**American Journal of Water Resources**

## Prediction of Missing Hydro-Meteorological Data Series Using Artificial Neural Networks (ANN) for Upper Tana River Basin, Kenya

**Raphael M. Wambua**^{1,}, **Benedict M. Mutua**^{1}, **James M. Raude**^{2}

^{1}Egerton University Department of Agricultural Engineering, Kenya

^{2}Jomo Kenyatta University of Agriculture and Technology, SWEED, Kenya

Abstract | |

1. | Introduction |

2. | Artificial Neural Networks |

3. | Materials and Methods |

4. | Results and Discussions |

5. | Conclusions |

6. | Recommendations |

Acknowledgement | |

References |

### Abstract

Accurate prediction of missing hydro-meteorological data is crucial in planning, design, development and management of water resources systems. In the present research, prediction of such data using Artificial Neural Networks (ANN) based on temporal and spatial auto-correlation has been conducted for upper Tana River basin in Kenya. Different ANN models were formulated using a combination of numerous data delays in the ANN input layer. The findings show that the best models comprise of a feed-forward neural network trained on Levenberg-Marquardt algorithm with single hidden layer. Additionally, the best ANN architecture model for predicting missing stream flow data was at gauge station 4CC03 with correlation coefficient and *MSE* of 0732 and 0.242 respectively during validation. Temporal auto-correlation of the observed and the predicted stream flow values were evaluated using a correlation coefficient R that resulted to highest value of 0.756 at gauge station 4AB05. The best ANN model for prediction of missing precipitation data was at station 9037112 with R value of 0.970. In both cases the best performance was at epochs 9 and 20 respectively. The spatial auto-correlation show that the best ANN architecture model for prediction of missing stream flow data was at gauge station 4CC03 with R value of 0.723, while the one for precipitation was at station 9037096 with *R* value of 0.712 during the validation. The results indicate that the spatial auto-correlation of hydro-meteorological data using ANN is better than the temporal auto-correlation in the data prediction in upper Tana River basin.

**Keywords:** Prediction, hydro-meteorological data, ANN, data delay, auto-correlation, upper Tana River basin

**Copyright**© 2016 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- Raphael M. Wambua, Benedict M. Mutua, James M. Raude. Prediction of Missing Hydro-Meteorological Data Series Using Artificial Neural Networks (ANN) for Upper Tana River Basin, Kenya.
*American Journal of Water Resources*. Vol. 4, No. 2, 2016, pp 35-43. http://pubs.sciepub.com/ajwr/4/2/2

- Wambua, Raphael M., Benedict M. Mutua, and James M. Raude. "Prediction of Missing Hydro-Meteorological Data Series Using Artificial Neural Networks (ANN) for Upper Tana River Basin, Kenya."
*American Journal of Water Resources*4.2 (2016): 35-43.

- Wambua, R. M. , Mutua, B. M. , & Raude, J. M. (2016). Prediction of Missing Hydro-Meteorological Data Series Using Artificial Neural Networks (ANN) for Upper Tana River Basin, Kenya.
*American Journal of Water Resources*,*4*(2), 35-43.

- Wambua, Raphael M., Benedict M. Mutua, and James M. Raude. "Prediction of Missing Hydro-Meteorological Data Series Using Artificial Neural Networks (ANN) for Upper Tana River Basin, Kenya."
*American Journal of Water Resources*4, no. 2 (2016): 35-43.

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### At a glance: Figures

### 1. Introduction

Among the hydro-meteorological data in a river basin, precipitation and stream flow are the most important. This is because of their application in water resource systems analysis, water balance computations ^{[1]}, estimation of extreme events such as floods and drought that adversely affect socio-economic development ^{[2]} is vital. Scarcity of hydro-meteorological data in a river basin may be due lack of measuring instruments, damage of measuring instruments or negligence in measurements. It is not appropriate to discontinue or abandon a water resources project in any stage; planning, design or development due to incomplete hydro-meteorological data. Estimation of relevant missing hydro-meteorological data is inevitable for any river basin with specific hydrologic processes. Accurate estimation of the missing hydro-meteorological data increases the prospect and ensures success of a water resources project. According to ^{[3]} and ^{[4]}, efficient prediction of any missing hydro-meteorological data require the spatial and temporal variation of their magnitudes and related physical processes at basin scales.

