*2.5. Testing Scenarios*

In order to demonstrate the use of the model, we proposed a set of example scenarios:


crops are quite common in the area. Crop failure occurs when a crop has a stress less than or equal to 0.45 over a 5-day period (Table 2). The irrigation system is a furrow, and it is activated when the crop is at 0.6 stress. In case of competition for irrigation water, the farmer favors the crop with the highest stress level in order to avoid losing production quality.

4. Sc3: For Scenario 3, the farmer has the same cropping system and the same structural aspects as Sc2, but he decides to install a pond in addition. The functioning of this pond is different from that of Sc1. The pond in Sc3 is filled with water from the borewell in addition to the runoff, in order to store water on days when there is no irrigation demand, or if there is excess water after irrigation.


**Table 2.** Crop parameters regarding crop water stress (see A3 for details).

For all the scenarios, the farm size assumed is 1 ha with a typical black soil. We used the 15-year Maddur climatic series (Latitude: 12◦35 3.01 N; Longitude: 77◦02 41.64 E) to run the simulation. The full parametrization of Sc0 is given in Appendix B.

#### **3. Results**

#### *3.1. Model Graphic User Interface*

When the user opens NIRAVARI, only three worksheets are initially visible: (i) a "read me" sheet explaining how to use the model; (ii) a Climate sheet, allowing the integration of the requested climatic data; and (iii) an Init sheet, allowing the user to parametrize the simulation. The Graphic User Interface allows the user to parametrize the simulation (Figure 3) with different validation processes (based on "data validation" from Excel). Information is given to the user whereby they have to fill in some data. Only cells in yellow can be modified. Once the parametrization is performed, the user clicks on the "Run" button, allowing for the simulation to run. When the simulation is over, a new workbook is opened with the computed data and some standard graphs, to then analyze the simulation.

A second button, "Load", allows the user to load a previous run to test a modification on a base scenario.


**Figure 3.** The upper screen of the graphic user interface. This Graphic User Interface allows for parametrizing of the simulation. Information and data validation are performed at this step.

#### *3.2. Playing with the Model*

The first indicator we observed was the level of crop failure over the 15-year climatic period (Table 3). Crop failure process is explained in A3. Growing using a rainfed system, (Sc0) shows a failure of 15% of the crops developed over the 15 years. Adding a pond in the jeminu (Sc1) improves the result (8% failure). This is due to the use of some irrigation to remove water stress to crops. However, it is impossible to avoid all failures, since the amount of water in the pond is not sufficient to irrigate all the crops in case of drought years. Moving to a pump and borewell system with more water-sensitive crops (but more expected economic return), (Sc2) shows a higher percentage of crop failure (29%). This high level of crop failure, despite irrigation possibilities, is due to two factors. The first is the use of more water-deficit-sensitive crops (Table 2). The second is due to the irrigation process itself. All beles cannot be irrigated on the same day, and the amount provided to the crops due to the irrigation technique (furrow) implies long irrigation cycles. Some beles are therefore not irrigated when needed, increasing the crop water stress leading to crop failure. This demonstrates the impact of the choice of water-intensive crops in spite of the addition of a bore well. If a buffer pond is added (Sc3), the situation improves with only 8% of crop failure.


**Table 3.** Percentage of crop failure over the 15-year climatic serie.

The second indicator is an economic estimation (Figure 4). We used the net return indicator (*NR*) to compare the scenario estimated as (3):

$$NR = \sum\_{i=1}^{n} [A\_i \;/\, 10,000 \cdot ((Y\_i \* w\_i \* p\_i) - \mathbb{C}\_i)] \tag{3}$$

where *Ai*: crop area (m2), *Yi*: crop potential yield (T·ha−1), *wi*: mean crop water stress; *<sup>p</sup>*: crop price (Rs·t <sup>−</sup>1); *Ci*: crop costs (Rs·ha−1). We carried out a survey with farmers in the region to estimate the production costs, the market price and the potential yield for each crop. In case of crop failure, which can occur at any time during the crop cycle, we estimate that the farmer loses all production costs.

