# Optimizing the Sowing Date to Improve Water Management and Wheat Yield in a Large Irrigation Scheme, through a Remote Sensing and an Evolution Strategy-Based Approach

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## Abstract

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## 1. Introduction

#### 1.1. Background and Context

#### 1.2. State of the Art

## 2. Materials and Methods

#### 2.1. Study Area

^{2}in area (including approximately 3100 km

^{2}of irrigated area), characterized by a semi-arid continental climate, with low and irregular rainfall of 250 mm/year on average, a high temperature in summer (38 °C on average, in July) and low temperature in winter (5 °C on average, in February) [57]. Among the irrigated sectors of the Haouz plain, the R3 district (Figure 1b) was chosen as the main area to validate our research results. It is located about 40 km east of Marrakech city and covers an area of 2800 ha composed of around 745 individual fields, used mainly for cereal crops (45% in 2011–2012 and the remainder surface was occupied by annual crops, trees and fallow). R3 is flat and considered by many previous studies as a suitable area for satellite applications (e.g., [34,58,59,60]). At field level, water is applied by flooding method. A fixed water rate is received by each plot, at each irrigation round, without taking into account the type of crops, water requirement, and the cultivated area.

#### 2.2. The Proposed Approach

- At the beginning of the agricultural season, the spatiotemporal distribution of the sowing dates over the irrigation scheme is optimized, considering the irrigation network constraints and the adopted sowing scenario. The number of plots to be sown in a same day is defined based mainly on the capacity of the irrigation network, i.e., the maximum volume of water that can be delivered to the plots irrigated by the same canal, according to its maximum discharge and location (tertiary, secondary or primary). Thus, the total area that will be sown in a given day is determined such that it can be completely irrigated in one single day during an irrigation round;
- During the agricultural season, before starting each irrigation round, we elaborate an optimal irrigation planning (irrigation date and irrigation water requirement for each plot) over the irrigation scheme according to the sowing calendar scenario and the crop water stress levels in each field. The starting date of each irrigation round is calculated based on the water stress coefficient (Ks), which is used to measure the soil water deficit levels for the crop, as defined in the FAO56 model [61], based on the Normalized Difference Vegetation Index (NDVI), which is a common and widely used remote sensing index to assess the green biomass and the state and health of crops by measuring the difference between near-infrared and red light. Thus, the Ks is equal to 1 at the day of sowing (because the farmers sow after a heavy rainfall event or a pre-irrigation at the beginning of the season). Then, Ks is calculated using the daily soil water balance at the root zone (see Section 2.3). An irrigation round is decided when the Ks reaches a value less than 0.7 at most for 5% of the total cultivated area. This threshold of Ks has been identified as the value above which the water stress does not affect significantly wheat yield [36,62,63]. Then, for each irrigation round, the spatiotemporal irrigation planning is optimized based on the Irrigation Priority Index (IPI) [56] (see Section 2.4 and Section 2.6). When a plot is irrigated, the Ks coefficient becomes equal to 1 and the process continues to define the starting of the next irrigation round. Additionally, no more irrigation is decided for wheat crop at the end of the season when the canopy cover reaches the half of the maximum canopy cover during the senescence stage (see Section 2.2);
- At the end of the agricultural season, an evaluation of the irrigation water consumed and the final yield expected is conducted in order to decide on the most optimal spatiotemporal sowing date calendar to be adopted, i.e., the best recommendations concerning the cultivation schedule which will allow to increase incomes and reduce the use of water resources during the agricultural season.

#### 2.3. Dataset

#### 2.3.1. Meteorological Data

_{0}) is an indicator of the evaporative demand of the atmosphere and it is calculated using the FAO Penman–Monteith equation [61]. The climatic variables (air temperature and humidity, solar radiation and wind speed) needed to estimate ET

_{0}and rainfall were measured by an automatic weather station that was installed within the R3 district. More description about this weather station as well as the different sensors used for measuring the different climatic parameters are previously described by [59,64]. Figure 3 shows the daily ET

_{0}, temperature and rainfall calculated during the 2011–2012 agricultural season. The evolution of ET

_{0}is characteristic of semi-arid continental climate: it is moderate during the autumn (2 to 3 mm/day) and higher in summer (6 to 7 mm/day, in May–June). The annual precipitation is low (equal to 220.7 mm) and irregular and temperature is high in summer (33.5 °C, in June) and low in winter (4.33 °C, in February).

