Introduction

At high latitudes and at high altitude of mountainous terrain, permafrost (defined as soil in which temperatures remains continuously at or below freezing point for, at least, two consecutive years) and the active layer (which thaws seasonally) are the primary subsurface components of the land-atmosphere system. Permafrost restricts the mobility of soil-water, and infiltration. Thus, capillary action, infiltration, and percolation are rather inefficient in permafrost. An important aspect of permafrost is the local temporal equilibrium between the ice, gaseous, and liquid phase of water within the soil. Any changes in heat diffusion and conduction caused by a change in snow thickness, insolation at the soil surface or infiltration affect all three water phases in the soil and soil temperature simultaneously. Any change in soil temperature results in freezing, thawing, sublimation or water vapor deposition and a release of latent heat or consumption of energy, again altering soil state variables (soil temperature, soil volumetric liquid water, ice and water vapor content) and fluxes (e.g., soil heat flux, soil water flux, soil water vapor flux). Thus, freeze-thaw cycles affect the thermal and hydrological properties of soil because of the release of latent heat and consumption of energy accompanied with phase transition processes.

Ice changes the dynamics of soil thermal fluxes through the dependence of soil volumetric heat capacity and thermal conductivity on soil volumetric water and ice content. The specific heat capacity of water is twice that of ice and the thermal conductivity of ice exceeds that of water about four times.

Regions with permafrost are characterized by low winter air-temperatures, low saturation pressure of water vapor and frequently stable stratification of the atmospheric surface layer. All these conditions lead to low evaporation. Consequently, soil moisture remains stored in the frozen active layer. Thus, in spring the capacity of the soil to take up additional water will be limited even if some of the soil already thawed. In consequence of all these, this means that permafrost may enhance spring peak flood events (Cherkauer and Lettenmaier 1999). In summer, transpiration and evaporation depend on the active layer depth, soil and vegetation type as well as on meteorological conditions.

The hydrological and thermal surface conditions associated with permafrost and the active layer affect the near-surface atmosphere, and hence weather and climate, by the exchange of heat, moisture, and matter at the soil-atmosphere interface (e.g., Stendel and Christensen 2002, Molders and Walsh 2004). At the same time, the active layer depth is sensitive to weather; on the long-term, permafrost temperature and stability and active layer depth are sensitive to climatic change (e.g., Kane et al., 1991, Lawrence et al., 2006, Molders and Romanovsky 2006). Permafrost thawing not only can cause huge economic and infrastructure damages and ecosystem changes, it also releases water and trace gases; the related changes in trace gas and water cycle and ecosystems again can feedback to climate. (e.g., Esch and Osterkamp 1990, Cherkauer and Lettenmaier 1999, Oechel et al., 2000, Serreze et al. 2000, Romanovsky and Osterkamp 2001, Zhuang et al., 2001). The coupling between soil moisture and thermal processes is fundamental to high-latitude soil irritations. Therefore, this coupling has to be considered appropriately in numerical weather prediction models (NWPMs) to capture the annual soil-temperature cycle and 2m-temperatures in winter (e.g., Viterbo et al., 1999). For all these reasons permafrost, permafrost dynamics, and soil-

water freezing and soil-ice melting have also to be considered in climate and earth system modeling and for climate impact assessment.

Apparently permafrost variations have yet to receive a concerted effort within the context of global climate and earth system modeling. Recently, Luo et al. (2003) examined the performance of 21 modern land-surface models (LSMs) using their standalone versions and soil temperature observations along with fluxes and snow data from the 18-year Valdai dataset, a site without permafrost, but with regularly frozen ground in winter. Their study revealed that explicit inclusion of soil-water freezing and soil-ice melting improves the prediction of soil temperature and its seasonal and inter-annual variability. To appropriately represent the heat, moisture, and matter exchange at the soil-atmosphere interface, modern NWPMs, General Circulation Models (GCMs) and Earth System Models (ESMs) require suitable LSMs to simulate frozen ground and permafrost dynamics. For GCMs and ESMs such LSMs are indispensable for investigations of permafrost-climate feedbacks. ESMs also need to consider permafrost dynamics for examination on climate-permafrost-ecosystem change feedbacks.

Over the last decades geologists and geophysicists have developed site-specific permafrost models for investigation of permafrost dynamics (e.g., Goodrich 1982, Nelson and Outcalt 1987, Kane et al. 1991, Romanovsky and Osterkamp 1997, Smith and Riseborough 2001, Zhuang et al. 2001, Ling and Zhang 2003). Due to their fine vertical grid increments (<0.05 m) these kinds of permafrost models usually consume huge amounts of computational time. Since investigations of permafrost dynamics are typically oriented at decades or even centuries and the geological processes associated with changes in permafrost distribution are relatively slow, these kind of models typically run at large time steps (Molders and Romanovsky 2006). Furthermore, most permafrost models are site-specific and calibrated (e.g., Romanovsky et al. 1997, Osterkamp and Romanovsky 1999, Romanovsky and Osterkamp 2001), i.e. new data have to be collected for calibration when they are supposed to be applied elsewhere (Molders and Romanovsky 2006). Such calibration involves that the majority of available data at a site serves to determine optimal soil-transfer parameters, leaving the rest of data for model evaluation.

Applying a typical calibration technique certainly would lead to better predictions than those that are typically obtained with soil models designed for use in NWPMs, GCMs or ESMs. However, performing such a calibration technique for these models would require consistent soil temperature data for calibration for the typical domains of NWPMs and worldwide for GCMs or ESMs. As of today no such dataset exists making usage of calibrated permafrost models in NWPMs, GCMs or ESMs technically impossible. Furthermore, it has yet to be determined whether calibration coefficients may be climate sensitive. Coupling a permafrost model with a NWPM, GCM or ESM would also be a challenge because NWPM, GCM or ESM simulations require input of water and energy fluxes to the atmosphere at time steps of less than a minute to several minutes; consequently any vertically highly-resolved permafrost model would have to be run with this time-step making such coupled simulations computationally unattractive and in the case of weather forecasting even prohibitive. For all these reasons, the weather forecast, climate and earth system modeling communities do without calibration. They instead have developed various physically based concepts for predicting permafrost, active layer and soil frost processes. In doing so, knowledge and well-accepted concepts from permafrost and atmospheric sciences have been combined to build suitable soil models considering frozen soil physics for use in NWPMs, GCMs and ESMs.

All modern numerical NWPMs, GCMs and ESMs apply soil models embedded in their LSMs to simulate the thermodynamic and hydrological surface forcing (e.g., temperature, specific humidity, fluxes of water vapor and sensible heat) at the soil-atmosphere interface. The atmospheric scientific community has developed these soil models based on the best knowledge, and spent great efforts to evaluate and improve them (e.g., Yang et al. 1995, Shao and Henderson-Sellers 1996, Lohmann et al. 1998, Dai et al. 2003, Molders et al. 2003a). Incomplete knowledge of soil type and heterogeneity as well as soil initial conditions generally limits the predictability of the soil state, fluxes of heat, trace gases, water vapor, and water, and phase-transition processes within the soil and at the atmosphere-soil interface. Further errors in simulating soil conditions and fluxes result from the necessity to parameterize sub-grid scale processes, prescribe soil physical parameters, discretized partial differential equations and incorrectly simulated forcing (e.g., precipitation rate and amount, insolation).

In the following, the theory of soil physics, history and current state of modeling soil physics in atmospheric sciences is reviewed and evaluated; error sources for simulated permafrost quantities are discussed.

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