Sc0 situation allows farmers to earn 48,600 Rs (median), with a consequent number of years of loss. Adding a pond for protective irrigation (Sc1) drastically reduces the years of losses and low net return. The system with irrigated crops with a borewell (Sc2) improves the median net return (336,000 Rs), but makes it very variable due to the crops' failure and high-value crops' sensitivity to water shortages and droughts. Adding a buffer pond (Sc3) not only improves the median net return (489,000 Rs), but also reduces variability.

The third indicator is based on the pond water budget (Figure 5). This figure is more complex as it integrates the different components used to compute the dynamic of the pond water budget. The dynamic of the volume of the pond is given in clear blue on the first y-axis (left-hand). Input variables for the pond are on the first y-axis: rain (red), refill from the borewell (yellow) and runoff from the watershed (gray). The output variables are given on the second y-axis (right hand) in inverse order, the zero value being at the top of the graph: pond over flooding (orange), pumped for irrigation (lilac) and evaporation (light red). Depending on the parameters used for simulation, some of these variables will be null, or will change during the simulation. Scenarios Sc1 and Sc3 show two different modes of using the pond. In Sc1, the pond contributes to storing runoff water for irrigation when crops are most stressed. The pond is filled from time to time and quite slowly (Figure 5A). In Sc3, the pond is used as a buffer in order to store the water available by the pump and

by the runoff. The pond is therefore filled quite often. It is used when the pump flow rate is not sufficient to provide the required irrigation needs.

**Figure 4.** Net return distribution over the 15-year simulation period by scenario.

**Figure 5.** *Cont*.

**Figure 5.** Pond water budget for Sc1 (**A**) and Sc3 (**B**).

The last indicator we propose is water table evolution due to the use of the different systems (Figure 6). The use of the pond in Sc1 has a low impact on the water table (comparing Sc0 and Sc1). The slight decrease in water table levels in Sc1 comes from the reduction of crop failures, which consequently reduces the water that is drained into the groundwater, as it is used by the saved crops. The 100% irrigated cropping system of Sc2 impacts the level of the water table, because the long-term pumping pushes the water table to a quasi-constant decline. On the other hand, in Sc3, and in addition to the phenomenon explained before (the reduction of crop failure), the amount of water pumped is important because all the water available from the pump for one day is pumped even if there is no irrigation demand or if the irrigation demand is lower than the water available from the pump.

**Figure 6.** Evolution of the water table depth depending on the four scenarios of farming practices.

#### **4. Discussion**

So far, no model exists to deal with farmers' decision-making to irrigate their farms with multiple irrigation sources in the Indian context. NIRAVARI has been developed to be used as a tool by policy makers and technical advisors to assess different policies better placed to manage water resources in the broader context of climate change. To develop such a tool, we reused simple but robust, already existing models, such as the FAO model for crop growth and other simple models for other processes. The originalities of NIRAVARI regarding other irrigation models in India (see for example) are: (1) the decision-making model and its ability in testing a large range of decisions based on simple criteria; (2) its ability to study the distribution of water from the same source to different crops; (3) its ability to study two irrigation sources simultaneously; and (4) to consider the feedback between the cropping system and the water source.

Instead of using complex modelling languages, we chose a wide-spread language (VBA), allowing for object-oriented modelling and programming. Each element of our farm system is then modeled as an object, and a multiplicity of objects (such as beles or crops) are dealt with as structured containers. The use of Excel allows users to manage simple graphic user interfaces with validation processes in order to avoid any false input to the model parameters.

The scenarios tested show that rainfed systems can maintain a balance in the water table, but the income from these systems is very low and highly variable due to climate variability. However, adding a pond to this system reduces the vulnerability of these farms to climate variability while preserving the water table. On the other hand, a 100% irrigated system with high-added value crops leads to a significant improvement in income, but a drastic decrease in the water table. Indeed, this system leads to an instability of income that systematically decreases with the lack of water. Adding a pond buffer to this system limits the variability of income, but accentuates the decline of the water table, which limits the sustainability of the groundwater resource. These simulations can provide valuable considerations to policymakers, to decide on production systems and water storage technologies, and for their use to be promoted.

