A time series model to predict the runoff ratio of catchments of the Kalu ganga basin

Forecasting I-unoff ratio vat-iation is important since it can be used to calcula~c the runoff of a river catchment for a given rainfall on a particularday. The model SARIMA (Season,ll Auto-Regressive Integrated Moving Average) developed for this purpose which was based on Auto Correla t ion Func t ion (ACF) and Partial Au to Correction Filnction (PACF), w ~ s fitted to the runoff ratio data of the Katnpura catchment of the Kal~iganga basin. The dppropriateness of the sdme model was rested against two other catchments; Dela and Elluguwcl of the same river basin and found to be suitable.


INTRODUCTION
Water is one of the most important natural resources of the world.Proper management of this scare resource is everyone's responsibility, because availability of water for human usage is decreasing rapidly.In this context, management of rainwater also plays an important role.Rainwater runoff is another vital aspect in hydrological analysis.Therefore studies of the rainfall, runoff and runoff ratio are of immense value t o understand hydrological complexity.
In this study, the short-term variation of nlnoff ratio has been investigated.A model was derived to forecast the runoff ratio of the Rathnapura catchment of the Kalu ganga basin.SARIMA (Seasonal Auto-Regressive Integrated Moving Average) model was fitted to the runoff ratio.The data of Dela and Ellagawa catchments of the same river basin were used to verify the derived model.

METHODS AND MATERIALS
Rainfall data were obtained from the Department of Meteorology and discharge data were collected from t h e H y d r o l o g y Division of t h e D e p a r t m e n t of Irrigation.O n e hundred and ninety five monthly discharge data and rainfall data (from October 1978 to December 1994) were used in the analysis.Thiessen's Polygon method'was used to calculate the total average monthly rainfall of the relevant catchment using rainfall data measured in stations around the catchment.
The runoff component was calculated by subtracting the base flow from discharge data for each month.Runoff was divided by (monthly) the average rainfall to obtain the runoff ratio.A time series plot of the runoff ratio was used t o identify the trend and seasonal variation.The trend and seasonal variation were removed using differencing methods to make the series stationary.

Identification of the model was based on the graphs of A u t o Correlation Function (ACF) and Partial Corrlation Function (PACF).2
The model was fitted using Minitab (Version 14) software.Validity of the assumptions of the model was confirmed by analyzing residuals.

Applicability of t h e model derived f o r t h e
Ratnapura catchment was tested for the two catchments of Dela and Ellagawa.

RESULTS
The time series plot of calculated runoff ratio lor the Ratnapura catchment is shown (Figure 1).According t o the figure, a mild upward trend and a seasonal variation can be seen.The trend and seasonal variation were removed by using the method of differencing to make the series stationary.First difference was used to remove the trend.anddifference at lag 12 was used to Therefore the model fitted was identified using the graphs of ACF and PACF.It was found that p=O, d = l , q = l , P=O, D = l and Q=1.
x I -x t ., -x ,-,, + x [-,,= Z,+0.9068Zt~,,+O.8631Zt.,+0.78272L ., ,  In colnparison to Ratnapura and Dela, the gradient of the trend line of runoff ratio for Ellagawa was quite small (= 0.0002 per month).Almost all changes (affecting the runoff ratio) of the area had been completed before the beginning of the study period.The very small trend of the runoff ratio may be due to the above.

Auto-correlation Function for Ratio
I n conclusion, it can be stated t h a t t h e SARIMA(011)(011) 12 model is appropriate to model the runoff ratio of the catchments of Ratnapura, Dela and Ellagawa in the Kalu ganga basin.However, further investigation is necessary to conclude whether this model is appropriate t o forecast the runoff ratio of other catchments in Sri Lanka.

Figure 1 :
Figure 1: Runoff ratio of the Ratnapura catchment