A process-based water balance is simulated in iLand (Eq. 1), explicitly considering precipitation (P), interception and canopy evaporation (I), snow storage and melting, soil water content (Θ) and evapotranspiration (E, including transpiration and soil evaporation).
| \[\begin{aligned} P-I-R-\Delta \Theta -E=0 \end{aligned} \] | Eq. 1 |
Table of contents
precipitation and interception
Daily precipitation data are used as input to drive the hydrological cycle in iLand. Intra-daily variation in precipitation distribution is neglected. Canopy interception is modeled following the general scheme of Landsberg and Gower (1997) and implemented following the rendering of Seidl et al. 2005 in PICUS. Interception capacity depends on resource unit leaf area and differs for broadleaved and coniferous species. A leaf-area weighted average is used for mixed stands. In a rain event, the precipitation proportion not subject to direct throughfall (dependent on the rain intensity) through canopy gaps is routed to the interception storage (Eq. 2).
| \[\begin{aligned} imax_{needle} = P \cdot \left(1 - 0.9 \cdot \sqrt{1.03 - e^{-0.055\cdot P} } \cdot \frac{LAI_{needle}}{LAI_{total}} \right) \\ imax_{bl} = P \cdot \left(1 - 0.9 \cdot \left( 1.22 - e^{-0.055\cdot P} \right) ^{0.35} \cdot \frac{LAI_{bl}}{LAI_{total} } \right) \\ \end{aligned} \] | Eq. 2 |
,with imax the precipitation (in mm) that is not subject to throughfall, LAI the leaf area index of either coniferous species (needle), broadleaved species (bl) or both (total). The maximum interception storage is dependent on stand leaf area and on the share of coniferous/broadleaved species in the canopy (Eq. 3).
| \[\begin{aligned} storage_{max} = 2 \cdot \frac{LAI_{bl} }{LAI_{total}}+4 \cdot \frac{LAI_{needle}}{LAI_{total}} \\ storage = storage_{max} \left ( 1- e^{-0.5\cdot LAI_{total}} \right ) \end{aligned} \] | Eq. 3 |
The total interception is calculated following Eq. 4:
| \[\begin{aligned} i_{total} = min \left(P \: ; \: imax_{needle}+imax_{bl} \: ; \: storage \right) \end{aligned} \] | Eq. 4 |
The amount of precipitation per event exceeding the interception storage capacity is directly routed to soil (and if applicable: snow) pools. Evaporation of intercepted water from the canopy is calculated using the Penman-Monteith equation (see Eq. 7 below), with the canopy conductance set to infinity (cf. Landsberg and Gower 1997). The water not evaporated within one day is eventually channeled to the soil water pool as stemflow and drip.
snow water pool
If the daily mean temperature Td≤0°C, precipitation falls as snow and is routed to the snow water pool. On days with Td>0°C the snow water pool looses water to the soil water pool at a rate of 0.7 mm°C-1day-1 (Running and Coughlan 1988). It has to be noted that this representation of snow focuses on the snow water storage but does not give an accurate estimate of snow depth.
soil water pool
Soil hydraulic characteristics define the storage capacity of a one-layer bucket model. The volumetric plant-available water holding capacity (Θpaw) is derived as the the soil water at field capacity (Θfc with field capacity being defined as a soil water potential Ψ=-0.015 MPa) minus the water content at a minimum plant-available soil water potential (ΘΨmin) (Eq. 5)
| \[\begin{aligned} \Theta_{paw}=\Theta _{fc}-\Theta _{\Psi min} \end{aligned} \] | Eq. 5 |
The soil water characteristics curve to derive these points is defined by saturated soil water content (Θsat), saturated soil water potential (Ψsat) and bs the slope of the retention curve (in logarithmic space) (cf. Campbell and Norman 1998, Eq. 6)
| \[\begin{aligned} \Psi =\Psi _{sat}(\frac{\Theta }{\Theta _{sat}})^{b} \end{aligned} \] | Eq. 6 |
Θsat, Ψsat and bs can be derived by laboratory analysis of soil samples if available, but have also been estimated from large soil databases based on physical soil properties. In the absence of specific soil data we use the estimates of Cosby et al. (1984), who employed sand, clay and silt content as predictors. Their data has recently been successfully applied in the process-based forest model of Schwalm and Ek (2004).