Creating such a parsimonious, simple and handy model is also limited to the range of model applications, and the interpretation of some outputs should be considered with care. For example, the choice of the FAO-56 single coefficient formalism [33] implies that the model represents evaporation and transpiration as a single flux, and therefore, calculating the crop water use efficiency for different scenarios is not possible. Similarly, as in the FAO-56 formalism, there is no impact of the water stress on crop water demand, the stress is probably overestimated for rainfed crops—adapted to reduce their demand during drought—compared to strictly irrigated crops. Finally, the impact of water stress on the marketable yield, although drastically simplified (with no account for the disproportionate effect of stress during few critical phenologic stages and being more pronounced for water intensive crops than for more rustic ones), implies that the economic outputs of the model must be considered only as rough estimates.

Moreover, the size of the jeminu, the number and size of plots being fixed, the crop rotation being a forced variable for each simulation, and the adaptation of farmers to variations of water availability can be only partially accounted for in the model. This is the case of the "Jevons paradox" observed in Indian systems, where access to water-saving irrigation technologies can induce an increase of the irrigated area, and therefore, a faster depletion of the aquifer [37].

Finally, while one original feature of NIRAVARI is to account for the feedback between agricultural practices and groundwater resources, it can only represent one farm at a time, and therefore, the results of the simulations should not be interpreted as predictions of what is likely to happen in a farm, which could be surrounded by other farms with very different practices, all foraging the same aquifer. Instead, users should keep in mind that the type of questions to ask the model are rather of the type: "What is likely to happen if all farmers in a small region adopt the same practices as the one that is simulated in NIRAVARI?".

#### **5. Conclusions**

NIRAVARI was developed to help farmers and advisers, and to provide some analysis to policy-makers, move toward schemes they would like to implement. NIRAVARI can be used for a large range of questions and can, thanks to its simplicity (parsimonious) and genericity, be applied much beyond the Indian context. Crop parametrization, ground water transfer process and farm structure are easily changeable to represent a wide range of water management situations from countries other than India. Even if NIRAVARI was at first aimed at policy-makers, it can also be used as a training media for students to understand the impacts of irrigated agriculture on groundwater resources.

As a follow-up of the initial meeting with the policy-makers during a workshop held in Bangalore in March 2019, NIRAVARI is due to be presented to the officers of the Watershed Department in December 2022.

#### **6. Patents**

The NIRAVARI model is freely available on request to the main corresponding author.

**Author Contributions:** Software, J.-E.B.; validation, J.-E.B., MB and L.R.; conceptualization and methodology, J.-E.B. and M.B.; writing—original draft preparation, J.-E.B.; formal analysis, J.-E.B., M.B. and L.R.; writing—review and editing, J.-E.B., M.B., L.R. and M.S.; funding acquisition, L.R. and M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the ATCHA project [ANR-16-CE03-0006] and the Environmental Research Observatory M-TROPICS (https://mtropics.obs-mip.fr/, accessed on 11 October 2022), which is supported by the University of Toulouse, IRD and CNRS-INSU.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to thanks the different trainees who worked on the project and the different members of the ATCHA project for their constructive comments on the NIRAVARI model.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Equations of the Biophysical Model**

Let us call *b* the index to represent a bele and *t* the index for the time.

#### *Appendix A.1. Soil Water Budget*

The state variable of interest is the soil water content (*W*(*b*,*t*), m3). Water inputs (*iW*(*b*,*t*), m3·d−1) are irrigation (*I*(*b*,*t*), m3·d−1) and part of the rainfall in case of runoff (*Rf*(*b*,*t*), m3·d−1). Runoff is based on the curve number formalism [38]. Water outputs (*oW*(*b*,*t*), m3·d−1) are actual evapotranspiration (*Ea*(*b*,*t*), m3·d−1, see crop process) and drainage (*Dr*(*b*,*t*), m3·d−1). Drainage occurs when the soil water capacity is full (tipping bucket formalism, [39]).