#### 2.3.2. Irrigation Water Supply

#### 2.3.3. Wheat Fields Identification

#### 2.3.4. Applied Sowing Dates Identification

#### 2.3.5. Irrigation Network Identification

- Canals: line type, characterized by an id number, maximum discharge, the flow direction, the geographic coordinates, the category (primary, secondary or tertiary) and plots that are fed;
- Water intakes: point type, representing the devices that supply a plot or a set of plots. Each intake is characterized by an id number, the geographical coordinates, the maximum discharge, the number of plots it supply, the opening and closing times and the id number of the canal to which it is linked;
- Plots: polygon type, characterized by an id number, the farmer’s name, the type of crop, the id number of the canal and the water intake, the date of sowing, the overall area, the irrigated area and the effective irrigation water applied in 2011–2012 season (in terms of time and quantity).

#### 2.4. NDVI Profiles Simulation

- Exponential growth (CC <= CC
_{x}/2):$$\mathrm{CC}={\mathrm{CC}}_{0}{\mathrm{e}}^{\mathrm{tCGC}}$$ - Exponential decay (CC > CC
_{x}/2):$$\mathrm{CC}={\mathrm{CC}}_{\mathrm{x}}-0.25\frac{{\left({\mathrm{CC}}_{\mathrm{x}}\right)}^{2}}{{\mathrm{CC}}_{0}}{\mathrm{e}}^{-\mathrm{tCGC}}$$ - The decline in green crop canopy is described by:$$\mathrm{CC}={\mathrm{CC}}_{\mathrm{x}}\left[1-0.05\left({\mathrm{e}}^{\frac{3.33\mathrm{CDC}}{{\mathrm{CC}}_{\mathrm{x}}+2.29}\mathrm{t}}-1\right)\right]$$
_{0}is the initial canopy cover at t = 0 (%), CC_{x}is the maximum canopy cover at the start of senescence (t = 0), CGC is the canopy growth coefficient (% or cumulative growing degree days), CDC is the canopy decline coefficient (% or cumulative growing degree days), and t is time (days or cumulative growing degree days).

_{0}, CGC, CC

_{x}and CDC. CC

_{0}, CGC and CC

_{x}determine the time required to reach maximum canopy cover, whereas the canopy decline coefficient CDC determines the rate of the green canopy decline in the late season. For our proposed approach, we used the calibrated values of CC

_{0}, CGC, CC

_{x}and CDC obtained by [36] for wheat crop grown in the study area (R3) (Table 2).

_{min}= 0.14 as the minimum value of NDVI, associated with bare soil and dense vegetation in our study area [70].

_{x}/2). In the proposed approach, the optimization process (see Section 2.7) has been defined such that the irrigation window never overlaps the stopping irrigation window.

#### 2.5. Spatialized Estimates of Crop Water Needs and Water Stress Level

_{c}) as the product of the reference evapotranspiration (ET

_{0}) and a crop coefficient that account separately for the crop transpiration K

_{cb}(basal crop coefficient) and for the soil evaporation K

_{e}(soil evaporation coefficient). Additionally, in order to account for the level of the crop water stress to decide when to trigger irrigation, we evaluated the water stress coefficient (K

_{s}). Thus, the actual evapotranspiration (ET) is given by Equation (5):

_{cb}and K

_{e}are derived from NDVI observations using Equations (5) and (6) [64,70]:

_{cb}= 1.64 NDVI − 0.2296

_{e}= (0.2 (1 − CC))

^{3}m

^{−3}), ${\theta}_{\mathrm{WP}}$ is the water content at wilting point in [m

^{3}/m

^{3}] and Zr the rooting depth in (m) which varies according to the plant growth stages.

_{r,i}= D

_{r,i−1}− (P − RO)

_{i}− I

_{i}− CR

_{i}+ ET

_{c,i}+ DP

_{i}

_{r,i−1}and D

_{r,i}are respectively the root zone depletion at the end of day i − 1 and i (mm), and Pi is the precipitation, RO

_{i}is the runoff, Ii is the net irrigation depth, CR

_{i}is the capillary rise from the groundwater table, ET

_{c,i}is the crop evapotranspiration, and DP

_{i}is the water loss out of the root zone by deep percolation on day i (mm).

