Soil moisture (SM) is crucial in land-atmosphere (LA) interactions, regulating evapotranspiration and influencing moisture and energy budgets, which impact weather, precipitation, and the broader climate system. Despite efforts to quantify LA coupling using observational data, reanalysis, or combined observation-model products, challenges remain due to inconsistencies and discrepancies among datasets. This highlights the need for observational data to assess model performance, diagnose errors in model structures, and potentially improve their physical process. Flux tower sites, while valuable for in-situ observations, have limited global distribution and short durations. Conversely, satellite data offer high-quality, long-term, and globally distributed observations but are prone to random errors, which can degrade estimates of LA coupling. As a result, there is an incomplete picture of the reality of global LA coupling for model validation and calibration. This study introduces a method for deriving the Pearson correlation coefficient between SM time series from the Soil Moisture Active Passive (SMAP) satellite and observation-based latent heat flux (LE) products from the Global Land Evaporation Amsterdam Model (GLEAM), FluxCom, and Collocation-Analyzed Multi-source Ensembled Land Evapotranspiration (CAMELE). While SMAP data correlate closely with in-situ SM measurements, they exhibit stochastic random errors, which can reduce the accuracy of SM-LE correlation. On the other hand, SM variability typically resembles a first-order Markov process, enabling the estimation of the ratio between variance of random error and temporal variance in SM measurements. Given that the sequence of random error variances is unknown, it is not feasible to derive an error-free time series by eliminating random errors. As a solution, we propose a mathematical methodology to estimate the corrected correlation, considering random errors in satellite-based SM data. The accuracy of corrected correlations will be further evaluated using in-situ measurements (AmeriFlux network). We aim to construct a global depiction of SM-LE correlation from observationally gridded data with a quantification of uncertainties and potentially establish a new benchmark for model validation.