The freezing and thawing of the active layer of soil in the Arctic terrestrial drainage basin is simulated using a one-dimensional heat conduction model. Main forcing data are surface air temperature and snow thickness. Emphasis is placed on producing a topography-improved temperature data set from National Centers for Environmental Prediction (NCEP) reanalysis data, and a snow height data set compiled from SSM/I satellite data and observed climatological snow density. Soil bulk density, soil type and its relative composition are derived from the SoilData System of the IGBP-DIS. The model is run with 25 km × 25 km resolution and daily time steps for the period September 1998 through December 2000. We compare modeled thaw depths and active layer depths with those measured at Circumpolar Active Layer Monitoring (CALM) field sites. This study shows for the first time the highly variable daily thaw depth over permafrost and seasonally frozen ground depth in nonpermafrost areas, as well as freezing and thawing periods for the whole pan-Arctic landmass.
 Significant atmospheric and terrestrial changes have occurred in the Arctic and Sub-Arctic in recent decades [Serreze et al., 2000]. The hydrologic cycle in the Arctic land-atmosphere-ocean system is central to these observed changes. However, current understanding of the Arctic hydrologic system remains incomplete because of the complexities of permafrost terrain, difficulties in acquiring field data in harsh environments, the decline in routine monitoring of temperature, precipitation and river discharge, and a relative lack of interdisciplinary research [Vörösmarty et al., 2001].
 The hydrology community has long recognized the importance of permafrost and the freeze-thaw cycle of soils. Approximately 80% of the land in the Arctic drainage basin is underlain by permafrost [Brown et al., 1997; Zhang et al., 1999] and the remaining area experiences seasonal freezing. Freezing of soil moisture reduces the hydraulic conductivity, leading to either more runoff due to decreased infiltration or higher soil moisture content due to restricted drainage. The existence of a thin frozen layer near the surface essentially decouples soil moisture exchange between the atmosphere and deeper soils. Knowing whether the soil is frozen is important in predicting surface runoff and the spring soil moisture reserve [Willis et al., 1961; Cary et al., 1978]. The active layer is a stratum of soil or other Earth material above permafrost that experiences freezing and thawing on an annual basis. Changes in active layer thickness directly affect groundwater storage and river discharge through partitioning surface runoff [Kane et al., 1991; Kane, 1997; Kane and Reeburgh, 1998; Brown et al., 2000]. Permafrost limits the amount of subsurface water storage and infiltration that can occur, leading to wet soils and ponded surface water, unusual for a region with limited precipitation. Active layer thickness and permafrost conditions are largely controlled by the surface heat balance, coupling hydrology to the surface energy balance so closely that they cannot be quantified separately [Vörösmarty et al., 2001].
 In this study we simulate the highly variable thaw depth (DT) over permafrost, seasonally frozen ground depth (DF) in nonpermafrost areas, and lengths of freezing and thawing periods for the whole pan-Arctic landmass. This effort represents a contribution to Arctic-RIMS (Rapid Integrated Monitoring System for the pan-Arctic Landmass), which brings data sets and techniques together to provide readily accessible hydrologic products. Arctic-RIMS is a collaborative effort between University of Colorado, University of New Hampshire, Ohio State University, and the Jet Propulsion Laboratory. Data and more information is available from the Arctic-RIMS web page at http://rims.unh.edu.
1.1. Previous Work
 Active layer studies have a relatively long history in the Arctic and Sub-Arctic. In the early 1960s, a comprehensive field investigation on tundra ecosystems was conducted at Barrow, Alaska by Brown and Johnson . They initiated a systematic study of active layer processes, with emphasis on monitoring thaw depth. Their approaches have been widely adopted in the Circumpolar Active Layer Monitoring (CALM) program. The CALM program was initiated in the late 1980s to observe and understand the response of the active layer and near-surface permafrost to climate change. It currently incorporates more than 100 monitoring sites involving 15 investigating countries [Brown et al., 2000]. The CALM network is part of the Global Terrestrial Network for Permafrost (GTN-P) of the World Meteorological Organization (WMO).
 A network of eight instrumented deep boreholes in European mountains from Svalbard to the Sierra Nevada has recently been established within the PACE program (Permafrost and Climate in Europe) [Harris et al., 2001]. Near-surface atmosphere–active layer–permafrost heat fluxes over seasonal to decadal timescales are monitored at additional shallower (10–20 m) boreholes. Hoelzle et al.  used measurements of surface net radiation, sensible and latent heat fluxes, and heat conduction to model lateral heat transfers that are important for mountain permafrost.
Hinzman et al.  demonstrated that site hydrology is a key factor in determining thaw depth. Zhang et al.  illustrated that active layer thickness, in general, increases with a thawing index in northern Alaska. The general validity of this relationship is supported by other studies [e.g., Romanovsky and Osterkamp, 1997; Nelson et al., 1998a; Brown et al., 2000; Klene et al., 2001]. Pavlov and Moskalenko  describe a cooling effect of shallow ground vegetation on soil during early summer and a delay in the onset of thawing. They also report that for northwestern Siberia, the response of permafrost temperature to climate warming is more pronounced than the response of soil seasonal thawing, primarily because of changes in the snow insulation effect.
