Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Detecting novel climates in projections of 21st century terrestrial ecosystem change Mahony, Colin 2017

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2018_may_mahony_colin.pdf [ 24.94MB ]
Metadata
JSON: 24-1.0364414.json
JSON-LD: 24-1.0364414-ld.json
RDF/XML (Pretty): 24-1.0364414-rdf.xml
RDF/JSON: 24-1.0364414-rdf.json
Turtle: 24-1.0364414-turtle.txt
N-Triples: 24-1.0364414-rdf-ntriples.txt
Original Record: 24-1.0364414-source.json
Full Text
24-1.0364414-fulltext.txt
Citation
24-1.0364414.ris

Full Text

  DETECTING NOVEL CLIMATES IN PROJECTIONS OF 21ST CENTURY TERRESTRIAL ECOSYSTEM CHANGE  by  Colin Mahony  B.Sc., McGill University, 1997  A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  March 2018  © Colin Mahony, 2018 ii Abstract The emergence of locally unfamiliar climates due to anthropogenic global warming is compelling scientists and resource managers to seek ecological data and management strategies from non-local climates, known as climate analogs. In this context, novel climates—emerging conditions with no analog in the observational record—represent widening gaps in the ecological knowledge base. Identification of novel climates is essential to climate change adaptation. However, methods to detect novel climates have not kept pace with this necessity.  The goal of this dissertation is to advance methods for detection of novel climates in the context of ecology and forest management. I develop a multivariate metric for climatic novelty, sigma dissimilarity, that uses the local historical range of interannual climatic variability as a scale for measuring the ecological significance of climatic differences. I apply this metric at three scales—continental, jurisdictional, and local—each of which offers a distinct perspective on the implications of climatic novelty. At the continental scale, I assess the emergence of novel climates in North America, where they are an important source of extrapolation error in ecological modeling. I demonstrate the potential for novel climates to emerge throughout the continent, particularly at low topographic positions. At the jurisdictional scale, I assess the emergence of novel climates that are not represented in a structured knowledge system for forest management—the Biogeoclimatic Ecosystem Classification for British Columbia. A parallel novelty assessment using sigma dissimilarity and random forest classification indicates a robust pattern of novel climates in BC, for which analogs from outside BC must be identified. At the local scale, I demonstrate that dependencies among climate variables can produce larger and earlier departures from natural variability than is detectable in individual variables. This multivariate departure intensification effect—evident in distinct regions of the planet in global climate models—indicates adaptive challenges for ecological and human communities as their local climates become unfamiliar.  The identification of locally unfamiliar and regionally novel climates is an important step in anticipating and adapting to climate change. Further, the challenges presented by novel climates are yet another basis to advocate for global emissions reductions.  iii Lay Summary Anthropogenic global warming is producing new, unfamiliar climates. This dissertation explores the ways that local climates are departing from historical variability, and the extent to which these locally unfamiliar climates are novel, i.e., unlike any of the climate types historically present elsewhere in the landscape. I find that novel climates are projected to emerge in many landscapes of North America by the end of the 21st century, particularly at low elevations. At a regional scale, I project the mid-21st century emergence of novel climates that are not represented in the ecological climate classification for British Columbia. At local scales, I demonstrate conditions under which the climatic departures from historical range of variability can be underestimated if interdependent climate variables are assessed in isolation. These advances in the detection of locally unfamiliar and regionally novel climates assist with the challenge of anticipating and adapting to the ecological impacts of climate change.  iv Preface All research chapters have been published or accepted in peer-reviewed journals, listed below.  I designed the studies, performed all analyses, and solely wrote the manuscripts, with substantive guidance and review from the coauthors of each manuscript. Dr. Alex J. Cannon provided R script and methods for the quantile delta mapping transformations performed in Chapter 5.  Chapters 2 & 3 Mahony, C. R., A. J. Cannon, T. Wang, and S. N. Aitken (2017). A closer look at novel climates: New methods and insights at continental to landscape scales. Global Change Biology, 23(9), 3934–3955.   Chapter 4 Mahony, C. R., Will H. Mackenzie, and S. N. Aitken (accepted with minor revisions). Novel climates: Trajectories of climate change beyond the boundaries of a forest management knowledge system. Forest Ecology and Management.   Chapter 5 Mahony, C. R. and A. J. Cannon (accepted with minor revisions). Wetter summers can intensify departures from natural variability in a warming climate. Nature Communications.     v Table of Contents Abstract .......................................................................................................................................... ii Lay Summary ............................................................................................................................... iii Preface ........................................................................................................................................... iv Table of Contents ...........................................................................................................................v List of Tables ............................................................................................................................... vii List of Figures ............................................................................................................................. viii List of Abbreviations .................................................................................................................. xii List of Symbols ........................................................................................................................... xiv Acknowledgements ......................................................................................................................xv Dedication ................................................................................................................................... xvi Chapter 1: Introduction ................................................................................................................1 1.1 Emergence of locally unfamiliar climates .................................................................. 1 1.2 Restoring climatic familiarity using non-local climate analogs ................................. 2 1.3 The problem of novel (no-analog) climates ................................................................ 3 1.4 The subjectivity of climatic novelty ........................................................................... 4 1.5 Detecting ecologically novel climates ........................................................................ 5 1.6 Evaluating the interannual climatic variability hypothesis ......................................... 7 1.7 Research objectives, strategies, and contributions ...................................................... 8 Chapter 2: Sigma dissimilarity—Measuring climatic differences relative to interannual climatic variability .......................................................................................................................10 2.1 Calculation of Mahalanobis distance scaled to ICV ................................................. 10 2.2 Sigma dissimilarity ................................................................................................... 14 2.3 Discussion ................................................................................................................. 15 Chapter 3: Novel climates of North America ............................................................................17 3.1 Introduction ............................................................................................................... 17 3.2 Methods..................................................................................................................... 21 3.3 Results ....................................................................................................................... 25 3.4 Discussion ................................................................................................................. 37 Chapter 4: Novel climates of British Columbia: Trajectories of climate change beyond the boundaries of the Biogeoclimatic Ecosystem Classification.....................................................45 4.1 Introduction ............................................................................................................... 45 4.2 Methods..................................................................................................................... 50 4.3 Results ....................................................................................................................... 55 4.4 Discussion ................................................................................................................. 65 Chapter 5: Locally novel climates—Intensified climate departures in coupled climate variables ........................................................................................................................................70 5.1 Introduction ............................................................................................................... 70 5.2 Methods..................................................................................................................... 74 5.3 Results ....................................................................................................................... 76 5.4 Discussion ................................................................................................................. 81 Chapter 6: Conclusion .................................................................................................................84 6.1 Research conclusions and significance ..................................................................... 84 6.2 Future research directions ......................................................................................... 86 6.3 Closing remarks: The role of local ecological wisdom ............................................ 88 Bibliography .................................................................................................................................90 vi Appendix A Supplementary information for Chapter 3 ........................................................102 A.1 Selection of reference interannual variability data ................................................. 102 A.2 PCA truncation threshold ........................................................................................ 109 A.3 Subsampling the analog pool .................................................................................. 112 A.4 CMIP5 Ensemble models ....................................................................................... 114 A.5 Ensemble results ..................................................................................................... 115 A.6 Investigating analog outliers ................................................................................... 117 A.7 Accounting for non-normality in the distribution of ICV ....................................... 119 A.8 Null model analysis of elevation-novelty relationship ........................................... 122 A.9 Variation around mean novelty from multiple ICV proxies ................................... 124 A.10 Bias due to nonrandom weather station placement ................................................. 126 A.11 Variable selection.................................................................................................... 127 A.12 Comparison to standardized Euclidean distance. .................................................... 130 A.13 Assessment of error due to ICV sample size .......................................................... 134 Appendix B Supplementary Information for Chapter 4 ........................................................140 B.1 Biogeoclimatic subzone names ............................................................................... 140 B.2 Geographical distance to best analog ...................................................................... 141 B.3 Measuring analog dissimilarity with the RF proximity matrix ............................... 144 B.4 Effect of predictor availability on RF projections and novelty indicators .............. 146 B.5 Sensitivity analyses of North American analog search ........................................... 150 B.6 Relationship between elevation and novelty ........................................................... 154 Appendix C Supplementary Information for Chapter 5........................................................155 C.1 Timing of climate departures .................................................................................. 155 C.2 Sensitivity to univariate and multivariate normalization methods ......................... 158 C.3 Null model for departure differences ...................................................................... 161 C.4 Out-of-reference-period standardized anomaly bias ............................................... 163 C.5 CMIP5 Ensemble .................................................................................................... 164 C.6 Summer Tx-Pr correlations and orthogonality of climate change .......................... 165 C.7 Relative departures of temperature and precipitation ............................................. 166 C.8 Pseudocode for calculation of maximum departure difference. ............................. 167 C.9 Parallel analysis of hottest three consecutive months ............................................. 168  vii List of Tables Table A.1: Count of total North American stations in the CRU TS3.23 source observations ... 104 Table A.2: CMIP5 models included in the RCP8.5 and RCP4.5 ensemble mean projections ... 114 Table A.3:  Differences between the data used in Williams et al. (2007) and the benchmark scenario presented in Figure A.25, including probable effect on novelty. ........................... 131 Table B.1: Full names of biogeoclimatic subzones used as examples in Chapter 4 ................... 140 Table C.1: CMIP5 models included in Chapter 5 ....................................................................... 164  viii List of Figures Figure 2.1: Illustration of the procedure for analog identification using Mahalanobis distance scaled to local ICV .................................................................................................................. 13 Figure 2.2:  The theoretical basis of the multivariate sigma dissimilarity metric.. ....................... 14 Figure 2.3: Illustration of the use of the sigma dissimilarity metric to map analog dissimilarity. 15 Figure 3.1: Projected shifts in the North American temperature-precipitation envelope ............. 19 Figure 3.2: Simplified illustration of the novelty assessment. ...................................................... 21 Figure 3.3: An overview of the spatial variation in the input data to the novelty analysis ........... 24 Figure 3.4: Distribution of climatic novelty across North America ............................................. 26 Figure 3.5: Effect of variable selection on novelty of the RCP8.5 ensemble mean projection .... 28 Figure 3.6: Effect of variable selection on reference period (1971-2000) dissimilarity to a single location (Denver, CO) ............................................................................................................. 29 Figure 3.7: Comparison of the ensemble mean projections to individual RCP4.5 projections of the 15 models in the ensemble. ............................................................................................... 30 Figure 3.8: The first three dimensions of the North American climate envelope plotted in the localized climate space of Montreal, Canada ......................................................................... 32 Figure 3.9: Relationship between novelty and topographic position ............................................ 34 Figure 3.10: Elevational and latitudinal climate shifts (distance to best analog) in the RCP4.5 ensemble mean projection, and their relationship to novelty ................................................. 36 Figure 3.11: Relationships of novelty with elevational and latitudinal climate shifts .................. 37 Figure 4.1: Biogeoclimatic zones of British Columbia ................................................................ 47 Figure 4.2: Projected shifts in the British Columbian temperature-precipitation envelope ......... 48 Figure 4.3: Illustration of the linear method for measuring climatic novelty ............................... 50 Figure 4.4: Conceptual models for indicators of novelty in Random Forest projections ............. 52 Figure 4.5: Climatic differentiation among BGC units ................................................................ 55 Figure 4.6: Novelty of projected climates of British Columbia in the 2041-2070 period ............ 57 Figure 4.7: Spatial distribution of climatic novelty in current BEC zones and subzone-variants 58 Figure 4.8: Relationship between novelty measured with Mahalanobis distance and two hypothesized indicators of novelty ......................................................................................... 59 Figure 4.9: Analog similarity and ensemble agreement in BEC projections ................................ 61 Figure 4.10: End-of-20th century analogs for the mid-21st-century climates of BC ..................... 63 Figure 4.11: Locations in BC with non-BC North American analogs. ......................................... 65 Figure 5.1: Intensified departure from historical variability in a correlated temperature-precipitation regime ................................................................................................................ 73 ix Figure 5.2: Univariate and bivariate climate departures for summer precipitation (Pr) and mean daily maximum temperature (Tx) at selected locations .......................................................... 77 Figure 5.3: Intermodel variation in relative departures from natural variability in summertime temperature (Tx) and precipitation (Pr) .................................................................................. 79 Figure 5.4: Relationship of maximum departure difference to the correlation between summer mean daily maximum temperature (Tx) and precipitation (Pr) .............................................. 81 Appendix Figures Figure A.1: 1959-2013 interannual climatic variability of seasonal precipitation in North America, calculated from three gridded historical time series products ............................... 102 Figure A.2: Assessment of bias in coefficient of variation in the CRU TS3.23 interpolated grid and the JRA55 reanalysis ...................................................................................................... 103 Figure A.3: spatial distribution of CRU TS3.23 source stations ................................................ 105 Figure A.4: completeness of station data in the CRU TS3.23 source observations for North America ................................................................................................................................. 106 Figure A.5: number of complete years (data present for all seasons in both temperature and precipitation) in the 1951-1990 period for North American CRU TS3.23 source stations .. 108 Figure A.6: Local climate change signal (left) and North American spatial variation (right) within the localized data space of each reference station ..................................................... 110 Figure A.7: Local climate change signal (left) and North American spatial variation (right) expressed as standardized anomalies of the lesser principal components (PCs 10-12) of local interannual variability at each reference station ................................................................... 111 Figure A.8: Development of a weighted subsample of 8-km North American grid cells .......... 112 Figure A.9: novelty assessment for the reference period (1971-2000) ....................................... 113 Figure A.10: Novelty analyses for individual RCP4.5 projections of the 15-model CMIP5 ensemble ............................................................................................................................... 115 Figure A.11: The relationship (c) between novelty calculated from a single ensemble mean projection (b) and the average of 15 separate calculations for the 15 individual models in the ensemble (a). ......................................................................................................................... 116 Figure A.12: Seasonal temperature-precipitation plots of the North American analog pool ..... 117 Figure A.13: Outliers to the North American climate envelope do not have high analog importance............................................................................................................................. 118 Figure A.14: Illustration of data transformation using quantile matching to a fitted PDF ......... 119 Figure A.15: Example of decimal precision (black numbers in plot) required to perform quantile matching to a fitted gamma PDF .......................................................................................... 120 Figure A.16: Sensitivity analysis using raw instead of log-transformed precipitation data ....... 121 Figure A.17: Null model analysis of the relationship between relative elevation and novelty .. 123 x Figure A.18: Range of novelty calculated from the four ICV proxies for each grid cell, relative to their mean.............................................................................................................................. 124 Figure A.19: potential for missed novelty or false novelty relative to the 2σ threshold ............ 125 Figure A.20: Change in novelty relative to the Base Case when novelty is calculated using the single nearest weather station as an ICV proxy, rather than the four nearest stations .......... 126 Figure A.21: Effect of variable selection on novelty of the RCP4.5 ensemble mean projection 127 Figure A.22: Effect of variable selection on reference period dissimilarity to Montreal, Quebec................................................................................................................................................ 128 Figure A.23: Effect of variable selection on reference period dissimilarity to Yakima, WA. ... 128 Figure A.24: Effect of balancing the number of temperature (T) and precipitation (P) variables on reference period (1971-2000) dissimilarity ..................................................................... 129 Figure A.25: Approximate benchmarking of my dataset to the Williams et al. (2007) results .. 131 Figure A.26: Effect of variable selection on SED novelty in the RCP4.5 ensemble mean projection .............................................................................................................................. 132 Figure A.27: Reference period (1971-2000) sigma dissimilarity to Denver, CO, using Mahalanobis distance (a,b,c) and SED ................................................................................. 133 Figure A.28: ICV proxy sample size for map cells of the North American study area. ............. 134 Figure A.29: (a) Distribution of the 95% confidence interval of 120 bootstrapped novelty calculations for each map cell with novelty >1σ .................................................................. 136 Figure A.30: Map of the relative 95% confidence interval (a ratio of the median) of n=120 novelty calculations for each cell with bootstrap resampling of the ICV time series contributing to the PCA ........................................................................................................ 137 Figure A.31: Effect of bootstrapping on estimates of error at various sample sizes at a single map cell ......................................................................................................................................... 138 Figure A.32: Bootstrapping introduces a downward bias into calculations of sigma dissimilarity............................................................................................................................................... 139 Figure B.1: Geographical distances to the location of best British Columbian analogs for projected climates ................................................................................................................. 142 Figure B.2: Geographical distances to the location of North American climate analogs for projected climates ................................................................................................................. 143 Figure B.3: Ranked mean dissimilarity among BGC subzone-variants measured with RF proximity (var6). ................................................................................................................... 144 Figure B.4: Same as Figure B.3, but using the var44 variable set. ............................................. 145 Figure B.5: RCP4.5 ensemble mean BGC projections for the 2041-2070 period using Random Forest classification, at increasing predictor availability ...................................................... 147 Figure B.6: Analog similarity in the RCP4.5 ensemble mean Random Forest BGC projections for the 2041-2070 period at increasing predictor availability .................................................... 148 xi Figure B.7: Ensemble agreement among RCP4.5 Random Forest BGC projections for the 2041-2070 period by 15 CMIP5 global climate models ................................................................ 149 Figure B.8: End-of-20th century analogs for the mid-21st-century climates of BC, measured as proportional votes for climates projected to occur within BC .............................................. 150 Figure B.9: End-of-20th century analogs for the mid-21st-century climates of BC .................... 151 Figure B.10: Locations in BC with non-BC North American analogs for their RCP4.5 ensemble mean climate of the 2041-2070 period ................................................................................. 152 Figure B.11: Relationship of elevation to (a) novelty calculated with Mahalanobis distance, (b) log-transformed Random Forest analog proximity (a metric of analog similarity), and (c) non-BC Random Forest votes ............................................................................................... 154 Figure C.1: Relationship of the relative timing and the relative magnitude of climate departures in RCP4.5 ensemble projections of 6 CMIP5 models .......................................................... 155 Figure C.2: Departure year of the bivariate summer Tx-Pr climate signal from natural variability in the CMIP5 ensemble. ........................................................................................................ 157 Figure C.3: Timing of departure of the bivariate summer Tx-Pr climate signal relative to the departure of the univariate (max. of Tx or Pr) climate signals ............................................. 157 Figure C.4: Sensitivity of maximum departure difference to four different treatments of multivariate normality ........................................................................................................... 160 Figure C.5: Departure differences in the CMIP5 ensemble during the 2021-2050 period. ........ 161 Figure C.6: Null model for departure differences under global warming .................................. 162 Figure C.7: Overestimation bias in the 2σ proportion of non-reference-period standardized anomalies at reference period samples of nref = 30 to 600 normal variates .......................... 163 Figure C.8: Correlation between summer precipitation (smpr) and mean daily maximum temperature in the summer (smtx) in the pooled historicalNat runs of the six CMIP5 models................................................................................................................................................ 165 Figure C.9: Orthogonality of climate change projected by the six CMIP5 models .................... 165 Figure C.10: Relative departures (2σ proportions) of summer precipitation (smpr) and mean daily maximum temperature in the summer (smtx) in projections of the 2021-2050 period by six CMIP5 models................................................................................................................. 166 Figure C.11: Hottest three consecutive months in the r1i1p1 historicalNat run of each CMIP5 model used in this analysis. .................................................................................................. 168 Figure C.12: Correlation between precipitation (pr) and mean daily maximum temperature (tx) of the hottest 3 consecutive months .......................................................................................... 169 Figure C.13: Intermodel variation in relative departures from natural variability in temperature (Tx) and precipitation (Pr) of the hottest three consecutive months ..................................... 170 Figure C.14: Relationship of maximum departure difference to the correlation between mean daily maximum temperature (Tx) and precipitation (Pr) of the three hottest consecutive months ................................................................................................................................... 171 xii List of Abbreviations ANUSPLIN Australian National University thin plate spline smoothing algorithm AOGCM atmosphere-ocean general circulation model BC British Columbia BEC* Biogeoclimatic Ecological Classification BGC* biogeoclimatic CI  confidence interval CMIP5** fifth coupled model intercomparison project CRU TS Climatic Research Unit gridded time series  DEM digital elevation model DJF December-January-February ESM earth system model ESWG Ecological Stratification Working Group GCM global climate model GPCC Global Precipitation Climatology Centre GTOPO30 global 30 arc-second DEM historicalNat  historical natural forcings GCM run ICV Interannual climatic variability ID Identification code INDCs  Intended Nationally Determined Contributions JJA June-July-August JRA55 Japanese 55-year Reanalysis kde kernel density estimation km kilometer MAM March-April-May MAT  mean annual temperature MaxEnt  maximum entropy algorithm mbcn multivariate quantile mapping mm millimeters nref reference period sample size PC principal component PCA principal components analysis PDF probability density function PPT precipitation pqm parametric quantile mapping Pr precipitation PRISM parameter-elevation relationships on independent slopes model qdm quantile delta mapping RCP representative concentration pathway RF Random Forest algorithm smpr summer precipitation xiii smtx mean daily maximum temperature in the summer SON September-October-November SRES  Special Report on Emissions Scenarios Tave monthly mean temperature Tmax monthly mean of daily maximum temperature Tmin monthly mean of daily minimum temperature Tx monthly mean of daily maximum temperature USA United States of America USFS  United States Forest Service USGS United States Geological Survey WWF World Wildlife Fund *Biogeoclimatic Ecosystem Classification acronyms are defined in Figure 4.1 and Table B.1 **CMIP5 model acronyms are defined in Table C.1    xiv List of Symbols Da Mahalanobis-distance-based analog dissimilarity Dc Mahalanobis-distance-based magnitude of climate change Dmin Mahalanobis distance to best analog dT difference in MAT between the 2071-2100 and 1971-2000 normal periods. oC degrees Celsius Δ delta; the change from the reference condition to the projected future condition θ theta; the degree of orthogonality from the dominant mode of ICV σ sigma; signifies standard deviations of local historical ICV χ chi; the chi distribution  xv Acknowledgements I am deeply appreciative of my academic supervisor, Dr. Sally Aitken, for her patience, constancy, and wisdom as she guided me through my graduate studies. Thank you, Sally, for always having my back throughout this process.  I have been very lucky to have had the help of a supervisory committee that has been so much more: Dr. Alex Cannon, who very generously tutored me on climate science and became the best research collaborator I could wish for; Dr. Tongli Wang, whose work on biogeoclimatic projections is the inspiration for this research, and who invested much time in fruitful discussions and friendly review; and Dr. Suzanne Simard, who welcomed me to UBC with open arms and instilled in me the importance of science communication at every stage of the scientific process.  I am grateful to Jack Woods for his many contributions to this phase of my career, as a mentor, collaborator, advocate, and friend. Thanks to my officemates Ian MacLachlan, Joane Elleouet, and Susannah Tysor for companionship, ideas, and lots of fun. I greatly appreciate the patient help of the FCS administrative staff—Natasha Thompson, Rosemarie Cheng, Andrea Chan, and Christine Mutia—who quietly and competently keep everything running smoothly. I am indebted to Dr. Stephen Mitchell and Dr. Robert Guy for their generous help with the successful NSERC CGS application that got me started.  This dissertation is grounded in years of field work with my mentors in forest ecology and silviculture: Jeff McWilliams, Bob Green, Aaron Bigsby, Ben Andrew, and Bruce Blackwell. These foresters have profoundly informed my thinking on the role of climate in ecosystems.  This research was made possible by funding from a UBC Four Year Doctoral Fellowship, an NSERC/UBC TerreWEB PhD Fellowship, an NSERC Alexander Graham Bell Canada Graduate Scholarship (CGS-M), and an NSERC Discovery Grant to Dr. Sally Aitken. I am very grateful to the donor families and institutions of the Faculty of Forestry internal awards for the financial and moral support I received from the Peter Rennie Memorial Award, the FMIBC Scholarship, the Mary & David Macaree Fellowship, the Donald S. McPhee Fellowship, and the VanDusen Graduate Fellowship.Thank-you to the Faculty staff that administer these sources of support.  Finally, my greatest gratitude goes to my family: my partner in life, Suzanne von der Porten, who encouragement set me on the path to graduate school and sustained me throughout; my mother, Carol May Mahony, for boundless support of this project; and my father, Mick Mahony, whose lived wisdom continues to guide me.  xvi Dedication   To my children, Kye and Emily, who inspire me to protect their future and to take joy in the present.   1 Chapter 1: Introduction This dissertation is about the emergence of new, unfamiliar climates due to anthropogenic global warming in the 21st century. My goal is to contribute answers to two closely related questions. The first question relates to climatic familiarity at the local scale: How much will the future climate of any given location differ from its historical climate? The second relates to broader spatial scales: Are there observable climates elsewhere that resemble this projected future condition? Departure from familiar climatic conditions will put stress on ecosystems and on the knowledge systems that we have historically used to manage them. To some extent, our responses to locally unfamiliar conditions can be informed by our accumulated knowledge of comparable climates—climate analogs—elsewhere in the landscape. However, the necessity for climate analogs raises concerns about a broader level of unfamiliarity: climatic conditions with no analog, with which we have no personal or collective experience.  These novel climates represent gaps in the scientific, cultural, and evolutionary knowledge base for adaptation. Anticipating the ways in which local climates will become unfamiliar, and where novel climates will emerge, is a necessary scientific contribution to society’s response to climate change.  A central theme of this dissertation is that climate is subjective. Changes in climate that are impactful to one organism or ecosystem may be of little consequence to another. Climatic unfamiliarity, then, can only be definitively assessed in terms of the climate variables and their relative scales that matter in specific ecological contexts. However, there is a need for early warnings of types of climatic unfamiliarity that have general ecological significance. For this purpose, I adopt a widely-used assumption that the adaptive capacity of ecological communities is proportional to the interannual climatic variability of their local environments. This dissertation presents advances in the use of local climatic variability for estimating the ecological significance and novelty of projected climatic changes.  