ASCROM package documentation
Package ASCROM for vle-2.0.2
The ASCROM package provide four atomic models called
ClimaticWaterDemand, IrrigationDemand,
ActualIrrigation, WaterFlows and their
corresponding configuration in order to facilitate the use of the
models.
These four atomic models are intended to be coupled to simulate the
atmosphere/soil/plant system.
This coupled model is intended as an alternative to the Stics model when
testing the above and below ground water flows.
References: “Crop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56” - See documentation http://www.fao.org/3/X0490E/X0490E00.htm#Contents
ASCROM coupled model
Table of Contents
- Package dependencies
- Atomic model ClimaticWaterDemand
- Atomic model WaterFlows
- Atomic model IrrigationDemand
- Atomic model ActualIrrigation
- Atomic model Yield
- Atomic model Pond
- Atomic model IrrigationPriority
- Atomic model FarmIrrigationManager
- Annexe
Atomic model ClimaticWaterDemand
The ClimaticWaterDemand model (using extension class
DiscreteTimeDyn)
calculates the daily potential evapotranspiration. This calculation is
split in two parts: calculation of the potential crop transpiration and
calculation of the potential soil evaporation. We use the generic
approach based on Kcb (basal crop coefficient) and proposed by FAO
method, to estimate the potential transpiration. We calculate a
coefficient Ke to estimate the potential evaporation of soil. This model
also handles the dynamic of crop growth (growth of roots ).
Configuring a ClimaticWaterDemand Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| SoilDepth | double | [x] | soil depth [double] [m] |
| REW1 | double | [x] | soil surface layer readily evaporable water. Cumulative depth of evaporation (depletion) at the end of stage 1 [mm] see Table 4 |
| REW2 | double | [x] | soil deep layer readily ?? water. Cumulative depth of ?? (depletion) at the end of stage 1 [mm] see Table 4 |
| fw | double | [x] | average fraction of soil surface wetted by irrigation or light rainfalls (i.e rain < Rain_Threshold) [0.01 - 1]. If heavy rainfall, fw=1. See Table Table 4 |
| fw_Rain_Threshold | double | [x] | Rain threshold where fw=1. |
| Failure_Option | int | [x] | Choose crop failure option {0:none, 1:water, 2:yield, 3:water&yield, 4:water|yield}. |
| few_parameter | double | [] (default=1) | reference parameter for few computation. |
| isDrip | boolean | [] (default=False) | Drip option for few computation. |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- ET0 : Reference crop evapotranspiration (We
recommend to use values calculated by the Penman Monteith equation as it
is done in FAO approach) (mm.d-1) (double) (sync)
- WC_R1 : soil surface layer water content (mm)
(double) (nosync)
- WC_R2 : soil deep layer water content (mm) (double)
(nosync)
- RHmin : daily air minimal relative humidity (%)
(double) (sync)
- u2 : daily wind speed at 2m (m.s-1)
(double) (sync)
- Rain : daily rain (mm.d-1) (double) (sync)
- Is_Day_Without_Irrigation : detect if day has no
irrigation where it should have (bool) (double) (sync)
- YieldFraction : Yield/Yield_max fraction (-)
(double) (nosync)
- kcb_interp : kcb interpolation (-) (double)
(sync)
- kcini_interp : kcini interpolation (-) (double)
(sync)
- kcmid_interp : kcmid interpolation (-) (double)
(sync)
- h_interp : h interpolation (m) (double)
(sync)
- MaxDepthRoots_interp : MaxDepthRoots interpolation
(m) (double) (sync)
- Rain_Threshold_To_Reset_Days_Without_Water : water
threshold for water deficit counter. (mm) (double) (sync)
- Lethal_Threshold_Days_Without_Water : number of
days of water deficit after which the crop is failed. (days) (double)
(sync)
- Lethal_Threshold_YieldFraction : Crop YieldFraction
threshold for crop failure. (-) (double) (sync)
- NoFailurePeriod : Minimum duration since sowing before failure based on yield. (days) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- Kcb : Basal crop coefficient after specific adjustment in climates. Kcb+Ke<1,4. Kcb-Kcmin>= 0,01 (-) (double)
- h : the mean plant height during the mid or late season stage (m) (double)
- MaxDepthRoots : Maximum depth of roots (m) (double)
- kcini : () (double)
- kcmid : () (double)
- Ke : Soil evaporation coefficient. Kcb+Ke<1,4 (-) (double)
- RootDepth : Crop root depth (m) (double)
- Max_transp : Daily maximal crop transpiration (mm.d-1) (double)
- Max_evap : Daily maximal soil evaporation from soil surface layer (mm.d-1) (double)
- PET: Crop evapotranspration under standard conditions using a dual crop coefficient, one for transpiration (Kcb) and one for soil evaporation (Ke). (mm.d-1) (double)
- Kcmax : Maximum value of Kc following rain or irrigation. Kcmax [1,05 ; 1,3] (-) (double)
- Kr1 : Soil evaporation reduction coefficient. (-) (double)
- Kr2 : Soil ?? reduction coefficient. (-) (double)
- fc : Average soil fraction covered (or shaded) by vegetation [0.01 - 1] - see Table Table 3 (-) (double)
- few : Exposed and wetted soil fraction (-) (double)
- Days_Without_Water : number of consecutive days with water deficit (d) (double)
- Is_Failure_From_WaterSupply : detect if water deficit threshold has been reached for the current crop (bool) (double)
- Is_Failure_From_YieldFraction : detect if crop YieldFraction threshold has been reached for the current crop (bool) (double)
- Is_Failure : detect if crop has failed (bool) (double)
- Failure_counter : total number of failure (int) (double)
- Days_Since_Sowing : number of days since sowing (int) (double)
Details
State variables equations
Calculation of Kcb
Kcb(t) : Reference value of Kcb (after climatic correction). The calculation is first based on the linear interpolation from a set of pairs (Kc_params). In the FAO approach, the calculation is based on three pairs of values: Kcini, Kcmid, Kcend, provided in Table 1 (Annexe), and average stage durations for each crop, by climate are provided in Table 5 (Annexe).
We then also add a potential failure process based on consecutive days with water deficit (Days_Without_Water) and/or crop yield fraction (YieldFraction).
