Efficacy of statistical algorithms in imputing missing data of streamflow discharge imparted with variegated variances and seasonalities

Abstract

Streamflow missing data rises to a real challenge for calibration and validation of hydrological models as well as for statistically based methods of streamflow prediction. Although several algorithms have been developed thus far to impute missing values of hydro(geo)logical time series, the effectiveness of methods in imputation when the time series are influenced by different seasonalities and variances have remained largely unexplored. Therefore, we evaluated the efficacy of five different statistical algorithms in imputation of streamflow and groundwater level missing data under variegated periodicities and variances. Our performance evaluation is based on the streamflow data, procured from a hydrological model, and the observed groundwater data from the federal state of Brandenburg in Northeast Germany. Our findings revealed that imputations methods embodying the time series nature of the data (i.e., preceding value, autoregressive integrated moving average (ARIMA), and autoregressive conditional heteroscedasticity model (ARCH)) resulted in MSEs (Mean Squared Error) that are between 20 and 40 times smaller than the MSEs obtained from the Ordinary least squares (OLS) regression, which do not consider this quality. ARCH and ARIMA excelled in imputing missing values for hydrological time series, specifically for the streamflow and groundwater level data. ARCH outperformed ARIMA in both the streamflow and groundwater imputation under various conditions, such as without seasonality, with seasonality, low and high variance, and high variance (white noise) conditions. For the streamflow data, ARCH achieved average MSEs of 0.0000704 and 0.0003487 and average NSEs of 0.9957710 and 0.9965222 under without seasonality and high variance conditions, respectively. Similarly, for the groundwater level data, ARCH demonstrated its capability with average MSEs of 0.000635040 and average NSEs of 0.9971351 under GWBR1 condition. The effectiveness of ARCH, originated from econometric time series methods, should be further assessed by other hydro(geo)logical time series obtained from different climate zones.