A Novel Record-Extension Technique for Water Quality Variables Based on L-Moments

Extension of hydrological or water quality records at short-gauged stations using information from another long-gauged station is termed record extension. The ordinary least squares regression (OLS) is a traditional and commonly used record-extension technique. However, OLS is more appropriate for the substitution of scattered missing values than for record-extension as the OLS provides extended records with underestimated variance. Underestimation of the variance of the extended records leads to underestimation of high percentiles and overestimation of low percentiles given that the data is normally distributed. The Maintenance of Variance Extension techniques (MOVE) have the advantage of maintaining the variance in the extended records. However, the OLS and MOVE techniques are sensitive to the presence of outliers. Two new record-extension techniques with the advantage of being robust in the presence of outliers were recently proposed by the authors: the robust line of organic correlation (RLOC) and modified version of the Kendall-Theil Robust line (KTRL2). In this study a new robust technique is proposed. The new regression technique based on L-moments (LMOM) is a modified version of the RLOC and uses the same intercept as that of RLOC and KTRL2 while the estimated slope is based on the second L-moment. An empirical examination of the preservation of the water quality variable characteristics was carried out using water quality records from the Nile Delta water quality monitoring network in Egypt. A comparison between nine record-extension techniques (OLS, MOVE1 to MOVE4, KTRL, KTRL2, RLOC and LMOM) was performed to examine the extended records for bias and standard error in their statistical moment estimates and over the full range of percentiles. Results showed that the proposed LMOM technique outperforms other techniques by producing extended records that preserve variance as well as extreme percentiles.