Simulating Frozen Ground

Since the cross-effects are very small under most conditions and since volumetric heat capacity and thermal conductivity of the substrate influence each other only marginally, decoupled equations to describe the energy- and water-transport within the soil are commonly used (e.g., Deardorff 1978, McCumber and Pielke 1981, Groß 1988, Dickinson et al. 1993, Schlünzen 1994, Jacobson and Heise 1982, Eppel et al. 1995, Chen and Dudhia 2002, Dai et al. 2003). However, this decoupling is realized in various ways as described in the following. Table 1 lists the various methods used by recent soil models of NWPMs, GCMs, and ESMs.

Table 1. Classification of soil-models used in NWPMs, GCMs and ESMs with respect to parameterizations used and model approaches. The symbol X indicates free choice of the number of layers, values in brackets are the typical choice in the models indicated.

Name

Reference

Purpose

Number of layers for

Treatment of

nice

T 1 s

root

moisture

temperature

roots

Soil frost

SECHIBA

Ducoudre et al. 1993, Polcher

GCM

2

2

2

Top-to-bottom filling

NCEP

Chen et al. 1996

NWP

2

2

1

force-restore

BATS

Dickinson et al. 1986, 1993, Yang et al. 1997

GCM

3

3

3

Richard's equation

heat diffusion

Federer-Cowan-model

Uniform freezing to -4C, limited thermal diffusivity

BEST

Cogley et al. 1990, Pitman

3

3

2

diffusion

heat diffusion

Explicitly, ice and water co-exist

BASE

Verseghy 1991, Desborough 1997, Pitman et al. 1991, Slater et al. 1998

GCM

3

3

3

Richard's equation

heat diffusion

Explicitly, ice and water co-exist

PROGMOD

1

Acs et al. 2000

Substitutes surface flux data in diagnostic model

3

3

1

Richard's equation

force-restore

Hornet-approach, equal distributed

Bulk-heat capacity, freezing/ melting

SURF2

Claussen 1988

mesoscale modeling

2

5

0

Force-restore

heat diffusion

none

none

SURFW3

Claussen 1988, Mölders 1988, Fröhlich & Mölders 2002

mesoscale modeling

2

5

0

Force-restore

heat diffusion

none

none

HTSVS4

Kramm et al. 1994, 1996, Mölders et al. 2003, Mölders & Rühaak 2002, Mölders & Walsh 2004

Dry deposition, LSM in mesoscale modeling

X

X

X

Coupled diffusion equation including Richard's equation

Cowan-type, different in upper/lower root space

Explicitly, ice and water coexist

1 Used by Universität Wien, Universität Budapest, Universität Bayreuth

2 Used by GESIMA at GKSS, Universität Leipzig; similar LSMs are used by FITNAH at Universität Hannover or METRAS at Universität Hamburg, and Institut für

Troposphärenforschung Leipzig

3 Used by GESIMA at Universität Leipzig

4 used by MM5 at EURAD Universität zu Köln, Universität Leipzig, (older Version at Universität Frankfurt)

Table 1. (Continued)

Name

Reference

Purpose

Number of layers for

Treatment of

n nice

T 1 s

root

moisture

temperature

roots

Soil frost

OSULSM5

Chen & Dudhia 2001a,b

LSM in mesoscale modeling

X (4)

X (4)

3

Richard's equation

heat diffusion

none

MOSAIC

Koster & Suarez (1992)

