Stochastic modelling and forecasting of monthly groundwater levels in Ramotswa wellfield

Abstract

Ramotswa wellfield located in South Eastern Botswana is undergoing rapid urbanization with a significant population growth rate between 2-3% per annum. This along with unreliable rainfall pattern, has escalated the demand on fresh water supplies, hence pressure on the well field and supplies from the Gaborone Dam. Use of historical groundwater level records from observation boreholes provides valuable source of information for understanding the hydrological dynamics due to different stresses within the aquifer system and helps in anticipating future challenges that are likely to occur due to these stresses. In this study, an attempt has been made to model the fluctuation of monthly groundwater table data in Ramotswa wellfield both in space and time using geostatistical and stochastic models. By conducting time series modelling, monthly groundwater level data collected from 2002 to 2012 at 13 different wells were subjected to intervention analysis. This was done to detect any changes in the data due to natural and manmade causes. Cumulative Summation (CUSUM) results revealed that groundwater level data had undergone intervention at all the boreholes. Change which was confirmed by T-Statistic test at 5% significance level was identified at end of year 2007 and beginning of year 2008.Trend analysis was conducted using Mann Kendall test for data after time of intervention. The results revealed that trend was not statistically significant in most boreholes. For stochastic modelling, data at each borehole were subjected to two approaches namely Autoregressive Integrated Moving Average (ARIMA) and Thomas Fiering models to make three months forecasts. The most suitable model was chosen. It was found that in almost all cases ARIMA models gave the least error estimates in forecasting and hence was recommended for forecasting. For spatial interpolation of groundwater levels at unknown locations within the well field, geostatistical modelling approach was used for two scenarios; winter (July 2005) and wet season (i.e. after February 2006 floods). Based on the results of 3 semi-variogram models to the observed data, exponential model was found to provide the best fit for July 2005 scenario while for February 2006 it was the spherical model. The choice of the two models was supported by reasonable values of r2; which were 0.7 for July 2005 and 0.9 for February 2006. The nugget- to -sill ratios of 0.1 (< 0.25) for July 2005 scenario groundwater levels have strong spatial dependence while the ratio was 0.29 for February 2006 scenario indicating moderate spatial dependence. After interpolation by ordinary kriging, the results of the groundwater level at unknown were cross validated with known values at 5 boreholes within the radius of influence and the percentage errors were found to be low. The results indicated that groundwater levels are affected by topography and presence of water bodies and demonstrated the usefulness of stochastic modelling for temporal and geostatistics in spatial modelling of groundwater table in the study area, hence in water resources planning and management.