5.2. Canopy Hydrology

ADELM updates the solid and liquid canopy interception stores and diagnoses the fluxes routed from the canopy to the snowpack and soil surface.

Coupling to other components

• Precipitation Phase Partitioning provides rainfall_mmday and snowfall_mmday.

• Potential Evapotranspiration provides potential_canopy_evaporation and potential_canopy_sublimation.

• Shortwave Radiation provides canopy_net_radiation_Wm2 (used as energy limit for solid sublimation).

• Snow Hydrology uses snowfall_to_ground_mmday.

• Soil Hydrology uses throughfall_from_canopy_mmday.

1. Solid canopy interception

See also

model.processes.hydrology.calculate_canopy_solid_hydrology()

The solid canopy store canopy_solid_interception_storage [mm; State: snow water equivalent stored on the canopy] satisfies

(5.2.1)\[W_{\mathrm{can,sol}}^{\,t+1} = W_{\mathrm{can,sol}}^{\,t} + I_{\mathrm{can,sol}} - D_{\mathrm{can,sol}} - E_{\mathrm{sub}}\]

Atmospheric snowfall \(P_{\mathrm{snow}}\) (snowfall_mmday [mm day-1; Flux: solid precipitation reaching the canopy top]) is partitioned into an intercepted fraction and a direct-to-ground fraction using a Beer-law interception fraction:

(5.2.2)\[f_{\mathrm{int}} = 1 - \exp(-0.5\,\mathrm{VAI})\]

where \(\mathrm{VAI}\) is the vegetation area index. The intercepted solid input and the direct snowfall reaching the ground are

(5.2.3)\[I_{\mathrm{can,sol}} = f_{\mathrm{int}}\,P_{\mathrm{snow}}, \qquad P_{\mathrm{snow,g}} = (1 - f_{\mathrm{int}})\,P_{\mathrm{snow}}\]

The solid interception capacity is

(5.2.4)\[W_{\mathrm{can,sol,max}} = c_{\mathrm{snow}}\,\mathrm{VAI}\]

where \(c_{\mathrm{snow}}\) is canopy_solid_interception_capacity_coefficient [default: 1 mm (m2 m-2)-1; Fixed parameter: maximum snow water equivalent the canopy can hold per unit vegetation area index].

Actual canopy solid sublimation canopy_solid_sublimation_mmday [mm day-1; Flux: water flux sublimated from snow intercepted on the canopy] is limited to below-freezing conditions, bounded by an energy limit from canopy net radiation, and capped by the existing storage:

(5.2.5)\[E_{\mathrm{sub}} = \min\!\Bigl( W_{\mathrm{can,sol}}^{\,t},\; \min\!\bigl(E_{\mathrm{sub}}^\ast,\; E_{\mathrm{energy}}\bigr) \Bigr) \cdot \mathbf{1}[T_{\mathrm{a}} < T_{\mathrm{freeze}}]\]

where \(E_{\mathrm{sub}}^\ast\) is potential_canopy_sublimation [mm day-1; Diagnostic: atmospheric demand for sublimation of solid-phase water stored on the canopy] and \(E_{\mathrm{energy}} = \max(R_{\mathrm{can,net}}\,t_{\mathrm{day}}/L_{\mathrm{sub}},\,0)\) with \(R_{\mathrm{can,net}}\) the canopy net radiation (canopy_net_radiation_Wm2 [W m-2; Flux: net radiative flux at the canopy surface]).

Any store remaining above capacity after sublimation and new interception is unloaded to the ground:

(5.2.6)\[D_{\mathrm{can,sol}} = \max\!\left( W_{\mathrm{can,sol}}^{\,t} + I_{\mathrm{can,sol}} - E_{\mathrm{sub}} - W_{\mathrm{can,sol,max}},\;0 \right)\]

The total snowfall flux reaching the ground snowfall_to_ground_mmday [mm day-1; Flux: total snowfall reaching the ground, including direct throughfall and canopy unloading] is

(5.2.7)\[P_{\mathrm{snow,ground}} = P_{\mathrm{snow,g}} + D_{\mathrm{can,sol}}\]

2. Liquid canopy interception

See also

model.processes.hydrology.calculate_canopy_liquid_hydrology()

The liquid canopy store canopy_liquid_interception_storage [mm; State: liquid water stored on wet canopy surfaces] satisfies

(5.2.8)\[W_{\mathrm{can,liq}}^{\,t+1} = W_{\mathrm{can,liq}}^{\,t} + I_{\mathrm{can,liq}} - D_{\mathrm{can,liq}} - E_{\mathrm{can,liq}}\]

All rainfall is intercepted by the canopy: \(I_{\mathrm{can,liq}} = P_{\mathrm{rain}}\) where \(P_{\mathrm{rain}}\) is rainfall_mmday [mm day-1; Flux: liquid precipitation reaching the canopy top]. The liquid interception capacity is

(5.2.9)\[W_{\mathrm{can,liq,max}} = c_{\mathrm{liq}}\,\mathrm{LAI}\]

with \(c_{\mathrm{liq}}\) given by canopy_interception_capacity_coefficient [default: 0.2 mm (m2 m-2)-1; Fixed parameter: maximum liquid water the canopy can hold per unit leaf area index].

Throughfall to the soil surface throughfall_from_canopy_mmday [mm day-1; Flux: liquid precipitation reaching the soil surface without canopy interception] drains any rainfall in excess of capacity:

(5.2.10)\[D_{\mathrm{can,liq}} = \max\!\left(W_{\mathrm{can,liq}}^{\,t} + I_{\mathrm{can,liq}} - W_{\mathrm{can,liq,max}},\;0\right)\]

The water held in the canopy after accounting for throughfall is

(5.2.11)\[W_{\mathrm{can,int}} = \min\!\left(W_{\mathrm{can,liq}}^{\,t} + I_{\mathrm{can,liq}},\;W_{\mathrm{can,liq,max}}\right)\]

Actual wet-canopy evaporation canopy_liquid_evaporation_mmday [mm day-1; Flux: water flux evaporated from wet canopy surfaces] is bounded by this intercepted store:

(5.2.12)\[E_{\mathrm{can,liq}} = \min\!\left(E_{\mathrm{can,liq}}^\ast,\;W_{\mathrm{can,int}}\right)\]

where \(E_{\mathrm{can,liq}}^\ast\) is potential_canopy_liquid_evaporation [mm day-1; Diagnostic: atmospheric demand for evaporation from wet canopy surfaces]. The updated storage is \(W_{\mathrm{can,liq}}^{\,t+1} = W_{\mathrm{can,int}} - E_{\mathrm{can,liq}}\).