1.1 Emergence of locally unfamiliar climates Global mean surface temperature—driven up by increasing atmospheric greenhouse gas concentrations—departed from the range of its historical variability in the last quarter of the 20th century (Mann et al. 1998). However, the “noise” of year-to-year variability is much greater at the local scale, reducing societal perceptions of the climate change signal (Hansen et al. 2012). In most regions of the world, local mean annual temperatures are still within their historical range 2 of interannual variability (Hawkins and Sutton 2012). Nevertheless, emergence of the local warming signal is observable in relatively thermally stable tropical regions (Mahlstein et al. 2012a) and is projected to occur in the next 10-40 years at higher latitudes (Hawkins and Sutton 2012). Further, some regions of the world are projected to experience “climate departure” (Mora et al. 2013) in this century, in which the coolest year of future variability is hotter than the hottest year of historical variability (Diffenbaugh and Scherer 2011). Local climates are becoming increasingly unfamiliar to their inhabitants as anthropogenic global warming progresses in the 21st century (Frame et al. 2017).  1.2 Restoring climatic familiarity using non-local climate analogs As climatic unfamiliarity increases, localized strategies that organisms and human communities have developed to interact with their environments are becoming a source of maladaptation (Mcgraw et al. 2015). As a response, some organisms are migrating to maintain their adaptive advantage (Parmesan 2006). Human societies have the option, and often the necessity, of attempting to adapt in place.  A prominent approach to adapting to anticipated future climates is to adopt strategies—seed provenances, crop varieties, building codes—from other locations with similar historical climates. These non-local historical climates that match projected future conditions are called climate analogs (Mearns and Hulme 2001).  The use of climate analogs is a “space-for-time substitution”. Space-for-time substitution was traditionally used for studies of succession (Pickett 1989) but has been widely adapted for projecting global change impacts on ecosystems (Rastetter 1996). Despite the many pitfalls of this approach, its judicious use in ecological modeling has been extensively validated (e.g., Blois et al. 2013, Elmendorf et al. 2015).  The non-stationary climates of the 21st century are causing the use of climate analogs in space-for-time substitutions to expand beyond the research community and become a necessity for predicting and managing ecosystem responses. Climate analogs are used explicitly for a number of purposes, including projecting the future spatial distributions of ecological zones (e.g., Rehfeldt et al. 2012, Wang et al. 2012) and climate classifications (e.g., Baker et al. 2009, Torregrosa et al. 2013); identification of climate change impacts on individual ecosystems (e.g., Hogg and Hurdle 1995); calculation of climate velocity (Hamann et al. 2015); projecting the future performance of tree provenances (Franks et al. 2014); and intuitive communication of climate change (e.g., "city analogues" Kopf et al. 2008). While these explicit uses of climate analogs are becoming common, climate analogs are the implicit 3 basis of a much broader range of the ecological literature on climate change impacts.  Any statistical projection of biological responses in non-stationary climate conditions based on their observed historical relationship to climate predictors is implicitly using space-for-time substitution, and hence climate analogs.  Such models include species distribution models (Elith and Leathwick 2009) and population response functions (Rehfeldt and Jaquish 2010, Wang et al. 2010). Mechanistic ecological models are also dependent on observational data for parameterization and validation (Rastetter et al. 2003).  The space-for-time substitutions implicit in applications of bioclimatic models in non-stationary climates place climate analogs as a central pillar of ecology and ecosystem management in the 21st century.  1.3 The problem of novel (no-analog) climates Given the centrality of climate analogs to ecology in a changing climate, novel climates—emerging conditions with no analog in the observational record—represent an important knowledge gap. Novel climates have received particular attention in the context of ecological modeling, where prediction into novel climates is a form of extrapolation (Peterson et al. 2011). Correlative bioclimatic models (e.g., species distribution models) are statistically invalid in novel conditions where they are not supported by observational data on ecological responses to climate (Williams and Jackson 2007, Fitzpatrick and Hargrove 2009, Webber et al. 2011). Extrapolation into novel climates is therefore a source of model error that requires detection and quantification.  The significance of climatic novelty extends well beyond the realm of formal ecological modeling. Observations of the ecological responses to climate are not just training data for ecological models; they are the basis for a broader range of cultural ecological knowledge accumulated over millennia by indigenous peoples(Turner et al. 2000), and over generations of ecosystem managers (Haeussler 2011) and farmers (Mortimore 2010).  The context-specificity of local knowledge places novel climates as a confounding factor in cultural capacity for adaptation to climate change (Turner and Clifton 2009). For example, ecosystem managers working within formalized ecological knowledge systems (e.g., the Biogeoclimatic Ecosystem Classification for British Columbia; Pojar et al. 1987) are likely to be particularly challenged by novel climates that are not described by those systems.  The challenges of novel climates for cultural environmental knowledge have parallel challenges to the genetic adaptations of organisms to their environments. Locally-adapted populations may be at an adaptive disadvantage in the face of unfamiliar selective pressures 4 imposed by novel climates (Etterson and Shaw 2001, Anderson et al. 2012). At broader spatial scales, novel climates likely reduce the opportunity for local populations to benefit from adaptive gene flow from locally-adapted populations elsewhere in the landscape (Kremer et al. 2012). Opportunities for human-assisted migration of locally-adapted populations of species of economic or conservation concern (Aitken and Whitlock 2013) is likely to be less effective, and more error-prone, in novel climates. The environmental knowledge embedded in organismal genomes spans their evolutionary experience of climates through deep time, and thus samples a much broader range of climates that those historically observed by humans (Radeloff et al. 2015). Nevertheless, the current atmospheric CO2 level, and the minimum 2oC anthropogenic global warming projected for this century, are unprecedented in at least the past 3 million years (Martínez-Botí et al. 2015). This global departure from the climatic range of the Quaternary period indicates the potential for emergence of local climates that are novel at evolutionary timescales.  1.4 The subjectivity of climatic novelty Climatic novelty is context-dependent: it is only meaningful relative to the set of climatic conditions—the analog pool—for which ecological responses to climate have been observed. A general assessment of global climatic novelty may use all historically extant climates as the analog pool. However, more spatially constrained analog pools are more meaningful for specific applications. For projection of a population response function, the climates of the common gardens comprising the provenance trial are the relevant analog pool; predictions into any other climates are either interpolations or extrapolations. The same principle applies to point observations of presence and absence used as training data for a species distribution model. For ecosystem managers working within a jurisdictional knowledge system, the climates of the jurisdiction are the relevant analog pool. In special cases, such as for assessing disruption to an ecological community, the analog pool may be most meaningful if it is constrained to a single analog: the local historical climate. Absolute novelty—climates with no historical analog on the planet—is an abstraction that is useful for indicating broad risks to ecological knowledge and evolutionary potential. For practical purposes, however, novelty is only meaningful relative to a specific set of observed analogs. The scale of the relevant analog pool can range from global to local and may comprise only a sample of the climates within a geographic area.  5 Another source of subjectivity in novel climate detection is that biological responses to climate are complex and specific to each ecological context. The elements of climate—growing season frosts, wind speed, fog, solar insolation, extreme events, snow-free period, and so on—have varying relevance to different species in different environments. The scales and thresholds at which these climate elements are relevant is similarly context-specific. This suggests that the appropriate metric of climatic novelty depends on the study system. a climatic condition that is novel from the perspective of one species may be functionally familiar to another due to differences in the species’ climatic tolerances. Novelty is in the eye of the beholder. It is only meaningful relative to the set of climates sampled by the observational data, cultural experience, or evolutionary history of the system of interest, and to the climatic tolerances of those systems.  1.5 Detecting ecologically novel climates The subjectivity of climatic novelty in ecosystems suggests that it is most meaningfully measured using bioclimatic models of ecological responses to climate. Current bioclimatic modeling is predominantly done with machine learning algorithms such as MaxEnt (Phillips et al. 2006),  Random Forest (Breiman 2001), and support vector machines (Drake et al. 2006) due to their ability to model complex and localized bioclimatic relationships. However, the localized and non-linear structure of machine learning models confounds the direct detection and measurement of novel conditions. As a result, direct novelty detection methods for MaxEnt have not been developed. One-class novelty detection algorithms have been developed for support vector machines (Clifton et al. 2014), but have not been applied in bioclimatic modelling.  Many methods of Random Forest novelty detection have been proposed, including proximity-based outlier detection (Breiman 2001), one-class classification (Désir et al. 2013), and vote confidence distributions (Zhou et al. 2015). However, my preliminary trials of these methods suggest that they are not directly feasible for bioclimate classification problems, which are characterized by a large number of observations and classes. The “dummy class” approach demonstrated by Rehfeldt et al. (2012) in the context of bioclimate classification is promising, but it has not been independently validated or replicated (Gerald Rehfeldt, pers. comm. August 14, 2014), and my pilot analyses to implement this technique were unsuccessful. Direct novelty detection has proven elusive for bioclimate modeling applications of machine learning algorithms. In the absence of direct techniques, detection of machine learning extrapolation is almost exclusively done indirectly, i.e., outside the structure of machine learning bioclimatic models. 6 The most common approach, used with MaxEnt species distribution models, is multivariate environmental similarity surfaces (Elith et al. 2010), a univariate metric that measures extrapolation relative to the numerical range of training data in the individual predictor variables. A related multivariate approach measures outliers with a Mahalanobis distance calculated from the spatial covariance of training data in the model predictor variables (Roberts and Hamann 2012, Mesgaran et al. 2014). Both these methods can be called “study-area scaling”, because novelty and other climatic differences are measured relative to the spatial variation in the climate variables over the entire study area. Without careful tailoring of the study area to the ecological context, study area scaling can be arbitrary: some absolute climatic difference (e.g. 1oC) will be given a very small value for a large study area with high spatial climatic variation, and a very large value for a small study area with low spatial climatic variation. This scale dependence can confound interpretation of the ecological significance of novelty measured with study-area scaling.  Quantitative bioclimate classifications offer another approach to indirect novelty detection. Quantitative bioclimate classifications explicitly define climate variables and thresholds for ecologically distinct climate conditions, offering transparent identification of novel climates.  For example, the Rivas-Martinez Worldwide Classification System (Rivas-Martínez et al. 2011) has been effective in identifying novel projected climates in a small regional study area (Torregrosa et al. 2013). One limitation of this approach is that the extremes of each variable often are not bounded, particularly in recursively partitioned classifications such as the Koppen-Geiger global climate classification (Köppen 1936) and its automated equivalents (Cannon 2012). As a result, novel conditions are undetected in projections of these classifications (e.g., Rubel and Kottek 2010, Mahlstein et al. 2013). Another limitation of quantitative bioclimate classifications is that novelty at scales finer than the discrete classes will be undetected, but nevertheless may be ecologically significant.  The limitations of study-area scaling and quantitative bioclimatic classifications for novelty detection make interannual climatic variability (ICV) scaling relatively appealing. This approach uses the distribution of local interannual climatic variability in climate variables to assess dissimilarities among climate conditions. The appeal of ICV scaling is that the significance of climatic differences is assessed locally, using the logic that adaptive capacity in ecosystems is proportional to local historical interannual climatic variability. The seminal analysis of novel 7 climates (Williams et al. 2007) used a standardized Euclidean distance (SED) metric to measure dissimilarity of climate analogs in terms of standardized anomalies of local historical ICV. The SED metric of climatic novelty has been widely used at global and regional scales (e.g., Ackerly et al. 2010, Ordonez and Williams 2013, Ordonez et al. 2016).  Other ICV-based analog dissimilarity metrics are available (Grenier et al. 2013), notably the multivariate Kolmogorov-Smirnov goodness-of-fit test (Kopf et al. 2008). Novelty and other climatic differences measured relative to ICV have an intuitive ecological interpretation, since they reflect the range of climatic conditions that organisms have tolerated in order to persist in their local environments.  1.6 Evaluating the interannual climatic variability hypothesis The widespread use of ICV to contextualize climatic novelty and local climate change (e.g., Beaumont et al. 2011a, Mora et al. 2013) implicitly assumes that local adaptive capacity is proportional to interannual climatic variability. In other words, any absolute change in a climate variable, such as a 2oC increase in warm-season temperature, is assumed to be more impactful in locations with low interannual climatic variability in that variable (Mahlstein et al. 2011).  This assumption is closely related to the “climatic variability hypothesis” that intra-annual (seasonal) variation selects for higher thermal tolerance (Janzen 1967). This hypothesis is commonly used to explain the Rapoport Effect that species’ geographic ranges at low latitudes—where intra-annual (seasonal cycle) climatic differences are low—are smaller than in higher latitudes where species are subjected to large seasonal differences in climate (Stevens 1989, Pintor et al. 2015). The climatic variability hypothesis has been extensively reviewed (e.g., Addo-bediako et al. 2000) and has received substantial empirical support particularly with respect to ectotherms (e.g., Deutsch et al. 2008, Sunday et al. 2012). The equivalent hypothesis for interannual climatic variability (“ICV hypothesis” hereafter) does not appear to have received formal recognition or review as a general ecological hypothesis, despite being explicitly proposed for specific study systems (e.g., coral; Heron et al. 2016). Empirical support for the (intra-annual) climatic variability hypothesis is frequently cited as support for the ICV hypothesis (e.g., Mahlstein et al. 2011, Mora et al. 2013, Henson et al. 2017). However, the adaptive implications of intra-annual variation vs. interannual variability are distinct and should not be conflated. Intra-annual variation—the local seasonal cycle—is predictable cyclic variation for which organisms have evolved phenological adaptations such as winter dormancy. Interannual variability—year-to-year differences in each season—are essentially unpredictable except for the magnitude of the 8 variability itself. Evidence for the climatic variability hypothesis that intra-annual variation selects for higher environmental tolerances cannot stand in for evidence of the corresponding role of interannual climatic variability. The ICV hypothesis requires consideration on its own merits.  There is some theoretical, experimental, and observational support for the ICV hypothesis in the context of ecosystems.  In addition to the long-term average climate, the amount of year-to-year variability in climatic conditions is a defining characteristic of the environment to which organisms are adapted (Jackson et al. 2009a).  Environmental variability acts as a force of natural selection on life history, demographics, population genetic variation, and phenotypic plasticity of organisms (Chevin et al. 2010). Variability in climatic selection in successive cohorts of long-lived organisms can induce high population diversity in regeneration phenotypes for selection in future climates (Aitken et al. 2008, Jackson et al. 2009b). Variable environments can also select for higher phenotypic plasticity (Alpert and Simms 2002), expanding individual organisms’ range of physical or behavioral acclimations to climate change. Correlations between adaptive capacity and interannual variability have been observed in plants (Vázquez et al. 2017) and corals (Heron et al. 2016). Causal relationships have been inferred through experiments on yeast (Gonzalez and Bell 2013) and plants (Vázquez et al. 2017).  Despite this anecdotal support, cursory reviews of the ICV hypothesis for coral (Heron et al. 2016) and tropical rainforests (Corlett 2011) indicate that many more empirical studies are required to weigh the contexts in which ICV dominates other factors as an agent of adaptive capacity. Nevertheless, the ICV hypothesis is appealing as a coarse-filter indicator of ecological risks of climate change because of its intuitive logic, widespread use, and the absence of superior alternatives.  1.7 Research objectives, strategies, and contributions The goal of this dissertation is to aid efforts in climate change awareness and adaptation by advancing the detection of ecologically-relevant climatic novelty. The three research chapters explore distinct implications of novel climates at continental, jurisdictional, and local scales. These three research chapters share a common statistical method, which is described in a separate preceding chapter.   Chapter 2 describes sigma dissimilarity, a refinement of the standardized Euclidean distance novelty metric (Williams et al. 2007) that measures climatic differences relative to the 9 probability distribution of local interannual climatic variability. This metric is used to measure climatic novelty in Chapters 3 and 4, and local climatic unfamiliarity in Chapter 5.  Chapter 3 assesses novel climates at the continental scale, with an emphasis on the implications of novel climates for ecological modeling. I measure climatic novelty in end-of-21st century climate change projections for North America, providing new insights about the role of elevation gradients and topographic diversity in climatic novelty.  Chapter 4 assesses novel climates at the jurisdictional scale, with an emphasis on the challenges of novel climates for the formal ecological knowledge systems used in forest management. I present an assessment of the emergence of mid-21st-century climates with no analog among the historical climates described by the Biogeoclimatic Ecosystem Classification for British Columbia (BC), and the extent to which these novel climates are described by climate analogs elsewhere in North America. This chapter addresses a critical need for extrapolation detection in the projections of biogeoclimatic units that underpin many climate change adaptation initiatives in BC forestry. It also advances techniques for detection of novel climates by demonstrating indicators of model extrapolation in machine learning projections.   Chapter 5 assesses climatic novelty at the local scale, with an emphasis on maladaptation of ecological and human communities as their local climates become unfamiliar. I investigate the 21st-century departures of summertime temperature and precipitation from their joint natural variability on a global grid. This analysis demonstrates a “departure intensification” effect in which dependencies among climate variables can produce larger and earlier departures from local natural variability than is detectable in individual variables. This chapter contributes the first multivariate analysis to the literature on time-of-emergence and climate departures.  Each of the three research chapters is accompanied by an appendix containing supplementary methods and analyses that will be of interest to certain readers but that are not essential to the conclusions of the dissertation.  10 Chapter 2: Sigma dissimilarity—Measuring climatic differences relative to interannual climatic variability As discussed in Chapter 1, the seminal analysis of climatic novelty (Williams et al. 2007) used a standardized Euclidean distance (SED) metric. This method has enduring appeal because of the ecological rationale for measuring climatic dissimilarities relative to the historical range of local climatic variability. Despite exhibiting acceptable performance relative to several more complex analog detection metrics (Grenier et al. 2013), the SED metric has two important shortcomings. First, it is susceptible to variance inflation due to correlations in the raw variables. Second, it does not account for the effect of dimensionality (number of variables) on the statistical meaning of distance. These shortcomings confound interpretation of SED, particularly when comparing measurements with different dimensionality. In this chapter, I develop a new climatic novelty metric called sigma dissimilarity. Sigma dissimilarity incorporates two major modifications to the SED metric: (1) adapting SED into a Mahalanobis distance and (2) interpreting distances as percentiles of the chi distribution. Mahalanobis distance (Mahalanobis 1936) improves the scaling of variables relative to ICV, and removes variance inflation due to correlations. Interpretation using the chi distribution accounts for the effect of dimensionality on the statistical meaning of distance.  2.1 Calculation of Mahalanobis distance scaled to ICV The source data for calculating a Mahalanobian extension of SED are:   (a) Gridded study area climate normal data: [A] and [B] are (n x K) matrices of n spatially gridded observations of K climate variables over the study area, which is North America in Chapter 3 and British Columbia in Chapter 4. [A] is comprised of historical climate normals (typically 30-year means), and [B] is comprised of projected climate normals. The observations of these matrices, aik and bik, are normals for variable k at location i.   (b) Time series of reference ICV: [Cj] is a (T x K) matrix of T concurrent annual observations of the K climate variables at a location, j, for which novelty is to be calculated. The observations of [Cj], cjtk, are the values of variable k at year t of a historical reference period. sjk is the standard deviation of ICV in variable k.  11 The standardized Euclidean distance (SEDji) between the projected climate normals of a focal location j and the observed climate normals of any location i, as formulated by Williams et al. (2007), is   SED𝑗𝑗𝑗𝑗 = ���𝑏𝑏𝑗𝑗𝑗𝑗 − 𝑎𝑎𝑗𝑗𝑗𝑗�2𝑠𝑠𝑗𝑗𝑗𝑗2𝐾𝐾𝑗𝑗=1  (1) The corresponding Mahalanobis distance, Dji, is   D𝑗𝑗𝑗𝑗 = �D𝑗𝑗𝑗𝑗2 = ��𝒃𝒃𝑗𝑗′ −  𝒂𝒂𝑗𝑗′�T�Rj�−1�𝒃𝒃𝒋𝒋′ −  𝒂𝒂𝑗𝑗′� (2) Where [Rj] is the correlation matrix of [Cj] and 𝒂𝒂𝑗𝑗′ and 𝒃𝒃𝑗𝑗′ are row vectors of [A] and [B] at locations i and j, respectively, expressed as standardized anomalies of reference ICV [Cj].  Mahalanobis distance can be more intuitively understood as standardized Euclidean distance measured in the principal components of [Cj]. There are three steps to calculating Mahalanobis distance in this way (Figure 2.1).  Step 1—Re-expression as standardized anomalies Each observation in [Cj] can be expressed as a conventional standardized anomaly by subtracting the mean and dividing by the standard deviation of the time series for variable k:  𝑐𝑐𝑗𝑗𝑗𝑗𝑗𝑗′ = 𝑐𝑐𝑗𝑗𝑗𝑗𝑗𝑗 − 𝑐𝑐?̅?𝑗𝑗𝑗𝑠𝑠𝑗𝑗𝑗𝑗  (3) The result is a (T x K) matrix [C𝑗𝑗′] containing the column-wise z-scores of [Cj].   [A] and [B] can similarly be expressed as standardized anomalies of reference ICV:   𝑎𝑎𝑗𝑗𝑗𝑗′ = 𝑎𝑎𝑗𝑗𝑗𝑗 − 𝑐𝑐?̅?𝑗𝑗𝑗𝑠𝑠𝑗𝑗𝑗𝑗  (4) resulting in (n x K) matrices [A′] and [B′]. The outcome of this step is that each climate variable is scaled relative to ICV at focal location j (Figure 2.1b). Simple Euclidean distance in this scaled data space is equivalent to SED in the raw data space.  Step 2—Principal Components Analysis This step rotates the axes of the data space into alignment with the principal components of local ICV (Figure 2.1c).   The (K x K) correlation matrix of [Cj] is  12  �Rj� = 1T − 1 [C𝑗𝑗′]T[C𝑗𝑗′] (5) A principal components analysis is completed on [C𝑗𝑗′] by solving for the K ranked eigenvectors, ek, and corresponding K eigenvalues, λk, of [Rj]:   �R𝑗𝑗�𝐞𝐞𝑗𝑗 = λ𝑗𝑗𝐞𝐞𝑗𝑗 (6) The truncation criterion for retaining principal components is λk>0.01 (standard deviation >0.1). In other words, the dimensionality of the data space is reduced from K to M if any of the principal components of [C𝑗𝑗′] have trivial variance.   Eigenvectors meeting this criterion are assembled into [Ej], a (K x M) matrix whose columns are eigenvectors of [Rj].  �E𝑗𝑗� = [𝐞𝐞1 𝐞𝐞2 𝐞𝐞3 … 𝐞𝐞𝑀𝑀] (7) [A′], [B′], and [C𝑗𝑗′] are projected onto the eigenvectors of [Rj], to produce linearly transformed matrices [X], [Y], and [Zj], respectively.  [X] = [A′][E𝑗𝑗]  (8)  [Y] = [B′][E𝑗𝑗]  (9)  [Z𝑗𝑗] = [C𝑗𝑗′ ][E𝑗𝑗]  (10) Principal components are discarded (truncated) if they have variance less than 0.01 (rationale provided in Appendix A.2). In other words, the dimensionality of the data space is reduced from K to M climate variables if any of the principal components of [C𝑗𝑗′] have trivial variance.   Step 3—Calculation of Mahalanobis distance Mahalanobis distance in the raw data, Dji, can be calculated as standardized Euclidean distance (SED) in the rotated and truncated data space (Figure 2.1d):   D𝑗𝑗𝑗𝑗 = �� �𝑦𝑦𝑗𝑗𝑗𝑗 − 𝑥𝑥𝑗𝑗𝑗𝑗�2𝜎𝜎𝑗𝑗𝑗𝑗2𝑀𝑀𝑗𝑗=1  (11) where 𝜎𝜎𝑗𝑗𝑗𝑗2  is the standard deviation of ICV in each principal component, i.e. the column standard deviations of [Zj].   For each focal location j, Dji is measured to all of the other n grid locations in the study area analog pool. The minimum of these distances, Djmin identifies the location with the best end-of-20th century analog for the projected end-of-21st-century climate of focal location j.  13  Figure 2.1: Illustration of the procedure for analog identification using Mahalanobis distance scaled to local ICV, described mathematically in the text. Scatter plots (a,c,e,g) show the transformations of the data in two arbitrarily selected climate variables. Scree plots (b,d,f,h) show the relative spatial and temporal variation in the 12 dimensions of the data space at each step. The analog pool, [A], in this illustration is North America, and the focal location, grid cell j, is located on Melville Island (75oN, 107oW).  14 2.2 Sigma dissimilarity The effect of dimensionality on expected distances is a critical consideration for interpreting distances as dissimilarity. The probability distribution of squared Mahalanobis distances in multivariate normal data is described by the chi-square distribution with degrees of freedom equaling the number of dimensions in which the distance is measured (Wilks 2006). It follows that the chi distribution provides a null distribution for (non-squared) Mahalanobis distances, and that Mahalanobis distances can be expressed probabilistically as percentiles of the chi distribution (Figure 2.2). I express chi percentiles using the terminology of univariate z-scores; i.e., 1σ, 2σ, and 3σ (sigma) to describe the 68th, 95th, and 99.7th normal percentiles, respectively.  This “sigma dissimilarity” metric serves as a multivariate z-score.  Both interannual climatic variability and spatial climatic variation are affected by the effects of dimensionality on distance (Figure 2.3). Translation of distances into probabilities is necessary to account for the effect of dimensionality on the statistical meaning of climatic distance as a measure of dissimilarity.   Figure 2.2:  The theoretical basis of the multivariate sigma dissimilarity metric. The chi distribution is the probability density function of the non-squared Mahalanobis distances from multivariate normal observations to their mean. (a)  The chi distribution in 1 dimension is a half-normal distribution, and distances correspond to the sigma percentiles of the normal distribution. (b)  At increasing dimensionality, the sigma percentiles of the chi distribution shift away from the origin, providing a dissimilarity metric that accounts for the effects of dimensionality on the statistical meaning of distance.  15  Figure 2.3: Illustration of the use of the sigma dissimilarity metric to map analog dissimilarity. The projected climate of the focal location is the Ensemble Mean RCP4.5 projection for the 2071-2100 normal period.  (a) The expected probability density of reference ICV for the focal location is described by the chi distribution with degrees of freedom equaling the dimensionality of the data space, assuming multivariate normality. Distances (Dji) from the end-of-21st century focal condition to the end-of-20th century analogs are (a) classified and (b) mapped using the sigma percentiles of the chi distribution.  2.3 Discussion The analytical framework described in this chapter is a spatiotemporal analysis, in which dissimilarity is measured between the historical climate at one location and the projected future climate at another location. However, sigma dissimilarity also has purely spatial and purely temporal applications. Spatial applications of the metric include statistical climate classification (sensu Hargrove and Hoffman 2005) and measuring climatic transfer distances for the purposes of climate-based seed transfer (sensu O’Neill et al. 2017). A purely temporal application of sigma dissimilarity results in a multivariate standardized anomaly, a measure of the degree to which some year or time period differs from the historical range of variability. Chapters 2 and 3 are spatiotemporal applications of sigma dissimilarity, and Chapter 4 is a temporal application.  Out-of-sample bias Sippel et al. (2015) have recently observed that standardized anomalies outside of the reference sample used for standardization are subject to overestimation bias. The scale of this bias is substantial at the typical sample size of standardized anomalies: 29% overestimation in the probability of 2σ anomalies for a reference sample of n=30, assuming normality. Sigma dissimilarity as calculated in this dissertation is subject to this bias. The potential effect of this bias on the Chapter 3 results, which use a reference sample of n~40, has not been evaluated, and may particularly affect comparisons of results with differing dimensionality. Appendix C.4 16 demonstrates that the effect of this bias on the Chapter 5 results are negligible because the reference samples for standardization in that analysis are very large (n>400). The reference sample bias can be removed in univariate standardized anomalies by evaluating the probability of anomalies with Student’s t distribution, rather than the normal distribution (Sippel et al. 2015). The equivalent multivariate correction likely is to evaluate the probabilities of squared Mahalanobis distances against the F distribution instead of the χ2 distribution. Future formulations of sigma dissimilarity should incorporate a correction for out-of-sample bias.  17 Chapter 3: Novel climates of North America 3.1 Introduction Novel climates challenge the empirical basis of bioclimatic models (Webber et al. 2011), which are only statistically valid under the climatic conditions in which their correlations to biology were developed (Fitzpatrick and Hargrove 2009). In a formal sense, correlative inferences are not valid for novel climates. In practice, some amount of model extrapolation is necessary for ecological management in a changing climate. Nevertheless, the risk of inference error increases with the degree of extrapolation, and assessments of novel climatic conditions are due diligence in bioclimatic modeling (Peterson et al. 2011).  Species distribution models have evolved in recognition of the pitfalls of model extrapolation (Thuiller et al. 2004), and detection of multivariate model extrapolation continues to be an area of investigation (e.g., Mesgaran et al. 2014). Williams et al. (2007) introduced the concept of fundamentally novel climates that are broadly relevant to the whole ecosystem, rather than being defined with respect to individual species.  By measuring climatic differences relative to historical interannual climatic variability (ICV), Williams et al. (2007) demonstrated that the tropics and subtropics are susceptible to emergence of general novelty due to climate change in the 21st century. This result was corroborated at the global scale using an alternative method (García-López and Allué 2013). The standardized Euclidean distance (SED) method introduced by Williams et al. (2007) has been widely applied at regional and jurisdictional scales (e.g., Ackerly et al. 2010, Ordonez and Williams 2013). Alternative methods of assessing novelty have been applied at continental scales (Rehfeldt et al. 2012, Roberts and Hamann 2012), and the results of these studies suggest that novel climates may also emerge in temperate and Arctic climates. However, the relationship of these novelty inferences to each other, and to the global-scale assessment of Williams et al. (2007), is unclear. Further, the role of elevation gradients in moderating the emergence of novel climates has received little attention. A continental-scale analysis of general novelty in extratropical regions is required.  3.1.1 The continental climate envelope Most analyses of novel climates employ the conceptual model of the study-area climate envelope (sensu Williams et al. 2007). The observed climates of a study area occupy an identifiable volume—the climate envelope—within a multivariate data space made up of several 18 climate variables.  In a changing climate, this climate envelope will shift its position in multivariate climate space, resulting in the emergence of novel climates along the leading edge of the shifting climate envelope.   The simplest concept of the climate envelope is a convex hull with a single leading edge (sensu García-López and Allué 2013). This concept may be appropriate to small study areas or highly generalized climate classifications, but it neglects important features of observed climate envelopes. Two-dimensional seasonal climate envelopes for North America exhibit complex structure with several leading edges (Figure 3.1). In all seasons, the temperature-precipitation climate envelope of the North American continent has four prominent lobes associated with global-scale atmospheric circulation: tropical rainforest climates associated with upwelling of the Hadley cell; hot-dry subtropical climates associated with the downwelling of the Hadley cell; cool-wet temperate climates of Ferrel-polar frontal convergence; and cold-dry Arctic climates associated with the polar vortex. In other words, global atmospheric circulation superimposes an oscillating spatial precipitation pattern onto the relatively monotonic poleward temperature gradient, creating several leading edges in the North American climate envelope. In higher-dimensional climate space, there is also potential for elevational gradients to create other leading edges. Hence, global warming can be expected to produce regional and local occurrences of novel climates at all latitudes, rather than just in the warmest southern margins of the continent.    19  Figure 3.1: Projected shifts in the North American temperature-precipitation envelope in winter (a) and summer (b). Even in just two dimensions, there are several leading edges along which novel climates can form. Climate change trajectories for representative locations (c) are shown for reference.  3.1.2 Variable selection: defining climate.  An investigation of novel climates hinges on how climates are differentiated. The climate of any given location can be defined in terms of hundreds of biologically relevant variables, such as growing season frosts, wind speed, fog, solar insolation, extreme events, snow-free period, and so on. No two locations or time periods have the same combination of all of these characteristics; hence climate analogs cannot be defined in an objective sense. The climates of different locations can be considered ecologically equivalent only to the extent that some of their climatic differences are unimportant to the species or biological interactions under consideration. 20 Climatic similarities are subjective; a climate analog from the perspective of one species may not be an analog for another species.  