Water model documentation - Revision history

Fouad.Alkhouri at 01:07, 17 February 2023

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	<div>		<div>
	Please cite as: Steve Hedden, Hughes, Barry B. 2018. ''"IFs Water Model Documentation."'' Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY ~~<https://pardee.du.edu/wiki/Water_model_documentation>~~		Please cite as: Steve Hedden, Hughes, Barry B. 2018. ''"IFs Water Model Documentation."'' Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY

	The water model of the International Futures (IFs) system forecasts water demand by sector (municipal, industrial, and agricultural) and supply by source (surface water, groundwater, non-renewable groundwater, desalinated water, and treated wastewater) for 186 countries to the year 2100. Water supply and demand are equilibrated using a shadow price index, which is determined using a proportional-integral-derivate (PID) controller. There are no “forward linkages” from the water model to the rest of the IFs system; however, user-controlled parameters allow water scarcity to impact agricultural yields.		The water model of the International Futures (IFs) system forecasts water demand by sector (municipal, industrial, and agricultural) and supply by source (surface water, groundwater, non-renewable groundwater, desalinated water, and treated wastewater) for 186 countries to the year 2100. Water supply and demand are equilibrated using a shadow price index, which is determined using a proportional-integral-derivate (PID) controller. There are no “forward linkages” from the water model to the rest of the IFs system; however, user-controlled parameters allow water scarcity to impact agricultural yields.

Wikiadmin at 20:06, 7 September 2018

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	<div>		<div>
			Please cite as: Steve Hedden, Hughes, Barry B. 2018. ''"IFs Water Model Documentation."'' Pardee Center for International Futures, Josef Korbel School of International Studies, University of Denver, Denver, CO. Accessed DD Month YYYY <https://pardee.du.edu/wiki/Water_model_documentation>

	The water model of the International Futures (IFs) system forecasts water demand by sector (municipal, industrial, and agricultural) and supply by source (surface water, groundwater, non-renewable groundwater, desalinated water, and treated wastewater) for 186 countries to the year 2100. Water supply and demand are equilibrated using a shadow price index, which is determined using a proportional-integral-derivate (PID) controller. There are no “forward linkages” from the water model to the rest of the IFs system; however, user-controlled parameters allow water scarcity to impact agricultural yields.		The water model of the International Futures (IFs) system forecasts water demand by sector (municipal, industrial, and agricultural) and supply by source (surface water, groundwater, non-renewable groundwater, desalinated water, and treated wastewater) for 186 countries to the year 2100. Water supply and demand are equilibrated using a shadow price index, which is determined using a proportional-integral-derivate (PID) controller. There are no “forward linkages” from the water model to the rest of the IFs system; however, user-controlled parameters allow water scarcity to impact agricultural yields.

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	The following equation describes the four terms that are used by the PID controller to calculate the price index adjustment: the first term is the absolute change in the demand-supply ratio (the integral), the second term is the change in the demand-supply ratio from the previous year (the derivative), the third term is the impact that the integral has on the price index (0.3 but adjustable by user), and the fourth term is the impact that the derivative has on the price index (0.6 but adjustable by user).		The following equation describes the four terms that are used by the PID controller to calculate the price index adjustment: the first term is the absolute change in the demand-supply ratio (the integral), the second term is the change in the demand-supply ratio from the previous year (the derivative), the third term is the impact that the integral has on the price index (0.3 but adjustable by user), and the fourth term is the impact that the derivative has on the price index (0.6 but adjustable by user).

	<math>PriceAdjustment_r=PID(DemandSupplyRatio_{r,t}-1,(DemandSupplyRatio_{r,t}-DemandSupplyRatio_{r,t-1}),</math>		<math>PriceAdjustment_r=PID(DemandSupplyRatio_{r,t}-1,(DemandSupplyRatio_{r,t}-DemandSupplyRatio_{r,t-1}),</math> <math>ImpactofIntegralOnPrice,ImpactOfDerivativeonPrice)</math>
	<math>ImpactofIntegralOnPrice,ImpactOfDerivativeonPrice)</math>

	The change in the price index is then used to adjust water demand for each sector and water supply from each source.		The change in the price index is then used to adjust water demand for each sector and water supply from each source.

