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Land use effects on green water fluxes in Mato Grosso, Brazil Lathuillière, Michael Jacques 2011

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LAND USE EFFECTS ON GREEN WATER FLUXES IN MATO GROSSO, BRAZIL  by Michael Jacques Lathuillière  B.Sc., The University of British Columbia, 2002  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Resource Management and Environmental Studies)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2011  © Michael Jacques Lathuillière, 2011  Abstract  The blue water - green water paradigm has been increasingly used to describe water resources. Blue water represents liquid flows in rivers or aquifers, while green water (GW) represents vapour exchanges with the atmosphere either as evaporation from soil or as transpiration from plants. This study assesses the impacts of land use change on GW fluxes in the Brazilian state of Mato Grosso, an ideal candidate for the study of GW in light of recent deforestation for pasture and soybean expansion, and the near complete reliance of its agricultural land base on precipitation as the GW source. Fluxes were estimated for 2000-2009 by combining the MODerate Resolution Imaging Spectroradiometer (MODIS) evapotranspiration product with forest cover change from Brazil’s National Institute of Space Research (INPE), as well as guidelines from the Food and Agriculture Organization (FAO) to model soybean, maize, sugar cane, cotton and pasture GW. In 2000, forest cover represented one third of the state’s land base and returned half of the state’s water vapour to the atmosphere. Annual total GW volumes decreased by 10 % between 2000 and 2009 at a rate of 16.2 km3 y-1 per year. Deforestation explained up to 27 % of variance in annual total volumes while agricultural expansion, as cropland and pasture, explained up to 20 %. Cropland GW doubled within the study time period, 75 % to 83 % of which constituted soybean GW. Pasture GW was 5 times larger than soybean GW and offset the increase in cropland GW. The greatest uncertainty lies in the role played by residual land use GW fluxes which were attributed to Brazilian savanna (cerrado), the Pantanal wetland, as well as unaccounted agricultural land left as fallow.  ii  Table of Contents  Abstract .................................................................................................................................... ii Table of Contents ................................................................................................................... iii List of Tables ......................................................................................................................... vii List of Figures .......................................................................................................................... x List of Symbols and Abbreviations .................................................................................... xiv Acknowledgements ............................................................................................................ xviii Chapter 1: Introduction ........................................................................................................ 1 1.1  The blue water, green water paradigm ...................................................................... 1  1.2  Green water consumptive use for agriculture ........................................................... 3  1.3  Blue and green water trade-offs with land use change ............................................. 5  1.4  Study objectives and research questions ................................................................... 7  Chapter 2: Methodology...................................................................................................... 10 2.1  Site description........................................................................................................ 10  2.1.1  The Brazilian state of Mato Grosso .................................................................... 10  2.1.2  Land use change in Mato Grosso ........................................................................ 12  2.2  Green water flux modeling ..................................................................................... 14  2.2.1  Total green water flows (GWT) .......................................................................... 15  2.2.2  Forest green water flows (GWF) ......................................................................... 15  2.2.3  Crop and pasture green water flux calculation (GWC, GWP) ............................. 17  2.2.3.1  Meteorological data .................................................................................... 17  2.2.3.2  Crop coefficients and calendar.................................................................... 20  iii  2.2.3.3  Water productivity of crops ........................................................................ 22  2.2.3.4  Spatial characterization ............................................................................... 24  2.2.3.4.1 Municipal units...................................................................................... 24 2.2.3.4.2 Agricultural production information ..................................................... 25 2.2.3.4.3 Pasture area determination .................................................................... 25 2.3  R modeling tool....................................................................................................... 27  Chapter 3: Results................................................................................................................ 28 3.1  State level green water flows .................................................................................. 28  3.2  Cropland and pasture green water modeling results ............................................... 30  3.3  Municipality level green water flows ..................................................................... 32  3.3.1  Flows in 15 municipal units containing a meteorological station....................... 32  3.3.2  Flows in all 104 municipal units ......................................................................... 35  3.4  Relationships between green water fluxes and land use change............................. 42  3.5  Relationships among individual green water fluxes ............................................... 44  Chapter 4: Discussion .......................................................................................................... 47 4.1  Green water seasonality in Mato Grosso ................................................................ 47  4.2  Trends in green water fluxes ................................................................................... 49  4.2.1  Impact of deforestation on green water flows..................................................... 49  4.2.2  Green water use for agriculture........................................................................... 51  4.2.3  Impact of agricultural expansion on green water flows ...................................... 53  4.3  Shifts in green water use from land use change ...................................................... 54  4.4  Analysis of uncertainty and open questions............................................................ 59  4.4.1  Cropland and pasture evapotranspiration............................................................ 59  iv  4.4.1.1  Sensitivity of meteorological data on green water calculations.................. 59  4.4.1.2  Assumptions of FAO guidelines ................................................................. 60  4.4.2  MODIS ET assumptions ..................................................................................... 62  4.4.3  Land use maps for Mato Grosso ......................................................................... 62  4.4.3.1  Forest cover ................................................................................................. 63  4.4.3.2  Cropland and pasture .................................................................................. 65  4.4.3.2.1 Cropland practices ................................................................................. 65 4.4.3.2.2 Pasture estimate ..................................................................................... 66 Chapter 5: Conclusions ....................................................................................................... 69 References .............................................................................................................................. 71 Appendices ............................................................................................................................. 84 Appendix A Deriving green water fluxes through evapotranspiration ............................... 84 A.1  The Penman-Monteith equation .......................................................................... 84  A.2  Input data for the Penman-Monteith equation .................................................... 86  A.3  Remote sensing ................................................................................................... 91  Appendix B Gap filling for meteorological data ................................................................ 93 Appendix C List of municipal units of Mato Grosso.......................................................... 95 Appendix D Water productivity curves .............................................................................. 99 Appendix E Pasture estimate ............................................................................................ 105 Appendix F R scripts used in this research ....................................................................... 107 F.1  Reference ET calculation .................................................................................. 107  F.2  Crop coefficients MT ........................................................................................ 115  Appendix G Total and forest green water for Mato Grosso ............................................. 186  v  Appendix H Agricultural land use for 15 municipal units ................................................ 187 Appendix I Significant changes in total and forest green water fluxes in Mato Grosso .. 194  vi  List of Tables  Table 1. Precipitation partitioning of major biomes in 2003-2007 (Miralles et al., 2011) ....... 5 Table 2. INMET meteorological stations of Mato Grosso used in this study......................... 19 Table 3. Crop coefficients and average development stages for Mato Grosso. ...................... 20 Table 4. Planting scenarios for major crops and pasture considered in this study. ................ 22 Table 5. Meteorological stations and corresponding municipal units used to calculate water productivity of soybean, maize, sugar cane and cotton. ......................................................... 23 Table 6: Aggregated municipalities for 2000-2009. ............................................................... 24 Table 7: Animal unit conversion factors (fAU) for pasture determination in equation (2) (Ramos, 2005). ........................................................................................................................ 26 Table 8. R scripts produced for this study. ............................................................................. 27 Table 9. Mean annual crop (GWC) and pasture (GWP) potential and actual green water fluxes for 15 municipal units containing a meteorological station (2000-2009). Values are shown as a range with mean minimum and maximum values calculated between 2000 and 2009. Values in brackets represent the standard deviations (sd) for each minima and maxima across the 15 municipal units. ............................................................................................................ 31 Table 10. Annual mean potential and actual crop (GWC) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units) for soybean, maize, sugar cane and cotton. ............................................................................................................. 39 Table 11. Relationship between annual total green water (GWT) volumes and fluxes with annual deforestation (km2 y-1) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. ................................................................................................................................................. 42  vii  Table 12. Relationship between annual total and forest (GWT, GWF, km3 y-1) green water fluxes with annual expansion area (ha y-1) of pasture, cropland and agricultural land (sum of cropland and pasture) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. ........ 43 Table 13. Relationship between annual total and forest (GWT, GWF, km3 y-1) green water volumes with annual expansion area of pasture, cropland and agricultural land (sum of cropland and pasture) (ha y-1) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. ................................................................................................................................................. 44 Table 14. Analysis of effects of the change in annual forest (GWF), agriculture (GWAg), and soybean (GWSoy) green water volumes on the change in annual total (GWT) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). MUs with forest cover (n = 828), MUs with 50% forest cover in 2000 (n = 243). ................ 45 Table 15. Analysis of effects of the change in annual pasture (GWP), agriculture (GWAg) and soybean (GWSoy) green water volumes on the change in annual forest (GWF) volumes for for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. All municipal units (n = 936), municipal units with >50 % forest cover in 2000 (n = 243). .................................................. 46 Table 16. Sensitivity of reference evapotranspiration (ET0) to common corrections made to meteorological data obtained from INMET (2011). ............................................................... 59 Table 17. Sensitivity tests of reference ET (ET0) from possible errors in meteorological data. ................................................................................................................................................. 60 Table 18. Water productivity (WP) of soybean, maize, sugar cane and cotton for both scenarios. ................................................................................................................................. 65 Table 19. Common gaps filled in time series data for all conventional INMET meteorological stations. ................................................................................................................................... 93  viii  Table 20. Gaps filled using nearby meteorological stations. .................................................. 94 Table 21: Mean wind speed used for corrections at INMET conventional meteorological stations. ................................................................................................................................... 94 Table 22. Municipal units of Mato Grosso for 2000-2009 used in this study ........................ 95 Table 23. Water productivity of crops assuming no water stress (2000-2009). ..................... 99 Table 24. Water productivity of crops under water stress. ................................................... 100 Table 25: Mean pasture green water for 2000-2009. ............................................................ 100 Table 26: Monthly maximum and minimum green water volumes and fluxes in Mato Grosso for total (GWT) and forest (GWF) ......................................................................................... 186 Table 27. Average precipitation from 8 meteorological stations in Mato Grosso, 1961-1990 (INMET, 2009) ..................................................................................................................... 186 Table 28. Sum of harvested area and mean yield for 15 municipal units of Mato Grosso for 2000 and 2009. ...................................................................................................................... 190 Table 29. INPE forest cover for 15 municipal units (INPE, 2011)....................................... 191 Table 30. Breakdown of green water volumes in 15 municipalities for Aug 1st – Jul 31st hydrologic years between 2000 and 2009: total (GWT), forest (GWF), soybean (GWSoy), maize (GWMaize), sugar cane (GWSugar), cotton (GWCotton), pasture (GWP) with biggest drop in estimated area (Appendix E), and GWAg, as GWC + GWP. .............................................. 192 Table 31. Significant changes in total (GWT) and forest (GWF) green water volumes and fluxes (2000-2009). ............................................................................................................... 194  ix  List of Figures  Figure 1. The Brazilian state of Mato Grosso (left) and its major biomes (right) - rainforest (green), cerrado (pink), Pantanal wetland (white) - (IBGE, 2010d) (printed with permission). ................................................................................................................................................. 11 Figure 2. Agricultural production of annual crops in Mato Grosso (2000-2009) (IBGE, 2010a). .................................................................................................................................... 14 Figure 3. INMET meteorological stations in Mato Grosso (INMET, 2011). ......................... 19 Figure 4. Total (GWT) and forest (GWF) green water volumes (top panel) and fluxes (bottom panel) for Mato Grosso from 2000 to 2009. GWT represents GW for the entire state of Mato Grosso, while GWF is the statewide forest GW. In the top panel, GWF volume is included within the cumulative GWT volume. ...................................................................................... 30 Figure 5. Annual total (GWT) and forest (GWF) green water volumes for 15 municipal units containing a meteorological station for Aug 1st – Jul 31st hydrologic years between 20002009......................................................................................................................................... 32 Figure 6. Breakdown of forest (GWF), residual land use (GWR), potential agriculture (GWAg, as cropland and pasture) as a percentage of total (GWT) with soybean (GWSoy) and pasture (GWP) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (15 municipal units containing a meteorological station). Values for GWSoy are reported as actual (- a) and potential (- p) GW volumes, while GWP is given for two surface area estimates (sa1 and sa2)............................................................................................................ 33 Figure 7. Significant changes (p-value <0.05) in annual total (GWT), forest (GWF), pasture (GWP) and agricultural (GWAg, as cropland and pasture) green water for 15 municipal units  x  containing a meteorological station for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (km3 y-1 per year). Full table available in Table 30, Appendix H. ................................. 35 Figure 8. Significant changes (p-value <0.05) in annual total (GWT) and forest (GWF) fluxes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Full list available in Table 31, Appendix I. .......................................................................................... 36 Figure 9. Percent difference in annual total (GWT) and forest (GWF) green water volumes between hydrologic years 2000 and 2009 in municipal units with observed significant changes over time (Figure 8). ................................................................................................. 37 Figure 10. Breakdown of forest (GWF), residual land use (GWR), potential agriculture (GWAg, as cropland and pasture) as a percentage of total (GWT) with pasture (GWP1 and GWP2 for both estimates) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Values for GWP are reported as a mean volume post 2006. ................................................................................................................................ 38 Figure 11. Sum of annual potential (top) and actual (bottom) soybean (GWSoy), maize (GWMaize), sugar cane (GWSugar) and cotton (GWCotton) green water for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Error bars represent the standard deviation between the two scenarios. ....................................................................... 39 Figure 12. Differences in annual potential soybean (GWSoy) and pasture (GWP) green water volumes between the Aug 1st – Jul 31st hydrologic years 2000 and 2009 (all municipal units) (km3 y-1). Pasture results are based on a continuous increase in livestock density (Figure 23, Appendix E). ........................................................................................................................... 41  xi  Figure 13. Percent differences in annual soybean (GWSoy) and pasture (GWP) green water volumes between the Aug 1st – Jul 31st hydrologic years 2000 and 2009 (all municipal units). Pasture results are based on a continuous increase in livestock density. ................................ 41 Figure 14. Relationship between changes in annual pasture (GWP) and annual soybean (GWSoy) green water for 15 municipal units containing a meteorological station for Aug 1st – Jul 31st hydrologic years in 2000-2009. .................................................................................. 58 Figure 15. Rasterized forest cover for 9 municipal units which experienced an increase in forest (GWF) green water fluxes in 2000-2009 (1 km2 resolution). Close up on Jaciara (MU 52) and São Pedro da Cipa (MU 95). ...................................................................................... 64 Figure 16: Crop coefficients Kc during the crop development cycle (Allen et al., 1998) ...... 86 Figure 17. MODIS algorithm for determining evapotranspiration (Mu et al., 2011). ............ 92 Figure 18. Municipal units of Mato Grosso for 2000-2009 defined for this study................. 98 Figure 19. Water productivity curves using potential crop green water (GWC) in 15 municipal units containing a meteorological station (2000-2009) (scenario I). .................................... 101 Figure 20. Water productivity curves using potential crop green water (GWC) in 15 municipal units containing a meteorological station (2000-2009) (scenario II). ................................... 102 Figure 21. Water productivity curves using actual crop green water (GWC) for 15 municipal units containing a meteorological station (2000-2009) (scenario I). .................................... 103 Figure 22. Water productivity curves using actual crop green water (GWC) for 15 municipal units containing a meteorological station (2000-2009) (scenario II). ................................... 104 Figure 23. Annual pasture area estimate in 2000-2009 for assumed continuous increase in livestock density (sa1), stable livestock density of 1.21 livestock units ha-1 (sa2). Acrimat estimate is from the Mato Grosso Association of Breeders (Acrimat, 2011). ...................... 106  xii  Figure 24. Land use in 15 municipal units in Mato Grosso from forest, agriculture (as cropland and pasture) and residual land (INPE, 2011; IBGE, 2010a). Some MUs are represented by numbers (see Appendix C). .......................................................................... 187 Figure 25. Percent change in forest and agricultural land cover (as cropland and pasture) between 2000 and 2009. ....................................................................................................... 188 Figure 26. Cropland harvested area for 15 municipal units (IBGE, 2010a). ........................ 189 Figure 27. Estimated pasture area for 15 municipal units and two pasture estimates (sa1 and sa2) (IBGE, 2010a). .............................................................................................................. 189  xiii  List of Symbols and Abbreviations  AP  ha  α cp  Pasture area Surface albedo  1.013 MJ kg-1 oC-1  Heat capacity of water at constant pressure Inverse relative distance Earth-Sun  dr ∆  kPa oC-1  Slope of the vapour pressure curve as a function of temperature  δ  radians  Solar declination  ea  kPa  Actual vapour pressure  es  kPa  Saturation vapour pressure  es - ea  kPa  Vapour pressure deficit  eo(T)  kPa  Saturation vapour pressure at air temperature T  eo(Tmax)  kPa  Saturation vapour pressure at maximum air temperature  eo(Tmin)  kPa  Saturation vapour pressure at minimum air temperature  ε  0.622  Ratio of molecular weights of water vapour to dry air  ET  mm day-1, mm month-1  Evapotranspiration  ETC  mm day-1, mm month-1  Crop evapotranspiration  ET0  mm day-1, mm month-1  Reference evapotranspiration  FAO  Food and Agriculture Organization  FAO56  Food and Agriculture Organization, Irrigation and Drainage Paper 56 (Allen et al., 1998) xiv  FPAR  Fraction of photosynthetically active radiation  fAU  Animal unit conversion factor  G  MJ m-2 day-1  Ground heat flux  GIS  Geographic Information Systems  GMAO  Global Modeling and Assimilation Office  Gsc  0.0820 MJ m-2 min-1  GW  Solar constant Green water  GWAg  km3 y-1 , mm y-1  Agricultural green water (cropland + pasture)  GWC  km3 y-1 , mm y-1  Crop green water  GWP  km3 y-1 , mm y-1  Pasture green water  GWR  km3 y-1 , mm y-1  Residual land use green water  GWSoy  km3 y-1, mm y-1  Soybean green water  GWT  km3 y-1 , mm y-1  Total green water  γ  kPa oC-1  Psychrometric constant  IBGE  Brazilian Institute of Geography and Statistics  INPE  Brazilian National Institute of Space Research  INMET  Brazilian National Meteorological Institute  J  Day of the year  ϕ  radians  Latitude  Kc  Crop coefficient  Kc dev  Development phase crop coefficient  Kc end  Harvest crop coefficient  Kc ini  Initial phase crop coefficient xv  Kc late  Late season crop coefficient  Kc mid  Mid-season crop coefficient  kRs  0.16  LAI  Adjustment coefficient for the Hargreaves’ radiation formula Leaf area index  LSD  livestock units ha-1  Livestock density  λ  2.45 MJ kg-1  Latent heat of vapourization  λET  mm day-1  Latent heat flux  MODIS  MODerate Resolution Imaging Spectroradiometer  MOD12Q1  MODIS collection 4 land cover type 2  MOD15A2  MODIS FPAR/LAI  MOD16  MODIS evapotranspiration product  MU  Municipal unit  N  animals  Animal population  P  hPa  Atmospheric pressure  Peff  mm  Effective precipitation  PM  Penman-Monteith equation  PRODES  INPE’s Monitoring the Amazon Deforestation Project  Ra  MJ m-2 day-1  Extraterrestrial radiation  ra  s m-1  Aerodynamic resistance  RH  %  Relative humidity  RHmax  %  Maximum relative humidity  xvi  RHmean  %  Mean relative humidity  RHmin  %  Minimum relative humidity  Rn  MJ m-2 day-1  Net radiation  Rnl  MJ m-2 day-1  Net longwave radiation  Rns  MJ m-2 day-1  Net shortwave radiation  Rs  MJ m-2 day-1  Solar radiation  Rso  MJ m-2 day-1  Clear sky solar radiation  rs  s m-1  Bulk surface resistance  σ  4.903 10-9 MJ K-4 m-2 day-1  Boltzmann constant  ρa  kg m-3  Mean density of air at constant pressure  Τ  ºC  Air temperature Total livestock unit  TLU Τmax  ºC  Maximum air temperature  Τmin  ºC  Minimum air temperature  uz  m s-1  Wind velocity at altitude z above canopy  u2  m s-1  Wind velocity 2 m above canopy  WP  m3 tonne-1  Water productivity  ωs  radians  Sunset hour angle  z  m  Altitude of meteorological station  xvii  Acknowledgements  I would like to thank my supervisor Dr. Mark Johnson for supporting me through this research and helping me identify and own a project that truly made my UBC graduate experience exciting. I am also dearly thankful to Dr. Simon Donner for his great suggestions during and beyond the committee meetings. A special thanks to Iain Hawthorne from UBC Ecohydro Lab for his insight on instrumentation and statistical analysis of meteorological data, Brent Chamberlain from the Department of Forestry for his help on GIS analysis, and Qiaozhen Mu from the Numerical Terradynamic Simulation Group at the University of Montana, Missoula, for making the MOD16 data available. This project would not have been successful without the help of Brazilian researchers from the Universidade Federal de Mato Grosso in Cuiabá. More specifically: Dr. Eduardo Guimarães Couto for receiving me as a guest in the Agronomy department, Dr. José Holanda Campelo Júnior for his profound knowledge of Mato Grosso’s meteorological stations, and Dr. Francisco de Almeida Lobo for his kind suggestions regarding biosphere-atmosphere exchanges. I thank the entire faculty, staff and students from the UBC Institute for Resources, Environment and Sustainability for a very exciting two years in the program. They have really been an inspiration for me during and beyond my years on the campus. Finally, a very special thanks is owed to Caroline Guay who has supported me through the ups and downs of this exciting voyage.  xviii  Chapter 1: Introduction  Since the earliest settlements, civilizations have thrived through the planning of water resources for direct human consumption, irrigation for agriculture or navigation for trade. Despite a long history, water has had limited changes in its foundation for planning. Supplyside management has relied on large water projects built following forecasts on population growth, living standards and resulting increases in food consumption from irrigated agriculture (Gleick, 2000). Such management relies solely on the use of liquid water to meet human demand (e.g. rivers, lakes and aquifers) with little or no attention to the role of water vapour in the water cycle. Population pressures on rising water demand have led to calls for a change in water paradigm that would highlight new approaches to water planning (Gleick, 1998, 2000). One possible approach is to focus on vapour flows, which return almost two thirds of precipitation to the atmosphere through evapotranspiration processes (Oki & Kanae, 2006).  1.1  The blue water, green water paradigm The blue water, green water (GW) paradigm was proposed by Falkenmark &  Rockström (2006) to illustrate this shift in thinking for water resources. The paradigm emphasizes the link between precipitation and terrestrial ecosystems as a way to incorporate important water vapour flows that would otherwise be disregarded in conventional water management of aquifers and reservoirs (Rockström & Gordon, 2001; Falkenmark & Rockström, 2006). Blue water represents the liquid flows of surface and groundwater, while GW is comprised of water vapour, invisible in the landscape (Falkenmark & Rockström,  1  2004). Precipitation is partitioned at the soil; blue water is typically removed from the landscape by infiltrating into soil and recharging aquifers, or is transferred to streams and lakes by runoff and overland flow processes; potential GW remains in the soil’s unsaturated zone to regenerate precipitation either through soil evaporation or plant transpiration (together as evapotranspiration, or ET) (Falkenmark & Rockström, 2004). This distinction between liquid and vapour flows is particularly important when considering consumptive uses of water. GW is only used once as a means towards an ecosystem service (from a wetland, forest, pasture or cropland), whereas blue water can be used many times downstream (Falkenmark & Rockström, 2004: 6; Rockström & Gordon, 2001). In this context, water resource management becomes intimately tied to landscape management such that any change in land use impacts the partitioning of precipitation into blue and GW resources. From this proposed paradigm, it is apparent that water resource management has focused on blue water through the engineering of dams or wells (Falkenmark & Rockström, 2004: 8-9; 2006). Shifting the water source that is targeted for management to precipitation means emphasizing GW vapour flows in the water cycle, especially as input for source regeneration: close to 60 % of global precipitation is estimated to come from GW (Oki & Kanae, 2006) with recent estimates of annual global ET fluxes estimated at 62,800 km3 y-1 (Mu et al., 2011), 65,000 km3 y-1 (Jung et al., 2009) and 67,900 km3 y-1 (Miralles et al., 2011). As an emerging research paradigm, many studies have sought to provide detailed accounting of these sources of water at the river basin level (Sulser et al., 2010), national level (Iran : Faramarzi et al., 2009; Tunisia: Chahed et al., 2008), continental level (Africa: Schuol et al., 2009), and global level (Hoff et al., 2010).  