Abstracts Category : Other

Dealing with missing data in hydrology

by Yongbo Gao

Hydrological missing data is a common issue for hydrologists as it poses a serious problem for many statistical approaches in hydrology which require complete data sources since missing data is often harmful beyond reducing statistical power. For reasons of convenience, researchers often resort to simple solutions to deal with missing data such as simply discarding observations characterized by missing data or by replacing missing data with a statistical methodology. Despite its convenience, discarding is suboptimal as it reduces the quality of the conclusion to be drawn when analyzing the data. Actually, a variety of statistical techniques are available to treat missing data. My research is about finding the right techniques to deal with missing data problems in Hydrology and distinguishing in which certain circumstances which method works better.First, various imputation methods available to the hydrological researchers have been reviewed, including arithmetic mean imputation, Principal Component Analysis (PCA), regression-based methods and multiple imputation methods.Due to the time-series nature of hydrological data often requires more flexible non-linear model, we therefore put an emphasis on time-series regressions approaches that exploit the time series nature of hydrological data. Auto Regressive Conditional Heteroscedasticity (ARCH) models which originate from finance and econometrics and Autoregressive Integrated Moving Average (ARIMA) models are discussed regarding the applicability to hydrological contexts here. I focused the attention on discussing econometric time-series methods as they explicitly model the particular statistical properties of hydrological time-series (autocorrelation and heteroscedasticity) which are mostly neglected in algorithmic machine learning approaches.Second, the performances of imputation techniques which are widespread and easy to use but ignore the time series nature of hydrological data and imputation techniques exploiting their time series nature are compared. By running a hydrological model - Hydrologiska Byrns Vattenbalansavdelning (HBV) model we generated 5 different discharge time series that exhibit different patterns of volatility to analyze. The combination of Mean Squared Error (MSE) and Nash Sutcliff efficiency (NSE) as performance measures demonstrates that econometric time series models such as Autoregressive Integrated Moving Average (ARIMA) and Autoregressive Conditional Heteroscedasticity (ARCH) model outperform alternative imputation approaches such as mean imputation or Ordinary Least Squares (OLS) based regression methods. Furthermore, we examined how the inclusion of information beyond the time-series of the variable of interest itself can improve imputation results. Extensions of these models to incorporate additional exogenous regressors are readily available with ARIMAX and ARCHX models. Using discharge data from Brandenburg in the northeast of Germany, we compare the imputation performance of univariate ARIMA and ARCH models which have