Application of Ensemble Kalman Filter in Modelling of Water Reservoirs Hydrodynamics
Autor: Marcin Kawka
Promotor: prof. dr hab. inż Marek Nawalany
Promotor pomocniczy: Alfred Wüest
Praca doktorska obroniona z wyróżnieniem!
This thesis addresses the issue of data assimilation of water quality optical remote sensing products into hydrodynamic models. Currently, the assesment of surface waters ecological status is based mostly on traditional bottle-based, in-situ sampling. Due to logistical constraints, this approach is not capable of delivering results at high frequency and with high spatial density. A promising chance to overcome these limitations is the recent development of remote sensing methods.This thesis consists of three main parts, concerning the most important aspects of hydrodynamic modelling, remote sensing of water quality and data assimilation of measurements obtained by remote sensing to a hydrodynamic model, using Ensemble Kalman Filter. In the first part of the thesis, the theoretical foundations of hydrodynamic modelling – the Navier-Stokes equations are discussed, including the major assumptions and simplifications. Next, three exemplary applications of hydrodynamic modelling, used within this thesis are breifly discussed — a model of a hypothetical rectangular lake, the Zegrzy´nski Reservoir model and the Lake Greifensee model. All three applications were hydrodynamic models, including the impact of wind and heat exchange with the atmosphere. The Greifensee Lake model and the Zegrze Reservoir model were additionally supplemented with a simplified water quality model. To make the hydrodynamic part of the models, the Delft-3D package was used, and the modelling of water quality was done using the DELWAQ package. Measurement data used as boundary or initial conditions in the above mentioned models originated from routine, state monitoring measurements. The next section of the thesis discusses the processing of satellite images for the purpose of water quality remote sensing. As an example images acquired by ESA’s Sentinel-2A over the Zegrzy´nski Reservoir are used. The aim of the processing was to obtain a series of temporal spatial distributions of water quality parameters (chlorophyll concentration, suspended substances and colored dissolved organic matter). In order to calibrate the used model of optical properties of water, a field campaign was carried out on the Zegrzy´nski Reservoir, the scope and results of which were described in the thesis. Atmospheric correction of satellite images was based on near-infrared bands, in which spectral reflection was associated with the thickness of cirrus clouds, as well as the optical thickness of atmospheric aerosols. Finally, the problem of data assimilation was presented on the example of the Kalman Filter. The necessary mathematical apparatus was introduced gradually, starting from the basic, linear version of the Kalman Filter and ending with the Ensemble Kalman Filter used within this thesis. For each of the three above mentioned hydrodynamic and water quality models, a slightly different concept of assimilation was used. In the rectangular lake model, the spatial non-uniformity of the wind field was considered the most important source of model uncertainty. The ensemble of models launched within the Ensemble Kalman Filter data assimilation scheme was obtained by adding white noise to a spatially constant wind field. The assimilated variable was the time series of surface water temperature. The experiment with the simplified model confirmed the stability of the data assimilation scheme in the longer period of simulation (90 days) and the reduction of uncertainty related to the results of the model. The simplified case also allowed to assess the impact of the number of models launched within the ensemble (ensemble size) and the frequency of assimilation on the quality of results. The Second data assimilation experiment was performed on the Lake Greifensee model. The assimilated observation data originated from MERIS satellite, obtained in the summer 2011. Motivation of this experiment was to reproduce the double peak algal bloom, which occurred on Lake Greifensee in the summer 2011. As a source of uncertainty, driving the diversity of models within the ensemble, the growth rate of phytoplankton was selected. After each assimilation of satellite measurements, models run within the beam received corrected values of the phytoplankton growth coefficient. Modelling results with and without data assimilation were compared with measurements performed in-situ from a floating platform. In the Zegrzy´nski Reservoir model, as in the case of Lake Greifensee, the phytoplankton growth and mortality rates were used as the source of uncertainty. As observations for the data assimilation scheme – remote sensing measurements of chlorophyll concentration using the Sentinel-2A satellite from the summer of 2016 were used. The results were compared with routine RIEP measurements, which were carried out in the same period. As a summary, conclusions and recommendations regarding the perspective of assimilation using the Kalman Filter Team and satellite remote sensing of water quality in environmental monitoring are given.