$$\begin{cases} \begin{aligned} \text{IV}(b,b)&=l\text{IV}(b,t)-l\text{ov}(b,t) \\ \text{IV}(b,t)&=Rf(b,t)+l(b,t) \\ \text{ov}(b,t)&=E\_{a}(b,t) \\ Rf(b,t)&=[R(t)-r\text{conf}(t)] \ast \text{size}(b)/1000 \\ \begin{cases} \quad if(k\_{c}(b,t)>0)\text{ then} \\ \quad \text{else} \ E\_{a}(b,t)&=\min\left(W(b,t-1),\left(\frac{W(b,t-1)}{W\_{x}(b)}\right)\ast f\_{w}\ast k\_{c}(b,t)\cdot E\_{0}(t)\right) \\ \quad \text{else} \ E\_{a}(b,t)&=\min\left(W(b,t-1),k\_{c}\ast E\_{0}(t)\ast \text{size}(b)/1000\right) \\ \quad \text{if}\left(W(b,t-1)+\delta W(t)>W\_{x}(b)\right)\text{ then} \begin{cases} \text{Dr}(b,t) = \left(W(b,t-1)+\delta W(t)\right)-\mathcal{W}\_{\mathcal{X}}(b) \\ \qquad W(t)=W\_{x}(b) \end{cases} \end{cases} \end{cases} \end{cases} \tag{A1}$$

where *kc* is the evaporation crop coefficient (see Appendix A.2. Crop Processes), *ks* is the evaporation bare soil coefficient, *Wx*(*b*) is the maximum soil water capacity of bele *b* (m3) and *size*(*b*) is the size of the bele (m2)

*Appendix A.2. Crop Processes*

Let us call *A*(*t*) the age of the crops (in days). From crop sowing to crop harvest (see 2.3.1. ), *A*(*t*) follows a simple linear function: *A*(*t*) = *A*(*t* − 1) + 1.

Crop coefficient (*kc*(*t*)) is modelled by a multilinear function from FAO56 [33] (Figure A1)

$$\begin{cases} \begin{cases} \left(0 < A(t) < d\_1\right) \text{then } \text{kc}(t) = \text{kc}\_1 \\\\ \text{else if } (d\_1 < A(t) < (d\_1 + d\_2)) \text{ then } \text{kc}(b, t) = (A(t) - d\_1) \ast \frac{(\&\_2 - \&\_1)}{d\_1} + \text{kc}\_1 \\\\ \text{else if } ((d\_1 + d\_2) < A(t) < (d\_1 + d\_2 + d\_3)) \text{ then } \text{kc}(b, t) = \text{kc}\_2 \\\\ \text{else if } ((d\_1 + d\_2 + d\_3) < \text{age}(t) < (d\_1 + d\_2 + d\_3 + d\_4)) \text{ then } \text{kc}(b, t) = ((d\_1 + d\_2 + d\_3 + d\_4) - A(t)) \ast \frac{(\&\_2 - \&\_2)}{d\_1} + \text{kc}\_3 \\\\ \text{else } \text{kc}(b, t) = \text{kc}\_3 \end{cases} \end{cases} \tag{A2}$$

where *d*1, *d*2, *d*<sup>3</sup> and d4 are duration between growing phases (in days) and *kc*1, *kc2* and *kc3* are specific *kc* values. All these parameters are crop dependent.

**Figure A1.** The multistage crop coefficient. From FAO56 [33].

Representing Crop Water Stress

The crop water stress is calculated using a simple algorithm. If the crop requires water and no water is provided, its stress increases by one. If the level of stress reaches a given

threshold, then the crop dies. The level of stress can be zeroed if a sufficient amount of water is provided to the crop:

$$\begin{cases} \begin{cases} \begin{cases} \frac{A \text{ET}(t)}{M \text{ET}(t)} < p\_1 \text{ and } I(t) = 0 \end{cases} \end{cases} \text{then } \mathcal{N}\_{\mathbf{s}}(t) = \mathcal{N}\_{\mathbf{s}}(t - 1) + 1\\ \begin{cases} \begin{pmatrix} I(t) + R(t) > p\_2 \end{pmatrix} \text{then } \mathcal{N}\_{\mathbf{s}}(t) = 0\\ \begin{cases} \begin{pmatrix} I(\mathbf{s}) \end{pmatrix} \ge p\_3 \text{ then } \operatorname{crop} \operatorname{ die} \end{cases} \end{cases} \end{cases} \end{cases} \tag{A3}$$

where *AET*(*t*) is the actual evapotranspiration, *MET*(*t*) is the maximum evapotranspiration, *I*(*t*) is the amount of irrigation water provided, *Ns*(*t*) is the stress level, *R*(*t*) is the daily rainfall *p*1, *p*<sup>2</sup> and *p*<sup>3</sup> are crop dependant parameters. Modifying *p*1, *p*<sup>2</sup> and *p*<sup>3</sup> allows to represent different crop sensitivity to water stress.

