FORECASTING RUNOFF COEFFICIENTS USING ANN FOR WATER RESOURCES
MANAGEMENT: THE CASE OF NOTWANE CATCHMENT IN EASTERN
BOTSWANA.
B.P. Parida 1* , D.B. Moalafhi 2 and P.K. Kenabatho 1
1 Department of Environmental Science, Faculty of Science, University of Botswana,
P/Bag UB 00704, Gaborone, Botswana, Tel: 00267-3552522, FAX: 00267 3185097.
* paridab@mopipi.ub.bw
(correspondence author)
2 Department of Water Affairs, Hydrology and Water Resources Division, P/Bag 0029,
Gaborone, Botswana
ABSTRACT
Forecasting future response behaviour of a semi-arid catchment in terms of runoff coefficient being trivial, an attempt has been made to apply an Artificial Neural Network (ANN) model to forecast the runoff coefficients (ROC) for the rapidly urbanizing Notwane catchment system in
Botswana. Runoff coefficients computed from 1978 to 2000, by the water balance technique have been used to develop the optimal network architecture with appropriate choice of the size of input vectors, number of hidden layers and number of neurons in the hidden layers, training algorithms and transfer functions for the network. The developed network has then been used to simulate the runoff coefficients for the above period. Based on its performance in terms of reproducibility of the water balance runoff coefficients, the network was used to forecast the runoff coefficients up to 2020 and it was found that the increase in runoff coefficients varied from about 1% per year. Based on the weights given by the network to the input variables, it was found that while about 48% contribution came from the climatic factors, 52% came from the landuse/land cover aspects.
KEYWORDS
Artificial neural network, runoff coefficient, water balance method, principal component analysis
1

1. INTRODUCTION
A major task that still intriguing the present day hydrologists is in their attempt to establishing typical rainfall-runoff relationship for a given catchment such that forecast of the consequences of a storm can be done with greater accuracy and on time to save the ever increasing loss of life and property due to floods. This task becomes even more difficult for a semi-arid or an arid catchment due to the complexity involved in the process of transformation of rainfall to runoff and is further worsened while continuous changes in land-use/land-cover are taking place because of various anthropogenic and economic activities within the catchment. In spite of its location below 20 o
S of latitudes where climate is generally semi-arid with an annual average rainfall varying between 250-500mm together with a very high amount of evaporation which is of the order of about 2000 mm/annum, Botswana has been found to be suffering from flood related losses which between the years 1965 and 2000 aggregate to a total of about US$ 0.5 millions while affecting as high as about 160,000 people.
Although most of the rivers originating within Botswana are either ephemeral or intermittent, it is interesting to note that flooding has increasingly become a common problem in urban areas of
Botswana out of which two population clusters namely the Gaborone and Lobatse lying within the Notwane Catchment system have been among the hardest hit. Besides several economic activities in and around these cities leading to major and small-scale industrial, commercial, and institutional developments, the catchment has witnessed changes in land use due to growth in individual homesteads, settlements and mixed small-scale farming practices including poultry to support the urban population. Eventually, all these add to a compositely modified natural drainage system of the Notwane River which is part of one of the most important indigenous river systems viz the Limpopo system of Botswana.
2

While several attempts have been made to develop rainfall-runoff relationships, forecasting using these models would require knowledge of the input variable in future times. Knowledge of such input variables in future times is almost impossible due to climatic variability and dynamic landuse within the catchment. An estimate of these input variables by indirect methods would result in propagation of errors associated with the input variables, even if the forecast model performs accurately. In view of these, runoff coefficient, a ratio between total flow and total rainfall over the catchment in a year has been selected to represent the lumped flow characteristics with the assumption that the cross cutting effects due to changes in climate and land-use can be marginalized to some extent. Since, the time series of the runoff coefficients will usually be small and may be non-stationary; using time-series models to forecast some ten or twenty time steps ahead may not be possible or will yield erroneous results. In view of these, attempt to use the artificial intelligence through models like the ANN has been attempted in this paper, such that the results of this study can assist the policy makers to take decisions on the situation of land-use and land-cover in this catchment
2. METHODOLOGY
2.1 The Water Balance Model
When catchments are ungauged or the hydrological cycle is subjected to the effects of human interference, one of the methods found very useful in estimating runoff coefficient is the Water
Balance Method (Thornthwaite and Mather, 1955). Besides its reasonable representation of the physical processes through integration of the effects of climate and land-use (Dunne and
Leopold, 1978), the main advantage of this method lie in its simplicity and fewer data requirements.
3