The biological specificity of climatic analogs dictates that climatic novelty ultimately is specific to each bioclimatic model. Nevertheless, I agree with Williams et al. (2007) that novelty in basic aspects of climate such as seasonal temperature and precipitation is likely to have broad ecological significance. This “general novelty” represents an enhanced likelihood of species- or process-specific novelty relevant to modeling ecological impacts of climate change. Assessments of general novelty are useful to ecological modelers in that they provide a first approximation of geographic regions or time periods where the risk of model extrapolation is high. They are also useful for post-hoc evaluation of the many studies that neglect to include an assessment of model extrapolation.  In analyses of general novelty, there is a balance to be struck between defining climate too generally (not enough climate variables) and defining climate too specifically (too many variables). The simple, 4-variable definition of climate used by Williams et al. (2007) ensured that the potential for declaring novelty in ecologically equivalent climatic conditions was low. In other words, their method carried a low risk of false novelty (analogous to Type I inference errors). This robust approach produced strong evidence that bioclimatic models of 21st-century ecological change in the tropics and subtropics are susceptible to model extrapolation errors. However, this robustness came at the cost of a high potential of false analogs (analogous to Type II inference errors). Consequently, Williams et al. (2007) should be considered inconclusive for areas where novelty was not detected, i.e. the temperate and Arctic regions. A novelty analysis for these regions requires a more specific definition of climate.  The objective of this chapter is to provide a continental-scale assessment of general novelty that builds on the methods and results of Williams et al. (2007). This study is distinct in several respects. First, the sigma dissimilarity novelty metric facilitates comparison of results with different dimensionality. Second, analysis at much higher spatial resolution allows investigation of the role of elevation gradients in climatic novelty. Finally, drivers of novelty at continental to landscape scales are identified. The results provide a first approximation of model extrapolation risk for use in North American bioclimatic studies. More generally, this chapter advances conceptual and statistical models of climatic novelty that are globally applicable.  21 3.2 Methods In this chapter, I measure novelty as the sigma dissimilarity between the projected end-of-21st-century climate of a location of interest and its best analog among the observed end-of-20th-century climates of North America (Figure 3.2).   Variable selection  To facilitate continental- and landscape-scale novelty analysis, I used 12 seasonal climate variables to increase the differentiation of climates relative to Williams et al. (2007) four-variable analysis. This more specific definition of climate is intended to reduce the potential for false analogs (analogous to Type II errors) without unduly increasing the potential for false novelty (analogous to Type I errors). The 12 climate variables are mean daily minimum and maximum temperature (Tmin, Tmax) and total precipitation (PPT) for the four climatological seasons: winter (DJF), spring (MAM), summer (JJA), and autumn (SON). I log-transformed precipitation variables to provide a re-expression of the data in terms of relative magnitude.  Climate normals The reference period for this analysis is 1971-2000. Gridded reference period climate normals—The [A] matrix in the terminology of Section 2.1—were obtained using ClimateNA v5.10 (Wang et al. 2016). This publicly available application uses the delta method to downscale CMIP5 projections. The 1971-2000 base climatology (Figure 3.3) is compiled at 2.5-arcmin resolution from PRISM sources (Daly et al. 2008) for the contiguous US and Western Canada, and generated using the ANUSPLIN methodology (McKenney et al. 2011) for the remainder of the continent. I extracted data grids from ClimateNA at 4km resolution (2km for inset maps and 8km for sensitivity analyses) in a North American Equidistant Conic projection. The digital elevation models (DEMs) used to extract data from ClimateNA are gridded subsamples of USGS GTOPO30, thus conserving the elevation variance of this 30-arcsecond DEM.   Figure 3.2: Simplified illustration of the novelty assessment. Novelty is the distance between the projected future climate of a location of interest and its closest analog in the observed climates of the study area.  22 Analog pool To improve computational speed while conserving North American climatic diversity, I reduced the analog pool (the [A] matrix) to n=161,032 using a combination of regular and variable subsampling of the 30-arcsecond DEM.  This 12% sample of the 4km map grid adequately represents the diversity of climates present in the map grid, and results in minimal bias to the results of this chapter (Appendix A.3).  CMIP5 ensemble projections I assessed end-of-21st-century projections (2071-2100 climate normals; the [B] matrix) using an ensemble of the 15 CMIP5 projections (Taylor et al. 2012) available in ClimateNA: ACCESS1.0, CanESM2, IPSL-CM5A-MR, MIROC5, MPI-ESM-LR, CCSM4, HadGEM2-ES, CNRM-CM5, CSIRO Mk 3.6, GFDL-CM3, INM-CM4, MRI-CGCM3, MIROC-ESM, CESM1-CAM5, and GISS-E2R (Table A.2).  The ensemble models were chosen to represent the major clusters of CMIP5 GCMs identified by Knutti et al. (2013), and further selected based on the validation statistics of their CMIP3 equivalents (Wang et al. 2016). This chapter’s primary results are based on an “ensemble mean projection” calculated from the mean monthly anomaly for each variable in all 15 models (Figure 3.3).  Local ICV I estimated local ICV, [Cj], using weather station data from the CRU TS3.23 (Harris et al. 2014) source observations.  My use of point station data avoids variance reduction artefacts evident in gridded and interpolated time series (Director and Bornn 2015). I used a reference period of 1951-1990, due to higher risk of inhomogeneities prior to 1951 and a sharp decline in station observations after 1990.  Precipitation stations were assigned the temperature time series of the nearest temperature station, and discarded if no temperature station was available within 60km.  I discarded stations with less than 20 years of complete record north of 33oN, and <10 complete years south of this latitude (i.e., Mexico). This process selected 2304 CRU TS3.23 stations within the study area (Figure 3.3). I calculated sigma dissimilarity (novelty) separately for each of the four stations nearest to the focal location j, then averaged these values. Details of ICV data selection and processing are provided in Appendix A.1.  23 Emissions scenarios I evaluate novelty for the RCP4.5 and RCP8.5 scenarios (van Vuuren et al. 2011). I use the term emissions scenarios for simplicity, recognizing that these scenarios encompass other major components of radiative forcing such as atmospheric chemical cycles and land use change. RCP4.5 and RCP8.5 are most closely comparable to the B1 and A1F1 scenarios of the preceding SRES scheme (Rogelj et al. 2012). The RCP4.5 and RCP8.5 scenarios produce end-of-21st-century global warming of 2.4oC (1.7-3.3oC) and 4.3oC (3.2-5.5 oC), respectively, relative to the 1850-1900 period (IPCC 2013). The RCP4.5 scenario roughly corresponds to the 2.7oC (2.1-3.2oC) temperature rise consistent with the conditional INDCs of the Paris Agreement, and the RCP8.5 scenario roughly corresponds to the 4.1oC (3.1-4.8oC) warming consistent with an absence of emissions policies (Rogelj et al. 2016).  Novelty thresholds As a statistical measure of the departure from historical variability, sigma dissimilarity provides an intrinsically meaningful metric of the general ecological significance of climatic dissimilarities.  For this reason, I do not use a threshold analog dissimilarity level to define novelty. As a point of reference, however, note that Williams et al. (2007) used a threshold of SEDt=3.22 to define novel climates. Given that this SEDt was measured in a 4-dimensional climate space, it corresponds to a sigma dissimilarity of at least 2.11σ, depending on the correlations among the raw variables. I subjectively consider 2σ analog dissimilarity—the 95th percentile of local ICV—to be a moderate degree of novelty, and 4σ analog dissimilarity to be extreme novelty.  24  Figure 3.3: An overview of the spatial variation in the input data to the novelty analysis.  1971-2000 climate normals (a,b,c,d) are obtained from PRISM for the contiguous US and British Columbia, and ANUSPLIN elsewhere. Local ICV (e,f,g,h) is obtained from the 2304 CRU TS3.23 source stations. Projected climate change for the 15-model ensemble (i,j,k,l) is downscaled by the ClimateNA software using the delta method.  25 3.3 Results The RCP4.5 ensemble mean projection for the 2071-2100 normal period represents an increase of 3.5oC in the mean annual temperature (MAT) of North America, relative to the 1971-2000 normal period. In this projection, 2σ novelty emerges over 7% of the area of the continent (Figure 3.4a). Novel climates are primarily found adjacent to the Gulf of Mexico, the west coast of Mexico, the western high Arctic islands, and coast of northwest Alaska. Despite being limited in terms of area, novel climates are widespread: 80% of North American ecoregions contain some amount of 2σ novelty.  Novelty is emergent in many of the major basins and valleys of the Western Cordillera, including Death Valley, the Snake and Columbia Rivers, Puget Sound, the major valleys of southern British Columbia, and the northern portion of the California Central Valley. The RCP8.5 projection (6.2oC average MAT increase over North America) exhibits a much higher level of novelty, covering 40% of the area of the continent and found within 99% of ecoregions (Figure 3.4b). Patterns of novelty observed for RCP4.5 are largely accentuated in RCP8.5.  In addition, widespread novelty is emergent across the central and eastern portions of the continent with the exception of the Appalachian range and Labrador. Novelty is less widespread in the Western Cordillera, and is limited to lower elevations. In addition to the areas of emergent novelty in the RCP4.5 projection, several areas of the temperate rainforest climates of coastal British Columbia, Washington, and Oregon show pronounced (>3σ) novelty in the RCP8.5 projection.  26  Figure 3.4: Distribution of climatic novelty across North America in the (a) RCP4.5 and (b) RCP8.5 ensemble mean projections for the 2071-2100 normal period. The central Western Cordillera is shown in the inset to show elevation-related details.  27  Figure 3.4 (Cont’d) The range of variation in novelty calculated from the four ICV proxies is substantial in many grid cells, particularly in the RCP4.5 projection (Appendix A.9). This variation suggests some potential for local bias associated with averaging of ICV proxies. However, there are few locations with the potential for missed novelty or false novelty relative to a 2σ threshold. The main results of this analysis do not appear to be sensitive to differences among the four ICV proxies for each grid cell.  28  Figure 3.5: Effect of variable selection on novelty of the RCP8.5 ensemble mean projection. The 12-variable novelty (panel d) is the same as the main results presented in Figure 3.4. Novelty is highly sensitive to the use of seasonal mean daily temperature (Tave) instead of seasonal mean minimum and maximum daily temperature (Tmin, Tmax). Novelty is less sensitive to the use of two seasons instead of four. Results for RCP4.5 are provided in Appendix A.11.  29 As would be expected, novelty is sensitive to the variables used to define climate (Figure 3.5). The four-variable climate used by Williams et al. (2007)—average temperature and precipitation in summer and winter (Figure 3.5a)—produces a sharply reduced novelty throughout the continent, essentially eliminating the detection of novel climates in the Western Cordillera, boreal, and Arctic regions, even in RCP8.5.  Much of this reduction is associated with the substitution of mean temperature (Tave) for minimum and maximum temperature (Tmin, Tmax).  The use of two instead of four seasons has a relatively marginal effect on novelty.  The SED metric does not show this pronounced sensitivity to substituting Tmin and Tmax for Tave (Appendix A.12).   Figure 3.6: Effect of variable selection on reference period (1971-2000) dissimilarity to a single location (Denver, CO). The 12-variable climate space (panel d) corresponds to the default variable selection in this chapter. Seasonal mean minimum and maximum daily temperature (Tmin, Tmax) collectively provide a higher degree of climatic specificity than seasonal mean daily temperature (Tave). Maps for other locations are provided in Appendix A.11.  30 Figure 3.6 demonstrates the effect of variable selection on the climatic dissimilarity between a single location and all other locations in the 1971-2000 reference period.  Consistent with Figure 3.5, full seasonality has a marginal effect on climatic similarity, but variable sets including Tmin and Tmax yield a substantially more specific definition of climate than those using Tave. In particular, equivalent climates (<1σ dissimilarity) are regionally limited in the 12-variable climate space, but extend throughout the Southwest USA in the four-variable climate space.  A subjective assessment of several locations indicates that the relative sensitivity to variable selection is highly variable in different locations of the continent (Appendix A.11).  In addition, different locations show very large variation in the specificity associated with any given set of variables.   RCP4.5 novelty projections of the 15 individual models in the ensemble reveal large inter-model variation that exceeds the difference between mean projections for RCP4.5 and RCP8.5 (Figure 3.7 and Appendix A.5). Despite large inter-model variation, the RCP4.5 ensemble mean projection produces a pattern of novelty that is identical to the average of separate novelty calculations on the 15 individual ensemble models (Figure A.11). On average, the ensemble mean projection has a small bias towards lower novelty relative to the mean novelty of the individual ensemble models.    Figure 3.8 provides a visualization of the mechanism of widespread emergence of novel climates over the eastern continental interior evident in the RCP8.5 scenario. This plot was generated by performing a PCA on the [X′] matrix of Montreal, Quebec. The principal components are the dominant modes of spatial climatic variation across North America relative to the local ICV of Montreal. In the  Figure 3.7: Comparison of the ensemble mean projections to individual RCP4.5 projections of the 15 models in the ensemble. X-axis: North American dT, the difference in mean annual temperature between the 2071-2100 and 1971-2000 periods. Y-axis: average novelty over North America.  31 first two dimensions of the climate space (PC1 and PC2), Montreal appears to be in the interior of the climate envelope.  However, viewing the third dimension of the local climate space reveals that Montreal is located on or near an edge of the North American climate envelope that extends the length of the continent from the northern Gulf of Mexico coast (Houston, Texas) to the Arctic (Yukon Basin). This plot illustrates that novelty is a consequence of components of the climate change trajectory that don’t align with locally relevant spatial climatic gradients. Topographically uniform landscapes have fewer spatial climatic gradients, and consequently are more susceptible to the emergence of novel climates.  Despite being localized to Montreal, Figure 3.8a also illustrates the basis for emergence of novel climates in several other regions of the continent. The tropical rainforest (e.g., Chiapas, Mexico) and subtropical desert climates (e.g., Sonoran Desert) are on the leading edge of the temperature distribution of the continent. However, other leading edges are visible. The temperate rainforest climates represented by Prince Rupert, British Columbia form a pronounced lobe in the North American climate envelope due to their high precipitation. Similar but smaller elevation-associated lobes are visible for the Yukon River basin (locally warm/dry), and the upper elevations of Ellesmere Island (locally cold/wet). Each of these lobes has a leading edge relative to the climate change trajectory, resulting in the emergence of novel climates.  32   Figure 3.8: The first three dimensions of the North American climate envelope plotted in the localized climate space of Montreal, Canada (a: PC1xPC2; b: PC1xPC3). The individual RCP8.5 climate change trajectories of the 15-model ensemble are plotted for Montreal. The RCP8.5 ensemble mean trajectory is plotted for several other locations. Many of these locations are mapped in Figure 3.1c.  33 3.3.1 Relationship between novelty and topographic position There is a strong relationship between topographic position and novelty (Figure 3.9). In the RCP4.5 scenario, 2σ novelty is essentially limited to the lower half of the elevation range in all ecoregions with topographic relief (Figure 3.9c), and >4σ extreme novelty is limited to very low topographic positions. RCP8.5 novelty is also strongly associated with low topographic positions, and suggests an upslope movement of novelty as the magnitude of climate change increases. In addition, the low point density at the origin of Figure 3.9d indicates that low (<1σ) novelty is uncommon at low topographic positions in the RCP8.5 scenario. Comparison to a null model (Figure 3.9e,f) indicates that the relationship between topographic position and novelty is not simply an artefact of declining land area at higher topographic positions. The observed relationship between topographic position and novelty is statistically distinct from the null model in both RCPs at subsamples of the spatial grid (N=199,059) as low as n=15 (Appendix A.8), which can be assumed to eliminate the confounding effects of spatial autocorrelation on statistical significance (Gotelli and Ulrich 2012). This very high power provides strong evidence that the relationship between topographic position and novelty is greater than expected by chance.  34  Figure 3.9: Relationship between novelty and topographic position in RCP4.5 (a,c) and RCP8.5 (b,d). Topographic position is calculated as meters above the minimum elevation of each ecoregion (a,b), and alternately as a proportion of the elevation range within each ecoregion (c,d). (a,b) show results for all map cells in the continent (150 ecoregions, n=331,360), but observations in (c,d) are limited to ecoregions with an elevation range >1000m (97 ecoregions, n=199,056). Color shading is proportional to point density. (e,f) are null models for (c,d), generated by randomizing relative elevation; randomizing novelty produces an identical distribution.   35 3.3.2 Relationship between novelty and analog source distance Maps of analog source distances demonstrate the effect of topographical diversity on the geographical distance from which analogs must be sourced (Figure 3.10a,b). Analogs are primarily sourced from nearby downhill locations in the Western Cordillera and Appalachian range. In contrast, latitudinal analog distances are greater in the more topographically uniform central and eastern portions of the continent.  Very high (>4σ) novelty is associated with low elevational and latitudinal analog source distances (Figure 3.10c,d) There are several locations where the best analog is sourced from substantially higher relative elevations (>1000m), notably the great central valley of California, the Snake and Columbia basins of the Pacific Northwest, the Chilcotin plateau of British Columbia, and the Rocky Mountain foothills of Alberta (Figure 3.10a). As would be expected, these uphill analogs are sourced from distant southern locations (Figure 3.10b and Figure 3.11a). It is notable that these uphill analogs are associated with a moderate 1-2σ novelty (Figure 3.10c,d), i.e. poorly-matched analogs.  36  Figure 3.10: Elevational and latitudinal climate shifts (distance to best analog) in the RCP4.5 ensemble mean projection, and their relationship to novelty. (a,b): Analogs are generally sourced from lower elevations and/or southern latitudes, but not always (yellow shading). Downslope analogs are widely available in western North America, but analogues must be sourced over larger latitudinal distances in eastern North America.  (c,d): High novelty is associated with low elevational and latitudinal distances to the best analog.  Figure 3.11 further summarizes the relationship between elevation, latitude, and novelty. Uphill (downhill) analogs are exclusively associated with distant southern (northern) sources. Highly novel climates are strongly associated with nearby analogs. The reverse does not hold, 37 however: there are many locations with simultaneously low levels of elevational distance, latitudinal distance, and novelty (not shown).   Figure 3.11: Relationships of novelty with elevational and latitudinal climate shifts (distances to best analog), in the ensemble mean projection for the RCP4.5 (a) and RCP8.5 (b) scenarios. Highly novel climates are strongly associated with nearby analogs. 3.4 Discussion The results of this chapter build on the findings of Williams et al. (2007). Similar to Williams et al., the method used here suggests that the warmer southern margins of the continent and the western Arctic are particularly prone to the emergence of novel climates. In addition, localized emergence of novel climates is projected in lower topographic positions throughout the continent. Novel climates cover a limited area in the ensemble mean projection for the RCP4.5 emissions scenario (3.5oC average warming over North America), but are widespread in RCP8.5 (6.2oC warming). These three factors associated with a higher emergence of novel climates – regional susceptibility, topographic position, and the magnitude of projected climate change – can be viewed as a priori evaluation criteria for the credibility of bioclimatic projections. For example, species distribution model inferences for low topographic positions carry a higher burden of proof with respect to model extrapolation than other areas of the landscape. Other factors that limit analog availability, such as a sampling design that is truncated by a jurisdictional boundary, further increase the risk of model extrapolation and the burden of proof 38 for proponents of bioclimatic models (Thuiller et al. 2004).  The results of this chapter are a first approximation: novelty is ultimately specific to each bioclimatic model. The finding that most landscapes are prone to localized emergence of novel climates underscores the critical role of novelty assessments in validating projections of how species and ecosystems will respond to climate change. 3.4.1 Variable selection  Variable selection is a critical consideration in novel climate detection. In the absence of a measure of biological response, there is no objective basis to prefer the 12-variable climate used for primary results of this chapter over the 4-variable climate of Williams et al. (2007). These variable sets sit on a continuum from a very general (i.e. one-variable) characterization of climate, which would result in essentially no novelty, to a very specific one, which would result in nearly ubiquitous novelty. The art of novelty detection lies in finding an ecologically meaningful level of climatic specificity along this continuum. Broadly speaking, the 4-variable climate produces a generalized, biome-scale definition of climate, while the 12-variable climate produces a much more spatially constrained pattern of climatic similarity relevant to a finer ecological scale (Figure 3.6).   However, the similarity maps for specific locations (Appendix A.11) suggest that the climatic specificity of any given set of climate variables is highly variable among locations. This result suggests that the novelty associated with a single set of variables cannot be assumed to be relevant to a consistent scale of ecological differentiation, such as biomes or plant associations. Techniques for localized variable selection—mirroring the use of interannual variability for localized variable scaling—are an important priority in the future development of novelty detection methods. By generalizing distance measurements made at different dimensionalities, the sigma dissimilarity metric will facilitate progress in localized variable selection.  The use of Tave vs. Tmin and Tmax is the major factor driving the differences between novelty associated with the 4-variable and 12-variable climates. This sensitivity to replacing Tave with Tmin and Tmax is observed in the dissimilarity maps (Figure 3.6 and Appendix A.11), and therefore is not primarily attributable to inconsistencies between the observational (historical) and modeled (future) data. This sensitivity also cannot be attributed to an imbalance between the number of temperature and precipitation variables, since balancing the variable set with additional precipitation variables has little effect on climatic similarity (Figure A.24). These 39 analyses indicate that replacing Tave with Tmin and Tmax provides substantial additional information to differentiate distinct climates. Given that changes to the diurnal temperature range are a signature of an enhanced greenhouse effect (Braganza et al. 2004), and to the extent that diurnal temperature range can be considered to be ecologically relevant, the use of Tmin and Tmax appears to be an important consideration in detecting novelty.  3.4.2 Added value of Mahalanobis distance over SED Mahalanobis distance can either decrease or increase distance relative to SED, depending on whether or not the direction of measurement is aligned with the dominant variable correlations, which in this chapter are the dominant modes of historical climatic variability. Mahalanobis distance generally increases novelty and spatial dissimilarity relative to SED, though SED produced higher novelty in some locations (Appendix A.12). The differences between the two distance metrics were subtle in the 4-variable climate definition of Williams et al. (2007), but pronounced when Tave was replaced with Tmin and Tmax for the 6- and 12-variable climates.  The ability to accommodate the correlations of these variables is a key advantage of Mahalanobis distance over SED, given that goal of the distance measurement is to detect deviations from the historical pattern of variability. The advantages of Mahalanobis distance over SED may be marginal in simple definitions of climate (e.g., Williams et al. 2007), but are substantial in the larger and more correlated variable sets required for continental and landscape-level analyses.  3.4.3 Implications of ignoring interannual climatic variability (ICV) of the analog climate This chapter’s method hinges on the ICV of the location of interest, but ignores the ICV of candidate analogs. This asymmetry creates the potential for equivalencies to be drawn among climates with biologically relevant (Jackson et al. 2009) differences in modes of variability, such as the type and frequency of extremes. Metrics of goodness-of-fit of ICV, such as the multidimensional Kolmogorov-Smirnov statistic (Fasano and Franceschini 1987), are preferable for small analog pools (e.g., Kopf et al. 2008), but are computationally unfeasible for continental-scale analysis at high spatial resolution. Adding an ICV criterion to the analog dissimilarity metric would inevitably result in increased localization of climatic similarity, and thus higher novelty. For this reason, this chapter’s method can be expected to underestimate 40 novelty relative to a method that accounts for analog ICV, particularly at locations with geographically distant analogs. 3.4.4 Errors associated with observational data An important methodological difference between this chapter and Williams et al. (2007) is my use of observational data for the base climatology and ICV, instead of the internal climatology and variability of the ensemble models. High-resolution observational data is critical to adequately sampling the analog pool of the continent and to eliminating systematic downward biases in ICV due to grid cell averaging (Director and Bornn 2015). The disadvantage of combining high-resolution observational climatology with model projections is the loss of physical consistency in the analysis. For example, in the process of delta-downscaling, model projections may be transferred to regions of the climate space, such as hypermaritime and high-elevation climates, that are not represented in the coarse grid of the global climate model (Wilby et al. 2004). Another example is that the timing of multidecadal variability in the model runs may not be in phase with the observed climate used for delta-downscaling, resulting in exaggeration or damping of the climate change signal. These and other discontinuities between the observed historical and modeled future climate are an unquantified source of error in this analysis. These errors could be reduced through more sophisticated downscaling approaches that were out of scope for this first-approximation analysis. Note also that sigma dissimilarity assumes multivariate normality of ICV, and the results are sensitive to this assumption (Figure A.16). 3.4.5 Errors associated with ICV proxies I used weather station data as point-level estimates of climatic variability and covariance. Despite several advantages to this approach, it carries some particular sources of error. Incomplete years in the time series are unavailable to the PCA, which is expected to be unstable at small sample sizes. In this chapter, areas with very small sample size are limited (Figure A.28). Further, the similarity between the 12-dimensional results and the 6-dimensional results (Figures 8 and S21) suggests that limited sample size relative to dimensionality is not a major source of error in in this analysis.  However, reliable estimation of error in sigma dissimilarity is non-trivial (Appendix A.13), and the ratio of time series observations to the dimensionality of the sigma dissimilarity calculation should be maximized wherever possible.  41 The potential for bias due to nonrandom weather station placement is an inevitable limitation of the use of weather stations as proxies for local variability. High topographic positions are systematically undersampled by weather stations and therefore are likely to be poorly represented by their ICV proxies. However, my inferences of novelty at low topographic positions are robust to this source of error.  The potential for cross-contamination between the distinct ICV patterns of maritime and continental climates is another potential artefact of the use of weather stations as ICV proxies. Mexico, the contiguous US, and coastal British Columbia have sufficient station density in the coast-interior transition that conflation of distinct regional climates can reasonably be ruled out as a source of error. In contrast, very low station density in the boreal and Arctic regions suggests that results for these regions should be interpreted at a coarse spatial scale (Appendix A.10). The weather station data for Mexico is of poorer quality than for Canada and the United States, with longer distances between coupled precipitation and temperature stations (Figure A.3), lower number of complete years (Figure A.5), and higher potential for PCA artefacts (Figure A.7). In addition, novelty in southern Mexico is expected to be exaggerated due to the arbitrary truncation of the study area at the border with Guatemala, and hence the unavailability of analogs in Central America. For these reasons, novelty results for Mexico should be viewed with caution. These issues do not diminish the importance of Mexico as an analog pool for the US and Canada. 3.4.6 Inter-model uncertainty Inter-model variation exceeds the substantial difference between RCP4.5 and RCP8.5. This finding mirrors several species distribution modeling studies with inter-model uncertainty greater than scenario uncertainty (e.g., Real et al. 2010, Goberville et al. 2015) . Inter-model variation may be due to structural differences in the models, but may also be due to intrinsic variability of the modeled climate system (Hawkins and Sutton 2009) and downscaling biases. Internal variability can dominate inter-model variation at local scales in North America (Kay et al. 2015), particularly for precipitation variables (Deser et al. 2012a). Two of the high-novelty outliers in the RCP4.5 individual model projections, IPSL-CM5A-MR and GFDL-CM3, are based on only one model run (Table A.2), which increases the potential for these model projections to be influenced by internal variability. However, the greatest outlier, HadGEM-ES, is itself the mean of 4 runs of the model, which suggests that the very high novelty from this model is due to 42 structural model differences rather than internal variability. Despite the limited extent of novelty in the RCP4.5 ensemble mean projection, the presence of high-novelty projections in the RCP4.5 ensemble suggests that the potential for widespread emergence of novel climates cannot be disregarded even under a scenario of substantial global emissions reductions.  3.4.7 Drivers of novelty at low topographic positions The key outcome of this high-resolution analysis is the detection of novel climates at low topographic positions throughout the continent. This emergence of landscape-level novelty is strongly influenced by how specifically the climate is defined—it is absent in the 4-variable climate but prominent in the 6- and 12-variable climates—suggesting that localization of climatic similarity is the mechanism for this pattern of novelty. Warming climates at higher elevations are likely to have downhill analogs with a similar historical seasonality and diurnality. In contrast, analogs for the lowest topographic positions are inevitably in non-local regions that are more likely to have different patterns of seasonal and diurnal climatic variation, and thus higher sigma dissimilarity. The importance of this localized climatic signature is also suggested by the association of novel climates with geographically proximal analogs.  In some ways, this effect can be considered an artefact of the equal weight given to all variables within the sigma dissimilarity calculation, notwithstanding the scaling to ICV. For example, summer drought may be a critical factor driving an ecological community that can tolerate a wide range of winter conditions. In this hypothetical case, there may be many ecologically equivalent analogs in other regions that would not be detected by the method employed in this chapter. However, novelty could conversely be underestimated in other ecological situations requiring a more specific definition of climate. This distinction highlights the ultimate necessity for case-specific novelty assessments that are informed by relevant biological responses. Given the current scarcity of methods for case-specific novelty assessments, discussed below, the detection of low-elevation novelty in this chapter represents a useful first approximation of extrapolation risk at the landscape scale. 3.4.8 Relationship between climatic novelty and climate velocity The distance and elevation from which an analog must be sourced is relevant to several conservation and management considerations. Emergence of climates with distant analogs can, at first approximation, be considered to be more ecologically problematic than those with nearby 43 downslope analogs, because climatically adapted organisms are less likely to be locally available (Hamann et al. 2015). Distant analogs also are less credible, as they are more likely to have additional biologically important environmental differences not captured by the climate variables used in the analysis. The trade-off between elevation and geographical distance in sourcing analogs is central to the concept of climate velocity (Loarie et al. 2009), the speed at which climate conditions shift over the landscape in a changing climate. In the context of novel climates, the metric of interest is “backward velocity” from a future condition to a historical analog (Hamann et al. 2015). Backward velocity which can be thought of as the geographical distance from which ecological data must be sourced to match the evolving climate in a location of interest. In this chapter, novel climates are associated with analogs that are proximal to the focal location in both elevation and latitude. This result suggests an inverse relationship between climatic novelty and climate velocity, though the mechanism for this relationship is not clear from the results of this chapter. Low climate velocity can be due to the availability of downslope analogs, but it can also be due to a lack of good analogs in the study area. Similar to climatic novelty, backwards climate velocity is associated with low topographic positions (Hamann et al. 2015), yet novelty and velocity represent distinct risks to ecological knowledge and the validity of ecological models. Novel climates appear to be an important dimension in the measurement and interpretation of climate velocity.  3.4.9 Credibility of RCP8.5 bioclimatic projections The widespread emergence of novel climates in the RCP8.5 projections for the end of the 21st century underscores the pitfalls of modeling ecological responses to extreme climate change (Wiens et al. 2009). The scale of climate change under this scenario requires that analogs be sourced at large geographical or elevational distances, which likely removes analogs from a meaningful biophysical context. Hence even where analogs are found in an RCP8.5 end-of-century projection, their credibility is dubious. The results of this chapter suggest that bioclimatic model projections using the RCP4.5 scenario can be considered—at first approximation—to carry an acceptable risk of model extrapolation in areas where novel climates are not detected. However, the validity of end-of-century bioclimatic projections based on RCP8.5, in any location, should be carefully considered due to high risk of model extrapolation into novel climate space.  