Quantiles Trend Estimation of Variables of Annual Maximum Floods

Investigation of the basin floods in most cases is only based on flood peak trend analysis using conventional parametric or non-parametric (ordinary linear regression (OLR), Mann-Kendall, Sen) tests. In addition to the primary restrictions, these methods usually are provided to estimate the conditional mean or median and do not consider different quantiles while assessing the appropriate domain of conditional quantiles leads to a very good understanding of trend pattern. The objective of this study is using quantile regression (QR) to estimate the time trend (conditional quantiles) of flood variables including peak, volume and duration that result in better understanding of variables of annual maximum floods (AMF).
In the first step, AMF time series of Taleh-Zang hydrometry station located in southwestern Iran was considered and the time series of AMF peak flow, volume and duration were extracted.In the next step, trend analysis of AMF variables time series performed using OLR and their efficiency were investigated using fitting precision criteria, statistical significant test and residuals analysis. Then, QR lines were estimated for AMF variables trend analysis considering (0.05-0.95 with 0.01 steps) and their fitting precision criteria and statistical significant test were determined. Considering selected quantiles0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85 and 0.95 QR lines were plotted for AMF variables.
The OLR results indicated positive trends for AMF variables but complementary analysis showed that this method cannot be a suitable analysis for AMF variables trend analysis in this research. The QR application resulted in wide range of line slopes in comparison with OLR method. For all three variables 15% of estimated line slopes using QR were more than their estimation by OLR. Investigation of QR lines indicated statistical significant regression lines of AMF volume were related to upper bound quantiles while for AMF peak and duration were related to quantiles mid bound plus upper bound and there were a few acceptable QR lines for lower bound for all three variables so that for AMF peak, volume and duration 59%, 31% and 73% of QR lines were statistical significant considering 0.05 significance level. The fitting precisions of QR lines of upper and mid bounds were more than lower bound.
The quantile regression can be used without affecting the limitations of conventional methods for AMF variables trend analysis to access a wider range of applied trend analysis. Also there are certain differences between AMF variables trend slopes (especially for upper bound quantiles) in comparison with those estimated with OLR therefore the OLR method could not be a useful tool for trend assessment of extreme events. The results show trend of extreme flood variables are significantly more than those estimated by OLR and in other words the OLR led to underestimation of AMF variables increasing trend slope. Moreover, multiple variables flood trend analysis using QR revealed that considering significant trends for three flood variables, the flood potential risk are significantly more than those estimated using single variable analysis.