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The cumulative effects of forest disturbance on streamflow components and their scaling properties in… Li, Qiang 2018

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THE CUMULATIVE EFFECTS OF FOREST DISTURBANCE ON STREAMFLOW COMPONENTS AND THEIR SCALING PROPERTIES IN NESTED WATERSHEDS OF THE SOUTHERN INTERIOR OF BRITISH COLUMBIA   by  Qiang Li B. Eng., City College, Xi’an Jiaotong University, 2010 M.Sc., University of New Brunswick, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Environmental Sciences) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  October 2018   © Qiang Li, 2018  ii  The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a dissertation entitled:  THE CUMULATIVE EFFECTS OF FOREST DISTURBANCE ON STREAMFLOW COMPONENTS AND THEIR SCALING PROPERTY IN THE SOUTHERN INTERIOR OF BRITISH COLUMBIA submitted by Qiang Li in partial fulfillment of the requirements for the degree of Doctor of Philosophy               Dr. Xiaohua (Adam) Wei, Irving K. Barber School of Arts and Sciences  Supervisor  Dr. Allan D. Woodbury, University of Manitoba Supervisory Committee Member  Dr. David F. Scott, Irving K. Barber School of Arts and Sciences Supervisory Committee Member Dr. Rehan Sediq, School of Engineering  University Examiner Dr. Jianbing Li, University of Northern British Columbia External Examiner  iii  Abstract Cumulative forest change and climate variability are two dominant drivers of hydrological alterations in forested watersheds. Assessing their impacts on streamflow is critical for watershed management and ecosystem protection. Previous studies, however, focused on the cumulative effects (CEs) of forest disturbance on total streamflow, with limited attention given to baseflow and surface runoff. Five-nested watersheds (34.6~5580 km2) with significant forest disturbance, located in the southern interior of British Columbia, Canada were selected. The modified double mass curves were applied to each watershed to separate the relative effects of forest disturbance and climate variability on streamflow components. The analyses showed that cumulative forest disturbance increased streamflow components in all nested watersheds, while climate variability decreased them, despite inconsistent responses among study watersheds.    The CEs of forest disturbance on streamflow at various spatial scales of watersheds have been extensively studied. Researchers and land managers are seeking transfer functions for extrapolation of knowledge and data from one scale to another. In spite of substantial progress on scaling properties of hydrological variables, no studies have investigated scaling properties of the CEs of forest disturbance on streamflow. In this study, two methods including product moments and probability weighted moments were used to determine the scaling properties. The results showed that the CEs of forest disturbance on streamflow components obeyed the simple-scaling, which indicates the log-log linear relationship between the CEs and watershed areas. In addition, the coefficient of variation of the CEs of forest disturbance on streamflow was independent of spatial scales. More importantly, the scaling exponents of the CEs of forest disturbance on streamflow components were greater than 1, suggesting that the CEs increased with watershed iv  size. This conclusion is contrasted to the commonly-held perception of scaling exponents being less than 1 as larger watersheds normally are hydrologically resilient to forest change. The counterintuitive finding might be due to increased synchronization effects in snow-dominated systems, large variations in topography, and interactions between forests and climate in large watersheds. This study provided critical information for managing the CEs of forest disturbance on hydrology in the context of future forest disturbance and climate change.      v  Lay Summary Understanding cumulative effects (CEs) of forest disturbance on streamflow and their scaling properties is important for managing and protecting watershed functions and services. This study used advanced statistical approaches to quantify the CEs of forest disturbance in five-nested watersheds located in the southern interior of British Columbia, and then to determine scaling properties among them. The results show that forest disturbance increased annual streamflow components, while climate variability decreased them. Streamflow has distinct responses to cumulative forest disturbance. Results also suggest that the impacts of forest disturbance can be transferred from one scale to another with an increasing rate in the study region. This result is mainly attributed to the enhanced synchronization of snow-melt at different elevations, variation in topography, and promoted forest and climate interactions in larger watersheds. The results provide a useful guide for managing forest and water relations at different spatial scales.    vi  Preface This dissertation is submitted for the degree of Doctor of Philosophy in Environmental Sciences at the University of British Columbia Okanagan. This research was conducted under the supervision of Prof. Adam X. Wei in the Department of Earth, Environmental and Geographic Sciences at the University of British Columbia, Okanagan from September 2013 to August 2018. This dissertation is entirely original, for which I was the principal investigator and wrote the manuscripts under the supervision of Dr. Wei.   Chapter 2 is the literature review, and several parts of this chapter have been published (i.e., Li et al., 2017; Li et al., 2018b; Wei et al., 2018). I was responsible for research design, data collection, simulations, and manuscript writing. All co-authors commented on those manuscripts. A case study in Chapter 4 has been published as Li et al. (2018b), which is about one of the five-nested watersheds in this dissertation. In this paper, I designed the research, conducted data analysis, and wrote the manuscript. All authors commented on the research design. The data in Li et al. (2018a) were cited in Chapters 4 and 5. Part of Chapter 4 and Chapter 5 are in preparation for publications.   All the figures appeared in Chapter 2 were reprinted with permission of John Wiley & Sons.  Peer-refereed Journal Publications and Book Chapters 1. Li, Q., Wei, X., Yang, X., Giles-Hansen, K., Zhang, M., Liu, W. 2018a. Topography significantly influencing low flows in snow-dominated watersheds. Hydrology and Earth System Sciences, 22, 1947-1956. DOI: 10.5194/hess-22-1947-2018.  2. Li, Q., Wei, X., Zhang, M., Liu, W., Giles-Hansen, K., Wang Y. 2018b. Assessing cumulative forest disturbance and climate variability on hydrological processes in a large forested watershed. Journal of Hydrology. 557, 448-459. DOI: 10.1016/j.jhydrol.2017.12.056. vii  3. Wei, X.,* Li Q.,* Zhang, M., Giles-Hansen, K., Liu, W., Fan, H. 2018. Forest cover-another dominate factor in determining global water resources in forested regions. Global Change Biology. 24 (2) 186-795. DOI:10.1111/gcb.13983 (* denotes equal contribution and corresponding author). 4. Li, Q., Wei, X., Zhang, M., Liu, W., Fan, H., Giles-Hansen, K. 2017. Forest cover change and water yield in large forested watersheds: A global synthetic assessment. Ecohydrology. 10. E1838. DOI: 10.1002/eco.1838. 5. Zhang, M., Wei, X., Li, Q. 2017. Do the hydrological responses to forest disturbances in large watersheds vary along climatic gradients in the interior of British Columbia, Canada? Ecohydrology, 10(2), 1-13. DOI: 10.1002/eco.1840. 6. Zhang, M., Liu, N., Harper, R., Li, Q., Liu, K., Wei, X., Ning, D., Hou, Y., Liu, S. 2017. A global review on hydrological processes to forest change across multiple spatial scales: Importance of scale, climate, forest type, and hydrological regime. Journal of Hydrology, 546, 44-59. DOI: 10.1016/j.jhydrol.2016.12.040. 7. Liu, W., Wei, X., Li, Q., Fan, H., Duan, H., Wu, J., Giles-Hansen, K., and Zhang, H. 2016. Hydrological recovery in two large forested watersheds of southeastern China: the importance of watershed properties in determining hydrological responses to reforestation, Hydrology and Earth System Sciences (20), 4747-4756. DOI: 10.5194/hess-20-4747-2016.  8. Wei, X., Li, Q., Zhang, M., Liu, W., Fan, H., 2016, Forest cover change and hydrology in large watersheds. Chapter 11. Forest hydrology: processes, management, and assessment. Edited by Devendra Amatya, et al. CABI Publisher.  9. Zhang, M., Wei, X., Li, Q. 2016. A quantitative assessment on the response of flow regimes to cumulative forest disturbances in large snow-dominated watersheds in the interior of British Columbia, Canada. Ecohydrology, 9, 843-859. DOI: 10.1002/eco.1687. 10. Li, Q., Qi, J., Xing, Z., Li, S., Jiang, Y., Danielescu, S., Zhu, H., Wei. X., Meng, F-R., 2014. An approach for accessing impact of land use and biophysical conditions across landscape on recharge rate and nitrogen loading of groundwater. Agriculture, Ecosystems & Environment. 196, 114-124. DOI: 10.1016/j.agee.2014.06.028. 11. Li, Q., Xing, Z., Danielescu, S., Li, S., Jiang, Y., Meng. F-R., 2014. Data requirement for using combined conductivity mass balance and recursive digital filter method to estimate groundwater recharge in a small watershed New Brunswick, Canada. Journal of Hydrology, 511, 658-664. DOI: 10.1016/j.jhydrol.2014.01.073.   viii  Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ....................................................................................................................... viii List of Tables ................................................................................................................................xv List of Figures ........................................................................................................................... xxiv List of Symbols ........................................................................................................................ xxxii List of Abbreviations ............................................................................................................. xxxiii Acknowledgements ................................................................................................................ xxxiv Dedication .................................................................................................................................xxxv Chapter 1: Introduction ................................................................................................................1 Chapter 2: Literature Review .......................................................................................................7 2.1 Cumulative effects of forest disturbance on hydrology .................................................. 7 2.1.1 Cumulative forest disturbance .................................................................................... 7 2.1.2 Cumulative effects of forest disturbance on total streamflow in large watersheds .... 9 2.1.3 Relative contributions of climate variability and forest cover change to annual streamflow................................................................................................................. 15 2.1.4 Cumulative effects of forest change on baseflow and surface runoff ....................... 21 2.2 Scaling property of the cumulative effects of forest disturbance on hydrology ........... 25 2.2.1 Scaling properties of hydrological variables ............................................................. 25 2.2.2 Scaling properties of the cumulative effects of forest disturbance on hydrology ..... 32 2.3 Research methods ......................................................................................................... 33 ix  2.3.1 Research methods of assessing cumulative effects of forest cover change on streamflow components ............................................................................................ 33 2.3.2 Baseflow separation methods ................................................................................... 35 2.3.3 Scaling methods in hydrology .................................................................................. 38 Chapter 3: Research design and study watersheds ..................................................................41 3.1 Research framework ..................................................................................................... 41 3.2 Watershed selection ...................................................................................................... 42 3.3 Watershed data .............................................................................................................. 45 3.3.1 Climate data .............................................................................................................. 45 3.3.2 Hydrology and conductivity data .............................................................................. 46 3.3.3 Data and methods for quantification of cumulative forest disturbance levels .......... 47 3.3.3.1 Forest disturbance data ..................................................................................... 47 3.3.3.2 ECA calculation ................................................................................................ 47 3.3.3.2.1 H60 calculation ........................................................................................... 47 3.3.3.2.2 Hydrological recovery and ECA coefficient ............................................... 48 3.3.4 Watershed descriptions ............................................................................................. 51 3.3.4.1 Camp Creek watershed ..................................................................................... 53 3.3.4.2 Hedley Creek watershed ................................................................................... 56 3.3.4.3 Tulameen River watershed ............................................................................... 59 3.3.4.4 Similkameen River at Princeton ....................................................................... 62 3.3.4.5 Similkameen River near Hedley ....................................................................... 66 3.3.4.6 Summary of the cumulative forest disturbance levels in the five nested watersheds ......................................................................................................... 72 x  Chapter 4: Assessing cumulative effects of forest disturbance on streamflow components in the study watersheds ....................................................................................................................74 4.1 Overview ....................................................................................................................... 74 4.2 Research Methods ......................................................................................................... 76 4.2.1 Baseflow separation methods ................................................................................... 76 4.2.1.1 Conductivity mass balance method .................................................................. 77 4.2.1.2 Recursive digital filter method.......................................................................... 77 4.2.2 The method for estimating potential and actual evapotranspiration (PET and AET)78 4.2.3 Trend analysis of hydrometeorological variables ..................................................... 80 4.2.4 Cross-correlation between cumulative forest disturbance and streamflow components ............................................................................................................... 82 4.2.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow components ............................................................................................ 82 4.3 Results ........................................................................................................................... 84 4.3.1 Long-term baseflow separation ................................................................................. 84 4.3.2 Trend analysis of hydrometeorological variables ..................................................... 87 4.3.3 Cross-correlation between cumulative forest disturbance and streamflow components ............................................................................................................... 92 4.3.4 Separation of the cumulative effects of forest disturbance on streamflow components in nested watersheds ................................................................................................. 94 4.3.4.1 The cumulative effects of forest disturbance on streamflow components in Camp Creek watershed ..................................................................................... 94 xi  4.3.4.2 The cumulative effects of forest disturbance on streamflow components in Hedley Creek watershed ................................................................................... 97 4.3.4.3 The cumulative effects of forest disturbance on streamflow components in the Tulameen River watershed ............................................................................. 100 4.3.4.4 The cumulative effects of forest disturbance on streamflow components in the Similkameen River at Princeton ..................................................................... 103 4.3.4.5 The cumulative effects of forest disturbance on streamflow components in the Similkameen River near Hedley ..................................................................... 106 4.3.4.6 Synthesis assessment of the cumulative effects of forest disturbance on streamflow in the study watersheds ................................................................ 110 4.4 Discussion ................................................................................................................... 114 4.4.1 Baseflow separation methods ................................................................................. 114 4.4.2 The cumulative effects of forest disturbance on total streamflow .......................... 118 4.4.3 The cumulative effects of forest disturbance on baseflow and direct runoff .......... 120 4.4.4 Relative contributions of forest disturbance and climate variability to streamflow 121 4.5 Summary ..................................................................................................................... 123 Chapter 5: Scaling properties of the cumulative effects of forest disturbance on streamflow components .................................................................................................................................125 5.1 Overview ..................................................................................................................... 125 5.2 Methods....................................................................................................................... 127 5.2.1 Research design ...................................................................................................... 127 5.2.2 Product Moments method ....................................................................................... 128 5.2.3 Probability Weighted Moment method ................................................................... 130 xii  5.2.4 The physical property of the scaling exponent ....................................................... 131 5.2.5 Scaling property of observed streamflow in the study watersheds ......................... 132 5.2.6 Investigation of topographic indices as scaling parameters .................................... 134 5.2.7 The scaling property of the CEs of forest disturbance on streamflow, baseflow, and surface runoff .......................................................................................................... 134 5.3 Results ......................................................................................................................... 135 5.3.1 Scaling properties of streamflow components for different study periods ............. 135 5.3.2 Scaling properties of annual streamflow using topographic indices as scaling parameters ............................................................................................................... 143 5.3.3 Scaling property of the CEs of forest disturbance on streamflow components ...... 144 5.4 Discussion ................................................................................................................... 152 5.4.1 Scaling properties of observed streamflow components in study watersheds ........ 152 5.4.2 Scaling properties of annual streamflow and topographic indices ......................... 155 5.4.3 Scaling properties of the CEs of forest disturbance on streamflow components ... 157 5.4.4 Implications of scaling property of the cumulative effects of forest disturbance on streamflow components .......................................................................................... 160 5.5 Summary ..................................................................................................................... 161 5.6 Supplementary materials ............................................................................................. 163 Chapter 6: Conclusions, uncertainties and future studies .....................................................183 6.1 Conclusions ................................................................................................................. 183 6.1.1 Review of the effects of forest change on streamflow in large watersheds ............ 183 6.1.2 Baseflow estimation of the study region ................................................................. 183 xiii  6.1.3 Separation of the cumulative effects of forest disturbance and climate variability on streamflow components .......................................................................................... 184 6.1.4 Scaling properties of the cumulative effects of forest disturbance on streamflow components ............................................................................................................. 184 6.2 Uncertainties in this study ........................................................................................... 185 6.3 Future studies .............................................................................................................. 186 6.3.1 The cumulative effects of forest disturbance on streamflow components .............. 186 6.3.2 Assessing relative contributions of forest disturbance and climate variability on streamflow components .......................................................................................... 187 6.3.3 Topographic indices as the scaling parameters ....................................................... 187 6.3.4 Scaling properties of the cumulative effects of forest disturbance on the hydrological regimes ................................................................................................................................ 188 Bibliography ...............................................................................................................................189 Appendices ..................................................................................................................................222 Appendix A: The cumulative effects of forest disturbance on streamflow in the Deadman River watershed ...................................................................................................................... 222 A.1 Watershed description ................................................................................................. 222 A.2 Quantification of cumulative forest disturbance in the Deadman River watershed ... 223 A.3 Trend analysis of the annual and seasonal hydrometeorological variables ................ 224 A.4 Cross-correlation between CECA and annual streamflow in the Deadman River watershed .................................................................................................................... 225 A.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow................................................................................................................... 226 xiv  Appendix B: The cumulative effects of forest disturbance on streamflow in the Fishtrap Creek watershed ................................................................................................................................ 228 B.1 Watershed description ................................................................................................. 228 B.2 Quantification of cumulative forest disturbance in the Fishtrap Creek watershed ..... 229 B.3 Trend analysis of the annual and seasonal hydrometeorological variables ................ 230 B.4 Cross-correlation between the CECA and annual streamflow in the Fishtrap Creek watershed .................................................................................................................... 231 B.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow................................................................................................................... 232  xv  List of Tables Table 2.1 Reviews on the effects of forest cover change on baseflow or groundwater recharge . 23 Table 3.1 Hydrological recovery according to age (year) and height (m) of dominated tree species (Lodgepole pine) (Note: the heights of Lodgepole pine at 3, 5, 7 and 9 m correspond to ages of 5, 13, 20, and 25 years, respectively, based on the site index of 13) (Zhang, 2013) ........................................................................................................................... 49 Table 3.2 Hydrological recovery (%) according to age (year) and height (m) of Spruce (based on the site index of 13) (Zhang, 2013) ............................................................................. 49 Table 3.3 Hydrological recovery according to age (year) and height (m) of Douglas fir (based on the site index of 13) (Zhang, 2013) ............................................................................. 50 Table 3.4 Summary of characteristics of the selected watersheds ................................................ 51 Table 3.5 Summary of the cumulative equivalent clear-cut areas (CECA) by disturbance types (%) in the five study watersheds and Wolfe Creek watershed ................................... 73 Table 4.1 Mann-Kendall trend tests on hydrometeorological variables in the Camp Creek watershed from 1968 to 2013 (the bolded numbers indicate the statistical significance at the level of 0.05) ..................................................................................................... 89 Table 4.2 Mann-Kendall trend tests on hydrometeorological variables in the Hedley Creek watershed from 1974 to 2013 (Acronyms are shown in Table 4-1) ........................... 90 Table 4.3 Mann-Kendall trend tests on hydrometeorological variables in the Similkameen River at Princeton watershed from 1954 to 2013 (Acronyms are shown in Table 4-1) ....... 90 Table 4.4 Mann-Kendall trend tests on hydrometeorological variables in the Tulameen River watershed from 1954 to 2013 (Acronyms are shown in Table 4-1) ........................... 91 xvi  Table 4.5 Mann-Kendall trend tests on hydrometeorological variables in the Similkameen River near Hedley from 1967 to 2013 (Acronyms are shown in Table 4-1) ........................ 91 Table 4.6 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Camp Creek watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) ....................................... 92 Table 4.7 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Hedley Creek watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) ....................................... 93 Table 4.8 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Tulameen River watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) ......................... 93 Table 4.9 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Similkameen River at Princeton (the bolded numbers indicate the statistical correlations at the significance level of 0.05) ......................... 93 Table 4.10 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Similkameen River at Princeton (the bolded numbers indicate the statistical correlations at the significance level of 0.05) ......................... 94 Table 4.11 Tests on break points for the MDMC slopes of streamflow components in the Camp Creek watershed .......................................................................................................... 97 Table 4.12 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow components in the Camp Creek watershed from 1990 to 2013 ....................................................................................................... 97 xvii  Table 4.13  Break point tests for the MDMC slopes of the streamflow components in the Hedley Creek watershed ........................................................................................................ 100 Table 4.14 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Hedley Creek watershed from 1996 to 2013 ........................................................................................................................... 100 Table 4.15  Tests on break point for the MDMC slopes of streamflow components in the Tulameen River watershed ....................................................................................... 103 Table 4.16 Temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Tulameen River watershed ......................... 103 Table 4.17 Tests on break point for the MDMC slopes of streamflow components in Similkameen River at Princeton ..................................................................................................... 106 Table 4.18 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Similkameen River at Princeton watershed from 1985 to 2013 ................................................................................... 106 Table 4.19 Tests on break point for the MDMC slopes of streamflow components in Similkameen River at Hedley ......................................................................................................... 108 Table 4.20 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Similkameen River at Hedley watershed from 1985 to 2013 ................................................................................... 110 Table 4.21 Summary of the cumulative effects of forest disturbance on total streamflow in 10 watersheds in the southern interior of British Columbia using the MDMC approach (SD is standard deviation, and bolds are for five-nested watersheds) ...................... 112 xviii  Table 4.22 Descriptions of topographic indices of study watersheds and their relationship with the cumulative effects of forest disturbance on total streamflow (Bolds indicate statistical significance at the level of 0.05) (Li et al., 2018a) ................................................... 113 Table 4.23. Selected surface runoff conductivities (Cro), flows, and corresponding flow percentiles for the Similkameen River at Princeton from 1967 to 2013. The percentile indicates the exceedance probability. ....................................................................... 116 Table 4.24. Selected baseflow conductivities (Cbf), flow rates, and corresponding flow percentiles ................................................................................................................................... 117 Table 4.25 Trend tests of conductivities of surface runoff (Cro), baseflow (Cbf), and streamflow (Cq) ............................................................................................................................ 117 Table 5.1 Scaling exponents of annual streamflow, baseflow, and surface runoff in five-nested watersheds for the whole study period, reference period, and disturbance period, respectively in the southern interior of British Columbia. ........................................ 136 Table 5.2 Scaling exponents of annual streamflow in ten watersheds for the whole, reference, and disturbance periods, respectively in the southern interior of British Columbia. ...... 136 Table 5.3 Model summary of the log-log relationship between the first 10 orders product moments of annual streamflow and watershed sizes based on Eqn. (5-4) for the southern interior of British Columbia (Note: all the models are statistically significant P<0.05) ...................................................................................................................... 139 Table 5.4 Model summary of the log-log relationships between the first 10 orders PWMs of annual streamflow and their watershed areas based on Eqn. (5-8) for the southern interior of British Columbia (Note: all the models are statistically significant P<0.05). ................................................................................................................................... 142 xix  Table 5.5 Summary of the scaling exponents of annual streamflow in the five-nested and ten watersheds using the specific contributing area and perimeter as scaling parameters in the southern interior of BC. ...................................................................................... 144 Table 5.6 Summary of the scaling exponents of the cumulative effects of forest disturbance on streamflow components in the five-nested watersheds and annual streamflow in 10 watersheds in the southern interior of British Columbia. ......................................... 145 Table 5.7 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of the cumulative effects of forest disturbance on annual streamflow and watershed size of Eqn. (5-4) and Eqn. (5-8), respectively for five-nested watersheds located in the southern interior of British Columbia, Canada. (Note all the models are statistically significant P<0.05) ................................................................................. 146 Table 5.8 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of the cumulative effects of forest disturbance on annual baseflow and watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds located in the southern interior of British Columbia, Canada (Note all the models were statistically significant at P<0.05) ............................................................................. 147 Table 5.9 Model summary of log relationship between the first 10 orders PMs and PWMs of cumulative effects of forest disturbance on annual surface runoff and watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds located in the southern interior of British Columbia, Canada (Note all the models are statistically significant P<0.05) ................................................................................. 148 Table 5.10 Model summary of the log-log relationship between the expectation of the first 10 orders PMs and first 7 orders of PWMs of the cumulative effects of forest disturbance xx  on annual streamflow and their watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for ten watersheds located in the southern interior of British Columbia, Canada (Note all the models are statistically significant P<0.05) ............................ 150 Table 5.11 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual mean flow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) .................................................................................................... 163 Table 5.12 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual mean flow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) .................................................................................................... 164 Table 5.13 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) .................................................................................................... 165 Table 5.14 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) .................................................................................................... 166 xxi  Table 5.15 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) .................................................................................................... 167 Table 5.16 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) .................................................................................................... 168 Table 5.17 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) .................................................................................................... 169 Table 5.18 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) .................................................................................................... 170 Table 5.19 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the five-nested watersheds in the southern interior of British xxii  Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) .................................................................................................... 171 Table 5.20 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) ...................................................................................................................... 172 Table 5.21 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) ...................................................................................................................... 177 Table 5.22 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) ...................................................................................................................... 178 Table 5.23 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their specific catchment area of Eqns. (5-4) and (5-8), respectively in the five-nested watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.872. (Note all the models are statistically significant P<0.05). ............................................................. 179 xxiii  Table 5.24 Model summary of log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their perimeter of Eqns. (5-4) and (5-8), respectively in the five-nested watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.874. (Note all the models are statistically significant P<0.05). ................................................................................ 180 Table 5.25 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their specific catchment area of Eqns. (5-4) and (5-8), respectively in the ten watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.872. (Note all the models are statistically significant P<0.05). ................................................................................ 181 Table 5.26 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their perimeter of Eqns. (5-4) and (5-8), respectively in ten watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.874. (Note all the models are statistically significant P<0.05). ................................................................................ 