Revealing the error components of satellite-only precipitation products (SPPs) can help algorithm developers and end-users understand their error features and improve retrieval algorithms. Here, two error decomposition schemes are employed to explore the error components of the IMERG-Late, GSMaP-MVK, and PERSIANN-CCS SPPs over different seasons, rainfall intensities, and topography classes. Global maps of the total bias (total mean squared error) and its three (two) independent components are depicted for the first time. The evaluation results for similar regions are discussed, and it is found that the evaluation results for one region cannot be extended to another similar region. Hit and/or false biases are the major components of the total bias in most overland regions globally. The systematic error contributes less than 20 % of the total error in most areas. Large systematic errors are primarily due to missed precipitation. It is found that the SPPs show different topographic patterns in terms of systematic and random errors. Notably, among the SPPs, GSMaP-MVK shows the strongest topographic dependency of the four bias scores. A novel metric, namely the normalized error component (NEC), is proposed as a means to isolate the impact of topography on the systematic and random errors. Potential methods of improving satellite precipitation retrievals and error adjustment models are discussed.

To obtain more accurate formulas for precision estimation and to continue work on the adjustment of total least squares (TLS), the second-order approximation function method for the precision estimation of the TLS adjustment was investigated. According to least-squares (LS) criterion, the second-order Taylor expansions between parameter estimates or corrections and observational errors were derived. By the error propagation law, the formulas for biases in parameter estimates and residuals and the second-order approximate covariance and mean squared error matrices for the parameter estimates were obtained. Then, the implementation process of the second-order approximation function method for precision estimation was also designed. Results of the examples showed that the second-order approximation function method could effectively calculate biases and covariance or mean squared error matrices for precision estimation. The second-order approximation function method can provide more precision information for judging the qualities of parameter estimates and the nonlinear degree of the function model, contributing, in part, to the integrity of the theory on precision estimation of the TLS adjustment.