# Identifying Optimal Irrigation Water Needs at District Scale by Using a Physically Based Agro-Hydrological Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The FLOWS-HAGES Model

- Soil water contents and pressure potentials in the soil profile;
- Water uptake and actual evapotranspiration (actual water needs);
- Solute (e.g., nitrates, pesticides, salts, heavy metals) concentrations in the soil profile;
- Deep percolation water fluxes (return flow to the groundwater) and their quality in terms of solute (solute fluxes);
- Stress periods for each crop.

- To provide effective water requirement data to be used for optimal management of the irrigation network;
- To facilitate the decision-making process on the quantities of water to be allocated to agricultural users;
- To consider the most profitable cropping patterns given water availability restrictions imposed by the existing hydrological systems, and the potential yields reached in each irrigation district according to its productive characteristics, irrigation efficiency, economic scenario and external factors such as agricultural policies;
- To predict the impact of anticipated climate changes on the irrigation system under the current land use and vegetation cover;
- To predict the impact of human-driven changes in the land use on the irrigation system under current climate conditions;
- To predict the impacts on the irrigation system under mixed conditions 4–5.

_{gross}, as follows:

_{net}, to be supplied on day t is calculated as the difference between Irr

_{gross}and the eventual rain falling at the time when the irrigation starts.

_{gross}, irrigation water is not supplied.

_{act}, may be obtained by dividing Irr

_{net}by the on-farm irrigation efficiency, IE, of the irrigation system used for the crop considered, to give:

_{irr}, to satisfy a given Irr

_{act}at day t is

_{act}) for each field in the sector for day t, the model calculates the overall discharge to be delivered in that day (the discharge to be delivered at the sector head).

#### 2.2. Sector 6 of the Capitanata Irrigation Network

^{3}, which in turn is supplied with water by the Capacciotti dam. The hydraulic scheme of the low zone is presented in Figure 3b.

#### 2.3. Soil Characterization in Sector 6

_{s}at h = 0 by the gravimetric method and hydraulic conductivity K

_{s}at θ

_{s}by the falling-head method [14]. The θ(h) data points were measured using a sand-kaolin suction table. Water retentions were obtained at the following pressure heads: 1.0, 3.0, 7.0, 10.0, 15.0, 30.0, 70.0, 90.0, 130.0 and 180.0 cm (referring to the middle of the sample). We assumed that the average water contents actually corresponded to the indicated pressure head values [15].

#### 2.4. Crop Distribution and Actual Irrigation Volumes (Year 2016)

^{3}. The distribution network of Sector 6 supplies water to 31 delivery hydrants, and covers a total cultivated area of 129 ha, of which 64 ha of vineyards consumed, according to CBC, more than 73,000 m

^{3}in 2016 (Table 2).

^{3}, amounting to 38% of total water consumption. N/A means Not Available

#### 2.5. Evaluating Model Simulations by Direct Water Content Measurements

_{w}, volumetric water content, θ, tortuosity, τ, of the soil pore system, as well as on other factors related to the solid phase such as bulk density, clay content and mineralogy. Consequently, separating the effect of single soil properties (e.g., soil water) on ECa is no simple task (see for example, [17,18]). However, in two separate studies, [19,20] found spatial variation in soil water stored within the top 0.5 and 1.7 m to be highly correlated with the spatial variation in ECa measured with EMI sensors. Similar results were obtained by other authors (see for example, [21]. These studies demonstrated that in soils with low salinity, measurements of soil ECa can be used for estimating soil water stored in the soil profile. Estimating soil water content using ECa readings requires a site-specific calibration relating EMI measurements to simultaneous water contents measured by a different standard reference method. In this sense, the time-dynamics of water storage in the selected fields was measured by a Diviner 2000 (Sentek Pty Ltd, Stepney, South Australia) capacitance sensor. A Diviner access tube was installed in three sites of each field up to a depth of 1 m. The Diviner 2000 is a capacitance device consisting of a single sensor fitted to a square rod which can be lowered in a PVC plastic access tube (5.1-cm “i.d.”, 5.6-cm “o.d.”) [22].