182 Table A.1 Mann-Kendall trend test of the hydrometeorological variables in the Deadman River watershed from 1962 to 2013. .................................................................................. 225 Table A.2 Cross-correlation between the CECA and annual streamflow in the Deadman River watershed .................................................................................................................. 226 Table A.3 Temporal summary of the streamflow change to forest disturbance and climate variability and their relative contributions in the Deadman River watershed from 1990- 2013. ............................................................................................................... 227  xxiv  List of Figures Figure 2.1 The relationships between annual water yield variations and the changes in forest cover in 162 large watersheds, among which 89 watersheds are for the deforestation category and 73 for the reforestation category (Li et al., 2017). ................................ 11 Figure 2.2 Absolute changes in annual water yield responding to the absolute changes in forest cover (in every 5% increment). Bars are standard deviations within the intervals (Li et al., 2017). .................................................................................................................... 12 Figure 2.3 Hydrological sensitivity responds to watershed sizes (in logarithm scale) with an interval of log10(area) of 0.1 for 162 large watersheds. The hydrological sensitivity of the watersheds within the intervals was averaged. Bars are the standard deviations within the intervals (Li et al., 2017). ........................................................................... 13 Figure 2.4 Hydrological sensitivity responds to the aridity index (PET/P) with the PET/P interval of 0.1 for 162 large watersheds (Li et al., 2017). The hydrological sensitivity of the watersheds within the intervals was averaged. Bars are the standard deviations within the intervals. ................................................................................................................ 14 Figure 2.5 Hydrological sensitivity responds to precipitation with the precipitation interval of 100 mm. The hydrological sensitivity of the watersheds within the interval was averaged. Bars are the standard deviations within the intervals (Li et al., 2017). ....................... 15 Figure 2.6 (A) Boxplot of the relative contributions of forest cover changes (Rf) and climate variability (Rc) to annual water yield variations; and (B) Histogram of relative contributions of forest cover and climate variability to annual water yield variations. The averaged Rf and Rc are 50.1 ± 18.9% and 49.1 ± 19.5% respectively. (Li et al., 2017) ........................................................................................................................... 17 xxv  Figure 2.7 Spatial distributions of the relative contributions of vegetation changes to annual runoff changes (Rv) in 2000-2011 (the global average: 30.7 ± 22.5%) based on the Fuh model and Choudhury-Yang model. Boxplot shows the averaged Rv of eight forest biomes as defined by The Nature Conservancy (http://www.nature.org) (Adopted from Wei et al. 2018). .......................................................................................................... 19 Figure 2.8 Directional responses of relative contributions of forest cover changes (Rf) and climate variability (Rc) to variations of annual water yields. +/- indicate positive/negative effects of Rf and Rc to variations of annual water yields. (Note: numbers in graph denotes the numbers of case studies in the category) (Li et al., 2017) ....................... 20 Figure 2.9 An example of global patterns of the roles of vegetation cover and climate changes to the annual runoff in forested regions simulated by LAI (positive effects (+) indicate an increase in annual runoff, while negative effects (-) indicate a decrease in annual runoff) for the simulation period of 2000 to 2011 (adopted from Wei et al. 2018). ... 21 Figure 3.1 Research design ........................................................................................................... 42 Figure 3.2 Locations and elevations of the selected five nested watersheds in the Similkameen River watershed .......................................................................................................... 44 Figure 3.3 Locations and elevations of the 10 watersheds located in the southern interior of British Columbia ......................................................................................................... 45 Figure 3.4 ECA coefficients of different forest disturbance types (logging, fire, and mountain pine beetle (MPB) infestation) in the Similkameen River watershed (MS: Montane Spruce; SBPS: Sub-Boreal Pine Spruce; SBS: Sub-Boreal Spruce biogeoclimatic zone) (Zhang, 2013) .................................................................................................... 50 Figure 3.5 Annual discharge (mm year-1) for the study watersheds from 1974 to 2014. ............. 52 xxvi  Figure 3.6 Mean monthly discharge (mm month-1) of the study watersheds from 1974 to 2014. 52 Figure 3.7 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Camp Creek watershed located in the southern interior of British Columbia, Canada ........................................................................................... 54 Figure 3.8 Cumulative equivalent clear-cut areas (CECA) (%) of the Camp Creek watershed from 1970 to 2010 ............................................................................................................... 55 Figure 3.9 Annual disturbed area (%) in the Camp Creek watershed from 1970 to 2010............ 55 Figure 3.10 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Hedley Creek watershed located in the southern interior of British Columbia, Canada ........................................................................................... 57 Figure 3.11 Cumulative equivalent clear-cut areas (CECA) (%) of the Hedley Creek watershed from 1960 to 2011 ....................................................................................................... 58 Figure 3.12 Annual disturbed areas (%) in the Hedley Creek watershed from 1960 to 2011 ...... 58 Figure 3.13 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Tulameen River watershed located in the Southern Interior of British Columbia, Canada ....................................................................................... 59 Figure 3.14 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 20 2015 to June 21 2016 in the Tulameen River watershed .................................................................................................................... 60 Figure 3.15  Cumulative equivalent clear-cut areas (CECA) (%) of the Tulameen River watershed from 1954 to 2011 ....................................................................................................... 61 Figure 3.16 Annual disturbed areas (%) of the Tulameen River watershed from 1954 to 2011 .. 61 xxvii  Figure 3.17 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Similkameen River at Princeton located in the southern interior of British Columbia, Canada with a total area of 1810 km2, of which 530 km2 is in Washington State, USA. The headwaters of the watershed are on the USA side of the border draining north into Canada (Note: the upper reaches of the watershed are mainly located in the conservation parks where logging is prohibited) ..................... 63 Figure 3.18 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 19, 2015, to June 21, 2016 in the Similkameen River at Princeton ................................................................................................................. 64 Figure 3.19 Cumulative equivalent clear-cut areas (CECA) (%) of the Similkameen River at Princeton from 1954 to 2011 ...................................................................................... 65 Figure 3.20 Annual disturbed areas (%) of the Similkameen River at Princeton from 1954 to 2011 ..................................................................................................................................... 65 Figure 3.21 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Similkameen River near Hedley located in the southern interior of British Columbia, Canada .......................................................................... 67 Figure 3.22 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 19 2015 to June 21 2016 in the Similkameen River at Hedley ......................................................................................................................... 68 Figure 3.23 Cumulative equivalent clear-cut areas (CECA) (%) of the Wolfe Creek watershed from 1950 to 2011 ....................................................................................................... 69 Figure 3.24 Annual disturbed area (%) of the Wolfe Creek watershed from 1950 to 2011 ......... 70 xxviii  Figure 3.25 Cumulative equivalent clear-cut areas (CECA) (%) of the Similkameen River at Hedley from 1950 to 2011 .......................................................................................... 71 Figure 3.26 Annual disturbed areas (%) of the Similkameen River at Hedley from 1950 to 201171 Figure 3.27 Spatial distributions of forest logging, mountain pine beetle infestation, and wildfire in the five selected watersheds .................................................................................... 73 Figure 4.1 Annual baseflow (mm year-1) in Camp, Hedley, Princeton, Tulameen, and SRH from 1974 to 2013 ............................................................................................................... 85 Figure 4.2 Long-term mean monthly baseflow (mm month-1) in Camp, Hedley, Princeton, Tulameen, and SRH in 1974-2013 .............................................................................. 86 Figure 4.3 Long-term mean monthly baseflow index (baseflow/streamflow) in Camp, Hedley, Princeton, Tulameen, and SRH in 1974-2013 ............................................................ 87 Figure 4.4 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Camp Creek watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years). ........................................................................................................................ 96 Figure 4.5 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Hedley Creek watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years). ........................................................................................................................ 99 Figure 4.6 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Tulameen River watershed; xxix  (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years). ...................................................................................................................... 102 Figure 4.7 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Similkmeen River at Princeton watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years). .................................................................................... 105 Figure 4.8 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Similkameen River at Hedley; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years). .................................................................................................. 109 Figure 4.9 Long-term (1966-2013) discrete conductivity measurements and continuous streamflow data in the Similkameen River at Princeton ........................................... 115 Figure 4.10 The relationship between streamflow conductivity (Y) and streamflow (X) in the Similkameen River at Princeton ............................................................................... 115 Figure 5.1 Size distribution of the selected 70 watersheds located in the southern interior of British Columbia with the watershed sizes ranging from 20.8 km2 to 19600 km2 ... 133 Figure 5.2 Log-log relationship between the first five orders of product moments (A to E corresponds to 1st to 5th moments) of annual streamflow and watershed area based on Eqn. (5-4) in the southern interior of British Columbia ............................................ 138 xxx  Figure 5.3 The slope versus moment order of annual streamflow of Eqn. (5-6) for the 70 watersheds in the southern interior of British Columbia. The slope of the linear regression is the scaling exponent (1.031). ............................................................... 139 Figure 5.4 The log-log relationships between the first five orders of PWMs of annual streamflow (A to E corresponds to 1st to 5th probability weighted moments) and their watershed areas of Eqn. (5-8) for the southern interior of British Columbia. ........................... 141 Figure 5.5 The scaling exponent (H) vs. moment orders (k) of annual streamflow of Eqn. (5-8) in the southern interior of British Columbia (the averaged scale exponent is 1.019). .. 142 Figure 5.6 The log-log relationship between the expectation of the first five orders product moments (A to E corresponds to 1st to 5th moments) of the cumulative effects of forest disturbance to annual mean flow and their watershed size based on Eqn. (5-4) for 10 study watersheds in the southern interior of British Columbia, Canada (the squares represent the nested watersheds). .............................................................................. 149 Figure 5.7 The log-log relationships between the first five-order PWMs of the cumulative effects of forest disturbance on streamflow (A to E correspond to 1st to 5th probability weighted moments) and their watershed area based on Eqn. (5-8) in ten study watersheds in the southern interior of British Columbia (the squares represent the five nested watersheds. ..................................................................................................... 151 Figure 5.8 The log-log relationship between the first five orders product moments (A to E corresponds to 1st to 5th moments) of annual streamflow flow and their watershed sizes of Eqn. (5-4) for the ten study watersheds located in the southern interior of British Columbia, Canada. The squares represent the nested watersheds. ........................... 173 xxxi  Figure 5.9 The slope versus moment order of annual mean flow of Eqn. (5-6) for the study watersheds located in the southern interior of British Columbia. The slope of the linear regression is the scaling exponent (1.144) of the annual mean flow for study watersheds. ................................................................................................................ 174 Figure 5.10 The log-log relationships between the PWMs of annual mean flow (A to E corresponds to 1st to 5th probability weighted moments) and their watershed areas of Eqn. (5-8) in ten study watersheds in the southern interior of British Columbia. The squares represent the five nested watersheds. ........................................................... 175 Figure 5.11 The scaling exponent (H) vs. moment order (k) of the annual mean flow of Eqn. (5-8) for the ten study watersheds in the interior of British Columbia. The average scaling exponent is 1.171. ..................................................................................................... 176 Figure A.1 Location and spatial distributions of logging, mountain pine beetle, and forest fire in the Deadman River watershed. ................................................................................. 223 Figure A.2 The cumulative equivalent clear-cut area (CECA) in the Deadman River watershed from 1960 to 2012. .................................................................................................... 224 Figure A.3 The Modified Double Mass Curves (MDMC), which plots the cumulative annual streamflow (Qa) against the cumulative annual effective precipitation (Pae). ........... 227  xxxii  List of Symbols α  Recession constant BFa  Cumulative annual baseflow BFI  Baseflow index BFImax  Maximum baseflow index Cbf  Specific conductance of baseflow Cro  Specific conductance of surface runoff Cq  Specific conductance of streamflow K  Scaling parameter H  Scaling exponent of probability weighted moments P  Precipitation  Pae  Cumulative effective precipitation Qa  Cumulative annual streamflow Rf  Relative contribution of forest disturbance Rc  Relative contribution of climate variability  SRa  Cumulative annual surface runoff T  Temperature  ∆Q  Flow changes ∆Qf  Flow deviation due to forest disturbance ∆Qc  Flow deviation due to climate variability θ  Scaling exponent of product moments  xxxiii  List of Abbreviations AET  Actual evapotranspiration ARIMA Autoregressive integrated moving average CEs  Cumulative effects CECA  Cumulative equivalent clear-cut area CMB  Conductivity mass balance CV  Coefficient of variation LULC  Land use or land cover MDMC Modified double mass curves  MPB  Mountain pine beetle  PET  Potential evapotranspiration PMs  Product moments PWE  Paired watershed experiment PWMs  Probability weighted moments PUB  Prediction of ungauged basins RDF  Recursive digital filter SCA  Specific contributing area  TIs  Topographic indices  xxxiv  Acknowledgements I would like to express my deepest appreciation to my supervisor, Professor Adam Wei for his endless support of my Ph. D. study and research, for his patience, motivation, and immense knowledge over the past five years. I am also grateful to my Ph. D. committee members, Dr. Allan Woodbury, Professor Emeritus from the University of Manitoba, and Dr. David Scott from UBCO for their long-term commitment to help my research. Thanks for funding support from the Regional District of Okanagan and Similkameen and Natural Science and Engineering Research Council.    I would also like to show appreciation to my fellow graduate students, staffs, and faculty members in the Department at UBCO for aiding me with my work.   My thanks also go to all my friends in Canada and China for their help and encouragement.   Finally, my gratitude also goes to my parents, my wife, Caiyun Yang, and my son, Aaron Molin Li, - without their unconditional support and encouragement, I could not have accomplished this much.   xxxv  Dedication This dissertation is dedicated to my wife, Caiyun Yang, and my son, Aaron Molin Li.   1  Chapter 1: Introduction The relationship between forests and streamflow has long been studied (Wei et al., 2008; Zhou et al., 2015). Our understanding of the effects of forest cover change on water resource in forest dominated watersheds was mainly gained through paired watershed experiments (PWE) at the small watershed scale (<1000 km2). Various landmark reviews have summarized what we have learned in different eras (Hewlett and Hibbert, 1967; Bosch and Hewlett, 1982; Stednick, 1996; Andréassian, 2004; Brown et al., 2005). The general key messages from the PWE studies are that deforestation can increase annual runoff, magnify peak flows, and alter base flows, while reforestation can decrease annual runoff and reduce peak flows. Recently, reviews on the relationship between forest change and annual streamflow in large watersheds (>1000 km2) have concluded that deforestation increases annual streamflow, while reforestation decreases it (Li et al., 2017; Zhang et al., 2017b), which were consistent with the results from small watersheds. The implications of these reviews are pivotal for water supply, ecosystem protection, and engineering design. Yet, previous studies have mainly focused on how forest change affects total streamflow with limited attention given to its major streamflow components (i.e., baseflow and surface runoff). Considering all streamflow components can lead to a complete understanding of hydrological responses to forest change in a watershed.   Limited studies have examined the impacts of change in forest cover or land use on all streamflow components, including total streamflow, baseflow, and surface runoff. In small watersheds (<100 km2), field experiments and monitoring have been used as the major approaches to assess the effects of change in forest cover on baseflow or groundwater recharge.  Such effects can also be inferred from the dynamics in groundwater tables with relatively 2  consistent conclusions. For example, a rising of the groundwater table was observed after forest logging, indicating forest disturbance increased groundwater recharge or baseflow (Lane and Mackay, 2001; Smerdon et al., 2009), while the drying–up of streamflow in the ninth year after Eucalyptus plantation in South Africa demonstrated that an increase in forest cover decreased baseflow (Scott and Lesch, 1997). For large watersheds, hydrological models were often adopted to study the effects of forest change on streamflow components, and the conclusions from those model-based studies were inconsistent (Khoi and Suetsugi, 2014; Ma et al., 2009; Zhang et al., 2016a; Zhou et al., 2013). For instance, vegetation expansion has dramatically reduced total streamflow and surface runoff, but baseflow was increased using the Soil and Water Assessment Tool (SWAT) in the Kejie watershed (1755 km2), Southwestern China (Ma et al., 2009). Conversely, Khoi and Suetsugi (2014) concluded that a reduction in forest cover augmented total streamflow and surface runoff, while decreased baseflow in the Be River catchment (7500 km2), Vietnam. These contrasting results highlight large variations in streamflow response to forest and land cover changes, especially for baseflow (Juckem et al., 2008; Jutras et al., 2006; Jyrkama and Sykes, 2007). The limited studies, along with inconsistent results in large watersheds, demonstrate that more case studies are critically needed to advance our understanding of this emerging research topic (Black, 1998).     In large forested watersheds, forest change and climate variability are two major drivers influencing hydrological variation (Jimenez Cisneros et al., 2014; Sterling et al., 2013; Piao et al., 2010; Vörösmarty et al., 1998, 2000, 2010). Previous literature was focused on the effects of climate change/variability on water resources (Arnell, 2004, 2013; Immerzeel et al., 2010; Kundzewicz et al., 2007). To investigate the impacts of forest change on hydrology, the effects 3  of climate variability on streamflow must be either removed or taken into consideration (e.g. Bari and Schofield, 1991; Bell et al., 1990; Engel et al., 2005; Houser et al., 2006; Juckem et al., 2008). The interests in considering both drivers and their relative contributions to streamflow has been growing significantly (e.g., Foley et al., 2005; Creed et al., 2014; Li et al., 2017; Wei et al., 2013; Zhang et al., 1999, 2008).  However, a direct and quantitative assessment of how annual streamflow responds to both forest change and climate variability is challenging, particularly in large watersheds as it requires explicit consideration of climate variability when assessing the hydrological effects from forest change (Wei and Zhang, 2010; Zhang et al., 2012b; Dey and Mishra, 2017). It is even more challenging to study the relative contributions of climate variability and forest change to total streamflow, baseflow, and surface runoff.    Advanced statistical analyses have been used to explore the effects of land cover or forest change on total streamflow. For example, statistical techniques such as the sensitivity-based method (Dooge et al., 1999; Li et al., 2007; 2009), double mass curves (Stednick, 1996), simple water balance, time trend method (Zhao et al., 2010), Tomer-Schilling framework (Tomer and Schilling, 2009), and Budyko frameworks (Liang et al., 2015 a and b; ) have been developed and widely employed to quantify the effects of forest change and climate variability on streamflow (Wei et al., 2013; Dey and Mishra, 2017). Among them, Wei and Zhang (2010) used modified double mass curves (MDMC) and time series analysis to separate the relative contributions of forest change and climate variability to annual streamflow. As the MDMC method is based on water balance, it has the potential to separate the relative effects of forest change and climate variability on baseflow and surface runoff, respectively.   4  Understanding spatial hydrological variations and their scaling properties are the central issues in many aspects of hydrology (Blӧschl, 2006, 2013; Buttle and Eimers, 2009).  The purpose of studying scaling issue across various spatial scales are: 1) to estimate hydrological variables in ungauged basins [Prediction in Ungauged Basins (PUB)] to inform engineering design and watershed management (Blӧschl, 2013; Sivapalan, 2003; Sivapalan et al., 2003; Hrachowitz et al., 2013); and 2) to understand the underlying mechanism of regional hydrological processes (e.g., rainfall and streamflow generation; Gupta and Dawdy, 1995; Kumar and Foufoula-Georgiou, 1993).   The hydrological variables exhibiting spatial scaling indicate that their spatial structures remain invariant across spatial scales. Namely, the coefficient of variation (CV) of any hydrological variable of interest remains constant without changing with spatial scales (Gupta and Waymire, 1990; Smith, 1992; Gupta et al., 1994; Kumar et al., 1994). To present the strict sense of the statistical scaling, the simple- and multi-scaling were further introduced (Gupta and Waymire, 1990; Smith, 1992, Kumar et al., 1994). The simple-scaling is defined as the relationship between hydrological variables and watershed areas are log-log linear, while the CV of interested hydrological variables does not vary with spatial scales. In contrast, the log-log linear relationship also holds for the multi-scaling while the CV varies with spatial scales. Product Moments (PMs) (Smith, 1992) and Probability Weighed Moments (PWMs) (Kumar et al., 2004) are widely used statistical methods to examine the scaling properties of hydrological variables, such as floods, low, and annual mean flows (Yue and Gan, 2004; Buttle and Eimer, 2009). For instance, Gupta and Dawdy (1995) found that peak flow follows simple-scaling in the snow-dominated regions, while it obeys multi-scaling in rain-dominated regions.  5  Understanding the effects of forest change on hydrology across various spatial scales allows researchers and watershed managers to explore transforming functions so that knowledge and data can be transferred from one scale to another.  However, the results of the effects of forest disturbance on hydrology from the small watersheds cannot be simply extrapolated into large ones (>1000 km2) as large watersheds are characterized by more diverse landforms (e.g., wetlands, lakes), topographies, climates, and their interactions (Shuttleworth, 1988; Woods et al., 1997; Shaman et al., 2004; Yang et al., 2008), and hence are characterized with different hydrological processes. Several reviews indicate that the effects of forest cover on streamflow are attenuated with increasing watershed size (Li et al., 2017; Zhang et al., 2017b). Yet, there are nearly no studies to identify the scaling property of the CEs of forest disturbance on streamflow. The scaling properties of the CEs of forest disturbance on streamflow have significant implications for sustainable forest and watershed  management.   It is challenging to assess the scaling properties in association with the CEs of forest disturbance on hydrology for several reasons. Firstly, this type of study requires a large number of watersheds that experienced major forest disturbances with substantial hydrological alteration. Secondly, long-term data on climate, vegetation, and hydrology in those watersheds must be available, which is rarely the case for large watersheds with long-term monitoring data on both hydrology and forest disturbance in a region. Thirdly, there is a lack of suitable research methods for quantifying the CEs of forest disturbance on hydrology.  Current existing methods can only derive a periodic average of the CEs for forest disturbance on hydrology (Wei et al., 2013; Dey and Mishra, 2017). The annual flow variability resulting from forest disturbance are proved to be difficult to derive, especially for flood and low flows. Finally, the spatial heterogeneities of 6  climate, topography, soil, and vegetation can introduce great uncertainties for the watersheds of various spatial scales.    The major objectives of this Ph.D. study are: 1) to quantify the CEs of forest disturbance on streamflow, baseflow, and surface runoff in nested watersheds; 2) to determine the scaling properties of the CEs of forest disturbance on streamflow components; and 3) to discuss the implications of the results from this study for managing and protecting watershed functions and services in the context of future forest disturbance and climate change impacts.  7  Chapter 2: Literature Review 2.1 Cumulative effects of forest disturbance on hydrology 2.1.1 Cumulative forest disturbance Nearly all land use or land cover (LULC) change activities, directly and indirectly, modify watershed conditions including soil and vegetation, which in turn alters hydrological processes and nutrient cycles that cumulatively affect aquatic ecosystems individually or collectively (Dunne et al., 2001; Schindler and Lee, 2010; Seitz et al., 2011; Schreier and Lavkulich, 2015). In a watershed, cumulative effects (CEs) are defined as the combined results from actions that are individually minor but collectively significant when added to the past, present, and foreseeable future (Reid, 1998; Schindler et al., 2003; Schindler and Donahue, 2006; Jone, 2016). The classic example of the CEs is that the increased flood frequency and magnitudes, elevated sediment, and altered channel morphology in the San Francisco Bay, which are still in effect as a result of the banning of hydraulic mining in the Sierra Nevada 100 years later in the United States (Berg et al., 1996), which demonstrated that land cover or land use change can cumulatively affect watershed conditions over a long time. In Canada, the importance of cumulative effects has been well-recognized since the 1980s and is now a requirement for Environmental Impact Assessment (EIA) under the Canadian Environmental Assessment Act, and also under various provincial EIA laws and regulations (Hegmann et al., 1999; Seitz et al., 2010).  In contrast, the traditional EIA has mainly focused on an individual stressor and its impacts on water resources and aquatic habitat within the watershed boundary (Reid, 1998). Such EIA has significantly advanced our knowledge in understanding the impacts of an individual project on water resources and aquatic habitat (Bhaduri et al., 1997; Chen and Wei, 8  2008; Dunne et al., 2001). This traditional approach, however, ignores the additive effects and synergistic interactions of multiple stressors that are cumulative over space and time.  In forested watersheds, forest disturbances (e.g., logging, fire, and mountain pine beetle or MPB, infestation) and reforestation are the primary drivers to hydrological variation and alteration of aquatic habitat (Wei and Zhang, 2008). Quantification of spatial and temporal forest change in a watershed is a prerequisite for watershed assessment. Numerous indicators have been developed and applied to quantify the cumulative forest change in a watershed.   The first one is the forest coverage or land cover change percentage, which is a direct and straightforward indicator of the CEs and has been extensively used in hydrological studies (e.g. Liu et al., 2015a; Zhang et al., 2008). However, this indicator only describes net loss or increment of forest stands (e.g., logging and reforestation) without accounting for hydrological recovery due to forest regeneration after disturbance.   The second indicator is the equivalent roaded area (ERA), which was developed by the U. S. Forest Service (USFS) Region 5 to assess channel destabilization from various disturbance types (Mcgurk and Fong, 1995). For this indicator, the impacts of other types of LULC change are converted to the equivalent impacts from the road by an equivalent index. The sum of ERA represents the overall disturbance level for a given watershed. Clearly, ERA is a better indicator than forest coverage as ERA recognizes all types of disturbances. The accuracy of ERA is, however, limited because of its dependence on estimating the equivalent index, which is 9  empirically based. As a result, the accuracy of ERA may be questioned. In addition, hydrological recovery with the forest regeneration is not often considered in ERA.   The third indicator is the equivalent clear-cut area (ECA). Similar to the ERA, ECA has been extensively used in Western North America to quantify the cumulative effects of forest disturbance on hydrological regimes and degradation of aquatic habitat (Winkler et al., 2005; Redding et al., 2008). ECA captures dynamic vegetation changes as well as accounts for hydrological recovery, and consequently has been intensively used to study forest-water relationship (Lin and Wei, 2008; Zhang et al., 2014; Winkler et al., 2017).   The fourth one is remote sensing-based vegetation indicators such as NDVI (Normalized Difference Vegetation Index), LAI (leaf area index), and FPAR (Fraction of Photosynthetically Active Radiation).  These remote sensing-based indicators have recently been applied to forest hydrological studies particularly in large-scale watersheds or regions (Wei et al., 2018). For example, Trancoso et al. (2017) employed FPAR to quantify the climate and forest change on baseflow in 315 catchments ranging from 6.8 to 3229 km2 in Australia. Although high-resolution remotely-sensed data have become available, e.g. a spatial resolution of 30-meter forest cover map at the globe (Hansen et al., 2013) and Canada (Beaudoin et al., 2014), little effort has been made to use those data for detailed watershed assessment with forest changes.   2.1.2 Cumulative effects of forest disturbance on total streamflow in large watersheds The relationship between changes in forest cover and water yield has been well studied (Hewlett and Hibbert, 1967; Sun and Li, 2005; Wei et al., 2008; Zhang et al., 2017b). Our understanding 10  of the effects of forest cover change on water resources in forest-dominated watersheds was mainly gained through paired watershed experiments (PWE). Various landmark reviews have summarized what we have learned in different eras (Hewlett and Hibbert, 1967; Bosch and Hewlett, 1982; Stednick, 1996; Andréassian, 2004; Brown et al., 2005). The key messages from PWE studies are that deforestation can increase annual runoff, magnify peak flows, and alter base flows, while reforestation can decrease annual runoff and reduce peak flows. However, PWE studies are conducted at the small watershed scale (<100 km2, most of which are less than 10 km2), and their results cannot be directly scaled up to large watersheds (>1000 km2) as large watersheds are characterized by more diverse landforms (e.g., forests, wetlands, and lakes), topography, climate, and their interactions (Shuttleworth, 1988; Woods and Sivapalan, 1997; Shaman et al., 2004; Yang et al., 2008). However, there are no review studies of the effects of forest change on water yield in large watersheds. It is not clear whether the conclusion based on small watersheds is still applicable to large watersheds. To fill this knowledge, data from 162 large watersheds were collected to study the effects of forest change, both deforestation and reforestation, on annual water yield (AWY), of which 17 with the areas from 500 to 1000 km2 are included to increase our sample size. Among those 162 studied large watersheds, 89 are associated with deforestation, while 73 with reforestation (Li et al., 2017). It was found that AWY is significantly related to forest cover change regardless of forest cover change categories: deforestation, reforestation, and general forest cover change (or their combinations) (Figure 2.1). The results reveal that deforestation increases AWY, while reforestation decreases it. In addition, along with Figure 2.2, larger forest cover change can lead to greater AWY variations. The conclusions derived from the current large watershed study are consistent with the results from 11  multiple watershed scales (e.g. Bosch and Hewlett, 1982; Stednick, 1996; Andréassian, 2004; Zhang et al., 2017b).   Figure 2.1 The relationships between annual water yield variations and the changes in forest cover in 162 large watersheds, among which 89 watersheds are for the deforestation category and 73 for the reforestation category (Li et al., 2017).    12   Figure 2.2 Absolute changes in annual water yield responding to the absolute changes in forest cover (in every 5% increment). Bars are standard deviations within the intervals (Li et al., 2017).  Watershed properties (e.g., watershed size, slope, and etc.) play a critical role in shaping flow path and residence time, and consequently water storage capacity and hydrological response magnitude (Zhou et al., 2015). To compare AWY per unit forest cover change, the hydrological sensitivity was defined as the ratio of AWY change to its associated forest cover change. As shown in Figure 2.3, hydrological sensitivities decrease significantly with increasing watershed size (P<0.01), suggesting that larger watersheds are more resilient to hydrological alterations resulting from forest cover change. As larger watersheds are generally characterized by more diverse land uses, landforms (e.g. wetlands, lakes), topography, and soil types etc., which buffer hydrological responses to the changes in forest cover and climate (Woods, 2003; Yang et al., 2008; Karlsen et al., 2016). Due to variation in hydrological sensitivities with watershed scales, any conclusions drawn from one watershed at a specific spatial scale may not be directly extrapolated to those at other spatial scales (Blöschl and Sivapalan, 1995).   13   Figure 2.3 Hydrological sensitivity responds to watershed sizes (in logarithm scale) with an interval of log10(area) of 0.1 for 162 large watersheds. The hydrological sensitivity of the watersheds within the intervals was averaged. Bars are the standard deviations within the intervals (Li et al., 2017).  Hydrological sensitivities were found to be positively related to dryness and negatively related to precipitation (Figures 2.4 and 2.5). This result is consistent with previous studies (Farley et al., 2005; Sun et al., 2006; Yang et al., 2009; Zhou et al., 2015; Zhang et al., 2015b; Zhang et al., 2017b). It is generally agreed that water is limited in drier regions, and the changes in evapotranspiration caused by forest cover change could have a larger impact on water yield in terms of percentage change.     