GCM

3

2

2

Darcy's law

Force restore

BUCKET

Manabe 1969, Robock et al. 1995, Schlosser et al. 2000

GCM

0

1

1

bucket

heat balance

PLACE

Wetzel & Chang 1988, Wetzel & Boone 1995

Flexible

7

50

2

Richard's equation

heat diffusion

SiB

Sellers et al. 1986, Xue et al. 1991, Sud & Moko 1999

GCM, mesoscale

3

2

2

diffusion

Force-restore

Federer-Cowan-model

SEWAB6

Mengelkamp et al. 1999, 2001, Warrach 2001

Macroscale hydrological, mesoscale atmospheric models

6

6

1

Richard's equation

heat diffusion

different in upper/lower root space

VEGMOD7

Schädler 1990, Grabe 2001

ECHAM8

Dümenil & Todini 1992

LSM in GCM

1

5

2

bucket

heat diffusion

Equally distributed

ECMWF9

Viterbo & Beljaars 1995

LSM in mesoscale modeling

4

4

3

Richard's equation

heat diffusion

Expon-ential decrease with depth

5 used by MM5 at EURAD Köln, LMU München, IFU Garmisch-Partenkirchen

6 used by GKSS

7 used by Universität Karlsruhe, Forschungszentrum Karlsruhe, IFU Garmisch-Partenkirchen

8 used by MPI Hamburg

9 used by ECMWF

| |

1 1 1

Name

Reference

Purpose

Number of layers for

Treatment of

n nice

Ts

root

moisture

temperature

roots

Soil frost

TERRA10

Jacobson & Heise 1982

LSM in mesoscale modeling

3

3

1

Force-restore

Force-restore

Resis-tance

no

WASIM11

Hydrology

none

BIOME_ BCG12

Running & Hunt 1993.

Ecology

1

1

1

Top-to-bottom flow (no upwards flow)

Force-restore

LSM_FU-Berlin

Blumel 2001

Determine H from satellite data

0

0

0

ISBA13

Noilhan & Planton 1989, Mahouf & Noilhan 1991, Douville et al. 1995, Boone et al. 2000

LSM in GCM, mesoscale modeling,

NWPM

2

2-3

1

Force-restore

Force-restore

Explicit, ice and water coexist

SWB

Chen et al. 1996, Schaake et al. 1995

hydrology

2

-■-

1

Richard's equation

1993, Chatta & le Treut

1994, de Ronag & Polcher 1998

GCM

3

3

3

Darcy's law

Heat diffusion

Linear, temperature dependent freezing/melting

AMBETI14

Braden 1995

Agricultural consulting

3

3

3

GISS

Abramopoulos et al. 1988, Lynch-Stieglitz 1994

GCM

6

6

Heat diffusion

10 Used by LM, DM at DWD, IfT, Universität Bonn, by REMO at MPI Hamburg, TU Cottbus

11 used by ETH Zürich

12 Used by Universität Bayreuth, BITÖK, PIK

13 Used by FOOT3D, Universität zu Köln, Institut für Geophysik und Meteorologie

14 used by DWD, Universität Bayreuth

Force-Restore Method

The force-restore method had been introduced by Deardorff (1978) and became standard for NWPMs in the mid-Eighties. A force-restore model (Fig. 4) considers at least a thin top layer of depth d1 and a deep soil layer of depth d2 for which the soil temperature and moisture states are calculated. The force-restore model considers two distinctly different time scales in soil. The conditions in the uppermost layer are governed by the rapid responses to atmospheric forcing (e.g., precipitation, evaporation, diurnal course of atmospheric heating). These changes are represented by the so-called force term. The deeper soil layer only responses slowly to the atmospheric forcing. It typically represents annual changes. The interaction between the upper and deeper soil is considered by the restore term that describes the supply of heat and soil moisture from the deep soil layer. Some versions of the forcerestore model consider a third layer that considers decadal variation. In all layers, prognostic equations are solved to determine soil temperature or moisture conditions. In doing so, soil temperature and moisture conditions are assumed to be independent from each other except if freezing/thawing is considered. Then these phase transitions lead to a change is soil temperature.

NWPMs that use the force-restore method are limited in resolving the various soil horizons (Montaldo and Albertson, 2001). High latitude soils, however, frequently show a very heterogeneous vertical stratification because they were formed by during the ice age. Moreover, the force-restore methods does not permit for simulating the vertical distributions of soil processes like the diurnal variation of the boundary between an unfrozen upper and a frozen deeper soil layer because it works with only two or three reservoirs. However, surface-water and energy fluxes are extremely difficult to predict without knowing the exact depth of the freezing line.