Some of the conventional techniques used in filling missing data include interpolation and extrapolation, Inverse Distance Weighting (IDW), differentials and formulation of kernel functions. These methods have successfully been applied by ^{[4, 5, 6, 7, 8]} respectively. The main challenge with these methods is that they are time consuming, sometimes giving errors in their results. The hydrological river basin processes are stochastic and non-linear in nature. These processes have always been explained using physically based methods which are complex. Numerous models have been developed to study stochastic hydrological processes. These include ANN models which have been extensively tested in modeling and forecasting of non-linear hydrological systems and extreme events such as droughts ^{[9]} and floods ^{[10, 11]} and ^{[12]}. Numerous methods have previously been used to address data lack or limitation of data availability in different river basins. For instance, ^{[13]} and ^{[14]} estimated potential evapotranspiration and reference crop evapotranspiration for 31 provinces in Iran using average data from 181 synoptic stations and three temperature-based formulae. Spatial interpolation method was used to obtain an average value for different stations. In addition, ^{[15]} used multivariate fractional polynomial (MFP), Bayessian regression and robust regression to estimate reference evapotranspiration for three arid regions within which water crises is critical.

### 2. Artificial Neural Networks

An artificial neural network (ANN) model is an information processing system developed with a structure and operation similar to that of a human brain ^{[16]}. The ANN models have been improved over time by various calibration techniques. With sufficient amount of data and complexity, the ANN model can be adapted to establish any correlation between series of independent and dependent variables ^{[17]}. ANNs have some advantages ^{[18, 19]} and ^{[11]} that attracted their use in this research. These advantages include:

i) the ability to process information based on their dynamic response to external input

ii) they can capture numerous kinds of relationships including non-linear functions which are not usually detected by other techniques

iii) they provide effective analytical techniques in modeling and forecasting systems

iv) the networks have the ability to model dynamic time series variables in Water Resources Engineering

v) the definition of physical processes need not be done and this. property makes it appropriate in processing large and complex data sets, including that of drought forecasting

The ANN model processes information through an elaborate network of neurons that are linked together. It predicts outputs based on defined inputs ^{[20]} by a working principle resembling that of human brain where the neuron receives a set of input signals and generates outputs. The nervous system of human beings is represented by a number of architectural structures that range from simple to complex structures. Whether the structures are simple or complex, the systems consist of neurons or neural cells as the chief building blocks.

An ANN model is similar to a biological neuron in that it has multiple input channels, data processing unit, and output channels called dendrites, cell body and the axon respectively as represented in Figure 1. The input signals (*X*_{1}*, X*_{2}*, . . . , X*_{p}) are passed to the neuron through the dendrites that represent different input channels. Each channel has its own weight referred to as connection weight that may be denoted as *W*_{1}*, W*_{2}*,. . . ,W*_{p}. The weights are very critical since they allow for collection and processing of signals based on their magnitude and effects on input functions. If a weight function gives a non-zero value at the synapse, it is allowed to pass through the cell body. Otherwise, if it has a value of zero, it is not allowed to pass the cell body. All the conveyed signals are normally integrated by summing up all the inputs ^{[21]}.

**Figure 1.**Fundamental parts of a typical neural network

The summation is achieved by application of a mathematical model referred to as activation function, within the cell body to generate an output signal. According to ^{[21]} and ^{[3]}, the relationship between the input and output signal within an ANN model is represented using different data combinations and weight attached. This result into a function defined as:

(1) |

Where;

*X*_{i} = the input signal *i*

*W*_{i} =the weight attached to the input signal *i*

*P* =the number of input signals

*b*_{k} =the bias at the cell of the body

*Y* = the output

*f=*activation function

Numerous activation equations or functions can be used within the neurons. The most common functions used in the ANN models include; the step-function, non-linear sigmoidal, hyperbolic tangent and linear activation functions ^{[22]} and ^{[16]}.

