Data Assimilation for Marine Ecosystem Models

Abstract

In the presence of environmental issues caused by climate change and eutrophication, ecosystem models capable of providing accurate predictions are of considerable interest. Even the most advanced ecological models are not capable of reproducing reality perfectly, therefore it is essential to integrate them with the available observations. Data assimilation techniques serve as tools to calibrate and improve model accuracy by combining it with the data from measurements. Although ecosystem models have evolved to be considered as relatively proficient predictive tools, they are still missing a unified set of rules to govern the whole system. This is compensated by adding various biogeochemical processes associated with a substantial number of uncertain parameters, which are an important source of uncertainty in ecosystem models. To date, these have been successfully established through manual calibrations, with help of available measurements. However, the manual process is often time consuming, and becomes more complicated as the number of parameters to be estimated increases. Moreover, the parameter values are usually dependent on the region for which they are calibrated, therefore the process often needs to be repeated when a new ecosystem region is considered. Data assimilation methods provide a semi-automatic tool for estimating many parameters simultaneously, which when combined with expert knowledge can be a significant improvement over manual calibration. Since the parameters are a primary source of uncertainty, their estimation is the main focus of this work. Additionally, as the initial conditions are not always well known, these are also included and updated together with the parameters. Based on available data assimilation methods, variational techniques were selected as the most suitable. These were first introduced in meteorology for initial condition estimation, and further it also proved to be a proficient tool for parameter estimation. The same method has already been used successfully for ecosystem calibration. However variational techniques require the implementation of the model derivatives, which is a challenge for the ecological models, since they are renowned for their high degree of nonlinearity and issues of non-differentiability. Moreover, as ecosystem models become more advanced and sophisticated, it is important to search for alternative solutions for obtaining their adjoint models. To address this issue, a model reduced four dimensional variational data assimilation (4D-Var) is used. The method was designed in such a way that the implementation of the adjoint of the tangent linear approximation of the original model is not required. Using an ensemble of simulations from the original model, a proper orthogonal decomposition is used to build a reduced model. Then the adjoint of the original model is approximated by the adjoint of the tangent linear approximation of the reduced model. The method is easily adapted to tackle initial condition estimation, which is proficiently estimated in the reduced space. To gain a better understanding of the model reduced 4D-Var method and its behaviour in a marine ecosystem application, the technique is first applied to a simple 1D ecological model. The method is demonstrated in a twin experiment framework, where synthetically generated surface phytoplankton data are used. Three parameters are calibrated in a combination with an estimation of the initial conditions. Different control strategies are explored, showing that updating the initial condition is essential to obtain accurate parameter calibrations, which motivates their combined estimation in the further applications. Although the system used to investigate the method is small, it allows us to address and identify important issues when applying data assimilation methods in ecosystem models before integration in real complex configurations. Based on the relatively good results obtained in the 1D ecological model, the next step is to apply the model reduced 4D-Var method and assess its performances in a realistic large scale ecosystem. Next, the technique is implemented in the 2D North Sea coupled physical-ecological model (BLOOM/GEM). The model consists of detailed hydrodynamics, suspended sediment and river loads. Among many other processes, it takes into account primary production, nutrient cycle, phytoplankton species competition and their adaptation to different limiting conditions. Justified by generally well mixed conditions in the North Sea a vertically mixed 2D version of the model is used. It is a result of many years of experience, and it has been repeatedly calibrated and validated. The main goal is to improve the model capability to predict the chlorophyll-a concentration, which is the main indicator of the water quality. Followed by sensitivity analysis, supported by expert opinion, a number of parameters were selected as the most significant in the BLOOM/GEM model. A number of twin experiments are performed aimed at the calibration of two leading parameters from the sensitivity list. Similar control strategies as in the simple ecosystem were applied, confirming that estimation of the initial condition enhances the parameter calibration in terms of accuracy and computational efficiency. Parameter estimation resulted in 80%-90% of improvement with respect to the prior error (100% corresponds to the error of the prior parameters), whereas the initial condition updated in the same experiments obtained a 10%-25% of improvement with respect to the prior error. Moreover, the results show that the method is capable of significantly improving the prediction of chlorophyll-a, reaching up to 35% of total improvement over two years. The relatively good performance of the model reduced 4D-Var method in the 2D North Sea BLOOM/GEM model demonstrates its potential as a calibration tool for enhancing the model predictions using real chlorophyll-a measurements derived from the remotely sensed MERIS data. Therefore, further experiments are performed, this time with the real data, following the same control vector strategies as for the twin experiments, where the parameters and initial conditions are estimated. The predictions of chlorophyll-a concentration resulting from data assimilation are validated against remotely sensed MERIS measurements during a nearly two year period after the assimilation. The performance of the assimilated model is enhanced with respect to the original model, showing that for some control strategies up to 10% improvement of the model occurs, which verifies the model reduced approach to be a useful tool for improving model predictions of chlorophyll-a.