A multi-collocation method for coastal zone observations with applications to Sentinel-3A altimeter wave height data

Abstract

In many coastal areas there is an increasing number and variety of observation data available, which are often very heterogeneous in their temporal and spatial sampling characteristics. With the advent of new systems, like the radar altimeter on board the Sentinel-3A satellite, a lot of questions arise concerning the accuracy and added value of different instruments and numerical models. Quantification of errors is a key factor for applications, like data assimilation and forecast improvement. In the past, the triple collocation method to estimate systematic and stochastic errors of measurements and numerical models was successfully applied to different data sets. This method relies on the assumption that three independent data sets provide estimates of the same quantity. In coastal areas with strong gradients even small distances between measurements can lead to larger differences and this assumption can become critical. In this study the triple collocation method is extended in different ways with the specific problems of the coast in mind. In addition to nearest-neighbour approximations considered so far, the presented method allows for use of a large variety of interpolation approaches to take spatial variations in the observed area into account. Observation and numerical model errors can therefore be estimated, even if the distance between the different data sources is too large to assume that they measure the same quantity. If the number of observations is sufficient, the method can also be used to estimate error correlations between certain data source components. As a second novelty, an estimator for the uncertainty in the derived observation errors is derived as a function of the covariance matrices of the input data and the number of available samples. In the first step, the method is assessed using synthetic observations and Monte Carlo simulations. The technique is then applied to a data set of Sentinel-3A altimeter measurements, in situ wave observations, and numerical wave model data with a focus on the North Sea. Stochastic observation errors for the significant wave height, as well as bias and calibration errors, are derived for the model and the altimeter. The analysis indicates a slight overestimation of altimeter wave heights, which become more pronounced at higher sea states. The smallest stochastic errors are found for the in situ measurements. Different observation geometries of in situ data and altimeter tracks are furthermore analysed, considering 1-D and 2-D interpolation approaches. For example, the geometry of an altimeter track passing between two in situ wave instruments is considered with model data being available at the in situ locations. It is shown that for a sufficiently large sample, the errors of all data sources, as well as the error correlations of the model, can be estimated with the new method.