Also, in view of the fact that the method works very well for areas (cells) representing uniform soil and climatic characteristics, this method is often applied through a multi-cell representation of the catchment as suggested by Fischer et al , (1996). Such cells, however, can be obtained by superimposing contours of long-term rainfall, evapotranspiration on the soil map of the catchment. Computed runoff from each cell is then lumped at the outlet to obtain the final runoff, hence the runoff co-efficient (Parida et al., 2003). However, the output from each cell computed by this model is sensitive to one of the factors, which is used for allocation of Total Available
Moisture for Runoff (TARO) between Detention (DET) and Runoff (RO). This factor being sensitive to the cell size needs to be calibrated such that the sum of square of deviation between the observed and the computed flows was the least.
2.2 Artificial Neural Network (ANN)
Artificial Neural Network comprises of a network of neurons and takes the cue from their biological counterparts, in the manner that neurons being capable of learning can be trained to find solutions, recognize patterns, classify data and even forecast future events (Clair and
Ehrman, 1998). As a result of these, they have found wide application in simulating very complex relationships and as such found wide application in modelling many hydrological problems including rainfall-runoff modelling and stream flow forecasting (Shamseldin ,1997;
Zealand et al, 1999; Uvo et al ., 2000; Anmala et al , 2000; Hsu et al ., 2002 and Riad et al .,
2004)
Such a network usually comprises of many layers arranged in series, each layer containing one or a group of neurons each of which have the same pattern of connections to the neurons in the other layer(s) (Shamseldin, 1997). The first and last layers are used for input and output variables and the intermediate layers are usually connoted as the hidden layer which can be one or many,
4

depending on the complexity of the problem. The weights to a neuron are automatically adjusted by training the network according to a specified learning rule until it properly simulates the past data or performs the desired task (Furundzic, 1997; Shamseldin, 1997, Zealand et al , 1999).
Mathematical functions, known as neuron transfer functions, are used to transform the input to output for each neuron. The log-sigmoid transfer function is commonly used for hidden layer neurons, especially with the back propagation algorithm (The MathWork, Inc. 1994-2002).
Two separate stages are involved in the hidden (intermediate) and output layers in transformation of their respective inputs to output. Firstly, an input to a neuron is multiplied by its corresponding weight, and the total sum of those input products, to such neuron, plus a constant term yields the neuron net input. The second stage entails transformation of the net input into output. The optimum network architecture (Plant Model) can then be used to predict future behaviour (forecasting) of the plant. An optimization algorithm is used to select the control input that optimizes future performance. Figure 1 shows a typical example of a one hidden layer feed forward neural network architecture.
3. THE STUDY AREA
The study area lies between the latitudes 24
º
23
'
S - 25
º
22
'
S and the longitudes 25
º
23
'
E - 26
º
00
'
E relates to the Notwane catchment covering an area of about 225 km
2
in the south-eastern
Botswana as shown in Figure 2. Although the catchment is drained by the Notwane, Taung,
Metsemaswaane and Nywane rivers, the catchment system bears its name from the main stream i.e. Notwane, which traverses from some eleven kilometres south of Ramotswa, along the boarder through north eastwards yielding into the Limpopo. The Notwane River being an intermittent one has been dammed at Gaborone to create an artificial reservoir for catering to the Gaborone City
5

and some other urban centres around it and passes the greater Gaborone area from southeast to northeast.
The area experiences an average annual rainfall between 450 and 550 mm south-westerly with temperatures varying between 37