14   Figure 2.4 Hydrological sensitivity responds to the aridity index (PET/P) with the PET/P interval of 0.1 for 162 large watersheds (Li et al., 2017). The hydrological sensitivity of the watersheds within the intervals was averaged. Bars are the standard deviations within the intervals.  In summary, this synthetic assessment on the effects of forest cover change on annual water yield indicates that smaller and dryer watersheds are more hydrologically sensitive to forest cover change. However, the large ranges in hydrological responses to forest cover change observed in larger watersheds are likely watershed-specific. Therefore, a broader context considering forest cover, climate, and watershed properties is needed to fully understand and effectively manage annual water yield changes at various watershed levels.     15   Figure 2.5 Hydrological sensitivity responds to precipitation with the precipitation interval of 100 mm. The hydrological sensitivity of the watersheds within the interval was averaged. Bars are the standard deviations within the intervals (Li et al., 2017).  2.1.3 Relative contributions of climate variability and forest cover change to annual streamflow Forest cover change and climate variability are the two primary drivers for the hydrological variation in large forested watersheds. Understanding relative contributions of climate and forest change to water resources have significant implications on both water resources and its associated ecological services (Zhang and Wei, 2012; Zhang et al., 2011; Zhang et al., 2017c). Previous studies, however, often considered the impacts from either forest change or climate change solely on the hydrological variations. Therefore, there is a lack of addressing their effects and associated interactions.   16  To acknowledge the role of forest change in water resources among assessed watersheds, in a recent study, the relative contributions of changes in forest cover (Rf) and climate (Rc) to AWY from 67 large watersheds were collected and averaged to evaluate magnitudes of forest cover and climate change to AWY variations (Figure 2.6A). The histograms of Rf and Rc were also plotted to show distributions of two factors across sampled watersheds (Figure 2.6B, Li et al., 2017). The analysis clearly shows that the averaged Rf and Rc to AWY variations are 50.1 ± 18.9% and 49.1 ± 19.5%, respectively (Figure 2.6A), suggesting that the changes in forest cover and climate are equally important to AWY variations. This contradicts to the common perception that climate is a primary dominator of annual water yield variations while the change in forest or land cover is secondary.  Three key reasons may contribute to our finding. Firstly, when conducting large watershed studies, researchers often selected the watersheds experiencing dramatic forest change such as severe forest disturbance (e.g. logging, wildfire, and urbanization) so that the significant hydrological effects of forest cover changes can be detected. As such, AWY variations due to changes in forest cover might be more pronounced in those studied watersheds. Secondly, the distinctions in terms of their impact directions. The effects of deforestation or reforestation on AWY variations are mono-directional, and their effects are cumulative over a specific period of either deforestation or reforestation. In contrast, the effects of climate variability on AWY variations tend to fluctuate or multi-directional, and consequently may lead to possible cancellations over the deforestation or reforestation period (also see Figure 2.7). Thus, the difference in the impact directions may make the hydrological effects of forest cover change more pronounced. Thirdly, our selected hydrological variable is AWY variation rather than its total magnitude. There is no doubt that total annual water yields in any given year are normally 17  determined by climate, but their variations can be associated with both the changes in forest cover and climate.      Figure 2.6 (A) Boxplot of the relative contributions of forest cover changes (Rf) and climate variability (Rc) to annual water yield variations; and (B) Histogram of relative contributions of forest cover and climate variability to annual water yield variations. The averaged Rf and Rc are 50.1 ± 18.9% and 49.1 ± 19.5% respectively (Li et al., 2017).  The synthetic analysis clearly illustrated the equal importance of forest change and climate variability in determining large watershed hydrology. Global forests have been dramatically disturbed over the past decades.  How the global forest change alters global water resources can advance our understanding of the relationship between forest and water further. Four remote sensing-based indices (Forest cover, FPAR, LAI, and NDVI) to represent changes in vegetation cover in forest land (forest coverage > 30%) were plugged into widely-used models such as the Fuh model (Fuh, 1989) and the Choudhury-Yang models (Choudhury, 1999; Yang et al., 2008) to quantify relative contributions of vegetation and climate changes to annual runoff variations from 2000 to 2011 in forested landscape (Wei et al., 2018). The simulations concluded that 30.7 18  ± 22.5% of the global average variation in annual runoff could be explained by changes in vegetation cover (Rv), while the rest by climate change (Figure 2.7).  For example, Rv values for tropical and boreal forests, where experienced the dramatic forest loss between 2000 and 2011, are 30.3 ± 22.0% and 32.8 ± 22.4%, respectively. Similarly, the Rv values in British Columbia, Canada are about 39.0 ± 27.4 % due to the large-scale mountain pine beetle infestation and salvage logging with forest cover losses of 2.3 ± 5.2%.   The effects of changes in forest cover and climate to AWY are directional (either positive or negative). As a result, their combined effects on AWY variations can be additive or offsetting. Among 162 case studies, only 67 watersheds assessed the relative contributions of climate variability and forest change, of which 51 studied watersheds exhibited additive effects, while 16 showed offsetting effects (Figure 2.7). In addition, directional responses in vegetation cover and climate in runoff showed large spatial distributions across the globe through the global simulations.  The LAI was used as an example to represent the spatial distributions of directional responses from those two drivers (Figure 2.9). Spatial coverage of additive and offsetting effects of vegetation cover change on annual runoff are evenly split, accounting for 50.6% and 49.4% of the study area, respectively. Among them, the positive role of climate change on annual runoff is found being 73.1% of the study area, while the negative role is 26.9%. The positive and negative roles of vegetation change on annual runoff account for 48.4% and 51.6% of the study area, respectively. Generally, high risk of extreme cases (floods or droughts) may happen if there are additive effects between the changes in forest cover and climate. On the contrary, limited or no significant water yield changes may occur if their effects are offsetting. Thus, both change 19  magnitudes and directions of forest cover and climate must be considered in predicting and assessing future water resources availability.   Note: Acronyms of global biomes are listed below. Numbers in brackets are averaged forest cover changes in each biome in 2000-2011. Boreal Forests (-2.6±5.6%); TBM: Temperate Broadleaf and Mixed Forests (-1.9±2.6%); TC: Temperate Conifer Forests (-3.2±5.2%); M: Mediterranean Forests (-1.0±3.0%); TSC: Tropical & Sub-tropical coniferous Forests (-3.1±3.9%); TSDB: Tropical & Sub-tropical Dry Broadleaf Forests (-4.5±4.3%); TSMB:  Tropical & Sub-tropical Moist Broadleaf (-3.5±4.9%); and TSGSS: Tropical & Sub-tropical Grassland, Savannas, and Shrub land (-2.7±2.8%).   Figure 2.7 Spatial distributions of the relative contributions of vegetation changes to annual runoff changes (Rv) in 2000-2011 (the global average: 30.7 ± 22.5%) based on the Fuh model and Choudhury-Yang model. Boxplot shows the averaged Rv of eight forest biomes as defined by The Nature Conservancy (http://www.nature.org) (Adopted from Wei et al. 2018).  20   Figure 2.8 Directional responses of relative contributions of forest cover changes (Rf) and climate variability (Rc) to variations of annual water yields. +/- indicate positive/negative effects of Rf and Rc to variations of annual water yields. (Note: numbers in graph denotes the numbers of case studies in the category) (Li et al., 2017)   Rc (+) Rf (+), 11Rc (+) Rf (-), 2Rc (-) Rf (+), 14Rc (-) Rf (-), 4021   Figure 2.9 An example of global patterns of the roles of vegetation cover and climate changes to the annual runoff in forested regions simulated by LAI (positive effects (+) indicate an increase in annual runoff, while negative effects (-) indicate a decrease in annual runoff) for the simulation period of 2000 to 2011 (adopted from Wei et al. 2018).  2.1.4 Cumulative effects of forest change on baseflow and surface runoff Compared to a large number of studies on the effects of forest change on annual water yield, limited studies have been done to examine the impacts of change in forest cover or land use on baseflow and surface runoff (Li et al., 2018c). In addition, the CEs of forest change on streamflow components (i.e., baseflow and surface runoff) are often separately studied. A global summary on this subject with watershed sizes ranging from plot level (<<1 hectare) to large watershed scale (>1000 km2) is provided in Table 2.1. In small watersheds (<100 km2), the field observation is the primary approaches to investigate the effects of forest change on groundwater and groundwater recharge. The impacts of changes in forest cover on baseflow or groundwater 22  recharge are mainly inferred from the change in the groundwater table. Additionally, the results are relatively consistent. For example, a rising of the groundwater table was observed after forest logging, indicating forest disturbance increased groundwater recharge or baseflow (Table 2.1; Smerdon et al., 2009), while streamflow dried up completely in the ninth year after Eucalyptus plantation in South Africa (Scott and Lesch, 1997), demonstrating that an increase in forest cover decreased baseflow. In contrast, hydrological models were often adopted to assess the CEs of forest change on streamflow components and groundwater resources in large watersheds (>1000 km2) where the experimental methods are not applicable. Moreover, the conclusions from those model-based studies were generally inconsistent (Khoi and Suetsugi, 2014; Ma et al., 2009; Zhang et al., 2016a; Zhou et al., 2013). For instance, vegetation expansion was found to dramatically reduce total streamflow and surface runoff, but increased baseflow with Soil and Water Assessment Tool (SWAT) in the Kejie watershed (1755 km2), Southwestern China (Ma et al., 2009). Interestingly, the land expansion of forests decreased streamflow, baseflow, and surface runoff using the SWAT model in Upstream of Huai River, China. Recently, Li et al. (2018b) adopted the advanced statistical approaches, and revealed that forest disturbance consistently increased total streamflow, baseflow, and surface runoff in a snow-dominated watershed. The limited studies, along with inconsistent results in large watersheds, demonstrate that more case studies are needed in this research topic.     23  Table 2.1 Reviews on the effects of forest cover change on baseflow or groundwater recharge No. Source Study Site Country MAP (mm) Area (ha) Land cover change type Changes in groundwater table, recharge, or baseflow 1 Ahiablame et al. (2017) Missouri River (99 stations) USA 255-1140 135000000 Agriculture land expansion  Every 1% of the agriculture land expansion leads to 0.2% decrease in baseflow  2 Barnett (1990) Murray River Basin South Australia 300 -- Land conversion from native mallee to crop Groundwater recharge increased from <0.1 to 0.2 mm/year to 3 to 30 mm/year as a result of land conversion  3 Bent (2001) Cadwell Creek Massachusetts, USA 1174 -- 34% of partial clearcut Groundwater recharge increased by 68 mm/year for six seasons following harvest 4 Bliss and Comerford (2002) Gainesville Florida, USA 1150 42 Clear-cut A 21-49 cm rise in the groundwater table after 900 days of treatment 5 Calder et al. (1992) Karnataka Southern India 800 -- Reforestation Groundwater recharge reduced by eucalyptus plantations 6 Cao et al. (2009) Motueka River Catchment New Zealand  -- 218000 Pine planation Pine planation would reduce total streamflow (-4.5%), baseflow (-4.5%), and surface runoff (-3.4%) 7 Cook et al. (1989) Western Murray Basin South Australia 340 14 Clear-cut Groundwater recharge increased by 20 mm/year 8 Dubé et al. (1995) St. Lawrence Low lands Quebec, Canada 957 Forest stands (<1 ha) Clear-cut A 7-52 cm rise in groundwater table 9 Evans et al. (2000) Moose Lake  Alberta, Canada 468 2.7 Clear-cut Groundwater table was 26 cm higher in the cut area compared to the uncut area 10 Fannin et al. (2000) Carnation Creek British Columbia, Canada 2100-4800 12 90% of clear-cut A 50-150 cm rise in groundwater table in the cut area 11 Hetherington (1997) Carnation Creek British Columbia, Canada 2100-4801 1000 41% of clear-cut A 30-50 cm rise in groundwater table for 10 years following harvest 12 Huang et al. (2016) Upper Du watershed China 728~1480 896100 Conversion of 5.3% farmland to forest Reforestation is a major factor with a negative impact on baseflow. 13 Khoi and Suetsugi (2014) Be River watershed Vietnam 2400 750000 16.3 % of deforestation An increase in streamflow (0.2 to 0.4%) and surface runoff (4.8 to 10.7%), meanwhile, a decrease in baseflow (3.5 to 7.9%) were found. 14 Ledue et al. (2001) Niamey Southwestern Niger 565 -- Land conversion of native savannah to millet field Groundwater table rise 0.01-0.45 m/year by land conversion of native savannah to millet field 15 Ma et al. (2009) Kejie watershed Southwestern China 967 175500 Reforestation An increase in baseflow and a decrease in surface runoff and streamflow were detected.                  24  No. Source Study Site Country MAP (mm) Area (ha) Land cover change type Changes in groundwater table, recharge, or baseflow 16 Marcotte et al. (2008) St. Lawrence Low lands Quebec, Canada 1126 Forest stands (<1 ha) Clear-cut An increase in groundwater table of 50-70 mm higher than pre-disturbance level after 10 years of clearcut, but had reached nearly 50% of the pre-cut level  17 Megahan (1983) Pine Creek Idaho, USA 890 0.97 63% clear-cut and burned A 90 cm rise in the groundwater table, decreasing to 40 cm after 2 years 18 Mishra et al. (2010) Wisconsin USA 710~866 16964000 30% of deciduous forest convert to agricultural land Annual surface runoff and baseflow increased by 40.4 mm and 469.1 mm, respectively.  19 Nepstad et al. (1994) Amazon River Basin  Pará, Brazil 1750 -- Land conversion of evergreen tropical forest to pasture An increment of 370 mm in plant available soil water  20 Peck and Williamson Collie River Basin (5 watersheds) Western Australia  820-1120 80 ~ 350 Clear-cut and partially cut Water table increased by 260 cm/year in the clear-cut area and 90cm/year in the partial clear-cut area 21 Pothier et al. (2003) St. Lawrence Low lands Quebec, Canada 510 Forest stands (<1 ha) Clear-cut and partially cut Up to 22 cm rise in groundwater table 22 Salama et al. (1993) Cuballing Catchments  Southwestern Australia 462 175 70% of land conversion of native eucalypt forest by grassland Groundwater recharge increased from 0.4-1.0 mm to 10-25 mm  23 Schofield and Bari (1991) Collie River Basin  Western Australia  713 127 35% of reforestation Groundwater level declined an average 1.47 m 10 year period of reforestation. 24 Scott and Lesch (1997) Mokobulaan experimental catchments South Africa  1135 26.2 100% of reforestation Streamflow dried up completely in the ninth year after Eucalyptus Grandis plantation  25 Scott and Lesch (1997) Mokobulaan experimental catchments South Africa  1135 34.6 100% of reforestation Streamflow dried up completely in the twelfth year after Pinus patula plantation  26 Shi et al. (2013) Xixian Basin China 1145 1019100 2.38% and 10.33% expand in forest and paddy area Land cover change decreased surface runoff (1.6%), baseflow (2.8%), and streamflow (2.1%) 27 Urie (1971) -- Michigan, USA 790 16.2 50% of partially cut A 100 cm rise as a result of higher snowpack  28 Xu et al. (2013) Iowa, Illinois, Indiana, and Ohio (55 stations) Midwest USA 966 5700~102600 Agriculture land expansion  Land surface change contributed more to baseflow (74%) than climatic variability (27%) in 20/55 watersheds 25  No. Source Study Site Country MAP (mm) Area (ha) Land cover change type Changes in groundwater table, recharge, or baseflow 29 Zhang and Schilling (2006) Mississippi River Basin (16 watersheds) USA 724~907 136200~4366980 Conversion of perennial vegetation to seasonal row crops Baseflow and streamflow were increased. 30 Zhang et al. (2016a) Heihe River Basin China 450 12800000 Conversion of 17.1% and 0.5% deduction in farmland and forest to Urbanization Reductions in surface runoff (-0.89%), baseflow (-0.54%), and streamflow (-0.31%) were detected.  31 Zhou et al. (2013) Xitiaoxi Basin China 1466 137100 5.9 % of decrease in forest and 178% increase in urban area Surface runoff was increased by 11.3% and baseflow decreased by 11.2% 32 Li et al. (2018a) This study Upper Similkameen River watershed British Columbia, Canada 889 181000 30 % of forest disturbance Forest disturbance increased streamflow (27.7 mm), baseflow (7.4 mm), and surface runoff (18.4 mm) 33 This study Tulameen River watershed British Columbia, Canada 928 178000 37 % of forest disturbance Forest disturbance increased streamflow (33.0 mm), baseflow (9.0 mm), and surface runoff (24.8 mm) 34 This study Similkameen River at Hedley British Columbia, Canada 808 558000 49 % of forest disturbance Forest disturbance increased streamflow (19.7 mm), baseflow (7.3 mm), and surface runoff (12.2 mm) 35 This study Hedley Creek watershed British Columbia, Canada 612 38800 59% of forest disturbance Forest disturbance increased streamflow (49.4 mm), baseflow (15.8 mm), and surface runoff (32.3 mm) 36 This study Camp Creek watershed British Columbia, Canada 724 3460 43 % of forest disturbance Forest disturbance increased streamflow (20.6 mm), baseflow (5.7 mm), and surface runoff (14.5 mm). However, the impacts are not statistically significant.  37 This study  Fishtrap Creek watershed  British Columbia, Canada 472 13500 93 % of forest disturbance Forest disturbance increased streamflow (12.2 mm), baseflow (6.0 mm), and surface runoff (11.4 mm)   2.2 Scaling property of the cumulative effects of forest disturbance on hydrology 2.2.1 Scaling properties of hydrological variables Observations and hydrological models are the two general approaches to investigate a hydrological process at different spatial and temporal scales, which can span about eight orders 26  of magnitude in space and time (Blӧschl and Sivapalan, 1995; Blӧschl, 2001; Sivapalan, 2003). For instance, hydrological observations and models are conducted at several meters for unsaturated flows in the soil profile to streamflow monitoring in millions of kilometres basins. Researchers have long been exploring the relationship that is allowed to aggregate or disaggregate the knowledge obtained from one scale to another (Sivapalan et al., 2003; Hrachowitz et al., 2013). Such aggregation or disaggregation of a hydrological process is defined as scaling in hydrology, and the problems associated with it are defined as scaling issue (Gupta et al., 2004; Blӧschl, 1999; Blӧschl et al., 2007).   Scaling is the central issue in many aspects of hydrology (Blӧschl, 2006; Buttle and Eimers, 2009), which stems from seeking connections of hydrological processes at different spatial and temporal scales (Gupta and Dawdy, 1995). The importance of scaling issues in hydrology has been recognized since the 1980s. The aims of scaling studies are: 1) to predict characteristics of hydrological variables in ungauged basins (Prediction in Ungauged Basins (PUB)) to inform engineering design and watershed management (Sivapalan et al., 2003; Hrachowitz et al., 2013); and 2) to understand the underlying mechanism of hydrological process, such as rainfall and streamflow generation process, in a region (Kumar and Foufoula-Georgiou, 1993; Yue and Gan, 2004). Thus far, numerous studies have been conducted to investigate the spatial scaling properties of hydrological variables (e.g., Smith, 1992; Yue and Wang, 2004).   A hydrological variable exhibiting spatial scaling indicates the spatial structure of the hydrological variable remains invariant within a broad range of spatial scales (Gupta and Waymire, 1989; Gupta and Dawdy, 1995; Smith, 1992; Skaugen and Vaeringstad, 1995). This 27  implies the power law relationship between hydrological variables and watershed areas. The power law is expressed as i jQ k Qθ= , where Qi and Qj are hydrological variables from the watersheds with the sizes of Ai and Aj, respectively; k is the ratio of Ai to Aj, and is defined as scaling parameter (Smith, 1992; Kumar et al., 1994). In addition, the watershed area has the capability to capture the mechanism of flow generation processes and has been used as the primary or sole descriptor of spatial scales. θ is the scaling exponent and is always larger than zero as hydrological variables cannot exhibit an inverse trend with increasing watershed area. The power law relationship provides a basis for understanding and predicting the physical and statistical structure of hydrological variables across spatial scales (Gupta et al., 1994).   It is worth mentioning that other indices (e.g. bankfull width) have also been used as the scaling parameter (Dingman and Palaia, 1999; Medhi and Tripathi, 2015). In addition, many topographic indices (TIs) have been developed to describe the spatial patterns of a landscape (Yokoyama et al., 2002), locate spatial patterns of species (Jenness, 2004), and simulate spatial soil moisture (Park et al., 2001). In describing the role of topography in hydrology, numerous TIs have been developed and applied to help understand hydrological processes and to explain the variations between watersheds (Moore et al., 1991). For example, Li et al. (2018a) recently reported that six TIs could be used as the indicators to distinguish the watersheds in the southern interior of British Columbia. These six TIs were developed based on the high-resolution DEM, which may infer some underlying mechanisms of hydrological processes, where the watershed area has limited explanatory power (Famiglietti et al., 1998). Therefore, whether these topographic indices can be used as the scaling parameters is an interesting question to explore.   28  Based on the power law assumption, the index flood method was the first attempt to investigate the scaling property of floods (Dalrymple, 1960), especially in the USA. However, the assumption of scaling invariance of floods was not fit for several regions, for example, in the Southeastern and Appalachia regions of the USA (Cadavid, 1988). Thereafter, regional multiple regression method was developed to predict flow quantities particularly for the regions where index flood method is not applicable (Benson, 1963; Thomas and Benson; 1970; Pandey and Nguyen, 1999; Ishak et al., 2011). To provide a more concise definition and overcome the shortcoming of the index flood method, two important scaling theories, simple- and multi-scaling, were developed and applied widely. Simple-scaling is determined as 1) the relationship between a hydrological variable and watershed area is log-log linear, and 2) the slope or scaling exponent of this relationship is constant and does not vary with statistical moments. In contrast, the log-log linear relationship still holds for multi-scaling but violates the constancy of invariance scaling exponent (Gupta and Waymire, 1990; Gupta and Dawdy, 1995; Jothityangkoon and Sivapalan, 2001). The assumption of simple-scaling is similar to those of index flood method, while multi-scaling explains scaling property where the index flood method is not applicable.   The concepts of simple- and multi-scaling provide a completed definition of spatial scaling, and have significantly advanced our knowledge in understanding regional hydrological processes. For example, Gupta et al. (2004) and Gupta and Dawdy (1995) indicated that floods exhibited simple-scaling in the snow-dominated regions where floods are mainly dominated by the snowpack and solar radiation over a homogenous climatic region, while multi-scaling was detected in the rain-dominated regions where the floods are mainly driven by the storms with 29  large spatial distributions. Similarly, Yue and Gan (2009) revealed that the multi-scaling held for Prairie Provinces, Northwestern forest, and Mackenzie River for annual maximum 1-, 5-, and 7-day flows, while the other regions in Canada showed the simple-scaling. The simple- and multi-scaling concepts were also applied to test the scaling properties in annual mean flows and low flows. For instance, Vogel and Sankarasubramanian (2000) and Yue and Wang (2004) concluded that annual mean flows obeyed simple-scaling in the USA and Canada, respectively. For low flow variables, Salazar et al. (2018) demonstrated that annual minimum flows, peak flows, and mean flows exhibited simple-scaling in the Amazonian region. The scaling concept, therefore, has significant implications for understanding and predicting regional hydrological processes.   In addition to simple- and multi-scaling of hydrological variables, the scaling exponent (θ) is also used to describe characteristics of a hydrological variable over a wide range of spatial scales. The mathematical property of the power law reveals the critical value or threshold of the scaling exponent of 1 (Salazar et al., 2018). If θ <1 (or θ >1), it indicates that hydrological variables show dampening (or amplification) processes with increasing watershed areas. Various flow variables exhibited both dampening and amplification processes in different regions.   Numerous studies have examined the scaling exponents of floods at different return periods (Smith, 1992), annual mean flows (Vogel and Sankarasubramanian, 2000), and low flows across various regions (Yue and Wang, 2004). Among them, the scaling exponent of floods was extensively studied in the literature (Eaton et al., 2002; Medhi and Tripathi, 2015). For instance, the first attempt to relate annual mean floods to drainage basin indicates that the scaling exponent of annual mean floods was 0.80 in the United States (Fuller, 1914).  Gupta and Dawdy 30  (1995) reported scaling exponents ranging from 0.3 to 1.0 for flood quantiles in Utah, New Mexico, and New York. In the United Kingdom, the scaling exponent was found as 0.77 (Hosking et al., 1985). While in Canada, Ribeiro and Rousselle (1996) obtained the scaling exponent being 0.64 in Southern Ontario. Similarly, Pandey (1998) reported 0.72 for Ontario streams and 0.76 for streams in southern Quebec. The scaling exponent for floods in south-central Ontario was higher (0.94) than that in the above-mentioned two studies. Yue and Gan (2009) investigated floods in various homogenous regions in Canada and derived the scaling exponents ranging from 0.5 to 0.9. Salazar et al. (2018) found the scaling exponents of peak floods ranging from 0.77 to 0.91 in the Amazon basin regions. Although different scaling exponent values have been reported, the scaling exponents of floods are always less than 1. This implies that the magnitudes of floods show a dampening effect with increasing of watershed size, which can be mainly explained by generation mechanisms of flood flows. The upper proportions of watersheds are often characterized by greater slopes, which generate higher surface runoff and lower baseflow. In addition, the orographic effects can also increase precipitation and consequently higher streamflow in the upper parts of watersheds. Meanwhile, gentler slopes and fewer reliefs in the lower reaches of watersheds can cause slower flow velocities and longer transit times. As such, peak flow magnitudes tend to spread up, and hence decrease the magnitudes of peak flows in the lower reaches. As a result, the scaling exponents of flood flows are lower than the threshold of 1.   For low flows, the scaling exponents varied considerably. For instance, Yue and Wang (2004) reported that scaling exponents spanned from 0.8 to 1.0 for 1-, 5-, and 7-day low flows across Canada. Buttle and Eimers (2009) reported that the scaling exponent of low flows in Northern 31  Ontario was 1.54. A larger scaling exponent was reported in the Amazonia regions with the highest value being 1.62 (Salazar et al., 2018). In a similar study, Modarres (2009) reported a scaling exponent of 0.6 for low flows in Iranian rivers. Compared to flood flows, both above and below the threshold of 1 were reported in the literature. The low flow generation processes are complicated in nature and are mainly controlled by groundwater discharge and many other factors (e.g., hydrological regimes, climate, topography, and land cover) (Farmer et al., 2015). For example, large watersheds tend to receive more baseflow or groundwater discharge, but the variations of magnitudes of baseflow rely on regional groundwater systems (e.g., aquifer types and its transmissivity across watersheds). Thus, the resultant interactions of the groundwater system, climate, topography, and other factors (e.g., land use) can lead to biased scaling exponents among regions.   The studies examining the scaling exponents of annual mean flows are quite limited in the literature, of which the scaling exponents of either less or greater than 1 were reported. For instance, in Canada, Yue and Gan (2004) reported that the scaling exponents of annual mean flows in coastal BC, Ontario, and Yukon were 1.04, 1.04, and 1.01, respectively. Buttle and Eimers (2009) estimated that the average scaling exponent of annual mean flows in 22 watersheds in Southern-Central Ontario was 1.06. Vogel and Sankarasubramanian (2000) found that the scaling exponents of annual average streamflow ranged from 0.6 to 1.1 for the continental USA, with 1.15 in California. In Amazon, scaling exponents of annual runoff ranged from 0.90 to 1.18 (Salzar et al., 2018). However, none of them provided reasons as to why the scaling exponents of annual mean flow were above or below the threshold of 1. We may assume the following reasons.  Firstly, annual streamflow is composited of various flow variables (e.g., 32  high, median, and lows flows), and the different magnitudes of those flow variables across spatial scales can have the scaling properties of the annual mean flow. Secondly, spatial variations of evapotranspiration and their possible feedbacks and interactions with climate can also affect flow magnitudes, and consequently the scaling property of annual mean flow.    Although a large number of studies exist, few studies have investigated the underlying mechanisms of the relationship between the scaling exponent and watershed conditions. Cathcart (2001) found that the scaling exponents of flood flow varied from low values (e.g., 0.60) for arid systems to high values (approaching 1.0) for humid systems in British Columbia, Canada. This study also indicated that the scaling exponent of flood flows increased with increase in humidity. Recently, Medhi and Tripathi (2015) analyzed the flood data from 1173 watersheds in the USA and concluded that the lower scaling exponents could be expected for the regions with higher potential evapotranspiration, average water capacity, average clay content, average baseflow index, average forest cover, and higher seasonality of precipitation.  However, no study has been done to investigate the relationship between scaling exponents of annual mean flows and low flows with watershed or climate conditions, which is still a significant knowledge gap requiring future studies.   2.2.2 Scaling properties of the cumulative effects of forest disturbance on hydrology Despite significant studies on scaling in literature, there are no studies on the determination of the scaling property of the CEs of forest disturbance on streamflow, as far as we know. However, there is a critical need to understand if the cumulative hydrological effects caused by forest disturbance have a scaling transfer function from one spatial scale to others. Such understanding 33  would significantly support resource managers to assess if the CEs would be aggregated or disaggregated at different spatial scales.  It is a challenging task to study the scaling property in association with the CEs of forest disturbance on hydrology due to the following reasons. Firstly, this type of study often requires a large number of watersheds experienced dramatic and similar levels of forest disturbance, which might not be available in many regions.  Secondly, where those watersheds do exist, long-term data on climate, vegetation, and hydrology must be available. Thirdly, there is a lack of commonly-accepted research methods for quantifying the CEs of forest disturbance on hydrology particularly in large watersheds (Wei et al., 2013).  Finally, the spatial heterogeneities of climate, topography, soil property and vegetation may introduce great uncertainty and complexity, which further hinder exploring of the scaling property on CEs in a region.   2.3 Research methods 2.3.1 Research methods of assessing cumulative effects of forest cover change on streamflow components  In large forested watersheds, forest change and climate variability are the two primary drivers for hydrological variations (Farley et al., 2000; Sterling et al., 2013). The challenge in a large watershed study lies in separating the effects of forest changes (e.g., disturbances) and climate variability on hydrology (Wei and Zhang, 2011; Zheng et al., 2008). It is commonly accepted that the effects of climate variability on hydrology must be either excluded or take into full consideration so that the hydrological impacts of forest cover changes in large watersheds can be quantified. In general, the CEs of forest change and climate variability on hydrology can be 34  studied with hydrological modelling and statistical analysis. The physical-based hydrological models, such as the Distributed Hydrology Soils and Vegetation Model (DHSVM), Variable Infiltration Capacity (VIC), MIKE-SHE, Soil and Water Assessment Tool (SWAT) are the most widely used models (e.g., Beckers et al., 2009; Eisenbies et al., 2007; Schewe et al., 2014; Schilling et al., 2008; Zhang et al., 2013b). To examine the CEs, a reference (no or limited disturbance) and disturbance (great disturbance) periods are required for a study. During the disturbance period, climate and land cover scenarios are alternated once at a time, which also known as a one-factor-at-a-time approach (OFAT). As such, the CEs of land cover change can be quantified. However, availability of extensive and long-term data on vegetation, soil, topography, land use, hydrology, and climate often limits the broad application of hydrological models (Kirchner, 2009; Stednick, 2008; Wei and Zhang, 2011). In addition, the land-atmosphere interactions are not constant at different periods, especially for the regions with extensive reforestation or deforestation practices (Ellison et al., 2012; Li et al., 2018b; Khanna et al., 2017). However, such interactions are difficult to simulate, and thus are not commonly considered in the OFAT approach.   To date, several statistical approaches, including sensitivity-based method (Li et al., 2007), time trend analysis (Zhao et al., 2010), Tomer-Schilling framework (Tomer and Schilling, 2009), modified double mass curves (Wei and Zhang, 2010), and climate elasticity method (Xu et al., 2014; Berghuijs et al., 2017), have been developed and applied to study how forest change affects hydrology in large watersheds. The empirical and experimental method, paired watershed experiment (PWE), has been used for a century for small watersheds (<100 km2, most of which are less than 10 km2) (Hewlett and Hibbert, 1967; Bosch and Hewlett, 1982; Stednick, 1996; 35  Andréassian, 2004; Brown et al., 2005). Currently, more than 252 PWE watershed are available (Zhang et al., 2017b). However, PWE is not suitable for large watersheds as it is challenging to locate comparable large watersheds as controls.  To implement statistical methods for large watersheds, long-term (>50 years) climate, hydrology, land cover data must be available to draw the robust inference.  Li et al. (2017) provided the first review on the CEs of forest change on annual water yield in large watersheds, in which 58 watersheds were studied by statistical approaches while 104 by hydrological modelling. Clearly, statistical methods and modelling are two common approaches for studying the CEs of forest change on hydrology in large watersheds, while PWE is a popular one for small watersheds.  2.3.2 Baseflow separation methods Baseflow is a critical component of total streamflow, and it regulates groundwater storage, and maintains the health and integrity of aquatic ecosystems (Zhang et al., 2013a; Li et al., 2014). Assessing the CEs of forest disturbance on total streamflow, baseflow, and surface runoff would help us to gain a complete picture of the CEs on hydrological processes, and to understand the role of vegetation in groundwater systems (e.g. Malana et al., 2011; Matheussen et al., 2000;  Orellana et al., 2012). Currently, various baseflow separation methods have been developed based on chemical, isotopic, and graphical principles (Brodie et al., 2008; Li et al., 2014; Nejadhashemi et al., 2004; Stewart et al., 2007; Uhlenbrook et al., 2002). They can be, generally, classified into two categories, non-tracer-based and tracer-based separation methods (Gonzales et al., 2009; Miller et al., 2014).   36  The non-tracer-based separation methods focus on the analysis of the recession curve of the hydrograph (Lott and Stewart, 2006). The low‐pass filter methods and graphical methods are two classic types of non-tracer-based methods. For instance, hydrograph separation program HYSEP (Sloto and Crouse, 1996) was developed by USGS based on low‐pass filter principles, while the Recursive Digital Filter (RDF) method is one of the commonly used low-pass filter methods due to its simplicity, accuracy, and less intensive data requirement. Like other filter methods, the RDF method is devised from the signal-processing theory (Nathan and McMahon, 1990; Chapman, 1999; Eckhardt, 2005). Surface runoff is considered as a high-frequency signal, whilst baseflow is low-frequency signals. The principle of the RDF is to filter out the high-frequency signals during processing data in the separation of lower-frequency baseflow from the higher-frequency event flow (Nathan and McMahon, 1990; Zhang et al., 2013a). However, the filtering results are primarily dependent on the watershed-specific parameters, i.e., baseflow index (BFI), a ratio of baseflow to total streamflow. Zhang et al. (2017a) compared four non-tracer-based baseflow results to those separated by isotopes in Eastern Australia and concluded that RDF is a relatively accurate method with an accurate estimation of BFI.  