 Modeling efforts to understand freezing and thawing processes of soils have primarily focused on one-dimensional process studies. Nakano and Brown  developed a one-dimensional heat conduction model with a finite freezing zone, which considers the effect of unfrozen soil water content on the thermal regime of the active layer and permafrost. This model was subsequently validated against field data and used to investigate the thermal processes of soils at Barrow, Alaska [Nakano and Brown, 1972]. Outcalt et al.  developed a numerical model simulating the snowmelt and soil thermal regime through the surface energy balance. A spatially distributed thermal model was developed by Hinzman et al.  for the Kuparuk river basin in Alaska. They distributed measured soil thermal properties for five typical vegetation units on the basis of a regional vegetation map. Goodrich [1982a] presented a detailed study of the effect of snow cover on long-term, periodic, steady state equilibrium ground temperatures. Goodrich's results show that calculated mean annual ground temperatures are extremely sensitive to the assumptions made in treating the snow cover. Zhang et al.  modified Goodrich's treatment of the seasonal snow cover by including a physical treatment of wind slab and depth hoar layers within the snowpack. The modified model was used to investigate the impact of snow cover on the soil thermal regime in northern Alaska.
 Although in situ measurements and numerical modeling provide valuable data and information on site-specific factors controlling seasonal freezing and thawing processes and active layer thickness, there are severe and perhaps intractable problems in characterizing variability at high resolution over large areas [Nelson et al., 1997]. Attempts have been made to map active layer thickness using visible and near-infrared satellite remote sensing data [Hall, 1982; Gross et al., 1990; Peddle and Franklin, 1992; Leverington and Duguay, 1996]. Such approaches require that the relationship between permafrost and its environmental factors is known in each area. This requirement limits the application to a few areas where intensive ground-based measurements are available for algorithm tuning.
 Microwave remote sensing data have been used to detect near-surface soil freeze-thaw status over large areas [Zuerndorfer and England, 1992; Chang and Cao, 1996; Judge et al., 1996; Kimball et al., 2001; Zhang and Armstrong, 2001]. Freeze/thaw algorithms from Special Sensor Microwave/Imager (SSM/I) radiometer brightness temperatures (TB) use a negative spectral gradient between TB (37V) and TB (19V) together with a cutoff brightness temperature at 37 GHz and vertical (V) polarization. Active microwave data are also sensitive to the freeze/thaw transition over broad landscapes because of marked differences in surface dielectric properties and radar backscatter [Rignot and Way, 1994; Way et al., 1997]. ku-band data from the NASA Scatterometer (NSCAT), that operated from 1996 to 1997, have been used to map daily surface freeze/thaw state at a 25-km resolution across Alaska and Canada [Frolking et al., 1999]. However, the penetration depth of microwaves is limited to a few centimeters of soil at maximum.
Nelson et al.  mapped weekly thaw depths for the summer of 1995 over the Kuparuk river basin on the North Slope of Alaska. They used a simplified Stefan solution [Hinkel and Nicholas, 1995] to estimate thaw depth based on a land-cover map, a digital elevation model, and a topoclimatic index using spatial analytic techniques including geographic information systems technology. They caution against extrapolating results based on point measurements to larger regions, especially for complex terrain. Recently, Shiklomanov and Nelson  presented a 13-year time series (1986–1999) of active layer depth and active layer volume for four landcover categories within the same region.
 Several studies have shown that active layer depth is highly variable both temporally and spatially [e.g., Nelson et al., 1998b, 1999; Gomersall and Hinkel, 2001; Anisimov et al., 2002]. Air temperature, snow depth and summer rainfall cause interannual variations whereas spatial variability is a function of soil properties, water/ice content, and vegetation. Nelson et al. [1998b] used spatial autocorrelation analysis to map variability on 1 km2 grids in northern Alaska. Temporally and spatially coherent patterns of thaw depth associated with topographic features of the soil moisture regime dominate the coastal plain. A sampling distance of 100 m is not sufficient to capture the scale of active-layer variability for the foothills, which occurs over distances of 30 m and less. Nelson et al.  found the largest variations in active layer depth of the coastal plain in the 100–300 m range, whereas for the foothills this value is 1–3 m. Gomersall and Hinkel  suggest that samples in the coastal plain be taken at 10 m intervals, and in the foothills at 1 m intervals. This sampling density would account for 60% of the variation within the 1 km2 plots.
Anisimov et al.  used a stochastic model together with a high-resolution vegetation map and statistical properties of local active-layer variability at several test sites in northern Alaska. For the 1995–1999 time period they derived the probability of active layer depth at 1 km × 1 km resolution for four depth ranges over the Kuparuk river basin.
 A semiempiric method was applied by Anisimov et al.  to estimate active layer depth of the circum-Arctic region. They used mean annual air temperature and its annual amplitude, modified by factors for snow and vegetation. Further parameters include snow cover thickness and density, and a mineral and an organic soil layer with adjustable thermal properties. Maps of maximum annual thaw depth are derived by assuming that all permafrost regions consist either of sand, silt, or peat, and have either low or high soil water contents.
 Our study uses a highly modified version of the one-dimensional Goodrich model, described in section 2, to simulate the soil thermal regime on a daily basis for the whole pan-Arctic landmass at 25 km × 25 km resolution. Forcing parameters (section 3) include daily surface air temperature, snow height and soil moisture content, used together with static fields of soil bulk density and soil type at different depths, peat concentration, and snow density.