Wikiadmin at 20:03, 7 September 2018

2018-09-07T20:03:44Z

Wikiadmin at 20:02, 7 September 2018

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Wikiadmin at 19:55, 7 September 2018

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	The water requirement per unit of irrigated land is the difference between total crop water requirements and the part supplied by precipitation. This is largely driven by the cropping intensity, or the ratio of harvested irrigated crop area over irrigated crop area<ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref><ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref>[[File:WaterRequirementsPerIrrigatedLand.png\|frame\|center\|Drivers of water requirements per unit of irrigated land]]		The water requirement per unit of irrigated land is the difference between total crop water requirements and the part supplied by precipitation. This is largely driven by the cropping intensity, or the ratio of harvested irrigated crop area over irrigated crop area<ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref><ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref>[[File:WaterRequirementsPerIrrigatedLand.png\|frame\|center\|Drivers of water requirements per unit of irrigated land]]

	Water use per unit of irrigated land in IFs is driven by the shadow water price:		Water use per unit of irrigated land in IFs is driven by the shadow water price:

	:<math>waterperha_{r}=\frac{WATDEMAND_{r,agriculture}}{LANDIRAREAACTUAL_{r}}(1+(percentincreaseinprice_{r}watdemandelas_{r,agricultural}))</math>		:<math>waterperha_{r}=\frac{WATDEMAND_{r,agriculture}}{LANDIRAREAACTUAL_{r}}(1+(percentincreaseinprice_{r}watdemandelas_{r,agricultural}))</math>

	Where waterperha is the water requirements per hectare of irrigated land, WATDEMAND is agricultural water demand, LANDIRAREAACTUAL is the area of irrigated land, percentincreaseinprice is the change in water price, and watdemandelas is the elasticity between water price and agricultural water demand, which is -0.1 unless otherwise specified by the user.		Where waterperha is the water requirements per hectare of irrigated land, WATDEMAND is agricultural water demand, LANDIRAREAACTUAL is the area of irrigated land, percentincreaseinprice is the change in water price, and watdemandelas is the elasticity between water price and agricultural water demand, which is -0.1 unless otherwise specified by the user.

	~~==== ====~~

	=== Municipal water demand ===		=== Municipal water demand ===

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	Where waterperha is the water requirements per hectare of irrigated land, WATDEMAND is agricultural water demand, LANDIRAREAACTUAL is the area of irrigated land, percentincreaseinprice is the change in water price, and watdemandelas is the elasticity between water price and agricultural water demand, which is -0.1 unless otherwise specified by the user.		Where waterperha is the water requirements per hectare of irrigated land, WATDEMAND is agricultural water demand, LANDIRAREAACTUAL is the area of irrigated land, percentincreaseinprice is the change in water price, and watdemandelas is the elasticity between water price and agricultural water demand, which is -0.1 unless otherwise specified by the user.

	==== ~~Irrigation efficiency~~ ====		==== ====

	~~The efficiency of irrigation can also change over time depending on the type of irrigation used and the technology behind it.~~

	The model assumes that the efficiency of irrigation remains relatively constant over time for each country. We include a parameter on agricultural water demand however, that allows the user to adjust the efficiency of irrigation for countries, regions or the world.

	=== Municipal water demand ===		=== Municipal water demand ===

Wikiadmin at 19:53, 7 September 2018

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	==== Water requirement per unit of irrigated land (WRCI) ====		==== Water requirement per unit of irrigated land (WRCI) ====

	The water requirement per unit of irrigated land is the difference between total crop water requirements and the part supplied by precipitation. This is largely driven by the cropping intensity, or the ratio of harvested irrigated crop area over irrigated crop area<ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref><ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref>[[File:WaterRequirementsPerIrrigatedLand.png\|frame\|~~right~~\|Drivers of water requirements per unit of irrigated land]]		The water requirement per unit of irrigated land is the difference between total crop water requirements and the part supplied by precipitation. This is largely driven by the cropping intensity, or the ratio of harvested irrigated crop area over irrigated crop area<ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref><ref>Fischer, G., Tubiello, F. N., van Velthuizen, H., & Wiberg, D. A. (2007). Climate change impacts on irrigation water requirements: Effects of mitigation, 1990-2080. Technological Forecasting and Social Change, 74(7), 1083–1107. https://doi.org/10.1016/j.techfore.2006.05.021</ref>[[File:WaterRequirementsPerIrrigatedLand.png\|frame\|center\|Drivers of water requirements per unit of irrigated land]]

	Water use per unit of irrigated land in IFs is ~~estimated using a linear regression between agricultural~~ water ~~withdrawals (dependent variable) and irrigated land (independent variable). The details of the regression are shown below.~~		Water use per unit of irrigated land in IFs is driven by the shadow water price:

	~~The regression used to forecast~~ agricultural ~~water demand uses the following data:~~		:<math>waterperha_{r}=\frac{WATDEMAND_{r,agriculture}}{LANDIRAREAACTUAL_{r}}(1+(percentincreaseinprice_{r}watdemandelas_{r,agricultural}))</math>

	~~'''SeriesLandIrAreaEquip'''~~		Where waterperha is the water requirements per hectare of irrigated land, WATDEMAND is agricultural water demand, LANDIRAREAACTUAL is the area of irrigated land, percentincreaseinprice is the change in water price, and watdemandelas is the elasticity between water price and agricultural water demand, which is -0.1 unless otherwise specified by the user.

