A review has been made to understand the hydrogeochemical behaviour of groundwater through statistical analysis of long term water quality data (year 2005–2013). Water Quality Index (WQI), descriptive statistics, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. WQI results showed that majority of samples fall in moderate category during 2005–2013, but monitoring site four falls under severe category (water unfit for domestic use). Brownian time series behaviour (a true random walk nature) exists between calcium (Ca²⁺) and electric conductivity (EC); magnesium (Mg²⁺) with EC; sodium (Na⁺) with EC; sulphate (SO²⁻₄) with EC; total dissolved solids (TDS) with chloride (Cl⁻) during pre- (2005–2013) and post- (2006–2013) monsoon season. These parameters have a closer value of Hurst exponent (H) with Brownian time series behaviour condition (H=0.5). The result of times series analysis of water quality data shows a persistent behaviour (a positive autocorrelation) that has played a role between Cl⁻ and Mg²⁺, Cl⁻ and Ca²⁺, TDS and Na⁺, TDS and SO²⁻₄, TDS and Ca²⁺ in pre- and post-monsoon time series because of the higher value of H (>1). Whereas an anti-persistent behaviour (or negative autocorrelation) was found between Cl⁻ and EC, TDS and EC during pre- and post-monsoon due to low value of H. The work outline shows that the groundwater of few areas needs treatment before direct consumption, and it also needs to be protected from contamination.

We have estimated soil moisture (SM) by using circular horizontal polarization backscattering coefficient (σ^o_RH), differences of circular vertical and horizontal σ^o (σ^o_RV− σ^o _RH) from FRS-1 data of Radar Imaging Satellite (RISAT-1) and surface roughness in terms of RMS height (RMS_height). We examined the performance of FRS-1 in retrieving SM under wheat crop at tillering stage. Results revealed that it is possible to develop a good semi-empirical model (SEM) to estimate SM of the upper soil layer using RISAT-1 SAR data rather than using existing empirical model based on only single parameter, i.e., σ^o. Near surface SM measurements were related to σ^o_RH, σ^o_RV−σ^o_RH derived using 5.35 GHz (C-band) image of RISAT-1 and RMS_height. The roughness component derived in terms of RMS_height showed a good positive correlation with σ^o_RH−σ^o_RH (R₂ = 0.65). By considering all the major influencing factors (σ^o_RH, σ^o_RV− σ^o_RH, and RMS_height), an SEM was developed where SM (volumetric) predicted values depend on σ^o_RH, σ^o_RV− σ^o_RH, and RMS_height. This SEM showed R² of 0.87 and adjusted R² of 0.85, multiple R=0.94 and with standard error of 0.05 at 95% confidence level. Validation of the SM derived from semi-empirical model with observed measurement (SM_Observed) showed root mean square error (RMSE) = 0.06, relative- RMSE (R-RMSE) = 0.18, mean absolute error (MAE) = 0.04, normalized RMSE (NRMSE) = 0.17, Nash–Sutcliffe efficiency (NSE) = 0.91 (≈1), index of agreement (d) = 1, coefficient of determination (R₂) = 0.87, mean bias error (MBE) = 0.04, standard error of estimate (SEE) = 0.10, volume error (VE) = 0.15, variance of the distribution of differences (S²_d) = 0.004. The developed SEM showed better performance in estimating SM than Topp empirical model which is based only on σ^o. By using the developed SEM, top soil SM can be estimated with low mean absolute percent error (MAPE) = 1.39 and can be used for operational applications.