- freely available
Sustainability 2017, 9(3), 456; doi:10.3390/su9030456
2. Materials and Methods
2.1. Modeling System
2.1.1. Hydrologic Model and Reservoir Module
2.1.2. Irrigation and Plant Growth Module
2.1.3. Economic Module
2.2. Climate Change
2.2.1. Delta Method
Conflicts of Interest
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|Parameters/Units||Inputs and Equations with Descriptions|
|Inflow (m3/day)||Input graphically using output data from the MESH hydrologic model on a daily time step.|
|Reservoir (m3)||Initial reservoir volume calculated based on cumulative output from the MESH hydrologic model from 1 January–14 April.|
|Outflow (m3/day)||=(3 × Weir_Coefficient × Length × Height1.5 × 86,400) − (Evaporation × Reservoir_Area)|
|The established engineering equation for discharge over a rectangular weir was multiplied by 86,400 to convert from m3/s to m3/day. Evaporation over the reservoir area was subtracted from the discharge equation .|
|Weir Coefficient (dimensionless)||=0.6, An established engineering value was used.|
|Length (m)||=12, Spillway length was taken from the engineering drawings for the Pelly’s Lake weir.|
|Height (m)||=IF (Reservoir Elevation − Spillway Elevation) > 0 THEN (Reservoir Elevation − Spillway Elevation) ELSE 0, An established engineering equation.|
|Reservoir Elevation (m)||=9 × 10−7 × Reservoir + 378.23|
|This equation was determined from the engineering storage rating curve for the Pelly’s Lake weir.|
|Spillway Elevation (m)||=379.1, This value was provided on the engineering drawings for the Pelly’s Lake weir.|
|Evaporation (m3/day)||=0.00182 (April)|
|Mean monthly evaporation values from 1981–2010 were converted to daily values at Brandon, MB . These values were used due to insufficient data available to calculate evaporation at the study site.|
|Reservoir Area (m2)||=85,867,480, calculated in ArcGIS.|
|Irrigation Abstraction (m3/day)||=Abstraction[Canola] + Abstraction[Wheat] + Abstraction[Barley]|
+ Abstraction[Alfalfa], This variable calculated the total water abstraction volume abstracted from the reservoir.
|Abstraction [Crop]||=Max Abstraction Amount × Fraction Abstraction|
This equation calculated irrigation withdrawal volumes for each crop.
|Max Abstraction Amount (m3)||=15,000, this amount was calibrated to allow the reservoir to drain at a rate to provide sufficient water for irrigation for the entire growing season.|
|Fraction Abstraction [Crop](dimensionless)||=IF ((Switch[Canola] + Switch[Wheat] + Switch[Barley] + Switch[Alfalfa]) > 0) THEN(Switch[Crop] × Fraction_Crop_Area[Crop]/(Switch[Canola] × Fraction_Crop_Area[Canola] + Switch[Wheat] × Fraction_Crop_Area[Wheat] + Switch[Barley] × Fraction_Crop_Area[Barley] + Switch[Alfalfa] × Fraction_Crop_Area[Alfalfa])) ELSE (0)|
|When water requirements were not being met by a specific crop, this algorithm directed water withdrawals to the crop requiring irrigation. It also ensured water was not applied unless required to optimize crop growth.|
|Fraction Crop Area||=0.46 (Canola)|
|Historical patterns of crop production in Manitoba were used to determine the fraction of total crop area each crop comprised [37,55].|
|Switch[Crop]||=IF (Actual Yield < Gap × Optimum Yield AND TIME > 30 THEN 1 ELSE 0|
|Irrigation was triggered for a specific crop if the crop’s actual yield fell below 80% of optimum yield on day 30 (15 May).|
|Gap||=0.8, Irrigation application occurred when available water only allowed for 80% or less of optimum yield growth. Yield reductions due to water stress occur when available water falls below 60% of optimum plant requirements. The threshold of 80% ensured there was always sufficient water available to the plant .|
|Irrigation (mm/day)||=(Irrigation Abstraction/Crop Area) × 1000|
|This equation served to convert irrigation from a volume to a depth.|
|Crop Area (m2)||=66,976,634, This was calculated in ArcGIS using data on land use downloaded from the Manitoba Land Initiative .|
|Plant Growth Module|
|Rain Depth (mm/day)||Input graphically using values from Environment and Climate Change Canada for Holland, MB .|
|Water Available [Crop] (mm/day)||=Rain Depth + Irrigation × Fraction Abstraction|
|Daily water available for crop growth .|
|Available Water Depth [Crop] (mm)||Initial value set at 0. Snowmelt would contribute to initial spring soil moisture, however for the purposes of the model soil moisture was assumed to be recharged solely from precipitation and/or irrigation water.|
|Water Sufficiency Curve [Crop]||These curves were input graphically and represented the unique optimal water requirements of each crop. They allowed for crop yield to be calculated based on water availability .|
|Max Yield [Crop](tonnes/m2)||= 0.000224124 (Canola)|
= 0.000336063 (Wheat)
|Max yield values were held constant for all simulations .|
|Actual Yield [Crop] (tonnes/hectare)||=Max Yield × Water Sufficiency Curve × 10,000|
|Crop yield was calculated based on water availability. Each crop’s water sufficiency curve provided a proportion of maximum growth based on water availability. This proportion was multiplied by max yield and 10,000 to convert from m2 to hectares.|
|Optimum Yield [Crop]||For each crop, values were input graphically. The variable represented the maximum yield of each crop over time when its water requirements were being met. Values were constant for all simulations.|
|Gross Income [Crop] ($)||=Actual Yield × Price × Crop Area × Fraction Crop Area/10,000|
Calculated landscape level gross income.
|Price [Crop] ($/tonne)||=418.87 (Canola)|
|Crop prices were not available for years before 2015. Thus, 2015 crop prices were used in all simulations .|
|RCP2.6||Radiative forcing will peak at approximately 3 W/m2 before 2100 and then levels will decline.|
|RCP4.5||Radiative forcing will stabilize at 4.5 W/m2 after 2100.|
|RCP6||Radiative forcing will stabilize at 6 W/m2 after 2100.|
|RCP8.5||Radiative forcing will rise resulting in 8.5 W/m2 in 2100.|
|Modeling Center||Institute ID||Model Name|
|Canadian Centre for Climate Modeling and Analysis||CCCMA||CanESM2|
|Meteorological Office Hadley Centre||MOHC||HadGEM2-ES|
|Max Planck Institute for Meteorology||MPI-M||MPI-ESM-LR|
|NOAA Geophysical Fluid Dynamics Laboratory||NOAA GFDL||GFDL-ESM2G|
|Decade||Mean Precipitation Total (mm)||Incremental Increase %||Mean Temperature (°C)||Temperature Increase (°C)|
|Year||Difference in Crop Gross Margins without Irrigation and Crop Gross Margins with Irrigation and Associated Variable and Infrastructure Costs ($/hectare)||Increase in Crop Gross Margins under Irrigation ($/hectare)|
|Year||Difference in Crop Gross Margins without Irrigation and Crop Gross Margins with Irrigation and Associated Variable and Infrastructure Costs ($/hectare)||Increase in Crop Gross Margins under Irrigation ($/hectare)|
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