“…Surface runoff ( R s , in m s −1 ) in the Noah LSM consists of infiltration excess runoff from the unfrozen part of the model grid and direct runoff from the impermeable frozen part ( f imp , ‐) [ Schaake et al ., ; Koren et al ., ]: where Δ t is the time step (s), W d is the soil water deficit within the soil column (m), P x is the precipitation falling on the ground (m), K dt is an empirical parameter taken as 3.0 d −1 , and the impermeable frozen fraction is as in Zheng et al . [] assuming a gamma probability distribution for the soil ice content ( W ice , m) within root zone: where Δ z is the soil depth (m), n root is the number of soil layers within the root zone (‐), θ ice is the soil ice content (m 3 m −3 ), W cr is the critical ice content above which the frozen ground is impermeable taken as 0.15 m, α is a shape parameter of the gamma probability distribution (‐) taken as 3, and v is the upper limit of an integral function representing the spatial variability of frozen depth [ Koren et al ., ].…”