44 3.4.10 Managing novel climates If bioclimatic models are unreliable in novel climates, what is the alternative? In the absence of directly applicable observational data, ecological prediction in novel climates is likely to be more art than science, demanding ecological wisdom that integrates diverse information sources (Dawson et al. 2011). Emerging novel climates will inevitably retain vestiges of their historical character, such as the relative characteristics of their seasonal cycle, ICV, and spatial pattern. Despite some enduring familiarity, however, novel climates are likely to be less tractable to accumulated ecological knowledge, and thus represent a higher risk of management failures (Williams and Jackson 2007). The widespread novelty detected in the RCP8.5 scenario likely represents a serious threat to the ability of ecological practitioners to plan for the future. Novel climates exacerbate the challenges of adaptation to climate change, and add to the urgency of greenhouse gas emissions reductions.  Since climate is a fundamental driver of ecological function, the use of climate analogs underpins ecology as a predictive science. When data collected from one place or time is used for ecological insight into another, the implicit assumption is that the two climatic contexts are sufficiently similar for this knowledge to be transferable. Yet understanding and communicating the limits to the transferability of knowledge is equally foundational to the discipline of ecology. Climate change is forcing ecologists to generalize available ecological information to locally unfamiliar conditions. Bioclimatic models are a valuable tool in this effort. Nevertheless, ecologists should be increasingly vigilant for climatic conditions that are poorly sampled by observational data. Identification of novel climates allows us to differentiate contexts in which bioclimatic models are likely to be informative from those in which other approaches are necessary. This chapter provided general risk factors for emergence of novel climates. However, operational and ecologically-specific detection of novel climates remains an open problem in the field of bioclimatic modeling. In the next chapter, I analyze novel climates in the more specific context of bioclimatic projections that are being used for operational climate change adaptation in British Columbia’s forest sector.  45 Chapter 4: Novel climates of British Columbia: Trajectories of climate change beyond the boundaries of the Biogeoclimatic Ecosystem Classification 4.1 Introduction 4.1.1 Emerging challenges to the “local is best” ethic in forest management The necessity to adopt non-local practices in response to climate change is a major new dimension in forest management. Historically, forest managers have developed specialized management regimes for their local ecosystems (Puettmann et al. 2009). The complex interactions of productivity, competition, stress, and disturbance are often idiosyncratic to individual places, leading forest managers towards a “local is best” ethic with respect to silvicultural systems, stand-tending practices, and species and provenance selection (Seymour et al. 2002, Ying and Yanchuk 2006). These local idiosyncrasies are strongly driven by climate (Pojar et al. 1987), but the climates of the 20th century were sufficiently stable for forest managers to understand climate as a stationary quality of place. The non-stationary climates of the 21st century are a fundamental challenge to this place-based understanding of climate and ecosystem function (Millar et al. 2007). Forest managers have entered an era in which the “local is best” ethic is no longer reliable, and are looking to other locations for species, provenances, and management regimes that may be better suited to the anticipated future climates of their jurisdictions (Potter and Hargrove 2012, Williams and Dumroese 2013). This use of non-local climate analogs is an emerging cornerstone of 21st century forestry management, and underlies assisted migration through remote provenance selection (Aitken and Whitlock 2013), assisted range expansion (Rehfeldt and Jaquish 2010), and in situ tree species conservation (Hamann and Aitken 2013).  Moreover, climate analogs are essential to maintaining the relevance of accumulated practitioner knowledge in a changing climate. As climate zones shift across the landscape, so must the ecological knowledge with which they are associated.   Where analogs for anticipated future climates are available within local jurisdictional boundaries—e.g., from downhill locations—forest managers are able to draw on their familiar local knowledge systems. However, the projected magnitude of climate change over forest management timescales is compelling forest managers to look for climate analogs in the relatively unfamiliar climates of other jurisdictions (Potter and Hargrove 2012).  While some locally unfamiliar climates may have historical analogs in nearby jurisdictions, previous research 46 suggests the potential for novel climates that have no historical analogs at continental (Rehfeldt et al. 2012) and even global (Williams et al. 2007, García-López and Allué 2013) scales. These truly novel climates represent conditions for which little knowledge is available from observational experience (Williams and Jackson 2007), and therefore for which ecological predictions are unreliable (Fitzpatrick and Hargrove 2009). Forest management in a changing climate will inevitably involve some extrapolation of accumulated knowledge into novel, unfamiliar conditions. Nevertheless, the risk of management failures will likely increase with the degree of extrapolation (Peterson et al. 2011, pp. 126-8).  Measurement of novelty in projections of climate change indicates the degree of confidence that we can put in climate analogs for forest management guidance. 4.1.2 Novel climates in the British Columbia forest management context The use of climate analogs for climate change adaptation is in the early stages of being operationalized in British Columbia. For the past 50 years, forest practices and legislation in British Columbia have been organized under a province-wide structured knowledge system named the Biogeoclimatic Ecosystem Classification (BEC; Pojar et al. 1987, Haeussler 2011).  BEC includes, as one of its central pillars, a hierarchical climate classification with 16 zones (Figure 4.1), ~100 subzones, and ~200 subzone-variants. Though BEC climates were originally conceived as static map units, spatial shifts in BEC climate units have been projected by using these units as analogs for the future climates projected by global climate models (Hamann and Wang 2006, Wang et al. 2012). BEC unit projections are being used in an overhaul of the BC government’s tree seed transfer framework, in which seed transfer limits are defined by BEC units and shifted in space in accordance with their projected future spatial distribution (O’Neill et al. 2017). BEC unit projections are also being used to incorporate climate change into provincial government’s tree species suitability guidelines, by demoting or promoting individual species based on their historical suitability to the range of BEC units projected for a planting site. In providing a pool of climate analogs that are richly embedded with ecological knowledge, BEC is a coherent framework to guide the transfer of locally-adapted forest management strategies among regions and sites as their climates change.   47  Figure 4.1: Biogeoclimatic zones of British Columbia, the highest level of the BEC climate classification. Representative locations for a small sample of BEC subzones (see Table B.1 for full names) are provided for reference in subsequent figures. The emergence of climates that are not described by the BEC system is an open problem in the use of climate analogs for forest management in British Columbia. Mismatch between future conditions of some locations and their BEC analogs should be expected, since current BEC projections do not draw on analogs from outside British Columbia. Further, the potential for emergence of climates with no analogs in North America or beyond cannot be ruled out a priori. Two-dimensional seasonal temperature-precipitation envelopes for BC indicate that the warm edge of the BC climate envelope will develop novel climates (relative to historical BC climates) as it shifts due to climate change (Figure 3.1). These simplified representations of climatic shifts suggest that the potential for novel climates is not limited to the and driest areas of the province (e.g., the CDFmm subzone in the Georgia Basin and the PPxh subzone in the Okanagan Valley), but spans the warm margin of the climate envelope along the full range of precipitation regimes. The emergence of climates that are unfamiliar to the BEC system is an inevitable consequence of climate change. Further, previous research indicates the potential for future climates in British Columbia with no analogs in North America (Rehfeldt et al. 2012, Mahony et al. 2017). 48  Figure 4.2: Projected shifts in the British Columbian temperature-precipitation envelope in winter (a) and summer (b). RCP4.5 ensemble mean projection for the 2041-2070 period. Novel climates emerge along the leading edge of the shifting climate envelope. Climate change trajectories for a selection of BEC subzones (mapped in Figure 1) are shown for reference, linking end-of-20th-century climates (blue dots) to the projected mid-21st-century climate (red dots).  The apparent potential for climate change to produce some amount of jurisdictionally novel climates indicates that BEC projections are susceptible to extrapolation errors. Current BEC projections (Wang et al. 2012) provide the analog with the best match to projected conditions. The best match, however, is not necessarily a good match. Where extrapolation into novel climates results in a poor match between the projected future climate condition and its assigned analog within the BEC system, the BEC analog is likely to provide misleading guidance (Fitzpatrick and Hargrove 2009). Undiagnosed use of poor-quality analogs has the potential to produce management failures due, for example, to inappropriate provenance or species selection for reforestation. It is essential to identify poor-quality analogs associated with novel climates, so that other sources of management guidance can be pursued.  4.1.3 Linear vs. machine-learning approaches to measuring climatic novelty As discussed in section 1.4, climatic novelty is subjective to the ecological context under consideration: a climatic condition that is novel from the perspective of one ecological community may be functionally familiar to another. The context-dependence of climatic novelty 49 has important implications for how it is measured. The most prominent approach to novel climate detection defines novelty as the climatic distance (Dmin) between the projected climate and its closest historical analog (Williams et al. 2007, Mahony et al. 2017). This distance is measured using a set of climate variables that is universal to all locations in the study. The relative magnitude (the scaling) of these climate variables is defined by standardizing them to their local interannual climatic variability. Although this linear scaling approach is localized, it does not necessarily reflect the complex and non-linear biological responses to climate that are idiosyncratic to each ecosystem. In contrast, BEC projections are currently produced using a machine learning algorithm, Random Forest (Breiman 2001), that models the relationship between BEC units and climate using localized climate variable selection and non-linear scaling. Climatic novelty measured within the model structure of Random Forest BEC classifications could be much more ecologically meaningful than novelty measured with the linear Dmin approach. However, there currently are no established methods for novelty detection in Random Forest bioclimatic classifications, despite the availability of novelty detection methods for simpler classification problems (Désir et al. 2013, Zhou et al. 2015) and the promising approach developed by Rehfeldt et al. (2012). In the absence of direct novelty detection with Random Forest, the linear Dmin approach can provide a necessary approximation of which areas of British Columbia are susceptible to the emergence of novel climates. Further, the Dmin approach can provide a point of comparison for evaluating indicators of novelty in Random Forest BEC projections and investigating how Random Forests behaves in the context of extrapolation.  4.1.4 Study objectives The objectives of this study are to provide an assessment of where novel climates in British Columbia are likely to emerge by mid-21st-century and to demonstrate the utility of this approach to forest management. We focus on the projected climates of the 2050s (2041-2070) as this period roughly corresponds with the midpoint of the 50- to 100-year harvest rotations typical of British Columbia and is of immediate significance to current reforestation and timber supply management decisions (O’Neill et al. 2017). I use distance metric of sigma dissimilarity in parallel with Random Forest classification to evaluate (1) the robustness of novel climate inferences and (2) the extent to which these projected novel climates are described by climate analogs elsewhere in North America. In addition to providing specific insights for British Columbia, I find that overestimation of analog similarity and ensemble agreement are general 50 characteristic errors of extrapolation into novel climates. I demonstrate that these quantities can be used as indicators of climatic novelty in machine learning bioclimatic projections.  4.2 Methods 4.2.1 Linear novelty detection method I calculate linear novelty (Dmin) as the Mahalanobis distance (Mahalanobis 1936) between the projected mid-21st-century (2041-2070) climate of a location of interest and its closest analog among the observed end-of-20th-century (1971-2000) climates of an analog pool (Figure 2.1). The analog pool is either British Columbia or North America depending on the analysis.  This Mahalanobis distance is scaled to the historical interannual variability of the climate variables for the location of interest. Unlike the analysis of Chapter 3, I do not interpret Mahalanobis distances probabilistically using the chi distribution; novelty distances are instead interpreted in this chapter in terms of the minimum distances between BEC units.   Figure 4.3: Illustration of the linear method for measuring climatic novelty.  The local ICV of a location of interest is used to scale a Mahalanobis distance to identify the closest end-of-20th-century analog for the projected future climate of the location of interest.  4.2.2 Random forest classification Indicators of novelty in Random Forest projections I propose two indicators of extrapolation into novel climates in Random Forest projections: Analog similarity and ensemble agreement (Figure 4.4). Analog similarity—the similarity 51 between a location’s 20th-century climate and the 20th-century analog for its projected 21st century climate—can be expected to be greater for novel climates than for projected climates with good analogs. Where there is a good analog for the projected climate (location 1 in Figure 4.4a), the analog dissimilarity (Da) will be the same magnitude as the climate change trajectory (Dc). Where the climate change trajectory extends beyond the edge of the study area climate envelope (locations 2 and 3 in Figure 4.4a), analog dissimilarity may in some cases (e.g., location 2 in Figure 4.4a) be less than the magnitude of climate change (Da < Dc). In extreme cases of novelty, where the climate change trajectory extends perpendicular from the leading edge of the study area climate envelope (e.g., the PPxh trajectory in Figure 3.1), analog dissimilarity will be near zero because the best analog for the end of the trajectory is its origin. This conceptual model of analog similarity suggests that it is a precise but not highly sensitive indicator: it is expected to produce few type I errors (novelty inferred when the climate is not novel), but many Type II errors (novelty not detected when the climate is novel; e.g., location 3 in Figure 4.4a). Analog similarity can be measured as a distance (0-Da) in linear classification and approximated in Random Forest using proximity matrices, as described below in the section “BEC Proximity matrix”.  Ensemble agreement—the uniformity of class (e.g., BEC subzone) predictions for different global climate model projections—is another potential fingerprint of novelty detectable in Random Forest projections (Figure 4.4b).  Where good analogs are available (location 1 in Figure 4.4b), variation in the climate change trajectories of different global climate model projections will produce variation in class predictions for any given location. In the absence of good analogs (locations 2 and 3 in Figure 4.4b), the ensemble predictions are more likely to fall into a smaller number of classes located at the edge of the study area climate envelope. This conceptual model suggests that ensemble agreement is likely to be a more sensitive indicator of novelty than analog similarity (lower type II errors), but a less precise one (higher Type I errors). There are several ways to measure ensemble agreement; in this chapter I use the proportion of models that predict the majority class, as demonstrated in Figure 4.4.   52  Figure 4.4: Conceptual models for indicators of novelty in Random Forest projections: (a) Analog similarity and (b) ensemble agreement. The grey polygon signifies the study area climate envelope, and arrows indicate trajectories of climate change.  (a) Novel climates can be reliably inferred where the analog dissimilarity (Da) is less than the magnitude of climate change (Dc). (b) Novel climates are expected to produce higher agreement on the class (portrayed as subdivisions of the study area climate envelope; e.g., BEC subzones) assigned to the diverse projections of an ensemble of climate models. Random Forest classification  I trained Random Forest models to classify BEC subzone-variants from climate variables. Each model comprised 500 trees. To prevent class imbalances, each tree was grown using an n=50 bootstrap sample of grid cells each BEC subzone-variant, a technique called “tree-level downsampling.” Analyses on the ensemble mean projection were performed on a 2-km grid, using BEC subzone-variants as the class variable. To reduce computation time, CMIP5 ensemble analysis was performed on a 4-km grid, using BEC subzones as the class variable.  53 BEC proximity matrix The similarity between BEC subzone-variants within a Random Forest model was calculated with Random Forest proximity matrices. Random Forest proximity between two training observations is the proportion of trees within the forest in which the two observations are assigned to the same predicted class (same leaf node). For each RF model calculated on the full grid, I calculated a proximity matrix for an n=10,100 stratified subsample of the grid (50 grid cells for each of the 202 BEC subzone-variants). The proximity between two BEC subzone-variants is estimated as the average of their 50x50 submatrix within the proximity matrix. This calculation results in a 202x202 matrix of proximities among BEC subzone-variants. RF subzone-variant proximities are log10-scaled in this paper’s results. Examples of pairwise proximities are presented in Appendix B.3.  4.2.3 Climate Data Climate variables The primary climate variables used in this chapter are six “seasonal basic” variables: mean daily minimum and maximum temperature (Tmin, Tmax) and log-transformed total precipitation (PPT) for winter (Dec-Jan-Feb) and summer (Jun-Jul-Aug). These variables provide a simple characterization of climate, consistent with the objectives for the linear novelty analysis; they were already extensively validated in chapter 3; they avoid the conflation of distinct seasonal climate signals (e.g. as with mean annual temperature); they have approximately linear responses to increasing mean temperature (unlike e.g., number of frost-free-days); and they do not have highly non-normal distributions of interannual climatic variability. Random Forest models were trained on 5 nested variable sets of increasing dimensionality: the 6-variable “seasonal basic” set, the 44-variable set of Wang et al. (2012), and also on intermediate nested sets of 3, 12, and 24 variables (Appendix B.4). Observed and projected climate normals Gridded climate normals for the 1971-2000 and 2041-2070 periods were obtained using ClimateNA v5.10 (Wang et al. 2016). I extracted data grids from ClimateNA at 2km resolution for British Columbia and 8km resolution for North America in a North American Equidistant Conic projection. Observed 1971-2000 climate normals are interpolated from the PRISM climate surfaces for British Columbia. Projected 2041-2070 climate normals are the ensemble mean of 54 the 15 CMIP5 projections (Taylor et al. 2012; Table A.2) available in ClimateNA.  The ensemble mean projection is calculated from the mean monthly anomaly for each variable in all 15 models. I evaluate novelty for the RCP4.5 and RCP8.5 scenarios (van Vuuren et al. 2011).  Local interannual climatic variability I estimated local interannual climatic variation using the same set of CRU TS3.23 (Harris et al. 2014) source observations described in Section 3.2. This process selected 91 CRU TS3.23 stations within British Columbia. I calculated Mahalanobis distance (novelty) separately for each of the four stations nearest to the location of interest, then averaged these values.  4.2.4 North American climate analogs To identify North American analogs for the projected mid-21st-century climates of British Columbia, I conducted both a “backward” and a “forward” analysis (sensu Hamann et al. 2015).  The backward analysis trained Random Forest models on the projected 2041-2070 climate normals of pooled BEC units and North American ecoregions, and used these models to classify the historical 1971-2000 normals of North American raster grids. The forward analysis trained the model on historical normals and made class predictions on the projected normals. Tree-level downsampling was applied in all Random Forest models at n=15 per class per tree. For the purpose of sensitivity analysis, I created two alternative ecoregion classifications as class variables. The coarse-ecoregion set is composed of the World Wildlife Fund terrestrial ecoregions (Olson et al. 2001), totalling 145 ecoregions across the full extent of North America outside British Columbia. The fine-ecoregion set was compiled from US level IV ecoregions (Omernik 1987) and Canadian ecodistricts (Ecological Stratification Working Group (ESWG) 1995), totaling 751 non-BC ecoregions in Western North America (33oN-62 oN; 102 oW-140oW).  Each ecoregion set was gridded at 8km resolution and pooled with a 2km grid of BEC subzones (interior BC) and subzone-variants (coastal BC). Each of these two sets of training classes was paired with the 6-variable and 44-variable predictor sets, for a total of 4 Random Forest models each for the forward and backward analyses. Results of the 44-variable, coarse-ecoregion analysis are presented in this chapter, and all four model predictions are presented as sensitivity analyses in Appendix B.5.  55 4.3 Results 4.3.1 Distance between BEC units Climatic distances between BEC units (Figure 4.5) provide ecological context for interpreting novelty distances. Coastal (maritime) and interior (continental) BEC units have distinct distributions of nearest-neighbour distances. Coastal units are further apart from each other in climate space, on average, than interior units; a difference that is increasingly evident at higher levels of the BEC hierarchy (Figure 4.5c). This difference may be due to inconsistency in the application of the expert-based classification methodology between the two regions. However, the potential for this difference to be caused by lower vegetation sensitivity to climatic differences on the coast cannot be ruled out a priori. Although the ecological significance of the distinct distributions of coastal and interior regions is unclear, it nevertheless suggests that the two regions should be treated separately when interpreting climatic novelty. I use the median distance between nearest neighbour subzones as a threshold for novelty: Dmin > 2.7 in the coast region and Dmin > 1.5 in the interior region.   Figure 4.5: Climatic differentiation among BGC units. Differentiation is the distance between each BGC unit and its nearest neighbour in the “seasonal basic” climate space. Results are presented for the three hierarchical levels of the BEC climatic classification: (a) BGC subzone-variants (n=174); (b) BGC subzones (n=91); and (c) BGC zones (n=13). Boxplots for the coast and interior represent the pooled distances for all BGC units in each region.     56 4.3.2 Detection of novel climates with linear classification The pattern of novelty of projected mid-21st-century climates of British Columbia is consistent across emissions scenarios (Figure 4.6a-b). Under RCP4.5 (Figure 4.6a), BEC subzone-scale novelty (Dmin >1.5 in the interior) is projected for the major valley-bottoms of the southern interior, the Chilcotin Plateau, and northeastern BC.  Under RCP8.5 (Figure 4.6b), this spatial pattern of novelty intensifies to a level corresponding to the emergence of novel interior-region BEC zones (Dmin >2.5). On the coast, subzone-level novelty (Dmin >2.7) is limited to the small pockets of the coast under RCP4.5, but expands under RCP8.5 to large areas of the outer North Coast, Haida Gwaii, southern Vancouver Island, and the Lower Mainland. Expanding the analog search to all of North America substantially reduces novelty in Northeast BC, the Chilcotin Plateau (Central BC), and Rocky Mountain Trench (Southeast BC) (Figure 4.6c-d).  However, the pattern and magnitude of novel climates on the coast and the southern interior is essentially equivalent for the BC and North American analog pools. The lack of North American analogs for these locations in the linear novelty assessment indicates the potential for emergence of continental-scale climatic novelty in British Columbia.  Linear novelty is strongly associated with topographic position: novel climates (Dmin>1.5) predominantly occur at low elevations and there are very few low-elevation locations (<500m) with low novelty (Dmin<1) (Appendix B.6). As expected, climate analogs are predominantly sourced from downhill and southward locations (Appendix B.2). However, there are instances of uphill and northward analog sources, indicating that that climatic shifts may not follow intuitive geographic trajectories.  57  Figure 4.6: Novelty of projected climates of British Columbia in the 2041-2070 period.  (a,c) RCP4.5 and (b,d) RCP8.5 CMIP5 ensemble mean projections. Analog pools are (a,b) British Columbia and (c,d) North America.  The color scheme is scaled to the median climatic differentiation among BEC subzones in the coast (2.7) and interior (1.5).  58 The spatial distribution of projected novelty within the current map area of BEC zones is summarized in Figure 4.7a-b. With the exception of the BWBS and CDF, novelty does not align well spatially with BEC zones: zones that contain some areas of high novelty—i.e., the ICH, PP, SBPS, and BG zones—also contain areas of low novelty. The BEC subzone-variant is a more effective level of the BEC hierarchy to capture the spatial distribution of novelty (Figure 4.7c-f): in the interior, some BEC subzone-variants are occupied by novel climates on more than 75% of their area, even in RCP4.5. On the coast, however, few variants have a majority of their area as novel climates, even in RCP8.5.   Figure 4.7: Spatial distribution of climatic novelty in current BEC zones and subzone-variants. (a,b) Boxplots of the spatial distribution of climatic novelty within the current BEC zone map units, using the “seasonal basic” variable set for the (a) RCP4.5 and (b) RCP8.5 ensemble mean projections. (c-f) BEC subzone-variants with the highest median novelty over their spatial range on the (c,e) coast and (d,f) interior for (c,d) RCP4.5 and (e,f) RCP8.5. Boxplot whiskers indicate the minima and maxima. Red horizontal lines indicate the subzone-level novelty thresholds of Dmin=2.7 for the coast and Dmin=1.5 for the interior. 59 4.3.3 Evaluation of indicators of novel climates using linear classification  Analog similarity and ensemble agreement are both moderately correlated with climatic novelty (r=0.59 and r=0.57, respectively) in the linear classification of the RCP4.5 ensemble mean projection (Figure 4.8). High analog similarity exclusively occurs at high novelty (i.e., there are no Type I errors), indicating that analog similarity is a precise indicator of climatic novelty in the context of linear classification. Instances of simultaneously low analog similarity and high novelty (type II errors) indicate that the sensitivity of this indicator is not as high as its precision.  Despite being correlated with novelty, ensemble agreement exhibits both type I and II errors (Figure 4.8b), suggesting that it is not as precise an indicator of novelty as analog similarity. These results indicate that analog similarity and ensemble agreement have some utility in detection of model extrapolation in projections by machine learning algorithms such as Random Forest.    4.3.4 Indicators of novelty in Random Forest BEC projections Random Forest and linear classification produce similar BEC projections based on the RCP4.5 “seasonal basic” variable set  Figure 4.8: Relationship between novelty measured with Mahalanobis distance and two hypothesized indicators of novelty: (a) analog similarity and (b) ensemble agreement.  RCP4.5 ensemble mean projection of the “seasonal basic” variable set for British Columbia grid cells. (a) Scatter plot of analog similarity shaded by grid point density and contoured by 50th, 75th, and 95th percentiles. (b) violin plots indicating the novelty of grid points within each level of ensemble agreement, which is a discrete variable because it is the number of models voting for the majority class divided by the number of models in the ensemble.  60 (Figure 4.9a,d) despite their large methodological differences. The prominent trends of both of these projections, relative to the historical distribution of BEC zones (Figure 1), are: the uphill expansion of the CWH and ICH zones at the expense of the MH and wet belt ESSF, respectively; the expansion of the IDF and ICH into the central interior at the expense of the SBPS, MS, and SBS zones; the expansion of the ESSF and SBS zones into the Northern interior at the expense of the SWB and alpine (BAFA) zones, and the expansion of the CWH zone into montane elevations of the West Kootenays.  As expected due to their correlation (Figure 4.8a), analog similarity of the linear classification (Figure 4.9b) reflects the patterns and magnitude of climatic novelty measured directly in Figure 4.6a, notably the Alberta Plateau (BWBS zone), Okanagan valley, Georgia Basin, Chilcotin Plateau, and the outer coast. These patterns are also evident in the analog similarity of the Random Forest projection (Figure 4.9e). More broadly, the Coastal valleys and mountains and the valleys of the southern interior exhibit low analog similarity in the Random Forest projection. The coarse-scale patterns of RF analog similarity (Figure 4.9e) and ensemble agreement (Figure 4.9f) are similar. However, there are some occurrences of high ensemble agreement that are not matched in analog similarity, notably the northern Cariboo region and central Rocky Mountain Trench. This mismatch may indicate areas of genuinely high projection confidence (ecological equivalence among model projections), as opposed to spurious ensemble agreement produced by novel conditions. Examples of BEC subzone-variant similarities are presented in Appendix B.3. 61  Figure 4.9: Analog similarity and ensemble agreement in BEC projections made using Mahalanobis nearest neighbour (a-c) and Random Forest (d-f) classification; RCP4.5 ensemble mean projection for the 2041-2070 period, using the “seasonal basic” variable set. (a,d) BEC zone of best analog. (b,e) Climatic similarity between the best analog and the reference period condition. (c,f) proportion of a 15-model ensemble that voted for the majority subzone.     62 Progressively increasing the predictors available from the 6 “seasonal basic” variables up to 44 variables produces similar but somewhat more conservative Random Forest BEC projections (Figure B.5), notably removing the small occurrences of questionable analogs such as IDF in far northern BC and CWH (a coastal zone) in the interior wet belt.  Higher dimensionality produces subtle increases in analog similarity (Figure B.6) and ensemble agreement (Figure B.7), with some pronounced localized changes. Reducing the variable set to include only winter Tmin, summer Tmax, and mean annual precipitation produces an increase in questionable analogs (Figure B.5b) (e.g. extensive MS in the Boreal mountains), as would be expected due to insufficient predictors to differentiate distinct ecosystem climates. Analog similarity is somewhat higher in these 3-variable projections (Figure B.6b), but ensemble agreement is substantially lower (Figure B.7b), reflecting a higher level of analog availability in this low-dimensional climate space where ecologically distinct climates are not readily distinguished in terms of climate.  4.3.5 North American climate analogs The “backward” search for North American analogs trains a Random Forest model on the projected climates within the mapped distributions of pooled BEC subzones (within BC) and WWF ecoregions (outside of BC). This model is then used to assign a class label (subzone or ecoregion) to the historical climates of North America. The proportion of classification trees in the Random Forest that voted for a BC climate (Figure 4.10a) is an approximate measure of analog similarity to the future climates of British Columbia. Climate analogs are predominantly located in the Rocky Mountains as far south as Colorado and on the southwestern coast of Alaska. Southern climate analogs on the coast are limited small areas of the Oregon Cascades and the Sierra Nevada. Despite some low-similarity analogs in the Great Lakes and Canadian Maritimes regions, climate analogs are absent from central and eastern North America.  The class assigned to a grid cell in the “backward” analog search indicates the current BEC unit of the location to which the historical analog is matched (Figure 4.10b). For example, the large pink area in central British Columbia indicates analogs for the projected climates of the current subzones of the Montane Spruce (MS) BEC zone, and the purple areas in the Rocky Mountains of NW Montana indicate analogs for the projected climates of the current Engelmann spruce – subalpine fir (ESSF) subzones.  This backward prediction produced analogs for the future climates of current BG, ESSF, MS, SBPS and IDF subzones in Washington, Oregon, 63 Idaho, Montana, and Wyoming. There are relatively few analogs for ICH and PP subzones either within or outside of British Columbia. West-central Alberta contains large areas of analogs for BWBS subzones and small pockets of analogs for SWB subzones. Analogs for projected climates of CWH and CDF climates are limited to coastal Washington.   Figure 4.10: End-of-20th century analogs for the mid-21st-century climates of BC, as predicted by a Random Forest model trained on the 44-variable RCP4.5 ensemble mean 2041-70 climates of BEC units (within BC) and WWF ecoregions (outside BC). (a) Random Forest proportional votes for climates projected to occur within BC. (b) Dominant BEC zone predicted by the RF model, indicating the BEC zone that each climate analog represents.  This analog mapping is highly sensitive to variable availability and ecoregion generalization. Reducing the variable availability from 44 variables to the six-variable “seasonal basic” set produces a large expansion of analogs in the Northwestern United States (Figure B.8a and Figure 64 B.9a). The fine-scale ecoregionalization (replacing 145 ecoregions of North America with 751 ecoregions for western North America) produces a large contraction of analogs (Figure B.8d and Figure B.9d).  The ”forward” search for North American analogs trains a Random Forest model on historical climates of pooled BEC subzones and WWF ecoregions and assigns a class label to the projected climates of BC (Figure 4.11).  The proportion of classification trees in the Random Forest that voted for a non-BC climate is an approximate measure of climatic novelty to BC.  Non-BC votes are limited to the areas of novelty inferred from the linear analysis. However, some areas of novelty inferred from previous analyses are absent from the forward search of North American analogs. These absences, such as on the North Coast, suggest projected climates without North American analogs. In contrast to the backward analog search, the forward search is not sensitive to the coarseness of the non-BC classes (Figure B.10c-d). However, the forward search is sensitive to variable availability: the 6-variable predictor set produces an increase in non-BC Random Forest votes relative to the 44-variable set, particularly in the Chilcotin and Thompson Plateaus (Figure B.10a). Similar to linear novelty, non-BC Random Forest votes are strongly associated with low topographic positions (Appendix B.6).  