C in Summer and 10

C in Winter. Additionally the area experiences very high rates of evaporation, which stands at an average of about 1400 mm per year. The topography of the area is more or less undulating uplands, which are crossed by watercourses with hills and rocky outcrops and hardveld. Vegetation cover is mostly croton gratissimus woodland on hills and rocky outcrops. The hardveld, which contains the Taung and
Nywane rivercourses, is mostly vegetated with rhus leptodictya tree savanna. Generally, the area slopes gently into a northeasterly direction (Lungu and Sefe, 1989). The soils are mostly of the parent luvisols with field soil moisture capacity averaging about 90mm.
4. RESULTS AND DISCUSSIONS
4.1 Computation of Runoff coefficients using Water Balance Method
For the water balance model, monthly average rainfall values based on observations at Gaborone dam, Ramotswa, Lobatse, Molapowabojang, Ramatlabama and Goodhope raingauges have been used while for evaporation observations at Gaborone dam between the years 1978 and 2000 have been considered. Contours based on long-term annual average rainfall and potential evapotranspiration values were drawn over the soil map of the catchment and thirteen cells were identified as shown in Figure 3. For each cell, Water balance analysis was carried out using
Rainfall (P) and Potential Evapotranspiration (PET) and Field Moisture Capacity (FSMC) information for different years with equal distribution TARO between Detention and Runoff
6

(Parida et al., 2003). A typical Water Balance table for cell A and year 1996 is shown in Table
1.Runoff coefficients thus computed for this catchment from 1978 to 2000 have been tabulated in
Table 2. From these figures, it is observed that the ROCs increased at a rate of nearly 3 % per annum within this period.
4.2 Application of Artificial Neural Network
Application of ANN has been undertaken in two stages viz: development of optimal network architecture using the water balance computed ROCs and forecasting up to two decades i.e. 2020 to match with the Vision 2016 of the country.
4.2.1. Network Development and Validation of ROCs:
To take into account the contribution of several environmental variables including land cover/ land-use and many other climatic variables, network design was undertaken using five input variables viz: average basin rainfall, evaporation, temperature, field soil moisture capacity
(FSMC), and percent of urbanisation. Such vectors for different years were placed in a matrix of concurrent vector of output runoff coefficients computed from the water balance. For the input layer, most popularly known back propagation algorithm was used while t he log-sigmoid
(logistic) transfer function was used for the first/hidden layers while the linear transfer function
(purelin) was used for the output layer. The number of neurons in the input layer was decided based on the number of input variables. T he network architecture adopted was then used for training, validation and testing.
The optimum network architecture was a three neuron hidden layer using ‘One Step Secant
Algorithm’, trainoss and with early stopping. All the principal components were retained at 0.001 confidence level with all the input variables retained. This gave the best optimisation of the
7

performance function which was the Mean Squared Error (MSE). The ROC data was divided into three equal sub-sets for training, validation and testing. The network converged after 184 epochs with Mean Squared Error (MSE) of 0.0065 for training the subset. Optimization of the performance function for training, validation and testing subsets are shown in Figure 4.The output runoff coefficients obtained through simulation of the developed network were found to have a very good correlation between the target runoff coefficients (i.e. the ROCs computed from water balance model) at 0.996 and the plot between the two have been shown in Figure 5.
From the weighed activations of all the input variables into the hidden layer neurons, climatic variables were found to account for 48 % of the changes in Runoff while 52 % can be attributed to land use-drainage changes as shown by Table 2.
4.2.2 Forecast of ROCs:
After development of the optimal network, the Neural Network plant model was used for forecasting, which uses the previous plant input i(t) and output, a(t ) to predict future values of the plant output a m
(t+1) . The last value in an output array, a m
(t+1), is used to estimate proportionate values of i(t+1) and a p
(t+1) which are then added to the inputs in forecasting for a m
(t+2) . This was repeated until the forecasting reached the end of the chosen design period i.e. the year 2020.
Use of such a type of controller though requires a significant amount of on-line computation
(because of optimization algorithm is performed at each sample time to compute the optimal control input) is quite efficient in formulation of forecasts. The plot of simulated and forecasted
ROCs together have been shown in Figure 6. It was observed that the forecasted runoff coefficients also showed an upward trend with value of 0.0316 which is of the order 1 % rise.
8

