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Chapter 7. Land surface parametrization
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Chapter 1. Overview
Chapter 2. Radiation
Chapter 3. Turbulent diffusion and interactions with the surface
Chapter 4. Subgrid-scale orographic drag
Chapter 5. Convection
Chapter 6. Clouds and large-scale precipitation
Chapter 7. Land suface parametrization
Chapter 8. Methane oxidation
Chapter 9. Climatological data
REFERENCES
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7.6 Soil-water budget
The vertical movement of water in the unsaturated zone of the soil matrix obeys the following equation (see Richards (1931), Philip (1957), Hillel (1982), and Milly (1982) for the conditions under which Eqs. (7.57) and (7.58) are valid) for the volumetric water content
:
|
(7.57) |
is the water density (
), 
is the water flux in the soil (positive downwards, 
), and 
is a volumetric sink term (
), corresponding to root extraction. Using Darcy's law, 
can be specified as:
|
(7.58) |
(
) and 
(
) are the hydraulic diffusivity and hydraulic conductivity, respectively.Replacing (7.58) in (7.57), specifying
, and defining parametric relations for 
and 
as functions of soil water, a partial differential equation for 
is obtained; it can be numerically integrated
if the top boundary condition is precipitation minus evaporation minus surface
runoff. The bottom boundary condition assumes free drainage. Abramopoulos et al. (1988) specified
free drainage or no drainage, depending on a comparison of a specified geographical
distribution of bedrock depth, with a model-derived water-table depth. For
the sake of simplicity the assumption of no bedrock everywhere has been
adopted.7.6.1 Interception
The interception reservoir is a thin layer on top of the soil/vegetation, collecting liquid water by the interception of rain and the collection of dew, and evaporating at the potential rate. The water in the interception reservoir,
, obeys
|
(7.59) |
is the water evaporated by the interception reservoir (or dew
collection, depending on its sign), D represents the dew deposition
from other tiles, and 
(
) is the interception-the fraction of
precipitation that is collected by the interception reservoir and is later
available for potential evaporation. Because the interception reservoir
has a very small capacity (a maximum of the order of 1 mm, see Eq. (7.2)), it can fill up or
evaporate completely in one time step; special care has to be taken in order
to avoid numerical problems when integrating Eq.
(7.59). In addition, since El is defined in the vertical
diffusion code, it might impose a rate of evaporation that depletes entirely
the interception layer in one time step. In order to conserve water in the
atmosphere-intercepted water-soil continuum, the mismatch of evaporation
of tile 3 plus dew deposition from the other tiles (which is not explicitely
dealt with by the vertical diffusion) as seen by the vertical diffusion
and the intercepted water has to be fed into the soil.The equation is solved in three fractional steps: evaporation, dew deposition, and rainfall interception. The solver provides as outputs
(a) the inteception layer contents at time step
 ; |
| (b) Throughfall (ie, rainfall minus intercepted water); and |
| (c) The evaporation effectively seen by the intercepted layer in each tile i. |
First, the upward evaporation (
) contribution is considered; because 
depends linearly on 
(see Eq. (7.2)), an implicit version
of the evaporating part of (7.59) is obtained by linearizing
:
|
(7.60) |
is the new value of interception-reservoir content after the
evaporation process has been taken into account. After solving for 
, a non-negative value of evaporation
is obtained and the evaporation seen by this fractional time step is calculated
|
(7.61) |
The dew deposition is dealt with explicitely for each non-snow tile in succession, for tiles 3, 4, 6, 7, 8, where tile 7 is also considered because in the exposed snow tile, the canopy is in direct evaporative contact with the atmosphere. When the evaporative flux is downwards (
)
|
(7.62) |
where superscript 2 denotes the final value at the end of the this fractional time step.
The interception of rainfall is considered by applying the following set of equations to large-scale and convective rainfall
|
(7.63) |
is a modified convective rainfall flux,
computed by applying the heterogeneity assumption that convective rainfall
only covers a fraction 
of the grid box, 
is a coefficient of efficiency of interception of rain. The
total evaporation seen by the interception reservoir is 
for tiles 4, 6, 7, and 8 and 
for tile 3.The interception reservoir model described in this section is probably the simplest water-conserving formulation based on Rutter's original proposition (Rutter et al. 1972; Rutter et al. 1975). For more complicated formulations still based on the Rutter concept see, for instance, Mahfouf and Jacquemin (1989), Dolman and Gregory (1992), and de Ridder (2001).
