Gross Primary Production (GPP) is the amount of carbon dioxide (CO2) that is fixed by an ecosystem through photosynthesis. It is a key variable to understand the carbon cycle and biodiversity conservation. In-situ measurements of GPP are possible at a local scale. To estimate GPP on a global scale, models based on remote sensing data are used. One of them is the Penman-Montheith-Leuning (PML) model, which is constructed on physical processes.

In this thesis, a sensitivity analysis of the PML model is performed for the case study of Torgnon subalpine grassland. It is defined around three aspects: the application of the PML model to Torgnon subalpine grassland, the impact of the input data on the output data, and the reliability of the calibration procedure. We found out that the PML model can be applied to the study site, but the value of the parameters presented in the literature are not optimal (R2 = 0.57 using the literature calibration and R2 = 0.94 in the optimised case).

Moreover, the model is extremely sensitive to the Leaf Area Index (LAI), and, to a lesser extent, to temperature and Photosynthetically Active Radiations (PAR). However, it is weakly dependent on the CO2 concentration of the atmosphere. The analysis of the calibration procedure showed that a simplified PML model, that does not consider the CO2 concentration and Vapour Pressure Deficit (VPD), performs similarly to the initial model. An ensemble estimation of GPP is obtained by using an ensemble of optimal parameters. It suggests that errors in the calibration principally impact the spring and summer estimations.

This thesis presents a doctoral research where statistical concepts and techniques are applied to problems at the interface of marine and atmospheric processes. The research was conducted at the Statistics group of the Delft Institute of Applied Mathematics (TU Delft) and the Marine and Coastal unit of Deltares. The main objective of the work is to provide statistical tools to understand multi-dimensional climate and marine environmental datasets, as well as to offer ways for quantifying the uncertainties in the coastal ecological response that are driven by the climatic variation. Statistical quantification of uncertainties in data, models and predictions is therefore the central topic of the thesis.

The research is built on open source data (in-situ and satellite measured as well as numerically modelled) from the Copernicus Marine Environment Monitoring Service, the Dutch Directorate-General for Public Works and Water Management (Rijkswaterstaat), the Royal Netherlands Meteorological Institute, and the Euro-CORDEX regional climate modelling experiment. It also uses the open source numerical modelling software Delft3D from Deltares. All other statistical models and algorithms developed during the research are published and available open source.

The thesis starts by demonstrating the value of probabilistic predictions and uncertainty quantification for coastal ecosystems. That is done by constructing an ensemble modelling framework where certain chosen numerical model inputs and model process parameters are perturbed, to which the simulated coastal chlorophyll-a concentration is sensitive. The model perturbation was implemented using Latin Hypercube Sampling with Dependence (LHSD), and more than 150 ensemble members were produced using the Delft3D model. This ensemble prediction system is then compared to the deterministic model setup. A range of verification metrics that describe the goodness-of-fit, accuracy, reliability, and discrimination properties of both modelling experiments were computed. Apart from the verification metrics, the value of probabilistic predictions was also showcased by evaluating the benefit of having temporal and spatial estimates of uncertainty by producing ensemble band, predictive uncertainty intervals and standard deviations maps.

In Chapter 3 of the thesis, we work towards the quantification of climate change induced uncertainties in coastal phytoplankton response. The first necessary step is a comprehensive data exploration and dimension reduction, which also provides a statistical underpinning of atmospheric variable selection for the climate impact studies conducted later in the thesis. Here a range of existing dimension reduction techniques are described and applied to seven atmospheric variables (air temperature, solar radiation, eastward wind, northward wind, air pressure, relative humidity, and total cloud cover) and the chlorophyll-a data at hand. These techniques are applied in a structured way to include spatial and temporal correlation, as well as functional features in the multi-dimensional data. The applied methods include Principal Component Analysis (PCA), Principal Component Regression (PCR), Partial Least Squares (PLS) Regression, multi-way models (PARAFAC, Tucker and N-PLS), Dynamic Factor Analysis (DFA), and Functional PCA. Room for dimension reduction in the atmospheric data was identified, underlying temporal patterns in the chlorophyll-a signal at different locations were revealed, structural similarities (characterized by a mean function and functional variation) in the Euro-CORDEX climate projections were found, and the most influential atmospheric variables (solar radiation and air temperature) were chosen.

Building on these findings, we propose a way to quantify uncertainties in the climate scenarios that are used for the climate impact studies. The basis of this research step is the development of a stochastic climate generator, which is first tested on the solar radiation variable. This climate generator takes the existing Euro-CORDEX scenarios (a combination of Representative Concentration Pathways and Generic Circulation Model forcings) and enriches them by generating numerous new synthetic scenarios around them. These new generated scenarios are representative of the original ones due to the way the stochastic climate generator is constructed. The basis of the climate generator is a Bayesian multi-layered (hierarchical) model. In this model there are model parameters representing variation in the long term trend, seasonal amplitude, time shift, and additive residual. The generator estimates the distribution of each model parameter with Bayesian inference, and using data from all scenarios. Then, when sampling from the parameter distributions, numerous climate trajectories can be constructed. The climate generator is successfully tested on the solar radiation variable and the generated synthetic radiation projections are used in a demonstration study where uncertainties are further propagated to chlorophyll-a concentrations using the Delft3D numerical model.

In the final research step of the thesis, this Bayesian stochastic generator is extended to air temperature. This way we have numerous (>100) radiation and temperature projections available to propagate climate induced uncertainties to coastal chlorophyll-a response once again, this time covering the entire 21st century. In order to translate the climate signal into chlorophyll-a response, we make use of a Bayesian structural time series model. This model follows a piecewise linear trend and continues to repeat its multi-seasonal behavior, learnt from the past data, and most importantly also includes linear effects of the two climate variables. For the training of this time series model, we construct a historical chlorophyll-a signal by fusing in-situ and satellite measurements. This fused signal helps us to take advantage of the more frequent satellite measurements while correcting them with the more accurate in-situ measurements that are also available for a longer historical period. The Bayesian structural time series model is then trained on the fused chlorophyll-a signal and used for long term projection, taking the generated radiation and temperature scenarios as regressors. Since our main interest is the phytoplankton spring bloom dynamics, as a last step we extract yearly spring bloom cardinal dates (beginning, peak, end) from the long-term chlorophyll-a projections using a non-parametric shape constrained method (log-concave regression). The final result is therefore the estimation of climate change induced uncertainty in the coastal phytoplankton spring bloom dynamics.