5. CONCLUSIONS
The following conclusions have been drawn from this study undertaken to evaluate the possibility of using ANN in forecasting of Runoff coefficient up to 2020 for the Notwane catchment in Botswana. Conclusions drawn from this study can be summarised as follows:
(i) The optimal network developed for modelling the runoff coefficients from
Notwane catchment was a multi-layer feed forward type network with three layers operated through back propagation algorithm with layer using log-sigmoid transfer function and the output layer using purelin transfer function. The number neurons for the hidden layer were fixed at three with five and one for the input and output layers respectively. The training algorithm used was trainoss and with early stopping. The choice was confirmed with a very high correlation value of 0.996 between the simulated ROC values using the proposed network and the ROC values obtained from Water Balance model.
(ii) While, the simulated ROCs for the period 1978-2000 showed an increase of about
3 % per year, the forecasted ROCs for the next 20 years (upto 2020) showed a possible increase of about 1% per year. This indicates that the catchment is likely to see a reduction in the yield in the next 20 years.
(iii) From the weights attributed to various input variables used for simulation, it was found that between the years 1978 and 2000, while 52 % of the changes in ROCs can be attributed to land use-drainage changes, 48 % can be attributed due to climatic variables.
From the above, it can be concluded that, ANN provides not only an alternative modelling tool to forecast the possible combined impact of the current land-use practices together with climatic variability, on the yield expressed in terms of runoff coefficients, but also a means to find the
9

contribution of these environmental factors on the runoff co-efficient. The success of its applicability to a semi-arid catchment like the Notwane catchment speaks in favour of its use for other catchments in and around this country.
6. REFERENCES
Anmala, J., Zhang, B. and Govindaraju, R.S., (2000). Comparison of ANNs and Empirical
Approaches for Predicting Watershed Runoff. Journal of Water Resources. Planning &
Managmnt, ASCE, 126 (3): 156-166.
Clair, T. A. and Ehrman, J. M., (1998).Using Neural Networks To Assess Influence Of
Changing Seasonal Climates In Modifying Discharge, Dissolved Organic Carbon, And
Nitrogen Export In Eastern Canadian Rivers. Water Resources Research 34 (3): 447-455.
Dunne, T. and Leopold, L.B., (1978). Water in Environmental Planning. W.H. Freeman, San
Francisco.
Fischer, D.T., Smith, S.V. and Churchill, R.B., (1996). Simulation Of A Century Of Runoff
Across The Tomales Watershed, Marian County, California. Journal of Hydrology, 186: 253-273.
Furundzic, D., (1997). Application Example Of Neural Networks For Time Series Analysis:
Rainfall – Runoff Modelling, Signal Processing, 64: 383-396.
Hsu, K., Gupta, H.V., Gao, X., Sorooshian, S. and Imam, B., (2002). Self-Organizing Linear
Output Map (SOLO): An Artificial Neural Network Suitable For Hydrologic Modelling And
Analysis, Journal of Hydrology, 38 (12): 1-17.
Lungu, E.M., and F.T.K.. Sefe, (1989). Urban And Peri-Urban Hydrology – Groundwater
Pollution, Rural Dams And Flood Hazards. Swedeplan, Gaborone. Final report.
Parida, B.P., D.B.Moalafhi and P.K.Kenabatho. (2003) Effect of Urbanization on Runoff
Coefficient - A Case Study of Notwane Catchment in Botswana, Proceedings of the Intl. Conf. on
Water and Environment (WE-2003), Dec.15-18, 2003, Bhopal,'Watershed Hydrology', Allied
Publishers Pvt. Ltd.,123-131.
Riad, S., J. Mania, L.Bouchaou, Y. Najjar, (2004). Predicting Catchment Flow In A Semi-Arid
Region Via An Artificial Neural Network Technique, Hydrological Processes Journal, 18(13):
2387-2393.
Shamseldin, A.Y., (1997). Application of A Neural Network Technique To Rainfall-Runoff
Modelling, Journal of Hydrology, 199: 272-294.
The Mathworks Inc. (2002). Neural Network Toolbox; For Use with MATLAB, User’s Guide
Version 4.
10