Kc evolution
\[ Is\_Failure\_From\_WaterSupply(t) = Is\_Failure\_From\_WaterSupply(t-1) | (Days\_Without\_Water(t-1) \geq Lethal\_Threshold\_Days\_Without\_Water(t)) \label{eq:Is_Failure_From_WaterSupply}\]
\[ Is\_Failure\_From\_YieldFraction(t) = Is\_Failure\_From\_YieldFraction(t-1) | (YieldFraction(t-1) \leq Lethal\_Threshold\_YieldFraction(t) \text{&} Days\_Since\_Sowing(t-1) > NoFailurePeriod(t)) \label{eq:Is_Failure_From_YieldFraction}\]
\[ Is\_Failure(t)=\left\{ \begin{array}{@{}ll@{}} (Kcb\_interp(t)>0) \text{&} Is\_Failure\_From\_WaterSupply(t), & \text{if}\ Failure\_Option=1 \\ (Kcb\_interp(t)>0) \text{&} Is\_Failure\_From\_YieldFraction(t), & \text{else if}\ Failure\_Option=2 \\ (Kcb\_interp(t)>0) \text{&} Is\_Failure\_From\_WaterSupply(t) \text{&} Is\_Failure\_From\_YieldFraction(t), & \text{else if}\ Failure\_Option=3 \\ (Kcb\_interp(t)>0) \text{&} (Is\_Failure\_From\_WaterSupply(t) \text{|} Is\_Failure\_From\_YieldFraction(t)), & \text{else if}\ Failure\_Option=4 \\ False, & \text{otherwise} \\ \end{array}\right. \label{eq:Is_Failure}\]
\[ Failure\_counter(t)=\left\{ \begin{array}{@{}ll@{}} Failure\_counter(t-1) + 1, & \text{if}\ (Is\_Failure(t-1)=0) \text{&} (Is\_Failure(t)=1) \\ Failure\_counter(t-1), & \text{otherwise} \\ \end{array}\right. \label{eq:Failure_counter}\]
\[ Days\_Without\_Water(t)=\left\{ \begin{array}{@{}ll@{}} Days\_Without\_Water(t-1), & \text{if}\ Is\_Failure(t) \\ Days\_Without\_Water = Days\_Without\_Water(t-1) + 1, & \text{else if}\ Is\_Day\_Without\_Water \\ 0, & \text{otherwise} \end{array}\right. \label{eq:Days_Without_Water}\]
with
\(Is\_Day\_Without\_Water = (Kcb\_interp(t)>0) \text{&} ((Rain(t)<Rain\_Threshold\_To\_Reset\_Days\_Without\_Water(t)) \text{&} (Is\_Day\_Without\_Irrigation(t))\)
\[ Kcb(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ Kcb\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:Kcb}\]
\[ h(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ h\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:h}\]
\[ MaxDepthRoots(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ MaxDepthRoots\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:MaxDepthRoots}\]
\[ kcini(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ kcini\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:kcini}\]
\[ kcmid(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ kcmid\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:kcmid}\]
\[ Days\_Since\_Sowing(t)=\left\{ \begin{array}{@{}ll@{}} Days\_Since\_Sowing(t-1) + 1, & \text{if}\ kcb(t) > 0 \\ 0, & \text{otherwise} \end{array}\right. \label{eq:Days_Since_Sowing}\]
Calculation of Ke
This requires the prior calculation of different variables or parameters: Kcmax, AWC1, Kr …
Kcmax: represents an upper limit on evaporation and transpiration from the cropped surface. Kcmax ranges from about 1.05 to 1.30
\[ Kcmax(t)=\max\left( \begin{array}{@{}ll@{}} 1.2 + (0.04 * (u2(t) -2) -0.004 * (RHmin(t) -45)) * (h(t)/3)^{0.3} \\ Kcb(t) + 0.05 \end{array}\right) \label{eq:Kcmax }\]
Kr1: Soil evaporation and transpiration reduction coefficient. [dimensionless] [double]
Soil evaporation and transpiration from the exposed soil can be assumed to take place in two stages: an energy limiting stage, and a falling rate stage. During Stage 1, the soil surface remains wet and evaporation and transpiration are predicted to occur at the maximum rate limited only by energy availability at the soil surface and therefore, Kr1=1. As the soil surface dries, the evaporation and transpiration rate decreases below the potential rate, and Kr1 becomes less than one. Kr1 becomes zero when no water is left for evaporation and transpiration in the top soil reservoir.
\[ Kr1(t)=\min\left( \begin{array}{@{}ll@{}} 1 \\ \frac{WC\_R1(t-1)}{REW1} \end{array}\right) \label{eq:Kr1}\]
Kr2: Soil transpiration reduction coefficient. [dimensionless] [double]
Soil transpiration from the soil deep reservoir can be assumed to take place in two stages: an energy limiting stage, and a falling rate stage. During Stage 1, the soil remains wet and transpiration is predicted to occur at the maximum rate limited only by energy availability at the soil and therefore, Kr2=1. As the soil surface dries, the transpiration rate decreases below the potential rate, and Kr2 becomes less than one. Kr2 becomes zero when no water is left for transpiration in the soil deep reservoir. \[ Kr2(t)=\min\left( \begin{array}{@{}ll@{}} 1 \\ \frac{WC\_R2(t-1)}{REW2} \end{array}\right) \label{eq:Kr2}\]
1 - fc : average exposed soil fraction not covered (or shaded) by vegetation [0.01 - 1] - see Table Table 3
fc can also be estimated using the relationship.
\[fc(t) = (\frac{Kcb(t) - Kcini(t)}{Kcmax(t) - Kcini(t)})^{1 + 0.5*h} \label{eq:fc}\]
Remark : fc()=0 when kcb()=0
few : Exposed and wetted soil fraction
\[few(t)=\left\{ \begin{array}{@{}ll@{}} \max\left( \begin{array}{@{}ll@{}} 1 - 2/3 * fc(t) \\ 0 \end{array}\right) * fw, & \text{if}\ isDrip \\ \min\left( \begin{array}{@{}ll@{}} \max\left( \begin{array}{@{}ll@{}} 1 - few\_parameter * fc(t) \\ 0 \end{array}\right) \\ fw\_Rain \end{array}\right), & \text{otherwise} \end{array}\right. \label{eq:few}\] with \[fw\_Rain=\left\{ \begin{array}{@{}ll@{}} fw, & \text{if}\ Rain(t) < fw\_Rain\_Threshold \\ 1, & \text{otherwise} \end{array}\right. \]
Ke(t): Soil evaporation coefficient, Ke, describes the evaporation component of ETP. Where the topsoil is wet, following rain or irrigation, Ke is maximal, it only depends of the energy available for the evaporation process. Where the soil surface is dry, Ke is small and even zero when no water remains near the soil surface for evaporation.
\[Ke(t)=\min\left( \begin{array}{@{}ll@{}} Kr1(t) * (Kcmax(t) - Kcb(t)) \\ few(t) * Kcmax(t) \end{array}\right) \label{eq:Ke}\]
RootDepth(t): Depth of roots (m). (0 to MaxDepthRoots)
\[RootDepth(t)=\min\left( \begin{array}{@{}ll@{}} MaxDepthRoots(t) \\ SoilDepth \\ MaxDepthRoots(t) * Kcb(t)/Kcmid(t) \end{array}\right) \label{eq:RootDepth}\]
Max_transp(t) : Maximum transpiration
\[Max\_transp(t) = Kcb(t) * ET0(t) \label{eq:Max_transp}\]
Max_evap(t) : Maximum evaporation
\[Max\_evap(t) = Ke(t) * ET0(t) \label{eq:Max_evap}\]
PET(t): Potential Evapotranspiration
\[PET(t) = Max\_transp(t) + Max\_evap(t) \label{eq:PET}\]
Atomic model WaterFlows
The WaterFlows model (using extension class DiscreteTimeDyn)
estimate water flows from climatic and irrigation demands and available
pumping water.
The water available for the crop is provided by rain and irrigation (and
soil stock).
The soil is splitted into a surface layer (where both soil evaporation
and a fraction of the total crop transpiration can occur), and a deep
layer where only remaining crop transpiration is possible.
The crop potential transpiration demand is splitted homogeneously among
the 2 soil layers according to the RootDepth.
In the case of unsatisfied transpiration demand in the surface layer,
the difference is added to the deep layer transpiration demand.