ANN models have previously been used for estimating missing data values. Some of the research that demonstrate the use of ANN in prediction and filling missing data include the work by [23-31]^{[23]} has showed that non-linear autoregressive neural network with exogenous input (NARNNX) was better than non-linear autoregressive neural network (NARNN) in forecasting precipitation in Gilan, Iran. However, the use of artificial neural networks in prediction of hydro-meteorological data in upper Tana River basin has not been explored. This basin is a key water resource in Kenya for hydro-electric power generation, water supply and agriculture. The main objective of this research was to predict and test the efficiency of estimation of missing hydro-meteorological data series using artificial neural networks (ANN), for upper Tana River basin.

### 3. Materials and Methods

**3.1. The Study Area**

The upper Tana River basin with an area of 17,420 km^{2} (Figure 2) was the focus of the presented research. The upper Tana River basin lies between latitudes 00^{0} 05' and 01^{0} 30' south and longitudes 36^{0} 20' and 37^{0} 60' east. The basin is fundamental in influencing the ecosystem downstream ^{[32]}. It drains nine counties namely; Muranga, Nyandarua, Kiambu, Kirinyaga, Laikipia, Machakos, Nyeri, Embu and Kitui ^{[33]}. The basin was selected because it is located within a fragile ecosystem that represents all agro-ecological zones of Kenya where water resource systems, hydro-electric power generation and food security are negatively impacted by frequent drought occurrence. The basin area regulates the hydrology of the Kenya’s largest river system called Tana River Basin with a total area of 126,000 km^{2} ^{[34]}. Within the upper Tana River basin, numerous socio-economic activities such as hydro-power generation, agriculture, and irrigation take place.

**Figure 2.**Map of Kenya showing the upper Tana River basin

**3.2. Stream Flow Data**

There were approximately fourteen gauge stations in the upper Tana River basin with complete and incomplete data records. However, only eight stations were selected for this study since they had sufficiently long and reliable data for the period 1970-2010 as required by this study. The stations were in addition considered a realistic representative of the basin as they are objectively located within low, lower middle, middle and higher elevations for different agro-ecological zones as required in the study. The names of the stations and gauge identification (ID) numbers, their spatial locations are shown in Figure 2 and Table 1 respectively.

**3.3. Precipitation Data**

In the upper Tana River basin, data from twenty four meteorological stations were obtained from the Ministry of Environment, Water and Natural resources. Such stations provided precipitation data. The stations were also objectively located within the low, lower middle, middle and high elevations so as to study drought characteristics at different agro-ecological basin of the basin.

**3.4. Temporal Auto-correlation Based on ANN Models**

The hydro-meteorological data was partitioned into 70% and 30% training and validation both for stream flow data and precipitation data at each station. By considering different input neurons with different time delays; *t, t-1, t-2,…,t-n*, in the input layer, the structure for each station was obtained. Hidden layer neurons initially 2*n*+1, increase and decrease using trial and error technique. The output was is the predicted variable. Thus the neural network has three layers; input layer, hidden layer and the output layer (Figure 3a and Figure 3b). The model at each station was trained using different structures (Table 3). The output layer comprise of neurons in all the networks that are equal to the next month’s predicted value (I_{t+1}). For the present study, feed-forward neural network (FFN) and recursive neural network (RNN) were tested in the model training. Initially three different training algorithms were applied to train the structures; Back-propagation (BP), Conjugate Gradient (CG) and Levernberg-Marquardt (LM). Preliminary results indicated that a three-layer feed forward neural network with different input and hidden neurons was the best in performance, and that the superlative results were also obtained using the LM training algorithm. Thus the results presented are for best structure of three-layer feed forward network based on LM training algorithm. The monthly data for different previous months was auto-correlated with the next month’s predicted value. The performance of the auto-correlation was done using performance criteria of the correlation coefficient R, and mean square error (MSE) presented in Equations 3 and 4.