NWPMs that use the force-restore method are, for instance, the Deutschland Model (DM) of the German Weather Service (e.g., Jacobson and Heise, 1982), the APREGE of Météo-France and the Spanish Weather Service that both use ISBA (Noilhan and Planton 1989, Mahfouf et al., 1995); GCMs using a force-restore method are CSIRO9, and the ARPEGE climate model (DéQué et al., 1994, Mahfouf et al., 1995). See also Table 1.

Multi-Layer Models

Multi-layer soil models (Fig. 4) are most suitable for permafrost simulation in NWPMs, CTMs, GCMs and ESMs because they permit for simulating the vertical distributions of soil processes like the diurnal variation of the boundary between an unfrozen upper and a frozen deeper soil layer. Consequently, huge efforts have been spent to enlarge multi-layer soil models by soil-frost processes (e.g., Koren et al., 1999, Boone et al., 2000, Warrach et al. 2001, Mölders et al. 2003a, Narapusetty and Mölders 2005, 2006). Koren et al. (1999), for instance, tested and evaluated a soil-frost model offline that now is included with modifications in the NCEP (National Center for Environmental Prediction) Eta model. Mölders et al. (2003a) included the physics of soil-water freezing and thawing of soil-ice into the soil-model of the Hydro-Thermodynamic Soil Vegetation Scheme (HTSVS; Kramm et al.

1994, 1996) that is used in several mesoscale meteorological models (e.g., GESIMA Molders and Ruhaak 2002; MM5 Molders and Walsh 2004).

Figure 4. Schematic comparison of different concepts used for soil modeling in atmospheric models.

The impacts of soil-water freezing and soil-ice thawing in the active layer and the related processes have received little systematic study in the context of their influence on short-term weather.

Obviously, the coupled equation set (1) and (2) includes cross-effects like the Dufour effect (i.e., a moisture gradient contributes to the heat flux and alters soil temperature) and Ludwig-Soret effect (i.e., a temperature gradient contributes to the water flux and changes soil volumetric water content). Such a set of equation has either to be solved simultaneously by an iteration technique or must be simplified to avoid the iteration required by the coupling due to the cross-effects. Typically the interactions between the soil thermal and moisture regimes by the Ludwig-Soret and Dufour effect are neglected because they are negligible small under many circumstances. These interactions become noteworthy when chemicals are considered, for which they should be considered in CTMs and ESMs, when soil conditions suddenly switch from the dry to the wet mode, when soil temperatures vary around the freezing point, during snow-melt, and over the long-term these processes may gain influence on other processes or variables (Molders and Walsh 2004). The Dufor-effect, for instance, was found to affect soil temperature up to 2 K, the Ludwig-Soret effect affects water recharge by 5 % of the total recharge over the long-term (Molders et al., 2003b). Changes in soil temperatures and moisture caused by these cross-effects may alter the exchange of heat and moisture at the atmosphere-soil interface under these conditions.

The partial differential equations have to be discretized by a numerical scheme. Typically in LSMs of CTMs, NWPMs, GCMs and ESMs the Crank-Nicholson-scheme sometimes in conjunction with GauB-Seidel-techniques are used (e.g., Kramm 1995). When using a Crank-Nicholson-scheme it is advantageous to introduce a logarithmic coordinate transformation into Eqs. (1) and (2) by E, = P ln(z/zD ) before integrating to apply equal spacing and central differences for well appropriate finite difference solutions. Here, zD is the lower boundary, and P is a constant which is to be chosen for convenience. Sensitivity studies showed that discretizing the partial differential equations by a type of Galerkin finite element scheme is advantageous for simulation of frozen soil physics (Narapusetty and Molders 2006).

