Multivariate autoregressive modelling and conditional simulation of precipitation time series for urban water models

Abstract

Precipitation is the most active flux and major input of hydrological systems. Precipitation controls hydrological states (soil moisture and groundwater level), and fluxes (runoff, evapotranspiration and groundwater recharge). Hence, precipitation plays a paramount role in urban water systems. It controls the fluxes towards combined sewer tanks and the dilution of chemical and organic compounds in the wastewater. Furthermore, small catchments (i.e., areas of about 20 ha) have a fast response to precipitation. Therefore, catchment average precipitation is a key component in urban water models. However, average catchment precipitation is not always accurately known when measured at rain gauges, because the location of the gauge might be outside the catchment boundaries or does not reflect the entire catchment. The objective of this paper is to develop a method to estimate the precipitation in a catchment given a known precipitation time series at a location outside of the catchment, while quantifying the uncertainty associated with the estimation. We developed a multivariate autoregressive time series model for conditional simulation of precipitation time series. The case study is a small sub-catchment (16.5 ha) in Luxembourg. The time series of precipitation outside of the sub-catchment are available for two stations and cover the year 2010. We calibrated the model using the R-package ‘mAr’ and applied the developed conditional simulation algorithm to generate multiple realisations of precipitation time series. The results show that the proposed method is suitable to estimate time series of precipitation at ungauged sites and can quantify the associated uncertainty. Read More