	*'''Definition: '''Area equipped for irrigation: total (1000 ha)
	*Source: AQUASTAT
	*'''Units:''' 1000 ha

	~~'''SeriesLandIrActual%Equip'''~~

	*'''Definition: '''Area equipped for irrigation: actually irrigated,~~ %~~
	*Source: AQUASTAT
	*'''Units:''' Percent

	~~'''SeriesWaterWithdAgriculture'''~~

	*'''Definition: '''Agricultural water withdrawal
	*Source: AQUASTAT
	*'''Units:''' Cubic Km

	~~We use a linear formulation for this regression. The results are shown below.[[File:WaterWithDAgRegression.png\|frame\|right\|Regression used to forecast~~ agricultural water demand]]

	~~We use this regression to calculate~~ the ~~expected level~~ of agricultural water demand ~~(given land under irrigation) in~~ the ~~first year. This residual is then applied in every subsequent year as a multiplier~~.

	==== Irrigation efficiency ====		==== Irrigation efficiency ====

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	:<math>LANDIRAREAEQUIP_{r}=</math>		:<math>LANDIRAREAEQUIP_{r}=</math>
	:<math>\frac{((21-year)(slandirareaequip_{r}LandIrAreaEquipGR_{r}))+((year-1)(Prediction_{r}LandIrAreaEquipResid_{r}))}{20}</math>		:<math>\frac{((21-year)(slandirareaequip_{r}LandIrAreaEquipGR_{r}))+((year-1)(Prediction_{r}LandIrAreaEquipResid_{r}))}{20}</math>

	Else		Else

	:<math>LANDIRAREAEQUIP_{r}=Prediction_{r}*LandIrAreaEquip_{r}</math>		:<math>LANDIRAREAEQUIP_{r}=Prediction_{r}*LandIrAreaEquip_{r}</math>

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	:<math>LANDIRAREAEQUIP_{r}=LANDIRAREAEQUIP_{r}</math>		:<math>LANDIRAREAEQUIP_{r}=LANDIRAREAEQUIP_{r}</math>
	:<math>((1+\frac{WATPRICE_{r,t=1}-100}{100})*landirareaequipelas_{r})</math>		:<math>((1+\frac{WATPRICE_{r,t=1}-100}{100})landirareaequipelas_{r})</math>
	:<math>((1+\frac{FPRI_{r,crop}-100}{100})*0.01)</math>		:<math>((1+\frac{FPRI_{r,crop}-100}{100})0.01)</math>

	Where WATPRICE is the shadow water price index, FPRI is the shadow food price index for crops, and landirareaequipelas is the elasticity between water price and land equipped for irrigation, which is initialized at -0.15.		Where WATPRICE is the shadow water price index, FPRI is the shadow food price index for crops, and landirareaequipelas is the elasticity between water price and land equipped for irrigation, which is initialized at -0.15.

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	If Year < 21 then		If Year < 21 then

	:<math>LANDIRAREAEQUIP_{r}=</math>		:<math>LANDIRAREAEQUIP_{r}=</math>
	:<math>\frac{((21-year)(slandirareaequip_{r}LandIrAreaEquipGR_{r}))+((year-1)(Prediction_{r}LandIrAreaEquipResid_{r}))}{20}</math>		:<math>\frac{((21-year)(slandirareaequip_{r}LandIrAreaEquipGR_{r}))+((year-1)(Prediction_{r}LandIrAreaEquipResid_{r}))}{20}</math>
			Else
			:<math>LANDIRAREAEQUIP_{r}=Prediction_{r}*LandIrAreaEquip_{r}</math>

			In all years, the variable is then adjusted based on changes to water price and food price.

			:<math>LANDIRAREAEQUIP_{r}=LANDIRAREAEQUIP_{r}</math>
			:<math>((1+\frac{WATPRICE_{r,t=1}-100}{100})*landirareaequipelas_{r})</math>
			:<math>((1+\frac{FPRI_{r,crop}-100}{100})*0.01)</math>

			Where WATPRICE is the shadow water price index, FPRI is the shadow food price index for crops, and landirareaequipelas is the elasticity between water price and land equipped for irrigation, which is initialized at -0.15.

			And it is then multiplied by a parameter (landirareaequipm, default value of 1).