#### 2.6. Grain Yield Estimation

#### 2.6.1. NDVI-Based Approach

#### 2.6.2. AquaCrop-Based Approach

^{2}), WP is the normalized water productivity (kg·m

^{−2}) and Tr is the crop transpiration (mm).

^{2}), B is the total ground biomass (kg/m

^{2}) and HI is the harvest index (%).

#### 2.7. The Optimization Methodology

#### 2.7.1. Irrigation Priority Index (IPI)

_{s}map that represent the most and less stressed plots, respectively. $\delta {t}_{\mathrm{i}}$ the time delay (in days) between the beginning time of the irrigation round and the irrigation time of plot i and T the duration of the irrigation round. Values of $\delta {t}_{\mathrm{i}}$ range between 0 and T and are chosen as the decision variables of the optimization process.

#### 2.7.2. Sowing Date Optimization

- (a)
**Inputs**: available water resources, geospatial data and meteorological data;- (b)
**Decision variables**: the sowing date of each plot. We have 116 plots to be sown, which means 116 decision variables are considered;- (c)
**Optimization constraints**: we identified five constraints which we present by a decreasing level of priority.- The capacity constraint: supplies must never exceed the total capacity of the canal. This constraint is expressed by Equations (16) and (17):$$\sum _{j=1}^{J}{Q}_{j}}\left(\delta t\right)\le \Theta \left(\delta t\right)$$$$\sum _{i,j=1}^{I,J}{q}_{ij}}\left(\delta t\right)\le {Q}_{j}\left(\delta t\right)$$
^{3}/s), i and j are respectively the tertiary and secondary canals’ number, opened at the same time; - The interval constraint: all the irrigation tasks must be scheduled within the specified irrigation round interval, expressed by Equations (18) and (19):$$\delta {t}_{start}\le \delta {t}_{i}\le E$$$$\delta {t}_{i}+{D}_{i}\le E$$
- The overlap constraint: all the practical actions must be applied dependably (not simultaneously), considering the geographical distance between water intakes and the irrigation time span required for each plot supplied by the same canal;
- The traveling time: the time required for the operator to travel from one canal gate to another to start/stop an irrigation which depends on the distance between canals that can be significant. This time is calculated linearly based on the spatial distance between two intakes and assuming a moving speed of 30 km/h;
- The daily working time of operators: each scheduled task (start/stop an irrigation) must be scheduled within the specified working time that is between 8:00 h and 18:00 h;

- (d)
**The objective function**: the first objective function aims to propose the best spatiotemporal sowing distribution which minimize the gravity irrigation network constraints by exploring the space of decision variables in an efficient manner. In case the constraints are not met, we adopt the penalty method by adding penalty function. Thus, the first objective function is defined by Equation (20):$${F}_{1}={\displaystyle \sum _{j=1}^{5}{r}_{j}{P}_{j}}$$_{j}is the weight associated to each constraint j, and P_{j}the corresponding penalty expressed by Equation (21):$${P}_{j}={\displaystyle \sum}_{k=1}^{N}{\vartheta}_{j,k}$$

#### 2.7.3. Irrigation Scheduling Optimization

_{s}), while considering the irrigation network constraints. For that, we consider that the best distribution is the one that minimizes the IPI index (in terms of absolute value). Thus, for the resolution of this second optimization problem, we applied the CMA-ES algorithm, such as:

- (a)
**Inputs**: available water resources, geospatial data, meteorological data, soil proprieties, NDVI profiles, and K_{s};- (b)
**Decision variables**: During each irrigation round, two types of decisions must be made: when to irrigate the plots and in what order (i.e., the sequence and scheduling of the irrigations). The answer to these two questions is integrated into a single decision variable that consists of defining the start date to irrigate each plot (the stopping date is calculated based on the water amount to be supplied to a plot given the calculated irrigation duration and the constant flow rate of the tertiary canal). The stating date to irrigate the plots can therefore be considered as the only decision variables in the optimization process. In this work, 116 plots are scheduled, which means that 116 decision variables are considered during the optimization process while considering the constraints related to the irrigation network;- (c)
**Optimization constraints**: the same as the first optimization (i.e., irrigation network constraints);- (d)
**The objective function**: the second objective function aims to propose the best spatiotemporal irrigation distribution, which minimize the IPI index and the gravity irrigation network constraints. Thus, the second objective function is defined by Equation (22):$${F}_{2}={\displaystyle \sum}_{k=1}^{N}{\left({\mathrm{IPI}}_{k}\right)}^{2}+{F}_{1}$$

_{s}coefficient is chosen for the next execution, which means that we first begin with the irrigation of the most stressed plots (depending on the canal flow rate), which imply to minimize the level of water stress within the block of plots irrigated by the same canal.