2  1.2  Green water consumptive use for agriculture Unlike blue water, GW is only consumed once. It often provides important ecosystems  services, especially in crops and pasture where water is consumed during photosynthesis to convert solar energy into chemical energy for food and fiber. GW flows are driven by solar energy transfers to the Earth’s surface, which in turn affect how vapour flows are exchanged between the biosphere and the atmosphere. These transfers occur either directly from the soil (as GW from evaporation), or indirectly during CO2 fixation from photosynthesis (as GW from transpiration) (Falkenmark & Rockström, 2006). The difference between transpiration and evaporation leads to the distinction between “productive GW” and “unproductive GW” where transpiration is considered productive GW from a crop productivity or plant water-use standpoint. Evaporation from soil and water surfaces is deemed unproductive GW in that it does not result in primary productivity. Several studies have looked at the global importance of GW in the context of rain-fed agriculture. In a model simulation from 1971-2000, Rost et al. (2008) determined that GW represented over 80 % of crop water consumed (estimated at 7200 km3 y-1). Liu et al. (2009) estimated that between 1998 and 2002, GW accounted for >80 % of crop water use (3823 km3 y-1 estimated) for the major crops studied. Hoff et al. (2010) synthesized findings from seven different hydrologic models which agree on the global importance of GW for food production. Global crop GW consumption from rain-fed agriculture was found to be 3 to 4 times larger than blue water consumption from irrigated agriculture at 4435 km3 y-1 ± 20 % (or about 7 % of global ET) during the crop period (from four of the models) (Hoff et al., 2010). Global crop GW consumption from combined irrigated and rain-fed agriculture  3  contribute 5320 km3 y-1 ± 6 % (or about 8 % of global ET) during the cropping period (from five of the models) with large spatial differences (Hoff et al., 2010). GW is given an important role in redefining sustainable agriculture for the many challenges to be faced this century (Rockström & Karlberg, 2010). Rockström et al. (2009) assessed water availability and requirements for the next 40 years and concluded that GW would have an important role to play in the context of climate change, increased atmospheric CO2 and population growth. Efficient GW use can help meet current and future food demand via a mix of scenarios: water producitivity improvements (growing more crops with the same amount of water), irrigation expansion, cropland expansion and virtual water imports (Hoff et al., 2010; Rockström et al., 2009). The concept of virtual water was introduced by Allan (1998) to define goods and services as they relate to quantities of water consumed. This purely economic approach allows for the assessment of water flows between areas of production and consumption through international trade, especially for crops (Hoekstra & Hung, 2005). Importing virtual water through agricultural products can relieve local water stresses. Given that 94 % of virtual water trade is GW dependent (Liu et al., 2009), GW has an important role to play in solving the future food and water challenges. Agricultural production for some regions of the world is almost entirely rain-fed and thus depends on GW. Such regions are also considered major centers of significant improvement for rain-fed agriculture, particularly the tropics. In the tropics, GW productivity, defined as the amount of water required to grow 1 tonne of grain, is not very different from other regions (Falkenmark & Rockström, 2004: 53). Agricultural land management is the source of greater differences in water producitivity between regions and can vary between 1000 to 6000 m3 of GW per tonne of grain produced mainly due to  4  evaporation processes in the warmer regions and increased crop water requirements (Falkenmark & Rockström, 2004: 53). Upgrading rain-fed agriculture means reducing evaporative losses – deemed unproductive – and maximizing the transpiration component of ET. This improvement in water productivity can be achieved by various land management practices such as dry planting or intercropping, which illustrate a so called “vapour shift” (Falkenmark & Rockström, 2004: 148). These are but some proposed ways of meeting current and future food demands alongside expansion of irrigation, soil water harvesting and increasing agricultural land, all of which come with specific trade-offs on the impact of the partitioning of blue and GW (Karlberg et al., 2009).  1.3  Blue and green water trade-offs with land use change Miralles et al. (2011) used a land surface evaporation model to provide a global  assessment of precipitation partitioning of biomes for 2003-2007, thus updating information presented by Falkenmark & Rockström (2004: 40) (Table 1). Table 1. Precipitation partitioning of major biomes in 2003-2007 (Miralles et al., 2011) -1  Biome Tropical forests Savanna Grassland Cropland  -1  Green water* (mm y ) (% precipitation)  Blue water** (mm y ) (% precipitation)  1182 (53) 806 (60) 462 (62) 542 (62)  1068 (47) 533 (40) 336 (38) 336 (38)  *as ET; **as precipitation minus ET  The biomes listed in Table 1 are a result of local soil properties as well as factors that affect the partitioning of the water source (precipitation) into green and blue water components (Falkenmark & Rockström, 2004: 39). In addition, the difference in green and blue water partitioning also affects the recycling of precipitation through ET processes. From Table 1, 53 % to 62 % of precipitation was returned to the atmosphere between 2003 and 2007. This  5  adds another dimension of the paradigm: a reduction in local GW may in turn affect the regeneration of local precipitation through soil moisture feedback (Krakauer et al., 2010). Each water decision is, in effect, a land management decision in the blue and green water paradigm (Falkenmark & Rockström, 2004). Thus, the trade-offs from land use impacts on water partitioning in blue and green components must be considered, especially in the context of ecosystem services. While aquatic ecosystems rely exclusively on blue water resources, terrestrial ecosystems rely on GW (Falkenmark & Rockström, 2004: 184-186). Such global dependence of terrestrial ecosystem services on GW was estimated at approximately 44,700 km3 y-1 of plant-transpired GW for the 1971-2000 period (Rost et al., 2008). Previously forested areas may be replaced with agriculture thus increasing GW use for food production, but also changing the partitioning of precipitation by increasing the potential for run-off (blue water). In addition, GW can decrease since crops generally produce less GW than forest ecosystems due to their smaller root systems (Falkenmark & Rockström, 2004: 11), smaller canopy interception, different growing cycles, and differing seasonality for crops relative to forests. Gordon et al. (2005) describe that while there exists a global offset of GW losses from deforestation with GW gains from the expansion of irrigated lands (Gordon et al., 2005), regional differences may still occur. This is the case for the Amazon where deforestation is not accompanied by complementary increases in irrigation vapour flows (Gordon et al., 2005). Rost et al. (2008) show decreases in ET (2.8 % globally) and increases in river discharge (5.0 % globally) from land use change, while irrigation increases ET (1.9 % globally) and decreases discharge. Many of these identified trade-offs have impacts on vapour flows from the landscape. Such changes have been studied at the global scale using  6  remote sensing techniques to assess global changes in ET. These techniques have been able to complement ground-based ET observations to allow for global water vapour flux assessments. A recent study evaluating global ET fluxes between 1982-2008 found an increase of 7.1 ± 1 mm y-1 per decade for 1982-1997 (Jung et al., 2009). This increase had been expected from the theorized acceleration of the water cycle due to climate change, but evidence of a decrease in soil moisture supply in Australia, Africa and South America also contributed to a decline in ET since 1998 (Jung et al., 2009). Soil moisture represents GW stocks that are replenished by precipitation before water is returned to the atmosphere. The ET drop resulting from decreased soil moisture supply suggests a possible decline in GW stocks in the Southern Hemisphere from Jung et al. (2009). Moreover, given the importance of GW to replenish precipitation via ET (Oki & Kanae, 2006), changes in soil moisture may in turn affect the water cycle.  1.4  Study objectives and research questions Global studies, although important, fail to provide a detailed mechanism at the regional  level. Water management decisions are closely linked to land management decisions as they affect water partitioning into blue and green components. Studying GW is a way of determining just how land use management is affecting the water cycle by returning water vapour to regenerate precipitation, the GW source. The South American continent is the largest global source of GW with estimated annual flows of 17,000 km3 y-1 for 2003-2007 (Miralles et al., 2011), but is also considered a centre for the drop in global soil moisture supply described by Jung et al. (2009) (along with Asia and Australia).  7  The objective of this study is to enhance the understanding of the changes in GW fluxes with land use. Within the role of South America in the global ET decline (Jung et al., 2009), the Brazilian state of Mato Grosso represents a model case for such a study for two reasons: (1) its near complete reliance on precipitation (GW) rather than irrigation (blue water) for crop water on its expanding agricultural land base; (2) its rapid land use change from agricultural expansion and deforestation which are believed to have had detectable effects on GW fluxes. There is extensive literature on land use change in Mato Grosso with some implications on the impacts on the water cycle. Those studies do not, however, specifically address GW. This study takes a water-focused approach by looking at GW fluxes for the entire state of Mato Grosso (900,000 km2) during the 2000-2009 period in order to address the following research questions: 1. What changes in GW were observed and what role did land use play on those changes? 2. What GW trade-offs has Mato Grosso faced in light of its land use change? To answer these questions, I assessed state-wide ET processes as they occured in cropland, pasture and forest using the PM equation. A remote sensing technique (MODerate Resolution Imaging Spectroradiometer, or MODIS and available since 2000) which derives ET from a combination of meteorological data and surface coverage information was used to provide a monthly snapshot of total GW. This information was parsed into forest GW digital forest cover maps. Then, a crop model based on Food and Agriculture Organization guidelines (Allen et al., 1998) was used in combination with agricultural production information in order to determine total crop and pasture GW fluxes. The combination of both methods  8  helped to estimate the GW contributions from different land cover classes and from subregions of Mato Grosso. The thesis begins with a description of the study area, and the documented land use changes. Then, the methods used to derive GW fluxes at the state and municipal level are provided (Chapter 2) with a detailed description of the PM equation and its use with meteorological data and MODIS information (Appendix A). Finally, a description of results (Chapter 3) and discussion of findings (Chapter 4) are provided.  9  Chapter 2: Methodology  This chapter describes the methodology used for determining GW fluxes for the major land uses of Mato Grosso (forest, pasture, cropland) at the state and municipal unit (MU) level, a sub-division which allows for proper comparison of political boundaries over the study time period. First, a general description of the study area with documented land use changes is outlined. Then, a detailed description of total GW fluxes is provided before outlining steps for modeling the crop and pasture GW (GWC and GWP) contributions using meteorological data in combination with the PM equation and guidelines from Food and Agriculture Organization (FAO) (Appendix A).  2.1 2.1.1  Site description The Brazilian state of Mato Grosso The state of Mato Grosso is one of nine states that make Brazil’s Legal Amazon1. It  occupies 900,000 km2 and extends approximately from latitude 6.5°S to 18°S and from longitude 50°W to 62°W (Figure 1). Mean annual temperatures are 25-27°C with total annual precipitation concentrated in a September-April rainy season and distributed on a gradient of increasing rainfall from south to north, from 1200 to 2200 mm y-1 (INMET, 2011). The state is home to three major biomes separated by transitional landscapes: rainforest in the north, which comprises the southern extent of the Amazon forest; cerrado or Brazilian savanna in the centre; and the Pantanal wetland in the south (Figure 1). The cerrado region itself is a  1  The Legal Amazon is a political boundary containing the states of Acre, Amapá, Amazonas, Pará, Rondônia, Rorainma, Tocantins, Mato Grosso and Maranhão 10  complex ecosystem containing a mixture of grasslands (campo cerrados), savanna (cerrado sensu stricto) and woodland (cerradão) (Jepson, 2005), while the Pantanal in the south is delimited by more than 138,000 km2 of seasonally flooded areas, 35 % of which is in Mato Grosso (Vila da Silva & Abdon, 1998). Elevation in the state ranges from 70 m to 1150 m with highest land surface elevation occurring in the central part of the state in the cerrado zone.  Figure 1. The Brazilian state of Mato Grosso (left) and its major biomes (right) - rainforest (green), cerrado (pink), Pantanal wetland (white) - (IBGE, 2010d) (printed with permission).  All three biomes extend far beyond the state boundaries: the rainforest expands north towards the states of Amazonas and Pará, while the Pantanal is shared south with Mato Grosso do Sul, and west into Bolivia and Paraguay. The cerrado spreads east to reach over 2 million km2. The cerrado biome has undergone extensive land use change to agriculture, with cerrado vegetation reduced in extent by half by land use change (Klink & Machado, 2005). The occurrence of cerrado vegetation is in part due to the acidic soil conditions (pH of 4.3 to 6.2), the high levels of aluminum saturation, and phosphorous deficiency with low cation exchange capacity (Furley & Ratte, 1988). In addition to plant breeding strategies, soil 11  management for acidity, water and nutrient content had an important role in developing the cerrado as a major agricultural region (Goedert, 1983).  2.1.2  Land use change in Mato Grosso Mato Grosso has undergone important land use changes from agricultural settlements  both in its rainforest and cerrado biomes. Since the 1970s, agriculture has been expanding north and getting closer to the Amazon forest with a greater emphasis on soybean and pasture for cattle (Fearnside, 2001; Simon & Garagorry, 2005). Brazil’s internal colonization was largely driven by the national Agrarian Reform of the 1960s which aimed to alleviate poverty by providing small farmers with access to land. This colonization policy was one of the more important drivers of deforestation in the 1980s with cattle ranching and road building for access to remote areas (Rudel et al., 2009). Deforestation dynamics changed in the 1990s as the country entered a more enterprise-driven deforestation (Rudel et al., 2009) for cattle ranching and soybean production (Fearnside, 2001; 2005). While deforestation is often a concern in the rainforest area of northern Mato Grosso, the cerrado has experienced deforestation rates much higher than the rainforest (Klink & Machado, 2005). This has been attributed to the Federal Forest Code that dictates land-use of rural property through a “Legal Reserve” under which a percentage of natural forest cover must be kept on a property (Fearnside & Barbosa, 2004). As of 2000, that percentage of a land holding that must remain in native vegetation can ranges from from 20 % in western Mato Grosso, to 35 % in eastern Mato Grosso, to 80 % in the Amazon region and other heavily forested areas, to 50 % in the cerrado-rainforest transition area (Fearnside & Barbosa, 2004; Brannstrom et al., 2008).  12  Determining the dynamics of land use change in the region and the impacts of agricultural expansion on the cerrado and the rainforest has been an important focus of research. While the disappearance of the cerrado has been closely linked to the expansion of pasture and soybean for smaller areas of Mato Grosso (Jepson, 2005), consensus on their condition and continent wide impacts have been more difficult due to reliance on remote sensing techniques and census information whose statistical analysis often cannot infer direct causality. Between 1980 and 1995, Mato Grosso experienced a 50 % increase in its agricultural land surface for planted pasture and cropland at the expense of natural pasture (Cardille & Foley, 2003). While forests were previously cleared exclusively for pasture, there is now more evidence of conversions of forest to cropland and pasture to cropland with the expansion of Brazil’s soybean production. Morton et al. (2006) observed an 87 % increase in cropland in Mato Grosso concurrent to 40 % new deforestation between 2001 and 2004. They also estimated that 36 % of cropland resulted from pasture conversions and 30 % from replacement of cerrado (Morton et al., 2006). Between 2001 and 2005, the average rate of soybean expansion increased 19.4 % y-1 with observed land use changes from pasture to soybean (Jasinski et al., 2005). Between 2000 and 2006, soybean moved further north with evidence of replacement of pasture, itself indirectly contributing to forest clearing for additional pastures established closer to the Amazon (Barona et al., 2010). In 2009, the major crops of Mato Grosso were soybean (5.8 million ha harvested), maize (1.7 million ha harvested), cotton (0.4 million ha harvested), rice (0.3 million ha harvested), and sugar cane (0.2 million ha harvested) (IBGE, 2010a) (Figure 2). All major crops are planted during the rainy season, thus eliminating the need for irrigation (blue water). Out of the total harvested area of 8,757,373 ha noted in the 2006 state census,  13  irrigated land accounted for only 148,425 ha, with more than 99 % of irrigation used for the five crops listed above (IBGE, 2010a).  Figure 2. Agricultural production of annual crops in Mato Grosso (2000-2009) (IBGE, 2010a).  2.2  Green water flux modeling In the context of the blue and GW paradigm, GW fluxes were modeled as ET where the  total GW (GWT) for Mato Grosso was determined annually for each municipal unit (MU2). GWT is the sum of the GW fluxes of forest (GWF), cropland (GWC), pasture (GWP), and residual land use (GWR) which includes water bodies, unaccounted forest and shrubs (cerrado), roads and cities. For each MU, GWT and GWF were determined using the MODIS ET product (MOD16) obtained from an algorithm developed by Mu et al. (2011) (Appendix A); GWC and GWP were modeled using the PM equation following FAO guidelines by Allen et al. (1998) (shortened as FAO56, described in Appendix A). GW was analyzed by looking at volumes and fluxes. Fluxes (in mm) determine mean GW flows from a point. Volumes (in km3, computed as flux times area) represent the amount of water vapour produced by a landscape and are representative of an ecosystem surface area.  2  Municipal units are aggregated political units such that their shape and size remained constant between 2000 and 2009 (see section 2.2.3.4.1) 14  Volumes help to understand the aggregate quantities of water evaporated and transpired at the state level, as well as the cumulative impact of land use change on vapour returns to the atmosphere. Fluxes allow for a comparison between different land uses based on environmental conditions. The August 1st – July 31st hydrologic years is the timeframe believed to best represent the changes in GW fluxes due to both agricultural practices which coincide with the rainy season and deforestation rates which are calculated from forest cover determined in the dry months.  2.2.1  Total green water flows (GWT) The monthly GWT flux was obtained for the entire state of Mato Grosso as well as  individual MUs (Appendix C) using MODIS images at 1 km2 resolution (0.833 decimal degrees) obtained from the algorithm developed by Mu, et al. (2011), available online (ftp://ftp.ntsg.umt.edu/pub/MODIS/Mirror/MOD16/). GWT fluxes were extracted from the MODIS images with a raster mask extraction tool of ESRI Geographic Information System ArcGIS 10 after converting MU polygons to rasters of cell size identical to the MODIS raster data. Raster values were then analyzed in ArcGIS 10 to provide the GWT volumes and fluxes. Volumes (in km3 mo-1) were determined by summing rasters from MOD16 (in mm mo-1) before converting to a volume from its representative area. Fluxes (in mm mo-1) were obtained by summing MOD16 data and dividing by the number of rasters of interest.  2.2.2  Forest green water flows (GWF) Forest cover was obtained from the Brazilian National Institute of Space Research  (INPE, Instituto Nacional de Pesquisas Espaciais) responsible for monitoring deforestation  15  in the Legal Amazon. INPE’s Monitoring the Amazon Deforestation Project (PRODES, Projecto de Estimativa do Desflorestamento da Amazônia) has monitored deforestation first through an analogue method involving the visual interpretation of photos (1998-2002, described in (INPE, 2002)), then by a digital method using computers to determine deforestation rates (Câmara et al., 2006). All images were obtained from Landsat then processed by INPE to provide areas of gross deforestation. Images are typically obtained in July or August to avoid interfering cloud cover. INPE provides shapefiles of deforestation for the 2000-2009 period available through their website (http://www.obt.inpe.br) at 60 m resolution (except for 2007 which is at 120 m). Images were classified following land use determined by the INPE methodology (Câmara et al., 2006). Forest (floresta) designates tropical forest to be differentiated from other types of vegetation included in the “not forest” (não-floresta) classification such as grassland and cerrado. In addition, INPE uses a separate classification for “deforestation extent” (extensão desflorestada), which is accumulated deforestation up to and including the previous year; “year’s deforestation” (desflorestamento do ano); “water bodies” (hidrografia); and “clouds” (nuvem). Polygons were obtained in shapefile format that were then processed in ArcGIS 10 to separate year to year forest cover and deforestation. Forest cover was only available for 2009, but not for earlier years. These were determined using deforestation polygons available for each year. Thus, the 2008 forest cover was obtained by adding the forest cover polygons of 2009 to the deforestation polygons of 2009 (respectively for all years going back to 2000). Finally, forest cover features were converted to rasters of resolution equal to the MOD16 raster data (1 km2) in order to extract the forest monthly GWF using the forest cover raster as  16  the extraction mask. Raster values for GWF were then analyzed in ArcGIS 10 to provide the flux (mm mo-1) and the volume (km3 mo-1).  2.2.3  Crop and pasture green water flux calculation (GWC, GWP) Both GWC and GWP fluxes were obtained from calculations of crop evapotranspiration  (ETC) and agricultural production information. ETC was calculated from ET0, which was obtained from the PM equation using meteorological data as described in FAO56 (Allen et al., 1998) (Appendix A). Crops and pasture were assumed to not experience nutrient deficiencies or disease. Precipitation was assumed as the only water source for the major crops (soybean, maize, sugar cane and cotton). Agricultural production data was obtained through the Brazilian Institute of Geography and Statistics (IBGE, Instituto Brasileiro de Geographia e Estadisticas) SIDRA website for 2000-2009 period (IBGE, 2010a). This information is collected by IBGE through expert surveys (IBGE, 2010b). ETC (mm) was then multiplied by the harvested area of each crop and the estimated pasture area (Appendix E) to obtain the respective GWC and GWP volumes (km3).  2.2.3.1  Meteorological data  Meteorological data was used to calculate daily ET0 and ETC from FAO56 (Appendix A). Data were obtained from meteorological stations maintained by the Brazilian National Meteorological Institute (INMET, Instituto Nacional de Meteorologia) for Mato Grosso available online (http://www.inmet.gov.br/) (INMET, 2011). Measurements are recorded three times a day (local time 8:00, 14:00 and 20:00, GMT minus 4 hours). Maximum daily  17  relative humidity was selected as the value recorded at 8:00, while minimum relative humidity was that of 14:00 local time. Two types of meteorological station networks were used in the present analysis (Table 2 and Figure 3). Thirteen stations were available from the conventional weather station network (Estação Meteorológica de Observação de Superfície Convencional) (INMET, 2010b). These stations record daily maximum and minimum temperatures, humidity, wind speed, wind direction, cloud cover and cumulative daily precipitation. Data is typically read and recorded by an observer (INMET, 2011) and is available from 2000 to present. Twentyseven additional stations were available from the data logger network (Estação Meteorológica de Observação de Superfície Automática) (INMET, 2010a) which provides hourly temperature (including maximum and minimum), relative humidity, dew point, atmospheric pressure, wind velocity, direction, solar radiation and precipitation, mostly since 2008. All 13 conventional stations were used in the study due to the range of data available. Only 3 of the data logger stations were used in the present study, and were only used to aid in gap-filling for conventional meteorological stations located in close proximity (Table 20, Appendix B). The wind speed was adjusted to a height of 2 m for calculating ET0 using equation (1) (Allen et al., 1998): u2 = u z  4.87 ln(67.10 z − 5.42)  (1)  where u2 is the wind speed (m s-1) at 2 m above the surface, uz is the wind speed (m s-1) at z meters above the surface (10 m for INMET conventional stations (Campelo, 2010)).  18  Table 2. INMET meteorological stations of Mato Grosso used in this study. Name  Number  Type  Aragarças 83368 Conventional Cáceres 83405 Conventional Campo Verde A912 Data logger Canarana 83270 Conventional Cuiabá* 83361 Conventional Diamantino 883309 Conventional Gleba Celeste 83264 Conventional Matupá 83214 Conventional Nova Xavantina 83319 Conventional Padre Ricardo Remetter 83364 Conventional Poxoréo 83358 Conventional Rondonópolis 83410 Conventional Rondonópolis A907 Data logger São José do Rio Claro 83267 Conventional São José do Rio Claro A903 Data logger São Vincente 83363 Conventional *Cuiabá was combined with Padre Ricardo Remetter  Altitude (m)  Longitude (W)  Latitude (S)  345 118 749 430 145 256 415 285 316 140 450 284 284 350 350 800  -52.23 -57.68 -55.08 -52.27 -56.11 -56.46 -56.50 -54.92 -52.35 -56.07 -54.38 -54.57 -54.57 -56.72 -56.67 -55.42  -15.90 -16.05 -15.31 -13.47 -15.62 -14.40 -12.20 -10.25 -14.70 -15.78 -15.38 -16.45 -16.45 -13.43 -13.45 -15.82  Figure 3. INMET meteorological stations in Mato Grosso (INMET, 2011).  Raw data of each station was downloaded and analyzed as a time series using Aquatic Informatics Aquarius version 2.7. Details on gap filling for meteorological data are outlined in Appendix B.  19  2.2.3.2  Crop coefficients and calendar  Crop coefficients (Kc) and development cycles were obtained for soybean (Glycine max), maize (Zea Mays), cotton (Gossypium hirsutum), sugar cane (Saccarum officinarum) and pasture (FAO Water 2002a, 2002b, 2002c, 2002d). Each crop was given four Kc values which vary with the development cycle of the crop (Figure 16, Appendix A) based on the initial (Kc ini), development (Kc dev), mid-season (Kc mid), and late season phases (Kc late) to harvest (Kc end). Kc values were often available from the literature as step functions over time, especially for the development and late stages. This differs from the FAO which proposes progressive changes over time for Kc dev and Kc late (Figure 16, Appendix A). Kc ini and Kc mid were obtained from the literature and represent local environmental conditions (Table 3). Kc end  for soybean was obtained from FAO Water (2002c). These described steps allowed for the  construction of a similar Kc curve as that of Figure 16 (Appendix A). Table 3. Crop coefficients and average development stages for Mato Grosso. Crop  Kc ini (days)  Kc dev slope (days)  Kc mid (days)  Kc late slope (days)  Kc end  Source  Soybean  0.56 (13)  0.024 (40)  1.50 (43)  -0.0333 (30)  0.50  Farias et al., 2001; FAO Water, 2002c  Maize  0.60 (30)  0.04 (20)  1.40 (20)  -0.027 (30)  0.60  Bastos et al., n.d.  Sugar cane  0.4 (30)  0.019 (45)  1.25 (225)  -0.083 (60)  0.75  Alves de Oliveira et al., 2010  Cotton  0.4 (20)  0.022 (30)  1.05 (65)  -0.022 (35)  0.65  Embrapa algodão, 2003  Pasture  0.30  NA  0.75  NA  NA  Allen et al., 1998  NA = not available  20  Both Kc dev and Kc late were calculated based on the slope of the Kc curve during the development stage such that Kc dev increased with each day. Similarly, Kc late was determined with the slope of the Kc curve between Kc mid and Kc end. Duration of development cycles are based on average values. In the case of maize, average Kc values were determined for Kc ini and Kc end as obtained from the last point constructed on the Kc curve (Bastos et al., n.d.). Sugar cane is typically harvested once a year on rotation and repeats the Kc cycle upon harvest (Alves de Oliveira et al., 2010). Finally two Kc values were used for pasture (extensive grazing from Allen et al., 1998). These represent average Kc taking into account possible cuts from harvests or animal consumption (Allen et al., 1998). Since pasture ET can respond to cuts and precipitation, the Kc values were alternated between Kc ini and Kc mid for the dry and wet events, where the threshold for a wet event was defined as having 7 mm and 10 mm of precipitation in two separate scenarios (Table 4). Planting days for crops were established based on current practices in Mato Grosso assuming these practices were consistent for 2000-2009. The major crops rely on precipitation as a water source, and thus planting occurs such that larger water requirements coincide with the rainy season. Typically soybeans are planted first (October-November) followed by maize and cotton for a harvest, locally known as safrinha (or little harvest), before the end of the rainy season. The safrinha maize constitutes the bulk of maize production in the state (IBGE, 2008). Sugar cane is planted on rotation, where part of the plant is cut for harvest at the end of the rainy season (April), allowing the plant to re-grow for the following year. For this study, it is assumed that all harvested sugar cane takes one year to develop before the following cut (known as cana-soca). Two planting scenarios were  21  evaluated to determine GWC and GWP (Table 4). The first scenario assumes an early planting of soybean (October 1st) followed 126 days later by maize and cotton as safrinha; pasture growth was based on precipitation as 10 mm threshold for growth. The second scenario assumed a later soybean planting date (November 1st) followed 126 days later by maize and cotton as safrinha; pasture growth was based on precipitation as 7 mm threshold for growth. Table 4. Planting scenarios for major crops and pasture considered in this study. Scenario  Crops  Planting dates st  (I) Early planting date, 10 mm precipitation threshold  Soybean Cotton, maize Sugar cane Pasture  Oct 1 2000 and subsequent years rd Feb 3 2001 and subsequent years th Harvest on Apr 30 and subsequent years 10 mm precipitation threshold for Kc mid  (II) Late planting date, 7 mm precipitation threshold  Soybean Cotton, maize Sugar cane Pasture  Nov 1 2000 and subsequent years th Mar 7 2001 and subsequent years th Harvest on Apr 30 and subsequent years 7 mm precipitation threshold for Kc mid  2.2.3.3  st  Water productivity of crops  Water productivity (WP) curves were used to estimate GWC for MUs that were not close to a meteorological station. WP of crops refers to the amount of water required to produce a crop based on GW and the harvested area, often expressed in m3 of water per tonne of grain3. The relationship with crop transpiration is understood to be linear, such that more transpiration means more growth (Falkenmark & Rockström, 2004: 142-143), therefore the production quantities reported by IBGE (in tonnes) can help estimate the GW use of crops (in m3). WP curves were obtained from the meteorological stations and nearby 15 MUs (Table 5). If the meteorological station was near a municipal divide, or in an area surrounded by  3  Water productivity may also be understood as the reciprocal of water use efficiency 22  small municipalities, then agronomic data for the relevant MUs were used to determine the local WP. One WP curve was generated using the modeled ETC which assumes that the crops always receive enough water (called potential GW in this study). A second WP curve was obtained using effective precipitation (Peff) as calculated from the USDA Soil Conservation Service (Dastane, 1978) and obtained from software package Cropwat 8.0 (FAO Water, 2011). Peff calculates the amount of water available for crops in the root zone. GWC was then determined for 10 day time steps following these conditions to calculate what is termed actual GW in this study, and is by definition a value less than that of potential GW: If ETC < Peff then GWC = ETC If ETC > Peff then GWC = Peff GWC could then be estimated using production quantities available by IBGE (IBGE, 2010a). Table 5. Meteorological stations and corresponding municipal units used to calculate water productivity of soybean, maize, sugar cane and cotton. Station Aragarças Aragarças Cáceres Caranara Diamantino São José do Rio Claro Gleba Celeste Matupá Matupá Nova Xavantina Padre Ricardo Remetter Padre Ricardo Remetter Padre Ricardo Remetter Poxoréo Rondonópolis São Vincente  Municipalities  Municipal unit  Barra do Garças Pontal do Araguaia Cáceres, Curvelândia, Lambari d’Oeste, Mirassol d’Oeste Canarana Diamantino, São José do Rio Claro Diamantino, São José do Rio Claro Vera Matupá Peixoto de Azevedo Nova Xavantina Cuiabá Varzéa Grande Santo Antônio do Leverger Poxoréo Rondonópolis Campo Verde  27 79 10 34 14 14 103 59 76 70 40 102 92 85 89 31  Municipal unit 14 (Diamantino, São José do Rio Claro) contained two weather stations which acted as a replicate for the calculation of GW estimates. Results from WP curves are available in Appendix D.  23  2.2.3.4  Spatial characterization  To determine GWC, information on agricultural land expansion is needed. State boundary maps were downloaded from IBGE in shapefile format and manipulated in ArcGIS 10. The analysis of the IBGE maps determined the extent of MUs prior to depicting the geographic location and timeline of agricultural activity within the state.  