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Table 1: Locations and elevations of the monitoring wells Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta Int. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 201

Table 1 Locations and elevations of the monitoring wells Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta Int. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 201

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Figure 1: Study area showing the locations of BWDB GWL monitoring stations Viethodology Figure 1: Study area showing the locations of BWDB GWL monitoring stations A stochastic modelling technique for predicting groundwater table fluctuations with time series analysis
Figure 1: Study area showing the locations of BWDB GWL monitoring stations Viethodology Figure 1: Study area showing the locations of BWDB GWL monitoring stations A stochastic modelling technique for predicting groundwater table fluctuations with time series analysis
Figure 2 Linear regression model for KUS-DP monitoring well results in a stationary mean value of approximately zero. A simple linear regression model is developed for the observed series to characterize the trend component (Figure 2). The results of regression analysis are shown in Table 2. The trend of the overall GWL fluctuations develops through time which depicts a downward trend. The reason is that the water suction rate gets high during the dry season due to irrigation purpose and other water evolved activities. The first insight into the statistical properties of the time series is shown in Table 3. Performing the first differencing on the groundwater level series reduces the series mean from 12.414 to -0.001. The first differencing often results in a stationary mean value of approximately zero. Table 2: Statistical results for KUS-DP monitoring well
Figure 2 Linear regression model for KUS-DP monitoring well results in a stationary mean value of approximately zero. A simple linear regression model is developed for the observed series to characterize the trend component (Figure 2). The results of regression analysis are shown in Table 2. The trend of the overall GWL fluctuations develops through time which depicts a downward trend. The reason is that the water suction rate gets high during the dry season due to irrigation purpose and other water evolved activities. The first insight into the statistical properties of the time series is shown in Table 3. Performing the first differencing on the groundwater level series reduces the series mean from 12.414 to -0.001. The first differencing often results in a stationary mean value of approximately zero. Table 2: Statistical results for KUS-DP monitoring well
Table 3: Statistics of observed data and data from the first differencing Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta 1t. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 20
Table 3: Statistics of observed data and data from the first differencing Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta 1t. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 20
Further illustration of the time series is obtained from the estimated autocorrelation function (ACF) and partial autocorrelation function (PACF). As shown in Figure 4, lags up to 160 weeks long are taken. The ACF in Figure 3 dies down slowly in a damped sine-wave pattern, indicating that the raw data is non-stationary. Significant correlations (It-valuel>1.6) exist at the lag 1 and lag 2 phases in Figure 4(a). The ACF exhibits a strong 52 weeks seasonal component. To remove seasonal nonstationarity of the series, the first seasonal differencing of lag 52 is applied (Figure 5), although some significant correlation exists and its magnitude appears to be small as compared the seasonal differencing. As the trend shows long-term effect, another difference of lag 1 has induced to obtain stationarity and ensured not to be over differenced. effect, another difference of lag 1 has induced to obtain stationarity and ensured not to be over differenced.
Further illustration of the time series is obtained from the estimated autocorrelation function (ACF) and partial autocorrelation function (PACF). As shown in Figure 4, lags up to 160 weeks long are taken. The ACF in Figure 3 dies down slowly in a damped sine-wave pattern, indicating that the raw data is non-stationary. Significant correlations (It-valuel>1.6) exist at the lag 1 and lag 2 phases in Figure 4(a). The ACF exhibits a strong 52 weeks seasonal component. To remove seasonal nonstationarity of the series, the first seasonal differencing of lag 52 is applied (Figure 5), although some significant correlation exists and its magnitude appears to be small as compared the seasonal differencing. As the trend shows long-term effect, another difference of lag 1 has induced to obtain stationarity and ensured not to be over differenced. effect, another difference of lag 1 has induced to obtain stationarity and ensured not to be over differenced.
Periodogram is been used to characterize the periodic behaviour of the time series. Time series representing GWL typically have an underlying annual periodicity. Building a model of time series, detecting periodicity is a must. A plot of the time series may not always uncover the annual periodicity because time series contain random fluctuations that often mask the underlying structure. The plot of the periodogram shows a sequence of peaks with the lowest frequency peak at a frequency less than 0.02. Each of the data points in the time series represents a week, so an annual periodicity corresponds to a period of 52 in the current data set. As period and frequency are reciprocals of each other, a period of 52 corresponds to a frequency of 1/52 (or 0.0192). Figure 2 shows the periodogram for the given data set. Periodicity 52 has been determined from the periodogram as it is showing the frequency about 0.0189. has been determined from the periodogram as it is showing the frequency about 0.0189.
Periodogram is been used to characterize the periodic behaviour of the time series. Time series representing GWL typically have an underlying annual periodicity. Building a model of time series, detecting periodicity is a must. A plot of the time series may not always uncover the annual periodicity because time series contain random fluctuations that often mask the underlying structure. The plot of the periodogram shows a sequence of peaks with the lowest frequency peak at a frequency less than 0.02. Each of the data points in the time series represents a week, so an annual periodicity corresponds to a period of 52 in the current data set. As period and frequency are reciprocals of each other, a period of 52 corresponds to a frequency of 1/52 (or 0.0192). Figure 2 shows the periodogram for the given data set. Periodicity 52 has been determined from the periodogram as it is showing the frequency about 0.0189. has been determined from the periodogram as it is showing the frequency about 0.0189.
Figure 5: Plot of (a) ACF and (b) PACF for the time series of KUS-DP monitoring well obtained from the
Figure 5: Plot of (a) ACF and (b) PACF for the time series of KUS-DP monitoring well obtained from the
Figure 6: Plot of (a) ACF and (b) PACF for the data of KUS-DP monitoring well obtained from additional
Figure 6: Plot of (a) ACF and (b) PACF for the data of KUS-DP monitoring well obtained from additional
Table 4: Estimated parameters of seasonal ARIMA model for KUS-DP monitoring well Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta [nt. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 201)
Table 4: Estimated parameters of seasonal ARIMA model for KUS-DP monitoring well Sajal Kumar Adhikary, Md. Mahidur Rahman, Ashim Das Gupta [nt. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 201)
Figure 8: Observed & forecasted values by seasonal ARIMA (1,1,1)X(1,1,1)s2 model for KUS-DP well
Figure 8: Observed & forecasted values by seasonal ARIMA (1,1,1)X(1,1,1)s2 model for KUS-DP well
Table 5: Forecasting performance of Seasonal ARIMA and Decomposition models
Table 5: Forecasting performance of Seasonal ARIMA and Decomposition models
Figure 9: Plot of actual and forecasted values for KUS-DP monitoring well by Decomposition model A stochastic modelling technique for predicting groundwater table fluctuations with time series analysis
Figure 9: Plot of actual and forecasted values for KUS-DP monitoring well by Decomposition model A stochastic modelling technique for predicting groundwater table fluctuations with time series analysis
Related topics:
Data AssimilationGroundwater HydrologyParticle filtersLand-atmosphere interactionsRemote sensing applicationsClimate Changes and Climate VariabilityStatistical and Dynamical DownscalingSurface and Subsurface HydrologyStatistical Methods Applications
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