1.2. Study Area
 The area of interest is the Arctic drainage (Figure 1), defined as land areas emptying into the Arctic Ocean, Hudson Bay, James Bay, Hudson Strait and the Bering Sea. This domain is used for all Arctic-RIMS spatial fields. It is defined in terms of nodes of the National Snow and Ice Data Center (NSIDC) north polar Equal-Area Scalable Earth (EASE) grid [Armstrong and Brodzik, 1995]. The domain comprises 39,926 grid cells with 25 km × 25 km resolution. With an area of 25.1 × 106 km2 it encompasses 77.6% of all permafrost regions and 96.1% of continuous permafrost regions in the Northern Hemisphere. Almost half of the Arctic drainage (42.5%) is underlain by continuous permafrost (Figure 1b), as defined by the International Permafrost Association (IPA) [IPA, 1998; Brown et al., 2000]. A further 10.6% of the drainage is classified as discontinuous permafrost, and 17.6% is sporadic and isolated permafrost. Nonpermafrost or seasonally frozen ground in the southernmost regions of the Arctic drainage area makes up 20.8%, and ice sheets, glaciers, and lakes cover the remaining 8.5% of the domain.
2. Model Description
 A finite difference model for one-dimensional heat conduction with phase change [Goodrich, 1982a] is used. This model has been shown to provide excellent results for active layer depth and soil temperatures [Zhang et al., 1996; Zhang and Stamnes, 1998] when driven with well-known boundary conditions and forcing parameters at specific locations. A detailed description of the model is given by Goodrich [1982a], Zhang , and Zhang et al. , and only a brief summary is included here. Our intent is to model soil freeze/thaw state for the entire Arctic drainage area. We still run the model one-dimensionally and assume no lateral heat transfer among the 25 km × 25 km grid cells.
 Soil is divided into three major layers (0–30 cm, 30–80 cm, and 80–1500 cm) with distinct thermal properties for frozen and thawed soil, respectively (see section 3.3). Calculations are performed on 54 model layers ranging from a thickness of 10 cm for the top 80 cm of soil to 1 m at 15 m depth (the lower model boundary). Thermal properties of mineral soils are determined from soil dry bulk density and water content according to Kersten , and Lunardini  for peat. For each day the model was run until the soil temperature profiles reached equilibrium with the upper boundary conditions. This equilibrium condition was taken to occur when the maximum difference of soil temperatures at all levels between the two successive time steps was <0.005°C.
 When snow cover is present, the upper model boundary is set to the snow surface, with the upper boundary condition represented by daily mean air temperature (section 3.1). When snow cover is absent, the upper boundary is the ground surface and is represented by the surface temperature Ts (in °C) derived from air temperature Ta by an exponential expression [Zhang et al., 1996]:
The seasonal snow cover is treated as a single layer with climatological two-weekly snow densities and density-dependent effective thermal conductivity (section 3.2). To summarize, the key simplifications are (1) the snow surface temperature is set equal to air temperature; (2) heat transfer is by conduction only within the snow layer; and (3) snow densities and thermal conductivities are climatological.
 Estimates of geothermal heat flux for the lower model boundary at 15 m depth are not available with pan-Arctic coverage. We prescribe an initial geothermal heat flux for every grid cell using a temperature gradient of 3 K per 100 m. Then, we run the model for 20 years with this condition and use the resulting temperature gradient between the lowest two model layers together with the bottom layer thermal conductivity to calculate the new geothermal heat flux. This derived flux varies spatially with values ranging from close to zero up to 0.10 W m−2. The average value is 0.053 W m−2. Compared to no geothermal heat flux, the effect on active layer depths (maximum annual thaw depth) is mostly less than 1% (or 1–2 cm).
 Initial soil temperatures are chosen according to the permafrost classification of the grid cell (Figure 1b) on the basis of the IPA Circum-Arctic Map of Permafrost and Ground-Ice Conditions on the NSIDC EASE-Grid [Brown et al., 1997; IPA, 1998; Zhang et al., 1999]. In areas of continuous permafrost the model is initialized for the first day of the simulation (31 August 1998) to −8°C at 15 m depth. Corresponding 15-m values for discontinuous and sporadic/isolated permafrost are −4°C and −1°C, respectively. A value of +5°C is used for seasonally frozen ground, and a linear temperature profile up to the soil surface is assumed. The model is then spun up for 365 days in order to obtain more realistic start conditions for temperatures for all model layers. Calculations are performed with a daily time step.
3. Data Sources
 Daily air temperature and snow depth are the main forcing variables. Soil type and soil bulk density for each of the three major model layers are constant temporally. A climatological daily soil water content is included for each of the three main model layers. All input data have to be defined for each of the 39,926 EASE-Grid cells.
3.1. Surface Air Temperature
 We use adjusted surface air temperatures from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis [Kalnay et al., 1996; Kistler et al., 2001]. The NCEP fields are available with a horizontal resolution of 2.5° × 2.5°. Use is made of daily-average values, archived at the Climate Diagnostics Center in Boulder, Colorado. The 2-m temperature is a standard variable in the NCEP reanalysis. It represents a linear interpolation between the surface skin temperature and the temperature at the lowest model sigma level (0.995). It is therefore strongly influenced by the modeled surface energy budget. The lowest sigma (0.995) level is not as strongly influenced by the modeled surface energy budget, and should provide for more realistic temperature variability.
 Our approach is to perform a topography correction of the 0.995 sigma-level data using the difference in NCEP and Digital Elevation Model (DEM) (Figure 1a) topography on the 25 km × 25 km EASE-Grid in conjunction with temperature lapse rates derived from NCEP tropospheric data. As elevation is a first-order determinant of the spatial variation in surface air temperature, our adjustments effectively improve the resolution of the NCEP data, making it more compatible with the snow cover data sets.
