Irrigation Priority between Beles

If different beles require irrigation the same day, priority rules are needed if not enough water is available. To calculate irrigation priorities, we use a weighted average approach corresponding to a priority index, , calculated for each bele (2). The priority bele is the bele with the smallest . This approach makes it possible to integrate all the factors that impact the decision-making related to the management of irrigation. The choice of factor coefficients makes it possible to build different irrigation strategies.

$$
\mathfrak{R} = a \cdot \mathbb{R}\_{crop} + b \cdot \mathbb{R}\_{stres} + c \cdot \mathbb{R}\_{ag\varepsilon} + d \cdot \mathbb{R}\_{techmic} \tag{2}
$$

where *a*, *b*, *c* and *d* are the weight coefficients.


larger amount of water to provide; or (ii) favor the irrigation technique with the less amount of water to provide.

 is calculated for each bele requiring irrigation. In case of ex aequo, a final factor is used, *Rbele*, the bele priority factor. The advantage of this formalism is that we separate the strategy from the code and give the user the chance to choose his own irrigation strategy. An example of this algorithm is given in Table 1. The first four lines of the table {1–4} provide the priority given to the four priority factors. *Rcrop* is priority one, *Rstress* priority 2, *Rage* priority 3 and *Rtechnic* is not considered. For *Rstress* and *Rage*, the option of how to consider stress and age is given, respectively. For *Rstress*, we favor the more stressed crop first; while for *Rage*, we favor first the more aged crop.


**Table 1.** An example of the algorithm to determine the priority between the different beles to be irrigated. In this case, the bele irrigated is bele 1 as it has the lowest . See text for details.

The next four lines {5–8} give the computation for the different weights (see (2)). For example, as *Rcrop* is priority 1 and that {priority(*Rcrop*) + priority(*Rstress*) + priority(*Rage*) + priority(*Rtechnic*)} equals 6, then (*a*) equals 1/6 = 0.167.

Lines {9–17} give the status of the system on an example day to demonstrate the computation: there are three beles, with each a different crop {10}. Priority between these different crops is given on {11}. These three beles can be irrigated with a different irrigation equipment {12} providing a given amount of water {13}. Lines {14–17} give the status of the crop regarding their age and their water stress. From this information the different priorities are calculated {18–21}. *Rcrop* is calculated using {11} and the same algorithm used to calculate the weights (see above); *Rstress* is calculated as {17}/{16}; *Rage* is calculated as 1- {15}/{14}; and *Rtechnic* is calculated as {13} divided by the value of the technic given the largest amount of water; here, it is a furrow with 50 mm. Line {22} calculates the final value of using (2). In the case of ex aequo, we use {23} to decide the bele to irrigate.