2.2.3.4.1  Municipal units  Each Brazilian state is sub-divided into municipalities (municipios) which form the basis of information collected by IBGE for agricultural production surveys and census. Mato Grosso contains 141 municipalities, but their number and boundaries changed in 2001, 2005 and 2007. Municipalities that changed shape and size were aggregated in this study so that the sum of municipal areas was constant between 2000 and 2009. These larger municipal units (MUs) allowed proper comparison of data collected at the municipal level based on an identical land surface area. A summary of the larger MUs are shown below (Table 6) and the complete list of MUs is available in Appendix C. Table 6: Aggregated municipalities for 2000-2009. Municipal Unit 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Municipalities Aripuanã, Rondolândia, Colniza São José do Xingu, Santa Cruz do Xingu Nova Mutum, Nobres, Rosário Oeste, Chapada do Guimarães, Nova Brasilândia, Santa Rita do Trivaleto Itaúba, Cláudia, Terra Nova do Norte, Santa Carmem, Nova Santa Helena Água Boa, Novo Nazaré Novo São Joaquim, Santo Antônio do Leste São Félix do Araguaia, Alto Boa Vista, Cocalinho, Ribeirão Cascalheira, Bom Jesus do Araguaia, Serra Nova Dourada, Novo Santo Antônio Villa Bella da Santissima Trinidade, Pontes e Lacerda, Jauru, Conquista d'Oeste, Vale de São Domingos Tangará da Serra, Barra do Bugres, Reserva do Cabaçal, Salto do Céu, Rio Branco Cáceres, Mirassol d'Oeste, Lambari d'Oeste, Curvelândia Tapurah, Sinop Juara, Nova Monte Verde Cotriguaçu, Juruena São José do Rio Claro, Diamantino  24  2.2.3.4.2  Agricultural production information  Agricultural production information was obtained from the IBGE-SIDRA query website, http://sidra.ibge.gov.br/ (IBGE, 2010a) under table 1612 (tabela 1612). Municipal agricultural production data (produção agrícola municipal) was available for each year from 2000 to 2009, while census data (censo agropecuário) was available for 1996 and 2006. Values for cotton, maize, soybean and sugar cane as well as animal population were obtained for each municipality and aggregated to corresponding MUs. Agricultural production from IBGE-SIDRA relies on expert surveys to infer total values of production, planted area, harvested area, and average yield for both annual and perennial crops. This is to be differentiated from the census data which takes all production into account. Results for the 2010 census which IBGE started in August 2010 (IBGE, 2011) were unavailable at the time of writing.  2.2.3.4.3  Pasture area determination  Pasture surface area information is only recorded in the census data (1996, 2006) and was inferred for the non census years using animal population from the agricultural production data following steps in Barona et al. (2010). Animal population was obtained through IBGE-SIDRA (IBGE, 2010a) under table 73 (tabela 73). The total livestock units (TLU) are determined for time t and MU i by equation (2) (Barona et al., 2010): TLU (t , i ) = ∑ N (i, t , k ) f AU (t , k )  (2)  k  where N is the population of animal k and fAU is the animal unit conversion factor (Table 7) as defined by the Brazilian Ministry of Agriculture for the state of Mato Grosso and the Pantanal region, the southern region of the state (Ramos, 2005). MUs containing the Pantanal  25  were selected according to results from Via da Silva et al. (1998): Barão de Melgaço (MU4 26); Cáceres, Mirassol d'Oeste, Lambari d'Oeste, Curvelândia (MU 10); Itiquira (MU 51); Nossa Senhora do Livramento (MU 61); Poconé (MU 78); Santo Antonio de Leverger (MU 92). Table 7: Animal unit conversion factors (fAU) for pasture determination in equation (2) (Ramos, 2005). Animal  Mato Grosso*  Pantanal  Cow Buffalo Horse Donkey Mule Sheep Goat  0.92 0.83 0.83 0.64 0.64 0.14 0.12  0.83 0.74 0.74 0.59 0.59 0.12 0.11  *without the Pantanal wetland  Pasture area is then estimated after Barona et al. (2010) extract pasture area from the defined livestock density: AP (t , i ) =  TLU (t , i ) LSD(t , i )  (4)  where AP is the estimated pasture area (ha), and LSD is the livestock density in total livestock units (from equation (2)) per ha of pasture. The census of 1996 and 2006 provide pasture areas such that LSD(1996,i) and LSD(2006,i) can be determined for each MU i. Both LSD(1996,i) and LSD(2006,i) were then plotted as a function of time to linearly interpolate LSD for each 2000-2005 and 2007-2009 year before extracting an estimate of AP(t,i) using the equation above. Again, the results of the 2010 agricultural census are not available at the time of writing. Results of pasture areas based on animal populations are available in Appendix E.  4  See Appendix C 26  2.3  R modeling tool  All information was gathered into scripts written in R (R Development Core Team, 2011). Table 8 outlines the stepwise scripts used to determine GWC and GWP fluxes. Script details for Reference ET Calculation and Crop coefficients MT are shown in Appendix F. Table 8. R scripts produced for this study. Name Reference ET Calculation  Crop coefficients MT  Ag Production MT AG Production MT AET ArcInfo Raster extraction  Description Application of FAO56 using meteorological station data to calculate ET0 Application of Kc values for soybean, maize, sugar cane and cotton. Planting dates for maize and cotton occur 126 days after soybean planting; pasture Kc fluctuated with a precipitation threshold Calculation of potential GW C using ETC and agricultural production data obtained from IBGE Calculation of actual GW C using ETC, Peff and agricultural production data obtained from IBGE Extract raster information obtained from MOD16 available in ArcInfo format from ESRI ArcGIS 10  Output Daily ET0 averaged over 10 consecutive days to provide st decadal ET0 from January 1 2000 st to December 31 2009  Decadal ETC values for all crops  Monthly and annual potential GW C for all MUs in Mato Grosso Monthly and annual actual GW C for all MUs in Mato Grosso GW T and GW F listed by MU for both volumes and fluxes  27  Chapter 3: Results  GWT and GWF volumes and fluxes were determined for Mato Grosso using MOD16 (Mu et al., 2011). GWT volume was further separated into GWC, GWP, agricultural GW (GWAg, as the sum of GWC and GWP) as well as residual land use (GWR) green water using the PM equation from FAO56 (Allen et al., 1998). This breakdown was first done for 15 MUs using the INMET meteorological stations they contained before extrapolating crop water use to all 104 MUs using WP curves (Appendix D). First, a general description of fluxes and volumes for the 2000-2009 period is given for the state wide GW fluxes and volumes before showing crop water use modeling results. Then, a description of changes in fluxes and volumes is given for the 15 MUs containing a meteorological station as well as all Mato Grosso MUs, followed by an evaluation of GW fluxes in relation to land use change.  3.1  State level green water flows Annual5 GWT volumes for the entire state of Mato Grosso decreased between 2000 and  2005 at a rate of 1.5 km3 mo-1 per year (18.4 km3 y-1 per year, R2 = 0.65, p = 0.10) before increasing at a rate of 2.2 km3 mo-1 per year (26.7 km3 y-1 per year, R2 = 0.55, p = 0.15) with smaller fluctuations in monthly fluxes between dry and wet seasons between 2005 and 2009 (Figure 4). This change in the baseline GWT was apparent in both volumes and fluxes with the lowest values recorded in September 2005 for both GWT (52.8 km3 mo-1 and 56.6 mm mo-1) and GWF (21.7 km3 mo-1 and 48.7 mm mo-1).  5  Where the hydrologic year is defined from Aug 1st to July 31st of each year (year 1 = Aug 1st 2000 to July 31st 2001, year 2 = Aug 1st 2002 to July 31st 2003, etc.) 28  Monthly GWT and GWF volumes were typically at their highest between January and March (127.2 ± 2.9* km3 mo-1 and 33.2 ± 3.7 km3 mo-1 respectively) and at their lowest in August or September (68.0 ± 6.0 km3 mo-1 and 50.9 ± 3.0 km3 mo-1), thus presenting a range of 59.2 km3 mo-1 and 17.7 km3 mo-1 (Table 26, Appendix G). All GWT volume peaks contained a local minimum in February for all years (113.6 ± 3.4 km3 mo-1). GWT fluxes did not show the same fluctuations as observed for volumes, although the lowest annual flux did occur mostly in August and September. Monthly GWF fluxes showed clear maxima (117.5 ± 2.6 mm mo-1) occurring on different months in the hydrologic years, and minima (62.7 ± 5.5 mm mo-1) occurring in August and September. A decrease in GWF annual volume for the entire state was observed between 2000-2009 at a rate of 16.2 km3 y-1 per year (R2 = 0.82, p-value <0.01). In 2000, approximately half of GWT volumes came from forests which then occupied one third of the land. GWF fluxes exhibited a 10 year mean of 110 mm mo-1, with monthly fluctuations ranging between 20 % and 50 % around this value. GWT – GWF volume was estimated at 79.3 ± 2.6 km3 mo-1 in the wet season and 33.1 ± 2.2 km3 mo-1 in the dry season; or 62 % of GWT volumes for the wet months, and 49 % for the dry months.  *  95% confidence level 29  Figure 4. Total (GWT) and forest (GWF) green water volumes (top panel) and fluxes (bottom panel) for Mato Grosso from 2000 to 2009. GWT represents GW for the entire state of Mato Grosso, while GWF is the statewide forest GW. In the top panel, GWF volume is included within the cumulative GWT volume.  3.2  Cropland and pasture green water modeling results Sugar cane had the largest potential GWC flux with a mean of 1630 mm y-1, followed  by soybean (638 mm y-1), cotton (459 mm y-1) and maize (369 mm y-1) (Table 9). The mean GWP across the meteorological stations was 861 mm y-1 and comparable to measurements made by Meirelles et al. (2011). Since the mid-season crop coefficient (Kc mid) changed with  30  set precipitation thresholds, there is no difference between potential and actual GWP. Actual GWC fluxes were lower when considering water stress from lack of precipitation: 1130 mm y-1 for sugar cane, 476 mm y-1 for soybean, 251 mm y-1 for cotton and 276 mm y-1 for maize. There was no difference in GWP whether 10 mm (scenario I) or 7 mm of precipitation (scenario II) triggered the increase in crop coefficient (Table 9). Table 9. Mean annual crop (GWC) and pasture (GWP) potential and actual green water fluxes for 15 municipal units containing a meteorological station (2000-2009). Values are shown as a range with mean minimum and maximum values calculated between 2000 and 2009. Values in brackets represent the standard deviations (sd) for each minima and maxima across the 15 municipal units. Crop  Potential green water -1 (mm y ) min (sd) – max (sd) scenario I*  Potential green water -1 (mm y ) min (sd) – max (sd) scenario II**  Actual green water -1 (mm y ) min (sd) – max (sd) scenario II**  n/a  Actual green water -1 (mm y ) min (sd) – max (sd) scenario I* 1010 (156) – 1250 (191) 822 (18) – 889 (77)  Sugar cane  1540 (92) – 1857 (54)  same as scenario I  Pasture  n/a  Soybean  589 (30) – 687 (20)  570 (29) – 663 (9)  412 (86) – 540 (26)  363 (58) – 469 (26)  Cotton  432 (25) – 543 (15)  399 (21) – 545 (17)  210 (50) – 292 (40)  150 (48) – 242 (31)  Maize  340 (20) – 416 (11)  315 (24) – 400 (13)  239 (54) – 312 (20)  157 (51) – 244 (15)  st  same as scenario I same as scenario I  th  *Plant soybean Oct 1 , maize and cotton 126 days later, sugar cane Apr 30 , 10 mm precipitation triggers higher pasture crop coefficient **Plant soybean Nov 1st, maize and cotton 126 days later, sugar cane Apr 30th, 7 mm precipitation triggers higher pasture crop coefficient n/a: There is no potential GWP since it is determined from a direct response to a precipitation threshold  These results were used to derive the WP curves for potential and actual GWC and GWP for the early and late soybean planting scenarios. This allowed for the determination of GW volumes for MUs that did not contain a meteorological station. WP results are shown in Appendix D.  31  3.3 3.3.1  Municipality level green water flows Flows in 15 municipal units6 containing a meteorological station GWT volumes for 15 MUs that contained a meteorological station increased from 138  to 151 km3 y-1 from 2000 to 2003 before dropping to a minimum in 2005 (134 km3 y-1). Volumes then increased steadily until 2009 to reach 164 km3 y-1. GWF volumes dropped continuously from 44 to 39 km3 y-1, or 32 % to 23 % of GWT volumes within the same time period (Figure 5). GW volumes are representative of 123,724 km2 of land, or 14 % of Mato Grosso (Table 29, Appendix H).  Figure 5. Annual total (GWT) and forest (GWF) green water volumes for 15 municipal units containing a meteorological station for Aug 1st – Jul 31st hydrologic years between 2000-2009.  Agricultural GW (as the sum of pasture and cropland, GWAg) volumes were driven by GWP which represented >78 % of GWAg volumes, followed by soybean GW (GWSoy) volumes which were <17 % of GWAg volumes (Figure 6). GWP volumes were relatively stable between 32 and 35 km3 y-1 before dropping in 2005. The drop in GWP volumes depended on the pasture estimate from the assumption of livestock density post 2006  6  See Appendix I for a description of land use for these 15 municipal units 32  (Appendix E). The difference from both estimates in 2009 translated to a 2.1 % difference in GWAg that year and differences of <2.1 % for 2007-2008 and 2008-2009. GWSoy volumes doubled between 2000 and 2009 in both potential and actual GWC cases but did experience a drop in the 2006-2007 period: GWSoy increased from 3.0 to 5.9 km3 y-1 as potential GWC volumes, and from 1.9 to 4.8 km3 y-1 when including possible water stresses and planting scenarios. GWAg volumes peaked in 2004-2005 at roughly 30 % of GWT volumes before GWP volumes started to decline and while both potential and actual GWSoy peaked. Given the noted changes in the volumes listed above, there was also an increase in GW volumes that are unaccounted for and which fall under GWR. GWR volumes increased from 58 km3 y-1 to close to 91 km3 y-1 including both scenarios and potential and actual GWC. This change represented an increase from 40 % to over 50 % of GWT volumes between 2000 and 2009. GWR fluxes also reached a minimum in 2004-2005 averaged at 56 km3 y-1 or 42 % of GWT for all scenarios and water stress conditions.  Figure 6. Breakdown of forest (GWF), residual land use (GWR), potential agriculture (GWAg, as cropland and pasture) as a percentage of total (GWT) with soybean (GWSoy) and pasture (GWP) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (15 municipal units containing a meteorological station). Values for GWSoy are reported as actual (- a) and potential (- p) GW volumes, while GWP is given for two surface area estimates (sa1 and sa2).  33  Significant increases in GWT with time were found in the southeastern part of the state, while the significant decreases in GWF volumes which occurred in 3 MUs were located in central and northern Mato Grosso (Figure 7). Ten MUs had increases in GWT volumes that ranged from 0.03 to 0.46 km3 y-1 per year and 3 MUs had decreases in GWF volumes between -0.20 and -0.41 km3 y-1 per year. Changes in GWP and GWAg volumes over time were scattered across the MUs with more significant changes observed for GWP (10 MUs) than GWAg (7 MUs). Changes in GWP volumes were mostly negative and ranged from -0.28 km3 y-1 per year to 0.03 km3 y-1 per year while changes in GWAg volumes ranged from -0.25 km3 y-1 per year to 0.15 km3 y-1 per year (Figure 7).  34  Figure 7. Significant changes (p-value <0.05) in annual total (GWT), forest (GWF), pasture (GWP) and agricultural (GWAg, as cropland and pasture) green water for 15 municipal units containing a meteorological station for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (km3 y-1 per year). Full table available in Table 30, Appendix H.  3.3.2  Flows in all 104 municipal units Of the 104 MUs, 20 experienced a significant increase in GWT fluxes of at least 1.74  mm y-1 per year for 2000-2009 (up to 2.95 mm yr-1 per year for Barão do Melgaço) (Figure 8 and Table 31, Appendix I). GWT fluxes decreased in 12 MUs between -1.53 and -2.60 mm y1  per year, all of which were located in the north western part of the state (Figure 8).  Seventeen MUs which experienced increases in GWT fluxes were located in the same southcentral and south-eastern part of the state, except for Luciara (2.32 mm y-1 per year, 35  northwest), Lambari do Rio Verde (2.22 mm y-1 per year) and Sorriso (1.57 mm y-1 per year, central east) both in central Mato Grosso (Figure 8). In 2000, half of GWT volumes came from forest for about 40 % of total land (INPE, 2011a) before dropping by 10 % in the study period (Figure 10). Ten MUs experienced increases in GWF fluxes between 1.30 and 3.56 mm y-1 per year, all of which were located in the south and southeastern part of the state and correspond to MUs with a forest cover of 10 % or less (INPE, 2011a). Twenty MUs had statistically significant decreases in mean GWF fluxes between -2.76 and -1.43 mm y-1 per year and were concentrated in the northwestern part of the state, except for Campos do Julio (-1.95 mm y-1 per year) and Comodoro (-1.79 mm y-1 per year) which are west (Figure 8).  Figure 8. Significant changes (p-value <0.05) in annual total (GWT) and forest (GWF) fluxes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Full list available in Table 31, Appendix I.  GWT fluxes dropped by up to 15 % in volumes in the northwestern part of the state and increased up to a 40 % the south central part of the state while decreases in GWF fluxes  36  decreases in volumes of close to 40 % (Figure 9). Three MUs which had GWF volumes increase close to 20 %, also had GWF volumes <1 km3 y-1 per year.  Figure 9. Percent difference in annual total (GWT) and forest (GWF) green water volumes between hydrologic years 2000 and 2009 in municipal units with observed significant changes over time (Figure 8).  Potential GWAg volumes fluctuated between 17 % and 22 % of GWT peaking in 20042005 at 254 km3 y-1 per year mostly represented by the GWP at 206 km3 y-1 per year which generally was the bulk of GWAg volumes (Figure 10). Both potential and actual GWC volumes increased for soybean and maize between 2000 and 2009. Soybean was the largest GWC volume contributor with over five times the volume than other crops in 2009 (Table 10, Figure 11). All potential GWC volumes increased significantly within the time period (pvalue <0.05) at rates of 2.27 km3 y-1 per year for soybean (R2 = 0.82), 0.56 km3 y-1 per year for maize (R2 = 0.89) and 0.16 km3 y-1 per year for sugar cane (R2 = 0.68) and 0.15 km3 y-1 per year for cotton (R2 = 0.68).  37  Figure 10. Breakdown of forest (GWF), residual land use (GWR), potential agriculture (GWAg, as cropland and pasture) as a percentage of total (GWT) with pasture (GWP1 and GWP2 for both estimates) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Values for GWP are reported as a mean volume post 2006.  Actual GWSoy and GWmaize were 74-76 % and 73-74 % of their potential GW fluxes respectively (Table 10). Actual annual GWSoy and GWMaize increased significantly at a rate of 1.74 km3 y-1 per year (R2 = 0.82) and 0.42 km3 y-1 per year (R2 = 0.89) respectively, while GWSugar and GWCotton increased at 0.11 km3 y-1 per year (R2 = 0.68) and 0.08 km3 y-1 per year (R2 = 0.61). In 2005-2006, GWSoy dropped by 12 %, GWMaize by 2 %, GWSugar by 12 % and GWCotton by 11 % for all volumes (Figure 11). Annual GWP volumes were over 5 times larger than GWSoy in 2009 and 10 times larger in 2000. Annual GWP volumes decreased from 205 to 187 km3 y-1 in the 2005-2009 period or 200 km3 y-1 based on the drop estimate considering the largest estimate drop in pasture area (Figure 23, Appendix E). GWP volumes from pasture area estimates (Figure 23, Appendix E) represented an 8 % difference in contribution to GWAg. The increases in GWC volumes, and particularly the soybean contribution are almost offset by the decline in GWP: annual potential GWAG flux volumes increased by 5 km3 y-1 from 234 to 239 km3 y-1 (early planting date scenario) while actual GWAG volumes increased 12 km3 y-1 from 208 to 220 km3 y-1  38  (late plating date scenario) in 2000-2009. These changes are reflected in the percent contributions to GWT volumes (Figure 10). Table 10. Annual mean potential and actual crop (GWC) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units) for soybean, maize, sugar cane and cotton. 3  -1  3  -1  Crop  Potential GWC (km y ) 2000(sd) – 2009 (sd)*  Actual GWC (km y ) 2000(sd)- 2009 (sd)*  Soybean Maize Sugar cane Cotton  19 (0.4) – 37 (1) 1.1 (0.1) – 6.2 (0.4) 2.0 – 3.7 1.2 (< 0.1) – 2.4 (< 0.1)  14 (1) – 28 (3) 0.8 (0.2) – 4.6 (0.9) 1.4 – 2.5 0.61 (0) – 1.3 (0)  *standard deviation from both scenarios  Figure 11. Sum of annual potential (top) and actual (bottom) soybean (GWSoy), maize (GWMaize), sugar cane (GWSugar) and cotton (GWCotton) green water for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). Error bars represent the standard deviation between the two scenarios. 39  GWR volumes increased from 397 km3 y-1 (33 % of GWT) to 564 km3 y-1 (46 % of GWT) between 2000 and 2009 including both scenarios and potential and actual GWC. GWR fluxes also reached a minimum in 2004-2005, averaged at 393 km3 y-1 or 34 % of GWT (Figure 10). Potential GWSoy volumes increased in the central part of the state while GWP decreased in the central east, southwestern and southeastern part of the state, but also increased in the northern part of the state (Figure 12). The largest change in potential GWSoy volumes occurred in the central, eastern and south-eastern part of the state where volumes increased up to 1000 % (Figure 13). A few MUs increased GWSoy volumes >1000%, particularly MU 10 and 7, as well as some in the north. Some MUs dropped their GWSoy volume by half between 2000 and 2009, mostly in the southeast (4 MUs), in the central region (3 MUs) and the north (1 MU). GWP volumes decreased by close to 40 % in 2000-2009 in central, southeastern and southwestern Mato Grosso when considering an increase in livestock density past 2006. Five MUs in the north actually increased their GWP volume by more than 100 % within the same time period.  40  Figure 12. Differences in annual potential soybean (GWSoy) and pasture (GWP) green water volumes between the Aug 1st – Jul 31st hydrologic years 2000 and 2009 (all municipal units) (km3 y-1). Pasture results are based on a continuous increase in livestock density (Figure 23, Appendix E).  Figure 13. Percent differences in annual soybean (GWSoy) and pasture (GWP) green water volumes between the Aug 1st – Jul 31st hydrologic years 2000 and 2009 (all municipal units). Pasture results are based on a continuous increase in livestock density.  41  3.4  Relationships between green water fluxes and land use change Some of the variance in GWT fluxes and volumes can be explained by deforestation  with, however, small slope coefficients (Table 11). Generally, the relationships between GWT with deforestation showed greater R2 when considering volumes instead of fluxes. When considering all 104 MUs (n = 936), the relationships between GWT fluxes and volumes showed an R2 of 0.12 respectively with deforestation. The relationship for both GWT fluxes and volumes with deforestation had an R2 of 0.23 and 0.24 when considering MUs which experienced significant changes between 2000 and 2009. This R2 value increased to 0.27 for GWT volumes when adding the condition of having >50 % forest cover in 2000 (n = 81). The biggest differences between relationships of deforestation and GWT were observed with MUs which had >50 % forest cover in 2000 (n = 243), while there was no significant relationship for fluxes, there was one with volumes (R2 = 0.13, p-value <0.01). Table 11. Relationship between annual total green water (GWT) volumes and fluxes with annual deforestation (km2 y-1) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. Relationship with GWT fluxes (mm) Municipal units considered All 104 MUs With 50% forest cover in 2000 27 MUs With significant changes in GW T fluxes in 2000-2009 52 MUs With significant changes in GW T fluxes in 2000-2009 and 50% forest cover in 2000 12 MUs With significant decreases in GW T fluxes 12 MUs 3 Relationship with GWT volumes (km ) Municipal units considered All 104 MUs With 50% forest cover in 2000 27 MUs With significant changes in GW T fluxes in 2000-2009 50 MUs With significant changes in GW T fluxes in 2000-2009 and 50% forest cover in 2000 9 MUs  2  n  Equation of best fit  R  936  y = -0.048x + 83.00  0.12**  243  y = -0.006x + 103.5  0.01  468  y = -0.0064x + 76.81  0.23**  108  y = -0.012x + 106.0  0.07**  108  y = -0.011x + 108.1  0.07**  n  Equation of best fit  R  936  y = -0.057x + 12.34  0.13**  108  y = -0.048x + 16.45  0.13**  450  y = -0.081x + 12.44  0.24**  81  y = -0.072x + 15.11  0.27**  2  **p-value <0.01  42  Linear regression models between GWT and GWF fluxes and volumes generally showed little correlation with pasture, cropland and agricultural expansion (as the sum of pasture and cropland). Though the R2 was small, there was a relationship between GWF fluxes and pasture area and between GWT volumes and pasture (Table 12 and 13). MUs which experienced significant increases in GWT fluxes were not highly correlated to changes in cropland and agricultural land with R2 <0.10 (n = 369). When considering GWF fluxes, only those MUs which experienced significant decreases between 2000 and 2009 showed little correlation to the relationship with land use when cropland was considered (n = 22, R2 <0.10). There was a significant relationship between GWF fluxes and pasture (R2 = 0.12) (Table 12). Table 12. Relationship between annual total and forest (GWT, GWF, km3 y-1) green water fluxes with annual expansion area (ha y-1) of pasture, cropland and agricultural land (sum of cropland and pasture) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. Relationship with GWT fluxes (mm) Municipal units considered All (pasture) 104 MUs All (cropland) 104 MUs All (agricultural land) 104 MUs With significant increase in GW T (cropland) 41 MUs With significant increase in GW T (agricultural land) 41 MUs Relationship with GWF fluxes (mm) Municipal units considered All with forest cover (pasture) 92 MUs With significant changes in GW F (pasture) 33 MUs With significant decreases in GW F (pasture) 21 MUs With significant decreases in GW F (cropland) 21 MUs With significant decreases in GW F (agricultural land) 21 MUs With significant increase in GW F (pasture, cropland and agricultural land) 10MUs  n 936  2  Equation of best fit  R  No significant relationship -5  0.01**  -6  0.01**  -6  0.02**  y = 4.55 10 x + 70.25  -6  0.03**  Equation of best fit  R  936  y = -1.67 10 x + 87.09  936  y = -5.18 10 x + 87.44  369  y = 9.59 10 x + 70.85  369 n  2  829  No significant relationship  297  No significant relationship  189 189 189 90  -5  y = 5.75 10 x + 7.03  0.12**  No significant relationship -6  y = -9.10 10 x + 11.43  0.03*  No significant relationship  * p-value <0.05; ** p-value <0.01  43  GWT and GWF volumes were slightly more correlated with agricultural expansion (Table 13). Significant relationships were observed between GWT volumes and pasture expansion for all MUs (R2 = 0.10) which increased when considering MUs with significant changes in GWT (R2 = 0.15 for pasture and R2 = 0.20 for agricultural land). No significant relationship was observed when considering cropland alone. The effects of agricultural expansion on GWF volumes remained insignificant (Table 13). Table 13. Relationship between annual total and forest (GWT, GWF, km3 y-1) green water volumes with annual expansion area of pasture, cropland and agricultural land (sum of cropland and pasture) (ha y-1) for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. 3  Relationship with GWT volumes (km ) Municipal units considered All (pasture) 104 MUs With significant changes in GW T (pasture) 50 MUs With significant increase in GW T (cropland) 39 MUs With significant increase in GW T (agricultural land) 39 MUs 3 Relationship with GWF volumes (km ) Municipal units considered All with forest cover (pasture) 92 MUs With significant decrease in GW F (pasture) 50 MUs With significant decreases in GW F (cropland) 21 MUs With significant decreases in GW F (agricultural land) 21 MUs  n  Equation of best fit  936  y = 2.56 10 x + 10.47  450  y = 2.96 10 x + 10.43  351  2  R  -5  0.10**  -5  0.15**  No significant relationship -5  351  y = 2.34 10 x + 4.51  0.20**  n  Equation of best fit  R  2  828  No significant relationship  450  No significant relationship -5  0.03*  -5  0.04**  189  y = -3.57 10 x + 19.77  189  y = 2.77 10 x + 11.27  *p-value <0.05; **p-value <0.01  3.5  Relationships among individual green water fluxes Of the changes in annual GWT volumes, 40 % of variance was explained by the annual  changes in GWF volumes at n = 135 (15 MUs) containing a meteorological station, 70 % at n = 936 (104 MUs), and 95 % at n = 243 (27 MUs) when only considering MUs which had at least 50 % forest cover in 2000* (see Table 14). GWP volumes had the greatest relationship  *  Alto Taquari (MU 20) was not included since deforestation activity began in 2007 44  with GWT volumes considering the 15 MUs containing a weather station which represented the bulk of the relationship with GWT volumes compared to GWSoy, the largest contributor of GWC. Table 14. Analysis of effects of the change in annual forest (GWF), agriculture (GWAg), and soybean (GWSoy) green water volumes on the change in annual total (GWT) green water volumes for Aug 1st – Jul 31st hydrologic years between 2000 and 2009 (all municipal units). MUs with forest cover (n = 828), MUs with 50% forest cover in 2000 (n = 243). Change in GWT volumes (n) Change in GW F (135) 15 MUs Change in GW F (828) 92 MUs Change in GW F (243) 27 MUs Change in GW P (135) 15 MUs Change in GW Ag (135) 15 MUs Change in GW Soy (135) 15 MUs  2  Equation of best fit  R  y = 1.81x + 0.29  0.40**  y = 1.27x + 0.23  0.70**  y = 1.219x + 0.32  0.94**  y = -1.34x + 0.09  0.06**  y = -1.38x + 0.14  0.09**  y = -2.33x + 0.21  0.04**  **p-value < 0.01  There were no relationships observed between changes in annual GWF volumes changes in both annual GWAg and GWSoy volumes (R2 <5 %) (Table 15). This was also confirmed by introducing a one year lag which did not improve the significance of those relationships. Expanding the test to n = 936 (104 MUs) and n = 243 (27 MUs) which had at least 50 % forest cover in 2000 (Table 15) did not improve the significance of the test.  45  Table 15. Analysis of effects of the change in annual pasture (GWP), agriculture (GWAg) and soybean (GWSoy) green water volumes on the change in annual forest (GWF) volumes for for Aug 1st – Jul 31st hydrologic years between 2000 and 2009. All municipal units (n = 936), municipal units with >50 % forest cover in 2000 (n = 243). Change in GWF volumes (n, lag in years) Change in GW P (n = 243, 0) 27 MUs Change in GW P (n = 243, 1) 27 MUs Change in GW P (n = 936, 0) 104 MUs Change in GW P (n = 936, 1) 104 MUs Change in GW Ag (n = 243, 0) 27 MUs Change in GW Ag (n = 243, 1) 27 MUs Change in GW Ag (n = 936, 0) 104 MUs Change in GW Ag (n = 936, 1) 104 MUs Change in GW Soy (n = 243, 0) 27 MUs Change in GW Soy (n = 243, 1) 27 MUs Change in GW Soy (n = 936, 0) 104 MUs Change in GW Soy (n = 936, 1) 104 MUs  2  Equation of best fit  R  y = -1.73x – 0.44  0.04**  No significant relationship y = -0.31x – 0.15  0.01*  No significant relationship y = -1.34x – 0.39  0.03**  No significant relationship y = -0.34x – 0.14  0.01*  No significant relationship No significant relationship No significant relationship y = -0.55x – 0.13  <0.01*  No significant relationship  **p-value <0.01  46  Chapter 4: Discussion  Results provided insight on the changes in Mato Grosso’s GW fluxes between 2000 and 2009 at the state and MU levels but also generated many questions on uncertainties for a better flux estimate. First, a general description of GW seasonality is provided based on MOD16, before assessing the role of land uses in observed GW flux trends to understand the changes experienced in Mato Grosso. Finally a description and discussion of uncertainties encountered in this research is presented.  