Comparison of model-produced active layer fields: Results for northern Alaska



[1] In this study we compare gridded active layer thickness (ALT) fields representing northern Alaska produced by the State Hydrological Institute (SHI), National Snow and Ice Data Center (NSIDC), and Geophysical Institute–University of Alaska Fairbanks (UAF-GIPL 2.0) spatial permafrost models. Comparison of model-produced ALT fields representing northern Alaska revealed substantial differences. The largest difference in modeled ALT was found in the interior of Alaska. However, the spatial distribution of observational sites, most of which are on the North Slope, precludes definitive conclusions about the accuracy of model prediction for the Alaskan interior. Accuracy of the model-produced ALT fields was assessed at a series of monitoring sites and over a 27,000 km2 region in north-central Alaska with known spatial ALT distribution. The NSIDC model is very accurate over the extent of the topographically homogeneous Coastal Plain but overestimates ALT in more complex terrain of the Brooks Range Foothills. The UAF-GIPL 2.0 model reproduced site-specific active layer values well but overestimated ALT on the Coastal Plain. Although the SHI model provided relatively accurate estimates, it was unable to reproduce interannual active layer dynamics. Large differences in ALT fields have primarily resulted from differences in approaches adopted in each model for characterization of largely unknown spatial distribution of surface (vegetation, snow) and subsurface (soil properties, soil moisture) conditions. Results from this study identify the nature and magnitude of error in ALT fields produced by permafrost models.

1. Introduction

[2] Permafrost is a central element of the cryospheric system. Its importance has become increasingly recognized in both scientific literature and popular media, especially in the last few years [e.g., Linden, 2000; Goldman, 2002; Nelson, 2003; Pearce, 2006]. Permafrost plays several critical roles in global change science, acting as a natural archive of Earth's near-surface thermal history, as a potential driver of climate change through release of greenhouse gases, and as a translator of climate change impacting both natural and human systems [Nelson et al., 1993; Anisimov et al., 2001].

[3] Until recently, data describing and measuring the thickness, variability, and thermal regime of the active layer were usually collected in support of specific ecological, geomorphic, or engineering investigations and programs. The significance of permafrost for assessing climate change and its impacts on Arctic environments has resulted in several major initiatives to create large geocryological databases [Brown et al., 2000; Burgess et al., 2000; Romanovsky et al., 2002; Anisimov and Polyakov, 2003; International Permafrost Association Standing Committee on Data Information and Communication, 2003, Nelson et al., 2004; Taylor et al., 2006].

[4] Despite rapid growth in its observation network, geocryology remains a data-limited science. Data for most variables are typically available only for isolated locations and times, making them insufficient to evaluate permafrost conditions over large regions. Although this situation is changing dramatically with the increasing availability of remote sensing data [Zhang et al., 2004; Duguay et al., 2005] and automated ground-based data logging systems, most of the new data are only indirectly related to the state of subsurface permafrost conditions. This situation has stimulated increased use of permafrost models to evaluate permafrost parameters over space and time, as well as permafrost-related impacts of global climate change [e.g., Nelson and Outcalt, 1987; Anisimov, 1989; Waelbroeck, 1993; Smith and Riseborough, 1996; Hinzman et al., 1998; Slater et al., 1998; Shiklomanov and Nelson, 1999; Zhang et al., 2000; Stendel and Christensen, 2002; Sazonova and Romanovsky, 2003; Yamaguchi et al., 2005].

[5] One of the major roles of spatial permafrost models is to generate spatial data sets pertaining to the seasonally thawed layer above permafrost (active layer) useful in a wide range of hydrologic, ecological, climatologic, and socioeconomic assessments in the terrestrial Arctic. The thickness of the active layer (ALT) affects many important hydrologic processes, including subsurface water storage [Quinton et al., 2005], runoff generation (including timing and magnitude) [Quinton and Marsh, 1999], and fluvial erosion [McNamara et al., 1999]. It also influences soil aeration, decomposition, and mineralization [Oechel et al., 1993] and determines the potential rooting depth of tundra vegetation and its access to nutrients and water [Chapin et al., 1988]. Because these factors affect the exchange of biogenic gases between Arctic tundra and the atmosphere and export of carbon and nutrients to rivers and seas, they have potential for creating important feedbacks to global climatic and hydrologic systems. Within the general framework of global change studies, continental- and circumpolar-scale permafrost models have the greatest potential for assessing processes and changes in the active layer over the extent of the terrestrial Arctic.