65  Figure 4.11: Locations in BC with non-BC North American analogs for their RCP4.5 ensemble mean climate of the 2041-2070 period, as predicted by a Random Forest model trained on the 1971-2000 climates of BEC units (within BC) and coarse ecoregions (outside BC). The map is shaded by the proportion of classification trees in the Random Forest that voted for non-BC ecoregions. 4.4 Discussion The results of this chapter suggest that a majority of British Columbia’s area will remain free of provincially novel climates in the middle of the 21st century. This result suggests that the BEC system will remain the dominant source of climate analogs for mid-21st-century forest management planning horizons. Nevertheless, I detected a robust pattern of novel climates in mid-21st-century climate projections at low elevations in the Boreal Northeast interior (BWBS zone), the Georgia basin (CDF zone), the Chilcotin Plateau, the North Coast, and the major valley systems of the southern interior (BG, PP, IDF and dry ICH zones). This analysis suggests that forest management in most of these novel climates can be informed by analogs from other jurisdictions in North America. However, the novel climates of the north coast do not appear to 66 have North American analogs. These results demonstrate that novel climate detection is an essential component of knowledge transfer with climate analogs. The necessity to identify novel climates applies to other structured forest management knowledge systems—e.g., those of Yukon Territory (Environment Yukon 2013) and Quebec (Saucier et al. 2003)—and also to the informal local knowledge base of individual land managers.  By identifying portions of their landscapes that are prone to emergence of novel climates, forest managers can avoid misinterpretation of model projections and prioritize their search for analogs beyond the jurisdictional boundaries of their ecological knowledge systems.  4.4.1 Novel climate detection in Random Forest projections I have used a linear classification framework to validate two novelty indicators that are measurable in Random Forest—analog similarity and ensemble agreement. The similarities in the spatial distributions of these indicators in linear and random forest classifications provide a robust indication of locations in British Columbia that are susceptible to emergence of novel climates. The indicators also indicate the types of extrapolation errors that are induced by climatic novelty: analog similarity and ensemble agreement cannot be interpreted at face value in Random Forest projections. In the presence of substantial climate change, the absence of a shift in projected bioclimatic zones at certain locations should be interpreted as an artefact of novel climates, rather than as an indicator that climate change is relatively benign in those locations. Similarly, ensemble agreement cannot be assumed to indicate locations where the confidence in the ensemble projection is higher. On the contrary, ensemble agreement more likely indicates locations where lower confidence in the ensemble projection is warranted due to errors of extrapolation into novel climates. These artefacts of novel climates highlight the importance of developing a reliable novelty metric for random forest bioclimate classifications. The Random Forest algorithm is widely preferred for operational climate analog identification because it performs non-linear, localized variable selection and scaling appropriate to the complex relationships between climate drivers and ecological responses. Linear classification methods, though highly amenable to measurement of novelty, produce less reliable analogs because the variables and their relative scalings are universal to all of the ecosystem climates being modelled and are not necessarily relevant to each or any of them. Further development of novelty metrics for Random Forest, such as the novelty indicators proposed here and the “dummy class” 67 approach demonstrated by Rehfeldt et al. (2012), is critical to the use of climate analogs for forest management.  4.4.2 Managing novel climates Novelty to the British Columbia analog pool indicates projected climates that are not described by BEC, and which therefore have no associated forest management strategies that are formalized in provincial legislation (e.g. species selection guidelines) and local practice (e.g. stand establishment and tending regimes). One remedy, which is currently being implemented by the BC government, is to extend biogeoclimatic mapping into adjacent jurisdictions to access climate analogs from which management strategies and observational data can be drawn. The results of my North American climate analog assessment (Figure 4.10 and Figure 4.11) suggest that North American climate analogs are available for many of the projected novel climates of interior British Columbia, particularly in Alberta, Washington, Oregon, Idaho, Montana and Wyoming. The very high sensitivity of Random Forest analog identification to the bioclimate classification (Figures B.9-11) suggests that extension of the BEC classification and mapping methodology into these jurisdictions is a prerequisite to accurate identification of climate analogs.  Drawing analogs from adjacent jurisdictions, however, can only partially ameliorate the problem of novel climates. For example, the scarcity of southern analogs for the coastal climates of BC in Figure 4.10 is consistent with the prior expectation that the climate trajectory of coastal BC, towards warmer but still wet conditions, may not follow the north-to-south climatic gradient of cool-wet to warm-dry. The linear novelty assessment (Figure 4.6), random forest novelty indicators (Figure 4.9), and the North American analog search (Figure 4.11) consistently indicate that the north coast in particular appears to be susceptible to the emergence of continental-scale novel climates. In such cases, a global-scale analog search may be informative, especially in locations where plantations of species native to British Columbia have been established. For example, species choices could be informed by the climates where Sitka spruce grows well in the British Isles (Cameron 2015) or where Douglas-fir is planted in Europe (Isaac-Renton et al. 2014). However, management decisions in the absence of climate analogs must inevitably rely on other approaches, such as species-specific climatic suitability modeling (e.g. Leites et al. 2012, Rehfeldt et al. 2014), not just of tree species but also of their major pests and pathogens (Woods 2011). Experimental climate modification experiments (e.g. Templer et al. 2017) can 68 also be informative, especially at the regeneration stage, and managers should consider prioritizing these experiments in ecosystems that are more likely to transition into novel climates. Novel climates intensify the uncertainties of forest management under climate change. Strategies for dealing with these uncertainties—including lowering risk exposure (e.g., reducing rotation length), hedging (e.g., mixed-provenance regeneration), bolstering resistance (e.g., retention of intact ecosystems), and adaptive management (Spittlehouse and Stewart 2003, Millar et al. 2007, Bolte et al. 2009, Vilà-Cabrera et al. 2018)—are particularly necessary in locations where novel climates are projected to emerge. 4.4.3 The limits to adaptation in unfamiliar climates The accumulation of local ecosystem management regimes, and an understanding of the range of conditions over which they could be successfully applied, was one of the defining accomplishments of 20th-century forest management. This structuring of ecological knowledge into climatic and edaphic classes based on the concept of ecological equivalence is exemplified by BEC, which provides a framework to define limits to the spatial transferability of management regimes, genetic resources, and natural resources legislation. Climate change undermines a core underpinning of this knowledge base—that the future will resemble the past on the timescales over which forests are managed. Climate analogs can assist forest managers with redeploying their hard-won knowledge across the changing climates of their land base, and with sourcing non-local management strategies for the locally unfamiliar climates of the 21st century. However, a distinct problem of managing ecosystems in a non-stationary climate is that predicted ecosystem responses, and the applicability of knowledge derived from climate analogs, cannot be verified except by waiting for events to unfold (Rastetter 1996), at which point the predictions are moot. In addition, the future state of local climates is subject to many uncertainties stemming from global climate models (Deser et al. 2012b, Knutti and Sedláček 2012).  These factors constrain the time horizon over which forest managers can place confidence in guidance from climate analogs.  The intensity of these constraints is determined by the magnitude and pace of climate change.  A greater magnitude of climate change requires sourcing analogs from more distant biogeographical contexts, which may have low ecological equivalency due to non-climatic factors such as photoperiod and biotic interactions, and from beyond jurisdictional boundaries, which involves the formidable task of assimilating new management regimes into the 69 jurisdictional knowledge system. Further, the magnitude of climate change increases the potential for climates with no analog and thus no observational knowledge base. The RCP4.5 scenario represents a disruptive change in climate that nevertheless stabilizes by the end of this century. This stabilization implies that the shifting climatic zones will settle into place, and that forest managers at the end of the 21st century may be able to reinitiate the accumulation of locally-specific ecosystem knowledge. In contrast, it is questionable whether forest managers and other applied ecologists will be able to keep pace with the perpetually transitory and increasingly novel climates projected under the RCP8.5 scenario (Williams and Jackson 2007). The limits to which the forestry knowledge base can be brought to bear on the problem of climate change adaptation is a basis for forest managers to advocate for global emissions reductions.   As discussed above, the magnitude and pace of climate change is an overarching limitation on the ability of socio-ecological systems to adapt. The novelty assessments of this chapter and the previous chapter measured the magnitude of climatic novelty in terms of the scale of local interannual climatic variability. In the next chapter, I use the same approach to measure the magnitude of climate change at the local level.   70 Chapter 5: Locally novel climates—Intensified climate departures in coupled climate variables 5.1 Introduction To adapt to climate change, we must anticipate its impacts. A critical challenge of climate change risk assessment is the identification of general drivers of climate impacts that bridge the idiosyncratic responses of individual species, ecosystems, and societies. One prominent approach to assessing broad ecological and economic risks is to quantify climatic changes relative to local climatic variability (Settele et al. 2014). The premise of this approach is that biological and human populations are locally adapted (Kawecki and Ebert 2004) to the year-to-year variability of their environments, and have coping mechanisms for climatic changes within this range of variability (Mahlstein et al. 2012a). The hypothesis that adaptive capacity scales with environmental variability has some theoretical (Alpert and Simms 2002, Chevin et al. 2010), experimental (Gonzalez and Bell 2013, Vázquez et al. 2017) and observational (Deutsch et al. 2008b, Heron et al. 2016, Vázquez et al. 2017) support in the context of ecosystems, where environmental variability is a component of natural selection on the life history, demographics, population genetic variation, and phenotypic plasticity of organisms.  Further, historical variability is the range of conditions in which cultural and scientific knowledge about ecosystems has developed (Mortimore 2010). Departures from historical variability not only increase the potential for ecological disruptions to food security and ecosystem services (Battisti and Naylor 2009), but also represent locally unfamiliar conditions in which adaptive responses may not be apparent to human communities (Frame et al. 2017). The magnitude of a departure from local interannual variability therefore is an important indicator of climate change risks to both ecosystems and socioecological systems. In this chapter, I use the term “natural variability” to encompass the pre-industrial historical variability of real-world climates as well as the non-anthropogenically-forced internal variability of climate models. Departures from natural variability are commonly measured using the signal-to-noise ratio (S/N), which expresses changes in one climatic variable (the signal) relative to the scale of natural variability in that variable (the noise) (Christensen et al. 2007). Typically, the noise is defined as standard deviations of interannual variability (symbolized with sigma, σ), in which case S/N is equivalent to a standardized anomaly. S/N was originally used for the 71 detection of climate change (Hasselmann 1993). However, following the general logic of local adaptation to natural variability, S/N has become a widespread metric in many fields of climate change impact assessment, such as the human perceptibility of climate change (Hansen et al. 2012, Lehner and Stocker 2015), heat extremes (Coumou and Robinson 2013), risks to natural (Beaumont et al. 2011) and agricultural (Battisti and Naylor 2009) ecosystems, and general societal risk (Frame et al. 2017).  The timing of departures from natural variability has received particular attention, in variables including temperature (Diffenbaugh and Scherer 2011, Hawkins and Sutton 2012, Abram et al. 2016), precipitation (Giorgi and Bi 2009, Mahlstein et al. 2012b), biogeochemical cycles (Keller et al. 2014, Lombardozzi et al. 2014), sea level (Lyu et al. 2014), and specific ecological drivers (Henson et al. 2017).  These “time-of-emergence” studies have identified regions of large and rapid departures from natural variability, notably the observed and projected warming of the tropics where human populations (Frame et al. 2017) and, socioeconomic vulnerability (Mora et al. 2013) are concentrated. These coarse-scale studies assist the prioritization of more detailed regional climate risk assessments (Sui et al. 2014).  Risk assessments based on departures from natural variability have predominantly analyzed individual climate variables (but see Hao and AghaKouchak 2013, Flach et al. 2017). Interactions and dependencies among climate variables are increasingly recognized as important contributors to climate change impacts (Leonard et al. 2014, Zscheischler and Seneviratne 2017), and have implications for departures from natural variability. For example, summer precipitation (Pr) and mean daily maximum temperature (Tx) are negatively correlated over most land areas (Trenberth and Shea 2005) (Figure 1a,b). This correlation is driven primarily by evaporative cooling, but also by reflection of sunlight by clouds, and land-atmosphere coupling (Berg et al. 2015). As a result of this relationship, natural variability in many terrestrial locations lies along an axis from warm-and-dry to cool-and-wet conditions, and excludes conditions that are simultaneously much warmer and wetter than average (Figure 1c).  A climate change trend perpendicular to this axis, towards warmer-wetter conditions, can produce a larger and earlier departure from natural variability than in either Tx or Pr alone. This type of climate change trajectory is projected by climate models to occur in many regions (Scoccimarro et al. 2013). This example illustrates how extreme conditions can arise from unusual combinations of climate variables that are individually not in an extreme state. I use the term departure intensification to describe a multivariate climate change signal that is stronger relative to natural variability than 72 the signals of its component variables. My use of the term “departure” is synonymous with the use of “emergence” in the S/N and time-of-emergence literatures mentioned previously (Giorgi and Bi 2009). Like all climate departures (Mora et al. 2013), departure intensification in summer temperature and precipitation is a coarse-filter indicator of ecological risk. Nevertheless, some specific potential impacts can be identified. Host-parasite interactions can be much more disruptive to the host species than the physiological effects of environmental change alone (Kawecki and Ebert 2004). Fungal and microbial plant pathogens are of particular concern because of their responsiveness to growing season temperature and precipitation (Garrett et al. 2015) and their impacts on food security, forest health, and ecosystem services. For example, the global increase in the incidence and severity of Dothistroma fungal needle blight outbreaks in pine plantations has been linked to anomalously warm and wet conditions in many regions (Woods et al. 2016). Mosquito-borne diseases such as malaria and dengue fever are also of concern, because both the vector and pathogen are responsive to heat accumulation and standing water availability (Patz et al. 2003). The departure intensification effect (Figure 5.1) suggests that the response of these agents to simultaneously warmer and wetter conditions may be out of proportion to their local historical response to unsynchronized anomalies of similar magnitude in temperature or precipitation alone. These disruptions could offset the benefits of increased precipitation in reducing “hotter droughts” (Allen et al. 2015) induced by regional warming. Assessment of departure intensification in precipitation, temperature, and other coupled variables can provide an early warning of rapid ecological change that would not be apparent in analysis of individual climate variables.  The goal of this chapter is to investigate the phenomenon of departure intensification using the example of summer Tx and Pr.  I use a multivariate S/N approach to examine inter-model variation in departure intensification in RCP4.5 projections from 6 Coupled Model Intercomparison Project Phase 5 (CMIP5; Taylor et al. 2012) global climate models for the 1850-2100 period. I also establish the magnitude of Tx-Pr correlation required to produce departure intensification and locate regions with this degree of coupling in the observational record. 73  Figure 5.1: Intensified departure from historical variability in a correlated temperature-precipitation regime. Mean daily maximum temperature (Tx) and precipitation (Pr) of the Boreal (JJA) and Austral (DJF) summer are negatively correlated over most land areas in a, CRU TS3.23(Harris et al. 2014) precipitation stations and b, the internal variability of six CMIP5 global climate models (see Figure C.8 for single-model correlations). c, As a result, climate change trajectories into warmer-wetter conditions can depart from the joint variability of Tx and Pr sooner than in Tx alone: The projected shift in 30-yr climate normals (black line) at Newcastle, Australia exceeds the 2σ (~95%) threshold of joint historical interannual variability of Tx and Pr (gray points) by mid-21st century (red circle), despite staying within this threshold in each variable (red lines).   74 5.2 Methods 5.2.1 Reference interannual climatic variability I used historical natural forcings (historicalNat) model runs as reference variability for each CMIP5 model. HistoricalNat runs exclude anthropogenic forcings such as greenhouse gas emissions and land use change over the period 1850-2005, but include historical natural radiative forcings (e.g., solar cycles, volcanic eruptions) (Taylor et al. 2012). Pre-industrial control (piControl) runs are an alternative source of reference variability, but may have slightly biased natural variability due to the absence of volcanic forcings. For each model, I pooled all of the historicalNat runs available (excluding perturbed physics runs), such that the reference variability encompasses several historicalNat realizations of the 1850-2005 period. For example, the CanESM2 model, with 5 historicalNat runs, has n = 5 runs * 156 years/run = 780 years of reference variability. This large sample size facilitates reliable characterization of the tails of the distribution of reference variability and minimizes overestimation of anomalies outside of the reference period (Sippel et al. 2015) (Appendix C.4). 5.2.2 Univariate standardized anomalies Climate variables (e.g., with units of oC or mm) can be expressed as standardized anomalies, with units of standard deviations (symbolized as σ) of interannual variability over a multidecadal reference period. Standardized anomalies are traditionally calculated as z-scores, by subtracting the reference period mean and dividing by the reference period standard deviation (Wilks 2006). However, climate variables are often not normally distributed (e.g., substantial skewness), with the result that z-scores can overestimate the probability of an anomaly on one tail of the distribution, and conversely underestimate it on the other. To overcome this problem, I normalized univariate standardized anomalies of both temperature and precipitation using a form of non-parametric quantile mapping (Cannon et al. 2015), which additionally preserves the magnitude of the climate change relative to reference variability. The results of this chapter are not substantially different under other methods of correcting for non-normality, including univariate parametric quantile mapping (as used in the standardized precipitation index (Guttman 1999)), bivariate kernel density estimation, and multivariate quantile mapping (Cannon 2017) (Appendix C.2).  The reason for this robustness is that, as a binary metric, the 2σ proportion (see 75 below) is unaffected by the effect of normalization on the magnitude of anomalies beyond the 2σ threshold.  5.2.3 Bivariate standardized anomalies I used sigma dissimilarity to measure deviations from the bivariate distribution of temperature and precipitation. First, absolute bivariate anomalies are calculated as Mahalanobis distances from the centroid (multivariate mean) of the reference variability. Then, the squared distances are converted to percentiles of the chi-square distribution, which can be expressed as sigma levels (i.e., 1σ, 2σ, and 3σ for ~68th, 95th, and 99.7th percentiles). The sigma units of this metric facilitate direct probabilistic comparison between univariate and bivariate anomalies (Section 0). Orthogonality of climate change (θ) is measured as the inverse tangent of the relative magnitude of the 2051-2100 normals (Δ) of the principal components (PC1 and PC2) of reference variability, providing degrees of angular displacement from the dominant axis of interannual variability: θ = arctan(ΔPC2/ΔPC1).  5.2.4 Climate departure metrics The anomalies of projected 21st century climate change commonly exceed 3σ (an ~ 1/(1-0.9973) = 1-in-370-year exceedance), and therefore exceed the limits of statistical inference from even very large samples of modeled reference variability. This precludes quantification of the mean anomaly as a measure of departure from natural variability. Instead, I quantify the magnitude of climate change as the proportion of years in the preceding 30-year period that are >2σ (~1-in-20-year) anomalies relative to the distribution of reference variability. I call this metric the 2σ proportion. I define the term departure difference as the difference between the bivariate and univariate 2σ proportions. Univariate 2σ proportions are calculated as the maximum of the 2σ proportions of temperature and precipitation. As a noise-reduction measure, I calculated the departure difference for each year from the mean of the 2σ proportions of several historical+RCP4.5 runs. The null values of departure difference are slightly negative (Appendix C.3): where the correlation is non-significant and there is no trend in precipitation, the bivariate 2σ proportion is less than the univariate 2σ proportion by up to 0.1 depending on the magnitude of the temperature change. Positive departure differences indicate that the bivariate S/N is stronger than the univariate climate S/N. Pseudocode for calculation of maximum departure difference is provided in Appendix C.8.     76 5.2.5 Model selection To provide a robust representation of natural variability and the anthropogenic climate change signal, I selected CMIP5 climate models with at least 3 historicalNat runs and 3 RCP4.5 runs (Appendix C.5). I excluded CCSM4, which is superseded by CESM1-CAM5 (Meehl et al. 2013). I did not exclude models on the basis of model diagnostics.  5.2.6 Observed Tx-Pr correlations To complement previous analyses of gridded variability, I assessed observed Pr-Tx correlations at the station level in order to obtain local-scale estimates of interannual variability that are relatively free from grid-box averaging artefacts (Director and Bornn 2015). This analysis is anchored on precipitation stations because spatial correlation of precipitation is much lower than in temperature (Mitchell and Jones 2005). I obtained CRU TS3.23 (Harris et al. 2014) precipitation station observations from the source station files. I excluded stations with less than 30 years of summer precipitation totals in the 1901-2013 period.  Since precipitation and temperature are often not assessed at the same station, I used the CRU TS4.0 gridded Tx time series at the location of each precipitation station.  5.3 Results 5.3.1 Factors contributing to departure intensification.  Departure intensification is dependent on two factors: the strength of correlation (r) among climate variables and the orthogonality (θ) of climate change (Figure 5.2). The strength of the projected climate change signal is stronger in temperature than precipitation in almost all grid cells (Appendix C.7). Nevertheless, the precipitation trend determines the alignment of climate change with interannual variability: Large departure intensification occurs where the bivariate trajectory of climate change is orthogonal (perpendicular) to the dominant mode of interannual variability, as in Figure 5.2b&e. Departure intensification does not occur if the Tx-Pr correlation is low (Figure 5.2c) or if the trajectory of climate change is aligned with the dominant mode of variability, i.e. towards warmer-drier conditions (Figure 5.2d), except where the Tx-Pr correlation is very high (Figure 5.2f). The maximum departure difference metric can underestimate departure intensification where the climate change signal is very strong (Figure 5.2g), as both the univariate and bivariate anomalies rapidly exceed a 2σ proportion of 1.  77  Figure 5.2: Univariate and bivariate climate departures for summer precipitation (Pr) and mean daily maximum temperature (Tx) at selected locations; CanESM2 RCP4.5 ensemble projection. a, Terrestrial regions where bivariate departures from natural variability exceed univariate departures, measured as maximum departure difference during the 1880-2100 period. b (main plot), Time series of univariate and bivariate 2σ proportions near Memphis, USA. Univariate values are the larger of the Tx or Pr 2σ proportions. Bivariate proportions are assessed against the joint distribution of Tx & Pr. Shaded regions of the time series indicate the spread of the 5-run CanESM2 ensemble; solid lines are the ensemble mean. The dashed horizontal line indicates the expected 2σ proportion of 0.046 in a stationary climate with Gaussian (normal) variability. b (inset), The orthogonality of climate change (θ) is the angular displacement of the bivariate climate change trajectory from the dominant axis of bivariate interannual variability in Tx and Pr. c-g, Equivalent plots for other locations.  5.3.2 Inter-model variation.  There is considerable intermodel variation in summer Tx-Pr correlations and the orthogonality of climate change (Appendix C.6), and as a result there is large inter-model variation in the magnitude and spatial pattern of departure intensification (Figure 5.3). Nevertheless, departure intensification is evident in all models. On average, 23% of the land area 78 of each model has a maximum departure difference greater than 0.2 (i.e., >6 more years of 2σ anomalies in the preceding 30 years). The IPSL-CM5A_LR and CanESM2 models represent the intermodel range of departure intensification, with maximum departure differences >0.2 on 9% and 34% of their land area, respectively.  Low departure intensification in IPSL-CM5A_LR is due to its low correlation between summertime Tx and Pr relative to the other models (Figure C.8f). The reduced intensification in the GISS-E2-R projection is likely due to its pronounced lower climate sensitivity (Table C.1).  5.3.3 Timing of Departures The S/N of summer Tx-Pr climate change is highest in the tropics (Figure C.2). However, departure intensification of Tx-Pr regimes is evident at most latitudes (Figure 5.3). It is generally absent from the Boreal and Arctic regions due to low Tx-Pr correlations (Figure 1a). There is a strong relationship between the magnitude of departure intensification and the relative timing of departure of the bivariate Tx-Pr climate signal. As suggested by Figures 2b-g, the bivariate climate departure can occur several decades prior to the departure of Tx alone (Appendix C.1). On average, 16% (intermodel range of 7-23%) of the land area of each model departs from the joint variability of Tx and Pr at least ten years prior to the departure of either Tx or Pr alone (Figure C.3). These departure timings are based on a threshold 2σ proportion of 0.25, which represents a 10-fold increase in the frequency of warm 2σ anomalies. The role of departure intensification in the relative timing of bivariate and univariate climate departures is strongly influenced by how climate departure is (arbitrarily) defined. Consequently, the relative timing of departures is a less reliable indicator of departure intensification than the maximum departure difference.   79  Figure 5.3: Intermodel variation in relative departures from natural variability in summertime temperature (Tx) and precipitation (Pr). a-f, maximum departure difference is calculated from the mean time series of univariate and bivariate 2σ proportions of a number of historical/RCP4.5 runs for each CMIP5 model, as illustrated in Figure2b. The number of runs in each ensemble is indicated in parentheses next to the model name. Departure difference is the frequency of bivariate 2σ proportions minus the frequency of univariate (greater of Tx or Pr) 2σ proportions, both with respect to the 1850-2005 historicalNat simulations in each model. Positive values indicate a greater frequency of departures in the bivariate Tx-Pr regime than in Tx or Pr alone. Summer months are JJA (Northern Hemisphere) and DJF (Southern Hemisphere). 80 5.3.4 Minimum Tx-Pr coupling for departure intensification.  Bivariate climate departures are detected in tropical and subtropical regions of most climate models by the year 2020 (Figure 5.2 and Appendix C.1). This suggests that departure intensification may be detectable in the observational record at low latitudes, consistent with other studies that have detected emergence of a local warming signal (Mahlstein et al. 2012a). In extratropical regions where the climate signal has not yet emerged from natural variability, departure intensification likely is not yet detectable in the observational record. Nevertheless, all models indicate that, regardless of the orthogonality of the bivariate climate change trajectory, substantial departure intensification only occurs where there is a strong negative correlation (r < -0.5) between summertime Tx and Pr (Figure 5.4). This general relationship provides a rule of thumb for evaluating the observational record for regions that are susceptible to intensified climate departures. CRU TS3.23 precipitation stations (Harris et al. 2014) with >30 years of record exhibit strong negative summertime Tx-Pr correlations in several distinct regions on all continents, particularly in China, central Asia, Australia, central USA, western Canada, Argentina, southern Africa, and the African Sahel (Figure 5.1a). These regions are a priority for detection of departure intensification in the observational record, determining the probable trajectories of precipitation change, and identifying specific local impacts of departure intensification.  81  Figure 5.4: Relationship of maximum departure difference to the correlation between summer mean daily maximum temperature (Tx) and precipitation (Pr) in RCP4.5 ensemble projections of 6 CMIP5 models.  Oceans and Antarctica are not plotted. A random sample of n=1500 grid cells is plotted for each model to equalize plotting density.  5.4 Discussion This chapter has demonstrated that a multivariate climate change trend can be stronger, relative to natural variability, than all of the individual trends of its component variables. This departure intensification effect occurs when the climate change trajectory is misaligned with the dominant mode of interannual variability in correlated climate variables.  In the case of summer Tx and Pr—the focus of this chapter—these conditions hinge on stable or increasing precipitation. There is considerable intermodel variation in the amount and spatial pattern of departure intensification, due largely to intermodel variation in projected regional precipitation trends and the strength of simulated Tx-Pr correlations. Nevertheless, pronounced departure intensification is consistently limited to simulated climates with a summer Tx-Pr correlation 82 stronger than -0.5. This result provides considerable direction for prioritizing regions for further risk assessments based on observed correlations.  The climate variables in this chapter—summer Tx and Pr—reflect the primary goal of demonstrating departure intensification at a global scale. I selected the Boreal and Austral summer (JJA and DJF, respectively) to approximate the warm season, and to be consistent with previous studies of temperature-precipitation coupling (Trenberth and Shea 2005, Berg et al. 2015) that are foundational to this chapter. However, this season selection is problematic in the tropics and some subtropical regions, and confounds comparison with other relevant studies (e.g., Zscheischler and Seneviratne 2017). A parallel analysis using an alternative definition of summer—the hottest three consecutive months in each grid cell—can be found in Appendix C.9. I selected Tx as the temperature element in recognition that daily mean temperature could conflate different and potentially opposing physical processes driving daytime vs. nighttime temperature-precipitation correlations in many regions (Berg et al. 2015). Daily mean or minimum temperatures may be more salient elements for some regions and ecological processes. Identification of departure intensification in other economically and ecologically important coupled climate variables is a priority for future research. The finding that departure intensification is limited to variability correlations stronger than -0.5 provides a guideline for interrogating the observational record for other coupled variables that are subject to departure intensification. The impacts of climate departures are subject to the timescales over which maladaptation to unfamiliar local conditions is mitigated by gene flow, innovation, and other non-disruptive adaptive processes. In contrast to studies using a recent reference period (Giorgi and Bi 2009, Hawkins and Sutton 2012, Mora et al. 2013), my use of a pre-industrial baseline ignores local adaptation that has occurred during the industrial period, and may overstate the timing and magnitude of some of the disruptions associated with climate departures. The timescales of local adaptation are an important consideration in the assessment of the specific impacts of climate departures.  This chapter demonstrates that precipitation can have an important role in climate departures at interannual timescales, even though precipitation signals themselves are generally not projected to emerge from interannual climatic variability at the local scale (Mahlstein et al. 2012b). CMIP5 models generally agree on the direction of 21st-century regional precipitation 83 trends but differ substantially in magnitude, not only due to structural differences among climate models (Knutti and Sedláček 2012), but also due to the internal variability of each model run (Deser et al. 2012b). The sensitivity of departure intensification to precipitation trends highlights the importance of precipitation as a source of uncertainty in projections of ecological responses to climate change.  Departure intensification is a decadal-scale “compound event”, a class of climate extremes that arise from interactions and dependencies among multiple climate variables (Leonard et al. 2014). The case of departure intensification illustrates that some compound events are primarily multivariate and can remain undetected in univariate indices that synthesize multiple climate variables, such as the standardized precipitation-evapotranspiration index (Vicente-Serrano et al. 2010) and wet-bulb temperature (Knutson and Ploshay 2016). The World Climate Research Programme has established compound events as a research priority (Alexander et al. 2016), and techniques for identifying multivariate climate extremes are emerging (Flach et al. 2017).  However, investigations of compound events are sparse in many fields of climate change detection, impacts, and adaptation. This chapter demonstrates a form of compound extremes arising from historically unusual combinations of conditions. These compound anomalies can occur both as single-year events and long-term climatic shifts.  Identifying ecological and agricultural impacts associated with compound events and compound climate departures is an important area for further research.  