These days human beings are facing many environmental challenges due to frequently occurring drought hazards. It may have an effect on the country’s environment, the community, and industries. Several adverse impacts of drought hazard are continued in Pakistan, including other hazards. However, early measurement and detection of drought can provide guidance to water resources management for employing drought mitigation policies. In this paper, we used a multilayer perceptron neural network (MLPNN) algorithm for drought forecasting. We applied and tested MLPNN algorithm on monthly time series data of
The demand of water has increased diversely due to expansion in agriculture, population, energy, and industrial zone. Many parts of the world suffered each year due to scarcity of water. Change in climatic condition and contamination in water play a key role in water scarcity, Aswathanarayana [
Drought can be recognized as disaster associated with climate that can have effect on a wide range of land. There are many factors that play a major role in drought occurrence including high wind, low relative humidity, temperature, and characteristics and duration of rain, intensity, and onset, Wilhite [
Several tools have been used for the assessment of drought. Drought indices are one of the most commonly used tools for assessing the drought conditions around the world and few of them are as follows: Rainfall Anomaly Index (RAI), Van Rooy [
Similar to drought assessment tools, several models have been developed for drought forecasting. Paulo and Pereira [
A few applications of ANN models in drought forecasting only comprised of Morid et al. [
The log linear model is class of generalized linear models that can explore the relationships among categorical variables, Agresti [
Conventionally, hydrological variables, like monthly precipitation and temperature, have been widely modeled using different linear techniques, such as Autoregressive Moving Average (ARMA) Salas and Boes [
In this study, due to the importance of drought forecasting, the capability of
Our study area is in Northern Area and KPK including capital territory of Pakistan. We collected monthly data on total rainfall and mean temperature from seventeen meteorological stations (Balakot, Kotli, Cherat, Chilas, Islamabad, Gupis, Peshawar, Saidu Sharif, Muzaffarabad, Bunji, DI Khan, Drosh, Garhi Dupatta, Dir, Gilgit, and Kakul) from 1975 to 2012. As these stations’ data are managed by the Pakistan Meteorological Department (PMD), Islamabad, we collected the data from the Karachi Data Processing Center via PMD. The selected locations represent fully precipitation regimes affecting the area where water is the main source for agriculture and hydropower for the flood plains in Pakistan. These stations have significant ecological role, including watershed and enhancing the lifespan of Tarbela Dam. This dataset contains catchments with minimum synthetic influences and have good hydrometric performance. In this paper, SPEI with four different time scales are calculated for each station.
VicenteSerrano et al. [
Different equations are used to estimate PET values according to the nature of data that linked PET values with temperature data. The most commonly used procedures for calculating PET are Thornthwaite equation, Thornthwaite [
In the above equation,
SPEI values were obtained by fitting the longterm record of difference between precipitation and PET for specified time interval of any location.
VicenteSerrano et al. [
The SPEI drought category classification provided by McKee et al. [
SPEI values  Drought classes 

≥2  Extremely wet 
1.5 to 1.99  Very wet 
1 to 1.49  Moderate wet 
.99 to −.99  Near normal 
−1 to −1.49  Moderate drought 
−1.5 to 1.99  Severe drought 
≤ 
Extreme drought 
Sönmez et al. [
Mathematically, the SPEI is based on the cumulative probability distribution function of a given quantitative values of rainfall occurrence for a specific station.
In this study, we calculate SPEI values by standardizing different probability distributions (e.g., Gamma, Generalized Extreme Values Distribution, LogLogistic Distribution, and Generalized Pareto Distribution) that fit the
McKee et al. [
Parameter estimation method for different distribution.
Probability distribution  Method of estimation 

Gamma  Method of moments 
Generalized Pareto  Method of Lmoments 
Generalized Pareto  Method of Lmoments 
Generalized Extreme Value  Method of Lmoments 
Generalized Extreme Value  Maximum likelihood method 
LogLogistic  Method of moments 
The resulting parameters of each distribution are then used to derive Cumulative Distribution Function (CDF). For undefined values of
If
The distribution function of each probability distribution is than transformed into standard normal distribution to obtain SPTI values having zero mean and unit variance.
Following Mishra and Desai and McKee et al., the current study employed the approximate transformation provided by Abramowitz and Stegun [
The average value of the SPEI is 0, and the standard deviation is 1. The SPEI is a standardized variable; therefore, it can be compared with other SPEI values over time and space. The SPEI value equal to 0 indicates a value corresponding to 50% of the cumulative probability of
There are several methods for the development and implementation of neural network model of forecasting. In many applications, feedforward neural network topology with backpropagation learning algorithm was used, while some used variant of this. Several researchers described the problem in finding the appropriate network size for predicting realworld time series, Zhang et al. [
The MLPNN model is the most extensively used type of ANN’s approach for modeling hydrological data, Wang et al. [
In MLPNN model, all the input nodes are in one layer and hidden layer is distributed into one or more hidden layers. Figure
An example of a simple feedforward network, Garson [
Suppose there are
Let
Let
Also, let
That is
For designing ANN architecture, one must determine the optimum number of the following layers:
The number of input layers
The number of hidden layers
The number of output layers
General architecture of multilayer perceptron neural network model, Sherrod [
In this research, MLPNN model of ANNs was used for drought forecasting.
Detailed explanation MLPNN model and its selection of parameters is given in the following section.
All neural networks have an input layer and an output layer; however, the number of hidden layers may vary. Basically, selection of these variables is domainspecific or depends on the problem. Many algorithms, such as the polynomial time algorithm, Roy et al. [
Literature shows that there is no systematic way to investigate these problems. Many researchers adopted trial and error methodology for a specific problem which is the basic cause of inconsistency in ANN literature, Sheela and Deepa [
The procedure for MLPNN consists of four parts:
Variable selection
Formulations of training, testing, and validation
Architecture
Model verification and forecasting
Current research employed the MLPNN model by using Zaitun time series software. Following Lipae et al. [
In this study, time series data on observed SPEI with different time scale are computed by standardizing the probability distribution that describes well behavior of difference between precipitation and evapotranspiration using Abramowitz and Stegun [
Figures
The performance for all study stations of multilayer perceptron models in validation phase.
Stations  SPEI1  SPEI3  SPEI6  SPEI12  

