Estimating terrestrial water storage variations from GNSS vertical displacements in the Island of Haiti

In the field of hydro-geodesy, ill-posed inverse problems are very common. Those problems need to be regularized to find a stabilized solution. Usually, to solve those problems, two regularization methods are often used, Tikhonov’s regularization and Truncated Singular Value Decomposition (TSVD), with some common regularization parameter choice methods such as L-curve or General Cross Validation (GCV).

This study aims to test the capacity of the Least Squares Collocation (LSC) method to estimate the terrestrial water storage variations as an original approach. First, for the forward model, we calculated the hydrological crustal loading deformation in the island of Haiti by convolving Farrell (1972) Green's function with the surface mass loading from the Global Land Data Assimilation (GLDAS). After, a dense synthetic Global Navigation Satellite System (GNSS) network is used with the LSC method to estimate the Terrestrial Water Storage (TWS) variations for the inverse problem.

LSC is a natural way to stabilize an ill-posed inverse problem. Unlike Tikhonov’s or TSVD regularization method, LSC allows us to stabilize the inverse problem by including more physical information. The latter is introduced through a covariance function characterizing the observations, the parameters, and the functional link between them. One of the advantages of the LSC method is that it does not require any regularization parameter.

First, we showed that, for the island of Haiti, the near field can extend until 24° around a GNSS station. Secondly, we proved that the hydrology-induced vertical deformation is part of the GNSS vertical displacement over the island. Finally, we demonstrated that the LSC may be used as a method to estimate TWS variations in dense GNSS network area.