In most LSMs of NWPMS and CTMs thermal conductivity is assumed to be either constant or parameterized by using McCumber and Pielke's (1981) empirical formula (see also Kramm 1995, Kramm et al., 1996)

With and Pf = 2 +10 log|. Many state-of-the-art LSMs of NWPMS, CTMs, GCMs and ECMs use this parameterizations or variations thereof. For soil-temperatures below the freezing point the LSMs of many NWPMs, CTMs, GCMs and ESMs assume a mass-weighted thermal conductivity depending on the amounts of liquid and solid volumetric water content present x=Xwn±xlBL (11)

n+ni

Here the indices w and i stand for the liquid and solid phase of soil-water. In doing so, either a fixed or calculated value of thermal conductivity for the liquid and a value of 2.31 J/(msK) or so is used for the solid phase.

Predicted soil-temperature is highly sensitive to the thermal conductivity of the soil. Molders and Romanovsky (2006) showed that the parameterization of thermal conductivity according to Eq. (4) provides much higher thermal conductivity values than typically found for permafrost soils; Eq. (4) also provides a decrease of thermal conductivity as the ground freezes, while observations typically indicate the opposite effect. In permafrost, thermal conductivity can be determined as Farouki (1981)

This formula is often applied in permafrost modeling (e.g., Lachenbruch et al., 1982, Riseborough 2002). Here, X>, X„(=0.57 W/(mK)), and Xi(=2.31 W/(mK)) are the thermal conductivity of dry soil, water, and ice, respectively. Typical values for Xs range between 0.06 and 0.25 W/(mK) (e.g., Pielke, 1984). In permafrost soils, typical values for X range between 0.7 and 2.4 W/(mK) (e.g., Romanovsky and Osterkamp 2000).

Since permafrost soil pores are typically totally ice-filled, Farouki's formulation does not consider the possibility of partially air-filled pores because permafrost soils are usually saturated. Freezing of soil-water, however, also frequently occurs in mid-latitude winter or deserts where soil-pores are often partially filled with air. Since in NWPMs, GCMs and ESMs have also to be able to predict soil-temperatures accurately under these conditions, Molders and Romanovsky (2006) enlarged the parameterization to include the impact of air

Here A,a(=0.025 W/(mK)) is the thermal conductivity of air. This formulation is consistent with Eqs. (1) to (3) that explicitly consider water vapor fluxes (third and first on the right side of Eqs. (1) and (2), respectively) and air (last term of Eq. (3)). It leads to Farouki's formulation in the case of permafrost soils that are usually saturated meaning (Hinkel et al.,

The empirical formulation with mass-weighted thermal conductivity values generally provides greater thermal conductivity values than Molders and Romanovsky's (2006) parameterizations (e.g., Fig. 5, their Fig. 3). These authors report that thermal conductivity calculated with Eq. (10) ranges between 0.292 and 5.745 W/(mK), while values of about 2.2 W/(mK) and 1.5 W/(mK) were observed in the deeper and upper soil. Using the modified version of Farouki's formula yields thermal conductivity values between 0.149 (uppermost layer after dry episode) and 1.52 W/(mK) with about 1.1 W/(mK) on average. Note that an uncertainty analysis using Gaussian error propagating techniques identified Eq. (10) as a critical source of errors in predicted soil temperature because the natural variance in empirical parameters (pore-size distribution index, saturated water potential, porosity) propagates to great uncertainty in calculated thermal conductivity (Molders et al., 2005). Uncertainty in parameters propagates less strongly when using the modified Farouki formula, for which parameter-caused statistical uncertainty in calculated thermal conductivity, soil temperatures, and soil-heat fluxes is lower than when using the mass-weighted formulation.

silt and some sand silt and some sand

0.2 0.4 0.6 0.8 1.0 relative volumetric water content

0.2 0.4 0.6 0.8 1.0 relative volumetric water content

Figure. 5. Thermal conductivity as obtained by Eqs. (10) and (12). Figures for other soil types show similar basic pattern

Since the phase transitions alter soil temperature by release or consumption of heat diagnosis of soil ice has to be solved iteratively. Typically a first-order Newton-Ralphson-technique is applied (e.g., Molders et al., 2003a).