 All NCEP fields are first interpolated to the 25 km × 25 km EASE-Grid. Equation (2) shows the formalism for deriving topography-corrected surface temperatures:
TS,topo and TS,0.995 are the adjusted and the original daily NCEP temperatures, respectively, ΔT/Δz is the daily atmospheric lapse rate, zDEM and zNCEP the elevations of the high-resolution DEM grid and the coarse-resolution NCEP grid. The lapse rate is computed from the temperature on the first standard pressure level at least 750 m above the NCEP surface and the 0.995-sigma level temperature. This captures the basic lower-tropospheric temperature structure but reduces the effect of very strong near-surface inversions in winter that can lead to spurious temperature adjustments. Temperatures are corrected up to a maximum elevation difference of 500 m.
 The coarse resolution of the unmodified reanalysis depicts topographic effects poorly (Figure 2a). During summer this yields temperatures that are too high over mountain ranges and too low over valleys and fjords. In winter these effects are reversed. As a result of our topography corrections, surface temperature in mountainous regions is mostly reduced for summer months (Figure 2b, compare to the topography of Figure 1a). Temperatures are increased during winter when temperature inversions are common. The topography-corrected daily temperatures of the summer example given in Figure 2 are modified by up to ±4 K in and adjacent to mountain ranges (Figure 2c), whereas for winter the changes range between −6 and +10 K.
 Using a higher resolution temperature data set is important. The SSM/I snow data set (section 3.2) is available on the 25 km × 25 km resolution grid and temperature and snow data sets have to match as forcing for the frozen ground model. Our adjustment procedure therefore avoids situations where temperatures in mountainous regions are too high (due to the coarse-resolution NCEP data set) with the snow on the ground at the same time. This would lead to an earlier transition to equilibrium temperatures in the snow and an earlier development of an active layer. On the other hand, lower or even subzero temperatures depicted in the coarse-resolution NCEP data set at the flanks of mountain chains where there is no snow would lead to increased heat transfer from the ground to the atmosphere and earlier and more rapid freezing of soil.
 For driving the permafrost model we apply a 31-day running mean to the temperature time series of every individual grid cell. This avoids frequent thawing and refreezing when the temperatures are around the freezing point and prevents the development of numerous phase planes in the ground. Since smoothing does not conserve energy (i.e., freezing and thawing indices or Degree Day Freezing (DDF) and Degree Day Thawing (DDT) would be reduced) we redistribute the missing degrees by multiplying daily temperatures above and below the freezing point by the appropriate factor for every grid cell, respectively. These factors range from 0 to ∼0.05.
3.2. Snow Cover
 For deriving snow cover we use data on the 25 km × 25 km NSIDC EASE-Grid from the polar orbiting passive microwave radiometer SSM/I. The algorithm to derive snow water equivalent (SWE) of Chang et al.  that was originally developed for the Scanning Multichannel Microwave Radiometer (SMMR) was modified (equation (3)), primarily to adjust for the difference between 18 GHz and 19 GHz channels [Armstrong and Brodzik, 2001]:
TB is brightness temperature at frequencies of 19 and 37 GHz at horizontal (H) polarization. The algorithm utilizes the fact that microwave energy emitted by the underlying soil is scattered by snow grains, with this scattering proportional to the SWE. The algorithm is applicable to dry snow conditions only. SWE cannot be determined when the snow is wet, that is, liquid water is present on the snow grain surface. Wet snow is primarily an emitter at microwave frequencies and thus the information derived from the scattered portion of the signal is lost. We use only early morning overpasses of the satellite (approximately 0600 LT) to mitigate melt effects in the snow. These daily radiometer swath data are assembled into weekly data based on the maximum SWE for each pixel over the 7-day period. Snow height (in meters) is derived from SWE values (kg m−2) by dividing by a climatological snow density (kg m−3) (see below) at the given location and time of year.
 Very thin snow cover often cannot be detected by passive microwave remote sensing because it does not provide a sufficiently strong scattering signal. Therefore we also use the EASE-Grid version of the NOAA-NESDIS weekly snow charts [Armstrong and Brodzik, 2002] for snow identification. The NOAA charts are based on information from several visible-band satellites. For grid cells where the SSM/I does not detect snow but the NOAA charts do, we assume a snow thickness of 3 cm. The NOAA charts are most useful at the beginning of the winter season and for the southern margin of Arctic snow cover. Erroneous SSM/I depictions of snow, sometimes occurring in the middle of summer, are eliminated through comparison with the NOAA snow charts.
 A 45-year time series of Canadian snow data (1955–1999), which includes density measurements [MSC, 2000], is used to define the climatological seasonal cycles of snow density for tundra, taiga, prairie, alpine and maritime regions. These snow classes were defined by Sturm et al.  on the basis of climatological values of temperature, precipitation, and wind speed. Tundra and taiga snow areas, for example, are both characterized by low temperatures and low precipitation whereas tundra snow areas experience higher wind speeds. It is assumed that the Canadian snow densities for these snow classes are representative for other parts of the Arctic.
