**2.3 Hydrological modeling with artificial neural network (ANN) model**

The rainfall and runoff data were simulated through the artificial neural network method using several inputs and outputs [9, 10]. This method imitates the function of the human nervous system and works in line with human learning patterns [11]. The backpropagation using a binary sigmoid activation function has been discovered to be a good ANN model for hydrology. This is due to the fact that the activation function is *Hydrological Drought Index Based on Discharge DOI: http://dx.doi.org/10.5772/intechopen.104625*

the net (network) of the linear combination of the inputs and their weights. It is important to note that this model fits the pattern characteristics of the input and output data which are required to follow a normal distribution in the range of 0–1 (0,10,9) [12, 13].

The determination of the hydrological data requires that the parameters recorded for January be influenced by the hydrological conditions in January of the previous year and the same trend is expected to continue from February to December. The data were also sorted from January to December at the end of the time series and the estimation was continued for the next few years. Moreover, the runoff model was designed in line with the rainfall data input based on the analysis of variables in the HDI analysis. Meanwhile, the architecture and equations of the backpropagation method used in this research are presented in **Figure 1** [14, 15].

Where P1 is the 1st data input, Pn is the nth data input, Z1.1 is the 1st auxiliary variable in hidden layer 1, Z1.2 is the 2nd auxiliary variable in hidden layer 1, Z2.1 is the 1st auxiliary variable in hidden layer 2, Z2.2 is the 2nd auxiliary variable in hidden layer 2, b (=1) is the specified bias value which is equal to one, and Qn is the nth data output.

$$z\\_net\_j = v\\_v\_{j0} + \sum\_{i=1}^{n} P\_i v\_{ji} \tag{2}$$

**Figure 1.** *ANN for discharge calculation.*

$$z\_j = f(z\_-net\_j) = \frac{1}{1 + e^{-x\_-net\_j}}\tag{3}$$

$$Q\\_net\_k = w\_{ko} + \sum\_{j=1}^{p} z\_j w\_{kj} \tag{4}$$

$$Q\_k = f(Q\_-net\_k) = \frac{1}{1 + e^{-Q\_-net\_k}}\tag{5}$$