NWPMs using multiple-layer soil models are, for instance, MM5 (Grell et al., 1994), WRF (Skamarock et al., 2005); GCMs and ESMs with multiple soil-layers are, for instance, the Community Climate System Model (CCSM) family, the ECMWF GCM and the Canadian GCM using CLASS (see also Table 1).

Hybrid Models

In hybrid soil models (Fig. 3), soil-wetness is determined by a force-restore-method (e.g., Deardorff 1978, Groß 1988, Schlünzen 1994, Jacobson and Heise 1982), while soil heat-fluxes and soil temperatures are calculated from a one-dimensional heat-diffusion equation (e.g., Claussen 1988, Groß 1988, Schlünzen 1994, Eppel et al., 1995). In these models, soil temperature layers typically differ from the two or three reservoirs used for soil moisture determination because the heat-diffusion equation is often solved for more than two or three layers to better capture the diurnal variation of soil temperature (e.g., Fig. 3). It is obvious that when soil temperature and soil moisture are calculated at different depths, permafrost hardly can be dealt with in this kind of soil model, for which they are not further discussed.

' ■

1 1 " I . I ' ' ■

clay organic matcr'als - +++4peat

• / 1

.++ +-++I+-+" 1 ■++l+"+

1 1 1 ■

Figure. 3. Dependence of maximum liquid water content on soil temperature for some selected soil-types. From Molders and Walsh (2004).

Vertical Resolution

In theory, fine soil-grid increments ensure accurate simulation of soil heat and moisture fluxes, temperature and moisture profiles. Unfortunately, global datasets of vertical distributions of soil type are not available. The of soil type and soil initial state data, and huge computational burden associated with a fine grid dictate the vertical grid resolution of soil models of CTMs, NWPMs, GCMs or ESMs. For reasonable turn-around times a compromise between efficiency and practical accuracy of soil-temperature is made. Modern CTMs and NWPMs typically use four to six (e.g., Smirnova et al., 1997, 2000, Chen and Dudhia 2001,

Skamarock et al., 2005, Grell et al., 2005, Molders and Kramm 2007), GCMs and ESMs about ten logarithmically spaced soil layers that cover a depth down to 2 to 3m (e.g., Bonan et al., 2002, Stendel and Christensen 2002, Dai et al., 2003). Obviously, the number and position of grid nodes plays a role in how accurately the active layer depth can be captures (Fig. 6).

Boundary Conditions

The Earth's surface is the only physical boundary condition in atmospheric models. While the soil surface is part of the lower boundary with respect to the atmosphere, it is the upper boundary with respect to the soil. The lower boundary of any soil, i.e. the bottom of a soil model, is an artificial one. Ideally, it is put at a level of nearly constant soil temperature and moisture in 20 or 30 m depths or so. Doing so is especially important in permafrost soils, where decadal soil temperature variations exist even below 15 m depth (e.g., Romanovsky et al., 1997, Molders and Romanovsky 2006). Most modern soil models used in atmospheric models have the lower boundary around 2 or 3 m depth (e.g., Kramm et al., 1995, Smirnova et al., 1997, 2000, Chen and Dudhia 2001, Dai et al., 2003, Molders and Walsh 2004). NWPMs and CTMs typically assume climatologic soil temperatures that vary monthly and spatially at the bottom of the soil model for at least a month. Doing so introduces artificial sources and sinks for heat and moisture (e.g., Stendel and Christensen 2002). A constant soil temperature, for instance, will act as a heat source (sink) if the actual temperature is lower (higher) at that depth. While this shortcoming may be of minor impact when regarded over the short integration times of NWPMs and CTMs and if the soil temperature is appropriately set (e.g., Narapusetty and Molders 2005), errors may accumulate over the long integration times (of at least 30 years=climate period) of GCMs and ESMs (Molders and Romanovsky 2006). Therefore, soil models of GCMs and ESMs usually assume constant soil moisture and heat fluxes at their lower boundary (e.g., Dai et al., 2003, Oleson et al., 2004). Most soil models of GCMs or ESMs assume zero-flux conditions at the lower boundary (e.g., Oleson et al., 2004, Nicolsky et al., 2007). However, various observations (e.g., Zhang et al., 1996, Romanovsky et al., 1997, Molders et al., 2003 a, b) show non-zero heat and moisture fluxes at 2 or 3 m, the depth typically used as the lower boundary in soil models of GCMs or ESMs. Therefore, Molders and Romanovsky (2006) performed simulations assuming zero-flux at 30 m depth where this assumption is generally fulfilled (see also Nicolsky et al., 2007). They found that a logarithmic grid-spacing with at least 20 layers is required to appropriately capture the diurnal cycle in the active layer (see also Fig. 6), the depth of the active layer, the annual soil temperature cycle, and the timing of thawing and freeze-up.