Configuring a WaterFlows Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| CurveNumber | double | [x] | RunOff CurveNumber parameter (??) |
| Ia_SoilType_param | double | [x] | RunOff Ia parameter (??) |
| TH1 | double | [x] | soil surface layer thickness (mm) |
| ThetaFC1 | double | [x] | soil surface layer water content at field capacity (%) |
| ThetaWP1 | double | [x] | soil surface layer water content wilting point (%) |
| BD1 | double | [x] | soil surface layer bulk density (-) |
| TH2 | double | [x] | soil deep layer thickness (mm) |
| ThetaFC2 | double | [x] | soil deep layer water content at field capacity (%) |
| ThetaWP2 | double | [x] | soil deep layer water content wilting point (%) |
| BD2 | double | [x] | soil deep layer bulk density (-) |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- Rain : daily rain (mm.d-1) (double) (sync)
- ActualIrrigation : water supply (mm.d-1) [double]
(sync)
- Max_evap : daily maximal soil evaporation from soil
surface layer (mm.d-1) (double) (sync)
- Max_transp : daily maximal crop transpiration
(mm.d-1) (double) (sync)
- RootDepth : crop root depth (m) (double)
(sync)
- few : Exposed and wetted soil fraction (-) (double) (sync)
- fc : Average soil fraction covered (or shaded) by vegetation [0.01 - 1] - see Table Table 3 (-) (double) (sync)
- Kr1 : Soil evaporation reduction coefficient. (-) (double) (sync)
- Kr2 : Soil ?? reduction coefficient. (-) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- max_trans_R1 : daily maximal crop transpiration from soil surface layer (mm.d-1) (double)
- max_trans_R2 : daily maximal crop transpiration from soil deep layer (mm.d-1) (double)
- actual_evap : daily soil surface actual evaporation
(mm.d-1) (double)
- actual_transp_R1 : daily crop actual transpiration
from soil surface layer (mm.d-1) (double)
- actual_transp_R2 : daily crop actual transpiration
from soil deep layer (mm.d-1) (double)
- actual_transp : daily crop actual transpiration
(mm.d-1) (double)
- Irrigation : daily actual irrigation (mm.d-1) (double)
- RunOff : daily soil surface runoff (mm.d-1)
(double)
- I_R1 : daily soil surface layer infiltration
(mm.d-1) (double)
- I_R2 : daily soil deep layer infiltration (mm.d-1)
(double)
- Drain : daily soil deep layer drainage (mm.d-1)
(double)
- WC_R1 : soil surface layer water content (mm)
(double)
- WC_R2 : soil deep layer water content (mm)
(double)
- WCtmp_R1 : temporary soil surface layer water
content (after gravitational infiltrations and before
evapotranspiration) (mm) (double)
- WCtmp_R2 : temporary soil deep layer water content
(after gravitational infiltrations and before evapotranspiration) (mm)
(double)
- stress_index : crop water stress index (-) (double)
- DailyBalanceControl : control for daily water budget checking (should always be 0) (m) (double)
Details
State variables equations
\[RunOff(t)=\left\{ \begin{array}{@{}ll@{}} \frac{(Rain(t) - Ia)^2}{Rain(t) - Ia - S}, & \text{if}\ Rain(t) > Ia\\ 0, & \text{otherwise} \end{array}\right. \label{eq:RunOff}\]
with
\(S = \frac{25400}{CurveNumber} - 254\)
and
\(Ia = Ia\_SoilType\_param * S\)
\[I\_R1(t)=\max\left( \begin{array}{@{}ll@{}} 0. \\ Rain(t) + ActualIrrigation(t) - RunOff(t) \end{array}\right) \label{eq:I_R1}\]
\[I\_R2(t)=\max\left( \begin{array}{@{}ll@{}} 0. \\ WC\_R1(t-1) + I\_R1(t) - AWC1 \end{array}\right) \label{eq:I_R2}\]
with
\(AWC1 = (ThetaFC1 - ThetaWP1) * BD1 * TH1\)
\[Drain(t)=\max\left( \begin{array}{@{}ll@{}} 0. \\ WC\_R2(t-1) + I\_R2(t) - AWC2 \end{array}\right) \label{eq:Drain}\]
with
\(AWC2 = (ThetaFC2 - ThetaWP2) * BD2 * TH2\)
\[WCtmp\_R1(t) = WC\_R1(t-1) + I\_R1(t) - I\_R2(t) \label{eq:WCtmp_R1}\]
\[WCtmp\_R2(t) = WC\_R2(t-1) + I\_R2(t) - Drain(t) \label{eq:WCtmp_R2}\]
\[max\_trans\_R1(t)=\min\left( \begin{array}{@{}ll@{}} 1. \\ \frac{TH1}{RootDepth(t)*1000} \end{array}\right) * Max\_transp(t) \label{eq:max_trans_R1}\]
\[max\_trans\_R2(t)=\max\left( \begin{array}{@{}ll@{}} 0. \\ \frac{RootDepth(t)*1000 - TH1}{RootDepth(t)*1000} \end{array}\right) * Max\_transp(t) \label{eq:max_trans_R2}\]
\[actual\_evap(t)=\left\{ \begin{array}{@{}ll@{}} Max\_evap(t), & \text{if}\ Max\_evap(t) + max\_trans\_R1(t) \le WCtmp\_R1(t) or Max\_evap(t)<few(t) * WCtmp\_R1(t)\\ few(t) * WCtmp\_R1(t), & \text{otherwise} \end{array}\right. \label{eq:actual_evap}\]
\[actual\_transp\_R1(t)=\left\{ \begin{array}{@{}ll@{}} max\_trans\_R1(t) * Kr1(t), & \text{if}\ Max\_evap(t) + max\_trans\_R1(t) \le WCtmp\_R1(t) \\ fc(t) * \min\left( \begin{array}{@{}ll@{}} max\_trans\_R1(t) * Kr1(t) \\ WCtmp\_R1(t) \end{array}\right), & \text{otherwise} \end{array}\right. \label{eq:actual_transp_R1}\]
\[actual\_transp\_R2(t)= \min\left( \begin{array}{@{}ll@{}} Kr2(t) * (max\_trans\_R1(t) - actual\_transp\_R1(t) + max\_trans\_R2(t)) \\ WCtmp\_R2(t) * fracRoot\_R2 \end{array}\right) \label{eq:actual_transp_R2}\]
with
\[fracRoot\_R2=\max\left( \begin{array}{@{}ll@{}} 0. \\ \frac{RootDepth(t)*1000 - TH1}{TH2} \end{array}\right) \label{eq:fracRoot_R2}\nonumber\]
\[actual\_transp(t) = actual\_transp\_R1(t) + actual\_transp\_R2(t) \label{eq:actual_transp}\]
\[WC\_R1(t)=\min\left( \begin{array}{@{}ll@{}} AWC1 \\ WCtmp\_R1(t) - actual\_transp\_R1(t) - actual\_evap(t) \end{array}\right) \label{eq:WC_R1}\]
\[WC\_R2(t)=\min\left( \begin{array}{@{}ll@{}} AWC2 \\ WCtmp\_R2(t) - actual\_transp\_R2(t) \end{array}\right) \label{eq:WC_R2}\]
\[stress\_index = \frac{actual\_transp(t)}{Max\_transp(t)} \label{eq:stress_index}\]
\[DailyBalanceControl(t) = \Delta WC(t) - Rain(t) - ActualIrrigation(t) + RunOff(t) + Drain(t) + actual\_evap(t) + actual\_transp\_R1(t) + actual\_transp\_R2(t) \label{eq:DailyBalanceControl}\]
with
\(\Delta WC(t) = (WC\_R1(t) + WC\_R2(t)) - (WC\_R1(t-1) + WC\_R2(t-1))\)
De(t) Cumulative depth of evaporation (depletion) from the soil surface layer after a day with “heavy precipitation” [m],
FAO equation : \(De(t) = max(0, De(t-1) -(P(t)-R(t)) - I(t)/fw + Max\_evap(t)/few + AWC1(t) + DPe(t))\) combined with
\(De(t) = AWC1 - WC\_R1(t)\)
→
\(AWC1 - WC\_R1(t) = max(0, AWC1 - WC\_R1(t-1) -(P(t)-R(t)) - I(t)/fw + Max\_evap(t)/few + AWC1(t) + DPe(t))\)
→
\(-WC\_R1(t) = max(-AWC1, - WC\_R1(t-1) -(P(t)-R(t)) - I(t)/fw + Max\_evap(t)/few + AWC1(t) + DPe(t))\)
→
\(WC\_R1(t) = min(AWC1, WC_R1(t-1) + (P(t)-R(t)) + I(t)/fw - Max\_evap(t)/few - AWC1(t) - DPe(t))\) combined with
\(P(t)=Rain(t)\)
\(R(t)=RunOff(t)\)
\(I(t)=Irrigation(t)\)
\(DPe(t)=I\_R2(t)\)
→
\(WC\_R1(t) = min(AWC1, WC_R1(t-1) + (Rain(t)-RunOff(t)) + Irrigation(t)/fw - Max\_evap(t)/few - AWC1(t) - I\_R2(t))\)
to be compared to WaterFlow eq (combination of above eq for WC_R1, WCtmp_R1, I_R1) :
\[WC\_R1(t)=\min\left( \begin{array}{@{}ll@{}} AWC1 \\ WC\_R1(t-1) + Rain(t) + Irrigation(t) - RunOff(t) - I\_R2(t) - actual\_transp\_R1(t) - actual\_evap(t) \end{array}\right) \label{eq:WC_R1.2}\nonumber\]
Atomic model IrrigationDemand
The IrrigationDemand model (using extension class DiscreteTimeDyn)
estimate daily irrigation demand.