In short, the advantage of non-tracer-based baseflow separation methods has the least data requirement. However, as BFI estimation often involves professional judgement due to insufficient measured data, the method may have a biased baseflow estimation (Nejadhashemi et al., 2004; Zhang et al. 2013; Miller et al., 2015).   The tracer-based baseflow separation method is based on the mass balance of flow components. The rationale of the method is that baseflow and surface runoff have different ion concentrations due to distinctive flow travel paths. Baseflow percolates through soil and bedrock, and 37  accumulates more ions along the flow path than surface runoff. Baseflow, therefore, has a higher ion concentration compared to surface runoff (Matsubayashi et al., 1993; Stewart et al., 2007; Miller et al., 2014). Thus far, heat, 2H, 18O, silica, chloride, N-NO3- and specific conductance have been used as tracers to determine the interactions between groundwater and surface water (Anibas et al., 2011; Leaney and Herczeg, 1995; Li et al., 2014; Miller et al., 2014; Pellerin et al., 2008; Penna et al., 2014; Zhang et al., 2017a). Among those tracers, specific conductance (hereafter conductivity) is relatively a stable and non-expensive tracer and has received broad applications in various climatic regions (Zhang et al., 2013a; Stewart et al., 2007; Saraiva Okello et al., 2018). One of the apparent shortcomings of the tracer-based baseflow separation method is the availability of continuous long-term conductivity measurements, which has significantly limited the application of the tracer-based method for estimating long-term baseflow (Li et al., 2014; Zhang et al., 2013a).   To overcome shortcomings and strengthen advantages of both tracer- and non-tracer-based methods, the efforts have been conducted to improve baseflow separation. For examples, Zhang et al. (2013) developed a combined method that used the four-month conductivity measurements to calibrate the parameter for the RDF method in a small watershed in Canada. Following this calibration, they then used the calibrated RDF method to separate long-term baseflow.  Li et al. (2014) further validated the data required for applying this combined method, and recommended that a minimum of 6-month consecutive conductivity measurements during low flow seasons are needed. Zhang et al. (2017a) also proved that baseflow separated by RDF derived more reliable results with the parameters calibrated by isotopic data. Saraiva Okello et al. (2018) applied this combined method in a large watershed in South Africa for their long-term study. Li et al. (2018b) 38  adopted this framework in a large watershed in British Columbia, Canada, and found that the separated baseflow is comparable to other studies in the region. In conclusion, this combined baseflow separation method is a good alternative for long-term baseflow separation.   2.3.3 Scaling methods in hydrology  Scaling of hydrological processes has long been extensively studied (Blӧschl, 1999; Blӧschl and Sivapalan, 1995; Gupta et al., 1994). Several scaling methods were initially developed for floods and then applied to other hydrological variables. The index flood method was firstly proposed by Dalrymple (1960) for regional flood estimations, and then widely employed by the United States Geological Survey (USGS). A fundamental assumption of index flood method is that floods at different spatial scales in a homogeneous region remain similar over the wide range of spatial scales, which implies that floods could be transferred to other scales using watershed size as a scale parameter or an index factor (Dalrymple, 1960).  As a result, the index flood method can be used to predict floods at any given locations in the region and to analyze characteristics of flood frequency within the region. The index flood method has been successfully applied to many regions in the USA (Vogel et al., 1993a), Australia (Pearson et al., 1991; Vogel et al., 1993b) and Southern Africa (Mkhandi and Kachroo, 1997) and South Africa (Kjeldsen et al., 2002).   However, the assumption of the constant coefficient of variation or homogeneity of floods over a large spatial scale of the index flood method was conditional (Cadavid, 1988; Gupta and Waymire, 1990; Gupta et al., 1994; Smith, 1992). An alternative method for regional floods analysis is regression approach. Flow variables are regressed against watershed characteristics (e.g. area, slope) and climate variables (e.g. precipitation intensity) in a power form function 39  (Pandey and Nguyen, 1999). The objective of regression analysis is more on the prediction of regional flow variables. The regression methods have been applied in USA (Benson, 1963) and Australia (Pandey and Nguyen, 1999). There are two notable drawbacks with regard to the regression method. Firstly, regression models are developed for specific regions, which cannot be directly applied to other regions. Secondly, the accuracy of the regression method is highly dependent on the length of the observation data. As the data on extreme events are typically limited due to the short length of data records, the models may have a limited capacity of predicting hydrological processes of extreme events.    To overcome difficulties in defining the homogeneity of a study region by index flood method, and limitation of the regression method, the statistical simple- and multi-scaling approaches were introduced to analyze the spatial scaling behaviour of flood flows by a log-log linear relationship between product moments (PMs) of interested hydrological variables and basin areas (Waymire et al., 1984; Gupta and Waymire, 1990; Smith, 1992; Gupta et al., 1994). The PMs method has been used to examine floods (Gupta and Waymire, 1990; Smith, 1992; Medhi and Tripathi, 2015), annual mean flow (Vogel and Sankarasubramanian, 2000; Yue and Gan, 2004), low flows (Yue and Wang, 2004; Salazar et al., 2018), and the scaling property of rainfall events (Blöschl, 2001; Burlando and Rosso, 1996; Kumar and Foufoula-Georgiou, 1993; Over and Gupta, 1994; Gupta et al., 1996). However, the extreme events in hydrological variables may affect the scaling property (Smith, 1992; Gupta and Dawdy, 1994; Kumar et al., 1994; Gupta et al., 1994). To address the problem with extreme events, Kumar et al. (1994) developed an approach based on the log-log linear relationship between drainage area and the probability weighted moments (PWMs) to assess the scaling behaviour of hydrological processes, which are more robust against 40  outliers than PMs method. In common situations, two methods can identify the same scaling relationship (simple- or multi-scaling) (e.g., Pandey, 1998; Yue and Gan, 2004; Yue and Wang, 2004) with similar scaling exponents.  Therefore, two methods are often used to investigate the scaling properties of hydrological processes (Vogel and Sankarasubramanian, 2000; Yue and Gan, 2004). 41  Chapter 3: Research design and study watersheds 3.1 Research framework  This study is designed to investigate the cumulative effects (CEs) of forest disturbance on streamflow components, and to explore the scaling properties of the CEs of forest disturbance on streamflow components as shown in Figure 3.1. Assessing the CEs of forest disturbance on all streamflow components (surface runoff, baseflow and total streamflow) for each selected watershed using statistical approaches (i.e. MDMC, cross-correlation, and baseflow separation methods) were conducted in the five-nested watersheds (Figure 3.2), which are located in the southern interior of British Columbia (Chapter 4). Two methods, product moments (PM) and probability weighted moments (PWM), were employed to explore scaling properties of the CEs of forest disturbance on streamflow components based on the results from all five-nested watersheds (Chapter 5). The CEs of forest disturbance on streamflow components in those five-nested watersheds presented in Chapter 4 were used as primary data inputs for scaling analysis in Chapter 5. In addition, another five non-nested watersheds located in the southern interior of British Columbia with dramatic forest disturbance were also selected to form a group of 10 watersheds to further confirm the results from the five-nested watersheds (Figure 3.3). This research design ensures the robust conclusions.   42   Figure 3.1 Research design  3.2 Watershed selection This study was to assess the scaling properties of the CEs of forest disturbance on streamflow components. To achieve this, watersheds must experience significant forest disturbance. Moreover, the long-term data (> 40 years) in climate, forest disturbance, and hydrology must be available. As a result, five-nested watersheds located in the Similkameen River watershed were selected, which includes the Camp Creek (34.6 km2) (hereafter Camp), Hedley Creek (388 km2) (hereafter Hedley), Tulameen River (1780 km2) (hereafter Tulameen), Similkameen River at Princeton (1810 km2) (hereafter Princeton), and Similkameen River near Hedley (5580 km2) 43  (hereafter SRH) (Figure 3.2). All five watersheds experienced significant forest disturbances from logging, mountain pine beetle (MPB) infestation and wildfire, and have been monitored for more than 40 years. In the selected watersheds, agricultural irrigation is the largest water use. However, its influences on annual streamflow components are minor and negligible (Table 3.1). It should also be noted that Camp is located outside of the Similkameen River watershed boundary. However, Camp is next to the Similkameen River watershed, and has similarities in climate, vegetation, and topography to the selected watersheds. More importantly, Camp is relatively small which enlarges the range of watershed sizes (i.e., from 34.6 to 5580 km2) for analysis. It is, therefore, appropriate to treat Camp as one of the nested watersheds. In summary, the five-nested watersheds were selected to study the CEs of forest disturbance on streamflow components and their scaling properties.   Another five severely-disturbed watersheds (Figure 3.3), which are also located in the southern interior of BC, were also selected, including Baker Creek (1550 km2), Deadman River (878 km2), Fishtrap Creek (135 km2), Moffat River (548 km2), and Willow River (2860 km2) watersheds (Figure 3.3). Thus, a total number of 10 watersheds across several biogeoclimatic zones with different topography (Pojar et al., 1987) were included for this study. In addition, the scaling properties derived from 10 watersheds also provide an opportunity to examine whether the conclusion from five-nested watersheds still holds for non-nested watersheds. It should be mentioned that the CEs of forest disturbance on streamflow in Baker Creek, Moffat River, and Willow River have been successfully quantified by Zhang (2013) using the same research methods. Therefore, the results from these watersheds were directly included in this study (Zhang, 2013).  44   Figure 3.2 Locations and elevations of the selected five nested watersheds in the Similkameen River watershed 45   Figure 3.3 Locations and elevations of the 10 watersheds located in the southern interior of British Columbia  3.3 Watershed data 3.3.1 Climate data Monthly mean (Tmean), maximum (Tmax), minimum (Tmin) temperatures, and precipitation of the study watersheds were generated from the Climate West North American (WNA) dataset for 1954-2013 (Wang et al., 2016) using ClimateWNA. It is a standalone program that extracts and downscales historical climate data from the Climate Research Unit at the University of East Anglia (Mitchell and Jones, 2005; Harris et al., 2014) from 1901 to 2014.  It simulates monthly and annual climate variables for any given location based on latitude, longitude and elevation 46  based on the bilinear interpolation methods (Wang et al., 2006). Given the large spatial variations in climate across the watersheds, monthly climate data were generated at a resolution of 500 x 500 m across study watersheds. ClimateWNA has been validated through more than 600 weather stations across BC (Wang et al., 2016). This dataset has been widely used in many disciplines in British Columbia, Canada (e.g., Hember et al., 2017; Montwé et al., 2016; Schnorbus et al., 2014; Sofaer et al., 2017).    3.3.2 Hydrology and conductivity data Daily stream discharge data were collected from the hydrometric stations that are operated and maintained by Environment Canada. Our study region is characterized by snow-dominated hydrological regimes. The highest discharge occurs in the snow-melting season (late March to June) of all watersheds. Agricultural irrigation is the largest water consumer in the watersheds and accounted for less than 6% of the annual mean flow in the selected nested watersheds (Summit, 2011, 2014, and 2015). The in-situ conductivity probes (CTD-Diver, DI 271, Schlumberger Water Service, Canada) were installed near the hydrometric stations of Princeton, Tulameen, and SRH to continuously measure conductivity at a frequency of 30 minutes from May 19, 2015, to June 21, 2016.  The conductivity measurements for each day were averaged to derive daily conductivity. The conductivity data were used to separate baseflow from total streamflow for all five nested watersheds.   47  3.3.3 Data and methods for quantification of cumulative forest disturbance levels 3.3.3.1 Forest disturbance data The Cutblocks 2010 and the Vegetation Resources Inventory (VRI) 2010, two provincial databases, were obtained from the British Columbia Ministry of Forests, Lands and Natural Resources Operations. The Cutblocks database is a spatial record of forest harvest size, location, and timing. The VRI database provides detailed tree characteristics and additional non-logging disturbance type (i.e., fire and insect infestation).  Therefore, two databases are complementary and were both used to quantify the forest disturbance history in the study watersheds. It should be noted that forest disturbance data are not available in the part of the watershed located in the USA. The quantification of forest disturbance was only made in the Canadian portion of watersheds.   3.3.3.2 ECA calculation 3.3.3.2.1 H60 calculation In the interior of British Columbia, the H60 line is defined as the elevation of snowline above which lies 60% of the watershed area is above. Snow cover above the H60 elevation significantly contributes to spring freshet. As such, forest disturbance in areas above H60 is typically characterized with higher impacts on high flows in the interior of British Columbia (Gluns, 2000; Whitaker et al., 2002; Winkler et al., 2005; Zhang and Wei, 2014). This concept has been widely utilized to evaluate the hydrological impacts of forest disturbance (IWAP, 2006).     48  3.3.3.2.2 Hydrological recovery and ECA coefficient Forest logging, wildfire, and MPB infestation are recognized as three major forest disturbance types in the selected watersheds. Equivalent clear-cut area (ECA) is defined as the area that has been clear-cut, fire-killed or infested by insects, with a reduction factor (ECA coefficient) to account for hydrological recovery due to forest regeneration (IWAP, 2006). An ECA coefficient of 100% means that no hydrological recovery occurs, while an ECA coefficient of zero represents a full hydrological recovery in disturbed areas. To address the H60 effects on hydrology, it is recommended that the disturbed areas above H60 are multiplied by a weighting factor of 1.5 for ECA calculation (IWAP, 2006). Because forest disturbances and their effects are cumulative over both space and time, the sum of annual ECA values, or cumulative equivalent clear-cut area (CECA) at the watershed scale, is treated as a comprehensive indicator that captures dynamic changes of all types of forest disturbances spatially and temporally with a consideration of hydrological recovery following forest disturbances. Therefore, CECA was used as an indicator for estimating cumulative forest disturbance levels in this study.   Hydrological recovery of a forest stand is determined by various factors, including but not limited to disturbance types, climate, tree species, and soil properties. Site index is a standard and explicit measure of forest productivity and growth. Relationships between tree growth and hydrological recovery rates were developed to estimate ECA after logging for various tree species. Such relationships of the dominant species in BC, such as spruce, Lodgepole pine, and Douglas fir were suggested by the IWAP guidelines (BC Ministry of Forests and Rangeland, 1999). Thus, the relationships between hydrological recovery and ages or height of dominated tree species were developed based on the dominant site index of 13 in the Similkameen River 49  watershed (Tables 3.1 to 3.3). Then, the time series of the ECA coefficients for different tree species after forest disturbance were established based on the IWAP guidelines (Figure 3.4).   Table 3.1 Hydrological recovery according to age (year) and height (m) of dominated tree species (Lodgepole pine) (Note: the heights of Lodgepole pine at 3, 5, 7 and 9 m correspond to ages of 5, 13, 20, and 25 years, respectively, based on the site index of 13) (Zhang, 2013) Average height of the main canopy (m) Corresponding age (years) Hydrological Recovery (%) 0~3 0-13 15 3~5 14-19 30 5~7 20-26 50 7~9 27-34 70 9~11 35-41 80 11~13 42-51 90 13~15 52-61 95 >15 >72 100  Table 3.2 Hydrological recovery (%) according to age (year) and height (m) of Spruce (based on the site index of 13) (Zhang, 2013) Average height of the main canopy (m) Corresponding age (years) Hydrological Recovery (%) 0~3 0-25 15 3~5 26-33 30 5~7 34-39 50 7~9 40-45 70 9~11 46-54 80 11~13 55-61 90 13~15 62-70 95 >15 >70 100   50  Table 3.3 Hydrological recovery according to age (year) and height (m) of Douglas fir (based on the site index of 13) (Zhang, 2013) Average height of the main canopy (m) Corresponding age (years) Hydrological Recovery (%) 0~3 0-11 15 3~5 11-19 30 5~7 17-27 50 7~9 23-33 70 9~11 28-40 80 11~13 34-51 90 13~15 41-62 95 >15 >63 100    Figure 3.4 ECA coefficients of different forest disturbance types (logging, fire, and mountain pine beetle (MPB) infestation) in the Similkameen River watershed (MS: Montane Spruce; SBPS: Sub-Boreal Pine Spruce; SBS: Sub-Boreal Spruce biogeoclimatic zone) (Zhang, 2013)  01020304050607080901000 5 10 15 20 25 30 35 40 45 50 55 60 65ECA coefficient (%)Time since disturbances (years)Logging/Fire-S(Spruce)Logging/Fire-PL(Pine)Logging/Fire-FD(Fir)MPB-MSMPB-SBPS/SBS51  3.3.4 Watershed descriptions Table 3.4 Summary of characteristics of the selected watersheds    Camp Creek Hedley Creek Tulameen River Princeton Similkameen Hedley Area (km2) 35 388 1780 1810 5580 H60 (m asl) 1124 1300 1300 1360 1305 Elevation ranges (m) 912~1926 912~1637 629~2302 630~2400 534~2400 Slope (degree) 13.4 11.3 16.7 14.1 13.8 Drainage Density (km/km2) 0.61 0.78 0.72 1.24 0.83 Mean Annual Precipitation (mm) 724 613 926 999 806 Mean Annual Temperature (ºC) 3.3 2.4 3.5 3.2 3.4 Mean Monthly Tmax (ºC) 8 7 8.7 8.1 8.6 Mean Monthly Tmin (ºC) -1.4 -2.1 -1.8 -2.2 -1.8 Annual Mean Runoff (mm) 139 198 391 423 296 Annual Mean Baseflow (mm) 42.3 63 100 107 108 Biogeoclimatic Zones IDF, ESSF, MP EESF, IDF, MS IDF, ESSF, MS, PP IDF, ESSF, MS IDF, ESSF, MS CECA (%) 44.9 66.9 36.7 37.1 55.7 Licensed Off-stream/Annual Mean Runoff (%) 0 0 3.7 2 5.8 Hydrometric Stations 08NM134 08NL050 08NL024 08NL007 08NL038 Study Periods 1968-2013 1974-2013 1954-2013 1954-2013 1967-2013 Note: MAP: mean annual precipitation; MAT: mean annual temperature; CECA: cumulative equivalent clear-cut area up until 2011; IDF: Interior Douglas Fir; ESSF: Engelmann Spruce-Subalpine Fir; MS: Montane Spruce; PP: Ponderosa Pine.  52   Figure 3.5 Annual discharge (mm year-1) for the study watersheds from 1974 to 2014.   Figure 3.6 Mean monthly discharge (mm month-1) of the study watersheds from 1974 to 2014.   01002003004005006007008001974 1979 1984 1989 1994 1999 2004 2009 2014Streamflow (mm year-1)CampHedleyPrincetonTulameenSRH0204060801001201401601 2 3 4 5 6 7 8 9 10 11 12Streamflow (mm month-1)MonthCampHedleyPrincetonTulameenSRH53  3.3.4.1 Camp Creek watershed The Camp Creek watershed (Camp, 34.6 km2) is the smallest watershed among the five-selected watersheds. Other watershed characteristics are listed in Table 3.1. Logging and MPB are the two dominant disturbances in the Camp Creek watershed, and their distributions are shown in Figure 3.7. The logging started in 1975, followed by three logging events in 1977 (4.9%), 1981 (10.4%), and 1985 (4.5%) (Figure 3.9).  The CECA from logging was 38.6% in 2010 (Figure 3.8). By contrast, the MPB infestation contributed less to the CECA (6.0%) in 2010. No forest fire occurred in Camp. Overall, the CECA experienced a steady increase from nothing in 1976 to the highest 58.3% in 1993, then drop to 45.5 % in 2010, mainly due to a reduction in forest disturbance and forest regeneration (Figure 3.8). In summary, the Camp Creek watershed was severely disturbed.  54   Figure 3.7 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Camp Creek watershed located in the southern interior of British Columbia, Canada  55   Figure 3.8 Cumulative equivalent clear-cut areas (CECA) (%) of the Camp Creek watershed from 1970 to 2010   Figure 3.9 Annual disturbed area (%) in the Camp Creek watershed from 1970 to 2010 0102030405060701970 1975 1980 1985 1990 1995 2000 2005 2010CECA (%)YearLogging MPB Logging + MPB All0246810121970 1975 1980 1985 1990 1995 2000 2005 2010Annual Disturbed area (%)YearLoggingMPBLogging+ MPB56  3.3.4.2 Hedley Creek watershed The Hedley Creek watershed is 388 km2 (Figure 3.10). The highest monthly flow was 10.6 m3/s in May, and the lowest monthly flow was 0.33 m3/s in February (Figure 3.6). Logging and MPB infestation are the dominant disturbances. As the leading forest disturbance before 2004 (Figure 3.11), the logged areas occurred in 1981, 1995, and 2003, respectively (Figure 3.12) were about 1.4%, 1.5%, and 1.9% of the watershed area. Until 2011, the CECA from logging was about 21.3%. The CECA from MPB dramatically increased from 4.1% in 2003 to 8.9% in 2004, and then reached 44.7% of the watershed area in 2011 (Figure 3.11). The total CECA is 66.9%, suggesting that the watershed was severely disturbed.     57   Figure 3.10 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Hedley Creek watershed located in the southern interior of British Columbia, Canada  58   Figure 3.11 Cumulative equivalent clear-cut areas (CECA) (%) of the Hedley Creek watershed from 1960 to 2011   Figure 3.12 Annual disturbed areas (%) in the Hedley Creek watershed from 1960 to 2011  0102030405060701960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010CECA (%)YearFireLoggingLogging + MPBMPBAll0246810121970 1975 1980 1985 1990 1995 2000 2005 2010Annual Disturbed area (%)LoggingMPBLogging+ MPB59  3.3.4.3 Tulameen River watershed The Tulameen River is the largest tributary (1780 km2) of the Similkameen River that flows into the Similkameen River at Princeton (Figure 3.13). The conductivity measurement was conducted at the hydrometric station from May 20 2015, to June 21 2016, which covers the whole hydrological year (i.e., September to August) (Figure 3.14). The measured conductivities captured both the low flow and snow-melt periods. The highest conductivity (237.2 μS cm-1) corresponds to the lowest flow (0.05 mm day-1) on August 5, 2015, while the lowest conductivity (74.67 μS cm-1) corresponds to the highest flow (8.5 mm day-1) on April 22, 2016 (Figure 3.14).   Figure 3.13 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Tulameen River watershed located in the Southern Interior of British Columbia, Canada 60   Figure 3.14 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 20, 2015 to June 21, 2016 in the Tulameen River watershed  Logging was the leading forest disturbance in this watershed. Since 1962, logging has steadily increased with an average annual clear-cut rate or 0.42% of the watershed area (Figure 3.15). Logging accelerated in 1976, 1977, 1991, and 1993, with about 1% cut rate in each of these years (Figure 3.16). Up until 2011, the CECA from logging reached 19.9% of the watershed area (Figure 3.15). MPB infestation was the second dominant disturbance type, which was minor before 2003 (Figure 3.15). Between 2003 and 2007, CECA from MPB dramatically increased to 20.0% of the total watershed area. Fires occasionally occurred on a small scale (Figure 3.17).  Overall, the Tulameen River watershed has experienced significant disturbance since 1954 with the CECA being 33.8% in 2011.  0501001502002500123456789106-May-15 25-Jun-15 14-Aug-15 3-Oct-15 22-Nov-15 11-Jan-16 1-Mar-16 20-Apr-16 9-Jun-16Conductivity (uS cm-1)Flow (mm day-1)StreamflowBaseflowConductivity61   Figure 3.15  Cumulative equivalent clear-cut areas (CECA) (%) of the Tulameen River watershed from 1954 to 2011   Figure 3.16 Annual disturbed areas (%) of the Tulameen River watershed from 1954 to 2011  05101520253035401954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009CECA (%)YearFireLoggingLogging + FireLogging + MPBMPBAll0246810121954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009Annual Disturbed Area (%)YearFireLoggingLogging + FireLogging + MPBMPB62  3.3.4.4 Similkameen River at Princeton  The Similkameen River at Princeton is 91 km in length, with a drainage area of 1810 km2, of which 530 km2 or 29.3% of the watershed area is in the USA (Figure 3.17). The highest monthly flow is 91.5 m3/s in June, and the lowest monthly flow is 5.4 m3/s in September (Figure 3.6). Currently, the licensed off-streamflow water volume is mainly used for agricultural irrigation and mining industries, accounting for 2% of total annual streamflow volume (Table 3.1). The conductivity was measured at the hydrometric station from May 20, 2015, to June 18, 2016. The highest conductivity (270.1 μS cm-1) corresponds to the lowest flow (0.09 mm day-1) on August 13, 2015, while the lowest conductivity (104.8 μS cm-1) corresponds to the highest flow on April 22, 2016 (7.5 mm day-1) (Figure 3.18).  63   Figure 3.17 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Similkameen River at Princeton located in the southern interior of British Columbia, Canada with a total area of 1810 km2, of which 530 km2 is in Washington State, USA. The headwaters of the watershed are on the USA side of the border draining north into Canada (Note: the upper reaches of the watershed are mainly located in the conservation parks where logging is prohibited)  64   Figure 3.18 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 19, 2015, to June 21, 2016 in the Similkameen River at Princeton  Logging or post-disturbance salvage logging was the dominant disturbance in the Princeton. However, the disturbance is widely scattered across the watershed.  The upper reaches of the watershed are a part of the E.C. Manning Provincial Park where logging is prohibited. The watershed portion located in the USA was less disturbed (Hansen et al., 2013). The annual area logged was only 0.38% of the watershed. Up until 2011, the CECA from logging was 17.5% of the watershed area (Figure 3.20). The largest forest fire happened in 1984 with about 1% of the watershed area being burnt (Figure 3.20). MPB had no influence until 2003 but slightly increased to1.4% and 2.3% of the watershed area in 2004 and 2007, respectively.  The CECA from all disturbance types was 37.1% of the total watershed area in the Princeton, of which 15.7% resulting from MPB.   0501001502002503000123456786-May-15 25-Jun-15 14-Aug-15 3-Oct-15 22-Nov-15 11-Jan-16 1-Mar-16 20-Apr-16 9-Jun-16Conductivity (uSS cm-1)Flow (mm day-1)StreamflowBaseflowConductivity65   Figure 3.19 Cumulative equivalent clear-cut areas (CECA) (%) of the Similkameen River at Princeton from 1954 to 2011   Figure 3.20 Annual disturbed areas (%) of the Similkameen River at Princeton from 1954 to 2011  05101520253035401954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009CECA (%)YearFireLoggingLogging + FireLogging + MPBMPBAll00.511.522.531954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009Annual Disturbed Area (%)YearFireLoggingLogging + FireLogging + MPBMPB66  3.3.4.5 Similkameen River near Hedley The catchment area of the Similkameen River near Hedley (SRH) is 5580 km2, of which 540 km2 is located in the USA (Figure 3.21). The hydrometric station is the last monitoring station on the Similkameen River before it flows into the USA. The highest and lowest monthly flows are 242.1 m3/s in June and 16.6 m3/s in September (Figure 3.6), respectively. The licensed off-streamflow water volume is roughly about 5.8% of the total volume measured at the hydrometric station (Table 3.6). The conductivity measurement was conducted at the hydrometric station between May 20, 2015, and June 21, 2016. The highest conductivity (241.8 uS cm-1) corresponds to the lowest flow (0.08 mm day-1) on August 13, 2015, while the lowest conductivity (97.4 uS cm-1) corresponds to the highest flow on April 22, 2016 (6.0 mm day-1) (Figure 3.22). 67   Figure 3.21 Spatial distribution of historical fire, logging, and mountain pine beetle (MPB) infestation occurred in the Similkameen River near Hedley located in the southern interior of British Columbia, Canada  68   Figure 3.22 Measured conductivity and streamflow, and separated baseflow using conductivity mass balance method from May 19 2015 to June 21 2016 in the Similkameen River at Hedley  Princeton, Tulameen River, and Wolfe Creek watershed are three major sub-watersheds of the Similkameen River near Hedley (SRH) watershed (Figure 3.21). The spatial forest disturbance map demonstrated that the Wolfe Creek watershed had contributed significantly to the forest disturbance in SRH (Figure 3.27). The CECA in the Wolfe Creek watershed was also calculated to understand the spatial distributions of forest disturbance in the Similkameen River. Logging and MPB infestation are the dominant disturbance types in the Wolfe (Figure 3.23). Logging was the leading forest disturbance type with logging activity steadily increasing over time.  The annual logging rate was 0.6% of the watershed area between 1954 and 2011 (Figure 3.23). Up until 2011, the CECA from logging was 33.2% of the watershed area (Figure 3.23). The CECA from MPB dramatically increased since 2003, and exceeded that from logging in 2007 (Figure 3.24).  Up until 2011, the CECA from MPB was 43.6%. Forest fire rarely occurred in the watershed, and the CECA from forest fire was only 0.04% of the watershed area in 2011. In 0501001502002503000123456706/05/15 25/06/15 14/08/15 03/10/15 22/11/15 11/01/16 01/03/16 20/04/16 09/06/16Conductivity (uS cm-1)Flow (mm day-1)StreamflowBaseflowConductivity69  summary, the Wolfe Creek watershed was heavily disturbed with the CECA being 79.3% of the total watershed area in 2011.    Figure 3.23 Cumulative equivalent clear-cut areas (CECA) (%) of the Wolfe Creek watershed from 1950 to 2011  010203040506070801950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010CECA (%)YearFireLoggingLogging + FireLogging + MPBMPBAll70   Figure 3.24 Annual disturbed area (%) of the Wolfe Creek watershed from 1950 to 2011  Logging and MPB infestation were the leading forest disturbance in the SRH watershed. Logging is the dominant forest disturbance type with the CECA from logging being 24.4% of the SRH watershed area in 2011 (Figure 3.25). The CECA from MPB began to exceed the CECA of logging in 2011 with the CECA from MPB being 25.7% in 2011. Forest fires only accounted for 1.2% of the watershed area. In summary, the CECA of the SRH watershed was about 55.7% of the watershed area in 2011.   00.511.522.531950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Annual Distrubed Area (%)YearFireLoggingLogging + FireLogging + MPBMPB71   Figure 3.25 Cumulative equivalent clear-cut areas (CECA) (%) of the Similkameen River at Hedley from 1950 to 2011   Figure 3.26 Annual disturbed areas (%) of the Similkameen River at Hedley from 1950 to 2011  01020304050601950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010CECA (%)YearFireLoggingLogging + MPBLogging + FireMPBAll00.511.522.531950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010Annual Disturbed Area (%)YearFireLoggingLogging + MPBLogging + FireMPB72  3.3.4.6 Summary of the cumulative forest disturbance levels in the five nested watersheds  Overall, selected watersheds have been experiencing significant forest disturbance. The Tulameen River has the lowest CECA (36.7%), while the Wolfe has the highest (79.3%). Such variations lead to a significant spatial distribution of forest disturbance in the SRH watershed.  The upper reaches of the Similkameen River watershed had a moderate forest disturbance level with the CECA being 37.1% and 36.7% in Princeton and Tulameen, respectively (Table 3.6). The CECA of the Wolf watershed dramatically increased the CECA in the SRH watershed. Among all disturbance types, Camp and Hedley have the highest logging and MPB infestation levels, respectively. Forest fire was a minor disturbance type in the study watersheds. The extensive and cumulative forest disturbance and their associated cumulative effects on hydrology provide an excellent opportunity to evaluate the cumulative effects of the forest disturbance on hydrology and their scaling property.   73   Figure 3.27 Spatial distributions of forest logging, mountain pine beetle infestation, and wildfire in the five selected watersheds  Table 3.5 Summary of the cumulative equivalent clear-cut areas (CECA) by disturbance types (%) in the five study watersheds and Wolfe Creek watershed Watersheds Watershed Area (km2)  Logging (%) MPB (%) Fire (%) CECA (%) Camp 34.6 36.6 7.3 0 44.9 Hedley 388 21.3 44.7 0.2 66.9 Tulameen  1780 19.9 16.7 0 36.7 Princeton  1810 17.5 15.7 1.4 37.1 Wolfe  1910 33.2 43.6 0.04 79.3 SRH 5580 24.4 24.3 1.2 55.7 74  Chapter 4: Assessing cumulative effects of forest disturbance on streamflow components in the study watersheds  4.1 Overview The impacts of changes in forest cover on streamflow have long been investigated across the globe (Andréassian, 2004; Brown et al., 2005; Farley et al., 2005; Stednick, 1996; Wei et al., 2013). All reviews on the relationship between forest change and water yield across multiple spatial scales have concluded that deforestation increases water yield, while reforestation decreases it (Bosch and Hewlett, 1982; Li et al., 2017; Zhang et al., 2017b). The implications of these reviews are pivotal for water supply, ecosystem protection, and engineering design. However, previous studies have mainly focused on how forest change affects total streamflow with limited attention given to its major streamflow components (i.e., baseflow and surface runoff). Considering all streamflow components can lead to a complete understanding of hydrological responses to forest change in a watershed.   Limited studies have examined the impacts of change in forest cover or land use on baseflow and surface runoff. A global summary on this subject with watershed sizes ranging from plot level (<<1 hectare) to large watershed scale (>1000 km2) is provided in Table 2.1, which shows limited number of studies conducted on this topic and results of these studies are inconsistent, especially for baseflow alteration to forest cover change or LULC changes. In large forested watersheds, forest change and climate variability are two major drivers influencing hydrological variation. To investigate CEs of forest change on hydrology, the effects of climate variability on flow must be either removed or taken into consideration. The interest in considering both drivers 75  and their relative contributions to streamflow has been growing significantly (e.g., Li et al., 2017; Wei et al., 2018; Zhang et al., 2008).  However, a direct and quantitative assessment of how annual streamflow responds to both forest change and climate variability is challenging, particularly in large watersheds as it requires explicit consideration of climate variability when assessing the hydrological effects of forest change (Wei and Zhang, 2010; Zhang et al., 2012a). It is even more challenging to study the relative contributions of climate variability and forest change to baseflow and surface runoff.     Advanced statistical analyses have been used to explore the effects of land cover or forest change on total streamflow. For example, statistical techniques such as the sensitivity-based method, double mass curves, simple water balance, and the time trend method have been developed and widely used (Wei et al., 2013; Dey and Mishra, 2017). Among them, Wei and Zhang (2010) used modified double mass curves (MDMC) and time series analysis to separate the relative contributions of forest change and climate variability to annual streamflow. As the MDMC method is based on water balance, it has the potential to separate the relative effects of forest change and climate variability on baseflow and surface runoff.   Therefore, the objectives of this chapter were: 1) to explore the CEs of forest disturbance on total streamflow, baseflow, and surface runoff in study watersheds; 2) to quantify the relative contributions of forest disturbance and climate variability to total streamflow, baseflow, and surface runoff; and 3) to discuss possible implications of our results for management of water resource and protection of aquatic functioning.  76  4.2 Research Methods This section introduced the research methods used for separating the cumulative effects of forest disturbance on streamflow, baseflow and surface runoff in this study.  Section 4.2.1 shows baseflow separation methods applied in this study, which adopted the short-term field measured conductivity data to calibrate parameters for a long-term baseflow method (i.e., recursive digital filter). Section 4.2.2 demonstrates the approaches of estimating watershed level potential evapotranspiration (PET) and actual evapotranspiration (AET). Section 4.2.3 presents trends analysis methods for understanding hydrometeorological variables, while Section 4.2.4 describes time series cross-correlation for examining the relationship between forest disturbance and streamflow components. Finally, modified double mass curves were used to separate the effects of forest disturbance and climate variability on streamflow, baseflow, and surface runoff, which is the key focus of Section 4.2.5 as well as this chapter.   