[6] Several algorithms for active layer calculations have been developed. Evaluation of their performance has been provided by Zhang et al. [1996], Romanovsky et al. [1997], and Zhang and Stamnes [1998]. Although algorithms have been shown to provide good results for simulating active layer thickness when driven with well-known boundary conditions and forcing parameters at specific point locations, their adaptation to geographic space is not straightforward. This process requires simplification, careful selection of climate forcing data, and treatment of surface and subsurface parameters with largely unknown distribution over the modeled domain. Differences in how permafrost models are adapted for spatial applications create the possibility of substantial divergence in results from various models. This, in turn, can create considerable uncertainty in estimates of active layer thickness and its variation over geographic space. In this paper we compare three gridded active layer fields with potential for use in climatologic, hydrologic, biochemical, and socioeconomic applications. The models used to create the fields were developed at the National Snow and Ice Data Center (NSIDC), the University of Alaska, Fairbanks–Geophysical Institute Permafrost Laboratory (UAF-GIPL) and the State Hydrological Institute in Russia (SHI). The comparison was conducted on subsets of active layer fields representing the diverse environmental conditions characteristic of northern Alaska.

2. Spatial Permafrost Models

[7] Spatial permafrost models have historically been used to assess permafrost distribution, permafrost temperature, and the depth of the annually thawed layer above permafrost, in order to provide baseline information required for engineering, hydrologic, and ecologic investigations in the Arctic. Spatial models are used increasingly to evaluate geographic trends and variability in permafrost parameters, and to simulate permafrost evolution under changing climate. Spatial permafrost models can be broadly classified according to their underlying methodology as either equilibrium or transient models.

[8] Equilibrium models are based on empirical and semiempirical relationships and/or relatively simple analytical formulations, which link climatic, surface, and subsurface parameters. They are most often used to predict the limits or lateral “boundaries” of permafrost extent, or to estimate “average” geocryological parameters and, until recently, dominated permafrost modeling at small geographical scales.

[9] A wide spectrum of spatially explicit equilibrium permafrost models is available to estimate the thickness of the active layer. These models differ in complexity, data requirements, and computational algorithm. The simplest approaches are based on several variations of the analytical Stefan solution [Jumikis, 1977] to the heat conduction problem with phase change. The Stefan-based methods range from straightforward computational algorithms requiring deterministic specification of input parameters (gridded fields of thawing degree days (DDT), thermal properties of soil, moisture/ice content and land cover characteristics, and terrain models) [Klene et al., 2001a] to establishing empirical and semiempirical relationships between variables based on comprehensive field sampling procedures [Nelson et al., 1997a; Shiklomanov and Nelson, 2002]. These methods were used for high-resolution mapping of the active layer in the Kuparuk River basin, a 27,000 km2 area of north-central Alaska [Nelson et al., 1997; Shiklomanov and Nelson, 2002]. The Stefan-based approach was also adapted for detailed spatial characterization of active layer thickness in an urbanized area in the Arctic [Klene, 2005], and has been used to develop regional stochastic models for probabilistic mapping of active layer thickness [Anisimov et al., 2002].

[10] Several variants of a more comprehensive model, based on an adaptation of the analytical solution by Kudryavtsev et al. [1974] to the geographic context, have been developed and used with Geographic Information System (GIS) technology to estimate active layer thickness spatially at regional [Shiklomanov and Nelson, 1999; Sazonova and Romanovsky, 2003] and circum-Arctic [Anisimov et al., 1997] scales. The advantages of equilibrium models are their relative simplicity and low data requirements. The major drawback of such models is their inability to resolve interannual variability, which is frequently required for ecological and hydrological studies in the Arctic. These limitations have led to recent spatial adaptations of transient numerical simulators.

[11] Transient models are constructed using sets of differential equations that explicitly include time as one of the variables. They account for the major processes governing development of the ground thermal regime, and are based on numerical solutions of the surface energy balance, the water balance, and heat transfer equations at the atmosphere/ground surface interface and in frozen/unfrozen soil. Transient computational algorithms have traditionally been developed for detailed process studies at point locations with well-known boundary conditions and forcing variables. Application of transient models for spatial assessment of permafrost conditions, including active layer thickness, has been limited, primarily because the requirements of such models are large in terms of both forcing data and model parameters. Forcing data usually consist of high-frequency (e.g., daily) gridded fields of surface meteorology variables (air temperature, precipitation, solar radiation, wind speed, dew point, etc.). Some models also require knowledge of snow depth, snow density, and soil moisture. Data requirements include such parameters as soil properties at different depths, land cover categories, digital elevation models, and initial soil temperatures at specified depths over the modeling domain. Obtaining such data at the appropriate spatial scale and extent has proved to be a major difficulty. However, several spatially adapted transient numerical simulators have been developed in recent years [e.g., Hinzman et al., 1998; Oelke et al., 2003, 2004; Yamaguchi et al., 2005]. They are constructed using similar principles but differ in computational details, parameterizations, and resolution.

