Here, we seek to understand how Arctic river inundation affects permafrost thermal state. Specifically, we develop afirstorder approach to simulate evolving river‐water temperature over the inundation period. Then, river temperature is employed as the upper temperature boundary condition in a permafrost model, which predicts the thermal state of the shallow subsurface permafrost. Our combined model is applied and validated for downstream reaches of the Kuparuk River, Arctic Alaska. Finally, we run simulations to investigate the response of permafrost temperatures and the active layer to changingflood timing and river discharge.

Our quantitative model of river temperatureTwis based on a heat budget approach . Heat fluxes considered in the model include net surface shortwave solar radiation (H_sr), net longwave radiation (H_lr), latent heat (Hl) due to evaporation and condensation, convective heat (H_c), and riverbed heat flux (H_b; Hebert et al., 2011). With these terms, the net heat balance of the water body ΔH_w is

 ΔH_w = ΔH_sr+H_sr+H_lr+H_l+H_c+H_b. 

Surface net solar radiation H_sr at the water surface is expressed as the direct solar irradiance penetrating the water surface, that is, the difference between incoming solar radiation (His) and reflected solar radiation(H_rs), or

H_sr=H_is−H_rs=(1−R)H_is

where R represents the water surface albedo.

Longwave radiation includes the radiation emitted by the atmosphere, water surface, and vegetation. We assume the vegetation canopy effect is negligible for the northernmost Arctic river flood plains. Net longwave radiation H_lr at the water surface is then the difference between atmospheric downward longwave radiation (H_dl) and the longwave radiation emitted from the water surface (Hel),

Quoted from : Changing Arctic River Dynamics Cause Localized Permafrost Thaw.