	==== Water requirement per unit of irrigated land (WRCI) ====		==== Water requirement per unit of irrigated land (WRCI) ====

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	:<math>LANDIRAREAACTUAL_{r}=slandirareaactualpercent_{r}LANDIRAREAEQUIP_{r}\mathbf{landirareaactualm_{r}}</math>		:<math>LANDIRAREAACTUAL_{r}=slandirareaactualpercent_{r}LANDIRAREAEQUIP_{r}\mathbf{landirareaactualm_{r}}</math>



	Where LANDIRAREAACTUAL is the area of land irrigated, slandirareaactualpercent is the portion of land equipped for irrigation that is irrigated (sometimes called the ‘utilization intensity’), LANDIRAREAEQUIP is the area of land equipped for irrigation, and landirareaactualm is a parameter that allows the user to exogenously impact the area of irrigated land.		Where LANDIRAREAACTUAL is the area of land irrigated, slandirareaactualpercent is the portion of land equipped for irrigation that is irrigated (sometimes called the ‘utilization intensity’), LANDIRAREAEQUIP is the area of land equipped for irrigation, and landirareaactualm is a parameter that allows the user to exogenously impact the area of irrigated land.
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	For the first 20 years of the projection, the historical growth rate of land equipped for irrigation drives land equipped for irrigation, but with a diminishing effect. This effect decreases to zero over 20 years. After 20 years, land equipped for irrigation is driven entirely by the predicted value (using precipitation), water price, and food price. The equation below describes how LANDIRAREAEQUIP is calculated as a weighted average of the predicted value based on the level of precipitation, and the extrapolated value based on the historical growth rate. In the first year of the forecast the value is driven entirely by the historical growth rate, and by year 20 of the forecast, the variable is driven entirely by the regression described above.		For the first 20 years of the projection, the historical growth rate of land equipped for irrigation drives land equipped for irrigation, but with a diminishing effect. This effect decreases to zero over 20 years. After 20 years, land equipped for irrigation is driven entirely by the predicted value (using precipitation), water price, and food price. The equation below describes how LANDIRAREAEQUIP is calculated as a weighted average of the predicted value based on the level of precipitation, and the extrapolated value based on the historical growth rate. In the first year of the forecast the value is driven entirely by the historical growth rate, and by year 20 of the forecast, the variable is driven entirely by the regression described above.

			If Year < 21 then
			:<math>LANDIRAREAEQUIP_{r}=</math>
			:<math>\frac{((21-year)(slandirareaequip_{r}LandIrAreaEquipGR_{r}))+((year-1)(Prediction_{r}LandIrAreaEquipResid_{r}))}{20}</math>

	==== Water requirement per unit of irrigated land (WRCI) ====		==== Water requirement per unit of irrigated land (WRCI) ====

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	Wastewater that is treated but not directly reused is then added to exploitable surface water resources.		Wastewater that is treated but not directly reused is then added to exploitable surface water resources.

	<math>WATRESEXPLOITRENEW_{surface}=</math><math>WATRESEXPLOITRENEW_{surface}+WASTEWATERSUPPLY_{treated}-WASTEWATERSUPPLY_{TreatedAndReused}</math>		:<math>WATRESEXPLOITRENEW_{surface}=</math><math>WATRESEXPLOITRENEW_{surface}+WASTEWATERSUPPLY_{treated}-WASTEWATERSUPPLY_{TreatedAndReused}</math>

	Wastewater supply is calculated for all years using the same regressions described above for all years. The residuals for each of the equations do not change. The only way to increase supply of wastewater is to adjust municipal demand (which will affect total wastewater produced) or to adjust the wastewaterportiontreated parameter. This parameter is initialized as 1 but can be adjusted by the user. If the user does not change this parameter, the portion of produced wastewater that is treated will be driven by GDP per capita. If the user changes this to a value between 0 and 1 then that is the portion of produced wastewater that is treated.		Wastewater supply is calculated for all years using the same regressions described above for all years. The residuals for each of the equations do not change. The only way to increase supply of wastewater is to adjust municipal demand (which will affect total wastewater produced) or to adjust the wastewaterportiontreated parameter. This parameter is initialized as 1 but can be adjusted by the user. If the user does not change this parameter, the portion of produced wastewater that is treated will be driven by GDP per capita. If the user changes this to a value between 0 and 1 then that is the portion of produced wastewater that is treated.
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	If '''wastewaterportiontreated''' != 1 Then		If '''wastewaterportiontreated''' != 1 Then

	<math>WASTEWATERSUPPLY_{treated,r}=WASTEWATER_{produced,r}*\mathbf{wastewaterportiontreated_r}</math>		:<math>WASTEWATERSUPPLY_{treated,r}=WASTEWATER_{produced,r}*\mathbf{wastewaterportiontreated_r}</math>

	Else		Else

	<math>WASTEWATERSUPPLY_{treated,r}=WASTEWATERSUPPLY_{produced,r}*TF(GDPPCP_r)</math>		:<math>WASTEWATERSUPPLY_{treated,r}=WASTEWATERSUPPLY_{produced,r}*TF(GDPPCP_r)</math>

	We use a log function of GDP per capita to forecast the portion of wastewater that is treated.		We use a log function of GDP per capita to forecast the portion of wastewater that is treated.
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	Treated wastewater is also affected by changes in the water price index, using a 0.5 elasticity. The equation below shows the water price index effect on treated wastewater. Treated wastewater is also bound by produced wastewater – a country cannot treat more wastewater than is produced.		Treated wastewater is also affected by changes in the water price index, using a 0.5 elasticity. The equation below shows the water price index effect on treated wastewater. Treated wastewater is also bound by produced wastewater – a country cannot treat more wastewater than is produced.