Thornthwaite, C. W. and Mather, J.R., (1955). The Water Balance: Laboratory Of Climatology.
Pub. No. 8, Centerton, N J.
Uvo, C.B., Tölle, U. and Berndtsson, R., (2000). Forecasting Discharge In Amazon Using
Artificial Neural Networks. International Journal of Climatology, 20: 1495-1507.
Zealand, C.M., Burn, D.H. and Simonovic, S.P., (1999). Short Term Streamflow Forecasting using Artificial Neural Networks. Journal of Hydrology 214: 32-48
11

Table 1. A typical table for Water Balance Computation for cell A for the year 1996 (in mm).
J F M A M J J A S O N D TOTAL
Precipitation (P) 200 175 157 52 14 0 0 0 45 53 52 67 777
Potential Evapo-
Transpiration (PET) 88 79 60 47 73 73 64 93 97 100 89 97 960
P-PET 112 96 97 5 -59 -73 -64 -93 -52 -47 -37 -30
Available Potential
Water Loss (APWL) 0 0 0 0 59 132 196 289 341 388 425 455
Soil Moisture (SM) 90 90 90 90 46 20 10 3 2 1 1 1
Change in Soil
Moisture (ΔSM) 89 0 0 0 -44 -26 -10 -6 -2 -1 0 0
Actual Evapo-
Transpiration (AET) 88 79 60 47 58 26 10 6 47 54 89 97
Deficit (DEF) 0 0 0 0 15 47 54 87 50 46 0 0
Surplus (SURP)
Total Available for
Run Off (TARO)
Run Off (RO)
23
57
28
96
125
62
97
160
80
5
85
42
0
43
21
0
22
11
0
11
5
0
6
3
0
3
2
0 74 30
2 74 67 655
1 37 33 325
Detention ( DET) 29 63 80 43 22 11 6 3 1 1 37 34
Table 2. Runoff Coefficients and Percentage Urbanization for the Study Area for the period 1978 – 2000.
Year Runoff Coeff % Urban
1978 0.37 15
1979 0.40 15.7
Year
1991
1993
Runoff Coeff % Urban
0.46
0.53
45.7
47
1980 0.41 16.5 1994 0.54 48
1981 0.49 17.7 1995 0.56 49
1982 0.45 20 1996 0.54 50
1986 0.55 32 1997 0.50 50.7
1987 0.54 34.5 1998 0.42 51.7
1988 0.35 38 1999 0.49 52.5
1989 0.47 41 2000 0.54 53.7
1990 0.51 44
Table 3. Contributions of climatic and land use changes to runoff for the Notwane catchment
% influence
TOTAL
Climatic variables
Precipitation
(mm)
21
Evaporation
(mm)
16
48
Temperature
(ºC)
11
Landuse-drainage changes
FSMC (cm/m) % Urban
20
52
32
12

Input neurons
First and hidden layer
Input array
Output layer
Output array
Figure 1. A typical Multi-layer feed forward neural network architecture showing seven neurons in input layer, eight neuron in a hidden layer and a single neuron in the output layer .
Figure 2. The study area showing the drainage patterns with location of rainfall stations used in the study
13

Figure 3. Multi-cell representation of the Notwane catchment.
Figure 4. Optimization of the performance function for training, validation and testing subsets using the five input variables.
14

0.6
0.55
0.5
0.45
0.4
predicted target
0.35
0.3
1978 1980 1982 1987 1989 1991 1994 1996 1998 2000
Years
Figure 5. Predicted and Water balance Target runoff coefficients using the five input variables
0.6
0.55
0.5
0.45
0.4
0.35
0.3
19
78
19
81
19
87
19
90
19
94
19
97
20
00
20
03
Years
20
06
20
09
20
12
20
15
20
18
Figure 6. Simulated and Forecasted runoff coefficients using the developed Network
15