Understanding and repairing the signal damage due to filtering of mass change estimates from the GRACE satellite mission

Abstract

Filtering noisy observations to extract meaningful information is an old and necessary exercise for engineers and scientists. Filtering affects both the signal and the noise. While the noise is reduced to a minimum, the filtered observation is a smoothed representation of the true signal. The amount and type of smoothing required depends on the noise level. The geodetic satellite mission, GRACE provides heavily contaminated time variable gravity field of the Earth. Therefore, we have to use a strong smoothing operator before the data can be used. Over the past decade, many types of filters have been developed for treating the noisy GRACE products, which damages the signal. Therefore, along with filters, a number of methods to restore the signal damage have emerged. However, the majority of these methods use hydrological models to compute correction terms, such as leakage, bias, or scale factors, in a setup that lacks a detailed mathematical understanding. We fill this gap by studying the convolution integral on the sphere, with a motivation to revert the signal changes in filtered GRACE products. Since the dominant time varying signal observed by GRACE comes from mass transports in the hydrosphere, we analyze the impact of filtering on catchment scale hydrology. We discuss the convolution integral in the spatial domain, which helps us to break the total impact of filtering into two parts: leakage and attenuation of catchment-confined signal, where leakage is only the contribution of signal from outside the catchment. We find that leakage changes the amplitude as well as the phase of the catchment-confined filtered signal. Previous contributions have addressed only the amplitude change due to filtering, usually with the help of a hydrological model. This practice propagates the error and the uncertainties in models to the corrected GRACE products. Therefore, we advocate avoiding models for computing correction terms. A mathematical dissection of the convolution integral leads us to two methods for approaching the true regional average: the method of scale and the method of deviation. The method of scale uses the uniform layer approximation, while the method of deviation avoids any approximation. In a noise-free closed-loop test, we show that the method of scale is able to approach the truth, while the method of deviation gives us the true value. These methods need accurate knowledge of leakage and the deviation integral, which are estimated in a data-driven framework employing once filtered and twice filtered GRACE fields. In a closed-loop simulation environment with GRACE-type noise, we demonstrate for 32 catchments that we are able to approach the true leakage and the true deviation integral. The efficacy of data-driven method of deviation is found to be superior to three popular model dependent approaches. After being satisfied with data-driven methods for hydrology, we intend to use them for assessing the ice mass loss in ice sheets such as Antarctica and Greenland, but we find that they fail for ice sheets. This is due to the physical difference between the spatial mass change distribution in an ice sheet and in a hydrological catchment: the former suffers from a mass change concentrated near coast, while the later experiences a mass change throughout the catchment. Therefore, we tailor a new approximation for ice sheets giving us the data-driven method for ice sheets. It is tested effective in a noisy closed-loop simulation environment. The data-driven methods are used to correct the filtered GRACE products and to analyze the total water mass loss over Aral sea, lake Urmia, lake Victoria, California, Antarctica, and Greenland. We report and compare our findings with previously reported figures. We find that the long term trend in mass change is suppressed by filtering, and overestimated by model dependent approaches. This thesis explores the signal damage at catchment scale due to filtering of GRACE products, and develops data-driven methods to repair the signal damage. In a realistic closed-loop simulation environment, we demonstrate that the corrected signal is closer to truth. The performance decays with the catchment size, but is still better than model dependent approaches. Furthermore, the data-driven method is less accurate over arid regions (desert), however, the performance is on a par with the model dependent methods. Nevertheless, we extract our confidence from the overall performance of the data-driven methods in closed-loop environments to believe that we get superior mass change estimates from GRACE. This contribution helps us to reduce the filtering induced uncertainty in GRACE products.