Reconstruction of Information for Short-gauged Water Quality Parameters Using a Robust Version of the Line of Organic Correlation Technique

Abstract

Missing data are a common problem in water quality management and operational hydrology. In such situations, filling in missing observations is warranted. However, sometimes the extension of hydrological or water quality time series at short-gauged stations is required. Records can be extended in time at short-gauged stations by exploiting the correlation between the station of interest and a nearby long-gauged station. Ordinary least squares regression (OLS) is a traditional and commonly used record extension technique. However, its purpose is to generate optimal estimates of each record rather than of the population characteristics, for which OLS tends to underestimate the variance in the extended records. This leads to underestimation of high percentiles and overestimation of low percentiles, given that the data is normally distributed. The development of the line of organic correlation (LOC) technique, also known as the maintenance of variance extension technique (MOVE), is aimed at correcting this bias. The LOC is preferable when the probability distribution of the estimates, and not just an individual estimate, is of interest. Given that water resources data in general, and water quality data in particular, are characterized by the presence of outliers, positive skewness and non-normal distribution of data, a robust record extension technique is more appropriate. In this study, three record extension techniques were investigated, and their properties were explored: OLS, LOC and a new technique proposed in this paper, the robust line of organic correlation technique (RLOC). RLOC includes the advantage of the LOC in reducing the bias in estimating the variance, but at the same time it is also robust to the presence of outliers. An empirical examination of the preservation of the characteristics of the water quality parameters was carried out using water quality records from the Nile Delta drainage system monitoring network in Egypt. Ten years of monthly records of Electric Conductivity and Chloride measured at eleven locations were used in this study. A comparison between the three record extension techniques was performed to examine the extended records for bias and standard error of the estimate of statistical moments and over the full range of percentiles. The results of this study show that the proposed RLOC technique outperforms the OLS and LOC techniques by producing extended records that preserve variability as well as high and low percentiles. As such, it is recommended that the newly proposed RLOC technique be further investigated using simulated records with specific characteristics and data sets from other geographical areas.