Univ.-Prof. Dr.-Ing. André Niemann

Institut für Wasserbau und Wasserwirtschaft Abteilung Bauwissenschaften

Fakultät für Ingenieurwissenschaften

Universität Duisburg-Essen Fakultät für Ingenieurwissenschaften Abteilung Bauwissenschaften Institut für Wasserbau und Wasserwirtschaft Universitätsstraße 15 45141 Essen

Kontakt: Univ.-Prof. Dr.-Ing. André Niemann

Raum V15 R04 H36 Tel. +49 201 183-2225 Fax. +49 201 183-2886

Master thesis topic

Development of Ensemble Kalman Filter data assimilation with limited perturbations using PERT probability distribution Introduction

Data assimilation is a commonly applied technique to obtain a better estimate of initial states and produce better forecasts with a consequent increase of performance skills. The idea behind is to combine observed information with simulated data and produce better initial model estimates that can be subsequently use in the forecast simulation. Among other techniques, Ensemble Kalman Filter (EnKF) has been widely used in multiple applications. The classical approach in order to produce the ensemble of simulations is to perturb the model inputs (aka. forcing variables) using normally distributed noise. This approach however, is limited by the boundary bands that should be enforced to produce physically meaningful results.

The aim of this research is to investigate the properties of the PERT distribution as a replacement of the normally distributed noise in the generation of ensemble members. The characteristics of the PERT distribution, which is fully constrained to upper and lower boundaries seems an appropriate alternative to produce better covariance structures for the EnKF data assimilation technique.

Figure 1: Dynamic Programming scheme (left) and Model Predictive Control (right).

Sources: F. Massonnet, Southern Ocean sea ice reanalysis, Université Catholique de Louvain, 2013.Pert distribution, ModelAssit for @RISK, EPIX Analy-tics. Website resource( link)

Objectives • Develop a perturbation module for EnKF data assimilation based on PERT distribution • Compare the classical perturbations using normal distributions with the PERT version • Provide insights to the process and conclude on the practical applications Activities The student will conduct his/her research at Uni. Duisburg-Essen. The main activities consist of: • Literature review on Ensemble Kalman Filter data assimilation and PERT distributions • Formulation of EnKF using PERT perturbations • Hindcasting assessment using a calibrated hydrological model • Comparison with previously implemented normal distributions Organization Supervisors are MSc Rodolfo Alvarado Montero and Prof. Dr.-Ing. André Niemann from University of Duisburg-Essen. It is the obligation of the student to deliver three hardcopies and a digital version of the thesis. Furthermore, a presentation of 20 min. and a defense of approximately 20 min are part of the evaluation procedure of the thesis. A modification of the proposal is possible in agreement with the supervisors; the modification has to be documented. Date 03.03.2017