4.2.1 Baseflow separation methods In literature, baseflow separation methods divide total streamflow into two components, surface runoff and baseflow. In this study, baseflow is treated as groundwater discharge that sustains streamflow during low flow period but is also a small component during the high flow period. Similarly, surface runoff occurs during the snow-melting period and rain storm, but the lateral flow is also included as the surface runoff.    77  4.2.1.1 Conductivity mass balance method The conductivity mass balance (CMB) method (Stewart et al., 2007) is expressed as:  q robf roC CBF QC C−=−      (4-1) where, BF is baseflow (m3 s-1), Q is daily streamflow discharge (m3 s-1), Cq is the conductivity of streamflow (µS cm-1), Cbf is the conductivity of baseflow (µS cm-1), and Cro is the conductivity of surface runoff (µS cm-1). Cro corresponds to the highest daily streamflow, while Cbf corresponds to the lowest daily streamflow. Assumptions of applying the CMB method are: 1) contributions from other streamflow components are negligible; 2) Cbf and Cro are constant over the specific period; and 3) Cbf and Cro values are different from each other as baseflow percolates through soil and rocks, and carries more ions on its route, and thus has higher conductivity than surface runoff (Li et al., 2014; Miller et al., 2014; Stewart et al., 2007).   4.2.1.2 Recursive digital filter method The recursive digital filter (RDF) method (Eqn. 4-2) proposed by Eckhardt (2005) was used for the long-term baseflow separation in study watersheds.   maxmax1max1)1()1(BFIQBFIBFBFIBF ttt ααα−−+−= −    (4-2) Subject to BFt ≤ Qt, where, BF is baseflow (m3 s-1); Q is daily streamflow discharge (m3 s-1); α is recession constant (dimensionless) and BFImax is the maximum value of the baseflow index (the ratio of baseflow to total streamflow). In the RDF method, α can be determined from the hydrograph. However, BFImax cannot be directly measured (Li et al., 2014; Miller et al., 2014). The accuracy of the baseflow results from the RDF method is more sensitive to the BFImax than 78  to the recession constant.  It is suggested that the BFImax should typically be estimated from a tracer method (Zhang et al., 2013a; Zhang et al., 2017a). In this study, the BFI calculated from the CMB method was used as the initial value of BFImax in the RDF method. Then, the recession constant α and BFImax were adjusted to minimize the residuals of total baseflow between the RDF and CMB.  The baseflow separated by paired α and BFImax with minimum residuals (i.e., root mean square error) compared to that by the CMB method were determined as the final parameters for the RDF method (Li et al., 2014; Zhang et al., 2013a). The calibrated RDF method was finally employed to separate the long-term baseflow (1954-2013) for the study watersheds.   4.2.2 The method for estimating potential and actual evapotranspiration (PET and AET) In this study, monthly potential evapotranspiration (PET) was estimated through the Priestley-Taylor method (Eqn. 4-3) and Hamon method (Eqns. 4-4 and 4-5). The average monthly PET estimates derived from the two methods were then used to calculate actual evapotranspiration (AET) using Budyko method (Eqn. 4-6) and Zhang (Eqn. 4-7) method (Budyko, 1974; Zhang et al., 2001). The average monthly AET from two methods were used as the watershed AET.  The monthly PET and AET were then aggregated to derive annual values. The above-selected methods have been validated and widely used for estimating PET and AET. For instance, the Priestley-Taylor method and Hamon method were suggested by Lu et al. (2005) and McMahon et al. (2013) for estimating reliable PET. Budyko method and Zhang method for estimating AET was suggested by McMahon et al. (2013). In addition, Zhang method has been validated across the globe with the parameter (w) representing vegetation (e.g., the w values for forest, mix-79  vegetation, and grass being assigned as 2, 1, and 0.5, respectively). Our approach utilized the above-mentioned two methods for estimating PET and AET.     −+∆∆=λλγα GRPET n       (4-3) )3.273(7.2161651.0+××××=TVKDPET s     (4-4) )3.23727.17exp(108.6+××=TTVs     (4-5) 0.5{ [1 exp( / )] tanh( / )}AET P PET P PET P PET= − − × ×   (4-6) 1 ( / )1 ( / ) /PET PAET PPET P P PETωω+=+ +     (4-7) where, Eqns. (4-3), (4-4 and 4-5), (4-6), and (4-7) are the methods of Priestley-Taylor (Priestley and Taylor, 1972), Hamon (Hamon, 1960), Budyko (Budyko, 1974), and Zhang (Zhang et al., 2001), respectively.  α is constant in the Priestley-Taylor (α = 1.26 in this study). ∆ is the slope of the vapour pressure curve (kPa ºC-1); γ is the psychrometric constant (kPa ºC-1); Rn is the net daily radiation at the evaporating surface (MJ m-2 day-1), and G is soil flux into the ground (MJ m-2 day-1). The calculation of the Priestley-Taylor followed the procedure provided in McMahon et al. (2013).  For the Hamon method, D is the time from sunrise to sunset in multiples of 12h; K is the correction coefficient; and Vs is saturated vapour pressure (Zhou et al., 2015). In Zhang method, P is monthly precipitation (mm); ET is monthly actual evapotranspiration (mm); and w is the plant-available water coefficient (w =2 was used for this study).  80  4.2.3 Trend analysis of hydrometeorological variables Trend analysis has been used to assess the significance of temporal trends in hydrometeorological data, which may provide vital information to improve our understanding of the dynamics of hydrometeorological variables. The Mann-Kendall (MK) trend analysis is nonparametric trend analysis and does not require data to fit a normal distribution. The statistics of MK are based on the rank of data rather than real values (Ryverg and Vecchia, 2012; Hamed, 2009). Therefore, the advantage of the MK test is that statistical significance is not affected by the actual distribution of data (Yue et al., 2002). The statistic (S) of the MK test is calculated as follows.  11 1sgn( )n nj kk j kS x x−= = += −∑ ∑      (4-8) 1 0sgn( ) 0 01 0if xx if xif x>= =− <     (4-9)  where, n is the number of sample size, xi and xj is the tested variable.   The null hypothesis of the MK test is that there is no trend existing in the tested data series. The distribution of S has a mean of zero and the variance expressed by Eqn. (4-10). The normal Z-test is then calculated as Eqn. (4-11). The alternative hypothesis is accepted at the significant level of α when|𝑍𝑍| >  𝑍𝑍1−𝛼𝛼/2, where Z(1-α/2) is the value of the standard normal distribution with a probability of exceedance of α/2. A positive Z value reveals an upward trend, while a negative represents a downward trend of the variable. In this study, the MK test was first adopted to examine statistical trends, at the significance level of 0.05, of annual and seasonal maximum, 81  minimum, and mean temperatures, (Tmax, Tmin, and Tmean), P, PET, AET, streamflow (Q), baseflow (BF), and surface runoff (SR) over the study period in each study watershed.   ( 1)( 2)var( )18n n nS − −=       (4-10) 1 0( )0 01 0var( )S if Svar SZ if xS if xS− >= = − <     (4-11)  Once a statistically significant trend is detected, the changing magnitude is often used to quantify hydrological variations. The slope of general linear regression is often used. It is, however, very sensitive to the outliers in the data series. To overcome this shortcoming, Sen (1968) developed a non-parametric method to estimate the slope.  The set of linear slopes of data series was calculated as  j ikX Xj iβ−=−(1 ≤ i ≤ j ≤ n)     (4-12) where, X is the variable of the interests. i and j are the sequence of the variable. Sen’s slope, b, is then calculated as the median values of the slope that were derived from all combinations of linear slopes and expressed as b= Median (βk).  In this study, the Sen’s slope was adopted to quantify and compare the change magnitudes of tested hydrometeorological variables among the study watersheds.  82  4.2.4 Cross-correlation between cumulative forest disturbance and streamflow components Cross-correlation of time series data is an effective method to test whether there are significant relationships among time series variables. Its advantages are that it can remove autocorrelations existing in data series and identify lagged causality between two data series (Zhang and Wei, 2014). In this study, cross-correlation was used to detect the relationships and lagged effects between CECA and annual streamflow, baseflow, and surface runoff, respectively. All the tested hydrological variables and CECA data were pre-whitened to remove autocorrelation by fitting ARIMA (Autoregressive Integrated Moving Average) models. Model residuals from the ARIMA model with the best performance, achievement of model stationary, and coefficient of determination were selected for cross-correlation analysis (Lin and Wei, 2008; Liu et al., 2015a).     4.2.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow components  The modified double mass curves (MDMC) developed by Wei and Zhang (2010) was used to quantify the relative contributions of forest disturbance and climatic variability to each streamflow component for each study watershed. The basic assumption of MDMC is that a linear relationship is assumed between cumulative effective annual precipitation (Pae) and cumulative annual total streamflow (Qa), baseflow (BFa), and surface runoff (SRa) (Liu et al., 2015a; Wei and Zhang, 2010; Yao et al., 2012; Zhang et al., 2012b; Zheng et al., 2009). The effective annual precipitation (Pe) is defined as the difference between annual precipitation and actual evapotranspiration. Each MDMC was plotted as Qa, BFa, and SRa respectively against Pae.  In this way, the effects of climate variability on each streamflow component were eliminated (Wei 83  and Zhang, 2010; Zhang and Wei, 2012). For a period with no or little forest disturbance, a straight line between each cumulative annual streamflow component and Pae is expected. Break points between periods with different slopes can be identified on MDMC if there are significant influences from non-climatic variables, such as forest disturbance in our study. The Pettitt break point test was used to test the statistical significance of break points (Pettitt, 1979). Before implementation of the Pettitt test, any autocorrelation existing in the slope of MDMC must be removed, following the method by Yue et al. (2002). The nonparametric Mann-Whitney U-test Z statistic was further adopted to compare the statistical difference of the MDMC slopes before and after each break point (Liu et al., 2015a). Once the statistical difference of each break point was confirmed, the whole study period was subsequently divided into reference (before the break point) and disturbance (after the break point) periods. The baseline relationship in the reference period was therefore employed to predict each cumulative annual streamflow component for the respective disturbance period. The difference between each observed and predicted annual streamflow component was treated as the deviations caused by forest disturbance (∆Qf). Thus, the deviations caused by climate variability on each annual streamflow component can be determined as:  fc QQQ ∆−∆=∆       (4-13) where, ∆Q, ∆Qf, and ∆Qc are the deviations of each annual streamflow component between disturbance and average values of those variables in the reference period, annual flow deviations caused by forest disturbance, and annual flow deviations caused by climate variability, respectively.   84  Thus, the relative contributions of forest disturbance and climate variability to streamflow components can be calculated as:  %100×∆+∆∆=cfff QQQR      (4-14) %100×∆+∆∆=cfcc QQQR      (4-15) where, Rf and Rc are the relative contributions of forest disturbance and climatic variability to annual streamflow components, respectively (Wei and Zhang, 2010).   4.3 Results 4.3.1 Long-term baseflow separation The one-year field conductivity measurements were only conducted for Tulameen, Princeton, and SRH. Therefore, the CMB method was only applied to these three watersheds. Accordingly, the BFIs derived from the CMB method for Princeton, Tulameen, and Hedley were 0.25, 0.26, and 0.31, respectively. The average recession constant (α) calibrated from long-term hydrographs were respective 0.90, 0.92, and 0.92 for Princeton, Tulameen, and SRH. As suggested by the Zhang et al. (2013), parameters (α and BFImax) of the RDF were further adjusted by comparing the baseflow estimations against those from the CMB method.  The final parameters (α and BFImax) of the RDF method were determined as (0.90 and 0.27), (0.92 and 0.27), and (0.92 and 0.31) for Princeton, Tulameen, and SRH, respectively with the minimum biases (e.g., root mean square) between baseflow values separated by the CMB method. Since the BFImax in three watersheds did not vary dramatically, the BFImax of Camp and Hedley was assumed as 0.30. As such, the parameters (α and BFImax) of the RDF for Camp and Hedley were 85  determined as (0.93 and 0.30) and (0.91 and 0.30), respectively. Subsequently, the long-term baseflow in the periods of 1968-2013, 1974-2013, 1954-2013, 1954-2013, and 1967-2013 were separated by the RDF method for Camp, Hedley, Tulameen, Princeton, and SRH, respectively.    Figure 4.1 Annual baseflow (mm year-1) in Camp, Hedley, Princeton, Tulameen, and SRH from 1974 to 2013  In order to have consistent comparisons between the study watersheds, baseflow values during the common period of 1974-2013 were selected for the five study watersheds (Figure 4.1).  The mean annual baseflow and its standard deviation for Camp, Hedley, Tulameen, Princeton, and SRH were 40 ± 14 mm, 63 ± 24 mm, 98 ± 28 mm, 107 ± 35 mm, and 99 ± 29 mm, respectively. The coefficient of variance (CV) were 0.34, 0.38, 0.29, 0.33, and 0.30 for Camp, Hedley, Tulameen, Princeton, and SRH, respectively. The CV in smaller watersheds is higher than those from larger watersheds, indicating the baseflow in larger watersheds is a more stable source to maintain streamflow. Like total streamflow (Figure 2.14), baseflow showed large seasonal 0501001502001974 1979 1984 1989 1994 1999 2004 2009 2014Baseflow (mm year-1)YearCampHedleyPrincetonTulameenSRH86  variations (Figure 4.2). The highest baseflow occurred in the snow-melt season, while the lowest baseflow was detected in winter (October to February). However, the seasonal baseflow variations existed among the study watersheds. For example, the highest monthly baseflow was in May for Camp (11.9 mm month-1), while Princeton had the highest baseflow (39.1 mm month-1) in June (Figure 4.2). Furthermore, the BFIs in all five study watersheds show a consistent seasonal trend. Namely, baseflow contributed substantially to summer streamflow, while it had a lower contribution in the snow-melt season. The summer BFI could reach up to 0.52 in July in SRH, while the lowest BFI (0.20) occurred in April in Tulameen.    Figure 4.2 Long-term mean monthly baseflow (mm month-1) in Camp, Hedley, Princeton, Tulameen, and SRH in 1974-2013  0510152025303540451 2 3 4 5 6 7 8 9 10 11 12Baseflow (mm month-1)MonthCampHedleyPrincetonTulameenSRH87   Figure 4.3 Long-term mean monthly baseflow index (baseflow/streamflow) in Camp, Hedley, Princeton, Tulameen, and SRH in 1974-2013  4.3.2 Trend analysis of hydrometeorological variables The MK trend analyses were conducted in the period of 1968-2013 for Camp, 1974-2013 for Hedley, 1954-2013 for Tulameen, 1954-2013 for Princeton, and 1967-2013 for SRH (Tables 4.1 to 4.5). Overall, hydrometeorological variables across all five watersheds showed inconsistent trends, but a significant climate warming occurred over the study periods. For annual variables, the significant upward trends (P>0.05) of annual Tmax were only detected in Tulameen and Princeton. In addition, the annual increment trend in Tulameen (0.03 ºC year-1) was higher than that in Princeton (0.02 ºC year-1). Conversely, the significantly increasing trends were consistently found for annual Tmin and Tmean across all five study watersheds. Moreover, the same increasing trend of annual Tmean (0.03 ºC year-1) was also detected for the study watersheds. Unlike temperature, no statistical trends were found in annual precipitation across five watersheds. While the significant increasing trends of PET were detected for Hedley and 00.10.20.30.40.50.61 2 3 4 5 6 7 8 9 10 11 12BFIMonthCamp HedleyPrinceton TulameenSRH88  Tulameen with the annual increasing trend of 0.35 mm year-1 (P=0.01) and 0.42 mm year-1 (P=0.02), respectively. Tulameen was the only watershed where the significant (P=0.02) upward trend of AET was detected. For annual streamflow components, the significantly (P<0.05) downward trends were detected in Tulameen. Additionally, surface runoff showed a higher decreasing trend (-1.35 mm year-1) than that from baseflow (-0.49 mm year-1) in Tulameen. Although no significant trends of annual streamflow components were detected in other four watersheds, it is presumed that the increase in temperature might play a negative role in regulating all annual streamflow components.  The MK trends analyses demonstrated seasonal changes of hydrometeorological variables in the five-nested watersheds. In spring, no statistical trends were detected in Tmax among the five watersheds. In contrast, Tmin trend was insignificant only in Hedley. The spring P in Camp, Princeton, and Tulameen increased significantly with the highest upward trend in Camp (0.97 mm season-1). The significant upward trends in AET in spring were detected in Tulameen and SRH. The increasing temperature in spring might increase the spring freshet. However, no statistical changes in streamflow components were detected across all five study watersheds. In summer, the significant increasing trends of Tmax, Tmin, and Tmean were detected for Princeton and Tulameen, which might be the primary culprit for the significant decreasing trends of streamflow components in those watersheds. Due to the significant increment in temperatures, PET in Hedley and Tulameen increased significantly. In winter, significant increasing trends in Tmin were consistently detected for all five watersheds, while only Tmean in Tulameen and Princeton were increased significantly. In summary, all five study watersheds experienced significant climate warming over the study period.  89  Based on the trend analyses, significant decreasing trends were detected for annual and summer streamflow components in Princeton and Tulameen, which may due to the increments in annual and seasonal warming in the watersheds. However, it should be noted that the trend analysis only examined change directions. The underlying mechanisms were not well understood.        Table 4.1 Mann-Kendall trend tests on hydrometeorological variables in the Camp Creek watershed from 1968 to 2013 (the bolded numbers indicate the statistical significance at the level of 0.05)  Tmax Tmin Tmean P PET AET Q BF SR Annual Z 1.30 3.60 2.60 -0.20 0.80 1.10 -0.20 -0.20 -0.20 P 0.20 <0.001 0.01 0.88 0.43 0.27 0.81 0.87 0.86 Slope 0.01 0.03 0.02 -0.14 0.20 0.53 -0.10 -0.03 -0.06 Spring Z 0.10 2.40 1.40 2.10 0.60 1.90 1.20 1.30 1.20 P 0.89 0.02 0.16 0.04 0.58 0.06 0.22 0.20 0.23 Slope 0.00 0.02 0.01 0.97 0.08 0.32 0.24 0.07 0.17 Summer Z 0.80 3.70 2.00 0.70 0.30 0.30 -1.00 -1.00 -1.20 P 0.40 <0.001 0.05 0.48 0.76 0.73 0.32 0.29 0.23 Slope 0.01 0.03 0.02 0.44 0.08 0.15 -0.28 -0.09 -0.16 Winter Z 1.00 2.50 1.90 -1.10 1.70 1.50 -0.20 -0.10 0.10 P 0.34 0.01 0.06 0.25 0.09 0.14 0.87 0.92 0.89 Slope 0.01 0.03 0.02 -1.17 0.13 0.09 -0.01 0.00 0.00 Note: Tmax, Tmin, and Tmean: maximum, minimum, and mean temperature; P: precipitation; PET and AET: potential and actual evapotranspiration; Q: streamflow; BF: baseflow; SR: surface runoff; Spring: March to May; Summer: June to September; and Winter: October to February.        90  Table 4.2 Mann-Kendall trend tests on hydrometeorological variables in the Hedley Creek watershed from 1974 to 2013 (Acronyms are shown in Table 4-1)  Tmax Tmin Tmean P PET AET Q BF SR Annual Z 0.15 2.70 2.00 -0.80 2.50 -0.60 0.20 0.20 0.20 P 0.18 0.01 0.05 0.44 0.01 0.52 0.83 0.84 0.81 Slope 0.01 0.03 0.02 -1.18 0.35 -0.37 0.24 0.06 0.17 Spring Z 0.20 1.00 0.60 0.70 0.90 1.00 1.70 1.70 1.40 P 0.84 0.30 0.53 0.51 0.38 0.34 0.10 0.08 0.17 Slope 0.00 0.01 0.01 0.45 0.07 0.20 0.76 0.21 0.54 Summer Z 1.60 2.80 2.30 -1.00 2.20 -1.40 -0.90 -0.50 -0.80 P 0.11 0.01 0.02 0.32 0.03 0.15 0.40 0.58 0.42 Slope 0.03 0.03 0.03 -0.87 0.26 -0.68 -0.55 -0.14 -0.34 Winter Z 0.50 1.80 1.20 -0.30 0.90 1.70 0.90 0.90 1.00 P 0.62 0.07 0.22 0.73 0.40 0.09 0.35 0.37 0.32 Slope 0.01 0.02 0.02 -0.33 0.05 0.13 0.09 0.03 0.06   Table 4.3 Mann-Kendall trend tests on hydrometeorological variables in the Similkameen River at Princeton watershed from 1954 to 2013 (Acronyms are shown in Table 4-1)  Tmax Tmin Tmean P PET AET Q BF DR Annual Z 2.50 3.90 3.40 -0.40 2.10 1.60 -1.80 -1.80 -1.80 P 0.01 0.00 <0.001 0.71 0.04 0.11 0.07 0.07 0.07 Slope 0.01 0.02 0.02 -0.40 0.38 0.46 -1.90 -0.48 -1.37 Spring Z 1.40 2.90 2.40 2.10 1.10 2.80 -0.20 0.00 -0.30 P 0.15 0.00 0.02 0.03 0.26 0.01 0.85 0.99 0.78 Slope 0.02 0.02 0.02 0.81 0.09 0.35 -0.07 0.00 -0.07 Summer Z 2.00 4.10 2.90 0.40 1.80 0.30 -2.00 -2.30 -1.90 P 0.05 <0.001 0.00 0.71 0.07 0.77 0.04 0.02 0.06 Slope 0.02 0.02 0.02 0.14 0.27 0.09 -1.53 -0.46 -1.06 Winter Z 1.70 2.30 2.00 -1.10 1.80 1.50 -0.30 -0.20 -0.20 P 0.08 0.02 0.05 0.26 0.07 0.12 0.79 0.83 0.87 Slope 0.01 0.02 0.02 -0.94 0.09 0.09 -0.03 -0.01 -0.01    91  Table 4.4 Mann-Kendall trend tests on hydrometeorological variables in the Tulameen River watershed from 1954 to 2013 (Acronyms are shown in Table 4-1)  Tmax Tmin Tmean P PET AET Q BF SR Annual Z 2.90 3.60 3.50 -0.40 2.40 2.30 -2.10 -2.10 -2.00 P 0.00 <0.001 <0.001 0.67 0.02 0.02 0.03 0.03 0.04 Slope 0.02 0.02 0.02 -0.42 0.42 0.62 -0.49 -0.49 -1.35 Spring Z 1.70 2.90 2.50 2.90 1.80 3.60 -0.80 -0.30 -0.90 P 0.10 0.00 0.01 0.00 0.07 <0.001 0.45 0.79 0.36 Slope 0.02 0.02 0.02 0.95 0.16 0.40 -0.24 -0.02 -0.26 Summer Z 2.10 3.50 2.80 1.00 2.00 0.80 -2.50 -2.60 -2.40 P 0.04 <0.001 0.01 0.31 0.05 0.43 0.01 0.01 0.02 Slope 0.02 0.02 0.17 0.49 0.28 0.19 -1.39 -0.42 -0.94 Winter Z 2.20 2.30 2.20 -1.40 1.80 1.70 -0.70 -0.60 -0.60 P 0.03 0.02 0.03 0.15 0.07 0.09 0.46 0.52 0.52 Slope 0.02 0.02 0.02 -1.22 0.08 0.01 -0.17 -0.04 -0.12  Table 4.5 Mann-Kendall trend tests on hydrometeorological variables in the Similkameen River near Hedley from 1967 to 2013 (Acronyms are shown in Table 4-1)  Tmax Tmin Tmean P PET AET Q BF SR Annual Z 1.30 3.10 2.20 -0.60 0.70 1.40 -0.20 -0.20 -0.20 P 0.20 0.00 0.03 0.53 0.46 0.16 0.88 0.82 0.88 Slope 0.01 0.03 0.02 -0.70 0.20 0.65 -0.25 -0.13 -0.14 Spring Z 0.40 2.40 1.50 1.40 1.00 2.50 0.80 1.10 0.90 P 0.72 0.02 0.12 0.15 0.33 0.01 0.40 0.28 0.39 Slope 0.00 0.02 0.01 0.71 0.09 0.37 0.37 0.11 0.25 Summer Z 0.70 2.80 1.40 0.70 0.70 0.70 -0.90 -0.90 -0.90 P 0.50 0.01 0.15 0.47 0.47 0.46 0.39 0.39 0.36 Slope 0.01 0.02 0.01 0.09 0.09 0.26 -0.55 -0.24 -0.38 Winter Z 1.30 2.30 1.80 -1.10 1.10 1.50 1.40 1.50 1.40 P 0.20 0.02 0.08 0.28 0.27 0.14 0.15 0.14 0.15 Slope 0.01 0.03 0.02 -1.07 0.07 0.09 0.19 0.09 0.14   92  4.3.3 Cross-correlation between cumulative forest disturbance and streamflow components Cross-correlations between the CECA and each streamflow component in five-nested watersheds are summarized in Tables 4.6 to 4.10.  As shown in Tables 4.6, forest disturbance was not significantly (P>0.05) related to streamflow components in Camp, which indicated that forest disturbance did not cause a significant change in annual streamflow, baseflow, and surface runoff. In contrast, forest disturbance and all streamflow components were significantly related (P<0.05) in Hedley, Tulameen, Princeton and SRH, suggesting that forest disturbance has significantly affected annual streamflow, baseflow, and surface runoff in those watersheds. In addition, the positive coefficients of cross-correlation indicated that forest disturbance significantly increased annual total streamflow, baseflow, and surface runoff in Hedley, Tulameen, Princeton and SRH. It should be noted that the CECA of Princeton was only calculated for the Canadian portion. Although the upper portion of Princeton is mainly located in the conservation parks of Canada and the USA, recent MPB infestation might have enhanced forest disturbance in these areas, which was not included in our analysis. Thus, the relationship between the CECA and the streamflow components in Princeton are conservative.    Table 4.6 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Camp Creek watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) Hydrological Variables Cross-correlation ARIMA Model Coefficient Lags Annual Streamflow (1, 1, 0) 0.400 3 Annual Baseflow (0, 1, 1) 0.266 1 Annual Direct Runoff (0, 1, 1) 0.242 3 CECA ARIMA Model (1, 2, 0) 93  Table 4.7 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Hedley Creek watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) Hydrological Variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (1, 2, 1) 0.348* 0 Annual Baseflow (0, 2, 1) 0.354* 0 Annual Direct Runoff (0, 1, 1) 0.347* 0 ARIMA model for CECA (0, 2, 1)  Table 4.8 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Tulameen River watershed (the bolded numbers indicate the statistical correlations at the significance level of 0.05) Hydrological Variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (0, 2, 1) 0.317* 5 Annual Baseflow (0, 2, 1) 0.317* 5 Annual Direct Runoff (0, 1, 1) 0.348* 5 ARIMA model for CECA (0, 2, 1)  Table 4.9 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Similkameen River at Princeton (the bolded numbers indicate the statistical correlations at the significance level of 0.05) Hydrological variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (0, 1, 1) 0.287* 2 Annual Baseflow (0, 1, 1) 0.294* 2 Annual Surface runoff (0, 1, 1) 0.296* 2 ARIMA model for CECA (0, 2, 1) 94  Table 4.10 Cross-correlations between the cumulative equivalent clear-cut area (CECA) and streamflow components in the Similkameen River at Princeton (the bolded numbers indicate the statistical correlations at the significance level of 0.05) Hydrological Variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (0, 1, 1) 0.353* 8 Annual Baseflow (0, 1, 1) 0.354* 8 Annual Surface Runoff (0, 1, 1) 0.353* 8 ARIMA model for CECA (0, 2, 1)  4.3.4 Separation of the cumulative effects of forest disturbance on streamflow components in nested watersheds 4.3.4.1 The cumulative effects of forest disturbance on streamflow components in Camp Creek watershed The Modified Double Mass Curves (MDMCs) of streamflow, baseflow, and surface runoff were established for Camp over the study period of 1968-2013 (Figure 4.4). Only one break point detected by the Pettitt test occurred in 1989 for total streamflow, baseflow, and surface runoff with the CECA being 56.8%. Mann-Whitney U tests further confirmed that the slopes of MDMCs before and after the break points were statistically different (P<0.001) (Table 4.11). However, Moore and Scott (2005) used the regression analysis approach to quantify the effects of forest logging on the total streamflow for the period of 1971-2000. The largest logging event in 1982 was selected as the break point to separate the reference and disturbance periods. The difference in break points between this study and the study by Moore and Scott (2005) might be due to different research methods as well as different study periods. In addition, like many other PWE studies, the determination of break point in Moore and Scott (2005) was subjective.  In 95  contrast, this study used two methods that consistently revealed the same breaking point. Therefore, the determination of break point in this study is more robust.   The cross-correlation suggested that forest disturbance did not result in significant effects on streamflow components in Camp. However, the MDMC revealed that forest disturbance increased streamflow components. This is consistent with the PWE study in Camp (Moore and Scott, 2005). The MDMC revealed that streamflow, baseflow and surface runoff were increased by 2.16 ± 16.87mm, 0.48 ± 5.14 mm, and 0.99 ± 11.90 mm, respectively, with its Rf to streamflow components being 44.29%, 46.27%, and 40.25%. Conversely, climate variability decreased them by 2.72 ± 16.87 mm, 0.55 ± 5.14 mm, and 1.47 ± 11.90 mm, respectively, with Rc to streamflow components being 55.71%, 53.73% and 59.75 % (Table 4.12). Overall, the effects of climate variability on all streamflow components were slightly higher than those from forest disturbance, indicating that forest disturbance and climatic variability played an equal role in streamflow variations in Camp. The CEs of forest disturbance on streamflow components also showed temporal variations due to forest regeneration since 1990. Therefore, the disturbance period was further divided into two sub-periods, including 1990-2001 and 2002-2013 based on the distinct change in the rate of forest disturbance (Figure 3.9).  The streamflow components due to forest disturbance in the period of 1990-2001 were lower than those in 2002-2013. In summary, climate variability played a more important role in the variations of all streamflow components over the disturbance period in comparison to forest disturbance, but in the opposite direction.   96   Figure 4.4 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Camp Creek watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years).   97  Table 4.11 Tests on break points for the MDMC slopes of streamflow components in the Camp Creek watershed  Pettitt test Mann-Whitney Z test   K P Z P Q 521 <0.001 -5.681 <0.001 BF 529 <0.001 -5.907 <0.001 SR 529 <0.001 -6.075 <0.001  Table 4.12 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow components in the Camp Creek watershed from 1990 to 2013  Flow variable Periods ∆Q (mm) ∆Qf (mm) ∆Qc (mm) ∆Qf/Q (%) ∆Qc/Q (%) Rf (%) Rc (%) CECA (%) Q 1990-2001 18.04 12.23 ± 17.95 5.81 ± 17.95 7.89 3.75 67.78  32.22  56.0 2002-2013 -19.16 -7.91 ± 15.80 -11.24 ± 15.80 -6.72 -9.55 41.29  58.71  47.5 1990-2013 -0.56 2.16 ± 16.87 -2.72  ± 16.87 1.58 -1.99 44.29  55.71  51.7 BF 1990-2001 5.58 3.58 ± 5.47 2.00 ± 5.47 7.72 4.31 64.19  35.81  56.0 2002-2013 -5.73 -2.63 ± 4.82 -3.11 ± 4.82 -7.49 -8.86 45.82  54.18  47.5 1990-2013 -0.08 0.48 ± 5.14 -0.55 ± 5.14 1.17 -1.36 46.27  53.73 51.7 SR 1990-2001 12.46 7.93 ± 12.65 4.54 ± 12.65 7.30 4.18 63.59 36.41  56.0 2002-2013 -13.43 -5.94 ± 11.14 -7.48 ± 11.14 -7.19 -9.05 44.28  55.72  47.5 1990-2013 -0.48 0.99 ± 11.90 -1.47 ± 11.90 1.04 -1.54 40.25  59.75 51.7 Note: ∆Q is the difference of streamflow components between the reference and disturbance periods. ∆Qf and ∆Qc are the streamflow changes attributed to forest disturbance and climate variability, respectively. Rf and Rc are the relative contributions of forest disturbance and climate variability to streamflow components.   4.3.4.2 The cumulative effects of forest disturbance on streamflow components in Hedley Creek watershed The MDMCs of the streamflow components were established for Hedley in 1974-2013 (Figure 4.5). A significant break point was found on each MDMC determined by the Pettitt test, which occurred in 1995 for total streamflow, baseflow, and surface runoff with the CECA being 12.8%. The statistical difference between the slopes (P<0.05) of MDMCs before and after the break point was further confirmed by Mann-Whitney U tests (Table 4.13).  98  MDMC revealed that forest disturbance increased annual streamflow, baseflow, and surface runoff by 50.70 ± 20.26 mm, 18.20 ± 6.97 mm, and 38.51 ± 15.01 mm, respectively, while climate variability decreased them by 46.60 ± 20.26 mm, 15.70 ± 6.97 mm, and 33.32 ± 15.01 mm, respectively. The Rf  to streamflow, baseflow, and surface runoff were 54.89%, 53.68%, and 53.62%, respectively (Tables 4.14), which demonstrated that the effects of climate variability on all streamflow components were slightly lower than those from forest disturbance. As shown in Figure 3.17, the CECA in Hedley increased steadily with the MPB infestation since 2003. Streamflow components, therefore, experienced an increasing trend accordingly. The temporal analyses indicated the variations of streamflow components due to forest disturbance in 2005-2013 were higher than those in 1996-2004. The climate variability also played a higher impact in 2005-2013 than those in 1996-2004 (Table 4.14). In summary, forest disturbance significantly increased streamflow, baseflow, and surface runoff consistently in Hedley, and its contribution to the variations of streamflow components was higher than climate variability, despite their opposite directions.    99   Figure 4.5 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Hedley Creek watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years).   100  Table 4.13  Break point tests for the MDMC slopes of the streamflow components in the Hedley Creek watershed  Pettitt test Mann-Whitney Z test  K P Z P Q 322 <0.001 -2.209 0.027 BF 290 <0.001 -4.887 <0.001 SR 290 0.003 -4.141 <0.001  Table 4.14 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Hedley Creek watershed from 1996 to 2013  Flow Variable Periods ∆Q (mm) ∆Qf (mm) ∆Qc (mm) ∆Qf /Q (%) ∆Qc/Q (%) Rf (%) Rc (%) CECA (%) Q 1996-2004 7.66 48.69 ± 21.38 -21.38 ± 21.38 24.10 -20.31 54.27 45.73 17.3 2005-2013 7.71 64.67 ± 19.14 -56.96 ± 19.14 32.00 -28.18 53.17 46.83 54.1 1996-2013 7.69 56.70 ± 20.26 -49.00 ± 20.26 28.05 -24.25 53.64 46.36 35.8 BF 1996-2004 2.46 15.62 ± 7.36 -13.20 ± 7.36 24.17 -20.37 54.27 45.73 17.3 2005-2013 2.53 20.79 ± 6.60 -18.26 ± 6.60 32.13 -28.22 53.24 46.76 54.1 1996-2013 2.49 18.20 ± 6.97 -15.70 ± 6.97 28.15 -24.30 53.68 46.32 35.8 SR 1996-2004 5.20 33.11 ± 15.81 -27.90 ± 15.81 24.09 -20.31 54.27 45.73 17.3 2005-2013 5.18 43.92 ± 14.20 -38.74 ± 14.20 31.97 -28.20 53.14 46.86 54.1 1996-2013 5.19 38.51 ± 15.01 -33.32 ± 15.01 28.03 -24.25 53.62 46.38 35.8  4.3.4.3 The cumulative effects of forest disturbance on streamflow components in the Tulameen River watershed The MDMCs of streamflow components were established for Tulameen in 1954-2013 (Figure 4.6). Unlike Camp and Hedley, the timings of breaking points on MDMC of total streamflow, baseflow, and surface runoff were not consistent. The Pettitt test identified that break points occurred in 1982 with CECA of 15.9% for streamflow and surface runoff, while it was found in 1985 with CECA being 17.0% for baseflow. Additionally, the statistical difference of the MDMC slope before and after the break point was confirmed by the Mann-Whitney U tests 101  (Table 4.13). Cumulative forest disturbance could enhance snow accumulation and ablation process, and thus lead to more surface runoff. Meanwhile, cumulative forest disturbance also reduces evapotranspiration and increases soil moisture, hence leading to more baseflow. However, the effects on baseflow could take longer flow paths, and thus more time to recharge stream than surface runoff. As such, the lagged effects in baseflow to forest disturbance were found in Tulameen.   Over disturbance periods, forest disturbance increased annual streamflow, baseflow, and surface runoff by 32.96 ± 25.29 mm, 9.02 ± 6.80 mm, and 24.81 ± 18.10 mm, respectively. The Rf to streamflow components were 52.12%, 52.44%, and 52.30%, respectively (Tables 4.16). Climate variability decreased annual streamflow, baseflow, and surface runoff of 30.27 ± 25.29 mm, 8.18 ± 6.80 mm, and 22.49 ± 18.10 mm, respectively, with its Rc were respective 47.88%, 47.57%, and 47.70% (Tables 4.16). The temporal analysis demonstrated that the climate variability had higher impacts on the streamflow variations with relatively minor CECA in 1983-1993. The CECA in Tulameen increased steadily with dramatic MPB infestation since 2003 (Figure 3.19). As a result, the alterations of streamflow components attributed to forest disturbance in 2005-2013 were higher than those in 1994-2003 and 2004-2013. In short, climate variability and cumulative forest disturbance played an offsetting role in the variations of streamflow components as forest disturbance did in Tulameen.   102   Figure 4.6 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Tulameen River watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years).   103  Table 4.15  Tests on break point for the MDMC slopes of streamflow components in the Tulameen River watershed  Pettitt test Mann-Whitney Z test  K P Z P Q 899 <0.001 -6.652 <0.001 BF 876 <0.001 -6.474 <0.001 SR 892 0.003 -6.575 <0.001  Table 4.16 Temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Tulameen River watershed  Flow Variables Streamflow ∆Q ∆Qf (mm) ∆Qc (mm) ∆Qf/Q (%) ∆Qc/Q (%) Rf (%) Rc (%) CECA (%) Q 1983-1993 -9.06 30.31 ± 25.24 -39.37 ± 25.24 6.00 -14.33 43.50 56.50 11.71 1994-2003 3.92 13.91 ± 26.99 -9.99 ± 26.99 -2.80 -8.07 58.21 41.79 16.13 2004-2013 9.54 45.98 ± 23.65 -36.44 ± 23.65 8.81 -9.53 55.79 55.79 28.13 1983-2013 2.69 32.96 ± 25.29 -30.27 ± 25.29 3.29 -10.19 52.12 47.88 17.98 BF 1988-1993 -1.76 23.93 ± 6.65 -11.81 ± 6.74 5.84 -14.23 48.23 51.77 12.64 1994-2003 1.02 3.58 ± 7.26 -2.56 ± 7.26 -2.88 -7.84 58.31 41.68 16.13 2004-2013 2.97 13.14 ± 6.36 -10.17 ± 6.36 9.23 -9.45 56.36 43.64 28.13 1989-2013 0.84 9.02 ± 6.80 -8.18 ± 6.80 4.07 -10.51 52.44 47.57 17.98 SR 1983-1993 -3.94 18.84 ±18.45 -32.31 ± 18.06 2.92 -10.25 45.26 54.73 11.71 1994-2003 2.90 10.03 ± 19.27 -7.12 ± 19.31 -2.64 -8.28 57.87 42.13 16.13 2004-2013 7.97 36.02 ± 16.88 -28.05 ± 16.93 9.49 -9.94 56.11 43.89 28.13 1983-2013 2.31 24.81 ± 18.22 -22.49 ± 18.10 3.24 -9.54 52.30 47.70 17.98   4.3.4.4 The cumulative effects of forest disturbance on streamflow components in the Similkameen River at Princeton One break point was detected for total streamflow, baseflow, and surface runoff, which occurred in 1984, 1985, and 1984, respectively. Like Tulameen, the lagged response of baseflow to forest disturbance was also found in Princeton. Additionally, Mann-Whitney U tests confirmed that the 104  slopes of MDMCs before and after the break points were statistically different (P<0.001) (Table 4.17). The break points coincided with the history of forest disturbance as the CECA increased from 7.8 % in 1983 to 12.9% in 1985 (Figure 4.7).   Cumulative forest disturbance increased annual streamflow, baseflow, and surface runoff by 22.5 ± 16.9 mm, 6.5 ± 4.4 mm, and 15.8 ± 15.6 mm, respectively, with its Rf to streamflow components being 24.4%, 27.6%, and 23.7% over the disturbance periods. In contrast, climate variability decreased them by 69.7 ± 16.9 mm, 17.0 ± 4.4 mm, and 50.7 ± 15.6 mm, respectively, with Rc to streamflow components being 75.6%, 72.4% and 76.3%, respectively (Tables 4.18). Overall, the effects of climate variability on all streamflow components were much higher than those from forest disturbance, indicating the streamflow variations in Princeton were mainly caused by climate variability. Although climate variability is the dominated factor for streamflow variations, the relative contributions of forest disturbance to all streamflow components were at similar magnitudes in 1995-2004 than those in 1985-1994 and 2005-2013. In summary, results demonstrated that climate variability played a more dominate role in all streamflow components in comparison to forest disturbance, but in the opposite direction.   