Figure S1. The prediction of HCC of the FXW-M3 model on different values of ha for different soil types (a) R2 . (b) RMSE .
Figure S1 shows the impact of different values ofha on the performance of the HCC estimation with the FXW-M3 model. Including the impact of soil structure (with non-zeroha ) does improve the estimation of HCC, represented by a higher value of R2 and a lower value of RMSElog10 (K ). Compared to the original FXW-M2 model, the FXW-M3 model substantially increases the value of R2 and reduces the value of RMSElog10 (K ) for especially sand, sandy loam, loam and silt loam soils. When it comes to silty clay and clay soils, only slightly improvement is achieved.
The optimized value of ha varies for the different soil types of the validated 152 soil samples. For sand, sandy loam and loam soils, the optimized value of ha is in the range from about −50 cm to −30 cm. Silt loam has a slightly higher optimized value of about −17cm. When it comes to silty clay and clay soils, ha has a much higher optimized value close to −5 cm. However, it should keep in mind that both the silty clay and clay soil types have a small number of soil samples. For all the 152 soil samples, the optimized ha is about −28 cm. This value is further applied in predicting the HCC for all soil samples as shown in section 4 in the main text.
Table S1 . The optimized and fixed parameters of different model settings. The number in the bracket demonstrates the lower and upper boundary of the optimized parameters.