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 Freezing and thawing front (FTF) depths have implications for surface and subsurface exchanges of energy and water, vegetation growth and organic matter decomposition. Long-term changes in FTF depths are an important indicator of climate change. The FTF is seldom represented explicitly in land surface schemes, but the 0°C isotherm is used as a surrogate for the front. However, when multiple FTFs occur within a soil column or when soil temperature hovers around the freezing point in the spring, the simulated 0°C isotherm exhibits large fluctuations though in reality, the fronts develop rather smoothly. To explicitly simulate the FTF depths, this study couples a Two-Direction Stefan Algorithm (TDSA) in the Community Land Model 3 (CLM3). Several modifications are also introduced to adapt the CLM3 to the northern region, including the addition of a peat cover to the soil column, retention of a minimum unfrozen water content in the frozen soil, and implementation of canopy heat storage. The modified scheme was tested using field data from a boreal forest site. The TDSA enables the simulated FTF to be defined properly. Sensitivity tests demonstrate that the modified scheme (addition of a peat cover, unfrozen water and canopy heat storage) greatly improves the match between the simulated fronts and the 0°C isotherm derived from measured soil temperatures. These modifications and the coupling of the TDSA are applicable to other lands surface schemes for the simulation of ground frost in the cold regions.
 Freezing and thawing fronts (FTFs) separate the frozen and the unfrozen segments of a soil column. Frozen soils may have limited infiltration capacity, encouraging the generation of large runoff during the spring snowmelt. Shanley and Chalmers  found that the ratio of snowmelt runoff to the sum of snowmelt and rainfall is correlated with the seasonal maximum frost depth in an agriculture basin. Change in FTF depth affects ecosystem carbon cycling. Goulden et al.  found that at an old black spruce forest site in Manitoba, Canada, organic matter decomposition rate in unfrozen soil was ten times higher than in frozen soils. The increase in soil respiration rate during mid-summer was explained by an increased thaw depth. Changes in FTF depths are also an important indicator of climate change [Frauenfeld et al., 2004]. In recent years, disproportionate and rapid warming has been observed in high latitudes [Berner et al., 2005]. Continued warming is projected by global climate models for different scenarios of greenhouse gas emission [Houghton et al., 2001]. Accurate simulation of FTFs allows an assessment of permafrost degradation which has significant implications for the integrity of northern infrastructures.
 FTF depths can be interpolated from measured or simulated soil temperatures [Flerchinger and Saxton, 1989; Frauenfeld et al., 2004; Kennedy and Sharratt, 1998], using the 0°C isotherm as the surrogate for the front. However, this isotherm usually exhibits large fluctuations during autumn freezing and spring snowmelt periods when soil temperature hovers around the freezing point. Zhang and Lu  used the fraction of liquid water and ice content in the soil column to determine the position of freezing front but difficulties arise when both freezing and thawing fronts coexists within the same soil layer. The Stefan's equation has been successfully used for simulating FTF depths. Fox  and Li and Koike  used the equation to calculate ground freeze or thaw using near-surface temperatures. Woo et al.  extended the application by implementing a Two-Directional Stefan Algorithm (TDSA), using near-surface and deep soil temperatures as the forcing variables. They used TDSA in a standalone mode, but the algorithm can be coupled to land surface schemes to accurately predict FTF depths. One such scheme is the Community Land Model version 3 (CLM3) used in the Community Atmosphere Model (CAM) and in the Community Climate System Model (CCSM) [Oleson, 2004]. CLM3 has sophisticated soil parameterization with the soil column divided in 10 logarithmic layers. Thickness of upper soil layer is about 1.75 cm while the bottom layer is about 114 cm. However, CLM3 does not consider organic or peat soil layers which are commonly found in subarctic soils. This omission may limit accurate simulation of heat and water exchanges in most soils of the high latitudes. Canopy heat storage is also absent in the default CLM3 and this can lead to a warm bias that produces rapid snow melt. Initial tests further indicated that snow depth is underestimated by the model, resulting in excessively low winter soil temperatures. In order to simulate ground freeze-thaw in a high latitude environment, this study introduces several modifications in the CLM3 to improve the simulation of soil freeze-thaw processes.
2. Study Site
 The southern old black spruce forest site, hereafter known as SOBS (53.98 °N, 105.12 °W) is located about 100 km northeast of Prince Albert, Saskatchewan, Canada. SOBS was established under the Boreal Ecosystem Atmosphere Study (BOREAS) and was continuously monitored under Boreal Ecosystem Research and Monitoring Sites (BERMS) and Fluxnet Canada Research Network (FCRN) initiatives. Black spruce forests are an important northern ecosystem, accounting for more than 70% of the boreal forest cover in North America. They contain a large amount of soil organic matter so that its decomposition under warmer temperatures may significantly impact the carbon balance of the boreal region. Table 1 shows the key SOBS parameters used in CLM3 which is driven by atmospheric forcings that include incident solar radiation, air temperature, wind speed, precipitation and humidity, all of which are measured at the SOBS site.