 Bi-weekly climatological snow density values (Figure 3) are computed by averaging all observations made within ±7 days centered over two-week target dates. Each average snow density is obtained from typically 500 observations. Mean snow densities start at values of 170–230 kg m−3 in October, and rise, first gradually, then faster because of spring melt, reaching values between 380 and 550 kg m−3 in June. The density increase is due to snow settlement and repeated melting and refreezing. Tundra and taiga snow types (bold lines), which are found over more than 90% of the Arctic drainage area (tundra: 48.7%, taiga: 42.2%), have contrasting density characteristics for most of the season but become very similar from April through June. Tundra snow is much denser because of stronger winds in that climate zone and the development of wind slab layers. Taiga snow of the forested regions shows lower densities, attributed to deep snowpack with depth hoar layers, but an earlier and stronger increase in late winter and spring. These differences are important determinants of the insulation properties of snow, and heat transfer into the ground. Our snow density cycles are in agreement with those given by Brown  for Canadian prairie and boreal (taiga) regions, which are not defined using the snow classification of Sturm et al. . Additionally, Brown  reports that there is no evidence of trends in snow density over the 1964–1993 period. Snow density measurements collected at the Soviet North Pole drifting stations over the Arctic Ocean between 1954 and 1991 [Radionov et al., 1997] show values of about 220 kg m−3 for September, that rise to about 340 kg m−3 in June. These are close to our tundra snow densities.
 Dry and light snow is a good insulator, but conductivity increases with snow density. Sturm et al.  calculated an effective snow thermal conductivity keff at a given density ρs by a logarithmic regression (equation (4)) based on conductivity measurements made up to 1991 (some as early as 1889):
For the range of snow densities of interest (150–550 kg m−3) (cf. Figure 3) snow thermal conductivities of between 0.1 and 0.7 W m−1 K−1 are derived. Additionally, nonconductive heat transfer mechanisms like convection may occur in sub-Arctic snowpack, which contains a high percentage of extremely permeable depth hoar [Sturm, 1991; Sturm and Johnson, 1991]. This would result in increased effective thermal conductivity, but the convection effect would be limited by the presence of low permeability wind slab layers within the snowpack.
3.3. Soil Properties
 Soil bulk density fields for the three major model layers (0–30 cm, 30–80 cm and 80–1500 cm) are derived from the SoilData System [Global Soil Data Task, 2000] of the International Geosphere-Biosphere Programme (IGBP). The SoilData System can generate maps of a number of parameters at user-selected depths and spatial resolution. It uses a statistical bootstrapping approach to link records of their Pedon Database of 1125 soil profile descriptions to the FAO/UNESCO Digital Soil Map of the World.
 The relative compositions of clay, silt, sand, and gravel for each grid cell are also extracted from the SoilData System. These concentrations are used to weigh the different thermal conductivities for (1) fine grained soils (clay and silt) and (2) coarse grained soils (sand and gravel), calculated according to Kersten's  equations for frozen and thawed states.
 Since the SoilData System only accounts for mineral soil types, we parameterize a percentage of organic soil for the two top major layers in each grid cell. We compare the concentrations of the fine-grained soils clay and silt (CClSi) from the SoilData System with maps of peat concentration for Canada [Tarnocai et al., 2000] and the Former Soviet Union [Velichko et al., 1998]. Almost no peat coverage is mapped for soil with less than 40% of CClSi. By contrast, the peat concentration increases with an increase of CClSi when CClSi is greater than 40%. We therefore modify soil density using a peat density of 500 kg m−3 for our two soil layers and the value of CClSi as peat fraction. Peat thermal conductivity is calculated using the soil-water-dependent expression of Lunardini  for frozen and for thawed conditions. No peat correction is done for grid cells with surface elevations above 1200 m for layer 1, and above 1000 m for layer 2, which accounts for a general decrease of peat thickness with elevation.
 Soil water content is based on output from the University of New Hampshire Permafrost/Water Balance Model (P/WBM) [Vörösmarty et al., 2000; Rawlins et al., 2003]. P/WBM runs on the same Arctic drainage domain used in this study and provides runoff, evapotranspiration, soil water storage, and soil moisture for variable root and deep soil layers. These are standard outputs of the Arctic-RIMS system. We input a climatological soil water content for every day of the year obtained from a 20-year model climatology (1981–2000).
4. Results for 1998–2000
 We present results from the heat conduction model for September 1998 through December 2000, which is the extensive intercomparison period for the different atmospheric and hydrologic products within Arctic-RIMS.
4.1. Comparison With Measurements at CALM Field Sites
 Within the CALM network, active layer depth has been monitored since 1990 at more than 100 stations worldwide [Brown et al., 2000], of which 79 are located within the Arctic drainage area. The CALM site data were collected primarily over 100 m × 100 m test areas at 10 m grid intervals or 1000 m × 1000 m areas at 100 m grid intervals yielding up to 121 data points. We are interested in data from Canada (C), Greenland (G), Norway (N), Poland (P, on Svalbard), Russia (R), Sweden (S), and the USA (U). Measured values are not available for all stations and every year. As such, we compare our model results for the year 2000 with measurements of thaw depth (DT) for the same year, made at 60 locations in regions of continuous or discontinuous permafrost (Figure 4; see Figure 1 for locations of the CALM stations).
Figure 4 compares the modeled and measured values for the day when the measurement was taken in the field, which is usually close to the annual late summer maximum. Also shown in Figure 4 are bars of ±1 standard deviation for 48 grid sites. The average range of ±1 standard deviation is 26.6 cm and the average range between the minimum and maximum values for the grids is 66.5 cm. Modeled thaw depth is a distance-weighed average between the four grid cells around the CALM site location.
 The comparison between modeled thaw depth based on 625 km2 averages of temperature, snow depth and soil bulk density and a measured at a much smaller scale (1 ha or 1 km2) should be viewed as an indication of model performance rather than a true validation. For complex terrain in particular, point measurements extrapolated to obtain large area averages will tend to be poorly representative of true area means [Nelson et al., 1997].