4.1  Green water seasonality in Mato Grosso The state wide analysis of GW fluxes show important biosphere-atmosphere  relationships and confirms previous results and research, particularly GW seasonality and forest ET processes. Figure 4 shows a clear seasonality in GW fluxes at the state level, illustrated by the changes in GWT volumes. GWT fluxes, though in phase with the rainy season, suggest complex processes with various contributions from land uses. GW originates as precipitation during the rainy season and is evaporated to a point where the landscape reaches potential ET, estimated by Ahn & Tateishi7 (1994) to be 132 mm mo-1 (January) and 126 mm mo-1 (March). Available evaporation data from INMET for 1961-1990 by Piché evaporimeter8 show a constant increase in atmospheric water demand to an average of 169 mm mo-1 between April and August for 6 stations of Mato Grosso9 (INMET, 2009). The combination of high atmospheric demand with decreased precipitation limits GW fluxes:  7  Dataset available from UNEP (2008) The evaporimeter measures the atmosphere’s demand for water as evaporated from a wetted filter paper 9 Cáceres, Cuiabá, Diamantino, Gleba Celeste, Poxoréo, Utiariti (not currently available from INMET) 8  47  available soil water stocks, leaf water potential and leaf area index (LAI) typically decline in the dry season (Vourlitis et al., 2002). This leads to a decline in GWT volumes which reached a minimum just before the start of the new rainy season when GW stocks are replenished. The dip observed in volumes for the months of February is due to a short dry period in the middle of the rainy season occurring most years (locally called the veranico) where ET exceeds precipitation. The change in annual GWT fluxes, although strongly correlated with time, was not significant. The lowest GWT and GWF fluxes and volumes were observed during 2005, when south and central Amazônia experienced a drought (Aragão et al., 2007). Such an event illustrates additional meteorological factors affecting ET processes, typically through the variation of net radiation (Rn), vapour pressure deficit, precipitation, and surface resistance as illustrated in the PM equation (Appendix A). Fisher et al. (2009) found that Rn and the vapour pressure deficit explained most of the variance in monthly ET in tropical forest (87 % and 14 % respectively) while precipitation explained 6 %. The 2004-2005 hydrologic year was one of three years in which the mean temperature reached 26.5ºC according to data recorded by the INMET stations. February 2005 had the highest recorded wet season mean temperature between 2000 and 2009 at 27.4ºC. The average annual precipitation from the 12 INMET meteorological stations for 2004-2005 was 1563 mm for a 1364-1748 mm y-1 precipitation range and an average equal to 97 % of the 1961-1990 long term average of 1610 mm y-1 (INMET, 2009). Given the seasonality of precipitation, it is important to consider the precipitation for January to March. The 2004-2005 hydrologic year had a veranico (February) with 185 mm mo-1 of rainfall, the second lowest of the time series and 25 % lower than the 1961-1990 average of 247 mm (INMET, 2009). A combination of greater Rn with  48  reduced precipitation that year meant less available water on the landscape for the dry season, thus explaining the larger drop in GWT for August 2005. Mean GWF fluxes were consistent with previous literature. Shuttleworth (1988) reported a mean forest ET of 110 mm mo-1 with fluctuations of 20 % near Manaus (Amazônia). Vourlitis et al. (2002) measured fluxes over forest near Sinop, northern Mato Grosso10, and observed similar seasonality in GWF with a maximum ET of 128 mm mo-1 for February (no data was available for March in the study). They found that ET declined in April-May to <98 mm mo-1 in July.  4.2 4.2.1  Trends in green water fluxes Impact of deforestation on green water flows The northern part of the state is home to the transition forest and the so called “arc of  deforestation”. Evidence of decreases in both GWT and GWF volumes suggested a possible correlation between deforestation and measured changes in GW fluxes, particularly considering the decline in annual GWF volumes (16.2 km3 y-1 per year). Table 11 shows a correlation between deforestation and decreases in GWT fluxes and volumes (R2 <0.30). Even when considering MUs with significant changes in GWT volumes and over 50 % forest cover in 2000, the R2 was 0.27 suggesting other factors are responsible for the drop in GWT flux drops in the past 10 years: meteorological as discussed above, but also economic as discussed in the next section. GWF volumes explained 40 % of variance in GWT for the 15 MUs containing a meteorological station, showing a strong atmosphere-biosphere relationship through the forest. Tropical forests were identified as being major sources of  10  Part of MU 11 in this research, see Appendix C 49  transpiration, or productive GW (Miralles et al., 2011), the difficulty remains in the isolation of the land use effect on such fluxes: many meteorological components fluctuated as the forest disappeared between 2000 and 2009. Nevertheless, the decrease in annual GWF volumes of 16.2 km3 y-1 per year is a land use effect given that the determination of these values is based on forest surface area as monitored by INPE multiplied by the MOD16 flux for forest area. As noted above, Rn is an important factor controlling seasonal ET in tropical forests (Fisher et al., 2009), but also vapour pressure deficit or surface conductance from which stomata exert a biological control over ET processes in dry rain forest (Costa et al., 2010). The lowest measured GWF volumes also coincided with the 2005 Amazônia drought and the drier veranico as suggested by mean temperature and precipitation data. In addition to Rn and stomatal control, the drop in GWF volumes in February 2005 could be a result of reduced evaporation from precipitation interception which is part of the algorithm used to obtained MOD16 data (Mu et al., 2011). Some researchers have suggested that the Amazon region might be subject to “savanization” from an ongoing reduction in precipitation, soil nutrient stress and change in evapotranspiration (Costa & Foley, 2000; Alves Senna et al., 2009). This analysis is an underestimation of the real contribution of forests to GW processes in the state and the impacts of deforestation on GWT. The INPE classification is different from that of other government bodies such as FEMA (Fundação Estadual do Meio Ambiente in Mato Grosso) which results in differing deforestation rates (Fearnside & Barbosa, 2004). According to INPE, forest cover in Mato Grosso dropped from about 378,000 km2 y-1 to 317,000 km2 y-1 between 2000 and 2009 (INPE, 2011a). As the INPE forest cover gets smaller so does the extract mask used to obtain the MOD16 data. But this drop only  50  represents a decrease in GW volume by forest as it is classified by INPE, which does not include cerrado. The largest differences between GWT and GWF volumes were observed in the wet months where the non-forest land uses – as classified by INPE – contribute to most of the water vapour volume. These originate from cerrado ecosystems, pasture (natural and planted) and cropland, but also cities, rivers and the Pantanal wetland. The inclusion of forest classified under cerrado would increase the contribution of forest to total fluxes and amplify the magnitude of the impact of deforestation on the drop in GWF over time. There is an anomaly with the 10 MUs that showed increases in GWF fluxes, all of which had 10 % forest cover or less in 2000. Six of those MUs had forest cover <100 km2 in 2000 and all experienced deforestation between 2000 and 2009 with the exception of São Pedro da Cipa which increased its forest cover by 0.7 km2 (INPE, 2011a). This anomaly might be a result of the method: the raster extract masks used to obtain the GWF fluxes might not be truly representative of the actual forest cover, especially if smaller than the 1 km2 MODIS resolution. Santo Antônio de Leverger and Poconé had over 1200 km2 of forest cover in 2000 but is also included as part of the Pantanal (Vila da Silva & Abdon, 1998). The flood waters which can be under the canopy and would have been included in MOD16 for a resulting increase in measured GWF. GWF volumes however did decrease in the study time period.  4.2.2  Green water use for agriculture The dynamics of GWC and GWP volumes depend on the respective changes in surface  area led by an expansion of soybean and a drop in pasture area. Pasture has a higher annual ETC as determined by FAO56 compared to soybean (861 mm y-1 and 638 mm y-1  51  respectively), which are both much lower than sugar cane (1639 mm y-1). However, the planting season and spatial extent of production are what determine the GW volumes. Therefore pasture and soybean are responsible for most of the changes in agricultural GW flux changes in Mato Grosso. The overwhelming contribution of GWP volumes compared to cropland (GWP >78 % of GWAg) make it an important variable in understanding the changes in GWAg volumes in the context of agricultural expansion. There mostly was an increase in GWC for soybean and maize in both potential and actual GWC. Barona et al. (2010) suggested deriving linear models from IBGE agricultural production data in order to identify possible uncertainties in the data obtained from expert surveys. While this might be suitable for understanding agricultural expansion from a land use point of view, it is questionable for understanding GW dynamics which depend on many factors such as Rn, vapour pressure deficit, precipitation and surface conductance. There is an additional economic factor to consider for GWC as producers will respond to market prices and abruptly change production quantities which in turn influence land use decisions. Barona et al. (2010) found a correlation between cattle price and deforestation (R2 = 0.5-0.6 for 1999-2007) and between soybean price and deforestation (R2 = 0.87 in 1999-2007) for the Amazon region. It is believed that the negative soy profits of 2004-2005 and 2005-2006 impacted soybean production (Aprosoja, 2011; Martins, 2011) and hence soybean GW (GWSoy). The general drop in pasture area mainly explains the mostly negative changes in GWP over the time period, particularly 2004-2006, and plays an important role in the drop of GWAg. Following previously documented research on land use change in Mato Grosso (Jasinski et al., 2005; Morton et al., 2006; Barona et al., 2010), GWC volumes are believed to  52  have increased mainly from agricultural expansion as discussed above, but some portion may also result from agricultural intensification. Yields, on a per hectare basis, have mostly increased in the time period except for sugar cane (Table 28, Appendix H). In the case of soybean, the leading crop in the state, an increase in yield means more production for the same surface area with two possible consequences: (1) an increase in GWSoy given the higher concentration of biomass per hectare of land leading to greater transpiration; (2) a decrease in GWSoy in the case of an improvement in WP; (3) other possible changes from soil management and fertilizer application which may lead to increases or decreases in GWSoy. This yield effect might counteract or exacerbate the effect of expansion observed in Figure 12. Despite these calculated increases in GWAg, their relationship at the state level was tested to be mostly insignificant.  4.2.3  Impact of agricultural expansion on green water flows Increases in GWT fluxes mostly occurred in the south central and south eastern part of  the state (Figures 8 and 9). This region typically contains more agriculture and residual land uses than INPE classified forest (Figures 24 and 25, Appendix H). These land uses were hypothesized to be responsible for some of the changes in GWT fluxes, particularly in areas which have no INPE classified forest (GWT flux increases of 2.41 mm y-1 per year and 2.26 mm y-1 per year in Acorizal and São José do Povo respectively) and those which contain the Pantanal wetland which acts as a GW source (GWT increased by 2.95 mm y-1 per year, 2.44 mm y-1 per year, and 2.19 mm y-1 per year for Barão de Melgaço, Santo Antônio de Leverger, and Poconé respectively). Pasture, cropland and agricultural land area (as the sum of cropland and pasture) did not show any strong relationship with GWT nor GWF volumes  53  and fluxes. The largest R2 of 0.20 described the relationship between annual GWT volumes and agricultural land area with a slope of 2.35 km3 ha-1 (2.4 mm). Just as with deforestation, agricultural expansion does not fully explain changes in GW volumes, particularly their increase within the study time period. Removing the drought in the 2004-2005 hydrologic year did not improve the relationship for pasture, the largest contributor of GWAg fluxes. Although it is clear that GW fluxes are increasing with soybean expansion, its effect on GWT fluxes is either too small, or shadowed by other effects as previously described. It is important to note that GWC volumes are particularly difficult to estimate given individual farmers’ decisions. Only harvested areas as they are reported by IBGE are used to model GWC. Farmers may decide to plant only part of their land, leaving the rest as fallow which would then be classified as GWR, a GW contribution which increased after the 2004-2005 season.  4.3  Shifts in green water use from land use change The drop in GWF fluxes from land use were most significant in the arc of deforestation  (Figures 8 and 9), which is believed to be for the purposes of agricultural expansion (Jasinski et al., 2005; Morton et al., 2006; Barona et al., 2010). The replacement of forest with other land uses significantly decreases transpiration and partial compensation from evaporation (Costa & Foley, 2000). A forest to cropland transition was accompanied by a decrease in daily transpiration in northern Mato Grosso (Pongratz et al., 2006). Gordon et al. (2005) claim that global decreases in vapour flows from deforestation are mostly compensated by irrigation, except in the Amazon region due to the lack of local irrigation expansion (Gordon et al., 2005). This may be the case in Mato Grosso as well since agriculture is >95% rain-fed.  54  Such a land use effect would need to be confirmed and isolated with a much larger data set that would allow a better understanding of the relationship with deforestation within the meteorological variations. Where deforestation occurs for agricultural expansion, there is a shift in GW use for the purpose of growing food and fiber. As shown in Figures 6 and 10, the breakdown of GWT volumes was different in its contributions from forest and agriculture. The 15 MUs containing meteorological stations are important agricultural centres with GWAg representing 22 to 30 % of GWT and with 8 % of Mato Grosso forest cover in 2000 (INPE, 2011a). While the state level GWT volumes decreased by 7 % between 2000 and 2005 before recovering by 9 %, GWT volumes for the 15 MUs increased 22 % after 2005. This rise was mainly driven by a 50 % increase in GWR volumes, some of which may include some unused cropland resulting from economic and meteorological related differences, as well as GW from the Pantanal wetland. In this case, GWT volume changes are also influenced by GWAg which explained 20 % of the variance in GWT volumes for 39 MUs. INPE classified forest contributed to about 50 % of Mato Grosso’s GWT during the wet season when crops are planted, and 40 % in the dry season (Figure 4). Therefore the presence or absence of forest will have a different impact on the changes in GWT. A disappearance of forest might have a much larger effect on total fluxes than the replacing land uses near the arc of deforestation, which could explain the role of deforestation on the overall drop in GWT at the state level. Although still important, the increase in agriculture and some parts of residual land may have simply been overweighed by the 16.2 km3 y-1 per year drop in annual GWF fluxes. The change in GW fluxes from the conversion of forest to agricultural land is unclear given the post 2006 land use and the mechanism of replacement of GWF by GWP fluxes. In a  55  previous study on land use change in the Legal Amazon, Barona et al. (2010) identified that there was a relationship between deforestation and change in pasture area in Mato Grosso from 2000 to 2006, but not between deforestation and soybean expansion. An extension of the study past 2006 is difficult given the sudden change in land use practices after 2005 believed to be due to negative soy profits (Aprosoja, 2011; Martins, 2011) , but also given the difficult extrapolation of pasture area with the lack of agricultural census information (soon to be available for 2010). A small reduction in daily transpiration was observed as a result of a land use change from transition forest11 to pasture from a simulation study in northern Mato Grosso (Pongratz et al., 2006): the change in carbon pathway from C3 (forest) to C4 (pasture) vegetation (physiological effect) was balanced by the change in surface roughness (morphological effect). Unlike C3 plants, C4 plants located in wet tropical areas are able to reduce stomata exposure to the environment, thus reducing transpiration during photosynthesis (Falkenmark & Rockström, 2004: 13). The change from a rough forest to a smooth pasture surface increases gas exchanges with the atmosphere which balanced the physiological effect (Pongratz et al., 2006). This drop in transpiration can be exacerbated by the inability of pasture to reach the same deep water reserves as forest (Costa & Foley, 2000; Vourlitis et al., 2008), as well as the change in albedo (Costa & Foley, 2000; Pongratz et al., 2006) which can affect evaporation. The question remains about the land distribution of deforestation and replacement by pasture in term of GW fluxes and their aggregated impact at the larger scale. A difference is expected in the measurement of changes in GW from MOD16 if there is a  11  Described as an area of mixed vegetation with cerrado and Amazon tree species (Pongratz et al., 2006) 56  small disaggregated deforestation rather than larger blocks which may explain part of the relationship between GW fluxes and land use change. Further evidence suggests other important dynamics within the agricultural land use, particularly given the large pasture area compared to soybean (between 21 and 23 million ha estimated for pasture compared to 5.8 million ha of soybean harvested for 2009 according to IBGE (2010a)). Variance in annual changes in GWT volumes is partially explained by the annual change in GWP and GWAg volumes (R2 = 0.15 and 0.20 respectively). Part of the drop in GWT may be due to agricultural expansion, as discussed above, but differences are most likely confounded by other factors as previously discussed. Also, the drop in GWP volumes from 2000-2009 is almost offset by the increase in potential GWSoy (19 to 37 km3 y-1), thus slowing down the increase in GWAg volumes (234 to 239 km3 y-1). When considering the possibility of land conversions from pasture to soybean which seems to constitute the bulk of agricultural land in Mato Grosso (IBGE, 2008), the relationship between fluxes is nonsignificant (Figure 14). Results already presented by Barona et al. (2010) show a strong relationship between pasture and soybean area in Mato Grosso between 2000 and 2006 indicating that the increase in soybean allocated land is slightly smaller than the loss in pasture land. Of the four main crops grown in Mato Grosso, maize and sugar cane are C4, while soybean is C3. The replacement of pasture by soybean changes the carbon pathway (C4 to C3) which in turn decreases transpiration rates from the more efficient use of water by the C4 plants (Pongratz et al., 2006). This is in line with the Kc values used in this study, particularly in the rainy season when crops are in the mid-season stage: Kc mid was 0.75 for pasture and 1.50 for soybean.  57  The land use decisions from year to year and other factors affecting GW lead to a lack of relationship between the change observed in annual GWP and GWSoy for the time period studied (Figure 14). Some years, fields are left as fallow which would be counted as GWR rather than GWC used for cropland and could adopt the ET processes of pasture. In which  -1.0  -0.5  0.0  3 −1  Change in annual GW P (km y )  0.5  case, the relationship between cropland and pasture would be more closely tied.  R squared is 0.02 -0.2  -0.1  0.0  0.1  0.2  0.3  3 −1  Change in annual GWSoy (km y )  Figure 14. Relationship between changes in annual pasture (GWP) and annual soybean (GWSoy) green water for 15 municipal units containing a meteorological station for Aug 1st – Jul 31st hydrologic years in 2000-2009.  58  4.4  Analysis of uncertainty and open questions  4.4.1  Cropland and pasture evapotranspiration  4.4.1.1  Sensitivity of meteorological data on green water calculations  The separation of GW contributions from GWT fluxes are based on information provided by FAO56 which depend on meteorological data from the 12 INMET stations in order to derive ET0 (Appendix A). The concern over the impacts of common gaps filled in meteorological data (Appendix B, Table 19) were addressed by checking the effects of those correction on ET0 (Table 16). Table 16. Sensitivity of reference evapotranspiration (ET0) to common corrections made to meteorological data obtained from INMET (2011). -1  Parameter (INMET station) Atmospheric pressure (Diamantino) Minimum temperature - Tmin (Caceres) Minimum humidity - RHmin (Sao Vincente) Wind speed (Caceres)  Change in ET0 (mm day ) (min. to max. change)  Test Check of effect of seasonality (978 to 983 hPa fluctuation)  -0.2 to +0.1  Decrease Tmin by 5ºC  0 to +0.8  Decrease RHmin by 10%RH  0 to -0.4  -1  Increase by 3.5 m s  +0.1 to +3.4  The largest impact of individual parameters was observed from wind speed which was given an uncertainty of 3.5 m s-1 followed by minimum temperature (Tmin) with an uncertainty of 5ºC. Tmin is used in many instances for determining ET0, namely vapour pressure (ea and es), net long wave radiation (Rnl) and solar radiation (Rs) as calculated using the Hargreaves’ model in equation (17) (Appendix A) which is a proxy used in the absence of direct solar radiation measurements. In order to understand the interaction between all components through the PM equation, two sensitivity tests were performed on data from two stations representing a dry and wet region of Mato Grosso: Cáceres located south and Matupa north, near the Amazon (Table 17).  59  Table 17. Sensitivity tests of reference ET (ET0) from possible errors in meteorological data. INMET Station Cáceres  Matupá  Test  -1  ET0 range* -1 (mm decade )  Impact on daily ET0 (mm day ) (min. to max. change)  2.4 – 5.7  +0.3 to +2.2  2.6 – 6.1  0 to +2.6  Tmin decrease by 5ºC, RHmin decrease by 10%RH, wind speed increase by 100% Tmin decrease by 5ºC, RHmin decrease by 10%RH, wind speed increase by 100%  *over entire series of 366 decades, where 1 decade is 10 days  The sensitivity analysis shows possible overestimation of ET0 by the combination of factors with greatest uncertainty in the meteorological data. Using Matupá as an example, potential GWSoy becomes 684-702 mm y-1 for both scenarios, or a 55 mm y-1 decrease, while pasture averages 1050 mm y-1, or a 189 mm y-1 increase. This change in pasture ETC represents a 73 km3 y-1 increase (28 %) in GWP for Mato Grosso in 2003 when considering the highest pasture estimate in 2000-2009. Such a rise in GWP would yet augment the importance of changes in GWP on GWT fluxes.  4.4.1.2  Assumptions of FAO guidelines  Assumptions were made pertaining to crop management. Crops were assumed to be healthy, without any nutrient or disease stress occurring in the 10 year study period. The lack of precipitation information for Mato Grosso complicates the use Peff for determining GWC fluxes, which was the main reason behind the use of WP curves for extrapolating GW fluxes to MUs that did not contain a meteorological station. This approach was considered more robust than extrapolating precipitation information to the entire state. Extrapolating precipitation would have brought additional uncertainty, namely: (1) the variations in precipitation within the state and within municipalities, (2) the lack of information on crop coefficients when crops are stressed, and (3) the lack of information on soils on which crops  60  are grown12. While this might not impact the GWC fluxes given their small contributions, those might be much more important for GWP whose fluxes depend on the variation of precipitation from place to place. Using WP curves to extrapolate GWC to other MUs is also based on calculations obtained from MUs that are mainly concentrated in the southern region of Mato Grosso which might not be ideal for MUs that are near the arc of deforestation. The spatial variability in cultivation practices and the crop coefficients introduce further uncertainty. Planting dates of crops were also a concern given that individual practices based on local weather will change decisions on the planting date as well as the decision to plant safrinha (i.e. maize or cotton). Two scenarios were used to determine the sensitivity of the planting dates on potential and actual GWC fluxes allowed for an estimation of the possible differences arising from water stresses. FAO56 relies on the use of crop coefficients (Kc) to derive ETC from ET0 (Appendix A), and thus, uncertainty in Kc will drive changes in ETC. The values found for this study were not always representative of the various climates of Mato Grosso and therefore should be refined if this work were to be repeated. According to Allen et al. (2011), Rn is the dominant factor in humid climates, which was confirmed for tropical forests (Fisher et al., 2009). Values for Rn were calculated based on location of the meteorological stations and temperature as a substitute for cloud cover using the Hargreaves’ method. INMET meteorological stations do provide cloud cover but in the case of a large data gap there is no other way to determine the amount of radiation reaching the Earth’s surface. Some more recently installed data loggers provide direct measurements of solar radiation (Rs) and may be used in the future to derive Rn, once there is enough historical data for another 10 year analysis.  12  Soil information for all of Mato Grosso is available by Batjes et al. (2004) 61  4.4.2  MODIS ET assumptions  The algorithm developed by Mu et al. (2011) (Appendix A) has gone through improvements over the years (Cleugh et al., 2007; Mu et al., 2007; Mu, 2011; Mu et al., 2011) and maintains uncertainties of its own (Mu et al., 2011). The combination of FAO56 with data obtained from this algorithm could be problematic when assumptions of the two models are different. When looking at MOD16, some differences with FAO56 stand out. Mu et al. (2011) calculate both daytime and nighttime ET, consider a non-zero ground heat flux (G) for daily time steps, and include evaporation from water saturated soil. These identified differences have to do with evaporation as assumed by the MOD16 algorithm. Such differences will likely increase the gap between the MOD16 data and the simulated GWC from FAO56. Stomata are assumed to be closed at night in MOD16 (Mu et al., 2011) and hence any nighttime ET would mainly come from evaporation processes governed by G which is assumed to be close to zero for daily time steps in FAO56. In addition to the extra evaporation accounted for with water saturated soils, the differences between MOD16 and FAO56, as used in this study, could diminish the actual contribution of cropland and pasture to the total calculated ET from MOD16.  4.4.3  Land use maps for Mato Grosso The study used FAO56 to perform a back calculation on the contributions of land use to  GW fluxes. With the exception of forest cover provided by INPE Landsat images, direct MOD16 data extraction by other land uses could not be performed due to uncertainties in global maps. Current land maps are based on specific classification methods for determining land use such as the Global Land Cover maps from the European Space Agency whose 2009  62  product is one of the latest, most complete sets available. The product description is particularly careful in warning users not to use the maps for comparison work with previous Globe Cover maps (Bontemps et al., 2011).  4.4.3.1  Forest cover  Forest cover as classified by INPE is obtained by analysis of Landsat images and available in ESRI shapefile format. Errors from the use of this data are related to space and time. The process of converting rasters into polygons using a Geographic Information System (GIS) always causes uncertainties. Forest cover information is first analyzed from raster information (Câmara et al., 2006) before converting to polygons for public access. The uncertainty in this raster to polygon conversion is unknown for the Mato Grosso wide data. In some cases, the forest polygons might be smaller than the 1 km2 MODIS resolution leading to an overestimation of forest cover when converting these polygons to raster. This is believed to partially explain the anomalies observed for 7 MUs whose GWF fluxes increased in 2000-2009 despite deforestation. Those MUs all had <100 km2 of forest cover in 2000 and some non forest ET might been included in the GWF volume as a result of the sparse forest distribution (Figure 15). For example, the 82 counts for Jaciara and São Pedro da Cipa (Figure 15) would represent 82 km2 of forested area for 2000 while INPE reports 22.1 km2 (2011a). Similarly, the 55 counts in 2009 would represent 55 km2 of forest area compared to 17.8 km2 reported by INPE (2011a). For areas with more aggregated INPE classified forest, such as northern Mato Grosso, such differences are not expected.  63  Figure 15. Rasterized forest cover for 9 municipal units which experienced an increase in forest (GWF) green water fluxes in 2000-2009 (1 km2 resolution). Close up on Jaciara (MU 52) and São Pedro da Cipa (MU 95).  Landsat images are typically obtained near August when there is little cloud cover (Câmara et al., 2006). This means that the representative forest cover for the whole year is given by one image updated every dry season. Annual GWF fluxes from August to August change with forest cover which was referenced to occur every January. The August 1st – July 31st timeframe is believed to best represent the changes in GW fluxes due to both and agricultural practices which coincide with the rainy season and deforestation rates which are calculated from forest cover determined in the dry months. Finally, higher resolution mapping should help identify other forests which are not classified as such in the current INPE classification method. This would include cerrado, second growth and agroforestry. The INPE project Terra class (INPE, 2011b) hopes to fill gaps in knowledge with respect to land uses and may address these issues in time.  64  4.4.3.2 4.4.3.2.1  Cropland and pasture Cropland practices  GWC fluxes modeled using FAO56 and calculated for 15 MUs using the 12 INMET meteorological stations were obtained from several assumptions that will impact the final outcome of the GWC. When considering water stresses, soybean WP agreed with previously reported numbers in the tropics (Falkenmark & Rockström, 2004: 55), while sugar cane fell within the wider FAO Water ranges (Table 16). Maize’s highest WP estimate overlapped with the FAO Water range, whereas cotton WP was more than half the previously reported values. Table 18. Water productivity (WP) of soybean, maize, sugar cane and cotton for both scenarios. 