Configuring a IrrigationDemand Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| Rule_Strat | string | [x] | strategy option for irrigation rule (choose from {None, Rain_Threshold, SoilWaterContent_Threshold, CropWaterStress_Threshold}) |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- Rain7days : cummulated rain over the last 7 days
(mm.d-1) (double) (sync)
- Irrigation7days : cummulated irrigation over the
last 7 days (mm.d-1) (double) (nosync)
- CropWaterStress : crop water stress index (-)
(double) (nosync)
- SoilWaterContent : soil water content (mm) (double)
(nosync)
- Is_Failure : detect if water deficit threshold has
been reached for the current crop (bool) (double) (nosync)
- IrrigationDose_interp : IrrigationDose
interpolation (mm.d-1) (double) (sync)
- Rain_Threshold_interp : Rain_Threshold
interpolation (mm) (double) (sync)
- SoilWaterContent_Threshold_interp :
SoilWaterContent_Threshold interpolation (mm) (double) (sync)
- CropWaterStress_Threshold_interp : CropWaterStress_Threshold interpolation (-) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- IrrigationDemand : daily irrigation demand of the
1st subplot (mm.d-1) (double)
- IrrigationDose : irrigation amount to be applied
(mm.d-1) (double)
- Rain_Threshold : Rain amount threshold for
Rule_Strat=Rain_Threshold (mm) (double)
- CropWaterStress_Threshold : Crop water stress
threshold for Rule_Strat=CropWaterStress_Threshold (-) (double)
- SoilWaterContent_Threshold : Soil water content threshold for Rule_Strat=SoilWaterContent_Threshold (mm) (double)
Details
State variables equations
By setting the value of parameter Rule_Strat the user is choosing one of the following irrigation strategy:
- None: No particular restriction, irrigation happens
ASAP
- Rain_Threshold: Irrigation event start restricted
by Rain7days and Irrigation7days daily
inputs and using Rain_Threshold_params parameters
- SoilWaterContent_Threshold: Irrigation event start
restricted by SoilWaterContent daily inputs and using
SoilWaterContent_Threshold_params parameters
- CropWaterStress_Threshold Irrigation event start restricted by CropWaterStress daily inputs and using CropWaterStress_Threshold_params parameters
\[ IrrigationDose(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ IrrigationDose\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:IrrigationDose}\]
Depending on the Rule_Strat option choosed, a criterion might be used to decide if a new irrigation event should start. (see below the different options).
\[Irrigation\_Demand(t) = IrrigationDose(t) \label{eq:Irrigation_Demand}\]
Rule_Strat=Rain_Threshold
The cummulated rain over the last 7 days is compared to a threshold value
\[ Rain\_Threshold(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ Rain\_Threshold\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:Rain_Threshold}\]
\[ start\_rule=(Rain7days(t) + Irrigation7days(t-1) < Rain\_Threshold(t)) \label{eq:start_Rain_Threshold}\]
Rule_Strat=SoilWaterContent_Threshold
The soil water content is compared to a threshold value
\[ SoilWaterContent\_Threshold(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ SoilWaterContent\_Threshold\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:SoilWaterContent_Threshold}\]
\[ start\_rule=(SoilWaterContent(t-1) < SoilWaterContent\_Threshold(t)) \label{eq:start_SoilWaterContent_Threshold}\]
Rule_Strat=CropWaterStress_Threshold
The crop water stress index is compared to a threshold value (Remark : for the crop water stress index defined in the WaterFlows model 0 is max stress and 1 no stress)
\[ CropWaterStress\_Threshold(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ Is\_Failure(t) \\ CropWaterStress\_Threshold\_interp(t), & \text{otherwise} \end{array}\right. \label{eq:CropWaterStress_Threshold}\]
\[ start\_rule=(CropWaterStress(t-1) < CropWaterStress\_Threshold(t)) \label{eq:start_CropWaterStress_Threshold}\]
Atomic model ActualIrrigation
The ActualIrrigation model (using extension class DiscreteTimeDyn)
estimate ….
Configuring a ActualIrrigation Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| Irrig_Efficiency | double | [x] | fraction of irrigation water reaching soil surface. |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- Irrigation : daily irrigation applied (mm.d-1) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- ActualIrrigation : water supply (mm.d-1) [double]
Atomic model Yield
The Yield model (using extension class DiscreteTimeDyn)
estimate ….
Configuring a Yield Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- CropWaterStress : crop water stress index (-)
(double) (sync)
- Is_Failure : detect if crop has failed (bool)
(double) (sync)
- YieldMax : ?? (??) (double) (sync)
- Ky : Yield response factor (-) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- StressReductionFactor : ?? (??) [double]
- Yield : ?? (??) [double]
- YieldFraction : ?? (??) [double]
Details
State variables equations
\[StressReductionFactor(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ !Is\_Crop \\ \frac{StressReductionFactor(t-1)*(daycounter(t)-1) + CropWaterStress(t))}{daycounter(t)}, & \text{otherwise} \end{array}\right. \label{eq:StressReductionFactor}\]
with
\(Is\_Crop = ((YieldMax(t) > 0) \text{&} !Is\_Failure(t))\)
and
\(daycounter(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ !Is\_Crop \\ daycounter(t-1)+1, & \text{otherwise} \end{array}\right.\)
\[Yield(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ !Is\_Crop \\ \max\left( \begin{array}{@{}ll@{}} YieldMax(t) * (1. - Ky(t) * (1. - StressReductionFactor(t))) \\ 0. \end{array}\right), & \text{otherwise} \end{array}\right. \label{eq:Yield}\]
\[YieldFraction(t)=\left\{ \begin{array}{@{}ll@{}} 0, & \text{if}\ !Is\_Crop \\ Yield(t)/YieldMax(t), & \text{otherwise} \end{array}\right. \label{eq:YieldFraction}\]
Atomic model Pond
The Pond model (using extension class DiscreteTimeDyn)
estimate the pond volume and water flows (Evaporation, percolation and
overflow internal processes and potential refilling/extraction from/for
external sources).