**Figure 3.**ANN model Architecture used for prediction of missing (a) meteorological and (b) stream flow data based on spatial auto-correlation

**3.5. Spatial Auto-correlation Based on ANN Models**

It was expected that there exist spatial-autocorrelation among the hydro-meteorological for stations at different time delays. Seven stations were used at a time to estimate and/predict the hydro-meteorological variables at one of the eight stations at a time. From each station, 70% of the data was used for training while 30% was used validation. Figure 3b shows the schematic diagram for the proposed spatially correlated ANN model. Different ANN models were formulated using different time delays and hidden neurons. The results of the spatially auto-correlated ANN structures and training epochs are shown in Table 5 and Table 6.

**3.6. Performance Evaluation of the Models**

In ANN the input and output variables used in the modelling were normalized by fitting their values between zero and one to speed up the forecasting process as stated by ^{[18]}. In the present study, the recorded stream flow and precipitation data values were scaled from a minimum to maximum value by applying the following function:

(2) |

Where;

*X*_{n}= normalized/standardized value

*X*_{min }= the selected minimum value for standardization

*X*_{max }= the selected maximum value for standardization

*X*_{o }= original variable value

*x*_{min }= minimum value present in the original data set

*x*_{max }= maximum value present in the original data set

For the purpose of this research the X_{min} and X_{max} were chosen as 0.1 and 0.9 respectively as these have been found to give reliable results in hydrological studies ^{[18]}. After standardization, the prediction of data values for numerous stations was conducted. For illustration purpose, the results of selected stations are presented in the present paper. The normalized data was partitioned into training and validation data sets. At each hydro-meteorological station, 70% of continuous data was used for training while the remaining 30% was used for validation purpose. In this research, two criteria were used to determine the efficiency of the ANN models. These included the correlation coefficient (R) and the mean square error (MSE).

The statistical relationship between the observed and the predicated data values within the upper Tana River basin was done using the correlation coefficient (R). The fundamental function was customized to the respective data input and outputs of the following general form:

(3) |

Where;

*R *= the correlation coefficient

*I*_{Obs }= the observed value of the hydro-meteorological variable

*= *mean of the observed values the hydro-meteorological variable

*I*_{For}= the forecasted value of the variable

*=* mean of the forecasted values of the hydro-meteorological variable

*n*=number of data points considered

The *R* is a measure of the strength of the relation between observed and forecasted *DI* values. It varies from 0 to 1. The values of 0 and 1 indicate a poor and perfect forecasting capability of the model respectively.

(4) |

Where;

*MSE *= the mean square error

*I*_{Obs }= the observed value of the variable

*I*_{for }= the forecasted value of the ANN model

n* *= number of data points

The MSE ranges from 0 to 1. The smaller the MSE value the better the forecasting capability of the model.

### 4. Results and Discussions

Temporal auto-correlation of the observed and the predicted stream flow values was evaluated using a correlation coefficient R, giving 0.756 and 0.731 at gauge stations 4AB05 and 4AC03 respectively. The architecture for the best ANNs models at these stations are 3-9-1 and 2-9-1. The best ANN model for filling missing precipitation data was at station 9037112 with R and *MSE* values of 0.970 and 0.056 respectively. In both cases the best performance was at epochs 9 and 20 respectively (Table 3 and Table 4). The prediction of stream flow was done for one month and or more to represent medium and long-term range that are critical to a hydrological risk such as drought (Morid *et al*., 2007) ^{[18]}.

**4.1. Spatial Auto-correlation of Hydro-meteorological Data**

According to the results of spatial auto-correlation the performance of ANN changed by decreasing or increasing the number of hidden neurons from the initial 2n+1. From the results, the best ANN structure obtained was 7-8-1 which defines ANN structure with seven, eight and one neurons in the input, hidden and output layers respectively trained at epoch 16 for station 4CC03. Comparing Table 1 and Table 2 shows that the spatial auto-correlation is superior to temporal auto-correlation in estimating the missing values based on the R and MSE. This high performance in spatial auto-correlation is attributed to the fact that hydrological processes exhibit spatial variability.