Table 1. List of Site Characteristics of SOBS
Leaf Area Index
Stem Area Index
3. Modifications to the CLM3
 We implemented TDSA into CLM3 as a diagnostic tool. Daily simulated soil temperature and moisture are passed to TDSA to calculate depths of the freezing and thawing fronts. Based on the position of FTF we construct a new soil array in TDSA, termed the combined layers (i.e., frozen and unfrozen layers). The number of frozen and unfrozen layers depends on the number of FTFs. For example, if there are one freezing and one thawing front in the second soil layer, then this layer is split into three layers and the total number of combined soil layers will be the number of original layers plus the number of fronts and two additional dummy layers. Dummy layers are reserved for new FTFs created from both the top and the bottom of a modeled soil column.
 Each new layer is assigned a set of properties for their frozen and unfrozen states and the thickness and position of FTFs. Soil porosity and dry thermal conductivity of the combined layers are kept the same as the original CLM3 soil layers. If the temperature of original soil layer in CLM3 is lower or higher than the freezing point, the thermal state of the corresponding combined soil layer in TDSA is updated accordingly. Based on the thickness and state of the combined soil layers, the ice and liquid water content of each soil layer are also updated.
 The Stefan's algorithm is applied to the combined soil layers from the top, following steps 2 to 6 in the work by Woo et al. . If a new freezing/thawing front passes through certain combined layers, then all these layers are changed to frozen/unfrozen state. If any adjacent combined layers have the same thermal state and are from the same original CLM3 soil layer, these layers are combined and properties of this new layer are reassigned. If a combined layer does not freeze or thaw completely, this combined layer will be split into two. Properties are calculated for these two layers based on those of the split layer. Next, the Stefan's algorithm is applied to the combined soil layers from the bottom in the same manner as that from the top. After the thermal states of the combined soil layers are updated, the FTF depths are derived. From top to bottom, the interface of frozen and unfrozen layer is the freezing front, or the interface of unfrozen and frozen layer is thawing front. There is no restriction on the number of FTFs being created in the combined soil layers in the TDSA and model can capture multiple freeze and thaw cycles.
 In addition to the TDSA, an organic/peat cover is added to the soil column in CLM3, following Letts et al. . Canopy heat storage capacity is also formulated following Niu and Yang . Depending on soil texture, unfrozen water can occupy up to 10% of soil by volume [Farouki, 1986]. In this study it is specified as 5%, a value obtained from field data of SOBS. However, Niu and Yang  have developed a physically based and more sophisticated frozen soil scheme in CLM3.
 Performance of the modified CLM3 model was evaluated in a boreal black spruce forest from 1999 to 2005 by performing sensitivity tests to assess the effects of these modifications, and by comparing the simulated results with the observed snow, soil moisture and ground thermal regimes.
4.1. Sensitivity Study
 Several experiments were performed, using meteorological data from SOBS as inputs, to investigate how the introduced modifications affect the performance of CLM3. They include (i) Run 1, using the default sandy/clay soil profile (ii) Run 2 with a 30-cm peat on top of the mineral soil, (iii) Run 3, using the same profile as Run 2 but with a minimum of 5% unfrozen volumetric water content in the frozen soil, and (iv) Run 4 which is the same as Run 3 but adding a canopy heat storage. Figure 1 shows all the simulated FTFs and the measured 0°C-isotherm for 1999–2000. A cumulative frost thickness measure (CFT, in meter-day) is introduced to indicate the annual frostiness of the soil:
where FTi is thickness of frost for day i, for i = 1,365 days. Table 2 lists the CFT and the annual maximum frost depths (MFD) for the test runs and from the observed data, for the periods September 1999 to August 2004.