The shape of the pond is a reversed truncated pyramid with a
rectangular shaped base : 
Configuring a Pond Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| X0 | double | [x] | Pond surface Length (m) |
| Y0 | double | [x] | Pond surface Width (m) |
| Z0 | double | [x] | Pond depth (m) |
| fx | double | [x] | Shape coefficient for X dimension (must be positive) (m/m) |
| Evap_coeff | double | [x] | Pond evaporation reduction coefficient (??) |
| Percol_coeff | double | [x] | Pond percolation coefficient (??) |
| Init_Pond_Frac | double | [x] | Pond initial volume as a fraction of V0 (-) |
Local parameters
The following are computed once from user parameters and then keep a fixed value during the simulation duration
| Parameter name | Type | Description |
|---|---|---|
| fy | double | Shape coefficient for Y dimension (m/m) |
| S0 | double | Pond surface area (m2) |
| X1 | double | Pond bottom Length (m) |
| Y1 | double | Pond bottom Width (m) |
| Z1 | double | Pyramid Apex depth (m) |
| S1 | double | Pond bottom area (m2) |
| V0 | double | Pond total volume (m3) |
| V1 | double | Trunk volume of the truncated pyramid (m3) |
\[fy = \frac{Y0 * fx}{X0} \label{eq:fy}\]
\[S0 = X0 * Y0 \label{eq:S0}\]
\[X1 = X0 - fx * Z0 \label{eq:X1}\]
\[Y1 = Y0 - fy * Z0 \label{eq:Y1}\]
\[Z1 = \frac{X0}{fx} = \frac{Y0}{fy} \label{eq:Z1}\]
\[S1 = X1 * Y1 \label{eq:S1}\]
\[V0 = \frac{1}{3} * Z0 * (S0 + S1 + \sqrt{S0 * S1}) \label{eq:V0}\]
\[V1 = \frac{1}{3} * (Z1 - Z0) * (S0 + S1 + \sqrt{S0 * S1}) = \frac{1}{3} * (Z1 - Z0)^3 * fx * fy \label{eq:V1}\]
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- ET0 : Reference crop evapotranspiration (We
recomend to use values calculated by the Penman Monteith equation as it
is done in FAO approach) (mm.d-1) (double) (sync)
- Rain : daily rain (mm) (double) (sync)
- RunOff : daily incoming surface runoff volume
(m3) (double) (sync)
- Pond_Irrigation : daily actual irrigation using
pond water (m3) (double) (sync)
- AvailableWater : daily available water for refilling the pond (m3) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- Evaporation : Pond daily surface Evaporation (m3) (double)
- Percolation : Pond daily bottom Percolation (m3) (double)
- Pump_water_refill : Pond daily Refill volume (m3) (double)
- Pond_Overflow : Pond water overflow loss (m3) (double)
- V : Pond water volume (m3) (double)
- X : Pond water Length (m) (double)
- Y : Pond water Width (m) (double)
- S : Pond water area (m2) (double)
- Z : Pond water height (m) (double)
Details
State variables equations
\[Percolation(t) =\min\left( \begin{array}{@{}ll@{}} Z(t-1) * S1 * Percol\_coeff \\ V(t-1) + Rain(t) * S0 / 1000. + RunOff(t) - Pond\_Irrigation(t) \end{array}\right) \label{eq:Percolation}\]
\[Evaporation(t) =\min\left( \begin{array}{@{}ll@{}} ET0(t) * Evap\_coeff * S(t-1) / 1000 \\ V(t-1) - Percolation(t) + Rain(t) * S0 / 1000. + RunOff(t) - Pond\_Irrigation(t) \end{array}\right) \label{eq:Evaporation}\]
\[Pump\_water\_refill(t)=\min\left( \begin{array}{@{}ll@{}} V0 - \min\left( \begin{array}{@{}ll@{}} V0 \\ (V(t-1) + Rain(t) * S0 / 1000. + RunOff(t) - Pond\_Irrigation(t) - Evaporation(t) - Percolation(t)) \end{array}\right) \\ AvailableWater(t) \end{array}\right) \label{eq:Pump_water_refill}\]
\[Pond\_Overflow(t)=\max\left( \begin{array}{@{}ll@{}} 0 \\ (V(t-1) + Rain(t) * S0 / 1000. + RunOff(t) - Pond\_Irrigation(t) - Evaporation(t) - Percolation(t) + AvailableWater(t)) - V0 \end{array}\right) \label{eq:Pond_Overflow}\]
\[V(t) = V(t-1) + Rain(t) * S0 / 1000. + Runoff(t) + AvailableWater(t) - Pond\_Overflow(t) - Pond\_Irrigation(t) - Evaporation(t) - Percolation(t) \label{eq:V}\]
and initialized with : \(V(0) = Init\_Pond\_Frac * V0\)
\[Z(t) = Z0 - Z1 + \sqrt[3]{\frac{3 * (V(t) + V1)}{fx * fy}} \label{eq:Z}\]
\(X(t) = (Z(t) + Z1 - Z0) * fx\)
\(Y(t) = (Z(t) + Z1 - Z0) * fy\)
\(S(t) = X(t) * Y(t) = (Z(t) + Z1 - Z0)^2 * fx * fy\)
\(V(t) = \frac{1}{3} * S(t) * (Z(t) + Z1 - Z0) - V1 = \frac{1}{3} * (Z(t) + Z1 - Z0)^3 * fx * fy - V1\)
\((Z(t) + Z1 - Z0)^3 =\frac{3 * (V(t) + V1)}{fx * fy}\)
\[X(t) = (Z(t) + Z1 - Z0) * fx \label{eq:X}\]
\[Y(t) = (Z(t) + Z1 - Z0) * fy \label{eq:Y}\]
\[S(t) = X(t) * Y(t) = (Z(t) + Z1 - Z0)^2 * fx * fy \label{eq:S}\]
Atomic model IrrigationPriority
The IrrigationPriority model (using extension class
DiscreteTimeDyn)
estimate the priority for irrigation among the different plots of the
farm. It is computed for each crops of each plots. The lowest value of
IrrigationPriority is the highest priority.
