**4.4 HDI1 and HDI2 in Kali Asem and Umbul sub-watersheds**

The calculation showed that the HDI1 for the Kali Asem sub-watershed at Qaw80 was 0.00, the HDI1 limit at Qaw50 was 0.0180, and at 70% Qaw80 was recorded to be 0.0123. Moreover, the result for the HDI1 in the Umbul sub-watershed at Qd80 was found to be 0.00, the HDI1 limits at Qd50 were 0.0200 while at 70% Qd80 was 0.0123.

The discharge prediction simulation model implemented the backpropagation ANN using the following parameters:

1.The model consists of one input, two hidden, and two output layers.

2.The network was formed using Descant Gradient Learning (trainingdm) with *logsig* used for activation in the hidden layer and *purelin* in the output layer.

**Figure 5.** *Deficit based on Qaw50 and Qaw80 in the AWLR of the Kali Asem sub-watershed [21].*

**Figure 6.** *Deficit of discharge, Qaw in 1991, 1997, 2003 [21].*

3.The model simulation stops at the specified epoh of 1000 epoh or a mean square error (MSE) of 0.05.

The "scatterplot" of the Qsimulated and Qobserved in **Figure 7** shows a straight line and coincides. This means the simulation data has a statistical character that is not significantly different from the observation data.

The HDI1 value also ranged from 0.002 to 0.024 while the HDI2 value ranged from 0.001 to 0.022 (Extremely Dry). Moreover, a shift was observed in the dry time and

**Figure 7.** *Suitability analysis for the simulation results based on the discharge at Umbul dam [21].*

## **Figure 8.**

*FDC analysis on the Q observation and simulation (Qobservation and Qsimulation, as well as IK observation and IK simulation [21].*

this means it is difficult for the simulation to accurately predict the start or end time for the drought condition (see **Figure 8**).

The calculation showed that the equation can be written in the form of a matrix as follows:

$$\begin{aligned} \bullet \text{ Input weight, } (\text{P} \rightarrow \text{Z}\_1) = \begin{bmatrix} -2, 434 & 2, 385 \\ -1, 422 & -1, 312 \\ -2, 730 & -1, 428 \\ 2, 198 & -2, 700 \\ 1, 798 & -0, 613 \\ -0, 823 & 3, 194 \\ 1, 206 & -0, 166 \\ -4, 729 & -3, 937 \end{bmatrix} \end{aligned} $$

• Input bias weight, b ¼ ½ � 5, 893 5, 369

$$\text{\textbullet Hidden layer weight} - \mathbf{1}, (\mathbf{Z}\_1 \rightarrow \mathbf{Z}\_2) = \begin{bmatrix} \mathbf{0}, \mathbf{7} \mathbf{5} \mathbf{5} & \mathbf{7}, \mathbf{68} \mathbf{5} \\ -\mathbf{7}, \mathbf{35} \mathbf{9} & \mathbf{2}, \mathbf{927} \end{bmatrix}$$

• Hidden layer bias weight � 1, b ¼ �½ � 8, 477 �1, 755

• Hidden layer weight � 2 Zð Þ¼ <sup>2</sup> ! Q

0, 021 �0, 033 0, 891 0, 762 �0, 087 0, 068 0, 748 �0, 101 �0, 022 0, 562 �0, 739 0, 987 0, 999 �0, 648 �0, 179 0, 332 � � *Hydrological Drought Index Based on Discharge DOI: http://dx.doi.org/10.5772/intechopen.104625*

• Hidden layer bias weight � 2 b ¼ ½ � 0, 713 0, 129 0, 236 0, 267 0, 681 0, 644 0, 389 0, 383

The model was simulated at Umbul Dam for verification and the results showed that the simulation data is within the tolerance limit (α) of 5% which indicates that it is not significantly different. A run test was also conducted on the drought parameter.