- if capacity = 30 L/s: flow = 0.03 × 3600 = 108 m
^{3}/h; - if capacity = 60 L/s: flow = 0.06 × 3600 = 216 m
^{3}/h; - if capacity = 90 L/s: flow = 0.09 × 3600 = 324 m
^{3}/h.

## 3. Results

#### 3.1. Optimization of the Spatiotemporal Sowing Date Distribution

#### 3.2. Effect of Sowing Date Optimization on Wheat Growth and Irrigation Schedules

_{s}reaches a value less than 0.7 at most for 5% of the total cultivated plots.

#### 3.3. Effect of Sowing Date Optimization on Water Requirements

#### 3.4. Effect of Sowing Date Optimization on Wheat Yield

## 4. Discussion

## 5. Conclusions

_{c}) with the observed irrigation amounts applied by farmers. Results showed that a reduction of up to −40% of water needs can be achieved. The simulated wheat yields after sowing dates optimization were compared with the estimated ones at the real case by applying two different approaches: NDVI-based approach and AquaCrop model. The results revealed that the early sowing scenarios lead to higher wheat yields compared to the late sowing scenarios for both approaches with a homogeneous distribution over the plots compared to the observed one, which implies a better equity among farmers.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Main irrigated sectors in the Tensift El Haouz basin; (

**b**) the gravity irrigation network in the R3 study area.

**Figure 2.**Flowchart of the proposed approach for yield and water resources optimization based on spatiotemporal sowing date optimization.

**Figure 3.**Reference evapotranspiration (ET

_{0}), rainfall amounts and air mean temperature during 2011–2012 agricultural season in the study area (R3).

**Figure 4.**Distribution of the sowing dates over the plots for each sowing scenario. Day number 1 is equal to the start date which change from one scenario to another.

**Figure 5.**Convergence of the objective function for each sowing scenario during the optimization process.

**Figure 8.**Stress coefficient (Ks) map of the first sowing scenario (

**a**) and the sixth sowing scenario (

**b**) at the beginning of the third irrigation round.

**Figure 9.**Variation of Ks coefficient and day of irrigation at the third irrigation round (IR), from one sowing scenario to another.

**Figure 10.**Distribution of the optimized IPI index at plot level for each sowing scenario (IRi represents the irrigation round number in the growing season).

**Figure 11.**IPI index distribution with sowing date optimization (for each sowing date) and without sowing date optimization (from previous study) at the third irrigation round of the 2011–2012 agricultural season.

**Figure 12.**Comparison of the variation of irrigation amount (mm), between simulated scenarios and the real case (observed irrigation at the 2011–2012 agricultural season). The statistical Student’s t-test shows that there are two groups of scenarios (S1, S5 and S6) and (S2, S3 and S4) at p > 0.05.

**Figure 13.**Variation of grain yield (t/ha), between simulated scenarios and the real case (2011–2012 agricultural season) based on the NDVI profiles (1st approach). The statistical Student’s t-test shows that S1 and S2 are identical (p > 0.05), and the other scenarios are significantly different (p ≤ 0.05).

**Figure 14.**Variation of grain yield (t/ha), between simulated scenarios and the real case (2011–2012 agricultural season) based on the AquaCrop model (second approach). The statistical Student’s t-test shows that S1 and S2 are identical (p > 0.05), and the other scenarios are significantly different (p ≤ 0.05).

**Figure 15.**Variation of the biomass (t/ha), between simulated scenarios and the real case (2011–2012 agricultural season) based on the AquaCrop model. The statistical Student’s t-test shows that S1 and S2 are identical (p > 0.05), and the other scenarios are significantly different (p ≤ 0.05).