MSE  MAE 

MSE  MAE 

MSE  MAE 

MSE  MAE 
 
Kakul  0.107  0.254  0.946  0.254  00.22  0.916  0.256  0.254  0.886  0.263  0.632  0.886 
Astor  0.100  0.241  0.949  0.089  0.248  0.947  0.094  0.741  0.947  0.258  0.263  0.925 
DI Khan  0.078  0.205  0.947  0.099  0.220  0.927  0.094  0.263  0.927  0.096  0.523  0.963 
Balakot  0.181  0.339  0.921  0.098  0.246  0.934  0.093  0.749  0.944  0.0589  0.236  0.780 
Bunji  0.099  0.217  0.944  0.099  0.230  0.914  0.091  0.746  0.944  0.089  0.856  0.942 
Chilas  0.100  0.244  0.946  0.104  0.207  0.941  0.121  0.785  0.941  0.123  0.856  0.936 
Dir  0.099  0.250  0.946  0.100  0.245  0.954  0.421  0.259  0.994  0.125  0.456  0.926 
Drosh  0.100  0.242  0.942  0.099  0.230  0.944  0.062  0.230  0.944  0.096  0.236  0.985 
Garhi Dupatta  0.099  0.251  0.945  0.099  0.243  0.876  0.290  0.245  0.876  0.091  0.226  0.872 
Kotli  0.121  0.258  0.940  0.100  0.239  0.948  0.123  0.485  0.948  0.105  0.256  0.923 
Cherat  0.175  0.321  0.917  0.100  0.224  0.939  0.101  0.785  0.939  0.103  0.845  0.926 
Islamabad  0.182  0.327  0.911  0.098  0.231  0.921  0.091  0.846  0.921  0.094  0.785  0.952 
Peshawar  0.022  0.109  0.987  0.099  0.222  0.934  0.093  0.856  0.934  0.097  0.159  0.942 
Muzaffarabad  0.102  0.238  0.950  0.099  0.248  0.994  0.098  0.286  0.984  0.09∖3  0.741  0.964 
Gilgit  0.187  0.332  0.887  0.140  0.275  0.900  0.145  0.869  0.900  0.126  0.451  0.970 
Gupis  0.027  0.126  0.985  0.097  0.225  0.930  0.045  0.856  0.930  0.087  0.236  0.910 
Saidu Sharif  0.100  0.244  0.945  0.100  0.243  0.944  0.145  0.265  0.944  0.115  0.263  0.894 
The observed and predicted values of SPEI using multilayer perceptron in the validation phase for Balakot station.
The observed and predicted values of SPEI using multilayer perceptron in the validation phase for Balakot station.
The observed and predicted values of SPEI using multilayer perceptron in the validation phase for Astor station.
The observed and predicted values of SPEI using multilayer perceptron in the validation phase for Astor station.
The model is potentially able to predict drought condition by using SPEI values with different time scale. The excellence of the forecast is reflected in the correlation coefficient between observed and estimated time series, the RMSE and MAE.
The accuracy of the selected model in all stations for each index is good in terms of correlation between observed and predicted SPEI values. From each observatory, correlation coefficient ranges lie in the interval 0.887 to 0.987 for SPEI1, 0.876 to 0.994 for SPEI3, 0.876 to 0.994 for SPEI6, and 0.780 to 0.970 for SPEI12. Figure
Actual versus predicted graph of SPEI1.
By using forecasted quantities of drought indices as input, model can be used to predict further by a multistep approach. No evidence was found about significant deviation between observed and predicted values of drought index for all indices.
In this study, multilayer perceptron neural network (MLPNN) algorithm is used for nonlinear drought forecasting of monthly time series data of average temperature and total precipitation that recorded from seventeen synoptic stations of Northern Area and KPK (Pakistan) from 1975 to 2012. SPEI values were estimated by fitting appropriate probability distribution of difference between precipitation and PET. We found that the MLPNN model is convenient for operational purposes (i.e., water resources and management) as variation between input data of observed and predicted SPEI values is not high.
Outcomes associated with the study show that ANNs have the power to capture the variation in selected drought indices with onemonth time scale. Water resources and management planner may take help from the developed neural network model to take action in advance to know about where water scarcity is increasing owing to insufficient rainfall in a particular region that may lead to drought condition.
The manuscript is prepared in accordance with the ethical standards of the responsible committee on human experimentation and with the latest version (2008) of Helsinki Declaration of 1975.
The manuscript is prepared by using secondary data.
The authors declared that there are no conflicts of interest.
The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through Research Group no. RG1437027.