 The modeled values nevertheless agree reasonably well with the measured ones within their standard deviation and capture the general picture of high-Arctic active layers. The Root Mean Square (RMS) error of 33.5 cm between measured and modeled thaw depth manifests some of the scale issues just described. Some grid cells were modeled with much lower thaw depths for the day of measurement in comparison to the measured thaw depths (G1, G2, C1). These test fields are at Greenland and Baffin Island fjords at much lower elevation than that of the higher and consequently colder corresponding model grid cell, resulting in shorter modeled thawing seasons and shallower active layer depths. The same effect contaminates comparisons with the four CALM sites on Svalbard, N1, N3, P1, and S1. The RMS error is reduced to 24.9 cm without these seven sites. Soil type and bulk density are also difficult to characterize on the coarse 25 km grid for complex terrain like mountain slopes.
 Separate thaw depths for mineral and for peat soils are available for the Swedish site of Kapp Linné on Svalbard (S1). The mineral soil thaw depths are almost twice as large as the peat soil thaw depths (111 cm versus 58 cm) and illustrate the small-scale dependency on soil type at the measured site. We average those values for comparison with model results because the areal extent of peat around Kapp Linné is unknown. The modeled thaw depth of 50.7 cm is much closer to the measured value for the peat case.
 A comparison between modeled thaw depth and the available 64 measurements at CALM sites for 1999 shows a similar behavior as for 2000, with a calculated RMS error of 30.5 cm. It is reduced to 27.8 cm without data from six sites that experience a cold bias adjacent to mountain ranges.
4.2. Sensitivity Study
 It is useful to examine the sensitivity of the model to altered forcing parameters and settings. Figure 5 summarizes results from modified parameters in terms of differences in RMS error between model thaw depth and CALM measurement in the year 2000 (section 4.1) compared to the standard run. The center points represent the standard run, which has a RMS error of 33.53 cm. The resulting changes in RMS errors (Figures 5a–5i) range between −0.52 cm and +0.43 cm for modifying the parameter by the listed value.
Figures 5a–5c show the effect of modified surface air temperature. A better agreement with CALM measurements (lower RMS error) can be obtained by increasing all daily values by 0.2 K (Figure 5a) or by increasing only the summer values (Figure 5b). Decreasing summer values (Figure 5c) has the opposite effect as increasing them. Since active layer depth is mostly influenced by summer temperatures, decreasing (Figure 5b) or increasing winter temperatures (Figure 5c) leaves the RMS error almost unchanged. The absolute RMS error change for warmer (Figure 5b) or cooler (Figure 5c) summers only is almost as big in comparison to decreasing or increasing every daily temperature value (Figure 5a).
 The effect of snow parameters is given in Figures 5d–5f. Lower snow height (Figure 5e) and higher snow density (Figure 5e) both result in lower RMS errors. Both lower snow depths and higher densities result in a larger heat transfer from the ground into the atmosphere. The influence of higher effective snow conductivity keff (Figure 5f), which takes the convective heat transfer process into account (section 3.2), is to reduce the RMS errors. A higher keff for sub-Arctic snow would therefore be a step into the right direction. Both a reduction and an increase in soil bulk density ρb give lower RMS errors (Figure 5g), because the comparison with some CALM sites improves while it gets worse for others. Lower initial soil temperatures (Tinit) before spinup (Figure 5h) improve the comparison slightly, as does a reduction in soil water content w (Figure 5i).
 The effects of these altered parameters and settings on the RMS error are clearly small. The largest effects result from changes in air temperature, snow parameters and soil bulk density. These calculations give an estimate for model sensitivity to single parameter changes. The remaining RMS error is attributed to scale differences between the relatively coarse model grid and the CALM measurements (as discussed in section 4.1), errors in forcing parameters and model shortcomings. In a combined run we used the settings that reduce the RMS error, for temperature (like in Figure 5a), snow density (Figure 5e), bulk density (Figure 5g), initial soil temperature (Figure 5h), and soil moisture content (Figure 5i). A somewhat better agreement with the measurements is reached with the RMS error reduced by 1.19 cm to 32.34 cm.
4.3. Time Series for Individual Model Grid Cells
 Here we present results from the standard model run for selected grid cells. The model is driven for the period 31 August 1998 through 31 December 2000, comprising two complete freezing and thawing seasons. Figure 6a shows for a selected grid cell the time series of surface air temperature T (including the 31-day running mean), snow height hS (shaded) and density ρS (dashed line) in the upper panel. The development of thawing (solid lines) and freezing planes (dashed lines) is shown in a vertical cross-section through the soil in the center panel, with thawed soil shaded in gray. The absolute value of thaw depth DT is in the bottom panel. This grid cell is located in southern Siberia in the Sayan Mountains at 51°N at 1664 m elevation in a region of continuous permafrost with taiga snow. An active layer with a maximum thickness of 177 cm develops in 2000, and it takes until the middle of the next winter until this thawed layer refreezes. Late freeze-up of the active layer is mainly due to the insulating effect of snow cover.
Figure 6b summarizes results from a second grid cell, located at 76°N on Prince Patrick Island in the Canadian high Arctic. As compared to the previous example, the grid cell is in a much colder climate zone with longer winters and shorter and colder summers. Air temperatures rise above freezing for only 60–70 days per year in contrast to 140–150 days in the previous example. Accordingly, the ground is snow covered for a longer period, but snow is thinner in this tundra area and its density is higher. An active layer no deeper than 45 cm develops. Refreezing in autumn is more rapid than the development of the active layer in spring because of the higher thermal conductivity of frozen soil as compared to thawed soil.
