Impact of missing observations in extreme precipitation trend and return level in non-stationary statistical model

Understanding the recurrence interval of heavy to extreme precipitation and its temporal trend is of great importance to water resources management. Empirical quantification of trends, however, is often complicated by the presence of missing observations. In this paper we quantify the impacts of missing observations on the perceived trends and 50-yr return levels of extreme precipitations through a data blockage experiment. The experiment isolates potential confounding factors by considering near-complete stations which do not have more than a week of missing values (baseline). In this experiment, missing observations of varying length of correlated missing observations are introduced to baseline stations. Number of baseline stations is 25 out of 663 available daily COOP stations in Ohio Basin. Time-series of missing observations subject to binomial distribution are repeated 300 times, and they are encoded to respective baseline station time-series. We use maximum likelihood (ML) fit with linear trend Generalized Extreme Value (GEV) distribution for both the baseline and the blocked records, and derive the parameter values – the trend coefficient for linear trend GEV and the 50-year return levels for each station. We find that the presence of missing values leads to under-estimation of return levels and deflation of their standard errors. Hence, incremental compensation of return levels, and inflation of standard errors of return levels are necessary in order to account for missing values. In this set-up, empirical compensation factor for 50-yr return level is 4.2%, and inflation factor to standard error is 5.8% at the minimum. However, difference in trends (missing value encoded series minus baseline series) does not seem to be conspicuous as those of 50-year return levels. More concern should be directed to the cause of numerical failure of optimization.