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Various climate and watershed characteristics determine the runoff coefficient (RC), and their interactions are complicated. Understanding the driving factors of the RC is important for understanding the long-term water balance and how it might change. Using the upper reaches of the Huaihe River Basin as the study area, remote sensing data were used to produce a RC map. The geographical detector was selected to quantify the individual and interactive influences of 13 driving factors on the RC. The results revealed that moderate resolution imaging spectroradiometer evapotranspiration (ET) data can be used to produce a mean average RC map based on the water balance equation. The dominant factors influencing the RC were found to vary at different scales. Precipitation had the largest correlation coefficient with the RC at the watershed scale. For the pixel scale, results from the geographical detector indicated that actual evapotranspiration (AET) and precipitation had the highest explanatory rate for the RC in the small watershed region and the whole study area (0.785 and 0.248, respectively). Climate factors, elevation, and normalized difference vegetation index had a substantial influence on the RC. Any two factors exhibited bilinear or nonlinear enhanced relationships in their interactions. The largest interactions between the factors were AET and precipitation, which exceeded 0.900. This study serves to better understand and explain runoff’s complex interrelationships.

The errors-in-variables (EIV) model is used for data processing in the field of geodesy. However, the EIV model may be ill-posed. By analyzing the decreasing regularization (D-regularization) characteristic of solutions for EIV models, algorithms using traditional methods such as singular value decomposition or the Tikhonov function can directly determine the irrationality of a model. When an EIV model is ill-posed, solutions in which the observation errors in the coefficient matrix are simulated by variables make the ill-posed nature of the model more serious. This is because the simulated observation errors are subtracted from the coefficient matrix in subsequent computations, which reduces the singular value of the normal matrix. This point is verified using an example. To account for the D-regularization of solutions in EIV models, a modified algorithm is derived by classifying the models into two categories, and the regularization parameters are iteratively revised based on the mean squared error. Finally, some conclusions are drawn from two separate examples. [ABSTRACT FROM AUTHOR]

The European land carbon uptake has been heavily impacted by several recent severe droughts, yet quantitative estimates of carbon uptake anomalies are uncertain. Atmospheric CO2 inverse models (AIMs) provide observation‐based estimates of the large‐scale carbon flux dynamics, but how well they capture drought impacts on the terrestrial carbon uptake is poorly known. Here we assessed the capacity of state‐of‐the‐art AIMs in monitoring drought impacts on the European carbon uptake over 2001–2015 using observations of environmental variability and vegetation function and made comparisons with bottom‐up estimates of carbon uptake anomalies. We found that global inversions with only limited surface CO2 observations give divergent estimates of drought impacts. Regional inversions assimilating denser CO2 observations over Europe demonstrated some improved consistency, with all inversions capturing a reduction in carbon uptake during the 2012 drought. However, they failed to capture the reduction caused by the 2015 drought. Finally, we found that a set of inversions that assimilated satellite XCO2 or assimilated environmental variables plus surface CO2 observations better captured carbon uptake anomalies induced by both the 2012 and 2015 droughts. In addition, the recent Orbiting Carbon Observatory—2 XCO2 inversions showed good potential in capturing drought impacts, with better performances for larger‐scale droughts like the 2018 drought. These results suggest that surface CO2 observations may still be too sparse to fully capture the impact of drought on the carbon cycle at subcontinental scales over Europe, and satellite XCO2 and ancillary environmental data can be used to improve observational constraints in atmospheric inversion systems. Plain Language Summary: Atmospheric CO2 inverse models (AIMs) are useful tools for quantifying the response of large‐scale carbon uptake to climate extremes, but their capacity for monitoring drought impacts, particularly at regional scales, is not fully explored. In this study, we assessed the capacity of state‐of‐the‐art AIMs for monitoring drought impacts on the European land carbon uptake over 2001–2015 using a large array of observational and model data sets. We found: (a) global inversions with only limited surface CO2 observations face a great challenge in monitoring drought impacts on the European carbon uptake; (b) Regional inversions assimilated denser CO2 observations over Europe, for the EUROCOM project, demonstrated some improved consistency but are still deficient, showing divergent estimates in interannual variability of carbon uptake for most years; and (c) A set of inversion systems that assimilated satellite XCO2 or assimilated environmental variables plus surface CO2 observations better captured annual and seasonal anomalies caused by droughts. Our study demonstrates that surface CO2 observations may still be too sparse to fully capture the impact of drought on the carbon cycle at subcontinental scales over Europe, whereby satellite XCO2 and ancillary environmental data can offer observational constraints for improving the estimates. Key Points: Global inversions with only limited surface CO2 observations give divergent estimates of drought impacts on the European carbon uptakeRegional inversions assimilating denser CO2 observations over Europe demonstrate some improved consistency but are still deficientThe inversions assimilating satellite XCO2 or environmental variables in addition to surface CO2 largely improve the estimates [ABSTRACT FROM AUTHOR]