	<math>WASTEWATERSUPPLY_{r,treated,t+1}=</math><math>Min(WASTEWATERSUPPLY_{r,produced},WASTEWATERSUPPLY_{r,treated,t}(1+(IncreaseInPrice0.05))</math>		:<math>WASTEWATERSUPPLY_{r,treated,t+1}=</math><math>Min(WASTEWATERSUPPLY_{r,produced},WASTEWATERSUPPLY_{r,treated,t}(1+(IncreaseInPrice0.05))</math>

	==== 3.2.3 Non-renewable (fossil) water withdrawals ====		==== 3.2.3 Non-renewable (fossil) water withdrawals ====
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	For some countries, we have data on fossil water withdrawals but not fossil water resources. This creates problems in the forecast since future water withdrawals are based on remaining fossil water resources. For these countries, we estimate that their total fossil water resources are 10 times their current fossil water withdrawals.		For some countries, we have data on fossil water withdrawals but not fossil water resources. This creates problems in the forecast since future water withdrawals are based on remaining fossil water resources. For these countries, we estimate that their total fossil water resources are 10 times their current fossil water withdrawals.

	<math>WATERRESFOSSIL = 10*WATERWITHDRAWAL_{fossil}</math>		:<math>WATERRESFOSSIL = 10*WATERWITHDRAWAL_{fossil}</math>

	We model fossil water in IFs using a stock and flow dynamic. Total fossil water resources are used as a stock and fossil water withdrawal is the flow. Fossil water withdrawals increase at a one percent growth rate. This increase is bounded by the total supply of fossil water remaining. A country cannot extract more than one seventh of their remaining fossil water resources in any year. This number is taken from current fossil water extraction rates. The highest rate of extraction globally, occurring in the Nubian Sandstone Aquifer, is about one seventh of remaining resources.<ref>UNESCO Non-Renewable Groundwater Resources. 2006. < http://portalsostenibilidad.upc.edu/archivos/fichas/informes/aguassubterraneasnorenovables.guiagestion..pdf></ref>		We model fossil water in IFs using a stock and flow dynamic. Total fossil water resources are used as a stock and fossil water withdrawal is the flow. Fossil water withdrawals increase at a one percent growth rate. This increase is bounded by the total supply of fossil water remaining. A country cannot extract more than one seventh of their remaining fossil water resources in any year. This number is taken from current fossil water extraction rates. The highest rate of extraction globally, occurring in the Nubian Sandstone Aquifer, is about one seventh of remaining resources.<ref>UNESCO Non-Renewable Groundwater Resources. 2006. < http://portalsostenibilidad.upc.edu/archivos/fichas/informes/aguassubterraneasnorenovables.guiagestion..pdf></ref>

	<math>WATERWITHDRAWAL_{t+1,f}=</math><math>Min(WATERWITHDRAWAL_{t,f}*1.01,\frac{WATERRESFOSSIL}{7})</math>		:<math>WATERWITHDRAWAL_{t+1,f}=</math><math>Min(WATERWITHDRAWAL_{t,f}*1.01,\frac{WATERRESFOSSIL}{7})</math>

	The subscript f represents fossil water.		The subscript f represents fossil water.
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	Desalinated water grows at an 8% growth rate, but this growth rate diminished over time. Desalinated water cannot decrease faster than 2% per year. Desalinated water increases based on an 8 percent growth rate ('''waterdesalinatedgr''') which can be changed by the user. Growth in desalinated water is also adjusted based on the change in the water price index, using a 0.5 elasticity.		Desalinated water grows at an 8% growth rate, but this growth rate diminished over time. Desalinated water cannot decrease faster than 2% per year. Desalinated water increases based on an 8 percent growth rate ('''waterdesalinatedgr''') which can be changed by the user. Growth in desalinated water is also adjusted based on the change in the water price index, using a 0.5 elasticity.

	<math>WATERDESALINATED_{r,t+1}=</math> <math>Min(WATERDESALINATED_{r,t}(1+(IncreaseInPrice0.05)),WASTERDESALINATED_{r,t}*(1+(\frac{\mathbf{waterdesalinated_r}}{100})))</math>		:<math>WATERDESALINATED_{r,t+1}=</math> <math>Min(WATERDESALINATED_{r,t}(1+(IncreaseInPrice0.05)),WASTERDESALINATED_{r,t}*(1+(\frac{\mathbf{waterdesalinated_r}}{100})))</math>

	Total water supply (WATERTOTALSUPPLY) is then calculated as the sum of these 5 water sources i.e. reused water, desalinated water, surface water, ground water, and fossil water.		Total water supply (WATERTOTALSUPPLY) is then calculated as the sum of these 5 water sources i.e. reused water, desalinated water, surface water, ground water, and fossil water.