Heterogeneity Of Soil

Data from lysimeters filled with natural soil cores taken at the same site show evidence that the natural heterogeneity of soils may lead to notable differences in ground water recharge even on relatively short-term (Molders et al., 2003a, b). It is obvious that such differences also impact soil-moisture and temperature condition. Such heterogeneity, however, is of subgrid-scale with respect to any soil model, and hence, not considered.

Other heterogeneity stems from the spatial variability of soils. Typically grid-cells of NWPMs and CTMs cover areas of several square-kilometers, while those of GCMs or ESMs encompass several 100 square-kilometers. Obviously soil type may vary or be even different over these areas. In most NWPMs and CTMs, the soil-type dominating within a grid-cell is assumed to be the representative one for the soil conditions within that grid-cell. This means soil temperature and moisture as well as heat and moisture fluxes are calculated using the soil parameters of the dominating soil. It also means that in areas of discontinuous permafrost either permafrost soil or no permafrost soil is assumed in a grid-cell. In both cases the neglecting of heterogeneity may lead to great errors in predicted soil temperature and hence active layer depth (see Fig. 7).

1993

1994

1995

1996

1993

1994

1995

1996

230321 48 139230321 48 139230321 48 139230 Day of Year

_ simulated observed soil temperature (°C)

230321 48 139230321 48 139230321 48 139230 Day of Year

_ simulated observed soil temperature (°C)

1993

1994

1995

1996

1993

1994

1995

1996

230321 48 139230321 48 139230321 48 139230 Day of Year

_ simulated observed soil temperature (°C)

230321 48 139230321 48 139230321 48 139230 Day of Year

_ simulated observed soil temperature (°C)

Figure. 6. Comparison of soil temperature as simulated at Barrow, Alaska with HTSVS and observed.In (a) 20 layers and in (b) 13 layers are logarithmically spaced to a depth of 30 m. Modified from Molders and Romanovsky (2006).

2002/03

2002/03

Day of Year

simulated observed soil temperature (°C)

2002/03

simulated observed soil temperature (°C)

2002/03

Day of Year simulated observed soil temperature (°C)

Figure. 7. Comparison of soil temperature as simulated with HTSVS and observed at Yakutsk, Siberia. In (a) soil type varies with depth, while in (b) a constant soil type, namely that of the uppermost layer is assumed. Observation data from Levine (2007; pers. communication

Some research meteorological models consider subgrid-scale spatial heterogeneity of soils by some kind of mosaic approach or subgrid-scheme (e.g., Molders and Raabe 1996, Molders et. al 1996). Considering subgrid-scale heterogeneity of soils can lead several Kelvin differences in soil temperature as compared to the strategy of dominant soil-type.

