Triple Collocation Analysis for Two Error-Correlated Datasets: Application to L-Band Brightness Temperatures over Land

Abstract

The error characterization of satellite observations is crucial for blending observations from multiple platforms into a unique dataset and for assimilating them into numerical weather prediction models. In the last years, the triple collocation (TC) technique has been widely used to assess the quality of many geophysical variables acquired with different instruments and at different scales. This paper presents a new formulation of the triple collocation (Correlated Triple Collocation (CTC)) for the case of three datasets that resolve similar spatial scales, with two of them being error-correlated datasets. Besides, the formulation is designed to ensure fast convergence of the error estimators. This approach is of special interest in cases such that finding more than three datasets with uncorrelated errors is not possible and the amount of data is limited. First, a synthetic experiment has been carried out to assess the performance of CTC formulation. As an example of application, the error characterization of three collocated L-band brightness temperature (TB) measurements over land has been performed. Two of the datasets come from ESA (European Space Agency) SMOS (Soil Moisture and Ocean Salinity) mission: one is the reconstructed TB from the operational L1B v620 product, and the other is the reconstructed TB from the operational L1B v620 product resulting from application of an RFI (Radio Frequency Interference) mitigation technique, the nodal sampling (NS). The third is an independent dataset, the TB acquired by a NASA (National Aeronautics and Space Administration) SMAP (Soil Moisture Active Passive) radiometer. Our analysis shows that the application of NS leads to TB error reduction with respect to the current version of SMOS TB in 80% of the points in the global map, with an average reduction of approximately 1 K over RFI-free regions and approximately 1.45 K over strongly RFI-contaminated areas.

Evaluation of SMOS L4 Sea Surface Salinity Product in the Western Iberian Coast

“…However, in terms of the standard deviation of the error, the product performed better than the analyzed satellite salinity products. Two metrics were used for the latter analysis: (i) the computation of the standard deviation of the difference between satellite and in situ salinity measurements, and (ii) correlated triple collocation analysis [40]. The authors also performed spectral and singularity [41] analysis and concluded that, while the effective spatial resolution of the analyzed L3 satellite salinity products was around 40 km, that of the L4 was very similar to the SST used in the multifractal fusion scheme, which was around 20 km.…”

Reply on RC1

“…Recently, a variant of TC especially adapted to deal with remote sensing measurements, has been introduced: The Correlated Triple Collocation (CTC) (González-Gambau et al, 2020). When applying CTC, the data is assumed to have the same spacetime sampling, that is, they represent the same spatial and time scales.…”

“…We have applied the CTC, following González-Gambau et al (2020), to characterize the SSS errors with 2016 data. We have taken three sets of collocated SSS maps: JPL SMAP v4.2 SSS, 8-day maps; BEC SMOS Arctic SSS v2.0, 9-day maps and BEC SMOS Arctic+ v3.1, 9-day maps.…”

Nine years of SMOS Sea Surface Salinity global maps at the Barcelona Expert Center

“…The major assumptions of TC are that errors must be uncorrelated with the target variable and also that the errors of the different data sets must be uncorrelated between them. Some refined formulations have been developed in recent years for taking into account the presence of cross-correlated errors between two of the data sets, but they require at least four data sets (Gruber et al, 2016;Pierdicca et al, 2017).…”