	<math>WATERTOTALSUPPLY=WASTEWATER_{TreatedAndReused}+DESALINATEDWATER+</math> <math>WATERWITHDRAWAL_{Surface}+WASTERWITHDRAWAL_{Ground}+WATERWITHDRAWAL_{FossilGround}</math>		:<math>WATERTOTALSUPPLY=WASTEWATER_{TreatedAndReused}+DESALINATEDWATER+</math>
			:<math>WATERWITHDRAWAL_{Surface}+WASTERWITHDRAWAL_{Ground}+WATERWITHDRAWAL_{FossilGround}</math>

	Because of the way we define water supply, demand can exceed supply of water resources. This usually means that the country is over exploiting their resources. This means that the country is using more surface water then their available yield, or withdrawing groundwater faster than the recharge rate. There are currently 23 countries that are over exploiting their water resources on a national level. It should be noted however, that since we are only looking at the national scale, local over-exploitation is not captured. This is particularly relevant to China and India—countries where over-exploitation is known to occur but not captured in our analysis. The top 5 countries in terms of national water exploitation are: Turkmenistan, Singapore, Egypt, Uzbekistan, and Syria, respectively.<ref>Singapore imports water from Malaysia. Water imports are not yet captured in the model.</ref>		Because of the way we define water supply, demand can exceed supply of water resources. This usually means that the country is over exploiting their resources. This means that the country is using more surface water then their available yield, or withdrawing groundwater faster than the recharge rate. There are currently 23 countries that are over exploiting their water resources on a national level. It should be noted however, that since we are only looking at the national scale, local over-exploitation is not captured. This is particularly relevant to China and India—countries where over-exploitation is known to occur but not captured in our analysis. The top 5 countries in terms of national water exploitation are: Turkmenistan, Singapore, Egypt, Uzbekistan, and Syria, respectively.<ref>Singapore imports water from Malaysia. Water imports are not yet captured in the model.</ref>
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	We pull in data on surface water withdrawal, groundwater withdrawal, and total water withdrawal from Aquastat. Since total water withdrawal is the sum of surface water withdrawal and groundwater withdrawal, we can estimate surface water withdrawal if we have total water withdrawal and groundwater withdrawal. Likewise, if we have total water withdrawal and groundwater withdrawal we can estimate surface water withdrawal. Since, however, Aquastat does not differentiate between renewable groundwater withdrawal and fossil groundwater withdrawal we must first subtract fossil water withdrawal from groundwater withdrawal using other data.		We pull in data on surface water withdrawal, groundwater withdrawal, and total water withdrawal from Aquastat. Since total water withdrawal is the sum of surface water withdrawal and groundwater withdrawal, we can estimate surface water withdrawal if we have total water withdrawal and groundwater withdrawal. Likewise, if we have total water withdrawal and groundwater withdrawal we can estimate surface water withdrawal. Since, however, Aquastat does not differentiate between renewable groundwater withdrawal and fossil groundwater withdrawal we must first subtract fossil water withdrawal from groundwater withdrawal using other data.

	<math>WATERWITHDRAWAL_{Ground}=</math> <math>WATERWITHDRAWAL_{Ground}-WATERWITHDRAWAL_{FossilGround}</math>		:<math>WATERWITHDRAWAL_{Ground}=</math> <math>WATERWITHDRAWAL_{Ground}-WATERWITHDRAWAL_{FossilGround}</math>

	If we have data on total water withdrawals but not surface water withdrawals and groundwater withdrawals then we estimate using global averages. We assume that 67% of a country’s water withdrawals come from surface water and 33% come from groundwater. If we do not have data on total water withdrawals we assume that a country’s total water withdrawals are equivalent to their total water demand. We then use the same global averages to determine which portion of this demand is met by surface water and which portion is met by groundwater. We do not yet reconcile total water demand with total water withdrawals, though, theoretically, they should be equivalent.		If we have data on total water withdrawals but not surface water withdrawals and groundwater withdrawals then we estimate using global averages. We assume that 67% of a country’s water withdrawals come from surface water and 33% come from groundwater. If we do not have data on total water withdrawals we assume that a country’s total water withdrawals are equivalent to their total water demand. We then use the same global averages to determine which portion of this demand is met by surface water and which portion is met by groundwater. We do not yet reconcile total water demand with total water withdrawals, though, theoretically, they should be equivalent.