3  -1  WP (m tonne ) range this study  Crop  (From potential and actual GWC)  Soybean Maize Sugar Cane Cotton  potential 1070 – 2140 720 – 790 230 1130 – 1160  actual 1530 – 1750 510 – 670 160 610 – 740  3  -1  WP (m tonne ) range (tropical)*  WP (m tonne ) range**  1250 – 1960 940 – 1460 100 – 150 2080 – 2160  1430 – 2500 625 – 1250 125 – 200 1670 – 2500  3  -1  *Falkenmark & Rockström, 2004:55; **FAO Water, 2002a, 2002b, 2002c, 2002d  Maize and cotton are typically planted towards the end of the rainy season when they are vulnerable to water stress as illustrated by the difference between potential and actual GWC. Most maize produced in Mato Grosso is planted after harvesting soybean (known as safrinha maize) (IBGE, 2008). Some however might be planted earlier, especially if there is no soybean produced, such as in Cuiabá (MU 40), Pontal do Araguaia (MU 79) and Varzea Grande (MU 102). The safrinha maize can often be a gamble since it is planted towards the end of the rainy season and may suffer from water stress which will in turn impact yields (Soler et al., 2007). Maize had the greatest variance of all crops and the lowest R2 for the linear models (Appendix D). This shows one of the consequences from the lack of information on the planting of maize from municipality to municipality and the realities of 65  planting maize after soybean. Similar comments can be made for cotton which was assumed to be safrinha in this study. The following MUs did not produce cotton for most of 20002009: Barra do Garças (MU 27), Canarana (MU 34), Cuiabá (MU 40), Matupá (MU 59), Peixoto de Azevedo (MU 76), Pontal do Araguaia (MU 79), Varzea Grande (MU 102). Other factors may also affect the differences in WP values. The normalization of planting dates for the crops might miss some connection between crop water use and recorded production. The Kc used for FAO56 assumed that crops across the state grow at the same rate and reach the development cycles at exactly the same time. This is probably not the case given that crops may experience various levels of water, nutrient or physical stresses based on the amount and frequency of precipitation, tropical storms and land degradation. This is true state-wide, as well as within each individual municipality. Moreover, the annual values reported by IBGE are obtained from expert surveys, not census, thus introducing further uncertainties in the calculation of WP. Moreover, there remains uncertainties related to practices at the regional level. Even in the situation where a land use map were available, the exact location, type and sequence of cultivated crops is difficult to know without additional on the ground information. This also includes cropland that is not cultivated in a given year and which was included as GWR. The use of agricultural production data remains one of the best ways for determining GWC and GWP fluxes at this point in time.  4.4.3.2.2  Pasture estimate  The use of animal population as a proxy for pasture area is particularly sensitive to information from IBGE. The increase in animal population with the decrease in pasture area suggested by the 1996 and 2006 census shows a greater concentration of cattle per hectare.  66  Barona et al. (2010) observed a 34 % increase in total livestock units with a 20 % increase in pasture area for the Legal Amazon. The livestock density determined in this study for Mato Grosso was close to that calculated for the Legal Amazon by Barona et al. (2010) for 20002006: 0.86 to 1.21 livestock units ha-1 (Barona et al., 2010) compared to 0.74 to 1.17 livestock units ha-1 in the present study. There is greater uncertainty in the 2006-2009 estimates due to missing census information post 2006. The 2010 census information is currently unavailable from IBGE and thus the post 2006 estimates rely on the assumed increase in livestock density over time. The pasture estimate should be repeated once the 2010 census data on pasture area becomes available. Animal population obtained from expert surveys can be lower or greater than what would have been obtained from a census (1996 and 2006), in turn underestimating or overestimating the pasture surface area. There is a 2 million ha difference between the highest estimate in the present study and the estimate provided by the Mato Grosso association of breeders (Figure 23, Appendix E) which corresponds to a difference of 17 km3 y-1 or <10 % for state-wide GWP volumes estimated in this study. Furthermore, the relationship between pasture area and animal population is not fixed in time. A producer may have a smaller animal population one year, while retaining the same pasture area on the property and temporarily changing the livestock density. Moreover, the pasture surface area implicitly assumes similar types of pastures and good pasture health with a strong correlation between animal unit and pasture area. This is probably not the case for all of Mato Grosso all of the time. The state is home to natural grasslands as well as planted Brachiaria pastures of different types (e.g. brizantha and marandu) which are known by Embrapa, Brazil’s main agricultural research organization, to have had serious degradation from premature death to  67  improper management and fertilization (Barbosa, 2006). All these factors will affect the correct determination of the pasture surface area and in turn the GW fluxes associated with the land use. Finally, establishing a correct Kc value for pasture is key for modeling GWP. Early work from Meirelles et al (2011) on measuring Brachiaria brizantha ET should be done over a longer period of time to better understand ET processes during the dry and wet seasons.  68  Chapter 5: Conclusions  This regional study identified possible trends and reasons for changes in total GW fluxes in Mato Grosso, Brazil, while generating questions about required information to gain better insight of land use effects on water vapour flows. Adapting a water-focused approach helped directly estimate the changes in GW fluxes between 2000 and 2009 while isolating land use effects on such changes. Also, important trade-offs in GW water use were identified in the study time period to provide important insight on water use in the state. Annual forest GW volumes represented 50 % of Mato Grosso’s annual GW volumes in 2000 and decreased by 10 % between 2000 and 2009 at a rate of 16.2 km3 y-1 per year as a result of deforestation which explained up to 27 % of variance in annual total GW volumes. Soybean, maize, sugar cane and cotton GW contributions mostly doubled between 2000 and 2009 despite a decline in 2005-2006 which followed a dry year. Increases in crop contributions to total GW volumes were balanced by the drop in pasture GW. GWP was 5 times greater than soybean while soybean represented between 75 % and 83 % of total crop GW. A sudden drop in GW fluxes and volumes observed in 2005-2006 raised questions about other factors affecting GW fluxes in Mato Grosso, namely the impact of meteorological conditions such as net radiation, vapour pressure deficit and precipitation, as well as market prices which affected farmers’ profits. Both factors also exert effects on GW fluxes and should be the focus of future studies. 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The expansion of agriculture in the Brazilian Amazon. Environmental Conservation, 32(3), 203-212.  82  Soler, C. M. T., Hoogenboom, G., Sentelhas, P. C., & Duarte, A. P. (2007). Impact of water stress on maize grown off-season in a subtropical environment. Journal of Agronomy and Crop Science, 193(4), 247-261.  Sulser, T. B., Ringler, C., Zhu, T., Msangi, S., Bryan, E., & Rosegrant, M. W. (2010). Green and blue water accounting in the Ganges and Nile basins: implications for food and agricultural policy. Journal of Hydrology, 384(3-4), 276-291.  United Nations Environmental Programme, UNEP - DEWA/GRID Europe. (2008). Ahn and Tateishi monthly potential & actual evapotranspiration & water balance. Retrieved June 20, 2011, from http://www.grid.unep.ch/GRID_search_details.php?dataid=GNV183  Vila da Silva, J. d S., & Abdon, M. d. M. (1998). Delimitação do Pantanal Brasileiro e suas sub-regiões. Pesquisa Agropecuaria Brasileira, Brasilia, 33(Numero Especial), 17031711.  Vourlitis, G. L., Priante, N., Hayashi, M. M. S., Nogueira, J. D., Caseiro, F. T., & Campelo, J. H. (2002). Seasonal variations in the evapotranspiration of a transitional tropical forest of Mato Grosso, Brazil. Water Resources Research, 38(6), 1094.  Vourlitis, G. L., Nogueira, J. D., Lobo, F. D., Sendall, K. M., de Paulo, S. R., Dias, C. A. A., et al. (2008). Energy balance and canopy conductance of a tropical semi-deciduous forest of the southern Amazon basin. Water Resources Research, 44(3), W03412.  83  Appendices  Appendix A Deriving green water fluxes through evapotranspiration  This Appendix is a condensed version of the FAO guidelines from Allen et al. (1998) (shortened as FAO56). It provides a detailed description of the PM equation and how it is used it to determine ETC using meteorological data. Then follows a description of the MOD16 algorithm developed by Qiaozhen Mu and colleagues at the University of Montana, Missoula (Mu et al., 2011).  A.1  The Penman-Monteith equation The PM equation is based on water and energy balances derived from both Penman  (1948) and Monteith (1965) to calculate ET. The need for a standard method for calculating ET was recognized by the FAO which published guidelines (FAO56) for implementing the PM equation (Allen et al., 1998; Allen et al., 2011). PM calculates the latent heat flux λET (in mm day-1) by: ∆ ( Rn − G ) + ρ a c p  λET =  (es − ea ) ra  r ∆ + γ (1 + s ) ra  (3)  where Rn is the net radiation and G is the soil heat flux (both in MJ m-2 day-1), ρa is the average density of the air at constant pressure (kPa), cp is the specific heat of the air (or heat capacity of water at constant pressure, 1.013 10-3 MJ kg-1 oC-1), (es – ea) is the vapour pressure deficit (kPa), ra is the aerodynamic resistance and rs is the bulk surface resistance  84  (both in s m-1), ∆ represents the slope of the vapour pressure curve (kPa oC-1), and γ is the psychrometric constant (kPa oC-1). FAO56 establishes a reference ET, or ET0, as “a hypothetical crop with an assumed height of 0.12 m having a surface resistance of 70 s m-1 and albedo of 0.23, actively growing and adequately watered” (Allen et al., 1998: 23). ET0 (mm day-1) incorporates local meteorological conditions from equation (3): 900 u 2 (e s − e a ) T + 273 ∆ + γ (1 + 0.34u 2 )  0.408∆( Rn − G ) + γ ET0 =  (4)  where u2 is the wind velocity (m s-1) 2 meters above the crop canopy, and T is the air temperature (oC). Crop ET, or ETC, is then determined by  ETc = K c ET0  (5)  where Kc represents a coefficient for a given crop in a specific environment. This coefficient changes during the development phases of the crop (Figure 16). It is important to note the assumptions that come with equations (3) to (5): ETC is calculated assuming ideal conditions: crops are disease free, well watered and adequately fertilized (Allen, et al. 1998). ET during the initial crop development phase is dominated by soil evaporation when the Leaf Area Index (LAI) is close to zero in Kc ini, before increasing to a higher crop coefficient Kc mid where transpiration exceeds evaporation in the crop coefficient. Kc end is the crop coefficient at harvest when the LAI drops at the end of the development cycle (Figure 16). Crop coefficients Kc dev and Kc late are also defined for the crop development stage and late season during which the crop coefficient gradually increases (Kc dev) and decreases (Kc late) with the LAI.  85  Figure 16: Crop coefficients Kc during the crop development cycle (Allen et al., 1998) (printed with permission from the Food and Agriculture Organization of the United Nations).  A.2  Input data for the Penman-Monteith equation All data required for the PM equation can be derived from meteorological data. The  sections below describe how data obtained from weather stations can be used to calculate ET0 with equation (4). The PM equation uses variables that can be derived from weather station data according to FAO56 (Allen et al., 1998) such as the vapour pressure deficit (es – ea), the slope of the vapour pressure curve (∆), the psychrometric constant (γ), and the surface and aerodynamic resistances (rs). In this study, daily ET0 was derived and then averaged over 10 consecutive days to provide a decadal ET0, as per recommendations of FAO56 (Allen et al., 1998).  86  Vapour pressure The vapour pressure deficit (es – ea) of equations (3) and (4) can be derived from humidity measurements. Generally, the vapour pressure (kPa) is expressed as a function of temperature (Allen et al., 1998). e o (T ) = 0.6108 exp  17.27T T + 237.3  (6)  where T is the temperature of the air (ºC). The saturation vapour pressure es is the pressure at which the air is saturated with water molecules (Allen et al., 1998). It is an average of the saturation vapour pressure for the daily maximum and minimum temperatures: es =  e o (Tmax ) + e o (Tmin ) 2  (7)  If the mean air temperature is used in the absence of Tmax and Tmin, then the saturated vapour pressure is underestimated, resulting in a smaller ET0 than expected (Allen et al., 1998). The actual vapour pressure can be derived by the relative humidity. Relative humidity represents the percentage of water molecules in the air in the gas phase to the total saturation vapour pressure. As a result, the actual vapour pressure is derived from the saturation vapour pressure and the relative humidity as follows (Allen et al., 1998):  e o (Tmin ) ea =  RH max RH min + e o (Tmax ) 100 100 2  (8)  where RHmax and RHmin represent the maximum and minimum relative humidity recorded at 8:00 and 14:00 respectively. In the absence of RHmin, ea can be estimated using RHmax: ea = e 0 (Tmin )  RH max 100  (9)  87  RHmin can also be estimated by assuming that the dew point temperature is equal to Tmin for the day (Allen et al., 1998: 58)  ea = e o (Tmin ) = 0.611exp  17.27Tmin Tmin + 237.3  (10)  or finally, by using the definition of actual vapour pressure: ea =  RH mean es 100  (11)  The slope of the curve representing the change in saturation vapour pressure with temperature is also needed for the PM equation. This slope ∆ (kPa ºC-1) is given by (Allen et al., 1998):  ∆=  4098e o (T ) (T + 237.3) 2  (12)  where T is the air temperature (ºC). Finally, the psychrometric constant (γ) describes the ability of water molecules to evaporate at a given atmospheric pressure by relating partial pressure of water in air and air temperature (Allen et al., 1998):  γ =  cP P  ελ  (13)  where ε is equal to 0.622 and represents the molecular weight ratio of water vapour to dry air, and λ is the latent heat of vapourization (2.45 MJ kg-1). Given the changes in air pressure with altitude, γ also changes with altitude.  88  Energy fluxes  Energy fluxes are an important component of the PM equation. Extraterrestrial radiation (Ra) is partitioned into various components which will impact ET in various ways (Allen et al., 1998): Solar radiation (Rs) is the radiation reaching the Earth’s surface after extraterrestrial radiation has travelled the upper atmosphere and clouds Net shortwave radiation (Rns) is the energy that is not reflected by the Earth’s surface Net longwave radiation (Rnl) is the energy emitted from the Earth terrestrial surface, without being absorbed from gases in the atmosphere The net solar radiation (Rn), is that which is fully available to the Earth surface for ET processes once energy fluxes transferred to the soil (G) have been taken into account In the absence of direct measurements at a weather station, energy fluxes can be derived using geographic location and cloud cover. Over daily time steps, G is negligible and is assumed close to zero. Rn (MJ m-2 day-1) is calculated using equation (14) (Allen et al., 1998): Rn = Rns − Rnl  (14)  where Rns is the net shortwave radiation gain and the Rnl is the net longwave radiation loss. Rns (MJ m-2 day-1) is the fraction that is not reflected by the surface and thus depends on Rs and the surface albedo α (at 0.23 for the reference crop) (Allen et al., 1998): Rns = (1 − α ) Rs  (15)  The net longwave radiation Rnl (MJ m-2 day-1) is the portion of the solar radiation emitted by the Earth’s surface as determined by Allen et al. (1998):  89  4  Rnl = σ (  4  Tmax + Tmin R )(0.34 − 0.14 ea )(1.35 s − 0.35) Rso 2  (16)  where σ is the Boltzmann constant (4.903 10-9 MJ K-4 m-2 day-1), Tmax and Tmin are the maximum and minimum temperatures (K), ea is the actual vapour pressure (kPa). Rs/Rso is the ratio of the solar radiation to the clear sky solar radiation. This ratio can be determined by maximum and minimum temperatures as well as altitude in the event of missing information on sunshine duration (Allen et al., 1998): Rs = k Rs (Tmax − Tmin ) Ra  (17)  This Hargreaves’ radiation formula calculates Rs using maximum and minimum temperatures (ºC), an adjustment coefficient kRs (0.16 for interior regions such as Mato Grosso), and Ra, the extraterrestrial radiation (MJ m-2 day-1). Rso = (0.75 + 2 ×10 −5 z ) Ra  (18)  where z is the altitude of the weather station (m). This calculation of Rso also assumes no information available for incoming radiation. Ra depends on the angle of incidence and can be calculated using geographical coordinates: Ra =  24(60)  π  Gsc d r (ω s sin(ϕ ) sin(δ ) + cos(ϕ ) cos(δ ) sin(ω s ))  (19)  where Gsc is the solar constant (0.0820 MJ m-2 min-1), φ is the latitude (radians), dr is the inverse relative distance Earth-Sun which depends on the day of the year J: d r = 1 + 0.33 cos(  2π J) 365  (20)  δ is the solar declination also depends on the day of the year J,  δ = 0.409 sin(  2π J − 1.39) 365  (21)  90  The sunset hour angle ωs is calculated using the latitude φ and solar declination δ:  ω s = arccos(− tan(ϕ ) tan(δ ))  A.3  (22)  Remote sensing MODIS is an instrument from the Earth Observation System (EOS) satellite launched  in 1999 (Terra spacecraft) and 2002 (Aqua spacecraft) with 36 spectral bands that view the entire planet every 1 to 2 days (Justice et al., 2002; NASA, 2011a). There are many MODIS products available including a product for ET (MOD16) and available globally at 1 km2 resolution (NASA, 2011b; Mu et al., 2011). MOD16 datasets have been perfected through the years (Cleugh et al., 2007; Mu et al., 2007; Mu, 2011; Mu et al., 2011) and use the PM equation to derive ET from remotely sensed and meteorological inputs available from the NASA Global Modeling and Assimilation Office (GMAO) (Mu et al., 2007; Mu, 2011) and compared to 46 eddy covariance flux towers which measure ET (Mu et al., 2011). Other remote sensing inputs for 8 and 16 days are (Mu, 2011) (Figure 8): Collection 4 land cover type 2 of MODIS (MOD12Q1) for global land cover 2 Fraction of photosynthetically active radiation and leaf area index (FPAR/LAI) from MODIS (MOD15A2) Collection 4 CMG MODIS albedo (MOD43C1) The daily meteorological observations are combined with the remote sensing inputs to determine total ET from the soil and the plant canopy using the algorithm illustrated in Figure 17.  91  Figure 17. MODIS algorithm for determining evapotranspiration (Mu et al., 2011)13.  13  Reprinted from Remote Sensing of Environment, 115, Mu, Q., Zhao, M., Running, S., Improvements to a MODIS global terrestrial evapotranspiration algorithm, 1781-1800, Copyright (2011), with permission from Elsevier. 92  Appendix B Gap filling for meteorological data  Data that did not follow dominant trends in seasonality (atmospheric pressure, minimum temperature in particular) were discarded with resulting gaps filled in order to determine daily values for ET0 (Table 19). Table 19. Common gaps filled in time series data for all conventional INMET meteorological stations. Measurement  Common gaps filled  Atmospheric pressure (P)  Zero value for P or P that did not follow seasonality replaced by a gap; 1-4 point gaps interpolated linearly; greater gaps replaced by monthly averages obtained from the entire time series of the meteorological station*  Temperature (T)  Zero and negative values for T replace by a gap; mean T of the air made equal to mean T** whenever there was a gap in Tmax or Tmin; large gaps in Tmax or Tmin replaced by monthly averages obtained from the entire time series of the meteorological station*  Relative humidity (RH)  Zero values for RH replaced by a gap; large gaps in RHmax or RHmin replaced by monthly averages obtained from the entire time series of the meteorological station*  Wind speed  Gaps in wind speed replaced by mean wind speed of entire time series of the meteorological station (see Table 21)  Vapour pressure deficit  Negatively calculated vapour pressure deficits replaced by zero  *In the larger gaps, often no data was recorded at all **Recall that mean daily temperature (Tmean) is calculated from maximum and minimum daily temperature (Tmax, Tmin)  In some cases, nearby meteorological station data was available to fill large gaps in data from the weather stations (Table 20).  93  Table 20. Gaps filled using nearby meteorological stations. Conventional station with gap  Station used to fill gap  Gaps filled  Padre Ricardo Remetter  Cuiabá*  P, RH and T (2003). Padre Ricardo Remetter was used as the one station for the nearby municipalities (both are 4ºS/W apart, 5 km)  São Vincente  Campo Verde**  P and RHmin (2008-2009). No P available; monthly averages from the data logger used to fill P (2000-2007)  Rondonópolis  Rondonópolis**  P, RHmin (2008-2009). No P on the conventional station. Monthly averages from the data logger used to fill P gaps for 2000-2007.  São José do Rio Claro  São José do Rio Claro**  RHmin, Tmin (2008-2009).Tmin had shifted to lower values in 2008  *Conventional station; **data logger  Wind speed is the more unpredictable meteorological variable and thus could not be approximated using seasonality. Gaps in wind speed were replaced by the mean of the entire time series for the weather station (Table 21). Table 21: Mean wind speed used for corrections at INMET conventional meteorological stations. Station Cáceres Gleba Celeste Padre Ricardo Remetter Poxoréo Rondonópolis São José do Rio Claro São Vincente  Mean wind speed (standard deviation) m s  -1  1.40 (0.89) 1.51 (0.62) 1.37 (0.80) 0.41 (0.60) 0.72 (0.75) 0.88 (0.55) 2.06 (1.14)  94  Appendix C List of municipal units of Mato Grosso  Many municipalities in Mato Grosso changed their size and shape between 2000 and 2009. As a result, municipal units (MUs) were created by aggregating political boundaries such that the total surface area of the unit remained unchanged in the time period of interest. Table 22 lists these MUs (from MU 1 to 14) as well as the municipalities which remained unchanged in the time period (from MU 15 to 104) (Figure 18). Table 22. Municipal units of Mato Grosso for 2000-2009 used in this study Municipal unit  Municipality  1 2  Aripuanã, Colniza, Rondolandia São Jose do Xingu, Santa Cruz do Xingu Chapada do Guimarães, Nobres, Nova Brasilandia, Nova Mutum, Rosario Oeste, Santa Rita do Trivaleto Claudia, Itauba, Nova Santa Helena, Santa Carmem, Terra Nova do Norte Agua Boa, Nova Nazaré Novo São Joaquim, Santo Antonio do Leste Alto Boa Vista, Bom Jesus do Araguaia, Cocalinho, Novo Santo Antonio, Ribeirao Cascalheira, Sao Felix do Araguaia, Serra Nova Dourada Conquista d'Oeste, Jauru, Vila Bela da Santissima Trinidade, Pontes e Lacerda, Vale de São Domingos Barra do Bugres, Reserva do Cabaçal, Rio Branco, Salto do Ceu, Tangara da Serra Caceres, Curvelandia, Lambari d'Oeste, Mirassol d'Oeste Ipiranga do Norte, Itanhanga, Sinop, Tapurah Juara, Nova Monte Verde Cotriguaçu, Juruena Diamantino, Sao José do Rio Claro * Acorizal Alta Floresta Alto Araguaia Alto Garças* Alto Paraguai Alto Taquari* Apiacas Araguaiana Araguainha* Araputanga Arenapolis Barão de Melgaço Barra do Garças Brasnorte Campinapolis Campo Novo do Parecis Campo Verde  3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  *  No forest cover reported by INPE 95  Table 22. Municipal units of Mato Grosso for 2000-2009 used in this study Municipal unit 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74  *  Municipality Campos de Julio Canabrava do Norte Canarana Carlinda Castanheira Colíder Comodoro Confresa Cuiabá Denise Dom Aquino Feliz Natal Figueiropolis d'Oeste Gaucha do Norte * General Carneiro Gloria d'Oeste Guaranta do Norte Guiratinga Indiavaí Itiquira Jaciara Jangada* Juina Juscimeira Lambari do Rio Verde Luciara Marcelandia Matupa Nortelandia Nossa Senhora do Livramento Nova Bandeirantes Nova Canaã do Norte Nova Garita Nova Lacerda Nova Marilandia Nova Maringa Nova Olimpia Nova Ubirata Nova Xavantina Novo Horizonte do Norte Novo Mundo Paranaita Paranatinga  No forest cover reported by INPE 96  Table 22. Municipal units of Mato Grosso for 2000-2009 used in this study Municipal unit 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104  *  Municipality Pedra Preta Peixoto de Azevedo Planalto da Serra Poconé * Pontal do Araguaia Ponte Branca* Porto Alegre do Norte Porto dos Gauchos Porto Espiridão Porto Estrela Poxoréo Primavera do Leste Querencia Ribeirãozinho Rondonópolis Santa Terezinha Santo Alfonso Santo Antonio do Leverger São Jose do Povo* São Jose dos Quatro Marcos São Pedro da Cipa Sapezal Sorriso Tabapora Tesouro* Torixoréu* União do Sul Varzea Grande* Vera Vila Rica  No forest cover reported by INPE 97  Figure 18. Municipal units of Mato Grosso for 2000-2009 defined for this study  98  Appendix D Water productivity curves  WP curves were developed using data available from the 15 MUs containing a meteorological station. Linear models were derived for each year of production and each crop in order to evaluate the validity of the assumption made for FAO56 and to extrapolate GWC volumes for MUs far from any meteorological station. Crops were assumed to be in perfect health and have sufficient nutrients for FAO56. In one case, the potential GWC was calculated assuming crops did not experience any water stress; the second case, the actual GWC was calculated using Peff calculated from the weather station’s precipitation data and the USDA Soil Conservation Service method (Dastane, 1978). The slopes of the lines of best fit represent the WP of each crop (Figures 19 to 22). These ranged from 2030 to 2450 m3 tonne-1 for soybean, 640 to 958 m3 tonne-1 for maize, 205 to 245 m3 tonne-1 for sugar cane, and 1020 to 1350 m3 tonne-1 for cotton. WP in m3 tonne-1 was not calculated for pasture given that production values reported by IBGE are not in tonnes but in animal population. Instead, mean values for GWP across the 15 MUs were determined (Table 25). No differences were observed between scenario I and II in which a precipitation threshold of 10 mm and 7 mm led to a change in crop coefficient for a greater GWP flux. Values ranged from 822 mm to 889 mm and standard deviations between 50 and 80 mm with the greatest variance recorded in 2007. Table 23. Water productivity of crops assuming no water stress (2000-2009). Crop Soybean Maize Sugar cane* Cotton  Year (scenario) I II I II I & II I II  2  Equation  R 6  y = 2140x + 5.73 10 6 y = 1070x + 6.20 10 6 y = 790x + 5.25 10 6 y = 720x + 4.76 10 6 y = 230x + 1.39 10 6 y = 1160x + 1.86 10 6 y = 1130x + 1.43 10  0.992 0.994 0.941 0.936 0.982 0.973 0.971  99  Table 24. Water productivity of crops under water stress. Crop Soybean Maize Sugar cane* Cotton  2  Year (scenario)  Equation  R  I II I II I & II I II  y = 1750x – 4.56 10 6 y = 1530x – 2.14 10 6 y = 670x + 2.25 10 6 y = 510x + 1.11 10 6 y = 160x + 1.79 10 3 y = 740x – 14.5 10 5 y = 610x – 3.25 10  6  0.983 0.986 0.943 0.945 0.930 0.957 0.957  Table 25: Mean pasture green water for 2000-2009. Year  Mean GWP (mm)  Standard deviation (mm)  ± 95% CI  2000 2001 2002 2003 2004 2005 2006 2007 2008 2009  822 865 859 865 865 848 836 848 859 889  56 50 59 48 54 63 68 80 59 77  35 31 37 30 34 39 42 50 37 48  CI: Confidence interval  Results for pasture were close to those measured by Meirrelles et al (2011).  100  2.0e+08  1000000  0  50000  150000  250000  Cotton  1500000  2.0e+08 1.0e+08  3 −1  1000000  0.0e+00  GWC (m y per municipal unit)  2.0e+08 1.0e+08  500000  tonnes per year per municipal unit  350000  3.0e+08  Sugar cane 3.0e+08  tonnes per year per municipal unit  R squared is 0.9823 0  1.0e+08  3 −1  600000  R squared is 0.9409  tonnes per year per municipal unit  0.0e+00  3 −1  200000  0.0e+00  GWC (m y per municipal unit)  2.0e+09  R squared is 0.9924 0  GWC (m y per municipal unit)  Maize  1.0e+09 0.0e+00  3 −1  GWC (m y per municipal unit)  Soybean  R squared is 0.9726 0  50000  150000  250000  tonnes per year per municipal unit  Figure 19. Water productivity curves using potential crop green water (GWC) in 15 municipal units containing a meteorological station (2000-2009) (scenario I).  101  2.0e+08  1000000  0  50000  150000  250000  Cotton  1500000  2.0e+08  350000  1.0e+08  3 −1  1000000  0.0e+00  GWC (m y per municipal unit)  2.0e+08 1.0e+08  500000  tonnes per year per municipal unit  3.0e+08  Sugar cane 3.0e+08  tonnes per year per municipal unit  R squared is 0.9823 0  1.0e+08  3 −1  600000  R squared is 0.9356  tonnes per year per municipal unit  0.0e+00  3 −1  200000  0.0e+00  GWC (m y per municipal unit)  2.0e+09  R squared is 0.9939 0  GWC (m y per municipal unit)  Maize  1.0e+09 0.0e+00  3 −1  GWC (m y per municipal unit)  Soybean  R squared is 0.9714 0  50000  150000  250000  tonnes per year per municipal unit  Figure 20. Water productivity curves using potential crop green water (GWC) in 15 municipal units containing a meteorological station (2000-2009) (scenario II).  102  2.0e+08 0  50000  150000  250000  Sugar cane  Cotton  1000000  1500000  350000  1.0e+08 0.0e+00  3 −1  1.0e+08  500000  tonnes per year per municipal unit  2.0e+08  tonnes per year per municipal unit  R squared is 0.9301 0  1.0e+08  3 −1  1000000  GWC (m y per municipal unit)  2.0e+08  600000  R squared is 0.9432  tonnes per year per municipal unit  0.0e+00  3 −1  200000  0.0e+00  GWC (m y per municipal unit)  2.0e+09  R squared is 0.9832 0  GWC (m y per municipal unit)  Maize  1.0e+09 0.0e+00  3 −1  GWC (m y per municipal unit)  Soybean  R squared is 0.9571 0  50000  150000  250000  tonnes per year per municipal unit  Figure 21. Water productivity curves using actual crop green water (GWC) for 15 municipal units containing a meteorological station (2000-2009) (scenario I).  103  2.0e+08 1.0e+08  1000000  0  150000  250000  Cotton  3 −1  1.0e+08  500000  1000000  1500000  tonnes per year per municipal unit  0.0e+00 5.0e+07 1.0e+08 1.5e+08  Sugar cane  R squared is 0.9301 0  50000  tonnes per year per municipal unit  GWC (m y per municipal unit)  2.0e+08  600000  R squared is 0.9452  tonnes per year per municipal unit  0.0e+00  3 −1  200000  0.0e+00  R squared is 0.9861 0  GWC (m y per municipal unit)  Maize  3 −1  GWC (m y per municipal unit)  1.0e+09 1.5e+09 0.0e+00 5.0e+08  3 −1  GWC (m y per municipal unit)  Soybean  350000  R squared is 0.9565 0  50000  150000  250000  tonnes per year per municipal unit  Figure 22. Water productivity curves using actual crop green water (GWC) for 15 municipal units containing a meteorological station (2000-2009) (scenario II).  104  Appendix E Pasture estimate  Pasture estimates were calculated for all MUs (Figure 23). The change in pasture area reflects the animal population in the state, more specifically as it relates to cattle which had the greatest heads in the states (from about 19 million in 2000 to 27 million heads in 2009). Pasture surface area increased until 2003 when it reached a peak of 24 million ha. Surface area then dropped by 13 % between 2003 and 2009 to reach 20.7 million ha in 2009 for an increase in livestock unit of 1.04 to 1.39 livestock units ha-1. To estimate the uncertainty in the pasture estimates post-2006, a second estimate was calculated assuming constant livestock densities for the 2006-2009 period. This revised pasture estimate increased almost 7 % between 2008 and 2009 to reach 23 million ha (as opposed to 21 million ha for the estimate based on increased animal concentration), and just 1 million ha lower than the 2003 estimate. The revised estimate is somewhat in disagreement with the hypothesis that pasture area is declining in Mato Grosso. Both results are 1 to 3 million ha lower than the values report by the Mato Grosso association of breeders (Associação dos criadores de Mato Grosso, (Acrimat, 2011). Values obtained for the estimate of pasture were then used to determine GWP volumes.  105  Figure 23. Annual pasture area estimate in 2000-2009 for assumed continuous increase in livestock density (sa1), stable livestock density of 1.21 livestock units ha-1 (sa2). Acrimat estimate is from the Mato Grosso Association of Breeders (Acrimat, 2011).  106  Appendix F R scripts used in this research  FAO guidelines (Allen et al., 1998) were adapted into statistical software R (R Development Core Team, 2011). Below is the code used for determining ET0 following equations listed in Appendix A (section F.1), as well as the crop development cycles for soybean, maize, cotton and sugar cane (section F.2). Please reference this thesis accordingly if you are going to use the code shown below.  F.1  Reference ET calculation  # by Michael Lathuilliere, UBC Institute for Resources, Environment and Sustainability. Land use effects on green water fluxes in Mato Grosso, Brazil.  ## Calculation of reference ET (ET0) as per FAO guidelines Irrigation and Drainage Paper 56  (FAO56)  ## Data should have first been analyzed and manipulated into Aquarius or other program, with an exported .csv ## file containing the following headings (stdev = standard deviation):  ## Date: month/day/year ## Tair mean: mean air temperature, in deg.C ## Tair.stdev: standard deviation of mean air temperature ## RHmean: mean relative humidity calculated at (RHmax + RHmin)/2, in % ## RH.stdev: standard deviation of the mean relative humidity ## P.mean: mean atmospheric pressure, in hPa ## P.stdev: standard deviation of atmospheric pressure ## Wspeed.mean: mean wind speed (record height of sensor), in m/s ## Wspeed.stdev: standard deviation of wind speed  107  ## Cloudcover.mean: mean cloud cover, as a fraction of 10 (/10), ## Cloudcover.stdev: standard deviation of cloud cover ## Tmax: maximum temperature over 24hr period, in deg.C ## Tmin: minimum temperature over 24hr period, in deg.C ## Precip: total precipitation over a 24hr period, in mm ## Tmean: mean temperature calculated as (Tmax+Tmin)/2, in deg.C ## RHmax: maximum humidity recorded at 8am ## RHmin: minimum humidity recorded at 2pm  ## All equations are numbered according to the FAO56 numbering  #-------------------------------------------------------------------------  rm(list = ls())  #------------------------------------------------------------------------##Input file location of .csv file for the climate station considered  Station <read.table("C:/Documents and Settings/BuddyLuv/My Documents/My Dropbox/Thesis/Aquarius/NovaXavantina/INMET_NovaXavantina_Aquarius.csv", header=TRUE, sep=",", na.strings="NA", dec=".", strip.white=TRUE)  #------------------------------------------------------------------------##Input altitude, latitude and name of the climate station  Location <- "NovaXavantina Station" z <- 316 #altitude in m lat <- -14.70 #latitude in decimal degrees  108  Wheight <- 10 #height of the sensor measuring wind speed, in m  #------------------------------------------------------------------------attach(Station)  ##Date conversions from the .csv file Date <- as.character(Date) Date <- as.Date(Date, "%m/%d/%Y") J <- as.numeric(format(Date, "%j")) #conversion to julian day  ## List of variables, constants used in the calculation uz <- Wspeed.mean #rename mean wind speed in m/s lambda <- ifelse(is.na(Tair.mean), 2.45, 2.501 - (2.361*0.001)*Tair.mean) #Temperature dependent latent heat of vapourization (MJ/kg) Cp <- 1.013*10^-3 #Specific heat capacity at constant P (MJ/kg.degC) sigma <- 4.903*10^-9 #Boltzmann constant in MJ/K^4m^2day u2 <- uz*(4.87/(log(67.8*Wheight-5.42))) #Wind speed at 2m height calculated from uz, equation (47)  #------------------------------------------------------------------------##Calculation of the psychrometric constant 'gamm' (kPa/degC), equation (8)  gamm <- (Cp*P.mean*0.1)/(0.622*lambda)  #------------------------------------------------------------------------##Calculation of the vapour pressure deficit (es - ea) (kPa)  109  ##Calculation of the saturation vapour pressure 'es' (kPa), equation (11)  eo.Tmax <- 0.6108*exp(17.27*Tmax/(Tmax+237.3)) eoTmax <- signif(eo.Tmax, digits = 3) ##keep 3 significant figures eo.Tmin <- 0.6108*exp(17.27*Tmin/(Tmin+237.3)) eoTmin <- signif(eo.Tmin, digits = 3) ##keep 3 significatn figures  es1 <ifelse(is.na(eoTmax)|is.na(eoTmin),0.6108*exp(17.27*Tmean/(Tmean+237.3)), (eoTmax+eoTmin)/2) ##if Tmax or Tmin are missing, 'es' is calculated using Tmean, eq(12) es <- signif(es1, digits = 3) ##keep 3 significant figures  ##Calculation of the actual vapour pressure 'ea' (kPa), equation (13) and equation (48)  ea1 <- ifelse(is.na(eoTmax)|is.na(RHmax)|is.na(RHmin), eoTmin,((eoTmin*RHmax/100) +(eoTmax*RHmin/100))/2) ##if Tmax, RHmax, RHmin missing, then assume Tmin = dewpoint temperature ##RHmean is determined by RHmax and RHmin, so eq(19) cannot be used ea <- signif(ea1, digits = 2) ##keep 2 significant figures (due to RH)  #Vapour pressure deficit (kPa)  Vap.deficit1 <- ifelse((es - ea)<0,0,(es-ea))  110  Vap.deficit <- signif(Vap.deficit1, digits = 2) ##keep 2 significant figures (due to ea)  #------------------------------------------------------------------------##Calculation of the slope of the saturated vapour pressure curve, Delta (kPa/degC)  Delta1 <- 4098*(0.6108*exp((17.27*Tmean)/(Tmean+237.3)))/((Tmean+237.3)^2) Delta <- signif(Delta1, digits = 3) ##keep 3 significant figures  #------------------------------------------------------------------------##Calculation of incoming radiation to determine ET0 using data from meteorological stations  ##Input longitude (fi) and latitude (lat) fi1 <- (pi/180)*(lat) ##in rad, equation (22) fi <- signif(fi1, digits = 4) ##keep 4 significant figures (from latitude) Gsc <- 0.0820 ##Solar constant in MJ/m2m-1  #Calculation of inverse relative distance Earth-Sun, equation (23) dr <- 1+0.033*cos(2*pi*J/365)  #Calculation of the solar declination, equation (24) delta <- 0.409*sin(-1.39+(2*pi*J/365))  #Calculation of sunset hour angle (rad), equation (26) ws1 <- acos(-tan(fi)*tan(delta))  111  ws <- signif(ws1, digits = 4) ##keep 4 significant figures (from fi)  #Calculation of extraterrestial radiation, in MJ/m2day, equation (28) Ra1 <(24*60/pi)*Gsc*dr*(ws*sin(fi)*sin(delta)+cos(fi)*cos(delta)*sin(ws)) Ra <- signif(Ra1, digits = 4) ##keep 4 significant figures (from fi)  #Calculation of clear sky solar radiation, in MJ/m2day, equation (37) Rso1 <- (0.75+z*2*10^-5)*Ra ##as and bs of equation (35) are unavailable Rso <- signif(Rso1, digits = 4) ##keep 4 significant figures (from Ra)  #Calculation of incoming solar radiation using Tmax and Tmin, in MJ/m2day, equation (50) Rs1 <- 0.16*Ra*(Tmax-Tmin)^0.5 #Hargreaves radiation formula using 0.16 for interior regions Rs <- signif(Rs1, digits = 3) ##keep 3 significant figures (from Temp)  #Calculation of net radiation from land surface albedo, in MJ/m2day, equation (38) Rns1 <- (1-0.23)*Rs ##albedo = 0.23 for reference crop Rns <- signif(Rns1, digits = 3) ##keep 3 significant figures (from Rs)  #Calculation of net outgoing longwave radiation, in MJ/m2day, equation (39)  112  Tmax.K <- Tmax + 273.16 #conversion deg.C to Kelvin Tmin.K <- Tmin + 273.16 #conversion deg.C to Kelvin Rnl1 <- sigma*(((Tmax.K^4)+(Tmin.K^4))/2)*(0.340.14*(ea^0.5))*(1.35*(Rs/Rso)-0.35) Rnl <- signif(Rnl1, digits = 2) ##keep 2 significant figures (from ea)  #Calculation of net shortwave radiation, in MJ/m2day, equation (40) Rn <- Rns - Rnl #for albedo = 0.23, reference crop  #------------------------------------------------------------------------#Calculation of reference ET (ET0), in mm/day, equation (6)  ref.ET1 <- (0.408*Delta*(Rn-0)+ gamm*(900/(Tmean+273))*u2*Vap.deficit)/(Delta + gamm*(1+0.34*u2)) ref.ET <- signif(ref.ET1, digits = 2) ##keep 2 significant figures (from ea)  Reference.Evap <- data.frame(Date, RHmean, Tmax, Tmin, Tmean, eoTmin, eoTmax, ea, ref.ET, Precip)  attach(Reference.Evap) decades <- 366 #enter the number of decades based on the availble data decade <- rep(1:decades, each=10) df1 <- aggregate(ref.ET, by = list(decade), mean, na.rm = TRUE) ET0.1a <- rep(df1$x, each = 10) ET0.1 <- signif(ET0.1a, digits = 2) ##keep 2 significant figures for ET0  113  df2 <- aggregate(ref.ET, by = list(decade), sd, na.rm = TRUE) ET0stdev.1a <- rep(df2$x, each = 10) ET0stdev.1 <- signif(ET0stdev.1a, digits = 2) ##keep 2 significant figures for ET0  detach(Reference.Evap)  #Creation of the new data frame and a graph Reference.ET <- data.frame(Date, RHmin, RHmax, RHmean, Tmax, Tmin, Tmean, Rn, u2, es, ea, Vap.deficit, ET0.1, Precip)  write.table(Reference.ET, file="C:/Documents and Settings/BuddyLuv/Desktop/NovaXavantina_decadal_ET0.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  ##Plotting of the data to check for calculation errors par(mfrow=c(3,1), mar=c(2,2,2,2), oma=c(1.5,2,1.5,1)) plot(Date,ET0.1, ylab = "", main="Net Radiation albedo = 0.23", col="red") plot(Date,Vap.deficit, ylab = "", main="Vapour Pressure Deficit (kPa)", col="blue") plot(Date,ET0.1, ylab = "", main="ET0 (mm/day), albedo = 0.23") title(Location, cex = 1.5, outer = TRUE) par(mfrow=c(1,1))  ##Export graph of time series of Rn, Vap.deficit, ETO dev.print(pdf, file="C:/Documents and Settings/m.lathuilliere.IRES/Desktop/NovaXavantina_Station_ET0.pdf", width=7.5, height=10, pointsize=5)  114  detach(Station)  #------------------------------------------------------------------------#### END #################################################################  F.2  Crop coefficients MT  # by Michael Lathuilliere, Institute for Resources, Environment and Sustainability. Land use effects on green water fluxes in Mato Grosso, Brazil.  ## This code calculates the crop ET (ETc) based on crop coefficients and crop calendars ## determined by the Food and Agriculture Organization and local practices.  ## It also contains a quick water balance (Precip - ETc) to assess how stressed ## the plants are during the growing season  #------------------------------------------------------------------------## Create a .csv files with the crops of interest, crop coefficients and time of ## each development stage  ## Kini crop coefficient of initial stage or time Kini.time ## Km  crop coefficient of middle stage, of time Km.time  ## Kl  crop coefficient of last stage, of time Kl.time  ## Kd  time is the crop development period  ## This code is specific to Mato Grosso, Brazil with planting dates occuring  115  ## late in the year (time series of ET0 from 2000-2010) #-------------------------------------------------------------------------  rm(list = ls())  #------------------------------------------------------------------------##Import of Reference ET calculated from the INMET stations # Change name of weather station to obtain ETc according to MT location  Crop.table <read.table("C:/Documents and Settings/BuddyLuv/My Documents/My Dropbox/Thesis/Aquarius/Crop_Coefficients.csv", header=TRUE, sep=",", na.strings="NA", dec=".", strip.white=TRUE)  Reference.ET <read.table("C:/Documents and Settings/BuddyLuv/My Documents/My Dropbox/Thesis/Aquarius/Caceres/Caceres_decadal_ET0.txt", header=TRUE, sep=",", na.strings="NA", dec=".", strip.white=TRUE)  #------------------------------------------------------------------------##Date reformating for the imported time series data  Date <- as.character(Reference.ET$Date) Date <- as.Date(Date, "%Y-%m-%d") J <- as.numeric(format(Date, "%j")) #day of the year doy <- seq.Date(as.Date("2001-01-01"), as.Date("2002-12-31"), by = 1) L <- as.numeric(format(doy, "%j")) jyear <- as.POSIXlt(Date)$year #specific year since 1900 d <- 1:3660 #day for the times series (necessary when dev and late stages  116  #occur between Dec and Jan  #------------------------------------------------------------------------########## Crop Calendar #################################################  #No climate data available for 1999 for the year 2000 harvest #all numbers in day of the year (to be repeated each year on the same day)  #Scenario 1: Early soy planting date (October 1st) followed immediately by maize and cotton #Scenarion 2: Late soy planting date (November 1st) follow immediately by maize and cotton #In both cases, pasture and sugar cane and planted all year round  plant.soy <- 274  # Oct 1st, day 274 (Oct-Dec for soy)  plant.maize <- plant.soy + 126  # Oct-Dec for Milho, Feb/Mar for  safrinha) plant.sugar <- 121  # May 1st, day 121 - Apr-May, planted  all year long and cut (typically Apr-May period) plant.cotton <- plant.soy + 126  # early Feb, immediate planting after  soybean  #------------------------------------------------------------------------#### Calculation of crop ET (ETc) based on crop development stages  ########## Soybean #######################################################  #Crop coefficients of soybean defined Kini.soy <- Crop.table[1,2] Km.soy <- Crop.table[1,3] Kl.soy <- Crop.table[1,4]  117  #Crop development cycles for all years, as a function of J (day of year) inisoy <- plant.soy inisoy.end <- plant.soy + Crop.table[1,5] - 1 Soy.ini <- J[inisoy:inisoy.end] devsoy <- inisoy.end + 1 devsoy.end <- inisoy.end + Crop.table[1,6] Soy.dev <- J[devsoy:devsoy.end] midsoy <- devsoy.end + 1 midsoy.end <- devsoy.end + Crop.table[1,7] Soy.mid <- J[midsoy:midsoy.end] latesoy <- midsoy.end + 1 latesoy.end <- midsoy.end + Crop.table[1,8] Soy.late <- J[latesoy:latesoy.end]  #Crop development cycles for all years, as a function of d (day of time series)  dSoy.ini <- d[inisoy:inisoy.end] dSoy.dev <- d[devsoy:devsoy.end] dSoy.mid <- d[midsoy:midsoy.end] dSoy.late <- d[latesoy:latesoy.end]  #Creates table of stages as a function of d for 2000-2009 alldSoy.ini <- sapply(0:9, function(j){d200jSoy.ini <- dSoy.ini + 365*j}) colnames(alldSoy.ini) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldSoy.dev <- sapply(0:9, function(j){d200jSoy.dev <- dSoy.dev + 365*j}) colnames(alldSoy.dev) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldSoy.mid <- sapply(0:9, function(j){d200jSoy.mid <- dSoy.mid + 365*j})  118  colnames(alldSoy.mid) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldSoy.late <- sapply(0:9, function(j){d200Soy.late <- dSoy.late + 365*j}) colnames(alldSoy.late) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009")  alldSoy.ini <- as.data.frame(alldSoy.ini) # redefined as a data frame alldSoy.dev <- as.data.frame(alldSoy.dev) alldSoy.mid <- as.data.frame(alldSoy.mid) alldSoy.late <- as.data.frame(alldSoy.late)  #Accounting of leap years for 2000, 2004 and 2008 (to re-align planting dates) alldSoy.ini[,2] <- alldSoy.ini[,2] + 1 #2001 alldSoy.dev[,2] <- alldSoy.dev[,2] + 1 alldSoy.mid[,2] <- alldSoy.mid[,2] + 1 alldSoy.late[,2] <- alldSoy.late[,2] + 1 alldSoy.ini[,3] <- alldSoy.ini[,3] + 1 alldSoy.dev[,3] <- alldSoy.dev[,3] + 1 alldSoy.mid[,3] <- alldSoy.mid[,3] + 1 alldSoy.late[,3] <- alldSoy.late[,3] + 1 alldSoy.ini[,4] <- alldSoy.ini[,4] + 1 alldSoy.dev[,4] <- alldSoy.dev[,4] + 1 alldSoy.mid[,4] <- alldSoy.mid[,4] + 1 alldSoy.late[,4] <- alldSoy.late[,4] + 1 alldSoy.ini[,5] <- alldSoy.ini[,5] + 1 #2004 alldSoy.dev[,5] <- alldSoy.dev[,5] + 1 alldSoy.mid[,5] <- alldSoy.mid[,5] + 1  119  alldSoy.late[,5] <- alldSoy.late[,5] + 1 alldSoy.ini[,6] <- alldSoy.ini[,6] + 2 alldSoy.dev[,6] <- alldSoy.dev[,6] + 2 alldSoy.mid[,6] <- alldSoy.mid[,6] + 2 alldSoy.late[,6] <- alldSoy.late[,6] + 2 alldSoy.ini[,7] <- alldSoy.ini[,7] + 2 alldSoy.dev[,7] <- alldSoy.dev[,7] + 2 alldSoy.mid[,7] <- alldSoy.mid[,7] + 2 alldSoy.late[,7] <- alldSoy.late[,7] + 2 alldSoy.ini[,8] <- alldSoy.ini[,8] + 2 alldSoy.dev[,8] <- alldSoy.dev[,8] + 2 alldSoy.mid[,8] <- alldSoy.mid[,8] + 2 alldSoy.late[,8] <- alldSoy.late[,8] + 2 alldSoy.ini[,9] <- alldSoy.ini[,9] + 2 #2008 alldSoy.dev[,9] <- alldSoy.dev[,9] + 2 alldSoy.mid[,9] <- alldSoy.mid[,9] + 2 alldSoy.late[,9] <- alldSoy.late[,9] + 2  #------------------------------------------------------------------------##Crop coefficient for development, Kdev  m1 <- (Km.soy - Kini.soy)/length(Soy.dev) ##slope of the line between Kini and Kmid df1 <- sapply(1:length(Soy.dev), function(i) {m1*i + Kini.soy}) Kdev.soy <- numeric(length(J)) hip.soy <- data.frame(jyear, Kdev.soy)  hip.soy <- data.frame(jyear, J, d, Kdev.soy) ##Year 2000 hip.soy[hip.soy$d > tail(alldSoy.ini[,1],1) & hip.soy$d < (head(alldSoy.dev[,1],1)  120  + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2001 <- data.frame(J,d, Kdev.soy) #Year 2001 hip.soy2001[hip.soy2001$d > tail(alldSoy.ini[,2],1) & hip.soy2001$d < (head(alldSoy.dev[,2],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2002 <- data.frame(J,d, Kdev.soy) #Year 2002 hip.soy2002[hip.soy2002$d > tail(alldSoy.ini[,3],1) & hip.soy2002$d < (head(alldSoy.dev[,3],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2003 <- data.frame(J,d, Kdev.soy) #Year 2003 hip.soy2003[hip.soy2003$d > tail(alldSoy.ini[,4],1) & hip.soy2003$d < (head(alldSoy.dev[,4],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2004 <- data.frame(J,d, Kdev.soy) #Year 2004 hip.soy2004[hip.soy2004$d > tail(alldSoy.ini[,5],1) & hip.soy2004$d < (head(alldSoy.dev[,5],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  121  hip.soy2005 <- data.frame(J,d, Kdev.soy) #Year 2005 hip.soy2005[hip.soy2005$d > tail(alldSoy.ini[,6],1) & hip.soy2005$d < (head(alldSoy.dev[,6],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2006 <- data.frame(J,d, Kdev.soy) #Year 2006 hip.soy2006[hip.soy2006$d > tail(alldSoy.ini[,7],1) & hip.soy2006$d < (head(alldSoy.dev[,7],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2007 <- data.frame(J,d, Kdev.soy) #Year 2007 hip.soy2007[hip.soy2007$d > tail(alldSoy.ini[,8],1) & hip.soy2007$d < (head(alldSoy.dev[,8],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  hip.soy2008 <- data.frame(J,d, Kdev.soy) #Year 2008 hip.soy2008[hip.soy2008$d > tail(alldSoy.ini[,9],1) & hip.soy2008$d < (head(alldSoy.dev[,9],1) + length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  #hip.soy2009 <- data.frame(J,d, Kdev.soy) #Year 2009, might not be calculated if planting date is too late #hip.soy2009[hip.soy2009$d > tail(alldSoy.ini[,10],1) & hip.soy2009$d < (head(alldSoy.dev[,10],1) +  122  #length(Soy.dev)),]$Kdev.soy = seq(head(df1, 1), tail(df1, 1), length = length(Soy.dev))  #------------------------------------------------------------------------#Crop coefficient for late season, Klate for soy  p1 <- (Kl.soy - Km.soy)/length(Soy.late) late.df1 <- sapply(1:length(Soy.late), function(i) {p1*i + Km.soy}) Klate.soy <- numeric(length(J))  hiplate.soy <- data.frame(J, d, Klate.soy) hiplate.soy[hiplate.soy$d > tail(alldSoy.mid[,1], 1) & hiplate.soy$d < (head(alldSoy.late[,1], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2001 <- data.frame(J, d, Klate.soy) #Year 2001 hiplate.soy2001[hiplate.soy2001$d > tail(alldSoy.mid[,2], 1) & hiplate.soy2001$d < (head(alldSoy.late[,2], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2002 <- data.frame(J, d, Klate.soy) #Year 2002 hiplate.soy2002[hiplate.soy2002$d > tail(alldSoy.mid[,3], 1) & hiplate.soy2002$d < (head(alldSoy.late[,3], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2003 <- data.frame(J, d, Klate.soy) #Year 2003  123  hiplate.soy2003[hiplate.soy2003$d > tail(alldSoy.mid[,4], 1) & hiplate.soy2003$d < (head(alldSoy.late[,4], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2004 <- data.frame(J, d, Klate.soy) #Year 2004 hiplate.soy2004[hiplate.soy2004$d > tail(alldSoy.mid[,5], 1) & hiplate.soy2004$d < (head(alldSoy.late[,5], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2005 <- data.frame(J, d, Klate.soy) #Year 2005 hiplate.soy2005[hiplate.soy2005$d > tail(alldSoy.mid[,6], 1) & hiplate.soy2005$d < (head(alldSoy.late[,6], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2006 <- data.frame(J, d, Klate.soy) #Year 2006 hiplate.soy2006[hiplate.soy2006$d > tail(alldSoy.mid[,7], 1) & hiplate.soy2006$d < (head(alldSoy.late[,7], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  hiplate.soy2007 <- data.frame(J, d, Klate.soy) #Year 2007 hiplate.soy2007[hiplate.soy2007$d > tail(alldSoy.mid[,8], 1) & hiplate.soy2007$d < (head(alldSoy.late[,8], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  124  hiplate.soy2008 <- data.frame(J, d, Klate.soy) #Year 2008 hiplate.soy2008[hiplate.soy2008$d > tail(alldSoy.mid[,9], 1) & hiplate.soy2008$d < (head(alldSoy.late[,9], 1) + length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  #hiplate.soy2009 <- data.frame(J, d, Klate.soy) #Year 2009 #hiplate.soy2009[hiplate.soy2009$d > tail(alldSoy.mid[,10], 1) & hiplate.soy2009$d < (head(alldSoy.late[,10], 1) + #length(Soy.late)),]$Klate.soy = seq(head(late.df1, 1), tail(late.df1, 1), length = length(Soy.late))  #------------------------------------------------------------------------##Crop ET for soy assuming only one harvest per year, for albedo = 0.23  #For albedo = 0.23 ETc.soy1a <- ifelse(d %in% alldSoy.ini[,1]| d %in% alldSoy.ini[,2]| d %in% alldSoy.ini[,3]| d %in% alldSoy.ini[,4]| d %in% alldSoy.ini[,5]| d %in% alldSoy.ini[,6]| d %in% alldSoy.ini[,7]| d %in% alldSoy.ini[,8]| d %in% alldSoy.ini[,9], Reference.ET$ET0.1*Kini.soy,0) ETc.soy1 <- signif(ETc.soy1a, digits = 2) ##keep 2 significant figures  125  ETc.soy2a <- ifelse(d %in% alldSoy.dev[,1], Reference.ET$ET0.1*hip.soy$Kdev.soy, 0) ETc2001.soy2a <- ifelse(d %in% alldSoy.dev[,2], Reference.ET$ET0.1*hip.soy2001$Kdev.soy, 0) ETc2002.soy2a <- ifelse(d %in% alldSoy.dev[,3], Reference.ET$ET0.1*hip.soy2002$Kdev.soy, 0) ETc2003.soy2a <- ifelse(d %in% alldSoy.dev[,4], Reference.ET$ET0.1*hip.soy2003$Kdev.soy, 0) ETc2004.soy2a <- ifelse(d %in% alldSoy.dev[,5], Reference.ET$ET0.1*hip.soy2004$Kdev.soy, 0) ETc2005.soy2a <- ifelse(d %in% alldSoy.dev[,6], Reference.ET$ET0.1*hip.soy2005$Kdev.soy, 0) ETc2006.soy2a <- ifelse(d %in% alldSoy.dev[,7], Reference.ET$ET0.1*hip.soy2006$Kdev.soy, 0) ETc2007.soy2a <- ifelse(d %in% alldSoy.dev[,8], Reference.ET$ET0.1*hip.soy2007$Kdev.soy, 0) ETc2008.soy2a <- ifelse(d %in% alldSoy.dev[,9], Reference.ET$ET0.1*hip.soy2008$Kdev.soy, 0) #ETc2009.soy2a <- ifelse(d %in% alldSoy.dev[,10], Reference.ET$ET0.1*hip.soy2009$Kdev.soy, 0)  # to activate if planting  date not too late in the year ETc.soy2bis <- ETc.soy2a + ETc2001.soy2a + ETc2002.soy2a + ETc2003.soy2a + ETc2004.soy2a + ETc2005.soy2a + ETc2006.soy2a + ETc2007.soy2a + ETc2008.soy2a #+ ETc2009.soy2a ## add in 2009 if required ETc.soy2 <- signif(ETc.soy2bis, digits = 2) ## keep 2 significant figures  ETc.soy3a <- ifelse(d %in% alldSoy.mid[,1]| d %in% alldSoy.mid[,2]| d %in% alldSoy.mid[,3]| d %in% alldSoy.mid[,4]|  126  d %in% alldSoy.mid[,5]| d %in% alldSoy.mid[,6]| d %in% alldSoy.mid[,7]| d %in% alldSoy.mid[,8]| d %in% alldSoy.mid[,9], Reference.ET$ET0.1*Km.soy,0) ETc.soy3 <- signif(ETc.soy3a, digits = 2) ## keep 2 significant figure  ETc.soy4a <- ifelse(d %in% alldSoy.late[,1], Reference.ET$ET0.1*hiplate.soy$Klate.soy, 0) ETc2001.soy4a <- ifelse(d %in% alldSoy.late[,2], Reference.ET$ET0.1*hiplate.soy2001$Klate.soy, 0) ETc2002.soy4a <- ifelse(d %in% alldSoy.late[,3], Reference.ET$ET0.1*hiplate.soy2002$Klate.soy, 0) ETc2003.soy4a <- ifelse(d %in% alldSoy.late[,4], Reference.ET$ET0.1*hiplate.soy2003$Klate.soy, 0) ETc2004.soy4a <- ifelse(d %in% alldSoy.late[,5], Reference.ET$ET0.1*hiplate.soy2004$Klate.soy, 0) ETc2005.soy4a <- ifelse(d %in% alldSoy.late[,6], Reference.ET$ET0.1*hiplate.soy2005$Klate.soy, 0) ETc2006.soy4a <- ifelse(d %in% alldSoy.late[,7], Reference.ET$ET0.1*hiplate.soy2006$Klate.soy, 0) ETc2007.soy4a <- ifelse(d %in% alldSoy.late[,8], Reference.ET$ET0.1*hiplate.soy2007$Klate.soy, 0) ETc2008.soy4a <- ifelse(d %in% alldSoy.late[,9], Reference.ET$ET0.1*hiplate.soy2008$Klate.soy, 0) #ETc2009.soy4a <- ifelse(d %in% alldSoy.late[,10], Reference.ET$ET0.1*hiplate.soy2009$Klate.soy, 0) ETc.soy4bis <- ETc.soy4a + ETc2001.soy4a + ETc2002.soy4a + ETc2003.soy4a + ETc2004.soy4a + ETc2005.soy4a + ETc2006.soy4a + ETc2007.soy4a + ETc2008.soy4a #+ ETc2009.soy4a ## add in 2009 if required  127  ETc.soy4 <- signif(ETc.soy4bis, digits = 2) ## keep 2 significant figures  ETc.soy <- ifelse(d < plant.soy, 0, ETc.soy1 + ETc.soy2 + ETc.soy3 + ETc.soy4)  #------------------------------------------------------------------------#Crop coefficients for soy  Kc.soy1a <- ifelse(d %in% alldSoy.ini[,1]| d %in% alldSoy.ini[,2]| d %in% alldSoy.ini[,3]| d %in% alldSoy.ini[,4]| d %in% alldSoy.ini[,5]| d %in% alldSoy.ini[,6]| d %in% alldSoy.ini[,7]| d %in% alldSoy.ini[,8]| d %in% alldSoy.ini[,9], Kini.soy,0) Kc.soy1 <- signif(Kc.soy1a, digits = 3) ##keep 3 significant figures  Kc.soy2a <- ifelse(d %in% alldSoy.dev[,1], hip.soy$Kdev.soy, 0) Kc2001.soy2a <- ifelse(d %in% alldSoy.dev[,2], hip.soy2001$Kdev.soy, 0) Kc2002.soy2a <- ifelse(d %in% alldSoy.dev[,3], hip.soy2002$Kdev.soy, 0) Kc2003.soy2a <- ifelse(d %in% alldSoy.dev[,4], hip.soy2003$Kdev.soy, 0) Kc2004.soy2a <- ifelse(d %in% alldSoy.dev[,5], hip.soy2004$Kdev.soy, 0) Kc2005.soy2a <- ifelse(d %in% alldSoy.dev[,6], hip.soy2005$Kdev.soy, 0) Kc2006.soy2a <- ifelse(d %in% alldSoy.dev[,7], hip.soy2006$Kdev.soy, 0) Kc2007.soy2a <- ifelse(d %in% alldSoy.dev[,8], hip.soy2007$Kdev.soy, 0) Kc2008.soy2a <- ifelse(d %in% alldSoy.dev[,9], hip.soy2008$Kdev.soy, 0) #Kc2009.soy2a <- ifelse(d %in% alldSoy.dev[,10], hip.soy2009$Kdev.soy, 0) # to activate if planting date not too late in the year  128  Kc.soy2bis <- Kc.soy2a + Kc2001.soy2a + Kc2002.soy2a + Kc2003.soy2a + Kc2004.soy2a + Kc2005.soy2a + Kc2006.soy2a + Kc2007.soy2a + Kc2008.soy2a #+ Kc2009.soy2a ## add in 2009 if required Kc.soy2 <- signif(Kc.soy2bis, digits = 3) ## keep 3 significant figures  Kc.soy3a <- ifelse(d %in% alldSoy.mid[,1]| d %in% alldSoy.mid[,2]| d %in% alldSoy.mid[,3]| d %in% alldSoy.mid[,4]| d %in% alldSoy.mid[,5]| d %in% alldSoy.mid[,6]| d %in% alldSoy.mid[,7]| d %in% alldSoy.mid[,8]| d %in% alldSoy.mid[,9], Km.soy,0) Kc.soy3 <- signif(Kc.soy3a, digits = 3) ## keep 3 significant figures  Kc.soy4a <- ifelse(d %in% alldSoy.late[,1], hiplate.soy$Klate.soy, 0) Kc2001.soy4a <- ifelse(d %in% alldSoy.late[,2], hiplate.soy2001$Klate.soy, 0) Kc2002.soy4a <- ifelse(d %in% alldSoy.late[,3], hiplate.soy2002$Klate.soy, 0) Kc2003.soy4a <- ifelse(d %in% alldSoy.late[,4], hiplate.soy2003$Klate.soy, 0) Kc2004.soy4a <- ifelse(d %in% alldSoy.late[,5], hiplate.soy2004$Klate.soy, 0) Kc2005.soy4a <- ifelse(d %in% alldSoy.late[,6], hiplate.soy2005$Klate.soy, 0) Kc2006.soy4a <- ifelse(d %in% alldSoy.late[,7], hiplate.soy2006$Klate.soy, 0)  129  Kc2007.soy4a <- ifelse(d %in% alldSoy.late[,8], hiplate.soy2007$Klate.soy, 0) Kc2008.soy4a <- ifelse(d %in% alldSoy.late[,9], hiplate.soy2008$Klate.soy, 0) #Kc2009.soy4a <- ifelse(d %in% alldSoy.late[,10], hiplate.soy2009$Klate.soy, 0) Kc.soy4bis <- Kc.soy4a + Kc2001.soy4a + Kc2002.soy4a + Kc2003.soy4a + Kc2004.soy4a + Kc2005.soy4a + Kc2006.soy4a + Kc2007.soy4a + Kc2008.soy4a #+ Kc2009.soy4a ## add in 2009 if required Kc.soy4 <- signif(Kc.soy4bis, digits = 3) ## keep 3 significant figures  Kc.soy <- ifelse(d < plant.soy, 0, Kc.soy1 + Kc.soy2 + Kc.soy3 + Kc.soy4)  t1 <- data.frame(Date, J, d, jyear, Reference.ET$ET0.1, ETc.soy, Kc.soy)  ########## Maize #########################################################  ##Crop coefficients defined Kini.maize <- Crop.table[2,2] Km.maize <- Crop.table[2,3] Kl.maize <- Crop.table[2,4]  ##Crop development cycles for all years inimaize <- plant.maize inimaize.end <- plant.maize + Crop.table[2,5] - 1 Maize.ini <- J[inimaize:inimaize.end] devmaize <- inimaize.end + 1 devmaize.end <- inimaize.end + Crop.table[2,6] Maize.dev <- J[devmaize:devmaize.end]  130  midmaize <- devmaize.end + 1 midmaize.end <- devmaize.end + Crop.table[2,7] Maize.mid <- J[midmaize:midmaize.end] latemaize <- midmaize.end + 1 latemaize.end <- midmaize.end + Crop.table[2,8] Maize.late <- J[latemaize:latemaize.end]  #Crop development cycles for all years, as a function of d (day of time series)  dMaize.ini <- d[inimaize:inimaize.end] dMaize.dev <- d[devmaize:devmaize.end] dMaize.mid <- d[midmaize:midmaize.end] dMaize.late <- d[latemaize:latemaize.end]  #Creates table of stages as a function of d for 2000-2009 alldMaize.ini <- sapply(0:9, function(j){d200jmaize.ini <- dMaize.ini + 365*j}) colnames(alldMaize.ini) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldMaize.dev <- sapply(0:9, function(j){d200jmaize.dev <- dMaize.dev + 365*j}) colnames(alldMaize.dev) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldMaize.mid <- sapply(0:9, function(j){d200jmaize.mid <- dMaize.mid + 365*j}) colnames(alldMaize.mid) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldMaize.late <- sapply(0:9, function(j){d200maize.late <- dMaize.late + 365*j}) colnames(alldMaize.late) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009")  131  alldMaize.ini <- as.data.frame(alldMaize.ini) alldMaize.dev <- as.data.frame(alldMaize.dev) alldMaize.mid <- as.data.frame(alldMaize.mid) alldMaize.late <- as.data.frame(alldMaize.late)  #Accounting of leap years for 2000, 2004 and 2008 (to re-align planting dates) alldMaize.ini[,2] <- alldMaize.ini[,2] + 1 #2001 alldMaize.dev[,2] <- alldMaize.dev[,2] + 1 alldMaize.mid[,2] <- alldMaize.mid[,2] + 1 alldMaize.late[,2] <- alldMaize.late[,2] + 1 alldMaize.ini[,3] <- alldMaize.ini[,3] + 1 alldMaize.dev[,3] <- alldMaize.dev[,3] + 1 alldMaize.mid[,3] <- alldMaize.mid[,3] + 1 alldMaize.late[,3] <- alldMaize.late[,3] + 1 alldMaize.ini[,4] <- alldMaize.ini[,4] + 1 alldMaize.dev[,4] <- alldMaize.dev[,4] + 1 alldMaize.mid[,4] <- alldMaize.mid[,4] + 1 alldMaize.late[,4] <- alldMaize.late[,4] + 1 alldMaize.ini[,5] <- alldMaize.ini[,5] + 1 #2004 alldMaize.dev[,5] <- alldMaize.dev[,5] + 1 alldMaize.mid[,5] <- alldMaize.mid[,5] + 1 alldMaize.late[,5] <- alldMaize.late[,5] + 1 alldMaize.ini[,6] <- alldMaize.ini[,6] + 2 alldMaize.dev[,6] <- alldMaize.dev[,6] + 2 alldMaize.mid[,6] <- alldMaize.mid[,6] + 2 alldMaize.late[,6] <- alldMaize.late[,6] + 2 alldMaize.ini[,7] <- alldMaize.ini[,7] + 2 alldMaize.dev[,7] <- alldMaize.dev[,7] + 2  132  alldMaize.mid[,7] <- alldMaize.mid[,7] + 2 alldMaize.late[,7] <- alldMaize.late[,7] + 2 alldMaize.ini[,8] <- alldMaize.ini[,8] + 2 alldMaize.dev[,8] <- alldMaize.dev[,8] + 2 alldMaize.mid[,8] <- alldMaize.mid[,8] + 2 alldMaize.late[,8] <- alldMaize.late[,8] + 2 alldMaize.ini[,9] <- alldMaize.ini[,9] + 2 #2008 alldMaize.dev[,9] <- alldMaize.dev[,9] + 2 alldMaize.mid[,9] <- alldMaize.mid[,9] + 2 alldMaize.late[,9] <- alldMaize.late[,9] + 2  #------------------------------------------------------------------------##Crop coefficient for development, Kdev  m2 <- (Km.maize - Kini.maize)/length(Maize.dev) ##slope of the line between Kini and Kmid df2 <- sapply(1:length(Maize.dev), function(i) {m2*i + Kini.maize}) Kdev.maize <- numeric(length(J)) hip.maize <- data.frame(jyear, Kdev.maize)  hip.maize <- data.frame(jyear, J, d, Kdev.maize) ##Year 2000 hip.maize[hip.maize$d > tail(alldMaize.ini[,1],1) & hip.maize$d < (head(alldMaize.dev[,1],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2001 <- data.frame(J,d, Kdev.maize) #Year 2001 hip.maize2001[hip.maize2001$d > tail(alldMaize.ini[,2],1) & hip.maize2001$d < (head(alldMaize.dev[,2],1) +  133  length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2002 <- data.frame(J,d, Kdev.maize) #Year 2002 hip.maize2002[hip.maize2002$d > tail(alldMaize.ini[,3],1) & hip.maize2002$d < (head(alldMaize.dev[,3],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2003 <- data.frame(J,d, Kdev.maize) #Year 2003 hip.maize2003[hip.maize2003$d > tail(alldMaize.ini[,4],1) & hip.maize2003$d < (head(alldMaize.dev[,4],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2004 <- data.frame(J,d, Kdev.maize) #Year 2004 hip.maize2004[hip.maize2004$d > tail(alldMaize.ini[,5],1) & hip.maize2004$d < (head(alldMaize.dev[,5],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2005 <- data.frame(J,d, Kdev.maize) #Year 2005 hip.maize2005[hip.maize2005$d > tail(alldMaize.ini[,6],1) & hip.maize2005$d < (head(alldMaize.dev[,6],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  134  hip.maize2006 <- data.frame(J,d, Kdev.maize) #Year 2006 hip.maize2006[hip.maize2006$d > tail(alldMaize.ini[,7],1) & hip.maize2006$d < (head(alldMaize.dev[,7],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2007 <- data.frame(J,d, Kdev.maize) #Year 2007 hip.maize2007[hip.maize2007$d > tail(alldMaize.ini[,8],1) & hip.maize2007$d < (head(alldMaize.dev[,8],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  hip.maize2008 <- data.frame(J,d, Kdev.maize) #Year 2008 hip.maize2008[hip.maize2008$d > tail(alldMaize.ini[,9],1) & hip.maize2008$d < (head(alldMaize.dev[,9],1) + length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  #hip.maize2009 <- data.frame(J,d, Kdev.maize) #Year 2009, might not be calculated if late planting date #hip.maize2009[hip.maize2009$d > tail(alldMaize.ini[,10],1) & hip.maize2009$d < (head(alldMaize.dev[,10],1) + #length(Maize.dev)),]$Kdev.maize = seq(head(df2, 1), tail(df2, 1), length = length(Maize.dev))  #------------------------------------------------------------------------#Crop coefficient for late season, Klate for maize  p2 <- (Kl.maize - Km.maize)/length(Maize.late)  135  late.df2 <- sapply(1:length(Maize.late), function(i) {p2*i + Km.maize}) Klate.maize <- numeric(length(J))  hiplate.maize <- data.frame(J, d, Klate.maize) hiplate.maize[hiplate.maize$d > tail(alldMaize.mid[,1], 1) & hiplate.maize$d < (head(alldMaize.late[,1], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2001 <- data.frame(J, d, Klate.maize) #Year 2001 hiplate.maize2001[hiplate.maize2001$d > tail(alldMaize.mid[,2], 1) & hiplate.maize2001$d < (head(alldMaize.late[,2], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2002 <- data.frame(J, d, Klate.maize) #Year 2002 hiplate.maize2002[hiplate.maize2002$d > tail(alldMaize.mid[,3], 1) & hiplate.maize2002$d < (head(alldMaize.late[,3], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2003 <- data.frame(J, d, Klate.maize) #Year 2003 hiplate.maize2003[hiplate.maize2003$d > tail(alldMaize.mid[,4], 1) & hiplate.maize2003$d < (head(alldMaize.late[,4], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2004 <- data.frame(J, d, Klate.maize) #Year 2004  136  hiplate.maize2004[hiplate.maize2004$d > tail(alldMaize.mid[,5], 1) & hiplate.maize2004$d < (head(alldMaize.late[,5], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2005 <- data.frame(J, d, Klate.maize) #Year 2005 hiplate.maize2005[hiplate.maize2005$d > tail(alldMaize.mid[,6], 1) & hiplate.maize2005$d < (head(alldMaize.late[,6], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2006 <- data.frame(J, d, Klate.maize) #Year 2006 hiplate.maize2006[hiplate.maize2006$d > tail(alldMaize.mid[,7], 1) & hiplate.maize2006$d < (head(alldMaize.late[,7], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2007 <- data.frame(J, d, Klate.maize) #Year 2007 hiplate.maize2007[hiplate.maize2007$d > tail(alldMaize.mid[,8], 1) & hiplate.maize2007$d < (head(alldMaize.late[,8], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  hiplate.maize2008 <- data.frame(J, d, Klate.maize) #Year 2008 hiplate.maize2008[hiplate.maize2008$d > tail(alldMaize.mid[,9], 1) & hiplate.maize2008$d < (head(alldMaize.late[,9], 1) + length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  137  #hiplate.maize2009 <- data.frame(J, d, Klate.maize) #Year 2009  to activate if planting date is not too late  #hiplate.maize2009[hiplate.maize2009$d > tail(alldMaize.mid[,10], 1) & hiplate.maize2009$d < (head(alldMaize.late[,10], 1) + #length(Maize.late)),]$Klate.maize = seq(head(late.df2, 1), tail(late.df2, 1), length = length(Maize.late))  #------------------------------------------------------------------------##Crop ET for maize assuming only one harvest per year, for albedo = 0.23  ETc.maize1a <- ifelse(d %in% alldMaize.ini[,1]| d %in% alldMaize.ini[,2]| d %in% alldMaize.ini[,3]| d %in% alldMaize.ini[,4]| d %in% alldMaize.ini[,5]| d %in% alldMaize.ini[,6]| d %in% alldMaize.ini[,7]| d %in% alldMaize.ini[,8]| d %in% alldMaize.ini[,9], Reference.ET$ET0.1*Kini.maize,0) ETc.maize1 <- signif(ETc.maize1a, digits = 2) ##keep 2 significant figures  ETc.maize2a <- ifelse(d %in% alldMaize.dev[,1], Reference.ET$ET0.1*hip.maize$Kdev.maize, 0) ETc2001.maize2a <- ifelse(d %in% alldMaize.dev[,2], Reference.ET$ET0.1*hip.maize2001$Kdev.maize, 0) ETc2002.maize2a <- ifelse(d %in% alldMaize.dev[,3], Reference.ET$ET0.1*hip.maize2002$Kdev.maize, 0) ETc2003.maize2a <- ifelse(d %in% alldMaize.dev[,4], Reference.ET$ET0.1*hip.maize2003$Kdev.maize, 0)  138  ETc2004.maize2a <- ifelse(d %in% alldMaize.dev[,5], Reference.ET$ET0.1*hip.maize2004$Kdev.maize, 0) ETc2005.maize2a <- ifelse(d %in% alldMaize.dev[,6], Reference.ET$ET0.1*hip.maize2005$Kdev.maize, 0) ETc2006.maize2a <- ifelse(d %in% alldMaize.dev[,7], Reference.ET$ET0.1*hip.maize2006$Kdev.maize, 0) ETc2007.maize2a <- ifelse(d %in% alldMaize.dev[,8], Reference.ET$ET0.1*hip.maize2007$Kdev.maize, 0) ETc2008.maize2a <- ifelse(d %in% alldMaize.dev[,9], Reference.ET$ET0.1*hip.maize2008$Kdev.maize, 0) #ETc2009.maize2a <- ifelse(d %in% alldMaize.dev[,10], Reference.ET$ET0.1*hip.maize2009$Kdev.maize, 0) ETc.maize2bis <- ETc.maize2a + ETc2001.maize2a + ETc2002.maize2a + ETc2003.maize2a + ETc2004.maize2a + ETc2005.maize2a + ETc2006.maize2a + ETc2007.maize2a + ETc2008.maize2a #+ ETc2009.maize2a ## add in 2009 if required ETc.maize2 <- signif(ETc.maize2bis, digits = 2) ## keep 2 significant figures  ETc.maize3a <- ifelse(d %in% alldMaize.mid[,1]| d %in% alldMaize.mid[,2]| d %in% alldMaize.mid[,3]| d %in% alldMaize.mid[,4]| d %in% alldMaize.mid[,5]| d %in% alldMaize.mid[,6]| d %in% alldMaize.mid[,7]| d %in% alldMaize.mid[,8]| d %in% alldMaize.mid[,9], Reference.ET$ET0.1*Km.maize,0) ETc.maize3 <- signif(ETc.maize3a, digits = 2) ## keep 2 significant figures  139  ETc.maize4a <- ifelse(d %in% alldMaize.late[,1], Reference.ET$ET0.1*hiplate.maize$Klate.maize, 0) ETc2001.maize4a <- ifelse(d %in% alldMaize.late[,2], Reference.ET$ET0.1*hiplate.maize2001$Klate.maize, 0) ETc2002.maize4a <- ifelse(d %in% alldMaize.late[,3], Reference.ET$ET0.1*hiplate.maize2002$Klate.maize, 0) ETc2003.maize4a <- ifelse(d %in% alldMaize.late[,4], Reference.ET$ET0.1*hiplate.maize2003$Klate.maize, 0) ETc2004.maize4a <- ifelse(d %in% alldMaize.late[,5], Reference.ET$ET0.1*hiplate.maize2004$Klate.maize, 0) ETc2005.maize4a <- ifelse(d %in% alldMaize.late[,6], Reference.ET$ET0.1*hiplate.maize2005$Klate.maize, 0) ETc2006.maize4a <- ifelse(d %in% alldMaize.late[,7], Reference.ET$ET0.1*hiplate.maize2006$Klate.maize, 0) ETc2007.maize4a <- ifelse(d %in% alldMaize.late[,8], Reference.ET$ET0.1*hiplate.maize2007$Klate.maize, 0) ETc2008.maize4a <- ifelse(d %in% alldMaize.late[,9], Reference.ET$ET0.1*hiplate.maize2008$Klate.maize, 0) #ETc2009.maize4a <- ifelse(d %in% alldMaize.late[,10], Reference.ET$ET0.1*hiplate.maize2009$Klate.maize, 0)  # to activate if  planting date not too late ETc.maize4bis <- ETc.maize4a + ETc2001.maize4a + ETc2002.maize4a + ETc2003.maize4a + ETc2004.maize4a + ETc2005.maize4a + ETc2006.maize4a + ETc2007.maize4a + ETc2008.maize4a #+ ETc2009.maize4a ## add in 2009 if required ETc.maize4 <- signif(ETc.maize4bis, digits = 2) ## keep 2 significant figures  ETc.maize <- ifelse(d < plant.maize, 0, ETc.maize1 + ETc.maize2 + ETc.maize3 + ETc.maize4)  140  #------------------------------------------------------------------------#Crop coefficients for maize  Kc.maize1a <- ifelse(d %in% alldMaize.ini[,1]| d %in% alldMaize.ini[,2]| d %in% alldMaize.ini[,3]| d %in% alldMaize.ini[,4]| d %in% alldMaize.ini[,5]| d %in% alldMaize.ini[,6]| d %in% alldMaize.ini[,7]| d %in% alldMaize.ini[,8]| d %in% alldMaize.ini[,9], Kini.maize,0) Kc.maize1 <- signif(Kc.maize1a, digits = 3) ## keep 3 significant figures  Kc.maize2a <- ifelse(d %in% alldMaize.dev[,1], hip.maize$Kdev.maize, 0) Kc2001.maize2a <- ifelse(d %in% alldMaize.dev[,2], hip.maize2001$Kdev.maize, 0) Kc2002.maize2a <- ifelse(d %in% alldMaize.dev[,3], hip.maize2002$Kdev.maize, 0) Kc2003.maize2a <- ifelse(d %in% alldMaize.dev[,4], hip.maize2003$Kdev.maize, 0) Kc2004.maize2a <- ifelse(d %in% alldMaize.dev[,5], hip.maize2004$Kdev.maize, 0) Kc2005.maize2a <- ifelse(d %in% alldMaize.dev[,6], hip.maize2005$Kdev.maize, 0) Kc2006.maize2a <- ifelse(d %in% alldMaize.dev[,7], hip.maize2006$Kdev.maize, 0) Kc2007.maize2a <- ifelse(d %in% alldMaize.dev[,8], hip.maize2007$Kdev.maize, 0) Kc2008.maize2a <- ifelse(d %in% alldMaize.dev[,9], hip.maize2008$Kdev.maize, 0)  141  #Kc2009.maize2a <- ifelse(d %in% alldMaize.dev[,10], hip.maize2009$Kdev.maize, 0) Kc.maize2bis <- Kc.maize2a + Kc2001.maize2a + Kc2002.maize2a + Kc2003.maize2a + Kc2004.maize2a + Kc2005.maize2a + Kc2006.maize2a + Kc2007.maize2a + Kc2008.maize2a #+ Kc2009.maize2a ## add in 2009 if required Kc.maize2 <- signif(Kc.maize2bis, digits = 3) ## keep 3 significant figures  Kc.maize3a <- ifelse(d %in% alldMaize.mid[,1]| d %in% alldMaize.mid[,2]| d %in% alldMaize.mid[,3]| d %in% alldMaize.mid[,4]| d %in% alldMaize.mid[,5]| d %in% alldMaize.mid[,6]| d %in% alldMaize.mid[,7]| d %in% alldMaize.mid[,8]| d %in% alldMaize.mid[,9], Km.maize,0) Kc.maize3 <- signif(Kc.maize3a, digits = 3) ##keep 3 significant figures  Kc.maize4a <- ifelse(d %in% alldMaize.late[,1], hiplate.maize$Klate.maize, 0) Kc2001.maize4a <- ifelse(d %in% alldMaize.late[,2], hiplate.maize2001$Klate.maize, 0) Kc2002.maize4a <- ifelse(d %in% alldMaize.late[,3], hiplate.maize2002$Klate.maize, 0) Kc2003.maize4a <- ifelse(d %in% alldMaize.late[,4], hiplate.maize2003$Klate.maize, 0) Kc2004.maize4a <- ifelse(d %in% alldMaize.late[,5], hiplate.maize2004$Klate.maize, 0)  142  Kc2005.maize4a <- ifelse(d %in% alldMaize.late[,6], hiplate.maize2005$Klate.maize, 0) Kc2006.maize4a <- ifelse(d %in% alldMaize.late[,7], hiplate.maize2006$Klate.maize, 0) Kc2007.maize4a <- ifelse(d %in% alldMaize.late[,8], hiplate.maize2007$Klate.maize, 0) Kc2008.maize4a <- ifelse(d %in% alldMaize.late[,9], hiplate.maize2008$Klate.maize, 0) #Kc2009.maize4a <- ifelse(d %in% alldMaize.late[,10], hiplate.maize2009$Klate.maize, 0)  ## to activate if planting date not too  late in the year Kc.maize4bis <- Kc.maize4a + Kc2001.maize4a + Kc2002.maize4a + Kc2003.maize4a + Kc2004.maize4a + Kc2005.maize4a + Kc2006.maize4a + Kc2007.maize4a + Kc2008.maize4a #+ Kc2009.maize4a ## add in 2009 if required Kc.maize4 <- signif(Kc.maize4bis, digits = 3) ## keep 3 significant figures  Kc.maize <- ifelse(d < plant.maize, 0, Kc.maize1 + Kc.maize2 + Kc.maize3 + Kc.maize4)  t2 <- data.frame(Date, J, d, jyear, Reference.ET$ET0.1, ETc.maize, Kc.maize)  ########## Sugar cane ####################################################  ##Crop coefficients defined Kini.sugar <- Crop.table[3,2] Km.sugar <- Crop.table[3,3] Kl.sugar <- Crop.table[3,4]  143  ##Crop development cycles for all years inisugar <- plant.sugar inisugar.end <- plant.sugar + Crop.table[3,5] - 1 Sugar.ini <- J[inisugar:inisugar.end] devsugar <- inisugar.end + 1 devsugar.end <- inisugar.end + Crop.table[3,6] Sugar.dev <- J[devsugar:devsugar.end] midsugar <- devsugar.end + 1 midsugar.end <- devsugar.end + Crop.table[3,7] Sugar.mid <- J[midsugar:midsugar.end] latesugar <- midsugar.end + 1 latesugar.end <- midsugar.end + Crop.table[3,8] Sugar.late <- J[latesugar:latesugar.end]  #Crop development cycles for all years, as a function of d (day of time series)  dSugar.ini <- d[inisugar:inisugar.end] dSugar.dev <- d[devsugar:devsugar.end] dSugar.mid <- d[midsugar:midsugar.end] dSugar.late <- d[latesugar:latesugar.end]  #Creates table of stages as a function of d for 2000-2009 alldSugar.ini <- sapply(0:9, function(j){d200jsugar.ini <- dSugar.ini + 365*j}) colnames(alldSugar.ini) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldSugar.dev <- sapply(0:9, function(j){d200jsugar.dev <- dSugar.dev + 365*j}) colnames(alldSugar.dev) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009")  144  alldSugar.mid <- sapply(0:9, function(j){d200jsugar.mid <- dSugar.mid + 365*j}) colnames(alldSugar.mid) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldSugar.late <- sapply(0:9, function(j){d200sugar.late <- dSugar.late + 365*j}) colnames(alldSugar.late) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009")  alldSugar.ini <- as.data.frame(alldSugar.ini) alldSugar.dev <- as.data.frame(alldSugar.dev) alldSugar.mid <- as.data.frame(alldSugar.mid) alldSugar.late <- as.data.frame(alldSugar.late)  #Accounting of leap years for 2000, 2004 and 2008 (to re-align planting dates) alldSugar.ini[,2] <- alldSugar.ini[,2] + 1 #2001 alldSugar.dev[,2] <- alldSugar.dev[,2] + 1 alldSugar.mid[,2] <- alldSugar.mid[,2] + 1 alldSugar.late[,2] <- alldSugar.late[,2] + 1 alldSugar.ini[,3] <- alldSugar.ini[,3] + 1 alldSugar.dev[,3] <- alldSugar.dev[,3] + 1 alldSugar.mid[,3] <- alldSugar.mid[,3] + 1 alldSugar.late[,3] <- alldSugar.late[,3] + 1 alldSugar.ini[,4] <- alldSugar.ini[,4] + 1 alldSugar.dev[,4] <- alldSugar.dev[,4] + 1 alldSugar.mid[,4] <- alldSugar.mid[,4] + 1 alldSugar.late[,4] <- alldSugar.late[,4] + 1 alldSugar.ini[,5] <- alldSugar.ini[,5] + 1 #2004 alldSugar.dev[,5] <- alldSugar.dev[,5] + 1  145  alldSugar.mid[,5] <- alldSugar.mid[,5] + 1 alldSugar.late[,5] <- alldSugar.late[,5] + 1 alldSugar.ini[,6] <- alldSugar.ini[,6] + 2 alldSugar.dev[,6] <- alldSugar.dev[,6] + 2 alldSugar.mid[,6] <- alldSugar.mid[,6] + 2 alldSugar.late[,6] <- alldSugar.late[,6] + 2 alldSugar.ini[,7] <- alldSugar.ini[,7] + 2 alldSugar.dev[,7] <- alldSugar.dev[,7] + 2 alldSugar.mid[,7] <- alldSugar.mid[,7] + 2 alldSugar.late[,7] <- alldSugar.late[,7] + 2 alldSugar.ini[,8] <- alldSugar.ini[,8] + 2 alldSugar.dev[,8] <- alldSugar.dev[,8] + 2 alldSugar.mid[,8] <- alldSugar.mid[,8] + 2 alldSugar.late[,8] <- alldSugar.late[,8] + 2 alldSugar.ini[,9] <- alldSugar.ini[,9] + 2 #2008 alldSugar.dev[,9] <- alldSugar.dev[,9] + 2 alldSugar.mid[,9] <- alldSugar.mid[,9] + 2 alldSugar.late[,9] <- alldSugar.late[,9] + 2  #------------------------------------------------------------------------##Crop coefficient for development, Kdev  m3 <- (Km.sugar - Kini.sugar)/length(Sugar.dev) ##slope of the line between Kini and Kmid df3 <- sapply(1:length(Sugar.dev), function(i) {m3*i + Kini.sugar}) Kdev.sugar <- numeric(length(J)) hip.sugar <- data.frame(jyear, Kdev.sugar)  hip.sugar <- data.frame(jyear, J, d, Kdev.sugar) ##Year 2000  146  hip.sugar[hip.sugar$d > tail(alldSugar.ini[,1],1) & hip.sugar$d < (head(alldSugar.dev[,1],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2001 <- data.frame(J,d, Kdev.sugar) #Year 2001 hip.sugar2001[hip.sugar2001$d > tail(alldSugar.ini[,2],1) & hip.sugar2001$d < (head(alldSugar.dev[,2],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2002 <- data.frame(J,d, Kdev.sugar) #Year 2002 hip.sugar2002[hip.sugar2002$d > tail(alldSugar.ini[,3],1) & hip.sugar2002$d < (head(alldSugar.dev[,3],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2003 <- data.frame(J,d, Kdev.sugar) #Year 2003 hip.sugar2003[hip.sugar2003$d > tail(alldSugar.ini[,4],1) & hip.sugar2003$d < (head(alldSugar.dev[,4],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2004 <- data.frame(J,d, Kdev.sugar) #Year 2004 hip.sugar2004[hip.sugar2004$d > tail(alldSugar.ini[,5],1) & hip.sugar2004$d < (head(alldSugar.dev[,5],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  147  hip.sugar2005 <- data.frame(J,d, Kdev.sugar) #Year 2005 hip.sugar2005[hip.sugar2005$d > tail(alldSugar.ini[,6],1) & hip.sugar2005$d < (head(alldSugar.dev[,6],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2006 <- data.frame(J,d, Kdev.sugar) #Year 2006 hip.sugar2006[hip.sugar2006$d > tail(alldSugar.ini[,7],1) & hip.sugar2006$d < (head(alldSugar.dev[,7],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2007 <- data.frame(J,d, Kdev.sugar) #Year 2007 hip.sugar2007[hip.sugar2007$d > tail(alldSugar.ini[,8],1) & hip.sugar2007$d < (head(alldSugar.dev[,8],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  hip.sugar2008 <- data.frame(J,d, Kdev.sugar) #Year 2008 hip.sugar2008[hip.sugar2008$d > tail(alldSugar.ini[,9],1) & hip.sugar2008$d < (head(alldSugar.dev[,9],1) + length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  #hip.sugar2009 <- data.frame(J,d, Kdev.sugar) #Year 2009, might not be calculated if late planting date  148  #hip.sugar2009[hip.sugar2009$d > tail(alldSugar.ini[,10],1) & hip.sugar2009$d < (head(alldSugar.dev[,10],1) + #length(Sugar.dev)),]$Kdev.sugar = seq(head(df3, 1), tail(df3, 1), length = length(Sugar.dev))  #------------------------------------------------------------------------#Crop coefficient for late season, Klate for sugar  p3 <- (Kl.sugar - Km.sugar)/length(Sugar.late) late.df3 <- sapply(1:length(Sugar.late), function(i) {p3*i + Km.sugar}) Klate.sugar <- numeric(length(J))  hiplate.sugar <- data.frame(J, d, Klate.sugar) hiplate.sugar[hiplate.sugar$d > tail(alldSugar.mid[,1], 1) & hiplate.sugar$d < (head(alldSugar.late[,1], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2001 <- data.frame(J, d, Klate.sugar) #Year 2001 hiplate.sugar2001[hiplate.sugar2001$d > tail(alldSugar.mid[,2], 1) & hiplate.sugar2001$d < (head(alldSugar.late[,2], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2002 <- data.frame(J, d, Klate.sugar) #Year 2002 hiplate.sugar2002[hiplate.sugar2002$d > tail(alldSugar.mid[,3], 1) & hiplate.sugar2002$d < (head(alldSugar.late[,3], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  149  hiplate.sugar2003 <- data.frame(J, d, Klate.sugar) #Year 2003 hiplate.sugar2003[hiplate.sugar2003$d > tail(alldSugar.mid[,4], 1) & hiplate.sugar2003$d < (head(alldSugar.late[,4], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2004 <- data.frame(J, d, Klate.sugar) #Year 2004 hiplate.sugar2004[hiplate.sugar2004$d > tail(alldSugar.mid[,5], 1) & hiplate.sugar2004$d < (head(alldSugar.late[,5], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2005 <- data.frame(J, d, Klate.sugar) #Year 2005 hiplate.sugar2005[hiplate.sugar2005$d > tail(alldSugar.mid[,6], 1) & hiplate.sugar2005$d < (head(alldSugar.late[,6], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2006 <- data.frame(J, d, Klate.sugar) #Year 2006 hiplate.sugar2006[hiplate.sugar2006$d > tail(alldSugar.mid[,7], 1) & hiplate.sugar2006$d < (head(alldSugar.late[,7], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2007 <- data.frame(J, d, Klate.sugar) #Year 2007 hiplate.sugar2007[hiplate.sugar2007$d > tail(alldSugar.mid[,8], 1) & hiplate.sugar2007$d < (head(alldSugar.late[,8], 1) +  150  length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  hiplate.sugar2008 <- data.frame(J, d, Klate.sugar) #Year 2008 hiplate.sugar2008[hiplate.sugar2008$d > tail(alldSugar.mid[,9], 1) & hiplate.sugar2008$d < (head(alldSugar.late[,9], 1) + length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  #hiplate.sugar2009 <- data.frame(J, d, Klate.sugar) #Year 2009  to activate if planting date not too late in the year  #hiplate.sugar2009[hiplate.sugar2009$d > tail(alldSugar.mid[,10], 1) & hiplate.sugar2009$d < (head(alldSugar.late[,10], 1) + #length(Sugar.late)),]$Klate.sugar = seq(head(late.df3, 1), tail(late.df3, 1), length = length(Sugar.late))  #------------------------------------------------------------------------##Crop ET for sugar assuming only one harvest per year, for albedo = 0.23  ETc.sugar1a <- ifelse(d %in% alldSugar.ini[,1]| d %in% alldSugar.ini[,2]| d %in% alldSugar.ini[,3]| d %in% alldSugar.ini[,4]| d %in% alldSugar.ini[,5]| d %in% alldSugar.ini[,6]| d %in% alldSugar.ini[,7]| d %in% alldSugar.ini[,8]| d %in% alldSugar.ini[,9], Reference.ET$ET0.1*Kini.sugar,0) ETc.sugar1 <- signif(ETc.sugar1a, digits = 2) ##keep 2 significant figures  151  ETc.sugar2a <- ifelse(d %in% alldSugar.dev[,1], Reference.ET$ET0.1*hip.sugar$Kdev.sugar, 0) ETc2001.sugar2a <- ifelse(d %in% alldSugar.dev[,2], Reference.ET$ET0.1*hip.sugar2001$Kdev.sugar, 0) ETc2002.sugar2a <- ifelse(d %in% alldSugar.dev[,3], Reference.ET$ET0.1*hip.sugar2002$Kdev.sugar, 0) ETc2003.sugar2a <- ifelse(d %in% alldSugar.dev[,4], Reference.ET$ET0.1*hip.sugar2003$Kdev.sugar, 0) ETc2004.sugar2a <- ifelse(d %in% alldSugar.dev[,5], Reference.ET$ET0.1*hip.sugar2004$Kdev.sugar, 0) ETc2005.sugar2a <- ifelse(d %in% alldSugar.dev[,6], Reference.ET$ET0.1*hip.sugar2005$Kdev.sugar, 0) ETc2006.sugar2a <- ifelse(d %in% alldSugar.dev[,7], Reference.ET$ET0.1*hip.sugar2006$Kdev.sugar, 0) ETc2007.sugar2a <- ifelse(d %in% alldSugar.dev[,8], Reference.ET$ET0.1*hip.sugar2007$Kdev.sugar, 0) ETc2008.sugar2a <- ifelse(d %in% alldSugar.dev[,9], Reference.ET$ET0.1*hip.sugar2008$Kdev.sugar, 0) #ETc2009.sugar2a <- ifelse(d %in% alldSugar.dev[,10], Reference.ET$ET0.1*hip.sugar2009$Kdev.sugar, 0)  ## to activate if  planting date not too late ETc.sugar2bis <- ETc.sugar2a + ETc2001.sugar2a + ETc2002.sugar2a + ETc2003.sugar2a + ETc2004.sugar2a + ETc2005.sugar2a + ETc2006.sugar2a + ETc2007.sugar2a + ETc2008.sugar2a #+ ETc2009.sugar2a ## add in 2009 if required ETc.sugar2 <- signif(ETc.sugar2bis, digits = 2) ## keep 3 significant figures  ETc.sugar3a <- ifelse(d %in% alldSugar.mid[,1]| d %in% alldSugar.mid[,2]| d %in% alldSugar.mid[,3]|  152  d %in% alldSugar.mid[,4]| d %in% alldSugar.mid[,5]| d %in% alldSugar.mid[,6]| d %in% alldSugar.mid[,7]| d %in% alldSugar.mid[,8]| d %in% alldSugar.mid[,9], Reference.ET$ET0.1*Km.sugar,0) ETc.sugar3 <- signif(ETc.sugar3a, digits = 2) ## keep 2 significant figure  ETc.sugar4a <- ifelse(d %in% alldSugar.late[,1], Reference.ET$ET0.1*hiplate.sugar$Klate.sugar, 0) ETc2001.sugar4a <- ifelse(d %in% alldSugar.late[,2], Reference.ET$ET0.1*hiplate.sugar2001$Klate.sugar, 0) ETc2002.sugar4a <- ifelse(d %in% alldSugar.late[,3], Reference.ET$ET0.1*hiplate.sugar2002$Klate.sugar, 0) ETc2003.sugar4a <- ifelse(d %in% alldSugar.late[,4], Reference.ET$ET0.1*hiplate.sugar2003$Klate.sugar, 0) ETc2004.sugar4a <- ifelse(d %in% alldSugar.late[,5], Reference.ET$ET0.1*hiplate.sugar2004$Klate.sugar, 0) ETc2005.sugar4a <- ifelse(d %in% alldSugar.late[,6], Reference.ET$ET0.1*hiplate.sugar2005$Klate.sugar, 0) ETc2006.sugar4a <- ifelse(d %in% alldSugar.late[,7], Reference.ET$ET0.1*hiplate.sugar2006$Klate.sugar, 0) ETc2007.sugar4a <- ifelse(d %in% alldSugar.late[,8], Reference.ET$ET0.1*hiplate.sugar2007$Klate.sugar, 0) ETc2008.sugar4a <- ifelse(d %in% alldSugar.late[,9], Reference.ET$ET0.1*hiplate.sugar2008$Klate.sugar, 0) #ETc2009.sugar4a <- ifelse(d %in% alldSugar.late[,10], Reference.ET$ET0.1*hiplate.sugar2009$Klate.sugar, 0) ETc.sugar4bis <- ETc.sugar4a + ETc2001.sugar4a + ETc2002.sugar4a + ETc2003.sugar4a + ETc2004.sugar4a + ETc2005.sugar4a + ETc2006.sugar4a + ETc2007.sugar4a +  153  ETc2008.sugar4a #+ ETc2009.sugar4a ## add in 2009 if required ETc.sugar4 <- signif(ETc.sugar4bis, digits = 2) ## keep 2 significant figures  ETc.sugar <- ifelse(d < plant.sugar, 0, ETc.sugar1 + ETc.sugar2 + ETc.sugar3 + ETc.sugar4)  #Crop coefficients for sugar Kc.sugar1a <- ifelse(d %in% alldSugar.ini[,1]| d %in% alldSugar.ini[,2]| d %in% alldSugar.ini[,3]| d %in% alldSugar.ini[,4]| d %in% alldSugar.ini[,5]| d %in% alldSugar.ini[,6]| d %in% alldSugar.ini[,7]| d %in% alldSugar.ini[,8]| d %in% alldSugar.ini[,9], Kini.sugar,0) Kc.sugar1 <- signif(Kc.sugar1a, digits = 3) ## keep 3 significant figures  Kc.sugar2a <- ifelse(d %in% alldSugar.dev[,1], hip.sugar$Kdev.sugar, 0) Kc2001.sugar2a <- ifelse(d %in% alldSugar.dev[,2], hip.sugar2001$Kdev.sugar, 0) Kc2002.sugar2a <- ifelse(d %in% alldSugar.dev[,3], hip.sugar2002$Kdev.sugar, 0) Kc2003.sugar2a <- ifelse(d %in% alldSugar.dev[,4], hip.sugar2003$Kdev.sugar, 0) Kc2004.sugar2a <- ifelse(d %in% alldSugar.dev[,5], hip.sugar2004$Kdev.sugar, 0)  154  Kc2005.sugar2a <- ifelse(d %in% alldSugar.dev[,6], hip.sugar2005$Kdev.sugar, 0) Kc2006.sugar2a <- ifelse(d %in% alldSugar.dev[,7], hip.sugar2006$Kdev.sugar, 0) Kc2007.sugar2a <- ifelse(d %in% alldSugar.dev[,8], hip.sugar2007$Kdev.sugar, 0) Kc2008.sugar2a <- ifelse(d %in% alldSugar.dev[,9], hip.sugar2008$Kdev.sugar, 0) #Kc2009.sugar2a <- ifelse(d %in% alldSugar.dev[,10], hip.sugar2009$Kdev.sugar, 0)  # to active if planting not too late in the  year Kc.sugar2bis <- Kc.sugar2a + Kc2001.sugar2a + Kc2002.sugar2a + Kc2003.sugar2a + Kc2004.sugar2a + Kc2005.sugar2a + Kc2006.sugar2a + Kc2007.sugar2a + Kc2008.sugar2a #+ Kc2009.sugar2a ## add in 2009 if required Kc.sugar2 <- signif(Kc.sugar2bis, digits = 3) ## keep 3 significant figures  Kc.sugar3a <- ifelse(d %in% alldSugar.mid[,1]| d %in% alldSugar.mid[,2]| d %in% alldSugar.mid[,3]| d %in% alldSugar.mid[,4]| d %in% alldSugar.mid[,5]| d %in% alldSugar.mid[,6]| d %in% alldSugar.mid[,7]| d %in% alldSugar.mid[,8]| d %in% alldSugar.mid[,9], Km.sugar,0) Kc.sugar3 <- signif(Kc.sugar3a, digits = 3) ##keep 3 significant figure  155  Kc.sugar4a <- ifelse(d %in% alldSugar.late[,1], hiplate.sugar$Klate.sugar, 0) Kc2001.sugar4a <- ifelse(d %in% alldSugar.late[,2], hiplate.sugar2001$Klate.sugar, 0) Kc2002.sugar4a <- ifelse(d %in% alldSugar.late[,3], hiplate.sugar2002$Klate.sugar, 0) Kc2003.sugar4a <- ifelse(d %in% alldSugar.late[,4], hiplate.sugar2003$Klate.sugar, 0) Kc2004.sugar4a <- ifelse(d %in% alldSugar.late[,5], hiplate.sugar2004$Klate.sugar, 0) Kc2005.sugar4a <- ifelse(d %in% alldSugar.late[,6], hiplate.sugar2005$Klate.sugar, 0) Kc2006.sugar4a <- ifelse(d %in% alldSugar.late[,7], hiplate.sugar2006$Klate.sugar, 0) Kc2007.sugar4a <- ifelse(d %in% alldSugar.late[,8], hiplate.sugar2007$Klate.sugar, 0) Kc2008.sugar4a <- ifelse(d %in% alldSugar.late[,9], hiplate.sugar2008$Klate.sugar, 0) #Kc2009.sugar4a <- ifelse(d %in% alldSugar.late[,10], hiplate.sugar2009$Klate.sugar, 0)  # to activate if planting date not too  late in the year Kc.sugar4bis <- Kc.sugar4a + Kc2001.sugar4a + Kc2002.sugar4a + Kc2003.sugar4a + Kc2004.sugar4a + Kc2005.sugar4a + Kc2006.sugar4a + Kc2007.sugar4a + Kc2008.sugar4a #+ Kc2009.sugar4a ## add in 2009 if required Kc.sugar4 <- signif(Kc.sugar4bis, digits = 3) ## keep 3 significant figures  Kc.sugar <- ifelse(d < plant.sugar, 0, Kc.sugar1 + Kc.sugar2 + Kc.sugar3 + Kc.sugar4)  156  t3 <- data.frame(Date, J, d, jyear, Reference.ET$ET0.1, ETc.sugar, Kc.sugar)  ########## Cotton ########################################################  ##Crop coefficients defined Kini.cotton <- Crop.table[4,2] Km.cotton <- Crop.table[4,3] Kl.cotton <- Crop.table[4,4]  ##Crop development stages inicotton <- plant.cotton inicotton.end <- plant.cotton + Crop.table[4,5] - 1 Cotton.ini <- J[inicotton:inicotton.end] Cotton.ini2 <- L[inicotton:inicotton.end] devcotton <- inicotton.end + 1 devcotton.end <- inicotton.end + Crop.table[4,6] Cotton.dev <- J[devcotton:devcotton.end] midcotton <- devcotton.end + 1 midcotton.end <- devcotton.end + Crop.table[4,7] Cotton.mid <- J[midcotton:midcotton.end] latecotton <- midcotton.end + 1 latecotton.end <- midcotton.end + Crop.table[4,8] Cotton.late <- J[latecotton:latecotton.end]  #Crop development cycles for all years, as a function of d (day of time series) dCotton.ini <- d[inicotton:inicotton.end] dCotton.dev <- d[devcotton:devcotton.end] dCotton.mid <- d[midcotton:midcotton.end] dCotton.late <- d[latecotton:latecotton.end]  157  #Creates table of stages as a function of d for 2000-2009 alldCotton.ini <- sapply(0:9, function(j){d200jCotton.ini <- dCotton.ini + 365*j}) colnames(alldCotton.ini) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldCotton.dev <- sapply(0:9, function(j){d200jCotton.dev <- dCotton.dev + 365*j}) colnames(alldCotton.dev) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldCotton.mid <- sapply(0:9, function(j){d200jCotton.mid <- dCotton.mid + 365*j}) colnames(alldCotton.mid) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009") alldCotton.late <- sapply(0:9, function(j){d200jCotton.late <dCotton.late + 365*j}) colnames(alldCotton.late) <c("2000","2001","2002","2003","2004","2005","2006","2007","2008","2009")  alldCotton.ini <- as.data.frame(alldCotton.ini) alldCotton.dev <- as.data.frame(alldCotton.dev) alldCotton.mid <- as.data.frame(alldCotton.mid) alldCotton.late <- as.data.frame(alldCotton.late)  #Accounting of leap years for 2000, 2004 and 2008 (to re-align planting dates) alldCotton.ini[,2] <- alldCotton.ini[,2] + 1 #2001 alldCotton.dev[,2] <- alldCotton.dev[,2] + 1 alldCotton.mid[,2] <- alldCotton.mid[,2] + 1 alldCotton.late[,2] <- alldCotton.late[,2] + 1 alldCotton.ini[,3] <- alldCotton.ini[,3] + 1 alldCotton.dev[,3] <- alldCotton.dev[,3] + 1  158  alldCotton.mid[,3] <- alldCotton.mid[,3] + 1 alldCotton.late[,3] <- alldCotton.late[,3] + 1 alldCotton.ini[,4] <- alldCotton.ini[,4] + 1 alldCotton.dev[,4] <- alldCotton.dev[,4] + 1 alldCotton.mid[,4] <- alldCotton.mid[,4] + 1 alldCotton.late[,4] <- alldCotton.late[,4] + 1 alldCotton.ini[,5] <- alldCotton.ini[,5] + 1 #2004 alldCotton.dev[,5] <- alldCotton.dev[,5] + 1 alldCotton.mid[,5] <- alldCotton.mid[,5] + 1 alldCotton.late[,5] <- alldCotton.late[,5] + 1 alldCotton.ini[,6] <- alldCotton.ini[,6] + 2 alldCotton.dev[,6] <- alldCotton.dev[,6] + 2 alldCotton.mid[,6] <- alldCotton.mid[,6] + 2 alldCotton.late[,6] <- alldCotton.late[,6] + 2 alldCotton.ini[,7] <- alldCotton.ini[,7] + 2 alldCotton.dev[,7] <- alldCotton.dev[,7] + 2 alldCotton.mid[,7] <- alldCotton.mid[,7] + 2 alldCotton.late[,7] <- alldCotton.late[,7] + 2 alldCotton.ini[,8] <- alldCotton.ini[,8] + 2 alldCotton.dev[,8] <- alldCotton.dev[,8] + 2 alldCotton.mid[,8] <- alldCotton.mid[,8] + 2 alldCotton.late[,8] <- alldCotton.late[,8] + 2 alldCotton.ini[,9] <- alldCotton.ini[,9] + 2 #2008 alldCotton.dev[,9] <- alldCotton.dev[,9] + 2 alldCotton.mid[,9] <- alldCotton.mid[,9] + 2 alldCotton.late[,9] <- alldCotton.late[,9] + 2  #------------------------------------------------------------------------##Crop coefficient for development, Kdev  159  m4 <- (Km.cotton - Kini.cotton)/length(Cotton.dev) ##slope of the line between Kini and Kmid df4 <- sapply(1:length(Cotton.dev), function(i) {m4*i + Kini.cotton}) Kdev.cotton <- numeric(length(J)) hip.cotton <- data.frame(jyear, Kdev.cotton)  hip.cotton <- data.frame(jyear, J, d, Kdev.cotton) ##Year 2000 hip.cotton[hip.cotton$d > tail(alldCotton.ini[,1],1) & hip.cotton$d < (head(alldCotton.dev[,1],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2001 <- data.frame(J,d, Kdev.cotton) #Year 2001 hip.cotton2001[hip.cotton2001$d > tail(alldCotton.ini[,2],1) & hip.cotton2001$d < (head(alldCotton.dev[,2],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2002 <- data.frame(J,d, Kdev.cotton) #Year 2002 hip.cotton2002[hip.cotton2002$d > tail(alldCotton.ini[,3],1) & hip.cotton2002$d < (head(alldCotton.dev[,3],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2003 <- data.frame(J,d, Kdev.cotton) #Year 2003 hip.cotton2003[hip.cotton2003$d > tail(alldCotton.ini[,4],1) & hip.cotton2003$d < (head(alldCotton.dev[,4],1) +  160  length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2004 <- data.frame(J,d, Kdev.cotton) #Year 2004 hip.cotton2004[hip.cotton2004$d > tail(alldCotton.ini[,5],1) & hip.cotton2004$d < (head(alldCotton.dev[,5],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2005 <- data.frame(J,d, Kdev.cotton) #Year 2005 hip.cotton2005[hip.cotton2005$d > tail(alldCotton.ini[,6],1) & hip.cotton2005$d < (head(alldCotton.dev[,6],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2006 <- data.frame(J,d, Kdev.cotton) #Year 2006 hip.cotton2006[hip.cotton2006$d > tail(alldCotton.ini[,7],1) & hip.cotton2006$d < (head(alldCotton.dev[,7],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  hip.cotton2007 <- data.frame(J,d, Kdev.cotton) #Year 2007 hip.cotton2007[hip.cotton2007$d > tail(alldCotton.ini[,8],1) & hip.cotton2007$d < (head(alldCotton.dev[,8],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  161  hip.cotton2008 <- data.frame(J,d, Kdev.cotton) #Year 2008 hip.cotton2008[hip.cotton2008$d > tail(alldCotton.ini[,9],1) & hip.cotton2008$d < (head(alldCotton.dev[,9],1) + length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  #hip.cotton2009 <- data.frame(J,d, Kdev.cotton) #Year 2009, might not be calculated if late planting date #hip.cotton2009[hip.cotton2009$d > tail(alldCotton.ini[,10],1) & hip.cotton2009$d < (head(alldCotton.dev[,10],1) + #length(Cotton.dev)),]$Kdev.cotton = seq(head(df4, 1), tail(df4, 1), length = length(Cotton.dev))  #------------------------------------------------------------------------#Crop coefficient for late season, Klate for cotton  p4 <- (Kl.cotton - Km.cotton)/length(Cotton.late) late.df4 <- sapply(1:length(Cotton.late), function(i) {p4*i + Km.cotton}) Klate.cotton <- numeric(length(J))  hiplate.cotton <- data.frame(J, d, Klate.cotton) hiplate.cotton[hiplate.cotton$d > tail(alldCotton.mid[,1], 1) & hiplate.cotton$d < (head(alldCotton.late[,1], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2001 <- data.frame(J, d, Klate.cotton) #Year 2001 hiplate.cotton2001[hiplate.cotton2001$d > tail(alldCotton.mid[,2], 1) & hiplate.cotton2001$d < (head(alldCotton.late[,2], 1) +  162  length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2002 <- data.frame(J, d, Klate.cotton) #Year 2002 hiplate.cotton2002[hiplate.cotton2002$d > tail(alldCotton.mid[,3], 1) & hiplate.cotton2002$d < (head(alldCotton.late[,3], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2003 <- data.frame(J, d, Klate.cotton) #Year 2003 hiplate.cotton2003[hiplate.cotton2003$d > tail(alldCotton.mid[,4], 1) & hiplate.cotton2003$d < (head(alldCotton.late[,4], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2004 <- data.frame(J, d, Klate.cotton) #Year 2004 hiplate.cotton2004[hiplate.cotton2004$d > tail(alldCotton.mid[,5], 1) & hiplate.cotton2004$d < (head(alldCotton.late[,5], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2005 <- data.frame(J, d, Klate.cotton) #Year 2005 hiplate.cotton2005[hiplate.cotton2005$d > tail(alldCotton.mid[,6], 1) & hiplate.cotton2005$d < (head(alldCotton.late[,6], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  163  hiplate.cotton2006 <- data.frame(J, d, Klate.cotton) #Year 2006 hiplate.cotton2006[hiplate.cotton2006$d > tail(alldCotton.mid[,7], 1) & hiplate.cotton2006$d < (head(alldCotton.late[,7], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2007 <- data.frame(J, d, Klate.cotton) #Year 2007 hiplate.cotton2007[hiplate.cotton2007$d > tail(alldCotton.mid[,8], 1) & hiplate.cotton2007$d < (head(alldCotton.late[,8], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  hiplate.cotton2008 <- data.frame(J, d, Klate.cotton) #Year 2008 hiplate.cotton2008[hiplate.cotton2008$d > tail(alldCotton.mid[,9], 1) & hiplate.cotton2008$d < (head(alldCotton.late[,9], 1) + length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  #hiplate.cotton2009 <- data.frame(J, d, Klate.cotton) #Year 2009  to activate if planting data not too late in the year  #hiplate.cotton2009[hiplate.cotton2009$d > tail(alldCotton.mid[,10], 1) & hiplate.cotton2009$d < (head(alldCotton.late[,10], 1) + #length(Cotton.late)),]$Klate.cotton = seq(head(late.df4, 1), tail(late.df4, 1), length = length(Cotton.late))  #------------------------------------------------------------------------##Crop ET for cotton assuming only one harvest per year, for albedo = 0.23  ETc.cotton1a <- ifelse(d %in% alldCotton.ini[,1]|  164  d %in% alldCotton.ini[,2]| d %in% alldCotton.ini[,3]| d %in% alldCotton.ini[,4]| d %in% alldCotton.ini[,5]| d %in% alldCotton.ini[,6]| d %in% alldCotton.ini[,7]| d %in% alldCotton.ini[,8]| d %in% alldCotton.ini[,9], Reference.ET$ET0.1*Kini.cotton,0) ETc.cotton1 <- signif(ETc.cotton1a, digits = 2) ##keep 2 significant figures  ETc.cotton2a <- ifelse(d %in% alldCotton.dev[,1], Reference.ET$ET0.1*hip.cotton$Kdev.cotton, 0) ETc2001.cotton2a <- ifelse(d %in% alldCotton.dev[,2], Reference.ET$ET0.1*hip.cotton2001$Kdev.cotton, 0) ETc2002.cotton2a <- ifelse(d %in% alldCotton.dev[,3], Reference.ET$ET0.1*hip.cotton2002$Kdev.cotton, 0) ETc2003.cotton2a <- ifelse(d %in% alldCotton.dev[,4], Reference.ET$ET0.1*hip.cotton2003$Kdev.cotton, 0) ETc2004.cotton2a <- ifelse(d %in% alldCotton.dev[,5], Reference.ET$ET0.1*hip.cotton2004$Kdev.cotton, 0) ETc2005.cotton2a <- ifelse(d %in% alldCotton.dev[,6], Reference.ET$ET0.1*hip.cotton2005$Kdev.cotton, 0) ETc2006.cotton2a <- ifelse(d %in% alldCotton.dev[,7], Reference.ET$ET0.1*hip.cotton2006$Kdev.cotton, 0) ETc2007.cotton2a <- ifelse(d %in% alldCotton.dev[,8], Reference.ET$ET0.1*hip.cotton2007$Kdev.cotton, 0) ETc2008.cotton2a <- ifelse(d %in% alldCotton.dev[,9], Reference.ET$ET0.1*hip.cotton2008$Kdev.cotton, 0) #ETc2009.cotton2a <- ifelse(d %in% alldCotton.dev[,10], Reference.ET$ET0.1*hip.cotton2009$Kdev.cotton, 0)  165  ETc.cotton2bis <- ETc.cotton2a + ETc2001.cotton2a + ETc2002.cotton2a + ETc2003.cotton2a + ETc2004.cotton2a + ETc2005.cotton2a + ETc2006.cotton2a + ETc2007.cotton2a + ETc2008.cotton2a #+ ETc2009.cotton2a ## add in 2009 if required ETc.cotton2 <- signif(ETc.cotton2bis, digits = 2) ## keep 3 significant figures  ETc.cotton3a <- ifelse(d %in% alldCotton.mid[,1]| d %in% alldCotton.mid[,2]| d %in% alldCotton.mid[,3]| d %in% alldCotton.mid[,4]| d %in% alldCotton.mid[,5]| d %in% alldCotton.mid[,6]| d %in% alldCotton.mid[,7]| d %in% alldCotton.mid[,8]| d %in% alldCotton.mid[,9], Reference.ET$ET0.1*Km.cotton,0) ETc.cotton3 <- signif(ETc.cotton3a, digits = 2) ## keep 2 significant figure  ETc.cotton4a <- ifelse(d %in% alldCotton.late[,1], Reference.ET$ET0.1*hiplate.cotton$Klate.cotton, 0) ETc2001.cotton4a <- ifelse(d %in% alldCotton.late[,2], Reference.ET$ET0.1*hiplate.cotton2001$Klate.cotton, 0) ETc2002.cotton4a <- ifelse(d %in% alldCotton.late[,3], Reference.ET$ET0.1*hiplate.cotton2002$Klate.cotton, 0) ETc2003.cotton4a <- ifelse(d %in% alldCotton.late[,4], Reference.ET$ET0.1*hiplate.cotton2003$Klate.cotton, 0) ETc2004.cotton4a <- ifelse(d %in% alldCotton.late[,5], Reference.ET$ET0.1*hiplate.cotton2004$Klate.cotton, 0)  166  ETc2005.cotton4a <- ifelse(d %in% alldCotton.late[,6], Reference.ET$ET0.1*hiplate.cotton2005$Klate.cotton, 0) ETc2006.cotton4a <- ifelse(d %in% alldCotton.late[,7], Reference.ET$ET0.1*hiplate.cotton2006$Klate.cotton, 0) ETc2007.cotton4a <- ifelse(d %in% alldCotton.late[,8], Reference.ET$ET0.1*hiplate.cotton2007$Klate.cotton, 0) ETc2008.cotton4a <- ifelse(d %in% alldCotton.late[,9], Reference.ET$ET0.1*hiplate.cotton2008$Klate.cotton, 0) #ETc2009.cotton4a <- ifelse(d %in% alldCotton.late[,10], Reference.ET$ET0.1*hiplate.cotton2009$Klate.cotton, 0) ETc.cotton4bis <- ETc.cotton4a + ETc2001.cotton4a + ETc2002.cotton4a + ETc2003.cotton4a + ETc2004.cotton4a + ETc2005.cotton4a + ETc2006.cotton4a + ETc2007.cotton4a + ETc2008.cotton4a #+ ETc2009.cotton4a ## add in 2009 if required ETc.cotton4 <- signif(ETc.cotton4bis, digits = 2) ## keep 2 significant figures  ETc.cotton <- ifelse(d < plant.cotton, 0, ETc.cotton1 + ETc.cotton2 + ETc.cotton3 + ETc.cotton4)  #------------------------------------------------------------------------#Crop coefficients for cotton  Kc.cotton1a <- ifelse(d %in% alldCotton.ini[,1]| d %in% alldCotton.ini[,2]| d %in% alldCotton.ini[,3]| d %in% alldCotton.ini[,4]| d %in% alldCotton.ini[,5]| d %in% alldCotton.ini[,6]| d %in% alldCotton.ini[,7]|  167  d %in% alldCotton.ini[,8]| d %in% alldCotton.ini[,9], Kini.cotton,0) Kc.cotton1 <- signif(Kc.cotton1a, digits = 3) ##keep 3 significant figures  Kc.cotton2a <- ifelse(d %in% alldCotton.dev[,1], hip.cotton$Kdev.cotton, 0) Kc2001.cotton2a <- ifelse(d %in% alldCotton.dev[,2], hip.cotton2001$Kdev.cotton, 0) Kc2002.cotton2a <- ifelse(d %in% alldCotton.dev[,3], hip.cotton2002$Kdev.cotton, 0) Kc2003.cotton2a <- ifelse(d %in% alldCotton.dev[,4], hip.cotton2003$Kdev.cotton, 0) Kc2004.cotton2a <- ifelse(d %in% alldCotton.dev[,5], hip.cotton2004$Kdev.cotton, 0) Kc2005.cotton2a <- ifelse(d %in% alldCotton.dev[,6], hip.cotton2005$Kdev.cotton, 0) Kc2006.cotton2a <- ifelse(d %in% alldCotton.dev[,7], hip.cotton2006$Kdev.cotton, 0) Kc2007.cotton2a <- ifelse(d %in% alldCotton.dev[,8], hip.cotton2007$Kdev.cotton, 0) Kc2008.cotton2a <- ifelse(d %in% alldCotton.dev[,9], hip.cotton2008$Kdev.cotton, 0) #Kc2009.cotton2a <- ifelse(d %in% alldCotton.dev[,10], hip.cotton2009$Kdev.cotton, 0) Kc.cotton2bis <- Kc.cotton2a + Kc2001.cotton2a + Kc2002.cotton2a + Kc2003.cotton2a + Kc2004.cotton2a + Kc2005.cotton2a + Kc2006.cotton2a + Kc2007.cotton2a + Kc2008.cotton2a #+ Kc2009.cotton2a ## add in 2009 if required Kc.cotton2 <- signif(Kc.cotton2bis, digits = 3) ## keep 3 significant figures  168  Kc.cotton3a <- ifelse(d %in% alldCotton.mid[,1]| d %in% alldCotton.mid[,2]| d %in% alldCotton.mid[,3]| d %in% alldCotton.mid[,4]| d %in% alldCotton.mid[,5]| d %in% alldCotton.mid[,6]| d %in% alldCotton.mid[,7]| d %in% alldCotton.mid[,8]| d %in% alldCotton.mid[,9], Km.cotton,0) Kc.cotton3 <- signif(Kc.cotton3a, digits = 3) ##keep 3 significant figure  Kc.cotton4a <- ifelse(d %in% alldCotton.late[,1], hiplate.cotton$Klate.cotton, 0) Kc2001.cotton4a <- ifelse(d %in% alldCotton.late[,2], hiplate.cotton2001$Klate.cotton, 0) Kc2002.cotton4a <- ifelse(d %in% alldCotton.late[,3], hiplate.cotton2002$Klate.cotton, 0) Kc2003.cotton4a <- ifelse(d %in% alldCotton.late[,4], hiplate.cotton2003$Klate.cotton, 0) Kc2004.cotton4a <- ifelse(d %in% alldCotton.late[,5], hiplate.cotton2004$Klate.cotton, 0) Kc2005.cotton4a <- ifelse(d %in% alldCotton.late[,6], hiplate.cotton2005$Klate.cotton, 0) Kc2006.cotton4a <- ifelse(d %in% alldCotton.late[,7], hiplate.cotton2006$Klate.cotton, 0) Kc2007.cotton4a <- ifelse(d %in% alldCotton.late[,8], hiplate.cotton2007$Klate.cotton, 0) Kc2008.cotton4a <- ifelse(d %in% alldCotton.late[,9], hiplate.cotton2008$Klate.cotton, 0)  169  #Kc2009.cotton4a <- ifelse(d %in% alldCotton.late[,10], hiplate.cotton2009$Klate.cotton, 0) Kc.cotton4bis <- Kc.cotton4a + Kc2001.cotton4a + Kc2002.cotton4a + Kc2003.cotton4a + Kc2004.cotton4a + Kc2005.cotton4a + Kc2006.cotton4a + Kc2007.cotton4a + Kc2008.cotton4a #+ Kc2009.cotton4a ## add in 2009 if required Kc.cotton4 <- signif(Kc.cotton4bis, digits = 3) ## keep 3 significant figures  Kc.cotton <- ifelse(d < plant.cotton, 0, Kc.cotton1 + Kc.cotton2 + Kc.cotton3 + Kc.cotton4)  t4 <- data.frame(Date, J, d, jyear, Reference.ET$ET0.1, ETc.cotton, Kc.cotton)  ########## Pasture #######################################################  ##Crop coefficients defined Kini.pasture <- Crop.table[5,2] Kmid.pasture <- Crop.table[5,3]  decades <- 366 #enter the number of decades based on the available data decade <- rep(1:decades, each=10) df5 <- aggregate(Reference.ET$Precip, by = list(decade), mean, na.rm = TRUE) Precip.1a <- rep(df5$x, each = 10) Precip.1 <- signif(Precip.1a, digits = 2) ##keep 2 significant figures for ET0 df6 <- aggregate(Precip.1, by = list(decade), sd, na.rm = TRUE) Precipstdev.1a <- rep(df6$x, each = 10)  170  Precipstdev.1 <- signif(Precipstdev.1a, digits = 2) ##keep 2 significant figures for ET0  #------------------------------------------------------------------------##Crop ET for pasture assuming that precipitation drives the ETc, for albedo = 0.23  ETc.pasture.1a <- ifelse(Precip.1 <= 1, Reference.ET$ET0.1*Kini.pasture, Reference.ET$ET0.1*Kmid.pasture) ETc.pasture <- signif(ETc.pasture.1a, digits = 2)  #------------------------------------------------------------------------##Crop coefficients for pasture  Kc.pasture <- ifelse(Precip.1 < 10, Kini.pasture, Kmid.pasture)  t5 <- data.frame(Date, J, d, jyear, Reference.ET$ET0.1, ETc.pasture, Kc.pasture)  #------------------------------------------------------------------------#Sum of all ETc at specific date  Sum.ETc <- (ETc.soy + ETc.maize + ETc.sugar + ETc.cotton + ETc.pasture)  #------------------------------------------------------------------------#### Summary table of ETc for all crops and years  Date3 <- format(Date, "%Y/%m") t6 <- data.frame(Date3, Sum.ETc, ETc.soy, ETc.maize, ETc.sugar, ETc.cotton, ETc.pasture)  171  attach(t6)  q1 <- aggregate(Sum.ETc, list(Date3), sum, na.rm = TRUE) # Total ETc (mm/month) q2 <- aggregate(ETc.soy, list(Date3), sum, na.rm = TRUE) # Total monthly Soybean ETc q3 <- aggregate(ETc.maize, list(Date3), sum, na.rm = TRUE) # Total monthly Maize ETc q4 <- aggregate(ETc.sugar, list(Date3), sum, na.rm = TRUE) # Total monthly Sugar Cane ETc q5 <- aggregate(ETc.cotton, list(Date3), sum, na.rm = TRUE) # Total monthly Cotton ETc q6 <- aggregate(ETc.pasture, list(Date3), sum, na.rm = TRUE) # Total monthly Pasture ETc  # Average daily ETc  count <- ts(diff(seq(as.Date("2000-01-01"), as.Date("2010-01-01"), by = "month")), start = c(2000, 01), freq = 12) days <- as.vector(count)  selection <- 1:120 # selection of 120 months to fit with the "days" data frame  q7a <- q1$x[selection]/days # in mm/day, average daily for all crops q7 <- signif(q7a, digits = 2) q8a <- q2$x[selection]/days # average daily ET (mm/day) Soybean q8 <- signif(q8a, digits = 2)  172  q9a <- q3$x[selection]/days # average daily ET (mm/day) Maize q9 <- signif(q9a, digits = 2) q10a <- q4$x[selection]/days # average daily ET (mm/day) Sugar cane q10 <- signif(q10a, digits = 2) q11a <- q5$x[selection]/days # average daily ET (mm/day) Cotton q11 <- signif(q11a, digits = 2) q12a <- q6$x[selection]/days # average daily ET (mm/day) Pasture q12 <- signif(q12a, digits = 2)  Summary.ETc <- data.frame(q1$Group.1[selection], 1:120,q1$x[selection], q7, q2$x[selection], q8, q3$x[selection], q9, q4$x[selection], q10, q5$x[selection], q11, q6$x[selection], q12)  colnames(Summary.ETc) <- c("Year/Month", "Month", "Total ETc (mm/mo)", "Average daily ETc (mm/d)", "Total Soy ETc (mm/mo)", "Average Soy ETc (mm/d)", "Total Maize ETc (mm/mo)", "Average Maize ETc (mm/d)", "Total Sugar ETc (mm/mo)", "Average Sugar Cane ETc (mm/d)", "Total Cotton ETc (mm/mo)", "Average Cotton ETc (mm/d)", "Average Pasture ETc (mm/mo)", "Total Pasture ETc (mm/d)")  #Export summary table to Desktop write.table(Summary.ETc, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_SumETc_annual.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  173  detach(t6)  #------------------------------------------------------------------------####Plot growing seasons of soy, maize, sugar cane and corn  plot(Date, ETc.sugar, ylab = "", main = "ETc fluxes at Caceres (mm)", col="red", pch = ".") mtext(expression(bold(paste("mm"," ", "day"^{-1}), sep = "")), side = 2, line = 2) lines(Date, ETc.sugar, type = "h", col = "red") points(Date, ETc.maize, pch = ".", col = "yellow") lines (Date, ETc.maize, type = "h", col = "yellow") points(Date, ETc.soy, pch = ".", col = "green") lines (Date, ETc.soy, type = "h", col = "green") points(Date, ETc.cotton, pch = ".", col = "orange") lines (Date, ETc.cotton, type = "h", col = "orange") points(Date, ETc.pasture, type = "h", col = "green2") legend("topleft", legend = c("sugar cane", "maize", "soy", "cotton", "pasture"), pch = c(15, 15, 15, 15, 15), col = c("red", "yellow", "green", "orange", "green2"), cex = 0.75, text.width = strwidth("sugar cane"), title = "Crop type")  ##to pdf dev.print(pdf, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_Station_ETc.pdf", width=8.5, height=5, pointsize=5)  #------------------------------------------------------------------------# Summary table of daily ETc and Precipiation  174  All.CropETc <- data.frame(Date,ETc.soy, ETc.maize, ETc.sugar, ETc.cotton, Reference.ET$Precip) colnames(All.CropETc) <- c("Date", "ETc.soy", "ETc.maize", "ETc.sugar", "ETc.cotton", "Precip")  write.table(All.CropETc, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_dailyETc_P_summary.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  #------------------------------------------------------------------------## 10 day P and decadal ETc comparison  cycle1 <- (27:63) #2001-2002 growing season cycle2 <- (64:99) #2002-2003 cycle3 <- (100:135) #2003-2004 cycle4 <- (136:172) #2004-2005 cycle5 <- (173:209) #2005-2006 cycle6 <- (210:245) #2006-2007 cycle7 <- (246:282) #2007-2008 cycle8 <- (283:360) #2008-2009  # Soybean df7 <- aggregate(t1$ETc.soy, by = list(decade), sum, na.rm = TRUE)  175  Soy.PET <- data.frame(df7, df5$x) # decadal ET Soy and aggregated Precip colnames(Soy.PET) <- c("decade", "Soy.ETc", "Precip")  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2001 <- Soy.PET[cycle1,] Soy.PET2001$occurence <- ifelse(Soy.PET2001$P.ET <0, 1, 0) occurence2001 <- sum(Soy.PET2001$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2002 <- Soy.PET[cycle2,] Soy.PET2002$occurence <- ifelse(Soy.PET2002$P.ET <0, 1, 0) occurence2002 <- sum(Soy.PET2002$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2003 <- Soy.PET[cycle3,] Soy.PET2003$occurence <- ifelse(Soy.PET2003$P.ET <0, 1, 0) occurence2003 <- sum(Soy.PET2003$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2004 <- Soy.PET[cycle4,] Soy.PET2004$occurence <- ifelse(Soy.PET2004$P.ET <0, 1, 0) occurence2004 <- sum(Soy.PET2004$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2005 <- Soy.PET[cycle5,] Soy.PET2005$occurence <- ifelse(Soy.PET2005$P.ET <0, 1, 0)  176  occurence2005 <- sum(Soy.PET2005$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2006 <- Soy.PET[cycle6,] Soy.PET2006$occurence <- ifelse(Soy.PET2006$P.ET <0, 1, 0) occurence2006 <- sum(Soy.PET2006$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2007 <- Soy.PET[cycle7,] Soy.PET2007$occurence <- ifelse(Soy.PET2007$P.ET <0, 1, 0) occurence2007 <- sum(Soy.PET2007$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2008 <- Soy.PET[cycle8,] Soy.PET2008$occurence <- ifelse(Soy.PET2008$P.ET <0, 1, 0) occurence2008 <- sum(Soy.PET2008$occurence)  Soy.PET$P.ET <- ifelse(Soy.PET$Soy.ETc == 0, 0, Soy.PET$Precip Soy.PET$Soy.ETc) Soy.PET2009 <- Soy.PET[cycle2,] Soy.PET2009$occurence <- ifelse(Soy.PET2009$P.ET <0, 1, 0) occurence2009 <- sum(Soy.PET2009$occurence)  Soy2001 <- c(occurence2001, range(Soy.PET2001$P.ET)) Soy2002 <- c(occurence2002, range(Soy.PET2002$P.ET)) Soy2003 <- c(occurence2003, range(Soy.PET2003$P.ET)) Soy2004 <- c(occurence2004, range(Soy.PET2004$P.ET)) Soy2005 <- c(occurence2005, range(Soy.PET2005$P.ET)) Soy2006 <- c(occurence2006, range(Soy.PET2006$P.ET))  177  Soy2007 <- c(occurence2007, range(Soy.PET2007$P.ET)) Soy2008 <- c(occurence2008, range(Soy.PET2008$P.ET)) Soy2009 <- c(occurence2009, range(Soy.PET2009$P.ET))  Soy.summary <- rbind(Soy2001, Soy2002, Soy2003, Soy2004, Soy2005, Soy2006, Soy2007, Soy2008, Soy2009) colnames(Soy.summary) <- c("Occurence", "min P.ET", "max P.ET")  # Maize df8 <- aggregate(t2$ETc.maize, by = list(decade), sum, na.rm = TRUE) Maize.PET <- data.frame(df8, df5$x) # decadal ET Maize and aggregated Precip colnames(Maize.PET) <- c("decade", "Maize.ETc", "Precip")  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2001 <- Maize.PET[cycle1,] Maize.PET2001$occurence <- ifelse(Maize.PET2001$P.ET <0, 1, 0) occurence2001 <- sum(Maize.PET2001$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2002 <- Maize.PET[cycle2,] Maize.PET2002$occurence <- ifelse(Maize.PET2002$P.ET <0, 1, 0) occurence2002 <- sum(Maize.PET2002$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2003 <- Maize.PET[cycle3,] Maize.PET2003$occurence <- ifelse(Maize.PET2003$P.ET <0, 1, 0) occurence2003 <- sum(Maize.PET2003$occurence)  178  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2004 <- Maize.PET[cycle4,] Maize.PET2004$occurence <- ifelse(Maize.PET2004$P.ET <0, 1, 0) occurence2004 <- sum(Maize.PET2004$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2005 <- Maize.PET[cycle5,] Maize.PET2005$occurence <- ifelse(Maize.PET2005$P.ET <0, 1, 0) occurence2005 <- sum(Maize.PET2005$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2006 <- Maize.PET[cycle6,] Maize.PET2006$occurence <- ifelse(Maize.PET2006$P.ET <0, 1, 0) occurence2006 <- sum(Maize.PET2006$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2007 <- Maize.PET[cycle7,] Maize.PET2007$occurence <- ifelse(Maize.PET2007$P.ET <0, 1, 0) occurence2007 <- sum(Maize.PET2007$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc) Maize.PET2008 <- Maize.PET[cycle8,] Maize.PET2008$occurence <- ifelse(Maize.PET2008$P.ET <0, 1, 0) occurence2008 <- sum(Maize.PET2008$occurence)  Maize.PET$P.ET <- ifelse(Maize.PET$Maize.ETc == 0, 0, Maize.PET$Precip Maize.PET$Maize.ETc)  179  Maize.PET2009 <- Maize.PET[cycle2,] Maize.PET2009$occurence <- ifelse(Maize.PET2009$P.ET <0, 1, 0) occurence2009 <- sum(Maize.PET2009$occurence)  Maize2001 <- c(occurence2001, range(Maize.PET2001$P.ET)) Maize2002 <- c(occurence2002, range(Maize.PET2002$P.ET)) Maize2003 <- c(occurence2003, range(Maize.PET2003$P.ET)) Maize2004 <- c(occurence2004, range(Maize.PET2004$P.ET)) Maize2005 <- c(occurence2005, range(Maize.PET2005$P.ET)) Maize2006 <- c(occurence2006, range(Maize.PET2006$P.ET)) Maize2007 <- c(occurence2007, range(Maize.PET2007$P.ET)) Maize2008 <- c(occurence2008, range(Maize.PET2008$P.ET)) Maize2009 <- c(occurence2009, range(Maize.PET2009$P.ET))  Maize.summary <- rbind(Maize2001, Maize2002, Maize2003, Maize2004, Maize2005, Maize2006, Maize2007, Maize2008, Maize2009) colnames(Maize.summary) <- c("Occurence", "min P.ET", "max P.ET")  # Sugar df9 <- aggregate(t3$ETc.sugar, by = list(decade), sum, na.rm = TRUE) Sugar.PET <- data.frame(df9, df5$x) # decadal ET Sugar and aggregated Precip colnames(Sugar.PET) <- c("decade", "Sugar.ETc", "Precip")  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2001 <- Sugar.PET[cycle1,] Sugar.PET2001$occurence <- ifelse(Sugar.PET2001$P.ET <0, 1, 0) occurence2001 <- sum(Sugar.PET2001$occurence)  180  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2002 <- Sugar.PET[cycle2,] Sugar.PET2002$occurence <- ifelse(Sugar.PET2002$P.ET <0, 1, 0) occurence2002 <- sum(Sugar.PET2002$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2003 <- Sugar.PET[cycle3,] Sugar.PET2003$occurence <- ifelse(Sugar.PET2003$P.ET <0, 1, 0) occurence2003 <- sum(Sugar.PET2003$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2004 <- Sugar.PET[cycle4,] Sugar.PET2004$occurence <- ifelse(Sugar.PET2004$P.ET <0, 1, 0) occurence2004 <- sum(Sugar.PET2004$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2005 <- Sugar.PET[cycle5,] Sugar.PET2005$occurence <- ifelse(Sugar.PET2005$P.ET <0, 1, 0) occurence2005 <- sum(Sugar.PET2005$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2006 <- Sugar.PET[cycle6,] Sugar.PET2006$occurence <- ifelse(Sugar.PET2006$P.ET <0, 1, 0) occurence2006 <- sum(Sugar.PET2006$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc)  181  Sugar.PET2007 <- Sugar.PET[cycle7,] Sugar.PET2007$occurence <- ifelse(Sugar.PET2007$P.ET <0, 1, 0) occurence2007 <- sum(Sugar.PET2007$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2008 <- Sugar.PET[cycle8,] Sugar.PET2008$occurence <- ifelse(Sugar.PET2008$P.ET <0, 1, 0) occurence2008 <- sum(Sugar.PET2008$occurence)  Sugar.PET$P.ET <- ifelse(Sugar.PET$Sugar.ETc == 0, 0, Sugar.PET$Precip Sugar.PET$Sugar.ETc) Sugar.PET2009 <- Sugar.PET[cycle2,] Sugar.PET2009$occurence <- ifelse(Sugar.PET2009$P.ET <0, 1, 0) occurence2009 <- sum(Sugar.PET2009$occurence)  Sugar2001 <- c(occurence2001, range(Sugar.PET2001$P.ET)) Sugar2002 <- c(occurence2002, range(Sugar.PET2002$P.ET)) Sugar2003 <- c(occurence2003, range(Sugar.PET2003$P.ET)) Sugar2004 <- c(occurence2004, range(Sugar.PET2004$P.ET)) Sugar2005 <- c(occurence2005, range(Sugar.PET2005$P.ET)) Sugar2006 <- c(occurence2006, range(Sugar.PET2006$P.ET)) Sugar2007 <- c(occurence2007, range(Sugar.PET2007$P.ET)) Sugar2008 <- c(occurence2008, range(Sugar.PET2008$P.ET)) Sugar2009 <- c(occurence2009, range(Sugar.PET2009$P.ET))  Sugar.summary <- rbind(Sugar2001, Sugar2002, Sugar2003, Sugar2004, Sugar2005, Sugar2006,  #this does not take into account the whole  growing Sugar2007, Sugar2008, Sugar2009) #season colnames(Sugar.summary) <- c("Occurence", "min P.ET", "max P.ET")  182  # Cotton df10 <- aggregate(t4$ETc.cotton, by = list(decade), sum, na.rm = TRUE) Cotton.PET <- data.frame(df10, df5$x) # decadal ET Cotton and aggregated Precip colnames(Cotton.PET) <- c("decade", "Cotton.ETc", "Precip")  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2001 <- Cotton.PET[cycle1,] Cotton.PET2001$occurence <- ifelse(Cotton.PET2001$P.ET <0, 1, 0) occurence2001 <- sum(Cotton.PET2001$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2002 <- Cotton.PET[cycle2,] Cotton.PET2002$occurence <- ifelse(Cotton.PET2002$P.ET <0, 1, 0) occurence2002 <- sum(Cotton.PET2002$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2003 <- Cotton.PET[cycle3,] Cotton.PET2003$occurence <- ifelse(Cotton.PET2003$P.ET <0, 1, 0) occurence2003 <- sum(Cotton.PET2003$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2004 <- Cotton.PET[cycle4,] Cotton.PET2004$occurence <- ifelse(Cotton.PET2004$P.ET <0, 1, 0) occurence2004 <- sum(Cotton.PET2004$occurence)  183  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2005 <- Cotton.PET[cycle5,] Cotton.PET2005$occurence <- ifelse(Cotton.PET2005$P.ET <0, 1, 0) occurence2005 <- sum(Cotton.PET2005$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2006 <- Cotton.PET[cycle6,] Cotton.PET2006$occurence <- ifelse(Cotton.PET2006$P.ET <0, 1, 0) occurence2006 <- sum(Cotton.PET2006$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2007 <- Cotton.PET[cycle7,] Cotton.PET2007$occurence <- ifelse(Cotton.PET2007$P.ET <0, 1, 0) occurence2007 <- sum(Cotton.PET2007$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2008 <- Cotton.PET[cycle8,] Cotton.PET2008$occurence <- ifelse(Cotton.PET2008$P.ET <0, 1, 0) occurence2008 <- sum(Cotton.PET2008$occurence)  Cotton.PET$P.ET <- ifelse(Cotton.PET$Cotton.ETc == 0, 0, Cotton.PET$Precip - Cotton.PET$Cotton.ETc) Cotton.PET2009 <- Cotton.PET[cycle2,] Cotton.PET2009$occurence <- ifelse(Cotton.PET2009$P.ET <0, 1, 0) occurence2009 <- sum(Cotton.PET2009$occurence)  Cotton2001 <- c(occurence2001, range(Cotton.PET2001$P.ET)) Cotton2002 <- c(occurence2002, range(Cotton.PET2002$P.ET))  184  Cotton2003 <- c(occurence2003, range(Cotton.PET2003$P.ET)) Cotton2004 <- c(occurence2004, range(Cotton.PET2004$P.ET)) Cotton2005 <- c(occurence2005, range(Cotton.PET2005$P.ET)) Cotton2006 <- c(occurence2006, range(Cotton.PET2006$P.ET)) Cotton2007 <- c(occurence2007, range(Cotton.PET2007$P.ET)) Cotton2008 <- c(occurence2008, range(Cotton.PET2008$P.ET)) Cotton2009 <- c(occurence2009, range(Cotton.PET2009$P.ET))  Cotton.summary <- rbind(Cotton2001, Cotton2002, Cotton2003, Cotton2004, Cotton2005, Cotton2006, Cotton2007, Cotton2008, Cotton2009) colnames(Cotton.summary) <- c("Occurence", "min P.ET", "max P.ET")  #Export summary tables write.table(Soy.PET, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_Soy_decETc.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  write.table(Maize.PET, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_Maize_decETc.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  write.table(Sugar.PET, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_Sugar_decETc.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  write.table(Cotton.PET, file="C:/Documents and Settings/BuddyLuv/Desktop/Caceres_Cotton_decETc.txt", sep = ",", na = "", dec = ".", row.names = FALSE, col.names = TRUE )  #------------------------------------------------------------------------#### END #################################################################  185  Appendix G Total and forest green water for Mato Grosso  Maximum and minimum GW volumes (km3 mo-1) and fluxes (mm mo-1) are shown in Table 26 below. The graph is available in Figure 4. Table 26: Monthly maximum and minimum green water volumes and fluxes in Mato Grosso for total (GWT) and forest (GWF) GWT 3 -1 (km mo ) 127.4 – 67.0 (Jan-Aug) 134.2 – 74.1 (Mar-Aug) 131.6 – 72.2 (Mar-Aug) 129.6 – 58.5 (Mar-Sep) 126.8 – 62.0 (Mar-Sep) 121.2 – 52.8 (Mar-Sep) 122.8 – 64.0 (Jan-Sep) 132.2-67.3 (Mar-Sep) 122.1 – 75.0 (Jan-Sep) 124.6 – 86.8 (Jan-Aug)  Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009  GWF 3 -1 (km mo ) 37.0 – 58.7 (Aug-Nov) 58.0 – 41.8 (Mar-Sep) 55.5 – 39.8 (Mar-Aug) 50.2 – 27.0 (Mar-Sep) 29.8 – 49.9 (Sep-Dec) 47.5 – 21.7 (May-Sep) 30.9 – 48.4 (Sep-Nov) 47.3 – 33.8 (Apr-Sep) 35.9 – 45.5 (Feb-Jul) 34.1 – 47.8 (Apr-Oct)  GWT -1 (mm mo ) 84.3 – 133.7 (Aug-Nov) 134.8 – 97.0 (Mar-Sep) 132.6 – 94.9 (Mar-Aug) 123.8 – 66.5 (Mar-Sep) 75.7 – 126.7 (Sep-Dec) 123.9 – 56.6 (May-Sep) 81.2 – 127.2 (Sep - Nov) 125.3 – 89.5 (Apr-Sep) 96.2 – 122.0 (Feb-Jul) 91.7 – 128.3 (Apr-Oct)  GWF -1 (mm mo ) 117.6 – 61.8 (Jan-Aug) 123.9 – 68.4 (Mar-Aug) 121.5 – 66.7 (Mar-Aug) 119.6 – 54.0 (Mar-Sep) 117.0 – 57.2 (Mar-Sep) 111.9 – 48.7 (Mar-Sep) 113.4 – 59.1 (Jan-Sep) 122.1 – 62.1 (Mar-Sep) 112.7 – 69.3 (Jan-Sep) 115.0 – 80.1 (Jan-Aug)  Precipitation data from INMET (2009) is available between 1961 and 1990 for 8 stations in Mato Grosso: Cáceres, Cuiabá, Diamantino, Gleba Celeste, Meruri, Poxoreo, Rosario do Oeste, and Sangradouro (Table 27). Table 27. Average precipitation from 8 meteorological stations in Mato Grosso, 1961-1990 (INMET, 2009) Month  Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec  (mm)  275.3  247.6  220.5  113.1  52.6  98.1  7.5  14.8  60.8  138.2  205.2  262.3  186  Appendix H Agricultural land use for 15 municipal units  GWT volumes were broken down into GWF, GWC, GWP, GWAg, and GWR volumes for 15 MUs containing a meteorological stations in order to understand the dynamics of the changes in GW fluxes between 2000 and 2009. Residual classes represent the cerrado ecosystems, cities, rivers and the Pantanal wetland. Depending on the location, the size of the residual land can vary from 8 % to 83 % in 2000 and from 12 % to 87 % in 2009 (Figures 24 to 27 and Table 28).  Figure 24. Land use in 15 municipal units in Mato Grosso from forest, agriculture (as cropland and pasture) and residual land (INPE, 2011; IBGE, 2010a). Some MUs are represented by numbers (see Appendix C).  187  Figure 25. Percent change in forest and agricultural land cover (as cropland and pasture) between 2000 and 2009.  GWC and GWP volumes were determined using fluxes calculated from FAO56 in combination with information collected from IBGE (IBGE, 2010a). As a result, any change in either harvested area or animal population will induce a change in calculated GW volumes. All crops have increased in harvested area between 2000 and 2009: in the 15 MUs considered, soybean increased from 476,717 ha to 912,060 ha (90 % increase), maize from 75,047 ha to 223,134 ha (200 % increase), sugar cane from 13,434 ha to 37,606 ha (180 % increase), cotton from 63,717 ha to 90,372 ha (40 % increase) (IBGE, 2010a). Total pasture area decreased in size between 2000 and 2009 from 3,723,700 ha to 3,227,100 ha (or 17 %) for the first estimate assuming continuous increase in livestock density post 2006, and 3,606,100 ha (11 %) assuming constant livestock density (Figure 27, Table 28). Moreover, average yields have increased between 2000 and 2009 for the 15 MUs (IBGE, 2010a): yields for soybean increased from 3007 kg ha-1 to 3954 kg ha-1, maize from 3197 kg ha-1 to 4988 kg  188  ha-1, sugar cane from 42,033 kg ha-1 to 58,892 kg ha-1 and cotton from 3611 kg ha-1 to 4239 kg ha-1 (Table 28).  Figure 26. Cropland harvested area for 15 municipal units (IBGE, 2010a).  Figure 27. Estimated pasture area for 15 municipal units and two pasture estimates (sa1 and sa2) (IBGE, 2010a).  189  Table 28. Sum of harvested area and mean yield for 15 municipal units of Mato Grosso for 2000 and 2009. Crop Soybean Maize Sugar cane Cotton Pasture*  Sum of harvested area in 2000 (ha) 476,717 75,047 13,434 63,717 3,723,700  Sum of harvested area in 2009 (ha) 912,060 223,134 37,606 90,372 3,227,100**/3,606,100  Mean yield in 2000 -1 (tonne ha ) (sd) 3007 (929) 3197 (1820) 42,033 (41034) 3611 (1968)  Mean yield in 2009 -1 (tonne ha ) (sd) 3717 (1833) 4988 (2646) 37,715 (24,723) 4239 (1403)  sd: standard deviation; *estimated area from animal population;**two estimates based on differing livestock densities (Appendix E)  190  Differences in land use between 2000 and 2009 are shown in Table 30 below for forest (INPE, 2011), agriculture (as cropland and pasture) (IBGE, 2010a) as well as the residual land uses. Table 29. INPE forest cover for 15 municipal units (INPE, 2011). Municipalities Year Barra do Garças Pontal do Araguaia Cáceres, Curvelândia, Lambari d’Oeste, Mirassol d’Oeste Canarana Diamantino, São José do Rio Claro Vera Matupá Peixoto de Azevedo Nova Xavantina Cuiabá Varzéa Grande Santo Antônio do Leverger Poxoréo Rondonópolis Campo Verde  2  Size (km ) (MU)  2  INPE forest cover (km ) (% total)  2  Agricultural land (km ) (% total)  2  Residual land (km ) (% total)  9147 (27) 2755 (79)  2000 285.4 (3) 0 (0)  2009 226.1 (2) 0 (0)  2000 3490 (38) 1120 (41)  2009 2800 (31) 847 (31)  2000 5380 (59) 1630 (59)  2009 6130 (67) 1910 (69)  27610 (10)  2644.9 (10)  2107.6 (8)  9080 (38)  7830 (28)  15900 (52)  17700 (64)  10839 (34)  2513.3 (23)  2178.3 (20)  4210 (39)  5220 (48)  4120 (38)  3440 (32)  12700 (14)  4296.6 (34)  3522.3 (28)  4310 (34)  6130 (48)  4100 (32)  3050 (24)  2961 (103) 5153 (59) 14402 (76) 5527 (70) 3539 (40) 938 (102)  1696.6 (57) 3750.3 (73) 11032.3 (77) 324.0 (6) 181.6 (5) 0 (0)  1006.8 (34) 3054.9 (59) 9758.7 (68) 273 (5) 173.3 (5) 0 (0)  396 (13) 980 (19) 1300 (9) 3150 (57) 758 (14) 174 (19)  1520 (51) 1470 (28) 1726 (12) 3100 (56) 554 (10) 224 (24)  868 (29) 422 (8) 2070 (14) 2050 (37) 4590 (83) 764 (81)  437 (15) 633 (12) 2920 (20) 2150 (39) 4800 (85) 714 (76)  12270 (92)  1210.5 (10)  1111.9 (9)  5990 (49)  4770 (39)  5070 (41)  6390 (52)  6923 (85) 4166 (89) 4794 (31)  132.3 (2) 297.3 (7) 64.2 (1)  96 (1) 274.3 (7) 53.1 (1)  3480 (50) 2410 (58) 2680 (56)  3370 (49) 2240 (54) 3100 (65)  3310 (48) 1460 (35) 2050 (43)  3460 (50) 1650 (40) 1630 (34)  191  Table 30. Breakdown of green water volumes in 15 municipalities for Aug 1st – Jul 31st hydrologic years between 2000 and 2009: total (GWT), forest (GWF), soybean (GWSoy), maize (GWMaize), sugar cane (GWSugar), cotton (GWCotton), pasture (GWP) with biggest drop in estimated area (Appendix E), and GWAg, as GWC + GWP. Municipality Caceres, Curvelandia, Lambari d’Oeste, Mirassol d’Oeste1 Diamantino, São José do Rio Claro  Municipal unit  GWF (km3 y-2)  14 27  Campo Verde  31  Canarana  34  Cuiabá  40  Matupá  59  Nova Xavantina  70  -0.20** (0.84) 0.23* (0.46) 0.15** (0.84) 0.22* (0.53) 0.11* (0.55) -0.12* (0.49) 0.11* (0.50)  no soybean  89  Santo Antonio de Leverger1  92  Varzea Grande  102  Vera  103  0.025** (0.80) no cotton  -0.00015* (0.49)  GWAg (km3 y-2)  -0.28* (0.50)  -0.25* (0.45)  0.000071* (0.55) 0.00036* (0.57)  -0.14** (0.89) -0.075** (0.83)  -0.13** (0.86)  0.034** (0.60)  0.035* (0.56)  -0.044** (0.87) -0.056* (0.69) -0.028* (0.45) -0.13** (0.84)  -0.044** (0.87)  no cotton no cotton  no cotton no soybean  0.019* (0.60)  no forest  GWPasture (km3 y-2)  -0.074** (0.86)  -0.21** (0.80)  no forest  Rondonópolis  GWCotton (km3 y-2)  0.025** (0.92)  0.033* (0.46)  79 0.22* (0.69) 0.11* (0.58) 0.46* (0.60) 0.03* (0.46) 0.15* (0.84)  0.077* (0.55)  GWSugar (km3 y-2)  0.019** (0.82)  -0.41* (0.61)  85  GWMaize (km3 y-2)  0.013** (0.74)  76  Poxoréo  GWSoy (km3 y-2) 0.0055** (0.75)  10  Barra do Garcas  Peixoto de Azevedo Pontal do Araguaia  GWT (km3 y-2)  no soybean  -0.00014* (0.56) 0.0034** (0.70) 0.0065** (0.84) 0.0031* (0.56) 0.000072** (0.91) 0.019** (0.82)  0.00010* (0.45)  no cotton 0.0040** (0.77) -0.0078** (0.87)  0.0029* (0.51) 0.00021** (0.92)  -0.11** (0.82)  -0.075* (0.83)  *p-value <0.05; ** p-value <0.01; ***Municipal unit 14 contains 2 municipalities that each have a weather station; 1contains the Pantanal  192  Results provided for pasture consider the largest drop in pasture area post-2006, or a continuous increase in livestock density.  193  Appendix I Significant changes in total and forest green water fluxes in Mato Grosso  Simple linear regression was used to assess significant changes in fluxes and volumes between 2000 and 2009. Results are shown in Table 28 below. Table 31. Significant changes in total (GWT) and forest (GWF) green water volumes and fluxes (20002009). Municipal Unit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42  Changes in GWT volume 3 -2 km y -1.97  0.66  0.66  0.47  0.27 0.20 1.17  0.61 0.77 0.48  2  R  -0.76 -0.38  0.46 0.62  0.03  0.52  0.06 0.06 0.02 -0.63 0.16 0.01  0.71 0.47 0.76 0.51 0.48 0.51  0.01 0.50 0.23 -0.38 0.16 0.13 0.15  0.44 0.51 0.46 0.56 0.64 0.54 0.84  0.22  Changes in GWF volume 3 -2 km y -2.67  0.81  -0.20 -0.55  0.73 0.77  2  R  -0.26 -0.09  0.83 0.45  -0.66 -1.11 -0.67 -0.20  0.86 0.79 0.85 0.84  -0.35  0.80  -0.75  0.69  -0.01  0.54  -0.56  0.85  -0.02 -0.04  0.84 0.66  -0.04 -0.16 -0.03 -0.38 -0.22  0.69 0.87 0.65 0.69 0.73  0.53  -0.53  0.52  0.11  0.55  0.09  0.70  0.00  0.48  Changes in GWT flux -2 mm y -2.03  0.61  1.23  0.45  1.62 1.62 1.34  0.62 0.75 0.45  2  R  -2.13  0.57  2.41  0.50  1.16 1.98 0.91 -2.15 1.64 1.07  0.69 0.45 0.71 0.50 0.48 0.48  1.69 2.95 1.74 -1.68 1.82 0.93 2.04  0.45 0.52 0.48 0.58 0.62 0.57 0.84  1.37  0.52  -1.68  0.52  2.10  0.53  2.58  0.69  Changes in GWF flux -2 mm y -1.96  0.60  -1.47 -2.06 -2.01  0.53 0.44 0.53  -2.65  0.49  -2.12  0.49  -1.78  0.51  1.57 -1.96  0.63 0.57  -2.19  0.53  -1.79  0.46  3.00  0.68  2  R  194  Table 31. Significant changes in total (GWT) and forest (GWF) green water volumes and fluxes (20002009). Municipal Unit 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95  Changes in GWT volume 3 -2 km y  Changes in GWT flux -2 mm y  R  R  0.08  0.65  1.54  0.65  0.11  0.61  1.41  0.60  0.18 0.05  0.53 0.70  1.36 2.04  0.52 0.70  -0.72 0.08 0.12 0.14  0.58 0.68 0.75 0.79  -1.89 2.40 2.22 2.32  2  Changes in GWF volume 3 -2 km y  -0.15  -0.30  0.55  -0.25  0.54  0.11  0.50  2  R  Changes in GWF flux -2 mm y  R  -2.00  0.54  3.56  0.66  0.56 0.67 0.75 0.78  -1.98 2.61  0.53 0.54  2  0.88  2  -0.77  0.70  -0.02  0.62  -0.21 -0.01  0.80 0.45  -1.58  0.47  -1.88  0.48  -0.55 -0.15 -0.02 -0.10 -0.04 -0.49  0.85 0.80 0.76 0.80 0.88 0.83  -2.22  0.51  -2.10  0.46  -1.53  0.55  -1.43  0.46  -0.39  0.81 1.43  0.52  -0.02 -0.28 -0.29 -0.16  0.83 0.78 0.82 0.57  -1.81 -2.43 -2.76  0.45 0.48 0.45  -0.41  0.61 1.30 2.53  0.44 0.46  -2.60 0.94 2.09  0.45 0.50 0.54  0.65  1.55 2.19  0.62 0.45  0.01  0.48  1.11  0.47  -0.18  0.55  -1.83  0.54  -1.80  0.47  0.22 0.14  0.69 0.79  2.15 1.77  0.68 0.76  3.01  0.54  0.11  0.58  0.97 1.76  0.45 0.57  3.27  0.63  2.44 2.26  0.60 0.56  2.14  0.53  2.42  0.67  3.06  0.51  0.33 0.13  0.49 0.55  0.06  -0.38  -0.21 -0.02 0.46 0.02  0.60 0.57  0.01  0.67  0.00  0.86  0.63 0.82  0.51  195  Table 31. Significant changes in total (GWT) and forest (GWF) green water volumes and fluxes (20002009). Municipal Unit 96 97 98 99 100 101 102 103 104  Changes in GWT volume 3 -2 km y  R  0.21 -0.24 0.09  0.62 0.51 0.61  0.03  0.46  2  Changes in GWF volume 3 -2 km y -0.09 -0.09 -0.34  0.56 0.61 0.85  -0.11  0.57  -0.13 -0.36  0.76 0.77  2  R  Changes in GWT flux -2 mm y 1.52 -2.03 1.63  R  Changes in GWF flux -2 mm y  R  0.60 0.50 0.60  -1.97  0.45  2  2  196  

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