Table 2. Cumulative Frost Thickness (CFT) in Meter-Day and Maximum Freezing Front Depth (MFD in cm; in Parentheses) for Different Test Runs
 Run 1 usually overestimates the maximum freezing front depth (MFD) for all five simulation years as compared with the position of the observed 0°C isotherm. Simulated MFDs for Run 1 are 84, 96, 136, 152, and 65 cm for 1999–2004, respectively, compared to the observed depths of 40, 30, 55, 75, and 38 cm. The addition of a peat cover significantly improves the simulation of MFD. For example in 2000–2001, MFD decreases from 96 cm for default Run 1 to 29 cm for Run 2 (Table 2). Inclusion of 5% unfrozen soil water in Run 3 further improves the model performance. Table 2 indicates that the simulated MFDs and FDTs are smaller for Run 3 than for Run 2, producing a better agreement with observation. The default version of CLM3 does not provide for canopy heat storage, resulting in excessive heat transport to the upper soil/snow layers. This causes rapid melting of snow and hence thinner simulated snow depth than observed. Implementation of canopy thermal (heat) capacity improves the simulated soil thermal and hydrologic regimes as well as the depths of snow and ground frost (Table 2).
4.2. Improvement of FTF Simulation
 The TDSA provides a clear definition of the FTFs. Figure 2 is an example taken from the Run 4 simulation for 2002–03. It compares the simulated freeze-thaw fronts before (represented by the 0°C isotherm) and after the TDSA was applied (represented by the dots). The 0°C isotherm shows large fluctuations in March and April as latent heat is released by the refreezing of percolated snow meltwater to raise the soil temperature around the freezing point. Although the soil layers were still frozen during these periods, the freeze-thaw state cannot be depicted by the 0°C isotherm. This problem, common for all years, is overcome by the application of the TDSA to generate a gradual but realistic development of the FTF.
 Another drawback of the 0°C isotherm is related to the thickness of the soil layers specified by the model, as evidenced between January and March 2003. The 0°C isotherm remains at 40 cm for a protracted period (January to mid-February), and then suddenly descends to 62 cm, followed by unchanged depths until the end of March. This is because the model recognizes an entire layer to be either frozen or thawed. The situation is exacerbated for deeper layers as their thickness increases exponentially with depth. This problem is resolved by adding the TDSA to CLM3 to refines the FTF depths, thus eliminating the jumps produced in the simulations.
 The modified CLM3 was tested by performing five years of simulation and comparing the results with observed snow depth, surface soil temperature, root zone soil moisture, and the 0°C isotherm. For illustration purpose, only the results for years with the shallowest (2000–01) and deepest frost penetration (2002–03) are presented (Figure 3). Simulated snow depth compares well with observed snow depths for both years. Simulated volumetric soil water content (liquid) follows the seasonal variation measured by TDR probes. Simulated temperature for the top layer compares well with observation, except for a warm bias of several degrees for a short period in December 2000. Observed FTF depths are not available, therefore the 0°C isotherm is plotted instead. The simulated and observed maximum frost depth and frost duration are in agreement. The observed freezing isotherm tends fluctuate widely during the snow melt period (e.g., March of 2001, April and May of 2003) due to infiltration of snow meltwater into the frozen soil.
 These model tests demonstrate that the incorporation of an organic layer, the retention of some unfrozen water in the frozen soil and canopy heat storage capacity formulations in the CLM3 significantly improved its performance to simulate soil temperature, soil moisture, snow depth and freeze and thaw front depths.
 Most land surface schemes do not yield freezing and thawing fronts (FTF) explicitly as one of their outputs. This study implemented an algorithm in CLM3, a scheme used in the NCAR global climate model, to simulate the position of the FTFs using soil temperature and moisture modeled by CLM3 as inputs to the TDSA (two-directional Stefan's algorithm). The TDSA enables the frozen and thawed soil boundary to be distinguished, thus eliminating the difficulty of representing the fronts by the 0°C isotherm which shows much fluctuation during the snowmelt period, and which produces large jumps when freeze-thaw reaches the deeper layers (because layer thickness increases exponentially with depth in the CLM3).
 The soils in many northern regions have a peat layer but this feature is not accounted for in CLM3. Furthermore, canopy heat capacity is ignored and unfrozen water is absent in all frozen soils. Sensitivity experiments indicate that the absence of peat, the lack of canopy heat storage and the absence of unfrozen water can exaggerate soil thermal response to atmospheric forcing, leading to an overestimation of freeze-thaw depths. Modifications are added to CLM3 to rectify these shortcomings and the modified version was tested in a black spruce boreal forest site using five years of measured data. Results show a good match between the simulated and observed freeze and thaw front depths. From this study, we conclude that the organic soil cover, unfrozen water in the soil, and canopy heat storage are critically important to the modeling of freeze-thaw in the northern environment. It is unrealistic to project permafrost thaw if simulations are performed without proper attention to these factors.
 This study was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Mackenzie GEWEX (Global Energy and Water Cycle Experiment) Study and NSERC, Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) and Biocap Canada Foundation funded Fluxnet-Canada Research Network (FCRN). Observed data from BERMS initiatives are also acknowledged.