#### *Appendix A.3. Pump Process*

The pump flow rate (*f*, m<sup>3</sup> s−1) follows a power function depending on the depth of the ground watertable (see Appendix A.5. Water Table Processes). This is based on pump flows measurements on the Berambadi watershed [26,32].

$$f(t) = a \cdot H(t-1)^b \tag{A4}$$

where *a* and *b* are parameters and *H* represents the height of the water table (m)

#### *Appendix A.4. Pond Processes*

The pond is modelled as a right prism (Figure A2). Pond water contents (*Wp*(*t*), <sup>m</sup>3), depends on the water level in the pond (*hp*(*t*), m). Water input (*iWp*(*t*), m3·d−1) are rainfall (*Rp*(*t*), m3), refill by the pump when water is available (*Rf*(*t*), m3—see management processes) and runoff (*Ro*(*t*), m3). Water output are pumping for irrigation (*Ip*(*t*), m3—see management processes), surface evaporation (*Ep*(*t*), m3) and recharge of the ground water table if the pond is permeable (*Dp*(*t*), m3).

$$\begin{cases} \delta W\_{\mathcal{P}}(t) = iW\_{\mathcal{P}}(t) - \alpha W\_{\mathcal{P}}(t) \\ \begin{cases} iW\_{\mathcal{P}}(t) = R\_{\mathcal{P}}(t) + R f(t) + \operatorname{Ro}(t) \\ \
o W\_{\mathcal{P}}(t) = E\_{\mathcal{P}}(t) + I\_{\mathcal{P}}(t) + D\_{\mathcal{P}}(t) \\ R\_{\mathcal{P}}(t) = R(t) \* \operatorname{surf} 0/1000 \\ \begin{cases} if(\mathcal{R}(t) < \gamma\_1 \operatorname{l then } \operatorname{Ro}(t) = 0 \\ \operatorname{clse } \operatorname{Ro}(t) = \gamma\_2 \cdot (\mathcal{R}(t) - \gamma\_1) \\ E\_{\mathcal{P}}(t) = \min(\mathcal{W}\_p(t-1), \mathcal{E}\_{\mathcal{O}}(t) \cdot \operatorname{surf}(t-1)/1000 \\ D\_p(t) = \partial \cdot \mathcal{W}\_p(t-1) \end{cases} \end{cases} \tag{A5}$$

where *γ*<sup>1</sup> and *γ*<sup>2</sup> are parameters to deal with the runoff process, *surf* <sup>0</sup> is the upper surface area when the pond is full (m2), *surf*(*<sup>t</sup>* − 1) is the actual upper surface area (m2). Due the geometrical structure of the pond, there *Wp* and *surf* are linked. Detailed calculations are not given here.

**Figure A2.** The pond geometrical representation.

*Appendix A.5. Water Table Processes*

The ground watertable height (*H*(*t*), m) varies depending on the net recharge (*nR*(*t*), m3·d<sup>−</sup>1), ie the difference between input (drainage from the different beles and recharge by the pond) and output (irrigation to the different beles and lateral losses (*Q*(*t*), m3·d<sup>−</sup>1).

$$\begin{cases} \begin{aligned} \dot{H}(t) &= H(t-1) + nR(t) / S\_y \\ nR(t) &= \left( D\_p(t) + \sum\_{b=1}^n D(b,t) \right) - \sum\_{b=1}^n I(b,t) \\ \dot{H}\left(\dot{H}(t) > H\_x \right) \text{then } H(t) &= H\_x \\ Q(t) &= \left( H(t) - H \right) \cdot S\_y \cdot a' \\ H(t) &= H(t) - Q(t) \text{ / } Sy \end{aligned} \end{cases} \tag{A6}$$

where *H*(*t*) is an intermediate variable, *Sy* is the specific yield of the aquifer, *α* is the groundwater recession coefficient.


#### **References**


### **Appendix B**