## 3. Results and Discussion

#### 3.1. Irrigation Volumes Measured and Calculated by the Model

#### 3.2. Irrigation Volumes, Pressure Heads in the Root Zone and Deep Percolation Fluxes

#### 3.3. List of Hydrants to be Opened and Efficiency Indices

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. FLOWS-HAGES: Short Model Description

#### Appendix A.1. Water Flow

^{−1}) is the soil water capacity, h (L) is the soil water pressure head, t (T) is time, z (L) is the vertical coordinate being positive upward, K (h) (L·T

^{−1}) the hydraulic conductivity and S

_{w}(h) (T

^{−1}) is a sink term describing water uptake by plant roots.

#### Appendix A.2. Solute Transport

^{−3}) and Q (M·M

^{−1}) are the amount of solute in the liquid and adsorbed phases, respectively, q (L T

^{−1}) is the darcian flux, ρ

_{b}(M L

^{−3}) is the bulk density, D (L

^{2}T

^{−1}) the hydrodynamic dispersion coefficient. S

_{s}is a source-sink term for solutes. Hydrodynamic dispersion is related to the molecular diffusion constant of the substance in bulk water, D

_{0}(L

^{2}T

^{−1}), and the pore water velocity, v = q/θ, as:

#### Appendix A.3. Hydraulic Properties

_{e}is effective saturation and θ is the water content (θ

_{s}and θ

_{r}are the water content at h = 0 and for h→∞, respectively). α

_{VG}(cm

^{−1}), n and m = 1 − 1/n are shape parameters. Note the effective saturation, S

_{e}, is to be considered as a cumulative distribution function of pore size with a density function f(h) which may be expressed by:

_{r}to θ

_{s}consists of two f

_{i}(h) distributions obtained by Equation (A5), each occupying a fraction ϕ

_{i}of that pore space. Bimodal Durner model [27]:

_{i}is the weighting of the total pore space fraction to be attributed to the ith subcurve, and α

_{i}, n

_{i}and m

_{i}still represent the fitting parameters for each of the partial curves. Bimodal Ross and Smettem model [28]:

_{r}, to f(h) by the equation:

_{0}is the hydraulic conductivity at h = 0, and τ is a parameter accounting for the dependence of the tortuosity and the correlation factors on the water content.

#### Appendix A.4. Root Uptake

_{p}(d

^{−1}), is simulated macroscopically by distributing potential transpiration, T

_{p}(cm·d

^{−1}), over the root zone depth, Dr (cm), on the basis of a normalized root density distribution, g(z) (cm

^{−1}), with depth z. The normalized root density distribution may be obtained by normalizing the root length density distribution R

_{ld}(cm·cm

^{−1}) by its integral across the rooting depth, Dr:

_{ld}may be calculated as the ratio of the total length, Lr(z), of roots in a sample to the sample volume. Hereafter, we will define the denominator of Equation (A2) as root length density integral, R

_{Int}. g(z)dz is the fraction of roots located between z and z + dz. In the macroscopic approaches to root uptake, the function g(z) distributes the potential transpiration rate, T

_{p}, through the root zone in proportion to the root distribution [31,32]:

_{rw}and α

_{rs}being reduction factors depending on the local (at a given z) water pressure head, h (cm) and osmotic head, h

_{o}(cm), respectively.

_{a}being the actual transpiration rate and β a dimensionless water stress index integrated over the whole rooted profile [33,34], providing a measure of total plant stress. A value of β equal to 1 indicates that there is no stress in the soil root zone and that the actual transpiration rate T

_{a}is equal to the potential transpiration rate T

_{p}.

_{rw}= 1 and root uptake parameterization reduces to finding the factor α

_{rs}, depending on the osmotic potential (h

_{o}) induced by salts in the soil water.

#### Appendix A.5. Calculating the Water Stress Reduction Factor α_{rw}

_{rw}that have been proposed over the years. We mention here two general model types that have been used most often: piecewise linear functions and continuous smooth functions. To describe water stress, Feddes [31] proposed a piecewise linear reduction function parameterized by four critical values of the water pressure head, h

_{4}< h

_{3}< h

_{2}< h

_{1}:

_{2}or h < h

_{3}, and becomes zero when $h\le {h}_{4}orh\ge {h}_{1}$. In general, the value of h

_{3}is expected to be a function of evaporative demand.