105   Figure 4.7 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Similkameen River at Princeton watershed; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years).   106  Table 4.17 Tests on break point for the MDMC slopes of streamflow components in Similkameen River at Princeton   Pettitt test Mann-Whitney U test K P Z P Q 760 <0.001 -4.058 <0.001 BF 783 <0.001 -6.197 <0.001 SR 543 0.005 -2.706 0.007  Table 4.18 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Similkameen River at Princeton watershed from 1985 to 2013  Flows Periods ∆Q (mm) ∆Qf (mm) ∆Qc (mm) ∆Qf/Q (%) ∆Qc/Q (%) Rf (%) Rc (%) CECA (%) Q 1985-1994 -67 9.8 ± 16.6 -76.8 ± 16.6 2.7 -20.8 11.3 88.7 14.4 1995-2004 -11.1 46.9 ± 17.5 -57.9 ± 17.5 11 -13.6 44.7 55.3 20.6 2005-2013 -65.5  9.6 ± 16.5 -75.0 ± 16.5 2.6 -20.2 11.3 88.7  32.4 1985-2013 -47.2 22.5 ± 16.9 -69.7 ± 16.9 5.8 -17.9 24.4 75.6  21.4 BF 1986-1995 -11.8 2.8 ± 4.5 -14.6 ± 4.5 2.7 -13.9 16.2 83.8 14.7 1996-2006 -10.0 5.5 ± 4.5 -15.5 ± 4.5 8.1 -14.5 26.2 73.8  17.4 2007-2013 -9.4 13.2 ± 4.2 -22.5 ± 4.2 7.8 -21.3 36.9 63.1  34.1 1986-2013 -8.6 6.5 ± 4.4 -17.0 ± 4.4  6.1 -16.0 27.6 72.4  21.7 SR 1985-1994 -49.3 6.6 ± 15.3 -55.9 ± 15.3 2.4 -20.7 10.5  89.5 14.4 1995-2004 -8.5 33.6 ± 16.1 -42.1 ± 16.1 10.8 -13.5 44.4 55.6  20.6 2005-2013 -48.3 6.3 ± 15.4 -54.5 ± 15.4 2.3 -20.1 10.3 89.7  32.4 1985-2013 -34.9 15.8 ± 15.6 -50.7 ± 15.6 5.5 -17.8 23.7 76.3  21.4   4.3.4.5 The cumulative effects of forest disturbance on streamflow components in the Similkameen River near Hedley MDMC showed that one break point was consistently detected for total streamflow, baseflow, and surface runoff, which occurred in 1990 with the CECA being 16.8% (Figure 4.8). Mann-Whitney U tests further confirmed that the slopes of MDMCs before and after the break points 107  were statistically different (P<0.001) (Table 4.19). Unlike Princeton and Tulameen, the timing of baseflow responded to forest disturbance was as similar as surface runoff and total streamflow. This might due to forest disturbance in the Wolfe has substantially affected the baseflow and promoted the baseflow response to forest disturbance in the SRH.  Over the disturbance period, cumulative forest disturbance increased annual streamflow, baseflow, and surface runoff by 19.70 ± 21.22 mm, 7.30 ± 7.78 mm, and 12.23 ± 13.51 mm, respectively, with its Rf  to total streamflow, baseflow, and surface runoff being 48.72%, 48.40%, and 48.97%, respectively. In contrast, climate variability decreased total streamflow, baseflow, and surface runoff by 22.13 ± 21.22 mm, 8.19 ± 7.78 mm, and 13.76 ± 13.51 mm, respectively, with its Rc to streamflow components being 51.28%, 51.60% and 51.03%, respectively (Tables 4.20). In summary, the effects of climate variability and forest disturbance on all streamflow components were at the similar magnitude in SRH. Recall that Rc to streamflow components in Princeton was>70%, while about 55% in Tulameen. This indicated that forest disturbance might dramatically increase streamflow components in Wolfe. Consequently, such increment may offset negative effects from climate variability in Princeton, leading to the similar role of Rf and Rc in SRH. As such, the spatial effects of the CEs of forest disturbance on streamflow components must be considered for large watersheds.  To examine the temporal variations of forest disturbance and climate variability, the disturbance period was further divided into three sub-periods (Table 4.20).  With significant forest disturbance since 2003, the Rf to all streamflow components in the 2006-2013 was higher than those in 1991-1997 and 1998-2004. In turn, the Rc to all streamflow components is higher in 108  1991-1997 and 1998-2004 than 2006-2013. In summary, climate variability and forest disturbance play an offsetting role in the streamflow variations with similar magnitudes in the SRH.    Table 4.19 Tests on break point for the MDMC slopes of streamflow components in Similkameen River at Hedley   Pettitt test Mann-Whitney U test K P Z P Q 364 <0.001 -3.873 <0.001 BF 552 <0.001 -5.874 <0.001 SR 546 <0.001 -5.810 <0.001   109   Figure 4.8 (A) Modified Double Mass Curves (MDMC) of the cumulative annual streamflow (Qa) against cumulative effective precipitation (Pae) in the Similkameen River at Hedley; (B) MDMC of the cumulative annual baseflow (BFa) against Pae; and C) MDMC of the cumulative annual surface runoff (SRa) against Pae (Triangles indicate break points (years).    110  Table 4.20 Mean temporal variations of the relative contributions of forest disturbance and climate variability to annual streamflow in the Similkameen River at Hedley watershed from 1985 to 2013  Flow Variables Periods ∆Q (mm) ∆Qf (mm) ∆Qc (mm) ∆Qf/Q (%) ∆Qc/Q (%) Rf (%) Rc (%) CECA (%) Q 1991-1997 6.6 29.01 ± 23.10 -22.41 ± 23.09 8.84 -6.84 47.73 52.27 14.81 1998-2004 -21.96 -4.00 ± 20.77 -17.96 ± 20.77 -1.51 -6.80 42.91  57.09  21.72 2006-2013 5.75 30.90 ± 20.10 -25.15 ± 20.10 10.20 -8.32 54.02  45.98  39.64 1991-2013 -2.43 19.70 ± 21.22 -22.13 ± 21.22 6.69 -7.52 48.72  51.28  24.68 BF 1991-1997 2.40 10.76 ± 8.47 -8.36 ± 8.47 9.66 -7.51 45.78  54.22  14.81 1998-2004 -8.15 -1.51 ± 7.62 -6.64 ± 7.62 -1.28 -7.40 43.31  56.69  21.72 2006-2013 2.19 11.46 ± 7.37 -9.27 ± 7.37 11.12 -8.99 54.38  45.62  39.64 1991-2013 -0.89 7.30 ± 7.78 -8.19 ± 7.78 -7.30 -8.19 48.40  51.60  24.68 SR 1991-1997 4.2 18.06 ± 14.70 -13.86 ± 14.70 9.37 -7.19 49.00  51.00  14.81 1998-2004 -13.81 -2.66 ± 13.22 -11.15 ± 13.22 1.71 -7.16 42.73  57.27  21.72 2006-2013 3.55 19.27 ± 12.80 -15.72 ± 12.80 10.80 -8.81 53.79  46.21  39.64 1991-2013 -1.53 12.23 ± 13.51 -13.76 ± 13.51 7.07 -7.95 48.97  51.03  24.68   4.3.4.6 Synthesis assessment of the cumulative effects of forest disturbance on streamflow in the study watersheds To further understand the underlying mechanisms of the CEs of forest disturbance on streamflow and its components, five non-nested watersheds in the interior of British Columbia were also included to enlarge sample size and draw a more generalized conclusion for the region. The CEs of forest disturbance on total streamflow in those watersheds were assessed using the same research methods as for the nested watersheds in this study. This would ensure that consistent methods are applied to all study watersheds so that the results from each watershed are comparable. The details regarding the assessment of the Deadman River and Fishtrap Creek watersheds are presented in Appendix A and Appendix B, respectively. As shown in Table 4.21, the sizes of ten watersheds range from 34.6 km2 to 5580 km2, PET/P values range from 0.5 to 1.3, and the CECA values range from 28.5% to 92.8%. This provides an opportunity to examine 111  how the CEs of forest disturbance on streamflow respond to various forest disturbance, climate, and watershed conditions in the southern interior of British Columbia.   The CEs of forest disturbance on total streamflow (∆Qf) in each watershed were then standardized with the CECA and shown as ∆Qf/CECA. The nonparametric Kendall tests were employed to examine the relationships between ∆Qf/CECA and climatic parameters (P, PET/P), and watershed characteristics (topographic indices) (Table 4.22). To date, numerous topographic indices have been developed to represent attributes of topography in a watershed.  Li et al. (2018a) identified 11 topographic indices that are sufficient to distinguish watershed topography in the southern interior of BC. Therefore, they were selected as the indicators for representing watershed properties in this study. The Kendall results revealed that no statistically significant (P>0.05) relationships were found between ∆Qf/CECA and P or PET/P. In contrast, statistically significant relationships were detected between ∆Qf/CECA and some topographic indices, including watershed area, downstream flow length, specific contributing area, topographic wetness index, and perimeter.  The positive correlations were detected for the watershed area, downstream flow length, specific contributing area, and perimeter, while negative correlations for topographic wetness index. This result indicates that the watersheds with the larger size, longer downstream flow lengths, higher specific catchment areas, and longer perimeters would have greater streamflow responses to forest disturbance. In contrast, the watersheds having higher topographic wetness indices would have a lower streamflow response to forest disturbance. In summary, watershed condition or topography is the vital factor influencing streamflow responses to the CEs of forest disturbance.  112  Table 4.21 Summary of the cumulative effects of forest disturbance on total streamflow in 10 watersheds in the southern interior of British Columbia using the MDMC approach (SD is standard deviation, and bolds are for five-nested watersheds) Watersheds Area (km2) CECA  (%) P (mm) PET/P ∆Qf  Average (mm year-1) ∆Qf  SD  (mm year-1) Camp Creek 34.6 43.4 724.1 0.5 24.4 31.5 Fishtrap Creek 135 92.8 471.9 1.3 47.8 43.4 Hedley Creek 388 59.3 612.3 0.7 56.7 78.5 Moffat Creek 548 71.5 672.3 0.8 45.6 18.0 Deadman River 878 41.3 470.2 1.0 30.6 22.3 Baker Creek 1550 71.8 536.8 1.0 39.5 21.5 Tulameen River 1780 36.7 928.2 0.5 30.7 98.0 Princeton  1810 30.1 999.0 0.8 27.7 127.6 Willow River 2860 28.5 603.3 1.0 70.5 61.6 SRH 5580 49 808.2 0.6 19.7 96.8    113  Table 4.22 Descriptions of topographic indices of study watersheds and their relationship with the cumulative effects of forest disturbance on total streamflow (Bolds indicate statistical significance at the level of 0.05) (Li et al., 2018a) Topographic indices  Description and references Kendall P Values Area Plan area of a watershed 0.58 0.02 Upslope contributing area UCA is the area that can potentially produce runoff to a given location (Erskine et al., 2006). 0.27 0.28 Downslope distance gradient DDG is a hydrologic measure of the impact of the local slope characteristics on a hydraulic gradient. Values are low on concave slope profiles and high on convex slope profiles (Hjerdt et al., 2004). 0.29 0.27 Downstream flow length The downslope distance of a pixel along the flow path to the outlet of a watershed (Greenlee, 1987). 0.51 0.04 Slope Length Factor LS is a combined factor of slope length and slope gradient. It represents the ratio of soil loss per unit area on a site to the corresponding loss from a 22.1 m long experimental plot with a 9% slope (Desmet and Govers, 1996). 0.30 0.24 Positive topographic openness Describe the degree of dominance or enclosure of a location on an irregular surface. Values are high for convex and low for concave forms, respectively (Yokoyama et al., 2002).  -0.45 0.12 Relief The difference between the highest and lowest elevations within a local analysis window. 11×11 grid cell window is used in this paper. 0.30 0.24 Specific contributing area (SCA) Upslope contributing area per unit length of contour (Quinn et al., 1991). 0.51 0.04 Slope degree Slope degree of each DEM pixel (Burrough et al., 2015). 0.28 0.28 Surface area The land area of each DEM, which may provide a better estimation of the surface roughness than the planimetric area (Jenness, 2004). A lower value indicates a gentler topography.   0.37 0.20 Terrain ruggedness index TRI expresses the degrees of difference in elevation among adjacent cells (Riley, 1999). It calculates the sum changes between a grid cell and its eight neighbour grid cells. Higher values indicate more ruggedness of a watershed. 0.34 0.17 Topographic wetness index TWI = ln (SCA/Tan(slope)), it shows the spatial distribution of zones of surface saturation and soil water content (Ambroise et al., 1996; Quinn et al., 1995). -0.47 0.09 Perimeter The perimeter of a watershed.  0.45 0.07  114  4.4 Discussion 4.4.1 Baseflow separation methods The mean annual baseflow for Camp, Hedley, Tulameen, Princeton, and SRH were 40 ± 14 mm (or 5.7% of average annual precipitation), 63 ± 24 mm (or 10.3% of average annual P), 98 ± 28 mm (or 11.3% of average annual P), 107 ± 35 mm (or 11.3% of average annual P), and 99 ± 29 mm (or 13.4% of average annual P), respectively. Our estimations of baseflow were comparable to groundwater recharge rates estimated by other studies near the region. For examples, average annual recharge rates were 88 mm or 19.7% of precipitation in Vernon, Northern Okanagan, British Columbia (Liggett and Allen, 2010) and 77.8 ± 50.8 mm or 15.7% of precipitation in the Deep Creek watershed in North Okanagan (Assefa and Woodbury, 2013).    Several studies at the small watershed scale indicated that forest disturbance increased the conductivity in streams as well as other hydro-chemical data (Caissie et al., 1996; Covino and McGlynn, 2007; Pike et al., 2010; Yarie et al., 1993). This may lead to a concern over the assumption of the conductivity being temporally constant for applying the CMB method (Halford and Mayer, 2000). To address this concern, the long-term discrete conductivity measurement in the Similkameen River collected at Princeton, which includes specific conductance, streamflow temperature, and other water quality data (e.g., copper, zinc, nitrogen and etc.) (Figure 4.9) were used for analysis. There was, however, the absence of 10-year data collection (1975-1984, 1986). From 1986 onwards, data collection was made roughly twice per month. A total of 823 samples from 1966 to 2013 were collected and presented in Figures 4.9 and 4.10. The conductivity ranged from 47.4 to 274.1 μS cm-1. As expected, a close relationship between conductivity and streamflow was shown in Figure 4.10.  115   Figure 4.9 Long-term (1966-2013) discrete conductivity measurements and continuous streamflow data in the Similkameen River at Princeton   Figure 4.10 The relationship between streamflow conductivity (Y) and streamflow (X) in the Similkameen River at Princeton  116  The accuracy of baseflow estimation using the CMB method is highly dependent on the selection of baseflow and surface runoff conductivities (Cbf and Cro). Like other baseflow separation methods, all contributed flow components are lumped into two broad components (i.e., baseflow and surface runoff). In practice, there are temporal variations in those two end-members (Miller et al., 2014). Therefore, annual Cbf and Cro were calculated for each hydrological-year (i.e., August to September) to minimize temporal variations in conductivity. Conductivities corresponding to the flow rates exceed 5% and non-exceed 95% percentiles in each year were averaged and treated as annual Cro and Cbf, respectively. As a result, a total number of 18 conductivities were selected as Cro, while 15 as Cbf (Tables 4.23 and 4.24).   Table 4.23. Selected surface runoff conductivities (Cro), flows, and corresponding flow percentiles for the Similkameen River at Princeton from 1967 to 2013. The percentile indicates the exceedance probability.  Year Flow (m3/s) Julian Date Cro Percentile 1967 169 171 51 2 1968 133 144 60.9 2 1969 141 134 56 1 1970 174 154 47.4 1 1984 117 172 55.3 4 1988 111 144 57.7 1 1994 103 130 57 1 1996 162 157 67 1 1998 128 125 57 1 1999 245 166 53 1 2001 117 149 58 2 2006 111 144 52 2 2007 159 156 50 1 2008 266 140 62 1 2009 121 152 56 1 2011 131 172 66 4 2012 106 143 73.7 4 2013 88.7 141 64 3 117  Table 4.24. Selected baseflow conductivities (Cbf), flow rates, and corresponding flow percentiles Year Flow (m3/s) Julian Date Cbf Percentile 1968 3.26 355 153 98 1984 2.25 340 252 98 1985 2.02 37 175 99 1991 1.67 302 274 100 1992 1.61 329 220 99 1994 1.4 326 248 99 1995 2.1 27 206 99 1996 3.51 325 216 100 2000 3 348 226 99 2002 1.15 330 218 100 2006 2.62 255 203 95 2008 1.9 350 230 99 2009 3.4 286 192 99 2010 2.89 327 200 99 2013 3.78 57 185 99  Table 4.25 Trend tests of conductivities of surface runoff (Cro), baseflow (Cbf), and streamflow (Cq)     Kendall tau Spearman rho Coefficient P value Coefficient P value Cro 0.296 0.09 0.437 0.07 Cbf -0.219 0.26 -0.207 0.46 Cq 0.033 0.15 0.047 0.18  Two non-parametric tests, Kendall tau and Spearman’s rho, were selected for the temporal trend detection at the significance level of 0.05 for Cro, Cbf, and Cq (Table 4.25). The analysis showed that no significant temporal trends were detected in those variables (P>0.05), indicating that cumulative forest disturbance did not cause statistically significant changes in Cro, Cbf, and Cq in the Similkameen River at Princeton. Therefore, the effects of forest disturbance did not significantly affect the applications of the CMB method in Princeton and other watersheds. In addition, Li et al. (2014) suggested that a minimum data requirement for this combined baseflow 118  separation method is 6 months over low flow period. The continuous conductivity data in this study were collected for one year to minimize the possible uncertainties in the baseflow separation method. Furthermore, the RDF method has been proven to be an accurate baseflow separation method with a reasonable estimation of BFImax from a tracer method (Zhang et al., 2017a). In addition, this combined baseflow separation method has also been applied to other regions (e.g., Saraiva Okello et al., 2018), which further validated the utility of this method. In summary, the selected baseflow separation method (RDF) is sound for this study, and its application provides reliable estimates of baseflow or groundwater recharge in the study watersheds.   4.4.2 The cumulative effects of forest disturbance on total streamflow    The cumulative forest disturbance has consistently increased total streamflow in the five-nested watersheds. The positive responses of total streamflow to forest disturbance are generally consistent with the results from many studies (e.g., Li et al., 2017). The key reasons for an increment of streamflow components are that forest disturbance removes vegetation, decreases evapotranspiration and consequently increases streamflow. However, there were large variations in the total streamflow responses among the study watersheds.  For example, 59.3% of CECA in Hedley has increased total streamflow by 56.7 mm or 28.05% of streamflow, while 43.4% and 49% of CECA in Camp and SRH have increased total streamflow by 2.16 mm (or 1.58% of total streamflow) and 19.7 mm (or 6.69% of streamflow), respectively. Zhang (2013) reported that 71.8% of CECA in Baker River watershed led to a total streamflow increase by 39.5 mm (or 46.9% of streamflow), while an increment in 70.5 mm or 9.8% of total streamflow was only attributed to a CECA of 28.5% in Willow River watershed. Similar to our study, large variations 119  of total streamflow response to forest disturbance have been extensively reported in both small (Zhang et al., 2017a) and large watersheds (Li et al., 2017).       The large variations in the responses of total streamflow to forest disturbance among the five studied watersheds are likely related to their different watershed properties. Our analysis shows the significant relationships between topographic indices and ∆Qf/CECA. In addition, the additional analysis with inclusion of all 10 watersheds also found significant positive correlations between ∆Qf/CECA and watershed area, downstream flow length, specific catchment area, and perimeter, while significantly negative correlations were detected between topographic wetness index and ∆Qf/CECA (Table 4.22). The positive correlations between ∆Qf/CECA and watershed area and perimeter imply that streamflow in larger areas has the greater responses to forest disturbance. This finding is contrary to the common perception that larger watersheds have higher buffering capacity due to more complexity in landforms (Li et al., 2017; Zhang et al., 2017a). The positive relationship between the responses of streamflow and watershed size might be due to the enhanced synchronization effects of forest disturbance (Zhang and Wei, 2014) as well as possible land-atmosphere interactions in snow-dominated systems (Li et al., 2018c). With watershed size increasing, the land-atmosphere interactions may be more pronounced due to the forest-climate feedback, which in turn may lead to a promoted response in larger watersheds (Zhang and Wei, 2012). The correlation tests also indicated that downstream flow length, specific catchment area, and topographic wetness index are significantly related to ∆Qf/CECA. As such, more complex topography in the larger watershed may amplify the ∆Qf/CECA.   120  The non-parametric Kendall correlation test shows that no statistically significant correlations were detected between ∆Qf/CECA and climatic variables (i.e., P and PET/P) (Table 4.21). This may be due to the fact that the study watersheds are located in a relatively similar climate condition. The lack of significant differences in climate might be the reason for the undetectable change in streamflow responses to forest disturbance among the study watersheds.     4.4.3 The cumulative effects of forest disturbance on baseflow and direct runoff In our study, forest disturbance increased baseflow and surface runoff in study watersheds. The increase in baseflow and surface runoff are likely attributed to the removal of vegetation, alteration of soil conditions and the associated loss of soil infiltration capacity after forest disturbance. In snow-dominated watersheds, more snow accumulation, and earlier and quicker melting are expected after forest disturbance (Winkler et al., 2005), which consequently results in an increase in surface runoff. Meanwhile, forest disturbance also increases soil moisture and groundwater recharge, leading to more baseflow.   The increasing of baseflow and surface runoff after forest disturbance is consistent with the results from the studies in both small and large watersheds. For example, in small watersheds, a 21-49 cm rise in groundwater table was observed after three years of clear-cut in Gainesville (0.42 km2), Florida, USA (Table 2.1; Bliss and Comerford, 2002). Other case studies in small watersheds can also be found in Table 2.1. In large watersheds, the land conversion from forests to agriculture land led to an increase in surface runoff and baseflow in Wisconsin, the USA (Mishra et al., 2010). Ahiablame et al. (2017) found that every 1% increase in the agricultural land can lead to 0.2% decrease in baseflow. However, the inconsistent baseflow and surface 121  runoff responses to forest change were reported in the literature. For instance, Ma et al. (2009) showed that reforestation decreased surface runoff and total streamflow, but increased baseflow. Zhou et al. (2013) also found that surface runoff was increased of 11.3% while baseflow was decreased by 11.2% due to forest deduction and increase in urban area in Xitiaoxi Basin (1371 km2), China. Thus, baseflow and surface runoff can be decreased or increased after forest disturbance or land use change mainly depending on altered soil conditions and associated changes in infiltration capacities (Bruijnzeel, 1990, 2004; Liu et al., 2015b; Liu et al., 2016).   Understanding the impacts of forest disturbance on baseflow has profound implications for managing groundwater resources. Dynamics of baseflow or groundwater recharge are critical for explaining the variations of groundwater storage and water quality in a watershed. For example, Zhang and Schilling (2006) found that elevated nitrate levels in streams were mainly from baseflow. Zhou et al. (2013) demonstrated that the expansion of urban area led to 11.3% increase in surface runoff and 11.2% decrease in baseflow. Such a pattern shift has important influence on droughts and consequently groundwater management. This also suggests that a comprehensive understanding of how various streamflow components respond to forest disturbance or land cover change can help understand and manage groundwater resources.  4.4.4 Relative contributions of forest disturbance and climate variability to streamflow Different magnitudes of relative contribution to forest disturbance (Rf) in the study watersheds were summarized. Specifically, the Rf in Camp, Hedley, Tulameen, Princeton, and SRH were 44.3% (CECA of 43.4%), 54.9% (CECA of 59.3%), 52.1% (CECA of 36.7%), 24.4% (CECA of 30.1%), and 48.7% (CECA of 49%), respectively. In the other non-nested watersheds, Rf was 122  42.7% in the Willow River watershed with CECA being 23.8%, while 40.4% in the Bake River watershed with CECA being 35.0%, 43.3% in the Moffat River watershed with CECA being 40.0%, 86.2% in the Deadman River watershed with CECA being 56.4%, and 60.4% in Fishtrap Creek watershed with CECA being 92.8%. Suprisely, the Rf  in Princeton was much lower than that in Tulameen as they are similar in watersheds sizes and experienced similar forest disturbance or similar magnitudes of CECA. Unlike Tulameen, Princeton has a mixed type of climate with a moist climate in the upper portion (mainly located in the conservation parks) of the watershed. This moisture climate may decrease the sensitivity of hydrological responses to forest changes as various studies demonstrate that the hydrological effects of forest changes in wet regions are less sensitive than those in dry regions (Zhou et al., 2015).  Nevertheless, the Rf values in this study demonstrated that forest disturbance and climate variability were equally important to streamflow alterations, which are consistent with a recent review by Li et al. (2017) and a recent global assessment by Wei et al. (2018).    Variations in the relative contributions of forest or land cover change and climate variability to streamflow components have been reported in the literature (Table 2.1). For examples, all streamflow components were more sensitive to climate variability than to the land cover changes in the Heihe River basin (12800 km2), in Northwest China (Zhang et al., 2016) and in Xixian Basin, China (10191 km2) (Shi et al., 2013a). Similarly, the application of the Variable Infiltration Capacity model in the Qingyi River watershed (13263 km2) showed that total streamflow and baseflow changes were mainly attributed to climate variability rather than land cover changes (Liu et al., 2013).  Conversely, land cover changes were reported to play a more dominant role in the changes of all major streamflow components in the Kejie watershed (Ma et 123  al., 2009) and Upper Du watershed (8961 km2) (Huang et al., 2016) in China. Those contrasting results suggested there are large variations in hydrological responses, which are mainly due to the different levels of disturbance, climate, and watershed properties. More case studies are needed to further strengthen our understanding of the relationship between forest changes and streamflow components.   Forest disturbance and climate variability can have offsetting or additive effects on annual streamflow (Wei and Zhang, 2010; Zhang et al., 2008; Zhang et al., 2012). Our study indicated that forest disturbance and climate variability played an offsetting effect on all streamflow components. Similarly, the offsetting effects of forest disturbance and climate variability on all streamflow components have been detected in the Be River catchment using SWAT (Khoi and Suetsugi, 2014). In contrast, Liu et al. (2013) detected that land cover changes enhanced the impacts of climate variability on all streamflow components in the Qingyi River watershed, China.  The offsetting effects can lead to less variations in water resources, while additive effects can cause river flows to either increase (e.g., higher chances of floods) or decrease (e.g., higher chances of droughts) (Li et al., 2017). Either offsetting or additive effects would have important implications for water supply, public safety and ecological functions (e.g. Power et al., 1999).  4.5 Summary Quantifying the cumulative effects of forest disturbance on streamflow components has rarely been reported in the literature. Five nested watersheds located in the southern interior of British Columbia, including Camp, Hedley, Tulameen, Princeton, and SRH, and experienced dramatic forest disturbance, were selected to study the hydrological effects caused by cumulative forest 124  disturbance. In the study region, the long-term annual baseflow index has been determined to be around 0.30 with slight variation between watersheds.  Our results show that the cumulative forest disturbance consistently increased total streamflow, baseflow, and surface runoff, while climatic variability decreased them. However, there were large variations in the cumulative effects of forest disturbance on all streamflow components. Such large variations may be associated with the variations in cumulative forest disturbance levels, altered soil conditions after forest disturbance, and watershed property. Moreover, topography has been shown to play a significant role in the cumulative hydrological effects of forest disturbance. In addition, our analysis clearly demonstrates that forest disturbance and climate variability played an important role in all streamflow components, but in the opposite directions. The conclusions from this study can support water or watershed managers to manage our forested watersheds sustainably in the context of future forest disturbance and climate change.      125  Chapter 5: Scaling properties of the cumulative effects of forest disturbance on streamflow components 5.1 Overview Scaling is the central issue in many aspects of hydrology (Blӧschl, 2006; Buttle and Eimers, 2009), which stems from seeking connections of hydrological processes at different spatial and temporal scales (Gupta and Dawdy, 1995; Smith, 1992). The importance of scaling issue in hydrology has been recognized since the 1980s for predicting magnitudes of floods in a region (NRC, 1988). The aims of scaling studies are: 1) to estimate hydrological variables in ungauged basins [Prediction in Ungauged Basins (PUB)] to support engineering design and watershed management (Sivapalan, 2003; Hrachowitz et al., 2013); and 2) to understand the underlying mechanisms of regional hydrological processes (e.g., rainfall and streamflow generation; Kumar and Foufoula-Georgiou, 1993).   The power law relationship laid a basis for understanding and predicting the physical and statistical characteristics of hydrological processes across various spatial scales (Gupta et al., 1994; Kumar et al., 1994). Based on this relationship, the index flood method was initially treated as the primary approach for regional flood analysis (Dawdy, 1961), which was developed on the assumptions of 1) the relationship between flood flows and watershed area being log-log linear; and 2) the ratio of floods to mean annual floods being not dependent on the drainage area. However, Cadavid (1988) could not verify the second assumption of the index flood method in the Southeastern Appalachia regions of the USA. Furthermore, Gupta et al. (1990) revealed that the premise of the index flood method lacked “homogeneity”, i.e. the CV (coefficient of 126  variation) of floods varied with spatial scales. Hence, to present the shortcoming of the index flood method, the simple- and multi-scaling concepts were further introduced (Gupta and Waymire, 1990; Smith, 1992, Kumar et al., 1994). The simple-scaling is defined as the log-log linear relationship between the hydrological variables and watershed area. Additionally, the CV of hydrological variables does not vary with spatial scales. In contrast, multi-scaling also holds the log-log linear relationship, but the CV varies with spatial scales. For instance, Gupta and Dawdy (1994) found that annual mean flood flows were simple-scaling in the snow-dominated regions, while they obeyed multi-scaling in the rain-dominated regions in the Appalachian region, USA.   Another critical issue existing in the scaling studies is that the watershed area has long been treated as the primary scaling parameter to represent spatial scales. Although the watershed area can significantly explain the variations of hydrological variables, it has the limited explanatory power in some regions for specific hydrological variables. For example, Dingman and Palais (1999) recommended that the bankfull width was a better scaling parameter than the watershed area for floods using the data from 36 gaging stations in New Hampshire and Vermont, USA. Similarly, basin physiography (e.g., drainage density, slope, peatland and pond coverage, baseflow index, etc.) has been demonstrated to explain the variations in scaling property (Buttle and Eimer, 2009; Medhi and Tripathi, 2015). In addition, numerous topographic indices (TIs) have been developed to describe the topography of watersheds and infer driving mechanisms of hydrological processes (Moore et al., 1991), such as soil moisture and watershed shapes, whereas watershed area not. Therefore, whether these topographic indices are suitable for being the scaling parameter is an open question to be answered.  127  Forest change or land cover change is an important component to drive hydrological alterations in any forested watersheds (Wei et al., 2018). To date, numerous studies have been carried out to assess the effects of forest or land cover change on hydrology at various spatial scales. Researchers and managers are seeking knowledge to extrapolate the effects of forest change on hydrology from one spatial scale to another to understand cumulative effects and design management strategies accordingly. As far as we know, there are no any studies that have investigated the scaling property of the CEs of forest disturbance on streamflow and as well as its components.   Therefore, the major objective of this chapter was to assess the scaling properties of the CEs of forest disturbance on streamflow components in the five-nested watersheds. The specific objectives included: 1) to examine scaling properties of the observed streamflow components in the study watersheds; 2) to investigate whether some topographic indices can be used as suitable scaling parameters; and 3) to explore scaling properties of the CEs of forest disturbance on streamflow components.   5.2 Methods 5.2.1 Research design The following three sections were designed to achieve the above-mentioned research objectives. In section I, two groups of the study watersheds were classified to investigate the scaling properties of observed streamflow. The first group includes the five nested-watersheds experienced dramatic forest disturbance. This will minimize the variations in watershed properties among watersheds (McNamara et al., 1998). While the second has an additional five 128  non-nested watersheds so that the second group has 10 ten watersheds in total. The aim of using the second group was to confirm or check the scaling properties derived from the first group watersheds. In addition, the derived scaling properties were further tested for applicability to annual streamflow in the southern interior of British Columbia to provide the regional scaling properties. In this section, three scenarios including the entire study period, reference period, and disturbance period were designed for those two groups of watersheds, respectively. The reference and disturbance periods were divided by the break points on the modified double mass curves (see Chapter 4 for the details). In Section II, several topographic indices were also examined and tested for the eligibility to be scaling parameters for each group. In Section III, the scaling properties of the CEs of forest disturbance on streamflow were examined for each group. In addition, the scaling properties of baseflow and surface runoff were also tested. As presented in Chapter 2, both the product moments and probability weighted moments were applied for assessing scaling properties for each scenario.   5.2.2 Product Moments method The scaling relationship of flow variables Q(Ai) and Q(Aj) in two watersheds (i and j) with size Ai and Aj can be written as  ( ) ( , ) ( )i i j jQ A f A A Q A≅    (5-1) where ≅  implies equality of the probability distribution of flow variables of i-th and j-th watersheds; and ( , )i jf A A is the scaling transformation function. The scale transformation can be a function of any watershed property parameters (e.g. watershed area, bankfull width). Here, the 129  watershed area is treated as a proxy for scaling parameter as it has been used extensively. Under the simple-scaling hypothesis, the transformation function is expressed as Eqn. (5-2).  ( , ) ii jjAf A AAθ =          (5-2) where, θ is the scaling exponent and is always greater than zero as the magnitude of hydrological variables increases with watershed area increasing. The ratio of Ai and Aj is defined as a scaling parameter. Gupta and Waymire (1990) and Smith (1992) demonstrated that under the simple-scaling hypothesis, the kth ordinary product moment of a flow variable is shown as: [ ( )] [ ( )]kk kii i j jjAE Q A E Q AAθ =        (5-3)  The basin j is treated as the reference watershed with unit area, which is equal to 1. Then, by taking the natural logarithm of Eq. (5-3), the following equation can be derived.  ln( [ ]) ln( )ki k k iE Q a b A= +      (5-4) ln( [ (1)])kk ja E Q=       (5-5) kb kθ=       (5-6)   If a hydrological variable (e.g., annual streamflow) obeys simple-scaling, then Eqns. (5-4) and (5-6) hold. Namely, the logarithm of the k-order moment of a flow variable is a linear function of the logarithm of drainage area. In addition, the slope is a linear function of the moment order k. If a hydrological variable obeys multi-scaling, then Eqn. (5-4) holds but Eqn. (5-6) does not, indicating the slope is not a linear function of the moment order k. 130  5.2.3 Probability Weighted Moment method The probability weighted moment (PWM) was developed to identify the scaling property of a hydrological variable across various spatial scales (Kumar et al., 1994). The estimation of scaling property by the PWMs is more robust against possible outliers than the PM method. Similar to the PM method, drainage area (Ai (j)) is used as a scaling parameter. Under the simple-scaling hypothesis, the following relationship holds.  ln( ) ln( ) ln( / )i jk kA A i jH A Aβ β= +     (5-7) where, H is the scaling exponent. Assuming Aj is reference watershed area (Aj =1), the Eqn. (5-7) can be rewritten as Eqn. (5-8) ln( ) ln( )ikA k iC H Aβ = +          (5-8) Where, 1ln( )kkC β= , and ikAβ is the k-th PWM of a flow variable of watershed i, and is expressed as Eqn. (5-9).  ( ) ( )0( )i i ik i kA Q A Q A iq F dF qβ∞= ∫      (5-9)  Where, ( ) Pr[ ]i iF q Q q= ≥ . The estimate of ikAβ from the sample data can be given by  ( )1111ii jn kkAjn jqknkkβ−=−   =+   + ∑      (5-10)  where, n is sample size, and{ }( )i jq  is the descending order of a hydrological variable (i.e., (1) (2) ( )i i i nq q q≥ ≥ ≥ ). If a flow variable obeys the simple-scaling law, the log-log linear relationship between the PWM and drainage area as given in Eqn. (5-8) holds for all moment 131  orders of k. In addition, the slope (H) is constant, and is independent of k. Otherwise, they hydrological variables follow the multi-scaling.   5.2.4 The physical property of the scaling exponent The magnitude of flow rates naturally increases with increasing of watershed size. However, the change rates of any hydrological variables exhibit either dampening or amplification processes with increasing of watershed size. The derivation of the physical property of the power law is described as follows.   The scaling transformation function or power law of the equation can be rewritten as  i jQ k Qθ=       (5-11) The first and second derivatives of Eqn. (5-11) are shown as Eqns. (5-12) and (5-13), respectively. 1ijQ k Qkθ θ−∂=∂      (5-12) 222 ( 1)ijQ k Qkθ θ θ−∂= −∂    (5-13)  The positive or negative value of the first derivative of a function indicates that the function is either increasing (e.g., 0iQk∂>∂) or decreasing (e.g., 0iQk∂<∂), respectively. Similarly, the positive and negative value of the second derivative implies that the shape of the function is either concave (e.g.,22 0iQk∂>∂) or convex (e.g., 22 0iQk∂<∂). From a hydrological perspective, the 132  magnitudes of hydrological variables increase with watershed size, suggesting θ > 0. As such, Eqn. (5-11) is the monotonous increasing function (i.e. 0iQk∂>∂). It should be noted that the positive or negative of the second derivative is determined by the values of scaling exponent (θ). Therefore, a critical point can be identified for the power function (Eqn. 5-14), where the equation of 22iQk∂∂changes from positive to negative or vice versa. When 0 < θ <1, the shape of 22iQk∂∂is convex, indicating that the increment rate of Qi diminishes with increasing of watershed sizes. When θ > 1, the shape of 22iQk∂∂is concave, suggesting the increment rate of Qj increases with watershed size. In short, the value of scaling exponent demonstrates significantly different hydrological processes in a region.   220 0 10 10 1iif Dampening processQ if Critical pointkif Amplificaton processθθθ< < <∂ = = =∂ > >  (5-14)  5.2.5 Scaling property of observed streamflow in the study watersheds Both the PMs and PWMs were performed for annual streamflow, baseflow, and surface runoff for the three different time spans (i.e., whole, reference, and disturbance periods) in the five-nested watersheds. The reference and disturbance periods were separated by the break point on the modified double mass curves (MDMC) for each watershed (see Chapter 4 for the details). The selection of three periods for examinations can provide insights on how the cumulative 133  forest disturbance affects observed streamflow, baseflow, and surface runoff. Then, the PMs and PWMs methods were also conducted for the second group of the watersheds to examine whether the conclusions from the first group remain valid for the second group.   It would be useful to compare the results on scaling properties from two groups of the watersheds with those from a much larger number of the regional watersheds. To do this, the watersheds in the southern interior region of BC were selected based on the following criteria: 1) the watershed size is larger than 20 km2, as smaller watersheds may have distinct hydrological processes (Eaton et al., 2002; Smith, 1992); and 2) watersheds must have long-term monitoring data (e.g., >30 years).  As a result, a total number of 70 watersheds were selected in the southern interior of BC with watershed sizes ranging from 20.8 km2 to 19600 km2. As shown in Figure 5.1, the sizes of our studied watersheds lie between 500 and 5000 km2, which the selected regional watersheds fall in.      Figure 5.1 Size distribution of the selected 70 watersheds located in the southern interior of British Columbia with the watershed sizes ranging from 20.8 km2 to 19600 km2 051015202550 100 500 1000 5000 >5000Frequency (%)Watershed area (km2)134  5.2.6 Investigation of topographic indices as scaling parameters In this study, a total number of 12 topographic indices, which were considered as the unique topographic indices to distinguish the topography of watersheds for the southern interior of BC were derived for ten watersheds (5 nested and 5 non-nested). These indices include upslope contributing area, downslope distance gradient, downstream flow length, slope length factor, positive topographic openness, relief, specific contributing area, slope degree, surface area, topographic ruggedness index, topographic wetness index, and perimeter (see Table 4.25 for their definitions). To test the eligibility of topographic indices as scaling parameters, the watershed area in the PMs and PWMs methods were replaced by each topographic index to examine whether the scaling relationship holds between the tested TIs and hydrological variables in the five-nested as well as the ten watersheds.   5.2.7 The scaling property of the CEs of forest disturbance on streamflow, baseflow, and surface runoff The CEs of forest disturbance on streamflow, baseflow, and surface runoff were investigated in first group watersheds (five-nested), while their impacts on total streamflow were examined in second group watersheds (ten watersheds). The CEs of forest disturbance on annual streamflow and its components (∆Qf) were derived by MDMC. Among the selected watersheds, the ∆Qf in each watershed was, therefore, attributed to various levels of cumulative forest disturbance. To eliminate the uncertainties, the changes of annual streamflow components due to forest disturbance (∆Qf) in each watershed were standardized with its CECA and marked as ∆Qf/CECA. As such, the cumulative effects of forest disturbance on the streamflow between watersheds were minimized. Then, ∆Qf/CECA in each watershed was served as the input for the 135  PMs and PWMs to explore the CEs of forest disturbance on streamflow components in the five-nested (the first group) as well as in the ten watersheds (the second group).   5.3 Results 5.3.1 Scaling properties of streamflow components for different study periods The PMs and PWMs were established for annual streamflow, baseflow, and surface runoff for the three different time spans (the whole, reference, and disturbance periods) in the five-nested watersheds.  The PMs and PWMs model parameters for the three periods were detailed for streamflow (Tables 5.11 to 5.13), baseflow (Tables 5.14 to 5.16) and surface runoff (Tables 5.17 to 5.19). Both the PMs and PWMs consistently revealed that annual streamflow, baseflow, and surface runoff in the five-nested watersheds obeyed the simple-scaling law in the three periods (i.e., Eqns. 5-4 and 5-6 hold for PMs and Eqns. 5-8 for PWMs) (The 70 watersheds in the Southern Interior of BC was used as an example to explain of how to determine the simple- and multi-scaling using PMs and PWMs in the following section). For example, the average scaling exponents of annual streamflow, baseflow, and surface runoff for the five-nested watersheds were 1.176, 1.189, and 1.172, respectively for the whole study period (Table 5.1). The result from the second group (10 watersheds) was consistent with those from the five nested watersheds (Table 5.2). In summary, the scaling properties of annual streamflow consistently followed the simple-scaling law based on our analyses of the two grouped watersheds. More importantly, the scaling exponents in all three periods were greater than 1, indicating that the annual streamflow in the selected watersheds exhibited amplification processes.   136  Table 5.1 Scaling exponents of annual streamflow, baseflow, and surface runoff in five-nested watersheds for the whole study period, reference period, and disturbance period, respectively in the southern interior of British Columbia.  Scaling Exponent Annual streamflow Baseflow Surface runoff PMs PWMs Average PMs PWMs Average PMs PWMs Average Whole  1.168 1.183 1.176 1.180 1.198 1.189 1.163 1.181 1.172 Reference 1.169 1.173 1.171 1.171 1.184 1.178 1.153 1.167 1.160 Disturbance 1.254 1.239 1.247 1.201 1.200 1.201 1.185 1.185 1.185   Table 5.2 Scaling exponents of annual streamflow in ten watersheds for the whole, reference, and disturbance periods, respectively in the southern interior of British Columbia. Scaling exponent  PMs PWMs Average Whole  1.144 1.171 1.158 Reference 1.148 1.152 1.150 Disturbance 1.172 1.194 1.183   The PMs were also established for annual streamflow in 70 watersheds in the southern interior of BC. Table 5.3 showed the coefficients (ak and bk in Eqn. (5-4)) of the estimated linear regression models between ln( [ ])kiE Q and ln( )kiA for the first ten orders of PMs (k =1, 2, …, 10). As shown, the linear regression models of the first ten orders of PMs were statistically significant (P<0.01) with all R2 being greater than 0.80, indicating watershed area explained the most of the annual streamflow variations in the study region. To visualize the regression models, the first five moment orders of regression lines were shown in Figure 5.2. The goodness-of-fit of the linear relationship (R2=0.999 and P<0.01) in bk = kθ were further confirmed (Figure 5.3). In addition, the intercept of Eqn. (5-6) is zero and thus subjective to the simple-scaling. Otherwise, 137  the intercept should not be zero and play a significant role in the linear regression model for the multi-scaling. As shown in Figure 5.3, the intercept of the regression model did not substantially affect the regression model (<20% of slope). To further confirm the minor contribution of the interception in Figure 5.3 or Eqn. (5-6), the slope was found as 1.055 when the intercept was set to be zero for the regression model, which was not much different from the slope (1.031) regression model with intercept. Therefore, the limited role of the intercept of Eqn. (5-6) in the regression model was acceptable. In summary, the annual streamflow in the southern interior of British Columbia obeyed the simple-scaling, and the averaged scaling exponent was 1.031.   138   Figure 5.2 Log-log relationship between the first five orders of product moments (A to E corresponds to 1st to 5th moments) of annual streamflow and watershed area based on Eqn. (5-4) in the southern interior of British Columbia 139   Figure 5.3 The slope versus moment order of annual streamflow of Eqn. (5-6) for the 70 watersheds in the southern interior of British Columbia. The slope of the linear regression is the scaling exponent (1.031).  Table 5.3 Model summary of the log-log relationship between the first 10 orders product moments of annual streamflow and watershed sizes based on Eqn. (5-4) for the southern interior of British Columbia (Note: all the models are statistically significant P<0.05) Moment Orders bk ak R2 1 1.119 -4.948 0.818 2 2.219 -9.665 0.816 3 3.302 -14.191 0.812 4 4.377 -18.599 0.809 5 5.547 -22.924 0.807 6 6.329 -27.190 0.807 7 7.365 -31.413 0.807 8 8.402 -35.607 0.807 9 9.439 -39.780 0.807 10 10.478 -43.939 0.807  The established PWMs for annual streamflow of 70 watersheds confirmed the results from the PMs method. As shown in Table 5.3, the linear regression models of the first ten orders were statistically significant (P<0.01) with their R2 being > 0.70, indicating watershed area alone explained the large variations in annual streamflow in the region. To visualize the regression y = 1.031x + 0.191R² = 0.999 P< 0.010246810120 1 2 3 4 5 6 7 8 9 10b kMoment order (k)140  models, the first five moment orders of regression lines were shown in Figure 5-4. The scaling exponent did not vary dramatically with statistical moments, indicating the scaling exponent of H was constant to all statistical moments (Table 5.4 and Figure 5.5). Therefore, annual streamflow in the southern interior of BC obeyed simple-scaling with the scaling exponent being 1.019, which was not dramatically different from the PMs method (1.031). Therefore, the averaged scaling exponent from both methods was determined as 1.025 for the study region.     In summary, the simple-scaling of annual streamflow was determined from the analyses of two grouped watersheds. In addition, our results those two grouped watersheds, as well as 70 watersheds located in the southern interior of BC, demonstrated that all scaling exponents were greater than 1, indicating annual streamflow exhibits an amplification process with watershed size in the study region. It also indicated that the selected study watersheds are representative of the region.   141   Figure 5.4 The log-log relationships between the first five orders of PWMs of annual streamflow (A to E corresponds to 1st to 5th probability weighted moments) and their watershed areas of Eqn. (5-8) for the southern interior of British Columbia. 142   Figure 5.5 The scaling exponent (H) vs. moment orders (k) of annual streamflow of Eqn. (5-8) in the southern interior of British Columbia (the averaged scale exponent is 1.019).  Table 5.4 Model summary of the log-log relationships between the first 10 orders PWMs of annual streamflow and their watershed areas based on Eqn. (5-8) for the southern interior of British Columbia (Note: all the models are statistically significant P<0.05). Moment orders H ck R2 1 1.140 -6.294 0.781 2 1.014 -10.956 0.716 3 1.011 -11.411 0.717 4 1.008 -11.773 0.717 5 1.006 -12.074 0.717 6 1.004 -12.332 0.717 7 1.003 -12.557 0.717 8 1.001 -12.757 0.717 9 1.000 -12.938 0.717 10 0.999 -12.102 0.717  Tables 5.1 and 5.2 indicated that the cumulative forest disturbance did not alter the simple-scaling of annual streamflow in two groups of watersheds as the simple-scaling holds for all three periods. However, the cumulative forest disturbance did result in a change in scaling exponents for both two groups of watersheds.  Specifically, the scaling exponents of streamflow 00.30.60.91.21.50 1 2 3 4 5 6 7 8 9 10HMoment order (k)143  components in the reference period in both groups of watersheds were smaller than those in the disturbance period. Hence, this might imply that forest disturbance further augmented the scaling exponents of streamflow and its components (more detailed results on the scaling properties of the CEs will be presented in section 5.3.3).   5.3.2 Scaling properties of annual streamflow using topographic indices as scaling parameters Both the PMs and PWMs demonstrated that 10 of 12 topographic indices did not hold for Eqn. (5-4) and Eqn. (5-8), respectively. They were upslope contributing area, downslope distance gradient, downstream flow length, slope length factor, positive topographic openness, relief, slope degree, surface area, topographic ruggedness index, and topographic wetness index. Therefore, those 10 indices cannot be used as scaling parameters. In contrast, the specific contributing area (SCA) and perimeter were good indices for scaling. In addition, SCA and perimeter were proved to obey the simple-scaling based on our analyses of both the five-nested and ten watersheds (Tables 5.23 and 5.25 for SCA, respectively, while Tables 5.24 and 5.26 for the perimeter, respectively). Thus, the scaling exponents derived by the PMs and PWMs methods were consistent, and were greater than 1 when using SCA and perimeter as scaling parameters. Specifically, the scaling exponents of annual streamflow using SCA and perimeter as scaling parameters were 2.288 and 2.242, respectively for the five-nested watersheds, while they were 1.872 and 1.874, respectively for ten watersheds.  This demonstrated that annual streamflow showed the amplification process with SCA and perimeter.    144  Table 5.5 Summary of the scaling exponents of annual streamflow in the five-nested and ten watersheds using the specific contributing area and perimeter as scaling parameters in the southern interior of BC. Topographic indices Five-nested watersheds Ten watersheds θ H Average θ H Average Specific contributing area 2.272 2.304 2.288 1.838 1.906 1.872 Perimeter 2.229 2.254 2.242 1.846 1.902 1.874   5.3.3 Scaling property of the CEs of forest disturbance on streamflow components The scaling properties of the CEs of forest disturbance on total streamflow, baseflow, and surface runoff were examined by the PM and PWM methods in the five-nested watersheds. The PM methods indicated that the relationships between the CEs of forest disturbance on streamflow, baseflow, and surface runoff and watershed area held for Eqn. (5-4), respectively (also see Figure 5.6). In addition, the goodness-of-fit of the linear relationships (R2=0.999 and P<0.01) indicated that bk = kθ also held.  This implied that the CEs of forest disturbance on streamflow, baseflow, and surface runoff obeyed simple-scaling (also see Table 5.7). Furthermore, the scaling exponents of the CEs of forest disturbance on streamflow, baseflow, and surface runoff were 1.592, 1.612, and 1.587, respectively. The model summaries of the PMs method for total streamflow, baseflow, and surface runoff were represented in Tables 5.7, 5.8, and 5.9, respectively. Similarly, the PWMs methods revealed that the CEs of forest disturbance on total streamflow, baseflow, and surface runoff followed the simple-scaling law. The scaling exponents of total streamflow, baseflow, and surface runoff were 1.444, 1.454, and 1.440, respectively, which were consistent with those from the PMs. The scaling exponents from the PWMs method regarding the CEs of forest disturbance on streamflow, baseflow, and surface runoff were summarized in Tables 5.7, 5.8, and 5.9, respectively.  145  To further validate the results in the five-nested watersheds, the PMs and PWMs were also adopted for the CEs of forest disturbance on total streamflow in ten watersheds. Figure 5.6 and Table 5.10 showed that the PMs method revealed the CEs in ten watersheds also obeyed the simple-scaling law. In addition, the scaling exponent was 1.561. Similarly, Figure 5.7 and Table 5.10 summarized the results of the scaling properties of the CEs from the PWMs method in ten watersheds, which showed the CEs of forest disturbance on total streamflow obeyed simple- scaling law with the scaling exponent of 1.427. It should be noted that the disturbance period of the Moffat River watershed was only seven years, which led to the first-seven moment orders can be calculated for the PWMs for the ten watersheds study. However, the conclusion of using the first seven-moment orders was not different from those using the first ten moments. In conclusion, the PMs and PWMs consistently revealed that the CEs of forest disturbance on total streamflow, baseflow, and surface runoff obeyed simple-scaling. Furthermore, the scaling exponents of streamflow components were greater than 1. This implied the CEs of forest disturbance on streamflow component showed amplification process, i.e., the larger watersheds had the larger responses to cumulative forest disturbance.   Table 5.6 Summary of the scaling exponents of the cumulative effects of forest disturbance on streamflow components in the five-nested watersheds and annual streamflow in 10 watersheds in the southern interior of British Columbia.   Scaling exponent ∆Qf/CECA ∆BFf/CECA ∆SRf/CECA PMs PWMs Average PMs PWMs Average PMs PWMs Average Five-nested watersheds 1.592 1.444 1.518 1.612 1.454 1.533 1.587 1.440 1.514 Ten watersheds 1.561 1.427 1.494 -- -- -- -- -- --  146  Table 5.7 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of the cumulative effects of forest disturbance on annual streamflow and watershed size of Eqn. (5-4) and Eqn. (5-8), respectively for five-nested watersheds located in the southern interior of British Columbia, Canada. (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.148 -0.985 0.965 1 1.354 -2.705 0.983 2 2.901 -3.628 0.987 2 1.398 -3.552 0.985 3 4.432 -5.671 0.993 3 1.421 -4.096 0.986 4 6.024 -7.424 0.991 4 1.437 -4.544 0.987 5 7.630 -9.557 0.993 5 1.449 -4.915 0.988 6 9.202 -11.179 0.992 6 1.460 -5.231 0.988 7 10.805 -13.172 0.990 7 1.469 -5.509 0.989 8 12.376 -14.798 0.992 8 1.477 -5.757 0.989 9 13.970 -16.681 0.993 9 1.485 -5.982 0.990 10 15.542 -18.331 0.993 10 1.492 -6.188 0.990 bk = 1.592 k – 0.352; R2 = 0.999; P< 0.01  Average  1.444        147  Table 5.8 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of the cumulative effects of forest disturbance on annual baseflow and watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds located in the southern interior of British Columbia, Canada (Note all the models were statistically significant at P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.161 -2.256 0.970 1 1.362 -4.851 0.843 2 2.924 -6.163 0.994 2 1.406 -5.475 0.886 3 4.473 -9.504 0.998 3 1.430 -5.957 0.908 4 6.085 -12.579 0.996 4 1.446 -6.349 0.922 5 7.705 -15.989 0.998 5 1.459 -6.682 0.932 6 9.296 -18.940 0.997 6 1.470 -6.973 0.939 7 10.913 -22.213 0.998 7 1.480 -7.237 0.945 8 12.503 -25.162 0.997 8 1.489 -7.466 0.950 9 14.111 -28.330 0.997 9 1.497 -7.680 0.954 10 15.772 -18.283 0.968 10 1.505 -7.878 0.958 bk = 1.612 k – 0.374; R2 = 0.999; P< 0.01 Average 1.454        148  Table 5.9 Model summary of log relationship between the first 10 orders PMs and PWMs of cumulative effects of forest disturbance on annual surface runoff and watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds located in the southern interior of British Columbia, Canada (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.136 -1.313 0.961 1 1.348 -3.045 0.979 2 2.892 -4.316 0.983 2 1.392 -3.862 0.980 3 4.413 -6.683 0.991 3 1.416 -4.438 0.987 4 6.004 -8.790 0.988 4 1.432 -4.880 0.983 5 7.603 -11.261 0.991 5 1.449 -5.260 0.984 6 9.172 -13.233 0.989 6 1.455 -5.771 0.985 7 10.769 -15.567 0.990 7 1.465 5.855 0.985 8 12.336 -17.538 0.989 8 1.473 -6.103 0.986 9 13.924 -19.763 0.990 9 1.480 -6.327 0.986 10 15.493 -21.756 0.989 10 1.487 -6.533 0.987 bk = 1.587 k -0.356; R2 = 0.999; P<0.01 Average 1.44      149   Figure 5.6 The log-log relationship between the expectation of the first five orders product moments (A to E corresponds to 1st to 5th moments) of the cumulative effects of forest disturbance to annual mean flow and their watershed size based on Eqn. (5-4) for 10 study watersheds in the southern interior of British Columbia, Canada (the squares represent the nested watersheds). 150  Table 5.10 Model summary of the log-log relationship between the expectation of the first 10 orders PMs and first 7 orders of PWMs of the cumulative effects of forest disturbance on annual streamflow and their watershed size based on Eqn. (5-4) and Eqn. (5-8), respectively for ten watersheds located in the southern interior of British Columbia, Canada (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.209 -1.604 0.927 1 1.365 -3.119 0.954 2 2.877 -4.294 0.951 2 1.401 -3.918 0.953 3 4.38 -6.664 0.949 3 1.421 -4.485 0.953 4 5.944 -8.737 0.947 4 1.435 -4.932 0.952 5 7.506 -11.134 0.945 5 1.445 -5.297 0.952 6 9.062 -13.168 0.944 6 1.455 -5.614 0.952 7 10.629 -15.464 0.943 7 1.468 -5.929 0.951 8 12.185 -17.514 0.943 8 -     9 13.75 -19.733 0.942 9 -     10 15.306 -21.798 0.942 10 -     bk = 1.561k – 0.302; R2 = 1; P<0.01 Average 1.427      151   Figure 5.7 The log-log relationships between the first five-order PWMs of the cumulative effects of forest disturbance on streamflow (A to E correspond to 1st to 5th probability weighted moments) and their watershed area based on Eqn. (5-8) in ten study watersheds in the southern interior of British Columbia (the squares represent the five nested watersheds. 152  5.4 Discussion 5.4.1 Scaling properties of observed streamflow components in study watersheds Our results showed that annual streamflow obeyed the simple-scaling in our separate analyses involving the five-nested watersheds, ten watersheds, and 70 watersheds with the averaged scaling exponents of the PMs and PWMs 1.176, 1.158, and 1.031, respectively for the whole study periods. The baseflow and surface runoff in the five-nested watersheds also followed the simple-scaling, and their averaged scaling exponents were 1.189 and 1.172, respectively for the whole period. In addition, the scaling properties of the reference and disturbance periods of streamflow and its components were consistent with the whole study period. Those scaling exponents were all greater than 1, indicating that the observed streamflow components (annual streamflow, baseflow and surface runoff) in the southern interior of BC all exhibited an amplification process.   The physical interpretations for the scaling exponents of baseflow exceeding the threshold of 1 in the southern interior of BC might be that with watershed size increasing, more groundwater discharge (baseflow) became available, and consequently led to greater incremental rates.  This explanation is supported by our comparison of the baseflow index (Section 4.3.1) among the studied watersheds as the baseflow index in SRH was greater than those from Princeton and Tulameen, which clearly indicated that the lower reaches or large watersheds of the Similkameen River watershed received greater groundwater increments. In addition, there are two regional aquifers located in the lower reaches of the Similkameen River watershed, while there is none in the upper reaches (Ministry of Environment, 2006). Those two regional aquifers are likely the key sources of greater baseflow in larger watersheds of the study area. Finally, Li et al. (2018a) 153  showed that the topography had a higher control on low flows in the study region, with the scaling exponents of two topography indices (SCA and perimeter) being greater than 1, demonstrating that topographies in larger watersheds are more complex and thus could promote a higher streamflow increment with watershed size increasing. This, in turn, explains that the scaling exponents of baseflow were greater than 1.    The scaling exponent of greater than 1 for surface runoff in our study is somewhat surprising. As surface runoff is typically associated with high flows or peak flows, a larger watershed tends to have a higher buffering capacity for high flow increasing, and thus a lower scaling exponent (<1) is normally expected. The followings are our explanations. Firstly, lakes and wetlands play an essential role in regulating streamflow in a watershed as they can buffer changes in streamflow. However, in the southern interior of BC, lake and wetland coverages are relatively low, and thus their roles in buffering and storing the streamflow are limited. This is supported by Li et al. (2018a) who detected that the coverage of wetland and lake was not significantly related to streamflow in 28 watersheds in the southern interior of BC (Table 4.22). Secondly, the unique snow-melting process in the study region may promote surface runoff in large watersheds. Normally, the snow melting in the lower elevations of a watershed are earlier and faster due to a higher temperature. With watershed size increasing, averaged watershed elevations are decreased, which can promote more synchronization of snow melting processes as compared with small watersheds when there are large variations in elevations.  Such promoted synchronization effects in larger watersheds could lead to higher percentages of surface runoff in our study region. In summary, it is highly possible to have higher percentages of surface runoff in larger watersheds.  154  The higher scaling exponents (> 1) for both base flow and surface runoff would logically lead to higher scaling exponents (>1) for annual streamflow, which has been confirmed in this study (Table 5.1). The simple-scaling with the scaling exponents being greater than 1 for annual streamflow is also consistent with some existing studies. For example, Yue and Gan (2004) investigated the spatial properties of annual streamflow across Canada and its 11 sub-climatic regions using the PMs and PWMs methods. In particular, their results showed that annual streamflow of 48 watersheds in the interior of BC exhibited simple-scaling, and the scaling exponent was determined as 1.00. Furthermore, annual streamflow in each sub-climatic zone also followed simple-scaling, but the scaling exponents in the Coastal BC, Ontario, and Yukon were 1.04, 1.04, and 1.01, respectively. Similarly, Buttle and Eimers (2009) found that annual streamflow in 22 watersheds ranging from 3.4 to 190.5 hectares in the Southern-Central Ontario followed the simple-scaling, and its scaling exponent was 1.06. The scaling property of annual streamflow was also examined in the Continental USA. For example, Vogel and Sankarasubramanian (2000) explored the spatial property of annual streamflow in 18 large basins in the Continental United States using data from 1433 watersheds with sizes ranging from 3.5 to 2,952,618 km2, and found annual streamflow obeyed simple-scaling with scaling exponents ranging from 0.64 to 1.15 based on the PM method. Similarly, the annual streamflow in the Amazon basin also obeyed simple-scaling with the scaling exponents ranging from 0.90 to 1.18. Clearly, annual streamflow was found to obey the simple-scaling in the literature, with the scaling exponents being either greater or less than 1.    155  5.4.2 Scaling properties of annual streamflow and topographic indices   The PMs and PWMs methods consistently suggested that specific contributing area (SCA) and perimeter were only two of the12 tested topographic indices that can be used as scaling parameters. The corresponding scaling exponents of SCA and perimeter were 1.872 and 1.874 for ten watersheds, and 2.288 and 2.242 for the five nested watersheds, respectively.      Although the watershed area has long been used as a measure of spatial scales, other parameters were also tested to present spatial scales. For example, bankfull width was preferred to drainage area for investigating the scaling property of floods using the data from 36 gaging stations in New Hampshire and Vermont, USA (Dingman and Palais, 1999). In this study, SCA and perimeter were proved to be a measure of spatial scales. In fact, the perimeter is also a direct measure of watershed size. Larger-sized watersheds usually have longer perimeters. More importantly, the perimeter can distinguish the shape of watersheds, which may affect the resident time and flow path of streamflow (McGuire et al., 2005). For example, long and narrow watersheds potentially have longer perimeter and consequently longer flow paths and higher annual streamflow. In a similar study, Li et al., (2018a) validated that perimeter and annual streamflow were positively and significantly correlated in the study region. Thus, perimeter could be used a scaling parameter, which has further advanced the utility of perimeter in hydrological studies.  Compared to perimeter and watershed size, SCA is a relatively abstract topographic index to visualize. SCA is defined as upslope contributing area per unit length of contour (Quinn et al., 1991), describing the possibility of the locations to receive water from upslope areas (Gruber and Peckham 2008).  SCA is often used as an indicator of soil moisture availability, which has long 156  been used for hydrological model simulations. For instance, topographic wetness index (TWI) is defined as: ln (SCA/tanβ), where β is slope, which is a required primary input for TOPMODEL and other hydrological applications (Beven, 1995; Beven and Kirkby, 1979; Quinn et al., 1995; McGlynn and Seibert, 2003). The positive correlations have been identified between SCA and soil moisture (e.g., Famiglietti et al., 1998; McGlynn and Seibert, 2003), indicating that larger values of SCA corresponded to higher soil moisture. As such, any watersheds with higher values of SCA potentially have higher soil moisture and thus higher streamflow. In this study, the Kendall revealed the positive correlation between the ∆Qf/CECA and SCA. In addition, the scaling exponent of SCA for annual exceeded the threshold of 1, demonstrating that the increment of streamflow was greater than the increment of SCA. It should be noted that SCA is positively but not linearly related to annual streamflow in our study, which may suggest an important research gap on further understanding of the relationship between annual streamflow and SCA.   Among all three scaling parameters (i.e., watershed size, SCA, and perimeter), SCA and perimeter also provide additional information regarding the watershed shape and hydrological processes (e.g., soil water content). SCA is also related to other hydrological functions, such as soil erosion and percolation. However, since the result on SCA and perimeter as scaling parameters were generated from the five-nested and ten watersheds in the study region, whether SCA and perimeter can still be used as the scaling parameters for annual streamflow at the regional scale is a research question that needs to be addressed. Nevertheless, the scaling exponents of SCA and perimeter are greater than the threshold of 1. The relationship between perimeter, SCA and annual streamflow are complicated in nature and has not well been 157  documented. Therefore, it is suggested that future studies can involve a large number of watersheds to explore the scaling properties further using SCA and perimeter as the scaling parameters.     5.4.3 Scaling properties of the CEs of forest disturbance on streamflow components The PMs and PWMs methods indicated that the CEs of forest disturbance on streamflow component obeyed the simple-scaling. Moreover, the scaling exponents of the CEs of forest disturbance on streamflow, baseflow, and surface runoff were 1.518, 1.533, and 1.514 for the five-nested watersheds, respectively. Similarly, the simple-scaling of the CEs of forest disturbance on streamflow also determined for ten watersheds with the scaling exponent being 1.494. In addition, higher scaling exponents were found during the disturbance period than those from the reference period in the five-nested and ten watersheds for the observed annual streamflow. All those results consistently indicated that the CEs of forest disturbance on streamflow and its components obeyed simple-scaling, and forest disturbance increased the scaling exponents of streamflow components in the study region.    Our study showed that the scaling exponents of the CEs of forest disturbance on streamflow components had exceeded the threshold of 1, demonstrating that larger watersheds corresponded to the hydrological impacts of forest disturbance at an increasing rate with watershed size. This conclusion is consistent with our results on the observed streamflow data as discussed in section 5.4.1, and thus the explanations on observed streamflow data with respect to the scaling exponents of greater than 1 can be applied on the CEs here. However, this conclusion contradicted to the common perception that the effects of forest change on streamflow were 158  attenuated with increasing of watershed size (Li et al., 2017; and Zhang et al., 2017b) as larger watersheds have a more buffering capacity of the CEs of forest disturbance on the streamflow. Those contrasting results may be ascribed to the following additional reasons.     Firstly, the enhanced synchronization of forest disturbance in snow-dominated systems could contribute to the more pronounced CEs on streamflow in larger watersheds. The synchronization and de-synchronization of forest disturbance on hydrological processes between different elevation bands of a watershed are widely recognized in British Columbia, Canada (e.g., Lin and Wei, 2008; Zhang and Wei, 2014). In the snow-dominated watersheds, forest disturbance in the lower elevations of a watershed could cause earlier and faster snow melting process due to the increased solar radiation and higher temperature following forest disturbance. This, in turn, may lead to desynchronization effects with those at higher elevations. With watershed size increasing, averaged watershed elevations are normally decreased, and more forest disturbance are concentrated in the lower elevations, which can promote more synchronization while weakening de-synchronization. The enhanced synchronization effects can lead to more snow-melt enhanced responses in annual streamflow in larger watersheds.  Thus, larger watersheds are likely to experience increased synchronization effects, and consequently lead to more increment in streamflow.   Secondly, the topography in the region played an important role in the response of the streamflow to the CEs of forest disturbance. As shown in Table 4.22, the Kendall tau correlation indicated that several topographic indices, including the downstream flow length, specific contributing area, topographic wetness index, and perimeter, were significantly related to the 159  CEs of forest disturbance on streamflow in our ten studied watersheds. In addition, the importance of the role of topography in streamflow responses to forest disturbance has been reported in the literature. For example, Zhang and Wei (2014) found that two neighbouring watersheds, i.e., Willow (2860 km2) and Bowron River (3420 km2) watersheds, experienced similar disturbance levels in the Interior of BC.  The significant hydrological alterations (i.e., annual streamflow) were detected in the Willow River watershed, while no significant changes in those hydrological variables were detected for the Bowron River watershed. The differences may stem from the difference in watershed conditions (e.g., land forms, slopes, disturbance elevations). The similar finding was also obtained in the subtropical region in China (Liu et al., 2016), where the difference in topography may contribute to the distinct responses between watersheds under similar forest recover rate. In addition, the positive correlations between topographic indices and the CEs of forest disturbance on streamflow indicate that larger watersheds in our study region are characterized by more complex topographies. Therefore, the interactions between topography and forest disturbance can amplify the CEs in larger watersheds.   Thirdly, land-atmosphere interactions between forest disturbance and climate in larger watersheds may be more pronounced and intensified than smaller ones. Forest change could alter local and regional climate conditions (Zemp et al., 2017). For example, reforestation could intensify hydrological cycle and increase water availability due to more ET and more moisture in the atmosphere, while deforestation may potentially have negative impacts on the hydrological cycle and thus decreases water availability in downstream or a large landscape (Ellison et al., 2012).  