Configuring a IrrigationPriority Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| nbBele | int | [x] | number of plots to manage |
| a | double | [x] | strategy weight coefficient for plot priority |
| b | double | [x] | strategy weight coefficient for crop water stress |
| c | double | [x] | strategy weight coefficient for crop cycle completeness |
| d | double | [x] | strategy weight coefficient for irrigation technics |
| RS_strategy | int | [x] | Ranking Stress strategy, {1:favor most stressed ; 2:favor least stressed} |
| RC_strategy | int | [x] | Ranking Cycle strategy, {1:favor latest in crop cycle ; 2:favor earliest in crop cycle} |
| BelePriorities | set < double > | [x] | Ranking of the different plots, all values must be different from each others |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- CropPriority_i : crop priority related to economic
factor and crop cycle length (-) (double) (sync)
- Days_Without_Irrigation_i : number of consecutive
days with no irrigation where it should have for plot i with i ∈ [1,
nbBele] (days) (double) (nosync)
- Lethal_Threshold_Days_Without_Water_i : number of
days of water deficit after which the crop is failed for plot i with i ∈
[1, nbBele] (days) (double) (sync)
- Days_Since_Sowing_i : number of days since sowing
for plot i with i ∈ [1, nbBele] (days) (double) (nosync)
- Crop_Cycle_Duration_i : total expected crop cycle
for plot i with i ∈ [1, nbBele] (days) (double) (sync)
- Irrigation_Technic_Factor_i : irrigation technic factor (from least to most demanding in water) for plot i with i ∈ [1, nbBele] (-) (double) (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- IrrigationPriority_i : Priority order (going from 1 to nbBele) of plot i with i ∈ [1, nbBele] (-) [int]
- R_i : Priority factor of plot i with i ∈ [1, nbBele] (-) [double]
- RE_i : Ranking Economy of plot i with i ∈ [1, nbBele] (-) [double]
- RS_i : Ranking Stress of plot i with i ∈ [1, nbBele] (-) [double]
- RC_i : Ranking Cycle of plot i with i ∈ [1, nbBele] (-) [double]
- RT_i : Ranking Technics of plot i with i ∈ [1, nbBele] (-) [double]
Details
State variables equations
RE (Ranking Economy) : Plot priority related to economic factors (investments, market prices, …) and crop cycle duration (also related to economic factors as most of the time long cycles are more investment demanding). The idea is to rank all crops used. ∈ [0, 1] \[RE\_i(t)= \frac{CropPriority\_i(t)}{sum_i(CropPriority\_i(t))} \label{eq:RE}\]
RS (Ranking Stress) : factor related to accumulated crop stress (number of days without irrigation). 2 strategies are possible : (i) favor the most stressed crops to avoid failure, or (ii) favor the least stressed crops, because the most stressed ones have disminished their potential yield. ∈ [0, 1] \[ RS\_i(t)=\left\{ \begin{array}{@{}ll@{}} \frac{Lethal\_Threshold\_Days\_Without\_Water\_i(t) - Days\_Without\_Irrigation\_i(t-1)}{Lethal\_Threshold\_Days\_Without\_Water\_i(t)}, & \text{if}\ RS\_strategy=1 \\ \frac{Days\_Without\_Irrigation\_i(t-1)}{Lethal\_Threshold\_Days\_Without\_Water\_i(t)}, & \text{else if}\ RS\_strategy=2 \\ \end{array}\right. \label{eq:RS}\]
RC (Ranking Cycle) : factor related to relative normalised crop cycle realisation. 2 strategies are possible : (i) favor the crops closest to the end of their cycle to ensure harvest, or (ii) favor crops at the begining of their cycle to ensure correct development during early stages. ∈ [0, 1] \[ RC\_i(t)=\left\{ \begin{array}{@{}ll@{}} \frac{Crop\_Cycle\_Duration\_i(t) - Days\_Since\_Sowing\_i(t-1)}{Crop\_Cycle\_Duration\_i(t)}, & \text{if}\ RC\_strategy=1 \\ \frac{Days\_Since\_Sowing\_i(t-1)}{Crop\_Cycle\_Duration\_i(t)}, & \text{else if}\ RC\_strategy=2 \\ \end{array}\right. \label{eq:RC}\]
RT (Ranking Technics) : factor related to the irrigation technic (drip, sprinkler, furrow, …). Rank crops by their irrigation technics from the least demanding in water to the most ones. ∈ [0, 1] \[RT\_i(t)= \frac{Irrigation\_Technic\_Factor\_i(t)}{max_i(Irrigation\_Technic\_Factor\_i(t))} \label{eq:RT}\]
\[R\_i(t)= a * RE\_i(t) + b * RS\_i(t) + c * RC\_i(t) + d * RT\_i(t) \label{eq:R}\]
IrrigationPriority_i(t) : rank of ascending ordered values of R_i(t), for ex-aequo values of R_i(t) the lowest value of BelePriorities is first
Atomic model FarmIrrigationManager
The FarmIrrigationManager model (using extension
class DiscreteTimeDyn)
estimate ….
All irrigation water is provided for plots on the first day but can be
removed from pump or pond during several consecutive days of a water
cycle
Configuring a FarmIrrigationManager Model
Parameters settings
List and information about all possible parameters (name, type, ismandatory, description with default value).
See documentation of DiscreteTimeDyn
to get all available extension parameters (for example
time_step)
| Parameter name | Type | Is mandatory? | Description |
|---|---|---|---|
| DbgLog | double | [] (default=0) | Debug messages verbosity level |
| nbBele | int | [x] | number of plots to manage |
| isPondForIrrigation | bool | [x] | define if pond water can be used for irrigation |
| isOptimize | bool | [x] | define if water from last day of a cycle can be used (see case 2.1) |
| isRefill | bool | [x] | define if water from pump can be used to refill the pond |
| V0 | double | [x] | pond total volume (m3) |
| PlotArea_i | double | [x] | plot area of the plot i with i ∈ [1, nbBele] (m2) |
Input settings
List and information about all possible input ports (name, type, description with units).
for model using extension discrete-time also include sync info
- V : Pond water volume (m3) (double) (nosync)
- AvailableWater : pump maximum available water
(m3.d-1) (double) (sync)
- PumpMaxVol : maximum water volume reachable by the
pump (m3 of water) (double) (sync)
- IrrigationDemand_i : daily irrigation demand of
plot i with i ∈ [1, nbBele] (mm.d-1) (double) (sync)
- Max_Irrigation_Duration_i : Maximal water cycle
duration for plot i with i ∈ [1, nbBele] (days) (double) (sync)
- IrrigationPriority_i : Priority order (going from 1 to nbBele) of plot i with i ∈ [1, nbBele] (-) [int] (sync)
Output settings
List and information about all possible output ports (name, type, description with units).