_{50}and p

_{1}are adjustable parameters. Equation (A23) was motivated by a study [36] that found that an S-shaped function described salt tolerance yield reduction data better that other functions, including the threshold-slope model of Maas and Hoffman [37].

#### Appendix A.6. Calculating the Salinity Stress Reduction Factor α_{rs}

_{o}, consistent with the Mass and Hoffman [37] model for crop salt tolerance (Equation (A6)), the effects of salinity stress on root water uptake can be described using the piecewise linear (threshold-slope) function:

_{2}and h

_{o,50}are the adjustable parameters, the latter being the osmotic pressure head where uptake is halved.

_{o}, is assumed to be a linear function of soil solution salinity EC

_{w}according to U. S. Salinity Laboratory Staff [45]:

#### Appendix A.7. Combined Water and Salinity Stress

_{rw}= α

_{rs}= 1. Although additivity has been inferred from a number of laboratory and field experiments (e.g., [46,47,48,49,50]), its general applicability remains uncertain [51], especially for field conditions subject to relatively wide ranges in pressure heads (wetting/drying cycles).

_{rw}and α

_{rs}can be calculated as described above. In this case, Equation (A27) becomes:

_{50}, p

_{50}, p

_{1}and p

_{2}are the presumably crop, soil and climate-specific parameters.

#### Appendix A.8. Root Density Distribution

#### Appendix A.9. Solute Sink Term

_{s}is:

^{−1}), R

_{pf}is the root uptake preference factor (dimensionless) accounting for positive or negative selection of solute ions relative to the amount of soil water that is extracted [23].

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**Figure 1.**Graphical view of the criterion used by the model to calculate the time for irrigation and the irrigation volume. (

**a**) hav higher than hcrit, no irrigation is required; (

**b**) hav lower than hcrit, irrigation is required to bring the pressure head at the field capacity, hfc.

**Figure 2.**Graphical view of the irrigation volume calculation according to the criterion shown in Figure 1.

**Figure 3.**The study area (

**a**). The hydraulic scheme of the low-zone (

**b**). Sector 6 of district 10 in the “Sinistra Ofanto” irrigation system (

**c**).

**Figure 4.**(

**a**) Soil profile distribution; (

**b**) Digging of a soil pit; (

**c**) details of the soil profile vegetation context.

**Figure 6.**Cumulative irrigation actually supplied by farmers and calculated by the model (the bold red line) for grape (

**a**) and peach (

**b**).

**Figure 7.**FARM G 2-3. (

**a**) Irrigation volumes (both per single day and cumulative) calculated by the model (MOD); (

**b**) irrigation volumes actually supplied by the farmer (ON-DEM); (

**c**) pressure head at 40 cm depth; (

**d**) percolation fluxes at 80 cm; (

**e**) comparison between the time evolution of the water storage predicted by the model (MOD) and that estimated starting from the electromagnetic induction technique (EMI) sensor apparent electrical conductivity (ECa) readings (MEAS).

**Figure 8.**FARM G 52-1. (

**a**) The irrigation volumes (both per single day and cumulative) calculated by the model (MOD); (

**b**) the irrigation volumes actually supplied by the farmer (ON-DEM); (

**c**) the pressure head at 40 cm depth; (

**d**) the percolation fluxes at 80 cm; (

**e**) comparison between the time evolution of the water storage predicted by the model (MOD) and that estimated starting from the EMI sensor ECa readings (MEAS).

**Figure 9.**FARM P 54-4. (

**a**) The irrigation volumes (both per single day and cumulative) calculated by the model (MOD.); (

**b**) the irrigation volumes actually supplied by the farmer (ON-DEM); (

**c**) the pressure head at 40 cm depth; (

**d**) the percolation fluxes at 80 cm; (

**e**) comparison between the time evolution of the water storage predicted by the model (MOD) and that estimated starting from the EMI sensor ECa readings (MEAS).

**Figure 10.**FARM P 49-5. (

**a**) Irrigation volumes (both per single day and cumulative) calculated by the model (MOD); (

**b**) irrigation volumes actually supplied by the farmer (ON-DEM); (

**c**) the pressure head at 40 cm depth; (

**d**) the percolation fluxes at 80 cm; (

**e**) comparison between the time evolution of the water storage predicted by the model (MOD) and that estimated starting from the EMI sensor ECa readings (MEAS).