Departures from natural climatic variability are a challenge to locally-adapted natural and agricultural ecosystems. Decoupling of the climate change trend from the dominant historical mode of interannual variability can accelerate the rate at which locally unfamiliar climates develop, which may be a limitation on the ability of some organisms and societies to adapt to climate change (Alpert and Simms 2002, Chevin et al. 2010, Deutsch et al. 2008, Gonzalez and Bell 2013, Heron et al. 2016, Vázquez et al. 2017). This chapter has focused on this effect in terrestrial summer temperature and precipitation. However, the cause of departure intensification—a climate change trajectory that is misaligned with natural variability—likely applies to other climatic drivers of ecosystem function. The potential for climate departures to be amplified in coupled climate variables is an important consideration for climate change risk assessments and adaptation planning.    84 Chapter 6: Conclusion 6.1 Research conclusions and significance Sigma dissimilarity—a multivariate standardized anomaly The standardized anomaly is one of the atmospheric sciences’ most basic metrics (Wilks 2006). Known more generally in statistics as the z-score (σ), standardized anomalies are calculated with respect to a sample (e.g., a time series of a climate variable) by subtracting the sample mean and dividing by the sample standard deviation.  Univariate standardized anomalies with respect to a historical baseline are a widely-used coarse-filter indicator of climate change risks (e.g., Battisti and Naylor 2009, Hansen et al. 2012, Hawkins and Sutton 2012), following the assumption that ecological and socioeconomic disruptions of climate change are proportional to the degree of departure from natural variability (Garcia et al. 2014).  However, multivariate standardized anomalies have received little attention in this context. There is a growing recognition of the necessity to detect multivariate anomalies and other forms of compound climate events (Leonard et al. 2014, Alexander et al. 2016, Flach et al. 2017). Sigma dissimilarity is a multivariate standardized anomaly that can be directly compared to univariate standardized anomalies and signal-to-noise ratios. As such, it facilitates a seamless expansion of the literature on climate departures (a.k.a. time of emergence) into multivariate analysis; Chapter 5 is the first multivariate analysis that I am aware of in this stream of literature. Further, the sigma dissimilarity metric removes the influence of dimensionality on anomaly measurements, which had previously confounded comparison of novelty assessments with difference variable sets, e.g., between the 8-variable analysis of Ordonez and Williams (2013) and the 4-variable analysis of Williams et al. (2007). Sigma dissimilarity is not a statistical innovation; it is simply a re-expression of the probability density of the chi-square statistic. Nevertheless, it is a novel and intuitive articulation of this statistic in the field of climate change risk assessment. Novel climates can emerge at all latitudes, especially in low topographic positions Chapter 3 is an assessment of general climatic novelty based on a simple and consistent characterization of climate.  This chapter built on the seminal global analysis of Williams et al. (2007) by assessing of end-of-21st-century novelty for North America at high spatial resolution and by refining the standardized Euclidean distance into an intuitive Mahalanobian metric called sigma dissimilarity. Like Williams et al. (2007), I found extensive novelty in end-of-21st-century 85 projections for the warm southern margin of the continent as well as the western Arctic. In addition, I detected localized novelty in lower topographic positions at all latitudes: by the end of the 21st century, novel climates are projected to emerge in 80% and 99% of ecoregions in the RCP4.5 and RCP8.5 emissions scenarios, respectively. Novel climates are limited to 7% of the continent’s area in RCP4.5, but are much more extensive in RCP8.5 (40% of area). The finding that continental-scale novel climates can emerge in any landscape emphasizes that model extrapolation is a concern for all bioclimatic projections of the 21st century.  The strong association of novel climates with low topographic positions provides ecological modelers with a rule of thumb for the portions of the landscape in which their projections require special scrutiny.  Novel climates are a source of error in mid-21st century BEC projections Chapter 4 is an assessment of the emergence of mid-21st-century climates with no analog in the 20th-century climates of British Columbia (BC), and the extent to which these novel climates are described by climate analogs elsewhere in North America.  The results suggest that a majority of the province’s area will remain free of novel climates over this time period, and therefore that BC’s ecological knowledge system, the Biogeoclimatic Ecosystem Classification, can remain the dominant source of climate analogs for mid-21st-century forest management planning horizons. Nevertheless, using linear novelty detection and random forest novelty indicators, I detected a robust pattern of novel climates in mid-21st-century climate projections at low elevations in the coastal, southern interior, and northeastern regions of BC.  There appears to be potential to inform forest management in some of these novel climates with analogs from adjacent states and provinces, though continental-scale novel climates are projected for the north coast of BC. These jurisdictionally novel climates produce two errors in projections of the future distribution of biogeoclimatic units: (1) underestimation of the magnitude of bioclimatic change and (2) underestimation of the uncertainty associated with inter- and intra-model variation in global climate model ensembles. Mitigating these errors will improve the effectiveness of BEC projections for climate change adaptation and communication.  Emergence of unfamiliar climates can be faster than indicated by individual climate variables.  Chapter 5 demonstrated that interactions among climate variables can produce larger and earlier departures from natural variability than are detectable in individual variables. Summer temperature (Tx) and precipitation (Pr) are negatively correlated in most terrestrial regions, such that interannual variability lies along an axis from warm-and-dry to cool-and-wet conditions. A 86 climate change trend perpendicular to this axis, towards warmer-wetter conditions, can depart more quickly from the range of natural variability than a warmer-drier trend. This multivariate “departure intensification” effect is evident in all six CMIP5 models that we examined: 23% (9-34%) of the global land area of each model exhibits a pronounced increase in 2σ anomalies in the Tx-Pr regime relative to Tx or Pr alone. Observational data suggest that Tx-Pr correlations are sufficient to produce departure intensification in distinct regions on all continents. Departures from the historical Tx-Pr regime may produce ecological disruptions, such as in plant-pathogen interactions and human disease systems, that could offset the drought mitigation benefits of increased precipitation. Assessment of departure intensification in climate model projections provides an early warning of ecological disruptions that might otherwise be unanticipated.  6.2 Future research directions Direct extrapolation detection for machine learning bioclimatic models.  The motivation of this dissertation is to improve the detection of ecologically-relevant climatic unfamiliarity. The challenge is that familiarity is highly contextual: a novel climate from the perspective of one species may be functionally familiar to another due to differences in the two species’ ecological tolerances. Machine learning algorithms are good at modeling these complex and localized ecological responses to climate. However, detection of extrapolation into novel (unfamiliar) conditions is non-trivial in bioclimatic applications of machine learning, to the extent that extrapolation detection methods are not available for even the most widely used bioclimatic modeling algorithms such as MaxEnt and Random Forest. In lieu of biologically-specific novelty detection, I used standardization against local interannual climatic variability as a coarse-filter indicator of the general ecological significance of climatic differences. The weakness of this approach is that it does not provide definitive (fine-filter) information for any one ecological system. The next frontier in anomaly and novelty detection is fine filter analysis with model-specific extrapolation detection. The novelty indicators proposed and validated in chapter 4 are a good first step in this direction. Importantly, these indicators are not limited to random forest, but can be expected to be equally informative for other modelling algorithms. Ensemble agreement is particularly useful as a general extrapolation indicator because it is measured directly from model output.  87 Random Forest provides numerous opportunities to measure model-specific climatic unfamiliarity. The proximity matrix is particularly promising. Random forest proximity is the proportion of terminal (leaf) nodes shared by two observations across the forest. The BEC proximity matrix constructed in chapter 4 for measuring analog similarity has other practical applications. For example, it can be used as a climatic dissimilarity matrix for climate-based seed transfer in BC, with all the advantages of a random forest BEC model over the currently proposed Euclidean distance approach (O’Neill et al. 2017). However, the effectiveness of proximities for extrapolation detection is unclear, and largely untested even in the broader literature on Random Forest. Another potential approach for Random Forest novelty detection in BEC projections is to classify based on the voting pattern, rather than just the majority vote. The emergence of an unusual combination of BEC units in the class votes for a location—such as votes for coastal subzones in the future climates of the bunchgrass zone of interior BC—may be an indicator of a novel climatic condition. Finally, the “dummy class” approach demonstrated by Rehfeldt et al. (2012) is promising and deserves further attention. It may be that none of these approaches provides definitive extrapolation detection in isolation. However, an ensemble of novelty indicators is likely to provide robust insights.  Evaluating the link between interannual climatic variability and adaptive capacity The foundational assumption of sigma dissimilarity’s ecological relevance is the “ICV hypothesis” that adaptive capacity is proportional to interannual climatic variability. More broadly, this assumption underpins the widespread use of interannual variability as a scaling factor for coarse-filter climate change risks. My cursory review of the theoretical, experimental, and observational support for the link between interannual climatic variability and adaptive capacity indicated that a comprehensive review and meta-analysis of the ICV hypothesis is overdue. Further, there is substantial opportunity to test this hypothesis with existing datasets. For example, the AdapTree dataset contains abundant genomic and phenotypic data for a broad sample of lodgepole pine and interior spruce provenances (Liepe et al. 2016, Yeaman et al. 2016, MacLachlan et al. 2017). These data provide an opportunity to test the relationship between interannual climatic variability and climatic tolerances in these two tree species.  Biogeoclimatic mapping of adjacent jurisdictions.  Analog identification and novelty detection are highly sensitive to the spatial classification of climates (Appendix B.5). This sensitivity suggests that biogeoclimatic mapping of adjacent 88 United States (Washington, Oregon, Idaho, Montana, and Wyoming) is essential to identification of analogs for the projected future climates of BC. This process is being undertaken by the BC government, using a random forest bioclimate model to spatialize an expert classification of USFS vegetation plots at the BEC subzone level. Extrapolation error is an important consideration in this initiative, since the spatial distribution of USFS vegetation plots is discontinuous. The extrapolation detection methods described in this dissertation can assist by indicating regions of the landscape that do not have sufficient training data to support BEC mapping.   Survey of climate variables that are susceptible to departure intensification Chapter 5 demonstrated that departure intensification has two requisite conditions: (1) strong correlation among climate variables and (2) a climate change trajectory that is out of alignment with (orthogonal to) the mode of this correlation. However, chapter 5 investigated departure intensification in only two climate elements of a single season. The next step in this area of research is to conduct a survey of the potential for departure intensification in a suite of other climate variables. This involves assessing variable correlations in observational data and then using climate models to assess the potential for orthogonal climate change; some correlated variables may be physically constrained to change along the mode of interannual variability. Another stream of research on departure intensification is its connection to specific ecological risks. For example, many fungal infections of plants are strongly associated with nighttime temperature and humidity at specific times of year (Garrett et al. 2015). Departure intensification may be a complementary lens through which to assess climate change risk in these specific systems. Finally, observational and experimental studies of the linkage between bivariate climate departures and ecological disruptions is required to establish the ecological relevance of departure intensification.  6.3 Closing remarks: The role of local ecological wisdom This dissertation has explored the theme of how climate change impacts the knowledge base of ecologists and ecosystem managers. The focus of this research has been on detection of unfamiliar climatic conditions in which accumulated observational and experiential knowledge of ecosystems can be uninformative and even misleading. Understanding the limits to the transferability of knowledge is foundational to the discipline of ecology and the practice of 89 ecosystem management. Many of the historical failures of ecosystem management have originated in the assumption that what has worked in one location will work in another. These hard lessons have instilled in ecologists the need for great care when generalizing knowledge spatially, between locations with differing climates. Climate change introduces the need for an equivalent ethic with respect to time. Historically skillful ecological models and ecosystem management practices can no longer be safely assumed to be valid. The erosion of local climatic stationarity is forcing ecologists and ecosystem managers to import ecological information from non-local climate analogs. However, many of the idiosyncratic aspects of local climates—such as chinook winds, lake effects and, most importantly, relative spatial differences across the landscape—can be expected to persist. The soils and physiography will remain. Further, the transition of ecological communities is likely to lag changes in climate by decades. These enduring features of the landscape place limits on the degree to which climate analogs from exotic biogeographical contexts can be informative. The task of judging the circumstances under which climate analogs are useful requires a nuanced understanding of the local ecological context and its history. Some aspects of local knowledge, both scientific and traditional, are undermined by the emergence of unfamiliar climates. Nevertheless, local ecological wisdom is likely to be ever more critical for navigating the changing climates of the 21st century.    90 Bibliography Abram, N. J., H. V. McGregor, J. E. Tierney, M. N. Evans, N. P. McKay, D. S. Kaufman, K. Thirumalai, B. Martrat, H. Goosse, S. J. Phipps, E. J. Steig, K. H. Kilbourne, C. P. Saenger, J. Zinke, G. Leduc, J. A. Addison, P. G. Mortyn, M.-S. Seidenkrantz, M.-A. Sicre, K. Selvaraj, H. L. Filipsson, R. Neukom, J. Gergis, M. A. J. Curran, and L. von Gunten. 2016. Early onset of industrial-era warming across the oceans and continents. Nature 536:411–418. Ackerly, D. D., S. R. Loarie, W. K. Cornwell, S. B. Weiss, H. Hamilton, R. Branciforte, and N. J. B. Kraft. 2010. The geography of climate change: Implications for conservation biogeography. Diversity and Distributions 16:476–487. Addo-Bediako, A., S. L. Chown, and K. J. Gaston. 2000. Thermal tolerance , climatic variability and latitude. Proceedings of the Royal Society B: Biological Sciences 267:739–745. Aitken, S. N., and M. C. Whitlock. 2013. Assisted gene flow to facilitate local adaptation to climate change. Annual Review of Ecology, Evolution, and Systematics 44:367–388. Aitken, S. N., S. Yeaman, J. A. Holliday, T. Wang, and S. Curtis-McLane. 2008. Adaptation, migration or extirpation: climate change outcomes for tree populations. Evolutionary Applications 1:95–111. Alexander, L., X. Zhang, G. Hegerl, S. Seneviratne, A. Behrangi, E. Fischer, O. Martius, F. Otto, J. Sillmann, and R. Vautard. 2016. Implementation Plan for WCRP Grand Challenge on Understanding and Predicting Weather and Climate Extremes: The “Extremes Grand Challenge.” Allen, C. D., D. D. Breshears, and N. G. McDowell. 2015. On underestimation of global vulnerability to tree mortality and forest die-off from hotter drought in the Anthropocene. Ecosphere 6:art129. Alpert, P., and E. L. Simms. 2002. The relative advantages of plasticity and fixity in different environments: When is it good for a plant to adjust? Evolutionary Ecology 16:285–297. Anderson, J. T., A. M. Panetta, and T. Mitchell-Olds. 2012. Evolutionary and ecological responses to anthropogenic climate change. Plant Physiology 160:1728–1740. Baker, B., H. Diaz, W. Hargrove, and F. Hoffman. 2009. Use of the Köppen-Trewartha climate classification to evaluate climatic refugia in statistically derived ecoregions for the People’s Republic of China. Climatic Change 98:113–131. Battisti, D. S., and R. L. Naylor. 2009. Historical warnings of future food insecurity with unprecedented seasonal heat. Science 323:240–245. Beaumont, L. J., A. Pitman, S. Perkins, N. E. Zimmermann, N. G. Yoccoz, and W. Thuiller. 2011. Impacts of climate change on the world’s most exceptional ecoregions. Proceedings of the National Academy of Sciences 108:2306–2311. Berg, A., B. R. Lintner, K. Findell, S. I. Seneviratne, B. van den Hurk, A. Ducharne, F. Cheruy, S. Hagemann, D. M. Lawrence, S. Malyshev, A. Meier, and P. Gentine. 2015. Interannual coupling between summertime surface temperature and precipitation over land: Processes and implications for climate change. Journal of Climate 28:1308–1328. 91 Blois, J. L., J. W. Williams, M. C. Fitzpatrick, S. T. Jackson, and S. Ferrier. 2013. Space can substitute for time in predicting climate-change effects on biodiversity. Proceedings of the National Academy of Sciences 110:9374–9379. Bolte, A., C. Ammer, M. Löf, P. Madsen, G. J. Nabuurs, P. Schall, P. Spathelf, and J. Rock. 2009. Adaptive forest management in central Europe: Climate change impacts, strategies and integrative concept. Scandinavian Journal of Forest Research 24:473–482. Braganza, K., D. J. Karoly, and J. M. Arblaster. 2004. Diurnal temperature range as an index of global climate change during the twentieth century. Geophysical Research Letters 31:2–5. Breiman, L. 2001. Random forests. Machine Learning 45:5–32. Cameron, A. D. 2015. Building resilience into sitka spruce (Picea sitchensis (Bong.) Carr.) forests in Scotland in response to the threat of climate change. Forests 6:398–415. Cannon, A. J. 2012. Köppen versus the computer: Comparing Köppen-Geiger and multivariate regression tree climate classifications in terms of climate homogeneity. Hydrology and Earth System Sciences 16:217–229. Cannon, A. J. 2017. Multivariate quantile mapping bias correction: an N-dimensional probability density function transform for climate model simulations of multiple variables. Climate Dynamics. Cannon, A. J., S. R. Sobie, and T. Q. Murdock. 2015. Bias correction of GCM precipitation by quantile mapping: How well do methods preserve changes in quantiles and extremes? Journal of Climate 28:6938–6959. Chevin, L., R. Lande, and G. M. Mace. 2010. Adaptation, plasticity, and extinction in a changing environment: towards a predictive theory. PLoS Biology 8:e1000357. Christensen, J. H., B. Hewitson, A. Busuioc, A. Chen, X. Gao, I. Held, R. Jones, R. K. Kolli, W.-T. Kwon, R. Laprise, V. M. Rueda, L. Mearns, C. G. Menéndez, J. Räisänen, A. Rinke, A. Sarr, and P. Whetton. 2007. Regional Climate Projections. Pages 847–940in S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller, editors.Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Clifton, L., D. A. Clifton, Y. Zhang, P. Watkinson, L. Tarassenko, H. Yin, and S. Member. 2014. Probabilistic Novelty Detection With Support Vector Machines 63:455–467. Corlett, R. T. 2011. Impacts of warming on tropical lowland rainforests. Trends in Ecology and Evolution 26:606–613. Coumou, D., and A. Robinson. 2013. Historic and future increase in the global land area affected by monthly heat extremes. Environmental Research Letters 8:34018. Daly, C., M. Halbleib, J. I. Smith, W. P. Gibson, M. K. Doggett, G. H. Taylor, and P. P. Pasteris. 2008. Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States. International Journal of Climatology 28:2031–2064. Dawson, T. P., S. T. Jackson, J. I. House, I. C. Prentice, and G. M. Mace. 2011. Beyond predictions: biodiversity conservation in a changing climate. Science 332:53–58. 92 Deser, C., R. Knutti, S. Solomon, and A. S. Phillips. 2012a. Communication of the role of natural variability in future North American climate. Nature Climate Change 2:775–779. Deser, C., A. Phillips, V. Bourdette, and H. Teng. 2012b. Uncertainty in climate change projections: The role of internal variability. Climate Dynamics 38:527–546. Désir, C., S. Bernard, C. Petitjean, and L. Heutte. 2013. One class random forests. Pattern Recognition 46:3490–3506. Deutsch, C. A., J. J. Tewksbury, R. B. Huey, K. S. Sheldon, C. K. Ghalambor, D. C. Haak, and P. R. Martin. 2008a. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences 105:6668–6672. Deutsch, C. A., J. J. Tewksbury, R. B. Huey, K. S. Sheldon, C. K. Ghalambor, D. C. Haak, and P. R. Martin. 2008b. Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences of the United States of America 105:6668–6672. Diffenbaugh, N. S., and M. Scherer. 2011. Observational and model evidence of global emergence of permanent, unprecedented heat in the 20th and 21st centuries. Climatic Change 107:615–624. Director, H., and L. Bornn. 2015. Connecting point-level and gridded moments in the analysis of climate data. Journal of Climate 28:3496–3510. Drake, J. M., C. Randin, and A. Guisan. 2006. Modelling ecological niches with support vector machines. Journal of Applied Ecology 43:424–432. Ecological Stratification Working Group (ESWG). 1995. A National Ecological Framework for Canada. Ottawa. Elith, J., M. Kearney, and S. Phillips. 2010. The art of modelling range-shifting species. Methods in Ecology and Evolution 1:330–342. Elith, J., and J. Leathwick. 2009. Species distribution models: ecological explanation and prediction across space and time. Annual Review of Ecology, Evolution, and Systematics 40:677–697. Elmendorf, S. C., G. H. R. Henry, R. D. Hollister, A. M. Fosaa, W. A. Gould, L. Hermanutz, A. Hofgaard, I. S. Jónsdóttir, J. C. Jorgenson, E. Lévesque, B. Magnusson, U. Molau, I. H. Myers-Smith, S. F. Oberbauer, C. Rixen, C. E. Tweedie, and M. D. Walker. 2015. Experiment, monitoring, and gradient methods used to infer climate change effects on plant communities yield consistent patterns. Proceedings of the National Academy of Sciences 112:448–452. Environment Yukon. 2013. Yukon Ecological and Landscape Classification (ELC) Guidelines Version 1.0. Whitehorse, YT. Etterson, J. R., and R. G. Shaw. 2001. Constraint to adaptive evolution in response to global warming. Science 294:151–154. Fasano, G., and A. Franceschini. 1987. A multidimensional version of the Kolmogorov-Smirnov test. Monthly Notices of the Royal Astronomical Society 225:155–170. Fitzpatrick, M. C., and W. W. Hargrove. 2009. The projection of species distribution models and 93 the problem of non-analog climate. Biodiversity and Conservation 18:2255–2261. Flach, M., F. Gans, A. Brenning, J. Denzler, M. Reichstein, E. Rodner, S. Bathiany, P. Bodesheim, Y. Guanche, S. Sippel, and M. D. Mahecha. 2017. Multivariate Anomaly Detection for Earth Observations: A Comparison of Algorithms and Feature Extraction Techniques. Earth System Dynamics 8:677–696. Forster, P. M., T. Andrews, P. Good, J. M. Gregory, L. S. Jackson, and M. Zelinka. 2013. Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models. Journal of Geophysical Research Atmospheres 118:1139–1150. Frame, D., M. Joshi, E. Hawkins, L. J. Harrington, and M. De Roiste. 2017. Population-based emergence of unfamiliar climates. Nature Climate Change 7:407–412. Franks, S. J., J. J. Weber, and S. N. Aitken. 2014. Evolutionary and plastic responses to climate change in terrestrial plant populations. Evolutionary Applications 7:123–139. García-López, J. M., and C. Allué. 2013. Modelling future no-analogue climate distributions: A world-wide phytoclimatic niche-based survey. Global and Planetary Change 101:1–11. Garcia, R. A., M. Cabeza, C. Rahbek, and M. B. Araujo. 2014. Multiple Dimensions of Climate Change and Their Implications for Biodiversity. Science 344:1247579–1247579. Garrett, K. A., M. Nita, E. D. De Wolf, P. D. Esker, L. Gomez-Montano, and A. H. Sparks. 2015. Plant pathogens as indicators of climate change. Pages 325–338in T. Letcher, editor.Climate Change: Observed Impacts on Planet Earth. Elsevier Science, Oxford. Giorgi, F., and X. Bi. 2009. Time of emergence (TOE) of GHG-forced precipitation change hot-spots. Geophysical Research Letters 36:L06709. Goberville, E., G. Beaugrand, N. C. Hautek??ete, Y. Piquot, and C. Luczak. 2015. Uncertainties in the projection of species distributions related to general circulation models. Ecology and Evolution 5:1100–1116. Gonzalez, A., and G. Bell. 2013. Evolutionary rescue and adaptation to abrupt environmental change depends upon the history of stress. Philosophical Transactions: Biological Sciences 368:41740110. Gotelli, N. J., and W. Ulrich. 2012. Statistical challenges in null model analysis. Oikos 121:171–180. Grenier, P., A. C. Parent, D. Huard, F. Anctil, and D. Chaumont. 2013. An assessment of six dissimilarity metrics for climate analogs. Journal of Applied Meteorology and Climatology 52:733–752. Guttman, N. B. 1999. Accepting the standardized precipitation index: a calculation algorithm. Journal of the American Water Resources Association 35:311–322. Haeussler, S. 2011. Rethinking biogeoclimatic ecosystem classification for a changing world. Environmental Reviews 19:254–277. Hamann, A., and S. N. Aitken. 2013. Conservation planning under climate change: Accounting for adaptive potential and migration capacity in species distribution models. Diversity and Distributions 19:268–280. 94 Hamann, A., D. R. Roberts, Q. E. Barber, C. Carroll, and S. E. Nielsen. 2015. Velocity of climate change algorithms for guiding conservation and management. Global Change Biology 21:997–1004. Hamann, A., and T. Wang. 2006. Potential effects of climate change on ecosystem and tree species distribution in British Columbia. Ecology 87:2773–2786. Hansen, J., M. Sato, and R. Ruedy. 2012. Perception of climate change. Proceedings of the National Academy of Sciences 109:E2415–E2423. Hao, Z., and A. AghaKouchak. 2013. Multivariate Standardized Drought Index: A parametric multi-index model. Advances in Water Resources 57:12–18. Hargrove, W. W., and F. M. Hoffman. 2005. Potential of multivariate quantitative methods for delineation and visualization of ecoregions. Environmental Management 34:39–60. Harris, I., P. D. Jones, T. J. Osborn, and D. H. Lister. 2014. Updated high-resolution grids of monthly climatic observations - the CRU TS3.10 Dataset. International Journal of Climatology 34:623–642. Hasselmann, K. 1993. Optimal fingerprints for the detection of time-dependent climate change. Hawkins, E., and R. Sutton. 2009. The potential to narrow uncertainty in regional climate predictions. Bulletin of the American Meteorological Society 90:1095–1107. Hawkins, E., and R. Sutton. 2012. Time of emergence of climate signals. Geophysical Research Letters 39:1–6. Henson, S. A., C. Beaulieu, T. Ilyina, J. G. John, M. Long, R. Séférian, J. Tjiputra, and J. L. Sarmiento. 2017. Rapid emergence of climate change in environmental drivers of marine ecosystems. Nature Communications 8:14682. Heron, S. F., J. A. Maynard, R. van Hooidonk, and C. M. Eakin. 2016. Warming Trends and Bleaching Stress of the World’s Coral Reefs 1985 – 2012. Nature Scientific Reports 6:38402. Hogg, E. H., and P. A. Hurdle. 1995. The aspen parkland in western Canada: A dry-climate analogue for the future boreal forest? Water, Air, and Soil Pollution 82:391–400. IPCC. 2013. Summary for Policymakers. Page in T. F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex, and P. M. Midgley, editors. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Isaac-Renton, M. G., D. R. Roberts, A. Hamann, and H. Spiecker. 2014. Douglas-fir plantations in Europe: A retrospective test of assisted migration to address climate change. Global Change Biology 20:2607–2617. Jackson, S. T., J. L. Betancourt, R. K. Booth, and S. T. Gray. 2009a. Ecology and the ratchet of events: Climate variability, niche dimensions, and species distributions. Proceedings of the National Academy of Sciences 106:19685–19692. Jackson, S. T., J. L. Betancourt, R. K. Booth, and S. T. Gray. 2009b. Ecology and the ratchet of events: Climate variability, niche dimensions, and species distributions. Proceedings of the 95 National Academy of Sciences 106:19685–19692. Janzen, D. H. 1967. Why Mountain Passes are Higher in the Tropics. The American Naturalist 101:233–249. Jones, P. D., T. J. Osborn, K. R. Briffa, C. K. Folland, B. Horton, L. V Alexander, D. E. Parker, and N. A. Rayner. 2001. Adjusting for sampling density in grid-box land and ocean surface temperature time series. Journal of Geophysical Research 106:3371–3380. Kawecki, T. J., and D. Ebert. 2004. Conceptual issues in local adaptation. Ecology Letters 7:1225–1241. Kay, J. E., C. Deser, A. Phillips, A. Mai, C. Hannay, G. Strand, J. M. Arblaster, S. C. Bates, G. Danabasoglu, J. Edwards, M. Holland, P. Kushner, J. F. Lamarque, D. Lawrence, K. Lindsay, A. Middleton, E. Munoz, R. Neale, K. Oleson, L. Polvani, and M. Vertenstein. 2015. The community earth system model (CESM) large ensemble project : A community resource for studying climate change in the presence of internal climate variability. Bulletin of the American Meteorological Society 96:1333–1349. Keller, K. M., F. Joos, and C. C. Raible. 2014. Time of emergence of trends in ocean biogeochemistry. Biogeosciences 11:3647–3659. Knutson, T. R., and J. J. Ploshay. 2016. Detection of anthropogenic influence on a summertime heat stress index. Climatic Change 138:25–39. Knutti, R., D. Masson, and A. Gettelman. 2013. Climate model genealogy: Generation CMIP5 and how we got there. Geophysical Research Letters 40:1194–1199. Knutti, R., and J. Sedláček. 2012. Robustness and uncertainties in the new CMIP5 climate model projections. Nature Climate Change 3:369–373. Kobayashi, S., Y. Ota, Y. Harada, A. Ebita, M. Moriya, H. Onada, K. Onogi, H. Kamahori, C. Kobayashi, H. Endo, K. Miyaoka, and K. Takahashi. 2015. The JRA-55 reanalysis: General specifications and basic characteristics. Journal of the Meteorological Society of Japan. Ser. II 93:5–48. Kopf, S., M. Ha-Duong, and S. Hallegatte. 2008. Using maps of city analogues to display and interpret climate change scenarios and their uncertainty. Natural Hazards and Earth System Science 8:905–918. Köppen, W. 1936. Das geographische System der Klimate. Handbuch der Klimatologie:7–30. Kremer, A., O. Ronce, J. J. Robledo-Arnuncio, F. Guillaume, G. Bohrer, R. Nathan, J. R. Bridle, R. Gomulkiewicz, E. K. Klein, K. Ritland, A. Kuparinen, S. Gerber, and S. Schueler. 2012. Long-distance gene flow and adaptation of forest trees to rapid climate change. Ecology Letters 15:378–392. Lehner, F., and T. F. Stocker. 2015. From local perception to global perspective. Nature Climate Change 5:731–734. Leites, L. P., A. P. Robinson, G. E. Rehfeldt, J. D. Marshall, and N. L. Crookston. 2012. Height-growth response to changes in climate differ among populations of interior Douglas-fir: a novel analysis of provenance-test data. Ecological Applications 22:154–165. Leonard, M., S. Westra, A. Phatak, M. Lambert, B. van den Hurk, K. Mcinnes, J. Risbey, S. 96 Schuster, D. Jakob, and M. Stafford-Smith. 2014. A compound event framework for understanding extreme impacts. Wiley Interdisciplinary Reviews: Climate Change 5:113–128. Liepe, K. J., A. Hamann, P. Smets, C. R. Fitzpatrick, and S. N. Aitken. 2016. Adaptation of lodgepole pine and interior spruce to climate: Implications for reforestation in a warming world. Evolutionary Applications 9:409–419. Loarie, S. R., P. B. Duffy, H. Hamilton, G. P. Asner, C. B. Field, and D. D. Ackerly. 2009. The velocity of climate change. Nature 462:1052–1055. Lombardozzi, D., G. B. Bonan, and D. W. Nychka. 2014. The emerging anthropogenic signal in land–atmosphere carbon-cycle coupling. Nature Climate Change 4:796–800. Lyu, K., X. Zhang, J. A. Church, A. B. A. Slangen, and J. Hu. 2014. Time of emergence for regional sea-level change. Nature Climate Change 4:1006–1010. MacLachlan, I. R., T. Wang, A. Hamann, P. Smets, and S. N. Aitken. 2017. Selective breeding of lodgepole pine increases growth and maintains climatic adaptation. Forest Ecology and Management 391:404–416. Mahalanobis, P. C. 1936. On the generalized distance in statistics. Proceedings of the National Institute of Sciences of India 2:49–55. Mahlstein, I., J. S. Daniel, and S. Solomon. 2013. Pace of shifts in climate regions increases with global temperature. Nature Climate Change 3:739–743. Mahlstein, I., G. Hegerl, and S. Solomon. 2012a. Emerging local warming signals in observational data. Geophysical Research Letters 39:L21711. Mahlstein, I., R. Knutti, S. Solomon, and R. W. Portmann. 2011. Early onset of significant local warming in low latitude countries. Environmental Research Letters 6:34009. Mahlstein, I., R. W. Portmann, J. S. Daniel, S. Solomon, and R. Knutti. 2012b. Perceptible changes in regional precipitation in a future climate. Geophysical Research Letters 39:L05701. Mahony, C. R., A. J. Cannon, T. Wang, and S. N. Aitken. 2017. A closer look at novel climates: new methods and insights at continental to landscape scales. Global Change Biology 23:3934–3955. Mann, M. E., R. S. Bradley, and M. K. Hughes. 1998. Global-scale temperature patterns and climate forcing over the past six centuries. Nature 392:779–787. Martínez-Botí, M. A., G. L. Foster, T. B. Chalk, E. J. Rohling, P. F. Sexton, D. J. Lunt, R. D. Pancost, M. P. S. Badger, and D. N. Schmidt. 2015. Plio-Pleistocene climate sensitivity evaluated using high-resolution CO2 records. Nature 518:49–54. Mcgraw, J. B., J. B. Turner, S. Souther, C. C. Bennington, M. C. Vavrek, G. R. Shaver, and N. Fetcher. 2015. Northward displacement of optimal climate conditions for ecotypes of Eriophorum vaginatum L. across a latitudinal gradient in Alaska. Global Change Biology 21:3827–3835. McKenney, D. W., M. F. Hutchiinson, P. Papadopol, K. Lawrence, J. Pedlar, K. Campbell, E. Milewska, R. F. Hopkinson, D. Price, and T. Owen. 2011. Customized spatial climate 97 models for North America. Bulletin of the American Meteorological Society 92:1611–1622. Mearns, L. O., and M. Hulme. 2001. Climate Scenario Development. Climate Change 2001: The Physical Science Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change:739–768. Meehl, G. A., W. M. Washington, J. M. Arblaster, A. Hu, H. Teng, J. E. Kay, A. Gettelman, D. M. Lawrence, B. M. Sanderson, and W. G. Strand. 2013. Climate change projections in CESM1(CAM5) compared to CCSM4. Journal of Climate 26:6287–6308. Mesgaran, M. B., R. D. Cousens, and B. L. Webber. 2014. Here be dragons: A tool for quantifying novelty due to covariate range and correlation change when projecting species distribution models. Diversity and Distributions 20:1147–1159. Millar, C. I., N. L. Stephenson, and S. L. Stephens. 2007. Climate change and forests of the future: Managing in the face of uncertanity. Ecological Applications 17:2145–2151. Mitchell, T. D., and P. D. Jones. 2005. An improved method of constructing a database of monthly climate observations and associated high-resolution grids. International Journal of Climatology 25:693–712. Mora, C., A. G. Frazier, R. J. Longman, R. S. Dacks, M. M. Walton, E. J. Tong, J. J. Sanchez, L. R. Kaiser, Y. O. Stender, J. M. Anderson, C. M. Ambrosino, I. Fernandez-Silva, L. M. Giuseffi, and T. W. Giambelluca. 2013. The projected timing of climate departure from recent variability. Nature 502:183–187. Mortimore, M. 2010. Adapting to drought in the Sahel: Lessons for climate change. Wiley Interdisciplinary Reviews: Climate Change 1:134–143. O’Neill, G. A., T. Wang, N. Ukraintez, L. Charleson, L. Mcauley, A. Yankcuhk, and S. Zedel. 2017. A Proposed Climate-based Seed Transfer System for British Columbia. Prov. B.C., Victoria, B.C. Tech. Rep. 099. Olson, D. M., E. Dinerstein, E. D. Wikramanayake, N. D. Burgess, G. V. N. Powell, E. C. Underwood, J. A. D’amico, I. Itoua, H. E. Strand, J. C. Morrison, C. J. Loucks, T. F. Allnutt, T. H. Ricketts, Y. Kura, J. F. Lamoreux, W. W. Wettengel, P. Hedao, and K. R. Kassem. 