- PondExtraction : daily actual irrigation using pond
water (m3) (double)
- PumpExtraction : daily actual water pumped
(m3) (double)
- PondRefill : water for refilling the pond
(m3) (double)
- WaterCycle_Duration : remaining duration of active
water cycle (int) (double)
- WaterCycle_RemainingAmount : remaining water amount
of active water cycle (m3) (double)
- WaterCycle_CurrentPlot : plot index of active water
cycle (int) (double)
- WaterCycle_CurrentDose : daily pumping water of
active water cycle (m3) (double)
- IrrigationAmount_i : daily actual irrigation for
plot i with i ∈ [1, nbBele] (m3) (double)
- Irrigation_i : daily actual irrigation for plot i
with i ∈ [1, nbBele] (mm.d-1) (double)
- Is_Day_Without_Irrigation_i : detect if day has no
irrigation where it should have for plot i with i ∈ [1, nbBele] (bool)
(double)
- Days_Without_Irrigation_i : number of consecutive days with no irrigation where it should have for plot i with i ∈ [1, nbBele] (days) (double)
- PondExtraction_i : daily actual irrigation using
pond water for plot i with i ∈ [1, nbBele] (m3)
(double)
- PumpExtraction_i : daily actual water pumped for plot i with i ∈ [1, nbBele] (m3) (double)
Details
State variables equations
- Some state variables use different equations depending on the
following cases and sub-cases :
- Current day is not in an active water cycle
1.1. No plot request any water
1.2. At least one plot request water
- Current day is in an active water cycle
- Current day is not in an active water cycle
Local variables defined and used in the following part are initialized as :
\[ pond\_AvailableIrrigationWater=\left\{ \begin{array}{@{}ll@{}} V(-1), & \text{if}\ isPondForIrrigation(t) \\ 0, & \text{otherwise}\ \\ \end{array}\right. \label{eq:pond_AvailableIrrigationWater_1_2_init}\]
\[pump\_AvailableIrrigationWater = AvailableWater(t) \label{eq:pump_AvailableIrrigationWater_1_2_init}\]
\[total\_AvailableIrrigationWater = pond\_AvailableIrrigationWater + pump\_AvailableIrrigationWater \label{eq:total_AvailableIrrigationWater_1_2_init}\]
\[pond\_extraction = 0 \label{eq:pond_extraction_1_2_init}\]
\[pump\_extraction = 0 \label{eq:pump_extraction_1_2_init}\]
\[cycle\_max\_amount = PumpMaxVol(t) + pond\_AvailableIrrigationWater \label{eq:cycle_max_amount_1_2_init}\]
For each plot the local variables defined and used in the following part are initialized as :
\[plot\_irrig\_demand\_i = IrrigationDemand\_i(t) * PlotArea\_i / 1000. \label{eq:plot_irrig_demand_1_2_init}\] ∀ i ∈ [1, nbBele]
\[plot\_cycle\_duration\_i = ceil(\frac{plot\_irrig\_demand\_i - total\_AvailableIrrigationWater}{AvailableWater(t)}) \label{eq:plot_cycle_duration_1_2_init}\] ∀ i ∈ [1, nbBele]
Case 1.1 : Current day is not in an active water cycle and No plot request any water
Case detection : if \((WaterCycle\_Duration(t-1) <= 0.)\) & \((sum_i(IrrigationDemand\_i(t))==0)\)
Local variables equations :
\[pond\_extraction = 0 \label{eq:PondExtraction_1_1}\]
\[pump\_extraction = 0 \label{eq:PumpExtraction_1_1}\]
State Variables equations :
\[WaterCycle\_Duration(t) = 0 \label{eq:WaterCycle_Duration_1_1}\]
\[WaterCycle\_RemainingAmount(t) = 0 \label{eq:WaterCycle_RemainingAmount_1_1}\]
\[WaterCycle\_CurrentPlot(t) = -1 \label{eq:WaterCycle_CurrentPlot_1_1}\]
\[WaterCycle\_CurrentDose(t) = 0 \label{eq:WaterCycle_CurrentDose_1_1}\]
\[IrrigationAmount\_i(t) = 0 \label{eq:IrrigationAmount_1_1}\] ∀ i ∈ [1, nbBele]
\[Is\_Day\_Without\_Irrigation\_i(t) = 0 \label{eq:Is_Day_Without_Irrigation_1_1}\] ∀ i ∈ [1, nbBele]
Case 1.2 : Current day is not in an active water cycle and at least one plot request water
Case detection : if \((WaterCycle\_Duration(t-1) <= 0.)\) & \((sum_i(IrrigationDemand\_i(t))>0)\)
Sequential loop over all plots requesting water using increasing values of IrrigationPriority_i(t), for each plot 3 cases are possible :
1.2.1. All the requested water can be provided in a single day using
the pump and pond.
1.2.2 All the requested water can be provided during a water
cycle.
1.2.3 Not all the requested water can be provided neither in a single
day nor during a water cycle.
Case 1.2.1 All the requested water can be provided in a single day using the pump and pond.
Case detection : if \((WaterCycle\_Duration(t) <= 0.)\) & \((plot\_irrig\_demand\_i <= total\_AvailableIrrigationWater)\)
Local variables equations :
\[pond\_AvailableIrrigationWater = pond\_AvailableIrrigationWater - pond\_flow \label{eq:pond_AvailableIrrigationWater_1_2_1}\]
with
\(pond\_flow =\min\left( \begin{array}{@{}ll@{}} pond\_AvailableIrrigationWater \\ plot\_irrig\_demand\_i \end{array}\right)\)
\[pump\_AvailableIrrigationWater = pump\_AvailableIrrigationWater - pump\_flow \label{eq:pump_AvailableIrrigationWater_1_2_1}\]
with
\(pump\_flow =plot\_irrig\_demand\_i - \min\left( \begin{array}{@{}ll@{}} pond\_AvailableIrrigationWater \\ plot\_irrig\_demand\_i \end{array}\right)\)
\[pond\_extraction = pond\_extraction + pond\_flow \label{eq:pond_extraction_1_2_1}\]
\[pump\_extraction = pump\_extraction + pump\_flow \label{eq:pump_extraction_1_2_1}\]
\[total\_AvailableIrrigationWater = pond\_AvailableIrrigationWater + pump\_AvailableIrrigationWater \label{eq:total_AvailableIrrigationWater_1_2_1}\]
\[cycle\_max\_amount = PumpMaxVol(t) - pump\_extraction + pond\_AvailableIrrigationWater \label{eq:cycle_max_amount_1_2_1}\]
State Variables equations :
\[IrrigationAmount\_i(t) = plot\_irrig\_demand\_i \label{eq:IrrigationAmount_1_2_1}\]
\[Is\_Day\_Without\_Irrigation\_i(t) = 0 \label{eq:Is_Day_Without_Irrigation_1_2_1}\]
Case 1.2.2 All the requested water can be provided during a water cycle.
Case detection : if \(( WaterCycle\_Duration(t)==0. )\) & \(( plot\_irrig\_demand\_i <= cycle\_max\_amount )\) & \(( plot\_cycle\_duration\_i <= Max\_Irrigation\_Duration\_i(t) )\)
Local variables equations :
\[pond\_extraction = pond\_extraction + pond\_AvailableIrrigationWater \label{eq:pond_extraction_1_2_2}\]
\[pump\_extraction = pump\_extraction + pump\_AvailableIrrigationWater \label{eq:pump_extraction_1_2_2}\]
\[pond\_AvailableIrrigationWater = 0 \label{eq:pond_AvailableIrrigationWater_1_2_2}\]
\[pump\_AvailableIrrigationWater = 0 \label{eq:pump_AvailableIrrigationWater_1_2_2}\]
\[total\_AvailableIrrigationWater = pond\_AvailableIrrigationWater + pump\_AvailableIrrigationWater \label{eq:total_AvailableIrrigationWater_1_2_2}\]
\[cycle\_max\_amount = PumpMaxVol(t) - pump\_extraction + pond\_AvailableIrrigationWater - (plot\_irrig\_demand\_i - total\_AvailableIrrigationWater) \label{eq:cycle_max_amount_1_2_2}\]
State Variables equations :
\[WaterCycle\_Duration(t) = plot\_cycle\_duration\_i \label{eq:WaterCycle_Duration_1_2_2}\]
\[WaterCycle\_RemainingAmount(t) = plot\_irrig\_demand\_i - total\_AvailableIrrigationWater \label{eq:WaterCycle_RemainingAmount_1_2_2}\]
\[WaterCycle\_CurrentPlot(t) = i \label{eq:WaterCycle_CurrentPlot_1_2_2}\]
\[WaterCycle\_CurrentDose(t) = AvailableWater(t) \label{eq:WaterCycle_CurrentDose_1_2_2}\]
\[IrrigationAmount\_i(t) = plot\_irrig\_demand\_i \label{eq:IrrigationAmount_1_2_2}\]
\[Is\_Day\_Without\_Irrigation\_i(t) = 0 \label{eq:Is_Day_Without_Irrigation_1_2_2}\]
Case 1.2.3 Not all the requested water can be provided neither in a single day nor during a water cycle.