← Older revision		Revision as of 20:02, 7 September 2018
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	Since total renewable water resources does not account for the overlap between surface water and groundwater, we must recalculate total renewable water resources by subtracting this overlap. We then recalculate total renewable surface water and total renewable groundwater using this adjusted total.		Since total renewable water resources does not account for the overlap between surface water and groundwater, we must recalculate total renewable water resources by subtracting this overlap. We then recalculate total renewable surface water and total renewable groundwater using this adjusted total.

	<math>WATRESTOTALRENEW_{r,w} = \frac{WATRESTOTALRENEW_{r,w}}{WATRESTOTALRENEW(Overlap)}*WATRESTOTALRENEW(No Overlap)</math>		:<math>WATRESTOTALRENEW_{r,w} = \frac{WATRESTOTALRENEW_{r,w}}{WATRESTOTALRENEW(Overlap)}*WATRESTOTALRENEW(No Overlap)</math>

	It is not possible, however, for exploitable water resources (excluding secondary water) to reach the TRWR limit. While exploitable water resources can increase, we assume that it cannot grow by more than 20%. We also assume that exploitable water resources cannot grow by more than .5% per year and that only one fortieth of remaining resources can be extracted in any year. Thus, the equation for exploitable water resources is:		It is not possible, however, for exploitable water resources (excluding secondary water) to reach the TRWR limit. While exploitable water resources can increase, we assume that it cannot grow by more than 20%. We also assume that exploitable water resources cannot grow by more than .5% per year and that only one fortieth of remaining resources can be extracted in any year. Thus, the equation for exploitable water resources is:

	<math>WATRESEXPLOITRENEW_{r,w}=</math> <math>Min(WATRESEXPLOITRENEW_{t-1,w}*1.005,((\frac{MaxExploitRenew_w-WATRESEXPLOITRENEW_{t-1,w}}{40}))+WATRESEXPLOITRENEW_{t-1,w}))</math>		:<math>WATRESEXPLOITRENEW_{r,w}=</math> <math>Min(WATRESEXPLOITRENEW_{t-1,w}*1.005,((\frac{MaxExploitRenew_w-WATRESEXPLOITRENEW_{t-1,w}}{40}))+WATRESEXPLOITRENEW_{t-1,w}))</math>

	Where		Where

	<math>MaxExploitRenew_{w,r}=\mathbf{iwatresexploitrenew_{w,r}}*1.2</math>		:<math>MaxExploitRenew_{w,r}=\mathbf{iwatresexploitrenew_{w,r}}*1.2</math>

	iwatresexploitrenew is the exploitable renewable water resources in the first year. The subscript “w” represents that the variable is dimensioned in terms of surface and ground water. We also include a parameter, watresexploitrenewm on the total volume of exploitable water resources so that the user may increase or decrease this supply over time. After this growth rate is applied to exploitable surface water resources the secondary component is added to WATRESEXPLOITRENEW (surface). Secondary water is the total volume of treated wastewater that is not directly reused.		iwatresexploitrenew is the exploitable renewable water resources in the first year. The subscript “w” represents that the variable is dimensioned in terms of surface and ground water. We also include a parameter, watresexploitrenewm on the total volume of exploitable water resources so that the user may increase or decrease this supply over time. After this growth rate is applied to exploitable surface water resources the secondary component is added to WATRESEXPLOITRENEW (surface). Secondary water is the total volume of treated wastewater that is not directly reused.
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	The equation below describes the forecast equation for surface water withdrawals. It is calculated as the minimum of two terms: the previous year’s surface water withdrawals multiplied by 20 percent of the GDP growth rate of the country, and one seventh of the remaining exploitable potential plus the current level of withdrawal.		The equation below describes the forecast equation for surface water withdrawals. It is calculated as the minimum of two terms: the previous year’s surface water withdrawals multiplied by 20 percent of the GDP growth rate of the country, and one seventh of the remaining exploitable potential plus the current level of withdrawal.

	<math>WATERWITHDRAWAL_{r,surface,t+1}=</math> <math>Min(WATERWITHDRAWAL_{r,surface,t}1+0.2IGDP_r),\frac{RemainingPotentialExploitable}{7}+WATERWITHDRAWAL_{r,surface,t})</math>		:<math>WATERWITHDRAWAL_{r,surface,t+1}=</math> <math>Min(WATERWITHDRAWAL_{r,surface,t}1+0.2IGDP_r),\frac{RemainingPotentialExploitable}{7}+WATERWITHDRAWAL_{r,surface,t})</math>

	In the second case, where surface water withdrawals exceed the exploitable surface water limit, they are forced to converge to the exploitable limit over a 50-year time horizon. This time horizon is a parameter in the model (waterrenewconverge) that can be adjusted by the user.		In the second case, where surface water withdrawals exceed the exploitable surface water limit, they are forced to converge to the exploitable limit over a 50-year time horizon. This time horizon is a parameter in the model (waterrenewconverge) that can be adjusted by the user.