7.6.2 Soil properties
Integration of Eqs. (7.57) and (7.58) requires the specification of hydraulic conductivity and diffusivity as a function of soil-water content. Mahrt and Pan (1984) have compared several formulations for different soil types. The widely used parametric relations of Clapp and Hornberger (1978) (see also Cosby et al. 1984) are adopted:
|
(7.64) |
is a non-dimensional exponent, 
and 
are the values of the hydraulic conductivity and matric potential
at saturation, respectively. A minimum value is assumed for 
and 
corresponding to permanent wilting-point water content.Cosby et al. (1984) tabulate best estimates of
, 
, 
and 
, for the 11 soil classes of the US
Department of Agriculture (USDA) soil classification, based on measurements
over large samples. Since the model described here specifies only one soil
type everywhere, and because the determination of the above constants is
not independent of the values of 
and 
, the following procedure is adopted.A comprehensive review of measurements of
and 
may be found in Patterson (1990). Starting from Patterson's
estimates of 
and 
for the 11 USDA classes, a mean of the
numbers corresponding to the medium-texture soils (classes 4, 5, 7, and
8, corresponding to silt loam, loam, silty clay loam and clay loam, respectively)
is taken. The resulting numbers are 
and 
. Averaging the values of Cosby et al. (1984) for soil
moisture and soil-water conductivity at saturation for the same classes
gives the numerical values 
and 
. The Clapp and Hornberger expression for the matric potential
|
(7.65) |
(-15 bar) and 
(-0.33 bar) (see Hillel 1982; Jacquemin and Noilhan 1990)
to find the remaining constants 
and 
. The results are 
and 
. The above process ensures a soil that has an availability
corresponding to the average value of medium-texture soils, and yields a
quantitative definite hydraulic meaning to 
and 
compatible with the Clapp and Hornberger relations (see Table 7.2 for a summary of the
soil constants).Finally, the water transport in frozen soil is limited in the case of a partially frozen soil, by considering the effective hydraulic conductivity and diffusivity to be a weighted average of the values for total soil water and a very small value (for convenience, taken as the value of Eq. (7.64) at the permanent wilting point) for frozen water. The soil properties, as defined above, also imply a maximum infiltration rate at the surface defined by the maximum downward diffusion from a saturated surface. If the throughfall exceeds the maximum infiltration rate, the excess precipitation is put into runoff. However, in practice the maximum infiltration rate is so large that this condition is never reached. Surface runoff is therefore only produced if the soil becomes saturated.
7.6.3 Discretization and the root profile
A common soil discretization is chosen for the thermal and water soil balance for ease of interpretation of the results, proper accounting of the energy involved in freezing/melting soil water, and simplicity of the code. Equations Eqs. (7.57) and (7.58) are discretized in space in a similar way to the temperature equations, ie, soil water and root extraction defined at full layers,
and 
, and 
the flux of water at the interface between layer 
and 
. The resulting system of equations represents an implicit,
water-conserving method.For improved accuracy, the hydraulic diffusivity and conductivity are taken as (see Mahrt and Pan 1984)
|
(7.66) |
where
. The boundary conditions are given by
|
(7.67) |
and surface runoff 
is the soil infiltration at the surface:
|
(7.68) |
and
, with a similar equation for 
. The evaporation at the top of the soil layer, 
, is computed as the sum of the evaporations of tile 8
plus the contributions necessary to conserve water with the solver of the
interception layer: | (a) tile 3 mismatch(after the evaporated water used by the interception reservoir for the given tile is subtracted) ; and |
| (b) when the evaporative fluxes are downward (i.e., dew deposition), the evaporation for tiles 4, 6 and the canopy evaporation of tile 7. |
Root extraction is computed as
|
(7.69) |
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05.04.2002 |
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