The need for accurate estimation of hydrodynamic and water quality model variables arises from the UNITED project, which aims to create high-resolutional forecasting systems for monitoring the cultivation of seaweed and flat oysters and operating of the Belgian pilot of UNITED in the coastal area of the North Sea. Accurate observations of physical variables are usually only known for small domains of the model, on the water surface. Therefore, data assimilation is applied on different hydrodynamic models to search for improved estimates of waterlevel, water velocity and temperature. The sequential data assimilation algorithm, the Ensemble Kalman filter is considered. The algorithm is a Monte-Carlo approximation of the Kalman filter, both using accurate observations assimilated into the model, where the model each time is shifted towards the observations when available, providing an optimal trade-off estimation between the model estimations and observations. Two models are considered: a 1D model of the Western Scheldt estuary in Python and the 2D model with depth of the Western Scheldt estuary implemented with software packages Delft3D FM and OpenDA. Model estimates and estimates of model with assimilated observations are investigated in various experiments to look for improved predictions, using twin experiments to generate artificial observations over the whole domain. The various experiments contained the search for the effect of assimilation location on the estimates, of the effect of assimilation of different physical parameters, the effect of the observational error covariance and the effect of water surface assimilation on the estimation within the water column. In most cases, the Ensemble Kalman filter improved the estimate of waterlevel and water velocity with varying results up to a decrease in rmse of a factor four, while the assimilation of temperature gave a worse prediction. Furthermore, assimilation of waterlevel gave the best improvement in estimate. For the investigated models, assimilation of observations near the boundary conditions with implied noise gave the most improved estimates. Furthermore, assimilation of water surface observations improved the estimate within the water column for water velocity with a factor of 2, while temperature assimilation did not show any improvement. The result for temperature may be due to a collapsing Ensemble Kalman filter due to small standard deviations and a not realistic model setup for temperature. Therefore, assimilation of only observations at the surface may be used to accurately improves water column estimations for water velocity. For temperature, more research is needed. Advised is an experiment with a different model setup with more realistic and longer spin-up time of temperature. The collapsing Ensemble Kalman filter can be prevented by initialization of new ensembles before the the collapse happens. In further research, data assimilation can be applied on the DCSM model, a model involving the area of the Belgian pilot.

The aim of this research is to study a method to find exomoons and to find specific characteristics that point to the existence of exomoons. Exomoons are natural satellites orbiting an extrasolar (exo)planet in an extrasolar system. By looking at eclipses on exoplanets, we can find these characteristics. We consider the reflected light signals of exoplanets with an exomoon. The reflected light signal is the intensity of light the planet reflects from the host star towards the observer. We derive the reflected light signal in a planetary system with one exoplanet and in a system with an exoplanet and an exomoon. We made the assumptions that the exoplanets and exomoons have a homogeneous surface (albedo is 1) and move in circular orbits around a star with an inclination angle between the orbital planes. Along the orbit the planet and the moon have changing phases. The moon is always close to its planet, so the phases of the exomoon and the exoplanet are the same. For exoplanets, it is not possible to spatially separate a moon from its planet. One only sees the total signal of both bodies, the light originating from the star, reflected by the two bodies towards the observer. Maybe we can find an exomoon by examining eclipses. Eclipses occur when the exoplanet and exomoon are aligned with the star, so that the body closest to the star blocks the light towards the body farthest from the star. Finding eclipses is one of the few methods to discover exomoons. The systems are modeled with the assumption that any total eclipse happens every time r = R or −r = R, we see short dips in the reflected light signal. These dips are periodic and make the complete signal quasi-periodic. That is why we also calculate the Fourier transform of the reflected light signal. This quasi-periodicity causes the Fourier spectrum to have side bands that are repeated and are copies of themselves. In this research, the orbit of the exomoon is tilted to see the effect of inclination in the reflected light signal. The result is fewer eclipses. At most twice a year for a short amount of time an eclipse can occur. In the Fourier domain, this results in more peaks, but the pattern is still repeated. From this research, we cannot conclude whether or not an exomoon is present from measured data. What we learned, is that if an exomoon is present, short dips in the received light signal occur and this results in periodic side bands in the Fourier domain with respect to the system of one planet. The duration of an eclipse is very short, so the detection of the eclipse can easily be missed. The Fourier transform signal becomes stronger when a longer time has been measured.

Context. A double planet system or planet binary undergoes eclipses that modify the reflective light curve. In the time domain, the eclipse events are fast and weak. This would make their signal difficult to find and recognize in the phase light curve, even for small inclinations when eclipses happen frequently. However, due to the quasiperiodic nature of the phenomenon, the Fourier transform of the direct reflection signal consists of a double sum of sharp peaks. These peaks can be resolved for large close binaries and sufficiently long observation times with a star coronagraph. Aims. Eclipses modulate the phase curve, having an orbital period 2π/ω, with a contribution from the relative motion in the binary plane of a period 2π/Ω. This leads to a spectral structure with basis frequencies ω and Ω. We aim to characterize these spectra. Methods. We studied the regime of short eclipses that occur when the planet radii are small compared to the planet separation. We derived formulas for the peak amplitudes applicable to homogeneous (Lambertian) planet binaries in circular orbit with small inclination. Results. The effects of an eclipse and of double reflection appear as first- and second-order contributions (in planet radius over separation) in the reflection signal, respectively. Small peaks appear as observable side bands in the spectrum. Identical structures around mΩ are characteristic of short-duration eclipses. Deceasing side bands could indicate double reflection between companions. Conclusions. Fourier analysis of the light curve of non-transiting planets can be used to find planets and their moons. Difficulties in interpreting the structures arise for small planet separation and when there are several moons in mean-motion resonance.@en