	<math>WATERWITHDRAWAL_{r,surface,t+1}=</math> <math>WATERWITHDRAWAL_{r,surface,t}-(\frac{WATERWITHDRAWAL_{r,surface,t}-WATRESEXPLOITRENEW_{r,surface}}{\mathbf{waterrenewconverge}_{r,surface}})</math>		:<math>WATERWITHDRAWAL_{r,surface,t+1}=</math> <math>WATERWITHDRAWAL_{r,surface,t}-(\frac{WATERWITHDRAWAL_{r,surface,t}-WATRESEXPLOITRENEW_{r,surface}}{\mathbf{waterrenewconverge}_{r,surface}})</math>

	Where '''waterrenewconverge''' is the 50-year default convergence time.[[File:WaterwithdrawWhenWDExceedLimit.jpg\|frame\|right\|645x425px\|Conceptual model for forecasting water withdrawals when withdrawals exceed exploitable limit.]]		Where '''waterrenewconverge''' is the 50-year default convergence time.[[File:WaterwithdrawWhenWDExceedLimit.jpg\|frame\|right\|645x425px\|Conceptual model for forecasting water withdrawals when withdrawals exceed exploitable limit.]]
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	If groundwater withdrawals are less than the exploitable limit:		If groundwater withdrawals are less than the exploitable limit:

	<math>WATERWITHDRAWAL_{r,ground,t+1}=</math> <math>Min(WATERWITHDRAWAL_{r,ground,t}(1+0.2IGDP_r),\frac{RemainingPotentialExploitable}{7}+WATERWITHDRAWAL_{r,ground,t})</math>		:<math>WATERWITHDRAWAL_{r,ground,t+1}=</math> <math>Min(WATERWITHDRAWAL_{r,ground,t}(1+0.2IGDP_r),\frac{RemainingPotentialExploitable}{7}+WATERWITHDRAWAL_{r,ground,t})</math>

	If groundwater withdrawals exceed the exploitable limit:		If groundwater withdrawals exceed the exploitable limit:

	<math>WATERWITHDRAWAL_{r,ground,t+1}=</math> <math>WATERWITHDRAWAL_{r,ground,t}-\frac{WATERWITHDRAWAL_{r,ground,t}-WATRESEXPLOITRENEW_{r,ground}}{\mathbf{waterrenewconverge_{r,ground}}}</math>		:<math>WATERWITHDRAWAL_{r,ground,t+1}=</math> <math>WATERWITHDRAWAL_{r,ground,t}-\frac{WATERWITHDRAWAL_{r,ground,t}-WATRESEXPLOITRENEW_{r,ground}}{\mathbf{waterrenewconverge_{r,ground}}}</math>

	Both surface and groundwater withdrawals are adjusted based on the change in the water price index. A 0.5 elasticity is applied to the change in the water price index, which is then applied to both surface water withdrawals and groundwater withdrawals. Again, however, neither is permitted to grow faster than one seventh of the remaining exploitable potential.		Both surface and groundwater withdrawals are adjusted based on the change in the water price index. A 0.5 elasticity is applied to the change in the water price index, which is then applied to both surface water withdrawals and groundwater withdrawals. Again, however, neither is permitted to grow faster than one seventh of the remaining exploitable potential.

	<math>WATERWITHDRAWAL_{r,surface}=</math> <math>Min(WATERWITHDRAWAL_{r,surface}(1+(IncreaseInPrice0.05)),</math><math>{\frac{WATERWITHDRAWAL_{r,surface}-WATRESEXPLOITRENEW_{r,surface}}{7}})+WATERWITHDRAWAL_{r,surface}</math>		:<math>WATERWITHDRAWAL_{r,surface}=</math> <math>Min(WATERWITHDRAWAL_{r,surface}(1+(IncreaseInPrice0.05)),</math><math>{\frac{WATERWITHDRAWAL_{r,surface}-WATRESEXPLOITRENEW_{r,surface}}{7}})+WATERWITHDRAWAL_{r,surface}</math>

	The same logic and elasticity is applied to groundwater:		The same logic and elasticity is applied to groundwater:

	<math>WATERWITHDRAWAL_{r,ground}=</math> <math>Min(WATERWITHDRAWAL_{r,ground}(1+(IncreaseInPrice0.05)),</math><math>{\frac{WATERWITHDRAWAL_{r,ground}-WATRESEXPLOITRENEW_{r,ground}}{7}})+WATERWITHDRAWAL_{r,ground}</math>		:<math>WATERWITHDRAWAL_{r,ground}=</math> <math>Min(WATERWITHDRAWAL_{r,ground}(1+(IncreaseInPrice0.05)),</math><math>{\frac{WATERWITHDRAWAL_{r,ground}-WATRESEXPLOITRENEW_{r,ground}}{7}})+WATERWITHDRAWAL_{r,ground}</math>

	=== Wastewater ===		=== Wastewater ===