4.4. Arctic Drainage Area
 We now turn to results for the Arctic drainage area as a whole. A calculated thaw depth or frozen ground depth under the central Greenland ice sheet and other glaciated areas would be rather artifical. Therefore we mask out the Greenland ice sheet (Figure 1) but keep the meaningful results along the ice-free Greenland coast. We also mask ice caps in the Canadian Arctic Archipelago, on Svalbard, Novaya Zemlya, and elsewhere.
 The thermal soil model is run one-dimensionally on its 54 model layers for each of the 39,926 grid cells of the Arctic drainage area, and for the 854-day period from September 1998 through December 2000. The one-dimensional approach is justified compared to two- or three-dimensional modeling because the vertical length scale (1 m) is very much smaller than the horizontal length scale (25,000 m). Figure 7 summarizes development and decay of the active layer at 3-month intervals for 1999 (1 March, 1 June, 1 September, and 1 December). Figure 8 provides difference fields between 2000 and 1999. Thaw depth is calculated for the IPA-defined regions of continuous, discontinuous, and sporadic/isolated permafrost. It applies to the frozen parts of noncontinuous permafrost regions. Nonpermafrost seasonally-frozen ground regions are masked in black. There are regional differences in thaw depth between the two years. The thaw advance to the north is slower for much of the North American side of the Arctic drainage area in 2000 than in 1999 (as seen from the difference field of thaw depth for 1 June (Figure 8b)), whereas it is faster in 2000 for most of Eurasia except central Siberia. Also the retreat is faster in central Siberia in 2000, but generally slower in northern America (cf. December, Figures 7d and 8d).
 The slower advance on the North American side and the faster retreat in central Siberia in 2000 are consistent with lower values of Degree Day Thawing (DDT) (Figure 9) and an earlier maximum annual thaw depth or active layer depth (shown shortly). There is striking agreement in patterns of the difference in thawing index (Δ DDT, Figure 9c) and the difference in September thaw depth (Figure 8c) between the two years, pointing to surface air temperature as the main forcing parameter determining thaw depth.
 Thaw depth for the same days shown in Figures 7 and 8 is plotted in Figure 10 for a 6600 km-transect from Alaska over the Arctic Ocean to eastern Siberia (see Figure 7a for the location of the transect). Blue lines indicate 1 March, green ones 1 June, red ones 1 September, and orange ones 1 December. Together with a decreasing tendency toward the pole, southern and mountain areas stick out with larger thaw depths for every month. Most of the summer thawing occurs between 1 June and 1 September, but with a larger active layer increase during these three months on the North American side (grid cells one to about 100) compared to the Eurasian side. Mountain areas like the Brooks Range of Alaska or the Verkhoyanskiy and Cherskogo Ranges of eastern Siberia show lower thaw depths until June (Figures 7 and 10) before rising sharply through summer. We attribute this behavior to the higher soil bulk density in mountain regions and consequently higher thermal conductivity, lower soil water content, and remaining overestimates in surface temperature over high topography. These thaw depths are hard to verify because of the lack of measurements, although the higher thaw depth (nearly a factor of two) of mineral soils compared to peaty soils at Kapp Linné on Svalbard supports our results.
 Maximum annual thaw depth (DT,max) (or active layer depth) for 1999 and 2000 is presented in Figures 11a and 11b. There is general decrease with latitude in the active layer depth but with minimum values around coastal Greenland and for the Canadian Arctic Archipelago. The effects of topography stand out clearly. The active layer depth can reach values close to 250 cm in parts of southern Canada and southeastern Siberia. Northern central Canada northwest of Hudson Bay is characterized by bedrock areas with high bulk densities and high thermal conductivity, and higher active layer depths.
 The day of year when the maximum thaw depth was reached is displayed in Figures 11c and 11d. In general, as latitude increases, the date of maximum thaw depth becomes earlier, but differences between the two years are obvious. Deeper active layers develop when longer thawing occurs, with the day of maximum thaw depth found later in the year. The thawed layer on 1 September (cf. Figure 7c) has already retreated from its maximum (compare with Figures 11a and 11b, and to the air temperature field of 15 August 1999 in Figure 2) or is even completely refrozen in northern Canada and eastern Greenland while it is still increasing in southern regions. The maximum thaw depth is reached before 1 September in the high Arctic (Figures 11c and 11d) whereas the maximum for southern Canada, Scandinavia and western Russia is reached in October/November.
 Our results support a positive linear relationship between and active layer depth (ALD), suggested by several investigators [e.g., Nelson and Outcalt, 1987; Hinkel and Nicholas, 1995; Zhang et al., 1997; Brown et al., 2000] and based on measurements at CALM field sites. We present a similar plot, not for a time series at a single site but aggregating data for the complete Arctic drainage area (Figure 12). Two distinct linear relationships are evident for both years, reflecting different responses of surface thawing for different regions, but which break down for very high values of DDT. The linear cluster of points showing the larger change in ALD with DDT is populated by grid cells in mountain areas in Mongolia, southern and eastern Siberia, the northern Rocky Mountains, around Greenland, Svalbard, northern Norway, and bedrock areas of northern Canada. The linear cluster with the smaller change in ALD with DDT represents lowland grid cells in central and northern Siberia, the northern half of Alaska and central Canada.