Moreover, the climate of the southern interior of British Columbia is relatively dry and 160  warm at the lower elevations. It has been demonstrated that streamflow in the drier regions is more sensitive than the wetter ones to forest change (Li et al., 2017; Zhang et al., 2017; Zhou et al., 2015). In our study area, a higher percentage of dry areas is expected with watershed size increasing due decreasing of averaged watershed elevations. Thus, it is possible that more intensified interactions between forest disturbance and climate, and consequently more enhanced CEs with increasing of watershed size in our study area.      Finally, more groundwater discharge or baseflow with larger watersheds may also promote greater responses of the CEs to forest disturbance. In the five-nested watersheds, the baseflow index in the larger watersheds was greater than those of the smaller watersheds, indicating that the baseflow had a higher contribution to streamflow in larger watersheds. In addition, the scaling exponents of the CEs of forest disturbance on baseflow (1.189) were higher than those of total streamflow (1.176) and surface runoff (1.172). Hence, the CEs of forest disturbance on baseflow may further augment the CEs of streamflow to forest disturbance in our study area.   5.4.4 Implications of scaling property of the cumulative effects of forest disturbance on streamflow components The results of the scaling properties of the CEs of forest disturbance on streamflow components from this study are expected to have important implications for the management of regional forest resource and watersheds. First and foremost, the amplification effect was identified for the CEs of forest disturbance on annual streamflow and its components in the study area, indicating that the CEs of forest disturbance on streamflow components at the watershed scale is more pronounced with increasing of watershed size. This counterintuitive finding could change our 161  perception and management paradigm. In the past, it is often presumed that the CEs of cumulative forest disturbance would likely be diminished at larger watershed scales due to the increased buffering capacity. However, this is not the case in our study area. Forest harvesting could lead to more pronounced hydrological effects at larger spatial scales in our region. Such a conclusion would have important implications for designing sustainable forest harvesting levels and managing the CEs of forest disturbance in the southern interior of British Columbia.   Secondly, the scaling relationship determined in this study can be used to predict the CEs of forest disturbance on hydrology in the region with the watershed sizes similar to our study watersheds ranging from ten to several thousand square kilometres. This is useful and important given that forest disturbance is becoming more frequent, large-scale and extensive, and there is a general lack of long-term reliable data in many ungauged watersheds in the region. Thus, the established scaling relationship can provide a quick and accurate assessment regarding the CEs of forest disturbance on hydrology in the region.   Thirdly, this study also quantified that SCA and perimeter, in addition to the watershed area, can also be used as scaling parameters for the region. More research is needed to compare their utilities so that their selections can be scientifically sound and meaningful.  5.5 Summary This chapter adopted the product moments (PMs) and probability weighted moments (PWMs) methods to assess the scaling properties of the CEs of forest disturbance on streamflow and its components in both the five-nested and ten watersheds.  We conclude that annual streamflow 162  and its components, along with the CEs followed simple-scaling with the scaling exponents generally being greater than the threshold of 1, which demonstrated that the cumulative hydrological effects caused by forest disturbance were increased at an increasing rate with watershed size in the study region.  Two topographic indices including specific contributing area and perimeter were proved to be effective and significant scaling parameters for assessing regional hydrology at different spatial scales.  The results from this study would greatly help understand and predict the cumulative hydrological effects of forest disturbance at various watershed scales.     163  5.6 Supplementary materials Table 5.11 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual mean flow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.197 -6.094 0.987 1 1.190 -7.262 0.988 2 2.384 -12.019 0.987 2 1.188 -7.970 0.988 3 3.565 -17.800 0.988 3 1.186 -8.497 0.988 4 4.739 -23.451 0.988 4 1.185 -8.877 0.988 5 5.908 -28.987 0.989 5 1.183 -9.203 0.988 6 7.073 -34.429 0.989 6 1.182 -9.479 0.988 7 8.236 -39.799 0.989 7 1.181 -9.719 0.989 8 9.397 -45.119 0.990 8 1.180 -9.931 0.989 9 10.558 -50.405 0.990 9 1.179 -10.120 0.989 10 11.720 -55.669 0.990 10 1.179 -10.292 0.989 bk = 1.168k + 0.053; R2 = 1; P<0.01 Average 1.183        164  Table 5.12 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual mean flow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.189 -6.010 0.984 1 1.179 -7.147 0.985 2 2.364 -11.823 0.984 2 1.175 -7.846 0.985 3 3.537 -17.496 0.985 3 1.174 -8.355 0.986 4 4.706 -23.067 0.986 4 1.173 -9.755 0.986 5 5.876 -28.561 0.987 5 1.172 -9.083 0.987 6 7.045 -33.991 0.988 6 1.172 -9.361 0.987 7 8.214 -39.367 0.989 7 1.171 -9.602 0.988 8 9.382 -44.699 0.989 8 1.171 -9.816 0.988 9 10.549 -49.997 0.990 9 1.170 -10.007 0.989 10 11.715 -55.268 0.990 10 1.170 -10.180 0.989 bk= 1.169k+0.027; R2 = 1; P<0.01 Average 1.173        165  Table 5.13 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.217 -6.279 0.989 1 1.224 -7.551 0.990 2 2.441 -12.516 0.990 2 1.230 -8.323 0.990 3 3.674 -18.737 0.990 3 1.234 -8.878 0.990 4 4.916 -24.956 0.990 4 1.237 -9.310 0.989 5 6.166 -31.178 0.990 5 1.239 -9.664 0.989 6 7.423 -37.403 0.989 6 1.241 -9.965 0.989 7 8.685 -43.630 0.989 7 1.243 -10.227 0.989 8 9.951 -49.858 0.989 8 1.245 -10.460 0.989 9 11.220 -56.084 0.989 9 1.247 -10.671 0.989 10 12.494 -62.308 0.989 10 1.248 -10.862 0.989 bk = 1.254k -0.077; R2 =1; P<0.01 Average 1.239        166  Table 5.14 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.213 -7.354 0.998 1 1.206 -8.521 0.998 2 2.416 -14.536 0.998 2 1.203 -9.226 0.998 3 3.611 -21.566 0.998 3 1.201 -9.733 0.998 4 4.799 -28.460 0.998 4 1.199 -10.128 0.998 5 5.980 -35.234 0.999 5 1.198 -10.452 0.998 6 7.156 -41.911 0.999 6 1.196 -10.727 0.999 7 8.330 -48.516 0.999 7 1.195 -10.966 0.999 8 9.502 -55.070 0.999 8 1.194 -11.177 0.999 9 10.674 -61.592 1.000 9 1.193 -11.366 0.999 10 11.847 -68.091 1.000 10 1.192 -11.537 0.999 bk = 1.180 k + 0.062;  R2 =1, P<0.01 Average 1.198        167  Table 5.15 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.212 -7.320 0.997 1 1.200 -8.448 0.997 2 2.408 -14.415 0.997 2 1.194 -9.132 0.998 3 3.590 -21.316 0.998 3 1.191 -9.625 0.998 4 4.763 -28.059 0.999 4 1.188 -10.009 0.998 5 5.930 -34.684 0.999 5 1.185 -10.322 0.999 6 7.096 -41.231 0.999 6 1.182 -10.585 0.999 7 8.261 -47.730 1.000 7 1.180 -10.812 0.999 8 9.428 -54.203 1.000 8 1.177 -11.011 0.999 9 10.596 -60.662 1.000 9 1.172 -11.188 0.994 10 11.766 -67.112 1.000 10 1.173 -11.348 1.000 bk = 1.171k + 0.067; R2 =1; P<0.01 Average 1.184        168  Table 5.16 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual baseflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.210 -7.361 0.999 1 1.206 -8.553 0.998 2 2.415 -14.594 0.999 2 1.204 -9.269 0.998 3 3.617 -21.722 0.998 3 1.203 -9.782 0.998 4 4.817 -28.764 0.999 4 1.201 -10.182 0.998 5 6.016 -35.741 0.998 5 1.200 -10.511 0.998 6 7.214 -42.672 0.998 6 1.199 -10.792 0.998 7 8.414 -49.572 0.998 7 1.199 -11.037 0.998 8 9.615 -56.453 0.999 8 1.199 -11.256 0.998 9 10.818 -63.323 0.999 9 1.199 -11.455 0.998 10 12.022 -70.187 0.999 10 1.199 -11.636 0.998 bk = 1.201 k + 0.012; R2 = 1; P<0.01 Average 1.201        169  Table 5.17 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.195 -6.404 0.985 1 1.189 -7.574 0.986 2 2.381 -12.640 0.986 2 1.186 -8.282 0.986 3 3.560 -18.729 0.986 3 1.184 -8.792 0.987 4 4.731 -24.684 0.987 4 1.183 -9.189 0.987 5 5.895 -30.518 0.988 5 1.181 -9.514 0.987 6 7.054 -36.251 0.988 6 1.180 -9.789 0.987 7 8.210 -41.907 0.989 7 1.178 -10.028 0.988 8 9.364 -47.512 0.990 8 1.177 -10.239 0.988 9 10.518 -53.082 0.990 9 1.176 -10.428 0.988 10 11.673 -58.630 0.990 10 1.176 -10.600 0.989 bk = 1.163k + 0.062; R2 =1; P<0.01 Average 1.181        170  Table 5.18 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.195 -6.373 0.982 1 1.183 -7.503 0.983 2 2.373 -12.522 0.983 2 1.177 -8.188 0.984 3 3.538 -18.479 0.984 3 1.174 -8.683 0.985 4 4.694 -24.278 0.985 4 1.171 -9.067 0.986 5 5.845 -29.957 0.987 5 1.168 -9.380 0.987 6 6.992 -35.557 0.988 6 1.165 -9.643 0.987 7 8.140 -41.108 0.989 7 1.163 -9.869 0.988 8 9.289 -46.633 0.990 8 1.160 -10.068 0.988 9 10.440 -52.144 0.990 9 1.158 -10.245 0.989 10 11.592 -57.647 0.991 10 1.156 -10.405 0.990 bk = 1.153 k + 0.067; R2=1; P<0.01 Average 1.167        171  Table 5.19 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual surface runoff and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the five-nested watersheds in the southern interior of British Columbia, Canada for the disturbance period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.192 -6.409 0.989 1 1.188 -7.603 0.989 2 2.379 -12.695 0.989 2 1.187 -8.324 0.989 3 3.564 -18.883 0.989 3 1.186 -8.841 0.989 4 4.749 -24.993 0.989 4 1.185 -9.244 0.989 5 5.932 -31.042 0.989 5 1.184 -9.575 0.989 6 7.115 -37.046 0.989 6 1.183 -9.857 0.989 7 8.299 -43.018 0.989 7 1.183 -10.104 0.989 8 9.484 -48.968 0.989 8 1.183 -10.324 0.989 9 10.671 -54.904 0.989 9 1.183 -10.522 0.989 10 11.858 -60.831 0.989 10 1.183 -10.703 0.989 bk = 1.185k + 0.008; R2 =1; P<0.01 Average 1.185        172  Table 5.20 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the whole study period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.167 -6.157 0.911 1 1.168 -7.354 0.924 2 2.327 -12.158 0.914 2 1.169 -8.080 0.930 3 3.481 -18.029 0.916 3 1.170 -8.604 0.933 4 4.630 -23.788 0.918 4 1.171 -9.013 0.936 5 5.775 -29.452 0.919 5 1.171 -9.348 0.937 6 6.917 -35.039 0.920 6 1.172 -9.632 0.939 7 8.056 -40.567 0.920 7 1.172 -9.878 0.940 8 9.195 -46.053 0.920 8 1.172 -10.095 0.940 9 10.334 -51.511 0.920 9 1.171 -10.289 0.941 10 11.473 -56.948 0.920 10 1.171 -10.465 0.942 bk = 1.144 + 0.043; R2 =1; P< 0.01 Average 1.171      173   Figure 5.8 The log-log relationship between the first five orders product moments (A to E corresponds to 1st to 5th moments) of annual streamflow flow and their watershed sizes of Eqn. (5-4) for the ten study watersheds located in the southern interior of British Columbia, Canada. The squares represent the nested watersheds. 174   Figure 5.9 The slope versus moment order of annual mean flow of Eqn. (5-6) for the study watersheds located in the southern interior of British Columbia. The slope of the linear regression is the scaling exponent (1.144) of the annual mean flow for study watersheds.  y = 1.144x + 0.043R² = 1 P<0.010246810120 1 2 3 4 5 6 7 8 9 10b kMoment orders (k)175   Figure 5.10 The log-log relationships between the PWMs of annual mean flow (A to E corresponds to 1st to 5th probability weighted moments) and their watershed areas of Eqn. (5-8) in ten study watersheds in the southern interior of British Columbia. The squares represent the five nested watersheds.   176   Figure 5.11 The scaling exponent (H) vs. moment order (k) of the annual mean flow of Eqn. (5-8) for the ten study watersheds in the interior of British Columbia. The average scaling exponent is 1.171.   0.00.20.40.60.81.01.21.40 1 2 3 4 5 6 7 8 9 10HMoment orders (k)177  Table 5.21 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Equation (5-4) and Equation (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.166 -6.144 0.900 1 1.156 -7.288 0.903 2 2.320 -12.102 0.903 2 1.153 -7.992 0.906 3 3.469 -17.926 0.905 3 1.152 -8.507 0.907 4 4.616 -23.658 0.908 4 1.151 -8.913 0.909 5 5.763 -29.321 0.910 5 1.151 -9.247 0.910 6 6.910 -34.931 0.911 6 1.151 -9.530 0.910 7 8.058 -40.498 0.913 7 1.151 -9.775 0.912 8 9.205 -46.030 0.914 8 -     9 10.353 -51.535 0.914 9 -     10 11.500 -57.020 0.915 10 -     bk = 1.148 k + 0.023; R2=1; P< 0.01 Average 1.152        178  Table 5.22 Model summary of the log-log relationship between the first 10 orders PMs and PWMs of annual streamflow and watershed sizes of Eqn. (5-4) and Eqn. (5-8), respectively for the ten watersheds in the southern interior of British Columbia, Canada for the reference period. (Note all the models are statistically significant P<0.05) PMs PWMs Moments  bk ak R2 Moments  H ck R2 1 1.799 -6.229 0.931 1 1.186 -7.486 0.937 2 2.366 -12.409 0.934 2 1.190 -8.251 0.938 3 3.559 -18.559 0.936 3 1.193 -8.798 0.938 4 4.758 -24.692 0.936 4 1.195 -9.223 0.938 5 5.961 -30.812 0.936 5 1.196 -9.570 0.937 6 7.169 -36.921 0.936 6 1.197 -9.865 0.937 7 8.380 -43.021 0.936 7 1.198 -10.121 0.936 8 9.593 -49.114 0.936 8 1.198 -10.349 0.935 9 10.808 -55.199 20.935 9 -     10 12.025 -61.278 0.935 10 -     bk = 1.172 k + 0.196; R2=1; P< 0.01 Average 1.194         179  Table 5.23 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their specific catchment area of Eqns. (5-4) and (5-8), respectively in the five-nested watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.872. (Note all the models are statistically significant P<0.05). PMs PWMs Moments bk ak R2 Moments H ck R2 1 2.333 -21.676 0.995 1 2.319 -22.751 0.995 2 4.647 -43.056 0.995 2 2.314 -23.422 0.995 3 6.946 -61.188 0.995 3 2.310 -23.907 0.995 4 9.231 -85.097 0.995 4 2.307 -24.283 0.995 5 11.505 -105.810 0.995 5 2.304 -24.590 0.995 6 13.770 -126.360 0.995 6 2.302 -24.849 0.995 7 16.030 -146.810 0.995 7 2.300 -25.073 0.995 8 18.288 -167.190 0.995 8 2.298 -25.271 0.995 9 20.546 -187.540 0.995 9 2.296 -25.448 0.995 10 22.805 -207.880 0.995 10 2.294 -25.608 0.995 bk = 2.272 k + 0.113; R2 =1, P<0.01 H 2.304     180  Table 5.24 Model summary of log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their perimeter of Eqns. (5-4) and (5-8), respectively in the five-nested watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.874. (Note all the models are statistically significant P<0.05). PMs PWMs Moments bk ak R2 Moments H ck R2 1 2.280 -25.609 0.983 1 2.267 -26.663 0.984 2 4.542 -50.898 0.984 2 2.262 -27.329 0.984 3 6.791 -75.931 0.984 3 2.259 -27.812 0.984 4 9.030 -100.750 0.985 4 2.256 -28.188 0.984 5 11.259 -125.370 0.986 5 2.254 -28.495 0.985 6 13.482 -149.850 0.986 6 2.252 -28.754 0.985 7 15.701 -174.230 0.987 7 2.250 -28.979 0.985 8 17.919 -198.560 0.988 8 2.249 -29.178 0.985 9 20.138 -222.860 0.989 9 2.247 -29.356 0.986 10 22.359 -247.160 0.989 10 2.246 -29.518 0.986 bk = 2.229 k + 0.092; R2 =1, P<0.01 H 2.254        181  Table 5.25 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their specific catchment area of Eqns. (5-4) and (5-8), respectively in the ten watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.872. (Note all the models are statistically significant P<0.05). PMs PWMs Moments bk ak R2 Moments H ck R2 1 1.892 -17.724 0.848 1 1.897 -12.667 0.864 2 3.768 -35.170 0.849 2 1.900 -13.393 0.870 3 5.629 -52.377 0.849 3 1.903 -13.917 0.875 4 7.478 -69.383 0.848 4 1.905 -14.929 0.889 5 9.317 -86.220 0.847 5 1.907 -14.666 0.880 6 11.149 -102.930 0.847 6 1.908 -14.953 0.882 7 12.976 -119.540 0.846 7 1.909 -15.201 0.884 8 14.804 -136.090 0.845 8 1.909 -15.421 0.885 9 16.625 -152.610 0.844 9 1.909 -15.517 0.886 10 18.449 -169.110 0.843 10 1.909 -15.794 0.886 bk = 1.838 k + 0.1017; R2 =1, P<0.01 H 1.906    182  Table 5.26 Model summary of the log-log relationships between the first ten-order of PMs and PWMs for the annual streamflow and their perimeter of Eqns. (5-4) and (5-8), respectively in ten watersheds in the southern interior of British Columbia for the whole study period. The scaling exponent is 1.874. (Note all the models are statistically significant P<0.05). PMs-10 watersheds PWMs Moments bk ak R2 Moments H ck R2 1 1.890 -21.541 0.781 1 1.893 -22.777 0.794 2 3.767 -42.821 0.783 2 1.897 -23.538 0.800 3 5.633 -63.876 0.785 3 1.900 -24.090 0.804 4 7.490 -84.733 0.786 4 1.902 -24.521 0.807 5 9.337 -105.420 0.786 5 1.903 -24.872 0.810 6 11.178 -125.960 0.785 6 1.904 -25.166 0.812 7 13.014 -146.400 0.785 7 1.905 -25.418 0.813 8 14.847 -166.770 0.784 8 1.905 -25.639 0.814 9 16.680 -187.100 0.784 9 1.905 -25.833 0.812 10 18.513 -207.410 0.783 10 1.905 -26.007 0.810 bk = 1.845 k + 0.085; R2 =1, P<0.01 H 1.902   183  Chapter 6: Conclusions, uncertainties and future studies 6.1 Conclusions 6.1.1 Review of the effects of forest change on streamflow in large watersheds Although numerous case studies in large watersheds (>1000 km2) have been reported, there is no review that has synthesized the results of large watersheds. This study (Chapter 2) analyzed data from 162 large watersheds (Li et al., 2017), and concluded that deforestation increases water yield, while reforestation decreases it. This conclusion is consistent with the reviews of the small watersheds (Zhang et al., 2017b), which showed that the streamflow responses to forest change in larger and wetter watersheds are smaller than those in smaller and drier ones. In addition, the relative contributions of forest change and climate variability to streamflow revealed that forest change and climate change played equal roles in streamflow alterations. This highlighted the importance of forest change on streamflow alterations in watershed assessment and management.   6.1.2 Baseflow estimation of the study region Baseflow plays an important role in maintaining streamflow, and is an important indicator of surface and groundwater interactions. This study adopted one-year observed specific conductance data to calibrate the parameters for the long-term recursive filter digital method. The mean annual baseflow for Camp, Hedley, Tulameen, Princeton, and SRH were estimated to be 40 ± 14 mm, 63 ± 24 mm, 98 ± 28 mm, 107 ± 35 mm, and 99 ± 29 mm, respectively. The average baseflow index of Camp, Hedley, Tulameen, Princeton, and SRH were 0.30, 0.30, 0.27, 0.27, and 0.31, respectively. These results provide the useful estimates of regional baseflow or groundwater recharge.   184  6.1.3 Separation of the cumulative effects of forest disturbance and climate variability on streamflow components This study is the first study, as far as we know, that adopted statistical methods to separate the effects of forest change and climate variability on various streamflow components in large watersheds. The modified double mass curves revealed that cumulative effects of forest disturbance consistently increased total streamflow, baseflow, and surface runoff in the five-nested watersheds, while climate variability decreased them accordingly. The cumulative forest disturbance increased streamflow components from 20.1 mm year-1 in SRH to 56.7 mm year-1 in Hedley among the five nested watersheds. In addition, the roles of forest disturbance and climate variability in streamflow components showed large variations across the study watersheds. Such large variations were likely attributed to the differences in forest disturbance levels, climate, soil disturbance, and watershed topography.   6.1.4 Scaling properties of the cumulative effects of forest disturbance on streamflow components Annual streamflow, baseflow, and surface runoff in the southern interior of British Columbia obeyed the simple-scaling law with the scaling exponents being greater than the threshold of 1, indicating that increments of annual streamflow and its components in larger watersheds are higher than that of the watershed area. Two topographic indices including specific contributing area and watershed perimeter were identified as significant scaling parameters in addition to the watershed area. The cumulative effects (CEs) of forest disturbance on streamflow, baseflow, and surface runoff were also determined to follow the simple-scaling law with their corresponding scaling exponents being greater than the threshold of 1, further confirming that forest disturbance 185  would lead to more pronounced hydrological cumulative effects with increasing of watershed size.  This counterintuitive finding may be mainly due to increased synchronization effects by forest disturbance in the snow-dominated watersheds, large variations in topography, and promoted interactions between forests disturbance and climate in larger watersheds. The results of this finding should have important implication for predicting and managing cumulative hydrological effects of forest disturbance in the context of future forest disturbance and climate change as well as for ungauged watersheds.    6.2 Uncertainties in this study In this study, the modified double mass curves were introduced to separate the cumulative effects of forest disturbance and climate variability on streamflow, baseflow, and surface runoff. The uncertainties of this method may include the followings. First, the PET values were derived from the Priestley-Taylor method and Hamon method, based on the recommendation from Lu et al. (2005).  In this study, the averaged PET values from two methods were employed, which minimized a level of uncertainties introduced by adopting one method alone. However, various studies have demonstrated that the changes in surface humidity (Willett et al., 2008), vapour pressure, wind speed (McVicar et al., 2012), and net radiation (Wild et al., 2009) may have impacts on evaporative demand and thus PET. Yet, these factors were not considered in the PET calculations in this study.  Therefore, this might introduce a certain level of uncertainty in PET and AET, and the accuracy of the MDMC. Second, the changes in seasonal climatic patterns and their effects on streamflow were not considered (Berghuijs et al., 2014; Shen et al., 2017). For instance, Berghuijs et al. (2014) revealed that precipitation shift from snow to rain led to a decrease in streamflow. Third, possible feedbacks between forest change and climate (Feng et 186  al., 2016; Li et al., 2018) were not fully accounted for. For instance, reforestation can alter the precipitation either locally or remotely in the downwind direction and hence intensify the hydrological cycle (Ellison et al., 2012, 2017), while deforestation might affect local precipitation patterns (e.g. Khanna et al., 2017). Despite the above-mentioned possible uncertainties, their effects on our key conclusions are judged to be minimal since our study focused on comparisons among the study watersheds.  By using consistent methods among all study watersheds, the associated uncertainties are minimized.   The total number of the five-nested watersheds was selected to assess the scaling property of the CEs of forest disturbance on streamflow, baseflow, and surface runoff. There is a concern over the limited number of watersheds used for this study. There is no doubt that a larger number of watersheds would increase our assessment.  To minimize possible uncertainties, another five disturbed watersheds were also included in our analysis. The scaling properties of the observed streamflow in the five-nested and ten watersheds were found to be consistent for the study region. This research design, therefore, ensured our robust results from this study.     6.3 Future studies  6.3.1 The cumulative effects of forest disturbance on streamflow components In this study, the CEs of forest disturbance on hydrology were assessed in the five-nested watersheds. However, as shown in Table 2.1, there are few case studies on this subject, and their results were inconsistent. This further highlights that more case studies are needed to develop more general conclusions on the CEs of forest disturbance on streamflow components. Moreover, the previous studies mainly adopted hydrological models to study this topic. This 187  study suggests that either modelling or statistical methods or both can be used to assess the cumulative hydrological effects caused by forest disturbance.    6.3.2 Assessing relative contributions of forest disturbance and climate variability on streamflow components The land cover-climate interactions were not adequately considered in this study. Such interactions can play an essential role in local or regional climate patterns and thus hydrology. Future studies should include the land cover-climate interactions for assessing the effects of forest changes and climate on hydrology.    6.3.3 Topographic indices as the scaling parameters  A total number of 12 topographic indices were examined to determine which one could be used as a scaling parameter in the five-nested and ten watersheds. We found that specific contributing area (SCA) and the watershed perimeter has significant relations with streamflow components.    However, this conclusion was only drawn from a limited number of watersheds. A further study involving more watersheds would strengthen our selection. In addition, SCA and watershed perimeter could be used as the scaling parameters for annual streamflow. However, it is uncertain whether these two indices can be used for other hydrological variables, requiring future attention.    188  6.3.4  Scaling properties of the cumulative effects of forest disturbance on the hydrological regimes In this study, the CEs of forest disturbance on total streamflow, baseflow, and surface runoff were quantified, which has advanced our knowledge of the cumulative effects of forest disturbance on hydrology. Meanwhile, the cumulative forest disturbance could also have significant impacts on other flow regime variables (e.g., high and low flows, flow timing). 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Nature Communications, 6, 5918. Ziemer RR, Lewis J, Rice RM, Lisle TE (1991) Modeling the Cumulative Watershed Effects of Forest Management Strategies. Journal of Environmental Quality, 20, 36-42.     222  Appendices Appendix A:  The cumulative effects of forest disturbance on streamflow in the Deadman River watershed A.1 Watershed description The Deadman River watershed is located in the southern interior of British Columbia, Canada. The total drainage area is 878 km2, of which over 90% are forests. Elevation ranges from 527 m to 1779 m (Figure A.1).  The annual mean maximum, minimum, and mean temperatures were 8.9 ºC, -2.7 ºC, and 3.1 ºC, respectively. The annual precipitation and streamflow were about 470 mm and 65 mm, respectively during 1962-2013. Deadman River is a critical Salmonid bearing river that is a tributary of Thompson River.  In this study, the monthly climate data, including precipitation, maximum, minimum, and mean temperatures were generated from the ClimateWNA (Wang et al., 2006). The daily streamflow data were obtained from Environment Canada (Station ID: 08LF027). 223   Figure A.1 Location and spatial distributions of logging, mountain pine beetle, and forest fire in the Deadman River watershed.   A.2 Quantification of cumulative forest disturbance in the Deadman River watershed Forest logging and mountain pine beetle (MPB) infestation were the two leading forest disturbance types in the Deadman River watershed (Figure A.2). Up until 2012, the cumulative equivalent clear-cut area (CECA) was 41.3% of the total watershed area. The logging was the dominated disturbance type through the study period. The logging activity initiated since the 1970s with the annual logging rate of 1% until the late 1990s. In 2012, the CECA from logging was about 27.2% of the watershed area. The CECA from MPB infestation increased dramatically since 2003. The CECA of MPB in 2012 was 13.6%. The fire occasionally occurred in the 224  watershed with the CECA of 0.45% in 2012. Overall, the Deadman River watershed has experienced significant forest disturbance.    Figure A.2 The cumulative equivalent clear-cut area (CECA) in the Deadman River watershed from 1960 to 2012.   A.3 Trend analysis of the annual and seasonal hydrometeorological variables The Mann-Kendall trend analysis and Sen’s slope were adopted to study the annual and seasonal trends in hydrometeorological variables for the Deadman River watershed (Table A.1). The annual and seasonal Tmin experienced the significant upwards trends (P<0.05).  The significant increasing trend of maximum temperature was only detected for at annual time interval. The annual, spring, and summer Tmean showed the significant upward trends. As a consequence, the corresponding PET showed the significant upward trend.  The spring P was the only season that showed a significant increasing trend. The winter streamflow showed the increasing trend mainly 0510152025303540451960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015CCEA (%)LoggingFireMPBAll225  due to the snow-melt by increased temperature. The increasing trends in temperatures and PET may, therefore, play negative impacts on streamflow.   Table A.1 Mann-Kendall trend test of the hydrometeorological variables in the Deadman River watershed from 1962 to 2013.  Tmax Tmin Tmean P PET AET Q Annual Z 2.6 3.1 3.1 -0.1 3.4 0.7 1.3 P 0.01 0.001 0.002 0.96 <0.001 0.49 0.20 Slope 0.018 0.026 0.022 -0.045 0.414 0.240 0.354 Spring Z 1.6 2.6 2.2 2.5 2.2 2.6 0.9 P 0.11 0.01 0.03 0.013 0.03 0.009 0.364 Slope 0.017 0.024 0.021 0.127 0.666 0.348 0.145 Summer Z 1.8 3.6 2.7 0.2 2.8 0.2 0.8 P 0.064 <0.001 0.008 0.818 0.004 0.806 0.444 Slope 0.019 0.020 0.019 0.103 0.218 0.045 0.093 Winter Z 1.5 2.1 1.9 -1.3 1.4 1.1 2.5 P 0.128 0.034 0.057 0.182 0.153 0.28 0.012 Slope 0.018 0.030 0.024 -0.574 0.059 0.056 0.073  A.4 Cross-correlation between CECA and annual streamflow in the Deadman River watershed The cross-correlation test revealed that forest disturbance and annual streamflow were significantly correlated (P< 0.05). In addition, the positive coefficient indicated that the cumulative forest disturbance has significantly increased the annual streamflow (Table A.2).    226  Table A.2 Cross-correlation between the CECA and annual streamflow in the Deadman River watershed Hydrological Variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (1, 3, 0) 0.320* 8 ARIMA model for CECA (2, 2, 1)  A.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow One break point was detected in 1989 on the MDMC. Additionally, Mann-Whitney U tests confirmed that the slopes of MDMCs before and after the break point were statistically different (P<0.001). The break point coincided with the history of forest disturbance (Table A.3). Overall, the cumulative forest disturbance increased annual streamflow by 16.59 mm, with Rf to streamflow being 86.2%. In contrast, climate variability increased it by 2.66 mm with its Rc to streamflow of 13.8%, respectively. Overall, the effects of climate variability on streamflow were much lower than those from forest disturbance, indicating streamflow variations in the Deadman River watershed were mainly caused by cumulative forest disturbance. The disturbance period was further divided into five sub-periods to examine the temporal role of forest disturbance and climate variability in streamflow. As shown in Table A.3, the Rf and Rc to streamflow showed temporal variations. For example, with slightly forest recovery, the Rf was lower in 1995-1999 than other periods. In summary, our results demonstrated that forest disturbance played a more important role in the variations streamflow compared to climate variability.   227   Figure A.3 The Modified Double Mass Curves (MDMC), which plots the cumulative annual streamflow (Qa) against the cumulative annual effective precipitation (Pae).   Table A.3 Temporal summary of the streamflow change to forest disturbance and climate variability and their relative contributions in the Deadman River watershed from 1990- 2013. Periods ∆Q (mm) ∆Qf (mm) ∆Qc (mm) Rf (%) Rc (%) CECA (%) 1990-1994 17.53 13.71 3.82 78.23 21.77 14.56 1995-1999 30.53 14.23 16.30 46.62 53.38 17.32 2000-2004 3.02 4.63 -1.61 74.18 25.82 18.21 2005-2009 21.57 19.71 1.85 91.40 8.60 32.43 2010-2013 27.12 34.20 -7.08 82.85 17.15 51.67 1990-2013 19.95 16.59 2.66 86.20 13.80 24.68      050010001500200025003000350040000 2000 4000 6000 8000 10000Cumulative streamflow  (mm)Cumulative effective precipitation (mm)ObservedPredictedLn(Qa) = 0.910 Ln (Pae ) - 0.393R2 = 0.998 P<0.001Year: 1989228  Appendix B:  The cumulative effects of forest disturbance on streamflow in the Fishtrap Creek watershed B.1 Watershed description  Fishtrap Creek is located in the southern interior of British Columbia with the drainage area of 135 km2 (Figure B.1). The Fishtrap Creek is a tributary of the North Thompson River and flows into the mainstream in the south of the town of Barriere (Easton et al., 2010). The annual mean maximum and minimum temperatures were 12.0 ºC and 0.2 ºC, respectively. The annual precipitation and runoff were 477 mm and 182 mm, respectively. The watershed is mainly located in the biogeoclimatic zones of Interior Cedar-Hemlock, Interior Douglas fir, and Montane Spruce.  The daily climate data, including precipitation, maximum and minimum temperatures were obtained from climate station located in the Darfield, BC, (Station ID: 1162265), which is located the 10 km north of the watershed. The streamflow data were obtained from Environment Canada (Station ID: 08LB024). The hydrological station was destroyed by the fire and reconstructed in March 2004 for measurement. To fill missing streamflow data, the average annual runoff ratios (streamflow/precipitation) of specific years were derived, which had similar climate conditions (similar precipitation and temperature) with the year 2003 and 2004. Then, streamflow data for 2003 and 2004 were estimated by multiplying the corresponding precipitation with the average runoff ratio.   229   Figure B.1 Watershed location and spatial distributions of logging, fire, and mountain pine beetle infestation.  B.2 Quantification of cumulative forest disturbance in the Fishtrap Creek watershed Forest logging and wildfire were the two dominated forest disturbance types in the Fishtrap Creek watershed (Figure B.2). Up until 2010, the cumulative equivalent clear-cut area (CECA) was 92% of the total watershed area. The logging was the dominated disturbance type before 2003. In August 2003, the McLure forest fire caused the significant loss. Roughly about 62% of the watershed was burnt, which lead the dramatic increase in the CECA. In 2010, the CECA from the fire was 29.8% of the watershed area. Before 2001, the CECA from logging was the leading disturbance types, and the CECA in 2001 was 28.5%. Then, the salvage logging after forest first surged the sharp increase in CECA. Until 2010, the CECA from logging was 50.4%. 230  The MPB in 2003 also contributed to the CECA substantially. The CECA from MPB in 2010 was 12.7%. Overall, the Fishtrap Creek watershed has experienced significant forest disturbance.    Figure B.2 The cumulative equivalent clear-cut area (CECA) from 1960 to 2010 in the Fishtrap Creek watershed.  B.3 Trend analysis of the annual and seasonal hydrometeorological variables The Mann-Kendall trend analysis and Sen’s slope were adopted to study the annual and seasonal trends in hydrometeorological variables for the Fishtrap Creek watershed (Table B.1). The annual and summer Tmin experienced the significant upwards trends (P<0.05).  Other temperature variables did not experience significant alterations over the study periods. The annual PET was the only season that showed a significant increasing trend. No significant changes were detected for the annual streamflow variables.   01020304050607080901001960 1970 1980 1990 2000 2010CECA (%)FireMPBLoggingAll231  Table B.1 Mann-Kendall trend test of the hydrometeorological variables in the Fishtrap Creek watershed from 1962 to 2013. Trend Test  Tmax Tmin Tmean P PET AET Q Annual Z 0.2 2 1.3 -0.2 -2.6 -1.1 0.5 P 0.85 0.05 0.09 0.86 0.01 0.27 0.60 Slope 0.002 0.025 0.014 -0.180 -0.767 -0.514 0.515 Spring Z -0.6 0.7 0.2 0.8 0.3 -0.6 1.2 P 0.54 0.46 0.86 0.44 0.73 0.58 0.24 Slope -0.010 0.011 0.002 0.300 0.028 -0.028 0.762 Summer Z 0.3 3.3 1.70 -0.5 1.5 0.3 -0.9 P 0.778 0.001 0.09 0.633 0.124 0.779 0.386 Slope 0.006 0.031 0.010 -0.372 0.134 0.025 -0.300 Winter Z 0.7 1.9 1.3 1.4 -0.5 0.4 -0.9 P 0.62 0.06 0.18 0.16 0.60 0.68 0.39 Slope 0.010 0.026 0.015 0.488 -0.046 0.049 -0.094  B.4 Cross-correlation between the CECA and annual streamflow in the Fishtrap Creek watershed The cross-correlation tests revealed that forest disturbance and annual streamflow were significantly correlated (P< 0.05) (Table B.2). Furthermore, the positive coefficient (0.294) implied that the cumulative forest disturbance has significantly increased the annual streamflow in the Fishtrap Creek watershed.   Table B.2 Cross-correlation between the CECA and annual streamflow in the Fishtrap Creek watershed Hydrological Variables Cross-correlation ARIMA Model Coefficients Lag Annual Streamflow (0, 0, 1) 0.294* 4 ARIMA model for CECA (0, 1, 1)  232  B.5 Separation of the cumulative effects of forest disturbance and climate variability on streamflow  One break point was detected in 2003 on the MDMC. Additionally, Mann-Whitney U tests confirmed that the slopes of MDMCs before and after the break point were statistically different (P<0.001) (Figure B.3). The break point coincided with the history of forest disturbance. Overall, the cumulative forest disturbance increased annual streamflow by 37.3 mm, with its Rf to streamflow being 60.1%. In contrast, climate variability decreased it by 24.8 mm with its Rc to streamflow of 39.9%. Due to the large forest logging and extensive forest fire, the streamflow change due to forest disturbance was much higher than those from climate variability. The disturbance period was further divided into five sub-periods of 5-year to study the temporal role of forest disturbance and climate variability in annual streamflow. The Rf and Rc showed temporal variations (Table B.3). For example, with forest recovery, the relative contribution of forest disturbance streamflow was lower in 2009-2013 than the period 2004-2008 following the significant forest fire. In summary, results demonstrated that forest disturbance played a more dominated role in the variations streamflow compared to climate variability, but in the opposite direction.   233   Figure B.3 The Modified Double Mass Curves (MDMC), which plots the cumulative annual streamflow (Qa) against the cumulative annual effective precipitation (Pae).  Table B.3 Temporal summary of the cumulative effects of forest disturbance and climate variability and their relative contribution to streamflow   ∆Q (mm) ∆Qf (mm) ∆Qc (mm) Rf (%) Rc (%) 2004-2008 32.5 48.1 ± 12.7 -15.6 ± 12.7 75.5 24.5 2009-2013 -7.5 26.6 ± 11.3 -34.1 ± 11.3 43.8 56.2 2004-2013 12.5 37.3 ± 12.0 -24.8 ± 12.0 60.1 39.9   0100020003000400050006000700080000 1000 2000 3000 4000 5000 6000 7000 8000Cumulative streamflow (mm)Cumulative effective precipitation (mm)Year : 2003Ln (Qa) = 0.902* Ln (Pae) + 0.802R2 = 0.998 P<0.001

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