2001. Terrestrial ecoregions of the world: A new map of life on Earth. BioScience 51:933–938. Omernik, J. M. 1987. Map Supplement: Ecoregions of the Conterminous United States. Annals of the Association of American Geographers 77:118–125. Ordonez, A., and J. W. Williams. 2013. Projected climate reshuffling based on multivariate climate-availability, climate-analog, and climate-velocity analyses: Implications for community disaggregation. Climatic Change 119:659–675. Ordonez, A., J. W. Williams, and J. Svenning. 2016. Mapping climatic mechanism likely to favour the emergence of novel communities. Nature Climate Change Letters; O:1–8. Osborne, J. W., and A. B. Costello. 2004. Sample size and subject to item ratio in principal components analysis and exploratory factor analysis. Practical Assessment, Research & Evaluation 9:1–13. Parmesan, C. 2006. Ecological and Evolutionary Responses to Recent Climate Change. Annual 98 Review of Ecology, Evolution, and Systematics 37:637–669. Patz, J. A., A. K. Githeko, J. P. Mccarty, S. Hussein, U. Confalonieri, and N. De Wet. 2003. Climate change and infectious diseases. Pages 103–132in A. McMichael, D. Campbell-Lendrum, C. Corvalan, A. Ebi, K. Githeko, J. Scheraga, and A. Woodward, editors.Climate Change and Human Health. Risks and Responses. World Health Organization, Geneva, Switzerland. Peterson, A. T., J. Soberon, R. G. Pearson, R. P. Anderson, E. Martinez-Meyer, M. Nakamura, and M. B. Araujo. 2011. Ecological Niches and Geographic Distributions. Princeton University Press, Princeton. Phillips, S. J., R. P. Anderson, and R. E. Schapire. 2006. Maximum entropy modeling of species geographic distributions. Ecological Modelling 190:231–259. Pickett, S. T. A. 1989. Space-for-time substitution as an alternative to long-term studies. Pages 110–135in G. E. Likens, editor.Long-Term Studies in Ecology: Approaches and Alternatives. Springer-Verlag New York Inc., New York. Pintor, A. F. V., L. Schwarzkopf, and A. K. Krockenberger. 2015. Rapoport’s rule: Do Climatic Variability gradients shape range extent? Ecological Monographs 85:643–659. Pojar, J., K. Klinka, and D. V. Meidinger. 1987. Biogeoclimatic ecosystem classification in British Columbia. Forest Ecology and Management 22:119–154. Potter, K. M., and W. W. Hargrove. 2012. Determining suitable locations for seed transfer under climate change: A global quantitative method. New Forests 43:581–599. Puettmann, K. J., K. D. Coates, and C. Messier. 2009. A Critique of Silviculture: Managing for Complexity. Island Press, Washington, DC. Radeloff, V. C., J. W. Williams, B. L. Bateman, K. D. Burke, S. K. Carter, E. S. Childress, K. J. Cromwell, C. Gratton, A. O. Hasley, B. M. Kraemer, A. W. Latzka, E. Marin-Spiotta, C. D. Meine, S. E. Munoz, T. M. Neeson, A. M. Pidgeon, A. R. Rissman, R. J. Rivera, L. M. Szymanski, and J. Usinowicz. 2015. The rise of novelty in ecosystems. Ecological Applications 25:2051–2068. Rastetter, E. B. 1996. Validating models of ecosystem response to global change. BioScience 46:190–198. Rastetter, E. B., J. D. Aber, D. P. C. Peters, D. S. Ojima, and I. C. Burke. 2003. Using mechanistic models to scale ecological processes across space and time. BioScience 53:68–76. Real, R., A. L. Márquez, J. Olivero, and A. Estrada. 2010. Species distribution models in climate change scenarios are still not useful for informing policy planning: An uncertainty assessment using fuzzy logic. Ecography 33:304–314. Rehfeldt, G. E., N. L. Crookston, C. Saenz-Romero, and E. M. Campbell. 2012. North American vegetation model for land-use planning in a changing climate: a solution to large classification problems. Ecological Applications 22:119–141. Rehfeldt, G. E., and B. C. Jaquish. 2010. Ecological impacts and management strategies for western larch in the face of climate-change. Mitigation and Adaptation Strategies for Global 99 Change 15:283–306. Rehfeldt, G. E., L. P. Leites, J. Bradley St Clair, B. C. Jaquish, C. Sáenz-Romero, J. López-Upton, and D. G. Joyce. 2014. Comparative genetic responses to climate in the varieties of Pinus ponderosa and Pseudotsuga menziesii: Clines in growth potential. Forest Ecology and Management 324:138–146. Rivas-Martínez, S., S. Rivas-Sáenz, and A. Penas-Merino. 2011. Worldwide bioclimatic classification system. Global Geobotany 1:1–638. Roberts, D. R., and A. Hamann. 2012. Predicting potential climate change impacts with bioclimate envelope models: A palaeoecological perspective. Global Ecology and Biogeography 21:121–133. Rogelj, J., M. den Elzen, N. Höhne, T. Fransen, H. Fekete, H. Winkler, R. Schaeffer, F. Sha, K. Riahi, and M. Meinshausen. 2016. Paris Agreement climate proposals need a boost to keep warming well below 2 °C. Nature 534:631–639. Rogelj, J., M. Meinshausen, and R. Knutti. 2012. Global warming under old and new scenarios using IPCC climate sensitivity range estimates. Nature Climate Change 2:248–253. Rubel, F., and M. Kottek. 2010. Observed and projected climate shifts 1901-2100 depicted by world maps of the Köppen-Geiger climate classification. Meteorologische Zeitschrift 19:135–141. Saucier, J. P., A. Robitaille, and J. F. Bergeron. 2003. Vegetation Zones and Bioclimatic Domains in Québec. Schneider, U., A. Becker, P. Finger, A. Meyer-Christoffer, M. Ziese, and B. Rudolf. 2014. GPCC’s new land surface precipitation climatology based on quality-controlled in situ data and its role in quantifying the global water cycle. Theoretical and Applied Climatology 115:15–40. Scoccimarro, E., S. Gualdi, A. Bellucci, M. Zampieri, and A. Navarra. 2013. Heavy precipitation events in a warmer climate: Results from CMIP5 models. Journal of Climate 26:7902–7911. Settele, J., R. Scholes, R. Betts, S. Bunn, P. Leadley, D. Nepstad, J. T. Overpeck, and M. A. Taboada. 2014. Terrestrial and inland water systems. Pages 271–359in  and L. L. W. Field, C.B., V.R. Barros, D.J. Dokken, K.J. Mach, M.D. Mastrandrea, T.E. Bilir, M. Chatterjee, K.L. Ebi, Y.O. Estrada, R.C. Genova, B. Girma, E.S. Kissel, A.N. Levy, S. MacCracken, P.R. Mastrandrea, editor.Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part A: Global and Sectoral Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. Seymour, R. S., A. S. White, and P. G. DeMaynadier. 2002. Natural disturbance regimes in northeastern North America—evaluating silvicultural systems using natural scales and frequencies. Forest Ecology and Management 155:357–367. Sippel, S., J. Zscheischler, M. Heimann, F. E. L. Otto, J. Peters, and M. D. Mahecha. 2015. Quantifying changes in climate variability and extremes: Pitfalls and their overcoming. Geophysical Research Letters 42:9990–9998. Spittlehouse, D. L., and R. B. Stewart. 2003. Adaptation to climate change in forest 100 management. BC Journal of Ecosystems and Management 4:1–11. Stevens, G. C. 1989. The latitudinal gradient in geographical range: How so many species coexist in the tropics. The American Naturalist 133:240–256. Sui, Y., X. Lang, and D. Jiang. 2014. Time of emergence of climate signals over China under the RCP4.5 scenario. Climatic Change 125:265–276. Sunday, J. M., A. E. Bates, and N. K. Dulvy. 2012. Thermal tolerance and the global redistribution of animals. Nature Climate Change 2:686–690. Taylor, K. E., R. J. Stouffer, and G. A. Meehl. 2012. An overview of CMIP5 and the experiment design. Bulletin of the American Meteorological Society 93:485–498. Templer, P. H., A. B. Reinmann, R. Sanders-Demott, P. O. Sorensen, S. M. Juice, F. Bowles, L. E. Sofen, J. L. Harrison, I. Halm, L. Rustad, M. E. Martin, and N. Grant. 2017. Climate Change Across Seasons Experiment (CCASE): A New method for simulating future Climate in seasonally snow-covered ecosystems. PLoS ONE 12:e0171928. Thuiller, W., L. Brotons, M. B. Araujo, and S. Lavorel. 2004. Effects of restricting environmental range of data to project current and future species distributions. Ecography 27:165–172. Torregrosa, A., M. D. Taylor, L. E. Flint, and A. L. Flint. 2013. Present, Future, and Novel Bioclimates of the San Francisco, California Region. PLoS ONE 8:1–14. Trenberth, K. E., and D. J. Shea. 2005. Relationships between precipitation and surface temperature. Geophysical Research Letters 32:1–4. Turner, N. J., and H. Clifton. 2009. “It’s so different today”: Climate change and indigenous lifeways in British Columbia, Canada. Global Environmental Change 19:180–190. Turner, N. J., M. B. Ignace, and R. Ignace. 2000. Traditional ecological knowledge and wisdom of aboriginal peoples in British Columbia. Ecological Applications 10:1275–1287. Vázquez, D. P., E. Gianoli, W. F. Morris, and F. Bozinovic. 2017. Ecological and evolutionary impacts of changing climatic variability. Biological Reviews 92:22–42. Vicente-Serrano, S. M., S. Beguería, and J. I. López-Moreno. 2010. A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index. Journal of Climate 23:1696–1718. Vilà-Cabrera, A., L. Coll, J. Martínez-vilalta, and J. Retana. 2018. Forest management for adaptation to climate change in the Mediterranean basin: A synthesis of evidence. Forest Ecology and Management 407:16–22. van Vuuren, D. P., J. Edmonds, M. Kainuma, K. Riahi, A. Thomson, K. Hibbard, G. C. Hurtt, T. Kram, V. Krey, J. F. Lamarque, T. Masui, M. Meinshausen, N. Nakicenovic, S. J. Smith, and S. K. Rose. 2011. The representative concentration pathways: An overview. Climatic Change 109:5–31. Wang, T., E. M. Campbell, G. A. O’Neill, and S. N. Aitken. 2012. Projecting future distributions of ecosystem climate niches: Uncertainties and management applications. Forest Ecology and Management 279:128–140. Wang, T., A. Hamann, D. Spittlehouse, and C. Carroll. 2016. Locally downscaled and spatially 101 customizable climate data for historical and future periods for North America. PLoS ONE 11:e0156720. Wang, T., G. A. O’Neill, and S. N. Aitken. 2010. Integrating environmental and genetic effects to predict responses of tree populations to climate. Ecological Applications 20:153–163. Webber, B. L., C. J. Yates, D. C. Le Maitre, J. K. Scott, D. J. Kriticos, N. Ota, A. Mcneill, J. J. Le Roux, and G. F. Midgley. 2011. Modelling horses for novel climate courses: Insights from projecting potential distributions of native and alien Australian acacias with correlative and mechanistic models. Diversity and Distributions 17:978–1000. Wiens, J. A., D. Stralberg, D. Jongsomjit, C. A. Howell, and M. A. Snyder. 2009. Niches, models, and climate change: Assessing the assumptions and uncertainties. Proceedings of the National Academy of Sciences 106:19729–19736. Wilby, R. L., S. P. Charles, E. Zorita, B. Timbal, P. Whetton, and L. O. Mearns. 2004. Guidelines for Use of Climate Scenarios Developed from Statistical Downscaling Methods. Analysis 27:1–27. Wilks, D. S. 2006. Statistical Methods in the Atmospheric Sciences. Second Ed. Academic Press. Williams, J. W., and S. T. Jackson. 2007. Novel climates, no-analog communities, and ecological surprises. Frontiers in Ecology and the Environment 5:475–482. Williams, J. W., S. T. Jackson, and J. E. Kutzbach. 2007. Projected distributions of novel and disappearing climates by 2100 AD. Proceedings of the National Academy of Sciences 104:5738–5742. Williams, M. I., and R. K. Dumroese. 2013. Preparing for Climate Change: Forestry and Assisted Migration. Journal of Forestry 111:287–297. Woods, A. 2011. Is the health of British Columbia’s forests being influenced by climate change? If so, was this predictable? Canadian Journal of Plant Pathology 33:117–126. Woods, A. J., J. Martín-García, L. Bulman, M. W. Vasconcelos, J. Boberg, N. La Porta, H. Peredo, G. Vergara, R. Ahumada, A. Brown, and J. J. Diez. 2016. Dothistroma needle blight, weather and possible climatic triggers for the disease’s recent emergence. Forest Pathology 46:443–452. Yeaman, S., K. A. Hodgins, K. E. Lotterhos, H. Suren, S. Nadeau, J. C. Degner, K. A. Nurkowski, P. Smets, T. Wang, L. K. Gray, K. J. Liepe, A. Hamann, J. A. Holliday, M. C. Whitlock, L. H. Rieseberg, and S. N. Aitken. 2016. Convergent local adaptation to climate in distantly related conifers. Science 353:1431–1433. Ying, C. C., and A. D. Yanchuk. 2006. The development of British Columbia’s tree seed transfer guidelines: Purpose, concept, methodology, and implementation. Forest Ecology and Management 227:10.1016/j.foreco.2006.02.028. Zhou, Q.-F., H. Zhou, Y.-P. Ning, F. Yang, and T. Li. 2015. Two approaches for novelty detection using random forest. Expert Systems with Applications 42:4840–4850. Zscheischler, J., and S. I. Seneviratne. 2017. Dependence of drivers affects risks associated with compound events. Science Advances 3:e1700263.  102 Appendix A  Supplementary information for Chapter 3 A.1 Selection of reference interannual variability data Reference interannual variability is a foundation of the novelty analysis. Precipitation variability is particularly problematic because spatial correlation of precipitation is much lower than for temperature. In keeping with the use of observed historical climate normals instead of AOGCM/ESM-modeled historical normals, this study requires observational data for reference interannual variability. I evaluated three sources of gridded precipitation variability data: two interpolated from station data—CRU TS3.23 (Harris et al. 2014) and GPCC v6 (Schneider et al. 2014)—and the JRA55 reanalysis (Kobayashi et al. 2015). A visual assessment (Figure A.1) indicates that both of the station-based products (CRU and GPCC) are problematic in areas of low station density: the CRU dataset exhibits pronounced variance reduction associated with averaging among distant stations in Canada, as well as interpolation errors in the winter surface for Northeastern Alaska. The GPCC dataset, which assimilates many more stations than the CRU dataset, has several areas of anomalously high variability in the Arctic associated with individual station records that were excluded from the CRU dataset.     Figure A.1: 1959-2013 interannual climatic variability of seasonal precipitation in North America, calculated from three gridded historical time series products: CRU TS3.23 (interpolated station data), GPCC v6 (interpolated station data), and the JRA55 reanalysis.  103 These artefacts suggest that the long-term JRA55 reanalysis might be preferable. However, the JRA55 dataset substantially underestimates variability relative to the CRU TS3.23 source station observations (Figure A.2). This underestimation is expected, because the reanalysis provides an estimate of precipitation over the whole reanalysis grid cell, which is expected have lower variability than point observations at individual stations.  Figure A.2: Assessment of bias in coefficient of variation in the CRU TS3.23 interpolated grid and the JRA55 reanalysis. Bias is calculated relative to the CRU TS3.23 source station observations. Each point in (b) and (c) represents a time series extracted from the grid at the station location. Each grid-based time series excludes years without a station observation. As demonstrated above, gridded products have a recognized downward bias in interannual climatic variability due to variance reduction effects of interpolation and grid-box averaging (e.g., Jones et al. 2001, Director and Bornn 2015). To avoid these biases, I calculated interannual variability at the station level and used this variability in novelty calculations for nearby mapping grid cells.  I selected the CRU TS3.23 source station observations for this purpose.  The first step in preparing the CRU station data is matching up station time series for Tmin, Tmax, and PPT. Only 41% of precipitation stations in the North American study area have a station ID that matches the ID of the temperature stations (Table A.1).  A solution to the problem of poor station ID-matching between precipitation and temperature data is to assign the geographically closest temperature time series to each precipitation time series. If the search radius is kept small, then there is little risk of assigning an inappropriate temperature record. Even if the temperature record is not from the same station, the anomalies are likely to be applicable, due to high spatial autocorrelation of temperature anomalies documented in the CRU interpolation methods (Harris et al. 2014). This rationale does not hold 104 for precipitation anomalies, which have low spatial autocorrelation. It follows that precipitation stations are an appropriate “base” for reference variability in the novelty analysis.   Table A.1: Count of total North American stations in the CRU TS3.23 source observations for monthly mean daily minimum temperature (Tmin) monthly mean daily maximum temperature (Tmax) and total monthly precipitation (PPT). Off-diagonals indicate number of stations with identification numbers matching a station in the corresponding climate element.  # of stations Tmin Tmax PPT Tmin 3166   Tmax 3116 3146  PPT 1059 1059 2557  An appropriate distance cutoff needs to be selected for assigning nearest temperature stations. Most precipitation stations in Canada and the US have a temperature station within 3km (Figure A.3). These can be considered effectively the same location. However, the southwestern US and Mexico have a large proportion of P stations that are 10-100 km away from the nearest T station. A cutoff of 60km is required to retain sufficient precipitation records for these areas, but potential errors associated with linking P & T records at this distance won’t affect results for Canada and most of the US.  105  Figure A.3: spatial distribution of CRU TS3.23 source stations for precipitation (coloured dots) and temperature (black dots). Precipitation stations are color coded by their proximity to the nearest temperature station.  Note in Figure A.3 that there are also some clusters of precipitation stations that have only one temperature station among them. In this case, it is appropriate to assign that single 106 temperature record to all neighbouring precipitation stations, in recognition that the spatial autocorrelation of precipitation anomalies is much lower than temperature anomalies.     Figure A.4: completeness of station data in the CRU TS3.23 source observations for North America. (top) Number of stations with complete records in the 1946-2013 period). (bottom) cumulative exclusion of CRU stations at increasing thresholds for number of complete years in the 1951-1990 period.  The number of stations with complete records is fairly stable between 1950 and 1985, after which there is a steep decline in precipitation records followed by a sharp decline in temperature 107 records in 1990 (Figure A.4, top). This decline is related to the CRU prioritization of stations with records in the 1961-1990 period. I used a reference variability period of 1951-1990. There are few stations with complete precipitation and temperature records (i.e., observations available for all seasons in all of PPT, Tmin, and Tmax for a given year) for the full 1951-1990 period (Figure A.4, bottom); 32% of stations have fewer than 31 complete years, and 9% have fewer than 21 complete years.  Stations with insufficient records (<20 complete years) are predominantly in Mexico (Figure A.5). There are no problem-free solutions to this data shortfall. To simplify the analysis, I used a low cut-off of 10 complete years for station exclusion south of 33oN, and 20 complete years north of that point. The caveat is that the novelty analysis is substantially less reliable for Mexico, since interannual variability is poorly sampled there, both spatially and temporally. For the purposes of this novelty analysis, Mexico should be seen largely as an analog pool for the United States and Canada.  108  Figure A.5: number of complete years (data present for all seasons in both temperature and precipitation) in the 1951-1990 period for North American CRU TS3.23 source stations.   109 A.2 PCA truncation threshold Step 2 of the sigma similarity algorithm uses a truncation threshold of 0.1 standard deviations (eigenvalue > 0.01) for retention of principal components (PCs). This low truncation threshold is appropriate for the purpose of the principal components analysis (PCA) within this algorithm: to scale the data space, not to compress it. The PCA rotates the data space into alignment with the PCs of local reference interannual variability, providing the frame of reference and scaling of spatiotemporal climatic differences. The factors of interest are the spatial differences in climate (spatial variation) and the trajectory of climate change (the climate change signal). These two types of information are not expected to be aggregated into the high-eigenvalue PCs of interannual climatic variability. I am particularly interested in modes of spatial variation and climate change that are large relative to interannual variability. The basic rationale for Mahalanobis distance is that there is no intrinsic basis to assign relative importance to the modes of variation in data. In Mahalanobis distance, all PCs are given equal importance, i.e., unit variance. This rationale applies to interannual climatic variability. Since I am interested in conserving spatial variation and the climate change signal in the data space, there is a strong rationale for retaining most or all of the PCs of interannual variability.  The risk of retaining PCs with very low variance is that the spatial variation or climate change signal could be grossly and artificially amplified by standardizing to a trivial variance in interannual variability. However, the distributions of climate change signal and the North American spatial variation within the local climate space of the 2304 reference stations are similar across PCs (Figure A.6), with the exception of increasing numbers of outliers at higher PCs. This result indicates that the potential for artificial amplification of climate change or spatial climatic differences is isolated to these outlier stations.  110  Figure A.6: Local climate change signal (left) and North American spatial variation (right) within the localized data space of each reference station (n=2304 stations). Principal components are standardized to unit variance, which expresses the climate change signal and spatial variation as standardized anomalies of reference interannual variability. Note that these plots were made after truncating any PCs with reference variability less than 0.1SD. The stations with outlier spatial and climate change signals are predominantly located in Mexico (Figure A.7). The fact that the Mexican stations have large signals for both spatial variation and climate change suggests that this effect is most likely associated with weather stations with a low number of complete years. Alternatively, it could be a genuine aspect of the climates of Mexico (high precipitation variability and low temperature variability). Due to the uncertainty with the cause of the large signals, removing the stations is not warranted. It is sufficient to note that the novelty analysis for the United States and Canada is not affected by signal amplification artefacts.  111  Figure A.7: Local climate change signal (left) and North American spatial variation (right) expressed as standardized anomalies of the lesser principal components (PCs 10-12) of local interannual variability at each reference station (n=2304 stations). Stations with potential signal amplification artefacts are predominantly limited to Mexico.  112 A.3 Subsampling the analog pool The size of the analog pool is a major rate-limiting factor in the analog identification algorithm. To improve computational speed, I reduced the analog pool by subsampling the 4km map grid (1.3-million cells) in two steps. First, I subsampled the 30-arcsecond DEM grid into an 8km grid. Next, I applied a variable subsample inversely weighted on the standard deviation of elevation within WWF ecoregions (Olson et al. 2001). The purpose of this second subsample is to provide denser subsampling in areas of more complex terrain. Standard deviation was intentionally chosen over robust dispersion metrics in order to conserve the sensitivity of the method to elevation outliers. Sampling weights were calculated as standard deviation of the ecoregion divided by the 80th percentile of the distribution of ecoregion standard deviation across the continent, and were truncated at 0.2 and 1. This second subsample further reduced the number of analogs from by about one-half from n=333,866 grid cells to n=161,032 (Figure A.8), or 12% of the 4km map grid. St. dev of ecoregion elevation distribution Sample   Figure A.8: Development of a weighted subsample of 8-km North American grid cells (right), to reduce redundancy in the analog pool. Ecoregions were subsampled based on the standard deviation of their elevation distribution (left).   I conducted a novelty assessment for the reference period (1971-2000), providing the sigma dissimilarity between map grid cells and their best analog within the reduced analog pool (Figure A.9). Only 0.02% and 0.003% of map grid cells have >1σ and >2 σ dissimilarity, respectively, to their best analog in the reduced analog pool. These cells are dispersed, and are primarily located 113 at high elevations. This assessment indicates that reduced analog pool adequately represents the diversity of climates present in the map grid, and results in minimal bias to the results of this study.    Figure A.9: novelty assessment for the reference period (1971-2000), indicating locations whose climate is not adequately represented by the reduced analog pool. Note that he dissimilarity scale has been reduced from 4σ to 1σ. Only 0.02% of cells have >1σ dissimilarity to their best analog in the reduced analog pool.   114 A.4 CMIP5 Ensemble models Table A.2: CMIP5 models included in the RCP8.5 and RCP4.5 ensemble mean projections. The model projection is an average of several model runs, as specified in the last column.  Modeling Center (or Group)  Institute ID Model Name # runs Commonwealth Scientific and Industrial Research Organization (CSIRO) and Bureau of Meteorology (BOM), Australia CSIRO-BOM ACCESS1.0 1 Canadian Centre for Climate Modelling and Analysis CCCMA CanESM2 5 National Center for Atmospheric Research NCAR CCSM4 5 Community Earth System Model Contributors NSF-DOE-NCAR CESM1(CAM5) 3 Centre National de Recherches Météorologiques / Centre Européen de Recherche et Formation Avancée en Calcul Scientifique CNRM-CERFACS CNRM-CM5 1 Commonwealth Scientific and Industrial Research Organization in collaboration with Queensland Climate Change Centre of Excellence CSIRO-QCCCE CSIRO-Mk3.6.0 10 NOAA Geophysical Fluid Dynamics Laboratory NOAA GFDL GFDL-CM3 1 NASA Goddard Institute for Space Studies NASA GISS GISS-E2-R 5 Met Office Hadley Centre (additional HadGEM2-ES realizations contributed by Instituto Nacional de Pesquisas Espaciais) MOHC HadGEM2-ES 4 Institute for Numerical Mathematics INM INM-CM4 1 Institut Pierre-Simon Laplace IPSL IPSL-CM5A-LR  1 Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute (The University of Tokyo), and National Institute for Environmental Studies MIROC MIROC-ESM 1 Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology MIROC MIROC5 3 Max-Planck-Institut für Meteorologie (Max Planck Institute for Meteorology) MPI-M MPI-ESM-LR 3 Meteorological Research Institute MRI MRI-CGCM3 1   115 A.5 Ensemble results Novelty assessments for individual global circulation models reveal a very large spread in overall extent of novelty projected for the RCP4.5 scenario (Figure A.10). Differences among models are generally in magnitude rather than spatial pattern, except in the boreal and arctic regions.   Figure A.10: Novelty analyses for individual RCP4.5 projections of the 15-model CMIP5 ensemble. Models are ordered by the North American average dT, the difference in mean annual 116 temperature between the 2071-2100 and 1971-2000 normal periods. Other model attributes are quoted from Forster et al. (2013): transient climate response (TCR) of global surface temperature to a 1%/yr increase in CO2 and equilibrium climate sensitivity (ECS) to an instant quadrupling of CO2. (a) plots the relationship between North American average dT and novelty for each of the 15 models.  The average of 15 separate novelty assessments for the individual ensemble model projections is very similar to the result obtained from a single analysis of the ensemble mean projection (Figure A.11).  The ensemble analysis results in a slightly higher level of novelty, but the spatial pattern is equivalent.    Figure A.11: The relationship (c) between novelty calculated from a single ensemble mean projection (b) and the average of 15 separate calculations for the 15 individual models in the ensemble (a).    117 A.6 Investigating analog outliers Novelty can be underestimated if outliers from the North American climate envelope are identified as analogs for a large number grid cells. Seasonal temperature-precipitation plots of the North American analog pool (Figure A.12) show a few serious outliers in the analog pool. However, none of these visible outliers are acting as important analogs in the novelty analysis. In addition to the plots shown in Figure A.12, there were no important outlier analogs in any combinations of seasonal Tmin/Tmax/PPT for either RCP.    Figure A.12: Seasonal temperature-precipitation plots of the North American analog pool. Analog importance is measured as the number of grid cells for which a candidate analog is the best analog in the novelty calculation.  None of the visible outliers have high analog importance.  118 Maps of analog importance (Figure A.13, left) and analog outliers (Figure A.13, right) indicate that there are no outliers with high importance. A similar comparison was done for RCP8.5, with similar results (not shown). This strongly suggests that analog outliers do not have a major influence on the results of the novelty analysis.    Figure A.13: Outliers to the North American climate envelope do not have high analog importance. (left) Analog importance is measured as the number of grid cells for which a candidate analog is the best analog in the novelty calculation. (right) Outlier distance is measured as the localized climatic Mahalanobis (M) distance from each candidate analog to the furthest of its four nearest neighbours. This approach ensures that clusters of up to three outliers can be detected.   119 A.7 Accounting for non-normality in the distribution of ICV The novelty metric applied in chapters 3 and 4 doesn’t make any accommodations for non-normality in the distribution of ICV. The univariate ICV distributions could be normalized  using the approach commonly used to calculated the standardized precipitation index (Guttman 1999): fit a PDF (e.g. 3-parameter gamma), and use quantile matching to the standard normal PDF to translate the variability into z-scores (Figure A.14). This transformation would move the data towards multivariate normality by normalizing the marginal distributions, but would not necessarily achieve multivariate normality (which can't be convincingly detected/rejected anyways due to small sample size of ICV). This procedure could in theory be used as a substitute for z-standardization within the algorithm of the sigma dissimilarity metric, as was done in chapter 5.   Figure A.14: Illustration of data transformation using quantile matching to a fitted PDF: (1) a generalized gamma PDF is fitted to the data; (2) the data are expressed as percentiles of the fitted PDF; and (3) these percentiles are then expressed as values of the standard normal PDF, i.e. as z-scores. Unfortunately, the quantile matching approach doesn’t work for this novelty analysis because the range of climates in the focal neighbourhood (grid cells associated with any given reference climate station) can be well beyond the range of decimal precision of the fitted PDF (Figure A.15). Note that this precision issue would not be a limitation if the transformation was calculated at the cell level rather than the station level: values beyond the precision horizon of the cell’s local ICV would be irrelevant to the calculation of novelty. The quantile-matching 120 transformation approach is preferable to z-standardization for a multivariate standardized anomaly, but it is not feasible for this novelty analysis.   Figure A.15: Example of decimal precision (black numbers in plot) required to perform quantile matching to a fitted gamma PDF. In this case, the range of projected climates of map cells associated with the reference station are beyond a feasible decimal precision (>16 decimal places). This problem precludes quantile matching in this novelty analysis, though it would not be a problem for an analysis in which reference variability was calculated separately for each grid cell.   Given that normalization of the reference variability is not feasible for this analysis, it is worthwhile to investigate the impact of the assumed distribution on the results.  A sensitivity analysis using raw precipitation data (i.e. not log-transformed as in the base case) provides a bookend for the assumed distribution of precipitation data (Figure A.16). With the exception of the Gulf Coast of the US, the general effect is to increase novelty. The results are not dramatic, however, and suggest that the assumed distribution is not of overriding importance.  121   Figure A.16: Sensitivity analysis using raw instead of log-transformed precipitation data, for (a) RCP4.5 and (c) RCP8.5. (b) and (d) are comparisons with the Base Case (log-transformed precipitation).  122 A.8 Null model analysis of elevation-novelty relationship Two factors complicate a statistical analysis of the relationship between topographic position (relative elevation) and novelty: (1) uneven sampling of relative elevation, and (2) high spatial autocorrelation. The problem of uneven sampling can be addressed by statistical analysis against a null model. However, spatial autocorrelation confounds statistical analysis by violating assumptions of independence (Gotelli and Ulrich 2012). I minimized the effect of spatial autocorrelation by conducting null model analysis in very small subsamples (n<25) of the spatial data set (N=199,059).  The method of null model analysis presented here is:  1. Generate null data by randomizing relative elevation (the choice to randomize elevation instead of novelty is arbitrary; either approach produces identical results.) 2. for each sample size j between 5 and 25:  a. Randomly subsample the observed and null data to the specified sample size (e.g. n=j);  b. obtain a bootstrap distribution (B=n replicates) of Spearman rank correlation in the subsampled observed and null data; and  c. conduct a paired t test between the bootstrap replicates of observed and null correlation.  3. Repeat step 2 100 times to obtain a boxplot of t-test p-values at each sample size j.  Estimates of spearman rank correlation converge on ρ=-0.49 and ρ=0 in the observed and null data, respectively, as sample size increases. The bootstrap uncertainty in estimates of ρ, and consequently the t test p-values, declines with increasing n.  Using this method, the observed relationship between relative elevation and novelty is statistically distinct (p<α=0.05) at n>15 (Figure A.17). Spatial autocorrelation can reasonably be assumed to be nil in such a small (<0.01%) subsample of the observed data. Obtaining a statistically significant result in this small subsample is strong evidence that the observed relationship between relative elevation and novelty is stronger than would be expected by chance.  123  Figure A.17: Null model analysis of the relationship between relative elevation and novelty. The plot shows boxplots of p-values from 100 t tests of bootstrap estimates of Spearman rank correlation in the observed and null (randomized) relationship between relative elevation and novelty, at subsamples of the spatial data (N=199,059) ranging from n=5 to n=25.  Statistical significance (p<α=0.05) at n>15 provides strong support for the relationship between relative elevation and novelty.  124 A.9 Variation around mean novelty from multiple ICV proxies I calculate novelty at each grid cell as the distance-weighted average of novelty calculations for the four nearest climate stations used as proxies for the interannual climatic variability (ICV) of the grid cell. The range of variation in novelty calculated from the four ICV proxies is substantial in many grid cells, particularly in the RCP4.5 projection (Figure A.18). This variation suggests some potential for local bias associated with averaging of ICV proxies. However, there are few locations with the potential for missed novelty or false novelty relative to the 2σ threshold (Figure A.19). The main results of chapter 3 do not appear to be sensitive to differences among the four ICV proxies for each grid cell.   Figure A.18: Range of novelty calculated from the four ICV proxies for each grid cell, relative to their mean, for RCP 4.5 (a) and RCP8.5 (b). Range decreases as mean approaches 8σ because the maximum detectable novelty is ~8.2σ. 125  Figure A.19: potential for missed novelty or false novelty relative to the 2σ threshold, for RCP 4.5 (a) and RCP8.5 (b). 126 A.10 Bias due to nonrandom weather station placement The potential for cross-contamination among the distinct ICV patterns of maritime and continental climates is a potential artefact of the use of weather stations as ICV proxies. Mexico, the contiguous US, and coastal British Columbia have sufficient station density in the coast-interior transition that conflation of distinct regional climates can reasonably be ruled out as a source of error. In contrast, low station density in the boreal and Arctic regions suggests the potential for conflation of maritime and continental ICV proxies over much of Canada and Alaska. Widespread systematic bias due to this conflation is not apparent when grid cells are given only a single station as an ICV proxy (Figure A.20). Systematic bias would be indicated if coastal and interior areas had opposite colouring. Nevertheless, this bias cannot be definitively assessed without an independent sample of weather stations. The scarcity of weather stations in the boreal and Arctic regions highlights that results for these regions should be interpreted at a broad, regional scale.   