In modern GCMs and ESMs, the fact that soil type may vary horizontally in space is typically considered by some kind of mosaic or TOPMODEL approach (e.g., Dai et al., 2003, Essery et al., 2003, Oleson et al., 2005, Nui et al., 2005). Herein soil temperature and moisture conditions are determined for the various horizontal patches of different soil-type. The grid-cell soil temperature and moisture are then derived as an area-weighted average of the soil-temperatures of the various patches within the grid-cell.

Most modern soil models of NWPMs, GCMs and ESMs assume one soil-type for the entire soil column (e.g., Slater et al., 1998, Schlosser et al., 2000). Typically the uppermost soil-type is chosen to be representative for the entire soil column. The main reason is the lack of 3D-soil characteristic data. Nevertheless, some soil models of NWPMs (e.g., HTSVS in MM5) permit the user to consider vertical heterogeneity of soil for process research studies, rather than for general use in forecasts. Many soil models of modern GCMs or ESMs also are designed for consideration of vertically differing soil types, but basically make no use of the possibility due to the lack of 3D global distributions of soil-data. Examinations show that simulations without consideration of vertically varying soil characteristics miss many details in soil temperature and moisture patterns that result from the vertical profile of soil parameters (see Fig. 7). Mölders and Romanovsky (2006) found that even in the uppermost layer where the soil-type is the same, RMSEs between simulated and observed soil temperatures increased on average up to 0.3 K as compared to simulations with consideration of a vertically varying soil characteristic profile; moreover, simulations ignoring vertical soil characteristic profiles yield significantly different soil temperature variance than those considering it. Neglecting vertical soil characteristic profiles may yield to errors in predicting active layer depth and the timing of thawing and freeze-up of the active layer (e.g., Fig. 7).

Initialization Problem

One major problem is the initialization of soil moisture and temperature in NWPMs and CTMs. Unfortunately, global datasets of vertical distributions of soil temperature and moisture conditions do not exist.

In NWPMs and CTMs, usually the soil moisture and temperatures states obtained from the previous forecast are used as initial values for the following forecast. This procedure violates the assumption used to simplify the equations, namely that horizontal heat and moisture fluxes within the soil are negligibly small. In nature as in the model, mountains usually receive more precipitation than valleys (e.g., Müller et al., 1995). In nature, runoff on the short-term and lateral soil water fluxes on the long-term lead to moister valleys than mountains (except for glaciers where water is stored in the solid phase). Consequently, when initializing NWPMs and CTMs as described before the neglecting of lateral soil water fluxes leads to too high soil moisture in mountainous regions and too low moisture in the lower elevated terrain. In weather forecasts, these errors yield to incorrect prediction of local recycling of previous precipitation and hence wrong forecasts of convection, showers, and thunderstorms (e.g., Mölders and Rühaak 2002). In permafrost regions, some of the permafrost exists in the valleys and is fed by runoff from the mountains, i.e. in such cases cannot be appropriately captures due to the initialization method. These errors can be avoided by either inclusion of horizontal moisture transport (3D soil model), or coupling/using the soil model with a hydrological model (e.g., Mölders and Raabe 1997, Mölders et al., 1999, Mölders 2001, Walko et al., 2000, Mölders and Rühaak 2002).

Being aware that lateral soil-water movements may be important on longer time scales, in the nineties several authors (e.g., Kuhl and Miller 1992, Marengo et al., 1994, Miller et al., 1994, Sausen et al., 1994, Hagemann and Dümenil 1998) introduced parameterizations of different complexity to consider runoff in GCMs. Some kind of TOPMODEL-approach (e.g., Beven and Kirkby 1979) considers soil moisture heterogeneity (e.g., Dai et al., 2003, Essery et al., 2003, Nui et al., 2005) and permits also for consideration of discontinuous permafrost. GCMs and ESMs typically initialize soil temperature and moisture states homogenously worldwide and run the soil model with the forcing of one year for several centuries until an equilibrium soil state distribution is established.

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