## AquaCrop

AquaCrop model can simulate the yield of sugarcane response to water productivity in four significant steps which is depicted in Fig. 1 (Revathy and Balamurali 2019).

The growth of sugarcane and water productivity (WP) is mainly determined by crop canopy. The development of canopy cover (CC) differs with respect to various seasons which are calculated by process of disrupting radiations activated by photosynthesis (Steduto et al. 2009). But AquaCrop model estimates the CC based on level of crop leaf and its expansion that are derived from maximum temperature and unmaintained WP. Hence, CC is expressed as

CC = \(\frac{\text{G}\text{r}\text{e}\text{e}\text{n} \text{c}\text{a}\text{n}\text{o}\text{p}\text{y} \text{c}\text{o}\text{v}\text{e}\text{r}\text{i}\text{n}\text{g} \text{u}\text{p}\text{p}\text{e}\text{r}\text{m}\text{o}\text{s}\text{t} \text{l}\text{a}\text{y}\text{e}\text{r} \text{o}\text{f} \text{s}\text{o}\text{i}\text{l}}{\text{T}\text{o}\text{t}\text{a}\text{l} \text{u}\text{p}\text{p}\text{e}\text{r}\text{m}\text{o}\text{s}\text{t} \text{l}\text{a}\text{y}\text{e}\text{r} \text{o}\text{f} \text{s}\text{o}\text{i}\text{l} \text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e} }\) (1)

Since WP plays a vital part in AquaCrop to maximize the crop yield, it is referred as a supporting model for irrigation policy. The WP is defined as the quantity of biomass which could be acquired with certain amount of water that is expressed in kg (biomass) per m3 of water transpired which is given as below

WP = \(\frac{\text{b}\text{i}\text{o}\text{m}\text{a}\text{s}\text{s} \text{p}\text{r}\text{o}\text{d}\text{u}\text{c}\text{e}\text{d} \text{e}\text{x}\text{p}\text{r}\text{e}\text{s}\text{s}\text{e}\text{d} \text{a}\text{s} \text{K}\text{g}\left(\text{b}\text{i}\text{o}\text{m}\text{a}\text{s}\text{s}\right)}{\text{w}\text{a}\text{t}\text{e}\text{r} \text{t}\text{r}\text{a}\text{n}\text{s}\text{p}\text{i}\text{r}\text{e}\text{d} \text{e}\text{x}\text{p}\text{r}\text{e}\text{s}\text{s}\text{e}\text{d} \text{a}\text{s}{ \text{m}}^{3} \left(\text{T}\text{r}\right)}\) (2)

AquaCrop model requires sufficient climatic data, crop data, soil data and field management data in order to fix the irrigation strategy under various seasons for obtaining good CC and balanced WP (Bahmani and Eghbalian 2018).

**Deep Learning Model**

Deep learning is a set of machine learning algorithms that implements multiple hidden layers to increasingly classify the irrigation strategy from the corresponding weather data and soil data. Before training the data, data normalization process is required to feed into network (Alajrami and Abu-Naser 2020). Data normalization is a preprocessing method where the data should be scaled in the range of 0 to 1. Therefore, the input data are being normalized using Z- score normalization approach to scale the data to zero and a standard deviation of one. The mathematical formula to derive Z- score normalization is as follows:

$${Norm}^{\text{'}}=\frac{Norm-\stackrel{-}{A}}{{\sigma }_{A}}$$

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where \(\stackrel{-}{A}\) and \({\sigma }_{A}\) denote the mean value and standard deviation of the attribute Norm.

The normalized data are passed into deep learning network to classify irrigation methods in order to predict the future water administration. ANNs are composed of elements stated as neurons which are multiplied by its weight, and execute it through non-linear activation function (Santos et al. 2019). By implementing a number of hidden layers of neurons, each of the layer that receives information of the input data, and pass the output to the next layers, formally deep learning network hold of input, multiple hidden and output layers correspondingly. The sum of the weighted edges is calculated using gradient descent method and activation function is transmitted to the next layer (Tian et al. 2020).

The difference between simple neural network and deep learning network are schematically represented in Fig. 2. Once the weather and soil data are fed into network, deep learning can automatically optimize the parameters. So, the classification error is minimized during training of network.

**Firefly Optimization **

The firefly optimization (FFO) algorithm is an optimization algorithm that works on firefly behaviors and it’s blinking features. FFO is also called as metaheuristic optimization, since it is capable of finding the optimal results for complicated problems (Johari et al. 2013). FFO follows a set of rules as follows:

1. As fireflies fit into unisex group, the firefly creatures can be attracted by other fireflies.

2. As for any two fireflies, the lightning attractions are being proportional to brightness, the low brightened creature attracts high brightened firefly. When the usual distance extends among fireflies, it’s brightness also obviously decreases.

3. The fireflies travel randomly with the purpose of finding the other fireflies rather than the particular firefly.

**The Attractiveness and Movements of the Firefly **

The attractiveness F of firefly \(i\) is fascinated by firefly \(j\) with its brightness based upon its distance \(r\)as defined in the following equation,

$$F\left(r\right)= \frac{{F}_{ij}}{{r}^{2}}$$

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If there are \(n\) number of fireflies, \({x}_{i}\) is then equal to the solution of firefly\(i\). By means of objective function\(f\left({x}_{i}\right)\), the brightness of the firefly i gets attracted to each other. Finally the brightness \(B\) of the firefly is picked out to expose the current position of its objective function which is given in (5)

$$B= f\left({x}_{i}\right)$$

5

The lowest brighter firefly is always attracted and migrated towards to the brighter one and each firefly hold a definite attractiveness value *β*. The attractiveness value *β* is fairly calculated depend upon the distance between the fireflies. The function belongs to firefly attractiveness is defined as follows.

$$\beta \left(r\right)= {\beta }_{0 }{e}^{-\gamma {r}^{2}}$$

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where β0 denotes the attractiveness of the firefly at value r = 0 and γ refers to the coefficient of media light absorption (Yang et al. 2013) and (Mandal et al. 2015).

**Optimized Deep Learning Model – A Proposed Approach**

Combining deep learning model with FFO i.e., DL-FFO directs a well-developed model to improve the water management by classifying the irrigation strategies in sugarcane production. Seeing as deep learning neural network implements a lot of hidden layers that is processed by means of activation functions, the degradation issue may occur at the time of training the network (Murali et al. 2020).

FFO helps in practice to compensate the degradation issue because it is merged with the deep learning model internally; thus increasing the network functionality. Since DL-FFO model obtained efficient prediction1, FFO is implemented with deep learning for optimizing weights. The main optimization problem is finding the best fit of the network by learning the optimal values of weight (Mandal et al. 2015). Optimizing the weight of the model results that deep learning network obviously improves the accuracy efficiency and reduces the error value. The implementation of the proposed model is narrated in Fig. 3.