By means of effective rooting depth (i.e. the constraining value of maximum rooting depth and soil depth; for a compilation of species-specific max. rooting depth see Breuer et al. 2003), an important site variable, water input from throughfall and snowmelt can be converted to soil water potentials. Water exceeding the field capacity is simulated to percolate out of the system. For every day, the soil water potential Ψ, used as proxy for tree response to soil water status, can be derived following Eq. 6.
transpiration and canopy conductance
Plant available soil water (Θpaw) can be transpired back to the atmosphere by trees. We use the widely applied Penman-Monteith equation (Eq. 7) to simulate plant transpiration (T) and canopy evaporation of intercepted precipitation (E), following its implementation in 3-PG (Landsberg and Waring 1997).
| \[\begin{aligned} T=\frac{\Delta R_{n}+\rho \cdot c_{p}\cdot D\cdot g_{a}}{\lambda \left ( \Delta +\gamma \cdot \left ( 1+g_{a}/g_{c} \right ) \right )}\cdot t \\ E=\frac{\Delta R_{n}+\rho \cdot c_{p}\cdot D\cdot g_{a}}{\lambda \left ( \Delta +\gamma \right )}\cdot t \end{aligned} \] | Eq. 7 |
with Δ the slope of saturation vapor pressure, Rn the incoming radiation (PAR), ρ the density of air, cp the heat capacity of the atmosphere, D the saturation deficit of air, ga the boundary layer conductance, and gc the canopy conductance, λ the latent heat of vaporization of water, and γ the psychrometric constant. Eq. 7 captures the two environmental drivers of evaporation, the net radiant energy supply and the supply of dry air, with the two controls ga, the mixing power of the atmosphere, and gc the primary physiological control exerted by plants (cf. Landsberg and Gower 1997).
We follow Landsberg and Waring (1997) in defining a constant, species-specific maximum canopy conductance gc,max for closed canopies (defined as LAI > LAIgcx, with LAIgcx being typically around 3, cf. Kelliher et al. 1995), and a linear reduction of gc,max for LAI < LAIgcx (Eq. 8)
| \[\begin{aligned} g_{c,max}=g_{c,max}\cdot min(\frac{LAI}{LAI_{gcx}}\; ,\; 1) \end{aligned} \] | Eq. 8 |
Maximum stomatal and canopy conductance values for species and species groups are for instance reported by Körner 1994 and Breuer et al. 2003, however both Körner 1994 and Kelliher et al. 1995 report no significant differences between tree species. Actual conductance gc is derived by correcting gc,max for the effects of vapor pressure deficit response and soil water use, represented by fD,d and fsw,d on a daily basis (Eq. 9). A leaf area weighted canopy average gc is applied for mixed stands.
| \[\begin{aligned} g_{c}=g_{c,max}\cdot min(f_{D,d}\; ,\; f_{sw,d}) \end{aligned} \] | Eq. 9 |
Furthermore, following Landsberg and Waring (1997) fage also directly reduces gc, and a leaf-area weighted average over fage for all trees per RU is computed to account for age-related decline in canopy conductance. Furthermore, for the vegetation layer <4m in height, for which LA dynamics is not explicitly simulated in iLand, conductance is calculated as described here.
On dry days (i.e. days without precipitation) the water transpired to the atmosphere is calculated as T from Eq. 7. On wet days, the transition between E and T is modeled following the approach by Wigmosta et al. (1994). First, intercepted water in the canopy is evaporated at the potential rate (Eq. 10)
| \[\begin{aligned} I=min\left ( i_{max};E \right ) \end{aligned} \] | Eq. 10 |
Transpiration from dry vegetation is subsequently calcualted as Eq. 11
| \[\begin{aligned} T_{d}=(E-I)\cdot \frac{T}{E} \end{aligned} \] | Eq. 11 |
with T/E the rate between daily transpiration and evaporation rates (Eq. 7). This stepwise calculation allows the vegetation to go from wet to dry within one timestep. If the canopy remains completely wet (i.e. I>E) or completely dry (i.e. I=0), the method is equivalent to the Penman Monteith equations in Eq. 7.
evapotranspiration from ground vegetation and saplings
iLand explictly models the leaf area from mature trees (>4m height) but also considers the effect of saplings (cohorts of trees) and - in the absence of trees - a ground vegetation layer. More details on saplings and ground vegetation is linked to the water cylce is given on the transpiration and conductance in saplings page.
Sequence of steps
- Precipitation P
- Interception of P in the crown
- Snow water pool: P is either stored in pool, or snow melts and adds to the flow P
- P is added to the soil water container. Excess water is transferred to the Runoff/trickle off pool
- Evaporation E and transpiration T is calculated using the (relative) current water content at this point
- T is removed from the soil water pool, and intercepted water which was not evaporated is added to the soil water.
Seidl, R., Rammer, W., Scheller, R.M., Spies, T.A. 2012. An individual-based process model to simulate landscape-scale forest ecosystem dynamics. Ecol. Model. 231, 87-100.
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