Case detection : otherwise
\[IrrigationAmount\_i(t) = 0 \label{eq:IrrigationAmount_1_2_3}\]
\[Is\_Day\_Without\_Irrigation\_i(t) = 1 \label{eq:Is_Day_Without_Irrigation_1_2_3}\]
Case 2 : Current day is in an active water cycle
Case detection : if \((WaterCycle\_Duration(t-1) > 0.)\)
\[WaterCycle\_Duration(t) = WaterCycle\_Duration(t-1) - 1 \label{eq:WaterCycle_Duration_2}\]
\[WaterCycle\_RemainingAmount(t)=\max\left( \begin{array}{@{}ll@{}} 0 \\ WaterCycle\_RemainingAmount(t-1) - WaterCycle\_CurrentDose(t) \end{array}\right) \label{eq:WaterCycle_RemainingAmount_2}\nonumber\]
\[ WaterCycle\_CurrentPlot(t)=\left\{ \begin{array}{@{}ll@{}} WaterCycle\_CurrentPlot(-1), & \text{if}\ WaterCycle\_Duration(t)!=0 \\ -1, & \text{otherwise}\ \\ \end{array}\right. \label{eq:WaterCycle_CurrentPlot_2}\]
\[ WaterCycle\_CurrentDose(t)=\left\{ \begin{array}{@{}ll@{}} WaterCycle\_CurrentDose(-1), & \text{if}\ WaterCycle\_Duration(t)!=0 \\ 0, & \text{otherwise}\ \\ \end{array}\right. \label{eq:WaterCycle_CurrentDose_2}\]
\[pond\_extraction = 0 \label{eq:PondExtraction_2}\]
\[pump\_extraction=\min\left( \begin{array}{@{}ll@{}} WaterCycle\_CurrentDose(t) \\ WaterCycle\_RemainingAmount(t-1) \end{array}\right) \label{eq:PumpExtraction_2}\nonumber\]
\[IrrigationAmount\_i(t) = 0 \label{eq:IrrigationAmount_2}\] ∀ i ∈ [1, nbBele]
\[ Is\_Day\_Without\_Irrigation\_i(t)=1 \label{eq:Is_Day_Without_Irrigation_2}\] ∀ i ∈ [1, nbBele]
Case 2.1 : Current day is the last day of an active water cycle
If isOptimize option is activated.
In the case where it is the last day of an active water cycle we subsequently try to do 1 day irrigations (similar to case 1.2.1), using the remaining water and using pump volumes from the start of the water cycle.
Sequential loop over all plots requesting water using increasing values of IrrigationPriority_i(t).
Local variables defined and used in the following part are initialized as :
\[ pond\_AvailableIrrigationWater=\left\{ \begin{array}{@{}ll@{}} V(-1), & \text{if}\ isPondForIrrigation(t) \\ 0, & \text{otherwise}\ \\ \end{array}\right. \label{eq:pond_AvailableIrrigationWater_2_1_init}\]
\[pump\_AvailableIrrigationWater = WaterCycle\_CurrentDose(t-1) - WaterCycle\_RemainingAmount(t-1) \label{eq:pump_AvailableIrrigationWater_2_1_init}\]
\[total\_AvailableIrrigationWater = pond\_AvailableIrrigationWater + pump\_AvailableIrrigationWater \label{eq:total_AvailableIrrigationWater_2_1_init}\]
\[pond\_extraction = PondExtraction(t) \label{eq:pond_extraction_2_1_init}\]
\[pump\_extraction = PumpExtraction(t) \label{eq:pump_extraction_2_1_init}\]
For each plot the local variables defined and used in the following part are initialized as :
\[plot\_irrig\_demand\_i = IrrigationDemand\_i(t) * PlotArea\_i / 1000. \label{eq:plot_irrig_demand_2_1}\] ∀ i ∈ [1, nbBele]
if \((plot\_irrig\_demand\_i <= total\_AvailableIrrigationWater)\)
Local variables equations :
\[pond\_AvailableIrrigationWater = pond\_AvailableIrrigationWater - pond\_flow \label{eq:pond_AvailableIrrigationWater_2_1}\]
with
\(pond\_flow =\min\left( \begin{array}{@{}ll@{}} pond\_AvailableIrrigationWater \\ plot\_irrig\_demand\_i \end{array}\right)\)
\[pump\_AvailableIrrigationWater = pump\_AvailableIrrigationWater - pump\_flow \label{eq:pump_AvailableIrrigationWater_2_1}\]
with
\(pump\_flow =plot\_irrig\_demand\_i - \min\left( \begin{array}{@{}ll@{}} pond\_AvailableIrrigationWater \\ plot\_irrig\_demand\_i \end{array}\right)\)
\[pond\_extraction = pond\_extraction + pond\_flow \label{eq:pond_extraction_2_1}\]
\[pump\_extraction = pump\_extraction + pump\_flow \label{eq:pump_extraction_2_1}\]
\[total\_AvailableIrrigationWater = pond\_AvailableIrrigationWater + pump\_AvailableIrrigationWater \label{eq:total_AvailableIrrigationWater_2_1}\]
State Variables equations :
\[IrrigationAmount\_i(t) = plot\_irrig\_demand\_i \label{eq:IrrigationAmount_2_1}\]
\[Is\_Day\_Without\_Irrigation\_i(t) = 0 \label{eq:Is_Day_Without_Irrigation_2_1}\]
- State variable that use a single equation (computed at the end of daily loop) :
Irrigation_i with i ∈ [1, nbBele] (mm.d-1) unit conversion from (m3) \[Irrigation\_i(t)= \frac{IrrigationAmount\_i(t) * 1000.}{PlotArea\_i} \label{eq:Irrigation_i}\] ∀ i ∈ [1, nbBele]
Days_Without_Irrigation_i with i ∈ [1, nbBele] (day) counter of consecutive days where Is_Day_Without_Irrigation_i \[ Days\_Without\_Irrigation\_i(t)=\left\{ \begin{array}{@{}ll@{}} Days\_Without\_Irrigation\_i(t-1) + 1, & \text{if}\ Is\_Day\_Without\_Irrigation\_i(t)=1 \\ 0, & \text{otherwise}\ \\ \end{array}\right. \label{eq:Days_Without_Irrigation}\] ∀ i ∈ [1, nbBele]
\[PondRefill(t)=\left\{ \begin{array}{@{}ll@{}} \min\left( \begin{array}{@{}ll@{}} pump\_AvailableIrrigationWater \\ V0 - V(t-1) \end{array}\right), & \text{if}\ isRefill \\ 0, & \text{otherwise}\ \\ \end{array}\right. \label{eq:PondRefill}\] along with \(pump\_extraction = pump\_extraction + PondRefill(t)\)
\[PondExtraction(t)=pond\_extraction \label{eq:PondExtraction}\]
\[PumpExtraction(t)=pump\_extraction \label{eq:PumpExtraction}\]
