A Bivariate Copula Approach to Extreme Water Level Estimation

Abstract

Understanding the factors that drive extreme water levels is key to an accurate assessment of flood hazard. The city of Venice has always been affected by flooding due to extreme water levels. In this study, we examine the factors driving and influencing extreme water levels in the Venice lagoon, aiming at deriving accurate extreme water level estimates in the Venice lagoon.
Due to the shallowness of the Venice lagoon, extreme water levels are influenced by both atmospheric forcing (surge) and water level of the lagoon (tide and bottom level) and interactions between these two. Furthermore, these extreme water levels have been changing over time due to variations in the bottom level. These variations are reportedly due to local (anthropogenic and natural) subsidence and sea level rise. In this study we resort to the available long-term water level observations of the Punta della Salute tide-gauge. Given the effects of subsidence and sea level rise in these data, we start by homogenizing the data by removing these trends and jumps from the time-series. Using the homogenized time-series, we study the influence of the dependence between tide and surge components on the extreme water level estimates. Finally, we quantify the effect in the estimates of modelling this dependence in the extreme value models.
To homogenize the data and better understand the underlying trends, a time-series analysis was performed on the time-series of water level observations. Mann-Kendall tests for monotonic trend were performed, followed by an analysis using changepoint detection methods. Changepoint detection was performed using the RHtest and BEAST methods on the Punta della Salute time-series as well as time-series from neighbouring tide-gauge stations. Ultimately trend decomposition using the BEAST method was used to detrend and homogenize the Punta della Salute time-series.
After detrending, the tide and surge components were separated using tidal harmonic analysis and reconstruction. The relationship of these now separated components was quantified during extreme water levels using the Pearson r correlation and the Kendall τ rank correlation. This relationship between tide and surge was described using copulas to estimate extreme water levels. Different copula variants were evaluated and extreme water level estimates derived using copulas that describe dependence were compared to extreme water level estimates using a copula that describes tide and surge as independent components. Lastly, these were compared to those derived from univariate extreme value analysis to assess the influence of separation of tide and surge components combined with copulas as opposed to a more traditional univariate extreme value analysis.
The main conclusions of this study are as follows.
• The water level observations of the Punta della Salute tide-gauge are indeed affected by jumps and trends due to subsidence and sea level rise. These can be successfully removed using the applied techniques.
• There is a clear dependence between tide and surge in the Venice lagoon, with lower tide levels leading to higher surge levels. The non-inclusion of this dependence (by assuming independence) in the combined analysis of tide and surge signals to drive total extreme water levels leads to an overestimation of the total water level extremes.
• Extreme water level estimates from the combined analysis of the tidal and surge signal are higher, but compatible with those from the analysis of the total water level signal (without separation of tidal and surge signal). This gives confidence in the combined analysis accounting for the dependence between the signals and allowing for a further application of the models to account for projected climate changes.