[12] For comparison we have utilized results from spatial permafrost models representing both equilibrium and transient approaches to permafrost modeling.

3. Models and Input Data

3.1. State Hydrological Institute (SHI) Equilibrium Model

[13] The SHI permafrost model is an equilibrium model based on Kudryavtsev's computational algorithm [Kudryavtsev et al., 1974]. Kudryavtsev's formulation describes the exponential attenuation of temperature oscillations in snow and vegetation cover, and takes into account the temperature offset in the layer affected by seasonal thawing. The maximum depth of thawing is calculated in the model by means of a semiempirical equation for the thickness of a homogeneous layer of permafrost in thermodynamic equilibrium with the atmospheric climate. In the SHI model, Kudryavtsev's algorithm was modified to take into account the presence of an organic layer. The model requires a minimal set of forcing data, including the mean annual temperature, the annual amplitude of the air temperature, snow depth calculated from precipitation, and the volumetric heat capacity and thermal conductivity of snow, vegetation, and soil [Anisimov et al., 1997]. The mean annual air temperature and air temperature amplitude were estimated using adjusted surface temperatures from the National Centers for Environmental Prediction and the National Center for Atmospheric Research (NCEP/NCAR) reanalysis [Kalnay et al., 1996; Kistler et al., 2001]. Daily air temperature at 2 m height is a standard variable in the NCEP/NCAR reanalysis and is available with a horizontal resolution of 2.5° × 2.5°. A topographic correction of the 2 m air temperature was made using the difference between the NCEP and digital elevation model (DEM) topography on the 25 km × 25 km NSIDC EASE-Grid in conjunction with temperature lapse rates derived from NCEP tropospheric data [Oelke et al., 2003].

[14] Mean annual snow depth was calculated through winter precipitation using the snow model detailed by Anisimov et al. [1997]. The thermal properties of snow and vegetation, and the dry density of organic and mineral soils were fixed both spatially and temporally. For every grid cell the thickness of vegetation cover, organic layer thickness and soil moisture were varied stochastically within a range of published data, resulting in a range of geographically varying active layer estimates. The final active layer field was produced by averaging of intermediate results. The spatial active layer fields produced by the SHI model were used to assess CH4 emission over the Russian permafrost regions [Anisimov et al., 2005a, 2005b; Anisimov and Reneva, 2006] and for evaluating the potential impact of climate change on infrastructure built on permafrost [Nelson et al., 2001, 2002].

3.2. National Snow and Ice Data Center (NSIDC) Transient Model

[15] The NSIDC model [Oelke et al., 2003, 2004] is an explicit dynamic simulator of the ground thermal regime. It is based on a spatial adaptation of the finite difference algorithm for one-dimensional heat conduction with phase change and a snow routine [Goodrich, 1982]. Descriptions of the algorithm were provided by Goodrich [1982], Zhang [1993], and Zhang et al. [1996]. Details about the spatial adaptation of the model at the circum-Arctic scale were provided by Oelke et al. [2003, 2004]. The NSIDC model requires daily gridded fields of air temperature, precipitation, snow depth, and soil moisture content, as well as spatial representation of soil properties, land cover categories, and digital elevation data to evaluate the daily progression of freeze/thaw cycles over the modeling domain. Initial soil temperatures are prescribed from available empirical observations associated with permafrost classification from the International Permafrost Association's circum-Arctic map of permafrost and ground ice conditions [Brown, 1997; Zhang et al., 1997]. Climatically, the model was forced by the daily adjusted NCEP/NCAR reanalysis surface temperatures [Oelke et al., 2003]. Snow water equivalent was derived from the polar orbiting passive microwave radiometer SMMR and SSM/I on the 25 km × 25 km NSIDC EASE-Grid and data are available from the National Snow and Ice Data Center at [Armstrong et al., 2005]. A 45-year time series of Canadian snow data (1955–1999), which includes snow density measurements [Meteorological Service of Canada, 2000], is used to define the climatological seasonal cycles of snow density for tundra, taiga, prairie, alpine and maritime regions on the basis of work by Sturm et al. [1995] snow classification. Daily snow depth was obtained from snow water equivalent divided by snow density. Snow density data were also used to estimate effective thermal conductivity based on work by Sturm et al. [1997]. Soil bulk density fields for the three major model layers (0–30 cm, 30–80 cm, and 80–1500 cm) were derived from the Soil Data System [Global Soil Data Task, 2000] of the international Geosphere-Biosphere Programme (IGBP). Because the Soil Data System accounts only for mineral soil types, parameterization of organic content for the top two soil layers was conducted for each grid cell [Oelke et al., 2003]. Peat thermal conductivity was estimated using the soil-water-dependent expression of Lunardini [1988] for frozen and for thawed conditions. Soil water content is based on output from the University of New Hampshire Permafrost/Water Balance Model [Vorosmarty et al., 2001; Rawlins et al., 2003].