Feed-forward and RNN with different training algorithms; Back-propagation (BP), Conjugate Gradient (CG) and Levernberg-Marquardt (LM), were used to compare network performance using R MSE. The best structure was selected based on the best values of R and MSE during the training and validation periods as shown in Table 5 and Table 6. The results show that the best model was found to be a three-layer feed-forward neural network trained by the LM algorithm. This best model structure was then used to estimate the missing monthly hydro-meteorological data values. The simulated monthly time series of missing data values for the gauging stations 4AB05 and 4DC03 are as shown in Figure 3 and Figure 4, while those for meteorological stations 9037096 and 9037064 are given in Figure 5 and Figure 6 respectively. A plot of the observed and the predicted values show that the models are efficient on prediction capabilities. For instance the scatter plot obtained by plotting the predicted and observed values of stream flow for stations 4AB05 and 4AC03 show that the points are consistently distributed on the 1:1 line, with correlation coefficient R values of 0.756 and 0.731 in that order (Figure 8).

The spatial auto-correlation show that the best ANN model for filling missing stream flow data was at gauge station 4CC03 with *R* and *MSE* values of 0.723 and 0.326 respectively, while the best ANN architecture model for filling missing precipitation data was at station 9037096 with *R* and *MSE* values of 0.712 and 0.329 respectively during the validation (Table 5 and Table 6).

Monthly time series hydro-meteorological data were predicted for the period without data records. For instance at gauging stations 4AB05 and 4DC03, data was predicted for the period of years 2004 to 2010, and 2000 and 2010. The highest predicted stream flow values for the period for the stations were 12.44 and 15.65 m^{3}/s (Figure 4 and Figure 5). On the other hand, the highest predicted precipitation values are 550 mm and 10 mm at meteorological stations 9037096 and 9037064, for the period 2002 to 2007 and 2000 to 2010 respectively (Figure 6 and Figure 7).** **Based on the validation *R* values, the prediction capability of ANNs models at gauged stations can be arranged from the largest to the smallest in the order 4CC03, 4BC02, 4AC03, 4DA10, 4AD01, 4AB05, 4ED01 and 4DC03 respectively. On the other hand, the ANNs models prediction capability at the meteorological stations decline from the largest to the smallest in the order of 9037096, 9036212, 9037031, 9137123, 9037064, 9036288, 9037202 and 9037112 respectively. The best ANN models from this study can be applied in other river basins with appropriate calibration and validation.

**Figure 4.**Monthly time series of predicted stream flow values at gauging station 4AB05

**Figure 5.**Monthly time series of the predicted stream flow values at gauging station

**4DC03**

**Figure**

**6**

**.**Monthly time series of the forecasted values of missing data at meteorological station 9037096

**Figure**

**7**

**.**Scatter plot for observed against predicted stream flow at gauge station 4AB05)

**Figure 8**

**.**Scatter plot for observed against predicted stream flow at gauge station 4AC03

### 5. Conclusions

In the presented study the artificial neural networks (ANN) was used to establish the relationship between the input and output of specified hydro-meteorological data combination. The ANN was used to formulate the temporal and spatial auto-correlation functions for prediction of missing hydro-meteorological data in the upper Tana River basin. As shown by the R and MSE values, the results indicate that the spatial auto-correlation of station data using ANN is better than the temporal auto-correlation in predicting missing hydro-metric data for upper Tana River basin. From the three neural networks tested in this study, the most efficient network was found to be feed-forward neural network (FFN) which was trained using the Levernberg-Marquardt (LM) algorithm

### 6. Recommendations

It is recommended form this investigation that the methods and results of the research be applied to investigate temporal and spatial auto-correlation between numerous parameters for prediction of other hydrological processes such as soil erosion, sediment yield and runoff. Such prediction would be very useful in prioritized planning of the land use practices, agricultural practices, soil conservation and water supply within the upper Tana River basin.

### Acknowledgement

The authors of this paper acknowledge the scholars whose articles are cited and included in the references of this article. In addition, authors are grateful to the editors and publishers of journals and books from where the literature has been referred. The authors are grateful to the editorial board and the reviewers of the American Journal Water Resources who assisted in improving the quality of this article.

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