Irrigation Round | Start Date | End Date | Duration (Day) | Applied Water Amounts (mm) |
---|---|---|---|---|

1 | 3 December 2011 | 24 December 2011 | 21 | 46 |

2 | 1 January 2012 | 21 January 2012 | 20 | 52 |

3 | 9 February 2012 | 29 February 2012 | 20 | 52 |

4 | 1 March 2012 | 23 March 2012 | 22 | 100 |

5 | 22 April 2012 | 4 May 2012 | 12 | 24 |

Early Sowing | Late Sowing | |
---|---|---|

CC_{0} | 4.5 | 3.83 |

CC_{X} | 89.33 | 81.33 |

CGC | 0.0089 | 0.0089 |

CDC | 0.145 | 0.145 |

**Table 3.**Optimized irrigation windows, sowing windows, stopping irrigation window, number and mean duration of irrigation round (IR) and the mean gap between two successive irrigation rounds.

Scenario | Gap between IR (Day) | Mean IR Duration (Day) | Number of IR | All Irrigations Window | Stopping Irrigation Window | Sowing Window |
---|---|---|---|---|---|---|

1 | 16 | 18 | 5 | [14 December 2011–19 May 2012] | [30 May 2012– 12 June 2012] | [1 November 2011– 4 December 2011] |

2 | 14 | 21 | 5 | [15 December 2011–29 May 2012] | [7 June 2012– 17 June 2012] | [16 November 2011– 16 December 2011] |

3 | 18 | 18 | 5 | [30 December 2011–9 June 2012] | [13 June 2012– 25 June 2012] | [1 December 2011–31 December 2011] |

4 | 14 | 19 | 5 | [14 January 2012– 13 June 2012] | [17 June 2012– 29 June 2012] | [16 December 2011–15 January 2012] |

5 | 13 | 19 | 4 | [7 February 2012–4 June 2012] | [20 June 2012– 3 July 2012] | [1 January 2012– 31 January 2012] |

6 | 16 | 19 | 4 | [14 February 2012–17 June 2012] | [23 June 2012– 7 July 2012] | [16 January 2012– 15 February 2012] |

Observed irrigation | 15 | 19 | 5 | [3 December 2011–4 May 2012] | [7 June 2012– 25 June 2012] | [16 November 2011–31 January 2012] |

**Table 4.**Irrigation water demands (mm) estimated for each irrigation round (IR) compared to the applied irrigations at the 2011–2012 agricultural season.

IR 1 (mm) | IR 2 (mm) | IR 3 (mm) | IR 4 (mm) | IR 5 (mm) | Total (mm) | |
---|---|---|---|---|---|---|

1st Sowing Scenario | 10 | 19 | 30 | 35 | 47 | 141 |

2nd Sowing Scenario | 7 | 10 | 33 | 53 | 61 | 164 |

3rd Sowing Scenario | 6 | 11 | 32 | 54 | 75 | 178 |

4th Sowing Scenario | 6 | 11 | 27 | 48 | 75 | 168 |

5th Sowing Scenario | 8 | 24 | 45 | 79 | 156 | |

6th Sowing Scenario | 4 | 29 | 48 | 72 | 152 | |

Observed Irrigation | 46 | 52 | 52 | 100 | 24 | 274 |

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**MDPI and ACS Style**

Belaqziz, S.; Khabba, S.; Kharrou, M.H.; Bouras, E.H.; Er-Raki, S.; Chehbouni, A.
Optimizing the Sowing Date to Improve Water Management and Wheat Yield in a Large Irrigation Scheme, through a Remote Sensing and an Evolution Strategy-Based Approach. *Remote Sens.* **2021**, *13*, 3789.
https://doi.org/10.3390/rs13183789

**AMA Style**

Belaqziz S, Khabba S, Kharrou MH, Bouras EH, Er-Raki S, Chehbouni A.
Optimizing the Sowing Date to Improve Water Management and Wheat Yield in a Large Irrigation Scheme, through a Remote Sensing and an Evolution Strategy-Based Approach. *Remote Sensing*. 2021; 13(18):3789.
https://doi.org/10.3390/rs13183789

**Chicago/Turabian Style**

Belaqziz, Salwa, Saïd Khabba, Mohamed Hakim Kharrou, El Houssaine Bouras, Salah Er-Raki, and Abdelghani Chehbouni.
2021. "Optimizing the Sowing Date to Improve Water Management and Wheat Yield in a Large Irrigation Scheme, through a Remote Sensing and an Evolution Strategy-Based Approach" *Remote Sensing* 13, no. 18: 3789.
https://doi.org/10.3390/rs13183789