Surface water balance

Land surface models have precipitation given as an input and need to correctly distribute the water over the surface. Some of the precipitation is intercepted by the canopy structure before reaching the ground. The fraction of water that falls on the ground is denominated throughfall. Upon reaching the ground, part of the throughfall infiltrates into the per- meable unsaturated soil and part can flow above the surface as runoff. The equation representing the water balance at the surface is:

T + M = E + I + R (2.10)

where T , throughfall is precipitation minus intercepted water, M is the available water from melting snow. On the right hand side, E is the water lost via evaporation, I is the infiltration into the first soil layer and R is the surface runoff.

Canopy interception

water will evaporate more easily back to the atmosphere, as there is no stomatal or soil resistance involved. The amount of intercepted water is a very uncertain quantity, as its measurement presents many challenges. It depends on the type of leaf, leaf angle, type of precipitation, and the presence of wind. Horton (1919) conducted a very meticulous study on this subject in his own hydrologic laboratory.

In JULES the water intercepted by the canopy is calculated as a linear function of the leaf area index (LAI), with a maximum capacity. In CTESSEL the intercepted water is considered as an extra tile, the interception reservoir. It has its own water balance equation accounting for rainfall interception, loss by evaporation (or gain by dew collection) as well as dew deposition from other tiles. In both models there is a maximum capacity that can be held on leaves; if it is reached, the exceeding water will fall down to the ground. Infiltration and runoff

The water reaching the soil surface is then split into infiltration when the soil is unsaturated and lateral runoff of the excess water. The way this division is done varies from model to model. CTESSEL hydrology uses a variable infiltration capacity based on orography and soil type (Balsamo et al., 2009). The orographic complexity of the terrain reduces the infiltration and more water is left for surface runoff. JULES calculates the infiltration based on a typical surface infiltration rate (infiltration enhancement factors (Best, 2009) averaged for the tiles. Runoff is the remaining water, with adjustments to account for the finite timestep.

Subsoil water transfer

The vertical movement of water in the unsaturated zone obeys the following equation (Richards, 1931) for the volumetric water content θ:

ρw

∂θ ∂t = −

∂F

∂z + ρwSθ (2.11)

where soil moisture θ is defined for each soil layer, ρw is the density of water (kg m−3), F

is the downward water flux into the next layer (kg m−2 s−1) and Sθ is a volumetric sink

term associated with the root uptake (m3 m−3 s−1), which depends on the surface energy balance and root profile (Viterbo and Beljaars, 1995). The equation is solved for the same four layers as the energy transfer, with top layer’s flux being the infiltration and a bottom boundary condition of free drainage.

The flux of water is described using Darcy’s law: F = −ρw h λ∂θ ∂z − γ i (2.12)

where λ is the hydraulic diffusivity (m2 s−1 ) and γ is the hydraulic conductivity (m s−1). Both parameters control the flow of water through the porous medium and are a function of the soil moisture and the soil texture. The functional relationship of these parameters with soil moisture is of an empirical nature, based on observational studies. In some formulations (Clapp and Hornberger, 1978; Cosby et al., 1984) hydraulic diffusivity and hydraulic conductivity are calculated as a function of the volumetric soil content (θ). However, it has been argued that, instead of using θ as the variable to link the soil moisture content to the soil properties, the matric potential, ψ, represents better the pressure that the droplets experience within the soil pores. The matric potential depends on the soil water content as well as on the soil texture. Van Genuchten (1980) formulation uses the matric potential, ψ, or the related pressure head (h = −ψ/(ρw· g)) to determine the water

flow. The hydraulic diffusivity in Van Genuchten (1980) formulation as a function of the pressure head h (m) is:

γ = γsat

(1 + αhn₎1−1/n_{− αh}n−12

(1 + αhn₎(1−1/n)(l+2) (2.13)

where α, n and l are soil texture dependent parameters which are related to the soil composition of sand, silt and clay through pedotransfer functions (W¨osten et al., 1999). JULES allows the use of either Brooks and Corey (1964) or Van Genuchten (1980) for- mulations. CTESSEL switched from Clapp and Hornberger (1978) formulation, used in its previous model version TESSEL, to Van Genuchten (1980) with the revision of the hydrology (Balsamo et al., 2009).

The pressure head is related to the volumetric soil water content via the water retention curve, which varies with the soil texture class:

θ(h) = θr+

θsat− θr

(1 + (αh)n₎1−1/n (2.14)

where θr represents a soil moisture residual.

Some aspects of the land parameterization still make use of significant water content quan- tities in volumetric unit, in particular the soil moisture stress on vegetation growth (Eq.

2.76). The permanent wilting point is the level of soil moisture below which vegetation cannot survive. Soil moisture at field capacity is the amount of water that can be held by the soil against gravity, and soil moisture at saturation is the maximum soil moisture that the soil can hold. These levels of soil moisture are defined in terms of the matric potential as:

ψ(θpwp) = −1500kP a

ψ(θcap) = −10kP a

ψ(θsat) = −33kP a

(2.15)

Soil water uptake by roots

The soil moisture stress on vegetation is calculated as a function of the water availability in the root zone, which is determined by a root fraction at each layer. The fraction of roots in the soil layers follows an exponential distribution and is plant dependent. The soil moisture stress factor is averaged across the soil layers. The equations describing the root density at each layer are for JULES Eq. 50 in Best et al. (2011) and Eq. 8.13 in ECMWF (2015).