**Figure 11.**Maps of four indices: (

**a**) Ratio of irrigation volumes model/irrigation volumes on-demand (IR MOD/IR ON-DEM); (

**b**) ratio of drainage volumes model/drainage volumes on-demand (DR MOD/DR ON-DEM); (

**c**) ratio of drainage volumes model/irrigation volumes on-demand (DR MOD/IR ON-DEM); (

**d**) ratio of drainage volumes on-demand/irrigation volumes on-demand (DR ON-DEM/IR ON-DEM).

Profile | Horizon | Texture (%) | Texture Class (USDA) | ||
---|---|---|---|---|---|

Sand | Clay | Silt | |||

P1 | Ap1 | 7.95 | 33.75 | 58.30 | Silty-Clay-Loam |

Bw1 | 5.25 | 46.25 | 48.50 | Silty-Clay | |

Bw2 | 5.75 | 38.75 | 55.50 | Silty-Clay-Loam | |

Bw3 | 6.63 | 41.25 | 52.13 | Silty-Clay | |

P2 | Ap1 | 27.00 | 18.75 | 54.25 | Silty-Loam |

Ap2 | 33.48 | 18.75 | 47.78 | Loam | |

Bw1 | 34.70 | 21.25 | 44.05 | Loam | |

Bw2 | 34.90 | 21.25 | 43.85 | Loam | |

P3 | Ap | 20.45 | 26.25 | 53.30 | Silty-Loam |

Bw1 | 20.00 | 26.25 | 53.75 | Silty-Loam | |

Bw2 | 19.80 | 31.25 | 48.95 | Silty-Clay-Loam | |

Bw3 | 14.50 | 31.25 | 54.25 | Silty-Clay-Loam | |

P4 | Ap | 32.15 | 21.25 | 46.60 | Loam |

C1 | 35.55 | 18.75 | 45.70 | Loam | |

C2 | 40.30 | 18.75 | 40.95 | Loam | |

CK3 | 39.85 | 18.75 | 41.40 | Loam | |

P5 | Ap | 25.00 | 33.75 | 41.25 | Clay-Loam |

B/C | 47.25 | 23.75 | 29.00 | Loam | |

Bw1 | 28.25 | 33.75 | 38.00 | Clay-Loam | |

Bw2 | 29.70 | 33.75 | 36.55 | Clay-Loam |

Crop | Area (ha) | Water Consumption (m ^{3}) (Year 2016) | Water Consumption (%) |
---|---|---|---|

Vineyard | 64 | 73,640.3 | 60.4 |

Early peach | 30 | 46,320.7 | 38 |

Autumn winter cereals | 20 | N/A | N/A |

Vegetable | 6.5 | N/A | N/A |

Fallow | 5 | N/A | N/A |

Table Grape | 1 | 732.3 | 0.6 |

Apricot | 1 | 1163.7 | 1 |

Olive | 1 | N/A | N/A |

**Table 3.**List of hydrants to be opened day by day and volumes (m

^{3}) to be supplied during the growing season for grape (year 2016).

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**MDPI and ACS Style**

Coppola, A.; Dragonetti, G.; Sengouga, A.; Lamaddalena, N.; Comegna, A.; Basile, A.; Noviello, N.; Nardella, L.
Identifying Optimal Irrigation Water Needs at District Scale by Using a Physically Based Agro-Hydrological Model. *Water* **2019**, *11*, 841.
https://doi.org/10.3390/w11040841

**AMA Style**

Coppola A, Dragonetti G, Sengouga A, Lamaddalena N, Comegna A, Basile A, Noviello N, Nardella L.
Identifying Optimal Irrigation Water Needs at District Scale by Using a Physically Based Agro-Hydrological Model. *Water*. 2019; 11(4):841.
https://doi.org/10.3390/w11040841

**Chicago/Turabian Style**

Coppola, Antonio, Giovanna Dragonetti, Asma Sengouga, Nicola Lamaddalena, Alessandro Comegna, Angelo Basile, Nicoletta Noviello, and Luigi Nardella.
2019. "Identifying Optimal Irrigation Water Needs at District Scale by Using a Physically Based Agro-Hydrological Model" *Water* 11, no. 4: 841.
https://doi.org/10.3390/w11040841