Figure 13 gives the number of days with a frozen surface soil layer for the winters 1998–1999 (Figure 13a) and 1999–2000 (Figure 13b), together with the lengths of the 1999 (Figure 13c) and 2000 (Figure 13d) thawing seasons. The principal control by latitude is clearly seen. The length of the thawing seasons 1999 (Figure 13c) and 2000 (Figure 13d) generally corresponds to the maximum thaw depth reached during these years (Figures 11a and 11b). Despite higher thawing indices in the year 2000 for eastern and western Siberia (Figure 9) the day of maximum thaw depth is reached earlier in these regions.
 The differences in DDT also explain the contrasts in length of soil thawing season (Figure 13c and 13d). In particular, a later day of maximum thaw depth in 2000 compared with 1999 (Figures 11c and 11d) in the northeastern Canadian Arctic is driven by a higher thawing index, which results in deeper September thaw depths (Figure 8c).
 The difference in Degree Day Freezing (DDF) between the winters 1998–1999 and 1999–2000 (Δ DDF, Figure 14c) shows all of the Eurasian side and southern Alaska being milder for 1999–2000. It is instructive to examine how this pattern of Δ DDF relates to snow cover. Snow cover, of course, acts to insulate the soil. To this end, Figure 15 shows the snow cover index (SCI) for the two winters and the difference (Δ SCI) between them. The SCI is defined by Zhang et al.  as the sum of daily snow depths over a winter and is therefore a combined measure of snow duration and thickness. Figure 15c reveals that areas with a more negative Δ SCI in much of northern Siberia and parts of Alaska and southern Canada roughly coincide with a more negative Δ DDF. However, the area of maximum negative Δ DDF over Eurasia is west of where Δ SCI is most negative.
 The pattern of Δ DDF also explains the differences in maximum frozen ground depth (DF,max) (Figures 16a and 16b) and the day of DF,max (Figures 16c and 16d). Frozen ground depth for the freezing seasons 1998–1999 and 1999–2000 is derived for nonpermafrost parts of regions with discontinuous and sporadic/isolated permafrost, and for seasonally frozen ground regions. Continuous permafrost regions are masked out. Frozen ground depth can reach values close to 250 cm in northern Canada, Alaska and the mountains in southeastern Siberia. The ground freezes to depths of less than 50 cm during winter in parts of southern Canada, Europe and southwestern Siberia. The higher SCI in southwestern Siberia for 1999–2000 results in shallower DF,max, whereas the opposite can be seen in central Canada. Finally, an earlier day of DF,max (Figures 16c and 16d) coincides with a shallower maximum frozen ground depth, as seen for southern Canada in 1998–1999 and for western Siberia in 1999–2000 (Figures 16a and 16b).
 Thaw depth for permafrost areas and frozen ground depth for seasonally frozen ground areas are examined for the entire Arctic terrestrial drainage using a one-dimensional model driven by reanalyzed surface air temperature, remotely-sensed snow data and soil information from a large soil database. Using a topography correction, NCEP temperatures are adjusted for better compatibility with the 25 km × 25 km snow data set. Snow height is calculated from derived values of snow water equivalent and observed mean snow density. We show results for two complete freezing and thawing seasons. The active layer depth is typically between 30 cm and 80 cm in regions of continuous permafrost, but can range up to 250 cm in midlatitude isolated permafrost regions. The maximum seasonally frozen ground depth is as much as 250 cm in northern areas of discontinuous permafrost. Maximum thaw depth is shown to be driven mainly by surface temperature, as expressed in terms of thawing index, but snow cover and soil bulk density are also important. Large regional differences exist for the length of soil freezing season and the day when the maximum is reached. We find positive linear relationships with different slopes between thawing index () and active layer depth pointing to a certain predictability of active layer depth for given surface air temperatures and soil types.
 Comparison with measurements at 60 CALM field sites indicates that the main characteristics of thaw depth can be modeled even though the horizontal scale of the model is 4–5 orders of magnitude the scale of the observations. It is anticipated that the model at this resolution will be more useful in reproducing a larger-scale regional representation of thaw depth rather than site-specific characteristics. It would be desirable to monitor larger areas with respect to thaw depth in different climatic regions of the Arctic drainage to better facilitate mode evaluation.
 The Goodrich model has widely been used in the permafrost community and has shown to provide excellent results in the Arctic, especially in the continuous permafrost region where soil water content in the active layer is at or near saturation. Impacts of coupling between soil hydrologic and thermal regimes may be more pronounced in discontinuous and nonpermafrost regions. In future work we may include more explicit treatments of hydrologic processes in the model.
 The frozen-ground model is shown to provide realistic results for the whole pan-Arctic drainage region and, once applied to longer time series, could be used to address effects of Arctic warming on the soil thermal regime. Being able to simulate changes in active layer depth in response to warming is important for assessing the release of greenhouse gases stored in permafrost soil. However, seasonally frozen ground and active layer depth are not adequately represented in global circulation models. We plan to run the model for a period of at least 20 years in a future study.
 This study was supported by the National Science Foundation under the Arctic System Science (ARCSS) program grants OPP-9732461, OPP-9614297, OPP-9906906, OPP-9910315, OPP-9907541, NASA grant NAG5-6820, and the NOAA/CIFAR grant NAI7RJ1224. Thanks are extended to Ross Brown (Meteorological Service of Canada) for the calculations of seasonal snow density cycles from the CRYSYS snow data set and to Michael Rawlins (University of New Hampshire) for supplying the modeled soil moisture fields. CALM data are available from the CALM web site at http://k2.gissa.uc.edu/~kenhinke/CALM/. Passive microwave data were provided by the EOS Distributed Active Archive Center (DAAC) at the National Snow and Ice Data Center, University of Colorado, Boulder, Colorado, USA.