Figure A.20: Change in novelty relative to the Base Case when novelty is calculated using the single nearest weather station as an ICV proxy, rather than the four nearest stations. Weather stations used as ICV proxies are displayed as black dots.    127 A.11 Variable selection  Figure A.21: Effect of variable selection on novelty of the RCP4.5 ensemble mean projection. The 12-variable novelty (panel d) is the same as the main results presented in Figure 7 of the publication. Novelty is highly sensitive to the use of seasonal mean daily temperature (Tave) instead of seasonal mean minimum and maximum daily temperature (Tmin, Tmax). Novelty is less sensitive to the use of two seasons instead of four. Results for RCP8.5 are provided in Figure 8 of the publication.  128  Figure A.22: Effect of variable selection on reference period dissimilarity to Montreal, Quebec.   Figure A.23: Effect of variable selection on reference period dissimilarity to Yakima, WA.  129  Figure A.24: Effect of balancing the number of temperature (T) and precipitation (P) variables on reference period (1971-2000) dissimilarity to Montreal QC (a,b), Flagstaff AZ (c,d), and Yakima WA (e,f). The 6-variable climate (a,c,e) is composed of Tmin, Tmax, and PPT for winter (DJF) and summer (JJA). Precipitation in spring (MAM) and autumn (SON) are added to these variables to define the 8-variable climate (b,d,f). Balancing the number of T&P variables has minimal effect on climatic dissimilarity.    130 A.12 Comparison to standardized Euclidean distance.  This study builds on Williams et al. (2007) by making several methodological modifications: (1) high spatial resolution; (2) observational data for baseline climatology; (3) a 12-variable description of climate, instead of 4; and (4) a Mahalanobian sigma dissimilarity metric instead of SED. In this section, I perform a stepwise comparison of my results to those of Williams et al., focusing on sensitivity to the 12-variable climate and the sigma dissimilarity metric.  In the first step of this factorialized comparison, I performed an SED novelty calculation using four climate variables similar to those used by Williams et al. (2007), and attempted to match the colour scheme to Williams et al. (2007) (Figure A.25). Despite several differences in data (Table A.3), the benchmark results are broadly similar in pattern to those of Williams et al. (2007). The higher novelty present in the benchmark in the Gulf states of the USA and the west coast of Mexico can likely be attributed to the continental rather than global analog search. Lower novelty throughout the western cordillera and arctic can likely be attributed to a higher-resolution representation of terrain.  Converting SED distances to approximate sigma dissimilarity allows comparison between SED novelty (Figure A.26) and Mahalanobian novelty (Figure A.21). Sigma dissimilarity based on SED is an approximation because it does not account for correlations among variables, and therefore is biased towards underestimation of statistical dissimilarity.  For this reason, the observed reduction in novelty detected by SED (Figure A.26) relative to Mahalanobis distance (Figure A.21) is expected. Note, however, that there are only subtle differences between SED and Mahalanobis distance in the 4-variable climate used by Williams et al. (2012). The underlying differences in spatial climatic dissimilarity associated with SED and Mahalanobis distance are illustrated in Figure A.27.    131 RCP4.5/B1 RCP8.5/A2      Figure A.25: Approximate benchmarking of my dataset to the Williams et al. (2007) results. (A) and (B) are SED novelty based on the four climate variables used by Williams et al. (2007) for RCP4.5 and RCP8.5, respectively. (C) and (D) are excerpted from Williams et al. (2007) for the SRES B1 and A2 scenarios, respectively.  Table A.3:  Differences between the data used in Williams et al. (2007) and the benchmark scenario presented in Figure A.25, including probable effect on novelty.  Williams et al. (2007) Benchmark scenario Effect Global analog search Continental analog search + 1980-1999 GCM variability Detrended 1951-2000 station variability - CMIP3 Ensemble (A2/B1) CMIP5 mean projection (RCP8.5/4.5) ? 250km grid (i.e. poor sampling of analog pool) 8km grid (i.e. good sampling of analog pool) -  B A 132  Figure A.26: Effect of variable selection on SED novelty in the RCP4.5 ensemble mean projection.  Distances have been converted to sigma levels to account for dimensionality effects  133  Figure A.27: Reference period (1971-2000) sigma dissimilarity to Denver, CO, using Mahalanobis distance (a,b,c) and SED (d,e,f), Results are shown for three different variable sets: 12-variables (a,d; Tmin/Tmax/PPT for 4 seasons), 8 variables (b,e; Tave and PPT for 4 seasons), and 4 variables (c,f; Tave and PPT for winter and summer). SED generally reduces spatial climatic dissimilarity relative to Mahalanobis distance, particularly in the 12-variable climate.   134 A.13 Assessment of error due to ICV sample size Some of the ICV proxies—weather station records used as proxies for local interannual climatic variability (ICV) in each map cell—contain missing data that reduce the sample size contributing to sigma dissimilarity. In general, most map cells have few missing years: 50% of cells outside of Mexico are represented by ICV proxies with ≥37 complete years; 75% have ≥32 complete years; and 95% of have ≥24 complete years (Figure A.28). Despite the completeness of the 1951-1990 record for most of the study area, the sufficiency of these samples for calculation of sigma dissimilarity deserves consideration.   Figure A.28: ICV proxy sample size for map cells of the North American study area.  These results indicate that sample size has a negligible effect on the z-standardization component (steps 1 and 3) of the calculation of sigma dissimilarity (bootstrap analysis, not shown). However, the effect of reduced sample size is an important consideration for the principal components analysis (PCA; step 2) because even the maximum sample size of 40 years is small for a 12-dimensional PCA. Despite the commonly-cited rule of thumb that sample size should be greater than five times the dimensionality of the PCA, empirical analyses have demonstrated that the instability associated with low sample size is highly dependent on the covariance structure of the sample (Osborne and Costello 2004), and hence that a sufficient sample size cannot reliably be determined a priori. 135 I conducted a bootstrap analysis to estimate the error associated with the sample size of the ICV proxy time series. I ran 120 iterations of the novelty analysis, each using a bootstrap resample of the complete years contributing to the PCA. To reduce computation times, I conducted the analysis only on map cells with >1σ novelty in the main 12-variable analysis, and only for a single ICV proxy per map cell rather than four.  95% confidence intervals (CIs) for each cell are the 2.5th and 97.5th percentiles of these 120 novelty estimates. The “relative 95% CI” is the CI divided by the median.  As expected, error is high at small sample sizes (Figure A.29). A large relative error is observed at a sample size of 30 years, suggesting the complicating role of covariance structure in generating instability in the PCA.  The median relative confidence interval is approximately one at most sample sizes n>24 years, indicating that bootstrap error is moderate for most of the map cells with novelty greater than 1σ.  Figure A.30 shows the spatial distribution of PCA instability as indicated by bootstrap error.  136  Figure A.29: (a) Distribution of the 95% confidence interval of 120 bootstrapped novelty calculations for each map cell with novelty >1σ.  Distributions are stratified by the number of complete years in the proxy ICV time series representing the map cell. (b) Same as (a) but showing 95% confidence interval as a ratio of the median of the n=120 bootstrap distribution.   137  Figure A.30: Map of the relative 95% confidence interval (a ratio of the median) of n=120 novelty calculations for each cell with bootstrap resampling of the ICV time series contributing to the PCA. Map cells with novelty <1σ in the main analysis are excluded and shown as grey. Locations with high relative CI indicate areas where novelty estimates are potentially unreliable due to an unstable PCA.  The bootstrap error estimation above provides an indication of the relative effect of sample size on novelty error and locations where novelty results may be less reliable. The absolute confidence intervals are not reliable, however, because bootstrapping intrinsically reduces the stability of the PCA. Duplication of observations by bootstrap resampling reduces the effective sample size of the covariance matrix. Hence PCA errors can be expected to be higher for all 138 bootstrap resamples than for the full sample.  At the level of an individual map cell (Figure A.31), variance of novelty calculated by n=39 bootstrap resampling is much greater than n==39 subsamples of an N=40 ICV time series.   In this case, bootstrap resampling at n=39 produces the error equivalent to an n=20 subsample. For this one map cell, bootstrapping in small samples (n≤20) produces a substantial underestimation of novelty.  This underestimation can be seen across the full population of map cells with novelty >1σ (Figure A.32), particularly in that the majority median bootstrap novelty, and substantial proportion of the 97.5th percentile of bootstrap novelty, are located below the 1:1 line. These results indicate that bootstrap resampling produces a biased and exaggerated estimate of uncertainty in the novelty analysis.   Figure A.31: Effect of bootstrapping on estimates of error at various sample sizes at a single map cell. (a) The distribution of novelty calculated from subsamples of the 40-year time series converges as the sample size (n=10,20,30, & 39) approaches the population size (N=40). (b) Bootstrap resamples of the subsamples do not converge because the effective sample size of the PCA is reduced. Bootstrap estimates of novelty have a downward bias in small subsamples (n≤20).   139  Figure A.32: Bootstrapping introduces a downward bias into calculations of sigma dissimilarity. (a) Lower bounds of the 95% confidence interval for the n=120 bootstrapped novelty calculations for each map cell, plotted against the novelty for each map cell calculated from the full time series of the ICV proxy. Contours show the regions containing 50%, 75%, and 95% of the points. The grey 1:1 line indicates equivalence between the full-sample and bootstrapped novelty calculation. (b) and (c) show the medians and upper 95% CI bounds, respectively.  In conclusion, the ICV proxy time series with <40 complete years should be considered to be small samples in the context of a 12-dimensional principal components analysis.  Despite the potential for small samples to produce unstable novelty results, the similarity between the 12-dimensional results and the 6-dimensional results (Figure A.21) suggests that limited sample size is not a major source of error in the main novelty results presented in this publication. Areas with very small sample size (i.e., sample size less than double the dimensionality) are limited to 5% of the area outside Mexico. The bootstrap analysis indicates some isolated locations where novelty results may be unreliable due to PCA instability. However, bootstrapping overestimates novelty error because it reduces the effective sample size of the PCA. Estimation of error in sigma dissimilarity is non-trivial and an area for future research. In the absence of a reliable estimate of error, the ratio of time series observations to the dimensionality of the analysis should be maximized wherever possible. This could be achieved by parsimonious variable selection, higher thresholds for complete years in ICV proxies, and even pooling of monthly observations into each seasonal variable.    140 Appendix B  Supplementary Information for Chapter 4 B.1 Biogeoclimatic subzone names Table B.1: Full names of biogeoclimatic subzones used as examples in Chapter 4 Label Subzone name CWHdm Coastal western hemlock zone, dry maritime subzone CWHvm Coastal western hemlock zone, very wet maritime subzone MHwh Mountain hemlock zone, wet hypermaritime subzone MHmm Mountain hemlock zone, moist maritime subzone CDFmm Coastal Douglas-fir zone, moist maritime subzone ESSFmw Engelmann spruce - subalpine fir zone, moist warm subzone PPxh Ponderosa pine zone, very dry hot subzone IDFxk Interior Douglas-fir zone, very dry cool subzone  MSdm Montane spruce zone, dry mild subzone ICHxw Interior cedar-hemlock zone, very dry warm subzone  SBPSdc Sub-boreal pine-spruce zone, dry cold subzone SBSwk Sub-boreal spruce zone, wet cool subzone SWBmk Spruce-willow-birch zone, moist cool subzone BWBSmk Boreal white and black spruce zone, moist cool subzone     141 B.2 Geographical distance to best analog Climate analogs for projected climates are primarily sourced from downhill and/or southward locations (Figure B.1). However, the high elevations of southeast British Columbia (primarily ESSF) are notable for sourcing low elevation analogs from Northern British Columbia. Conversely, the low elevations of Northwest BC (primarily ICH and SBS) source analogs from higher elevations in southern locations. These patterns of analog source distances in Northwestern and Southeastern BC are not substantially different when the North American analog pool is available (Figure B.2). These cases illustrate that climatic shifts may not follow intuitive trajectories uphill and northward. In landscapes where lower elevations are substantially drier than higher elevations due to rainshadow effects, as in Southeast BC, warm-dry submontane locations are not expected to provide analogs for warmer versions of cool-wet montane and subalpine climates. Similarly, in regions where southern regions are drier than northern regions, as in northwest BC, warmer-drier submontane climates to the south are not expected to provide analogs for warmer or warmer-wetter versions projected for warm-wet submontane climates in the north. The necessity to source analogs from very different topographic positions in distant regions raises doubt about the low levels of novelty detected in submontane Northwest BC and montane/subalpine Southwest BC. The simple 6-variable climate spaces used in this study may be unable to detect ecologically important distinctions between the projected climates of these locations and their geographically distant analogs.  The relationship between analog source distances and novelty (c-d) demonstrates that novel climates are associated with low elevational and latitudinal distances to their best analog. In other words, the best analogs for novel climates tend to be geographically close to their reference locations. This supports the proposal that analog dissimilarity—the climatic difference between the reference climate (1971-2000) of a location and the reference climate of the best analog for the projected climate of that location—should be low for novel climates.   142  Figure B.1: Geographical distances to the location of best British Columbian analogs for projected climates. (a,c) Elevational and latitudinal distances to the climatically most similar analog in the “seasonal basic” climate space for the RCP4.5 ensemble mean projection, using the British Columbia analog pool. (b,d) elevational and latitudinal analog distance plotted against climatic novelty.   143  Figure B.2: Geographical distances to the location of North American climate analogs for projected climates. (a,c) Elevational and latitudinal distances to the climatically most similar analog in the “seasonal basic” climate space for the RCP4.5 ensemble mean projection, using the North American analog pool. (b,d) elevational and latitudinal analog distance plotted against climatic novelty.    144 B.3 Measuring analog dissimilarity with the RF proximity matrix Results are similar for the var6 (Figure B.3) and var44 (Figure B.4) variable sets:    Figure B.3: Ranked mean dissimilarity among BGC subzone-variants measured with RF proximity (var6). 145  Figure B.4: Same as Figure B.3, but using the var44 variable set.    146 B.4 Effect of predictor availability on RF projections and novelty indicators This section presents subzone-level random forest classification with five variable sets of increasing dimensionality, up to the 44 variables used in Wang et al 2012. Var6 is also the “seasonal basic” variable set.  var3: ["Tmin_wt", "Tmax_sm", "MAP"] var6: ["Tmin_wt", "Tmax_wt", "Tmin_sm", "Tmax_sm", "PPT_wt", "PPT_sm"] var12: var6 + ["MAT", "MAP", "DD_0", "DD5", "PAS", "CMD"] var24: var12 + ["TD", "PPT10", "Tmin11", "PPT06", "PPT12","Tmax02", "Tmax_sp", "PPT08", "PPT_sp", "PPT05", "PPT09", "PPT_at"] var44: ["TD","PPT10", "Tmin11", "PPT06", "PPT12","Tmax02", "Tmin_sm", "Tmax_sp", "PPT08","Tmax_wt", "PPT_sm","Tmax_sm", "PPT_sp", "PPT05", "PPT09", "PPT_at", "PPT07","Tmax11", "PPT_wt", "Tave_sm", "Tmax_at", "PPT04","Tmax10", "PPT11","Tmin_wt", "PPT01", "Tmin02", "PPT03","Tave_sp", "Tmax05", "Tmax01", "Tmin12", "Tmin_at","Tmax07", "Tmin10", "SHM","Tmax08", "Tmin06", "Tmin05", "Tmax09", "PPT02", "EMT","Tmin01", "PAS"]  147  Figure B.5: RCP4.5 ensemble mean BGC projections for the 2041-2070 period using Random Forest classification, at increasing predictor availability from (b) 3 variables to (f) 44 variables. Training classes are BGC variants, predictions are colour-themed by BGC zone.    148  Figure B.6: Analog similarity in the RCP4.5 ensemble mean Random Forest BGC projections for the 2041-2070 period at increasing predictor availability from (b) 3 variables to (f) 44 variables.   149  Figure B.7: Ensemble agreement among RCP4.5 Random Forest BGC projections for the 2041-2070 period by 15 CMIP5 global climate models. To reduce computation time, RF models are trained at the BGC subzone level (instead of BGC variant) on a 4km grid (instead of 2km).    150 B.5 Sensitivity analyses of North American analog search  Figure B.8: End-of-20th century analogs for the mid-21st-century climates of BC, measured as proportional votes for climates projected to occur within BC predicted by a Random Forest model trained on the (a,c) 6-variable or (b,d) 44-variable RCP4.5 ensemble mean 2041-70 151 climates of BGC units (within BC) and (a,b) coarse or (c,d) fine ecoregion sets.  Figure B.9: End-of-20th century analogs for the mid-21st-century climates of BC, as predicted by a Random Forest model trained on the (a,c) 6-variable or (b,d) 44-variable RCP4.5 ensemble 152 mean 2041-70 climates of BGC units (within BC) and (a,b) WWF ecoregions or (c,d) US level 4 ecoregions. Predictions are made at the subzone level but color-themed at the zone level.   Figure B.10: Locations in BC with non-BC North American analogs for their RCP4.5 ensemble mean climate of the 2041-2070 period, as predicted by a Random Forest model trained on the 153 (a,c) 6-variable or (b,d) 44-variable RCP4.5 ensemble mean 2041-70 climates of BGC units (within BC) and (a,b) coarse or (c,d) fine ecoregion sets. The map is shaded by the proportion of classification trees in the Random Forest that voted for ecoregions that occur outside BC.   154 B.6 Relationship between elevation and novelty There is a strong relationship between elevation and novelty (Figure B.11). In the linear classification (Figure B.11a), novel climates (Dmin>1.5) predominantly occur at low elevations and there are very few low-elevation locations (<500m) with low novelty (Dmin<1).  Random Forest analog proximity and non-BC votes, which previous results have indicated to be indicators of climatic novelty, are also negatively correlated with elevation (Figure B.11b-c).     Figure B.11: Relationship of elevation to (a) novelty calculated with Mahalanobis distance, (b) log-transformed Random Forest analog proximity (a metric of analog similarity), and (c) non-BC Random Forest votes. RCP4.5 ensemble mean projection of the “seasonal basic” variable set. Landscape elevation is calculated as meters above the minimum elevation of the ecoprovince within which each grid cell is located.  Color shading and contours indicate point density.   155 Appendix C  Supplementary Information for Chapter 5 C.1 Timing of climate departures   Figure C.1: Relationship of the relative timing and the relative magnitude of climate departures in RCP4.5 ensemble projections of 6 CMIP5 models. Positive values on both axes indicate a bivariate (summer Tx & Pr) climate signal that is stronger (x-axis) and earlier (y-axis) than the univariate (max of Tx or Pr) climate signal. The climate signal is the average 2σ ratio of a number of model runs, given in parentheses next to the model name.  Percentages in red are the proportion of the land area in each model with a maximum departure difference >0.2 or a relative departure timing of >10 years.  A major stream of the climate change detection literature has focused on the timing of the emergence of the climate signal from the noise of natural or historical variability. For most purposes, the time of emergence and the time of departure are equivalent concepts, and I treat 156 them as such here. In the absence of a specific biological response, the specific metric and threshold for defining the departure year is arbitrary, and there are many such definitions in the literature. Here, I define a departure threshold as a 2σ proportion of 0.25; i.e., the climate is said to have departed from natural variability when 25% of the anomalies in the preceding 30-yr period are 2σ extremes or greater. Since the one-tailed null probability of a 2σ anomaly is 2.3%, this threshold approximates an order-of-magnitude increase in the frequency of warm 2σ anomalies. The relative timing of departure is the number of years that the bivariate signal departs prior to the departure of the univariate climate signal (max. of Pr or Tx). Locations at which the univariate signal has not departed by the year 2100 are assigned a departure year of 2100; this produces a conservative estimate of the departure of the bivariate climate signal relative to the univariate climate signal.  As expected, there is a strong relationship between the relative timing and the relative magnitude of departure (Figure C.1).  On average across all of the models, the bivariate climate signal departs more than 10 years prior to the univariate climate signal in 17% of land area (intermodel range of 7-23%). If the 2σ proportion threshold for departure were increased from 0.25 to 0.5, the relative timing of departure would increase in some areas, but would decrease or be undetected in others because the univariate departure year occurs beyond the year 2100 (Figure 5.2). The relative timing of departure is negative in some locations where the maximum departure difference is low. This occurs because the bivariate climate signal is weaker than the univariate signal at low correlations (Appendix C.3).  The bivariate summer Pr-Tx signal crosses the 2σ-proportion threshold of 0.25 for climate departure as early as 1980 in the tropical regions of some models and as late as 2020 in others (Figure C.2).  The spatial pattern of departure year is generally consistent with other studies of the time of emergence of the mean summer temperature signal (Mahlstein et al. 2011, Hawkins and Sutton 2012): departure year increases with latitude, though in some models the high Arctic experiences early departure. Many regions with strong departure intensification (Figure 5.3), e.g. the SE USA in CanESM2, do not show pronounced early relative timing of departure (Figure C.3). This occurs because the bivariate and univariate climate signals are only beginning to diverge when they cross the 2σ-proportion threshold of 0.25 for climate departure (Figure 5.2b).   157  Figure C.2: Departure year of the bivariate summer Tx-Pr climate signal from natural variability in the CMIP5 ensemble.  Figure C.3: Timing of departure of the bivariate summer Tx-Pr climate signal relative to the departure of the univariate (max. of Tx or Pr) climate signals. Positive numbers indicate the number of years that the bivariate signal departs prior to the univariate signal. 158 C.2 Sensitivity to univariate and multivariate normalization methods Sigma dissimilarity assigns probabilities to Mahalanobis distances based on the assumption that reference period variability is multivariate normal (MVN). Violations of this assumption cause the probability of some anomalies to be underestimated and others to be overestimated.   Despite univariate normalization, historicalNat Pr-Tx distributions are qualitatively non-MVN in some locations of the CanESM2 model. This likely is also the case in the other CMIP5 ensemble models. In this section I test the sensitivity of departure intensification to one alternate method of univariate normalization and two methods of multivariate normalization. Based on this sensitivity analysis, I chose not to conduct multivariate normalization in order to maintain the simplicity and transparency of this study’s primary methods.  I used the following methods for sensitivity analysis:  Univariate normalization only:  1. qdm: quantile delta mapping + sigma dissimilarity. This form of non-parametric quantile mapping (Cannon et al. 2015) is used in the main results of Chapter 5. The reference variability is normalized non-parametrically while preserving the magnitude of the climate change signal.   2. pqm: parametric quantile mapping + sigma dissimilarity. Fit a generalized gamma distribution to the reference variability and match the quantiles of the fitted distribution with the quantiles of the standard normal distribution. Parametric quantile mapping is commonly applied in the calculation of the standardized precipitation index (Guttman 1999).  Univariate normalization plus multivariate normalization:  3. mbcn: multivariate quantile mapping + sigma dissimilarity. This multivariate generalization of quantile delta mapping (Cannon 2017) is used to map the bivariate distribution of the historicalNat reference variability onto a standard bivariate normal distribution while preserving changes in the quantiles of each variable in the historical+RCP4.5 projection.  4. kde: quantile delta mapping + bivariate kernel density estimation. Instead of normalizing the bivariate distribution, this method uses kernel density estimation to map the probability contours of the bivariate distribution of reference period variability, allowing non-parametric estimation of the probability of bivariate anomalies.  These methods produce subtle but discernable differences in the magnitude, though not the spatial pattern, of maximum departure difference (Figure C.4). Kernel density estimation produces reduced departure differences in all cells. This suggests that the other methods may be overestimating the univariate anomalies, since kde provides probability density estimates that are 159 relatively independent of variable scaling.   There are no discernible differences in the mbcn method relative to qdm, indicating either that non-normality is not an important factor in departure difference in the CanESM2 model, or that mbcn is not an effective multivariate normalization method for this particular application.  Despite these sensitivities, the occurrence and the spatial pattern of departure intensification is robust to the differences in the four methods tested here.  The 2σ proportion underlies the observed robustness of departure intensification to normalization methods. As a binary metric, the 2σ proportion is unaffected by the effect of normalization on the magnitude of anomalies beyond the 2σ threshold. The 2σ proportion only relies on statistical inferences that are strongly supported by the reference variability sample. This is a critical advantage over the signal-to-noise ratio (z-scores of reference variability).  160  Figure C.4: Sensitivity of maximum departure difference to four different treatments of multivariate normality: a,e, quantile delta mapping (qdm); b,f, parametric quantile mapping (pqm); c,g, multivariate quantile mapping (mbcn); and d,h, bivariate kernel density estimation (kde).     161 C.3 Null model for departure differences Departure difference can be positive or negative, as seen in maps for the 2021-2050 period (Figure C.5). Departure difference is negative in cases where there is little trend in precipitation and low correlation between temperature and precipitation. Given that the signal-to-noise ratio of precipitation is generally much less than temperature, the scenario of non-stationary temperature, stationary precipitation, and a zero correlation is an appropriate null model for departure difference.   Figure C.5: Departure differences in the CMIP5 ensemble during the 2021-2050 period. A simulation of two normal variables, x with a shifted mean (representing a non-stationary Tx signal) and y with a mean of zero (representing a stationary Pr signal). As the mean of x increases, the frequency of 2σ anomalies increases faster for x alone than for the bivariate distribution of x and y (Figure C.6). This occurs because the probability of a distance of 2 is lower for a bivariate normal distribution than for a univariate normal distribution (see Section 0). For a 2σ shift in the mean of x, the bivariate frequency of 2σ anomalies is 0.1 less than the univariate frequency.  162  Figure C.6: Null model for departure differences under global warming. a, Mean 2σ proportion of 10000 samples of two normal variables, x with a shifting mean and y with a mean of zero. b, Departure difference and departure ratio of univariate x anomalies and bivariate x-y anomalies.  163 C.4 Out-of-reference-period standardized anomaly bias The conventional method of calculating standardized anomalies uses the mean and standard deviation of variability during a reference period to assign sigma levels to observations.  This method systematically overestimates the frequency of extreme events outside of the reference period because variation in the sample mean and variance reduction in the sample variance both increase the variance of out-of-sample standardized anomalies (Sippel et al. 2015). For small reference samples, this bias has a substantial impact on the detection of extreme observations:  for a 30-“year” reference sample drawn from a normal distribution, the frequency of 2σ events in the out-of-sample period is overestimated by 29% (Figure C.7). In real observations, this bias can be expected to be greater because serial autocorrelation reduces the effective sample size of the reference period (Sippel et al. 2015).  This bias is directly relevant to my study, which uses the frequency of 2σ events as its primary metric.  The reference period bias can be removed by using the student’s t distribution instead of the normal distribution for inferring the probability (sigma level) of anomalies. I have not implemented this correction to the calculation of sigma dissimilarity in this study. However, the bias associated with the very large pooled historicalNat reference periods used in this study is negligible (Figure C.7); simulation indicates that the bias in the 2σ ratio is 2% beyond nref = 465 years (the minimum nref in this study).   Figure C.7: Overestimation bias in the 2σ proportion of non-reference-period standardized anomalies at reference period samples of nref = 30 to 600 normal variates (“years”).  The bias at each nref is the mean bias from 10000 simulations, each with out-of-reference-period samples of n= 250 normal variates. 164 C.5 CMIP5 Ensemble Table C.1: CMIP5 models included in Chapter 5. The number of historicalNat runs and historical + RCP4.5 runs used in this study are specified. Perturbed physics experiments were excluded. CMIP5 is described by Taylor et al. (2012) Model Modeling Center (or Group)  Institute ID lat resolution lon resolution TCR* ECS* histNat runs hist+RCP4.5 runs          CanESM2 Canadian Centre for Climate Modelling and Analysis CCCMA 2.8 2.8 2.4 3.7 5 5          CESM1-CAM5 Community Earth System Model Contributors NSF-DOE-NCAR 0.9 1.3 2.3 4.1 3 3          CSIRO-Mk3-6-0 Commonwealth Scientific and Industrial Research Organization in collaboration with Queensland Climate Change Centre of Excellence CSIRO-QCCCE 1.9 1.9 1.8 4.1 5 10          GISS-E2-R NASA Goddard Institute for Space Studies NASA GISS 2.0 2.5 1.5 2.1 5 6          HadGEM2-ES Met Office Hadley Centre (additional HadGEM2-ES realizations contributed by Instituto Nacional de Pesquisas Espaciais) MOHC 1.3 1.9 2.5 4.6 4 4          IPSL-CM5A_LR Institut Pierre-Simon Laplace IPSL 1.9 3.8 2 4.1 3 4 *Adjusted transient climate response (TCR) and equilibrium climate sensitivity (ECS) as reported by Forster et al. (2013), except for non-adjusted values for CESM1-CAM5 reported by Meehl et al. (2013).    165 C.6 Summer Tx-Pr correlations and orthogonality of climate change  Figure C.8: Correlation between summer precipitation (smpr) and mean daily maximum temperature in the summer (smtx) in the pooled historicalNat runs of the six CMIP5 models.   Figure C.9: Orthogonality of climate change projected by the six CMIP5 models. Orthogonality of climate change is measured as the arctan of the relative magnitude of the 2051-2100 normals (Δ) in PC1 and PC2 of reference variability, providing degrees of angular displacement from the dominant axis of interannual variability. 166 C.7 Relative departures of temperature and precipitation  Figure C.10: Relative departures (2σ proportions) of summer precipitation (smpr) and mean daily maximum temperature in the summer (smtx) in projections of the 2021-2050 period by six CMIP5 models. Negative numbers (blue) indicate locations where the smpr departure is greater than the smtx departure. The number of runs in each ensemble is given in parentheses next to the model name. Equivalent results for the 2071-2100 period are shown below.   167 C.8 Pseudocode for calculation of maximum departure difference.  The departure difference is calculated with the following steps:  1. For each cell in the grid of each CMIP5 model,  2. Start with [n,k] matrices XTx, XPr, and XBi of standardized anomalies for the Tmax, precipitation, and bivariate time series, respectively. Each of the n rows is a year in the annual time series 1850-2100, and each of the k columns is a historical+RCP4.5 run.  3. For each year 1880-2100 and each model run, divide the number of absolute values exceeding 2 (2σ exceedances) in the previous thirty years by thirty, producing [n-30,k] matrices YTx, YPr, and YBi, of 2σ proportions for the Tmax, precipitation, and bivariate time series, respectively. 4. For each element of YTx and YPr, i.e., each year of each model run, select the 2σ proportion for either YTx and YPr, whichever is greater, producing an [n-30,k] matrix YUni of univariate 2σ proportions.  5. For each year 1880-2100, calculate the mean of the 2sigma proportions across all model runs, producing one univariate time series, 𝑌𝑌𝑈𝑈𝑈𝑈𝑈𝑈����� and one bivariate time series 𝑌𝑌𝐵𝐵𝑈𝑈����.  6. The departure difference is an 1880-2100 time series of bivariate minus univariate 2sigma proportion, i.e., 𝑌𝑌𝑈𝑈𝑈𝑈𝑈𝑈����� minus 𝑌𝑌𝐵𝐵𝑈𝑈����.  7. The maximum departure difference is the maximum value in the departure difference time series.   The univariate 2σ proportion is calculated from 2σ proportions of Tx and Pr because the alternate approach of selecting the maximum anomaly of either Tx or Pr in each year would result in an overestimate of the univariate 2σ proportion. Another alternative approach would be to calculate maximum departure difference with respect to each variable separately (𝑌𝑌𝑇𝑇𝑇𝑇���� and 𝑌𝑌𝑃𝑃𝑃𝑃����), and select the minimum of these two values for each cell. The sensitivity of the results to this valid alternative approach are likely very low because the univariate departures are almost exclusively driven by the Tx climate change trend (Appendix C.7).  168 C.9 Parallel analysis of hottest three consecutive months I used Boreal and Austral summer (JJA and DJF, respectively) in the main analysis to facilitate comparisons to other papers that use this common definition of summer, in particular the analysis of summertime temperature-precipitation correlations by Berg et al. (2015). However, I acknowledge that this definition of summer is problematic in the tropics and some subtropical regions, and confounds comparison with other relevant studies (e.g., Zscheischler and Seneviratne 2017).  This section provides a parallel analysis which defines summertime as the hottest three consecutive months. This season is identified in each CMIP5 model from the mean monthly Tmax in the r1i1p1 historicalNat run (Figure C.11).    Figure C.11: Hottest three consecutive months in the r1i1p1 historicalNat run of each CMIP5 model used in this analysis.  169  Figure C.12: Correlation between precipitation (pr) and mean daily maximum temperature (tx) of the hottest 3 consecutive months (h3m) in the pooled historicalNat runs of the six CMIP5 models analyzed in this study. Figure C.8, reproduced with land masking below for comparison, is the equivalent analysis using Boreal and Austral summer (JJA and DJF).   170  Figure C.13: Intermodel variation in relative departures from natural variability in temperature (Tx) and precipitation (Pr) of the hottest three consecutive months. Figure 5.3, reproduced below for comparison, is the equivalent analysis using Boreal and Austral summer (JJA and DJF).  171  Figure C.14: Relationship of maximum departure difference to the correlation between mean daily maximum temperature (Tx) and precipitation (Pr) of the three hottest consecutive months in RCP4.5 ensemble projections of 6 CMIP5 models.  Oceans and Antarctica are not plotted. Figure 5.4, reproduced below for comparison, is the equivalent analysis using Boreal and Austral summer (JJA and DJF).   

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0364414/manifest

Comment

Related Items