3.3. University of Alaska Fairbanks–Geophysical Laboratory (UAF-GIPL 2.0) Transient Model

[16] The UAF-GIPL 2.0 Dynamic model [Tipenko et al., 2004] is a numerical model based on an implicit finite difference method for the nonlinear parabolic heat conduction equation. The basic mathematical model is the enthalpy formulation of the one-dimensional Stefan problem [Alexiades and Solomon, 1993; Verdi, 1994]. The special Enthalpy formulation of the energy conservation law makes it possible to use coarse vertical resolution without loss of latent heat effects in the phase transition zone, even under conditions of rapid or abrupt changes in the temperature fields. The implicit finite difference method [Marchuk, 1975] was used to achieve a numerical solution of the problem. The numerical scheme has an approximation order of O(h2 + Δτ), where h and Δτ are spatial and temporal steps respectively. In the UAF-GIPL 2.0 model the process of soil freezing/thawing occurs in accordance with the unfrozen water content curve, which is specific for each soil layer and for each geographical location. For each grid point a one-dimensional multilayer model of soil down to the depth of a constant geothermal heat flux (typically 500 to 1000 m) is employed. Snow and vegetation cover are treated as insulating layers with time-variable properties.

[17] The resulting model uses gridded fields of monthly air temperature, snow depth, soil moisture, and thermal properties of snow, vegetation and soil. Air temperature fields were provided by the Climate Research Unit database (CRU) [New et al., 2002]. Snow water equivalent output from the Terrestrial Ecosystem Model (TEM) [Euskirchen et al., 2006] was used to estimate snow depth. Extensive field observations, obtained from representative locations characteristic of the major physiographic units of Alaska, were used to develop Alaska-specific gridded fields of soil thermal properties and soil moisture conditions. The model is applied over the state of Alaska at 0.5° × 0.5° resolution, providing estimates of the thermal state of the ground at prescribed intervals of depth and time.

4. Methodology

[18] To produce gridded fields of active layer thickness, the NSIDC, SHI, and UAF-GIPL models were run at corresponding spatial and temporal resolutions over model-specific geographic domains (permafrost regions of the Northern Hemisphere for the SHI model, circum-Arctic drainage area for the NSIDC model, and the State of Alaska for the UAF-GIPL model). The dynamic models (NSIDC and UAF-GIPL) estimated active layer thickness as the maximum depth of annual propagation of the 0°C isotherm into the ground. The equilibrium model (SHI) provided annual active layer estimates by means of an analytical formulation. To represent contemporary conditions, modeled ALT output for years 1995–2000 was generated and averaged. Analysis of empirical active layer information obtained from the North Slope of Alaska, indicates that ALT during this period did not experience significant temporal trends [Shiklomanov and Nelson, 2002; Hinkel and Nelson, 2003]. The portion of the model-produced ALT fields representing terrestrial Alaska north of 65.5°N, which corresponds approximately with the continuous permafrost zone of Alaska, was used for comparison (Figure 1). The continuous permafrost zone of Alaska was chosen for two reasons: (1) Active layer thickness, on which primary emphasis is placed in this paper, is a less important parameter in the discontinuous and sporadic permafrost zones. Owing to the high spatial variability of permafrost conditions in the latter regions, the actual location of permafrost patches and their thermal state becomes of prime concern, compared to the relatively thick active layer. (2) In the early 1990s a series of observational sites was established in northern Alaska for standardized active layer monitoring [Nelson et al., 1998], providing a rich data set for evaluation of model-produced ALT fields. Because the main purpose of this study is to evaluate gridded active layer fields provided by spatial permafrost models for a range of potential applications (as opposed to a detailed evaluation of model performance), no standardization in forcing data was implemented. The effect of forcing climate data on predictive active layer modeling was addressed by Anisimov et al. [2007].

Figure 1.

Region of Alaska north of 65.5°N used for comparison of model-produced ALT fields. Colors represent elevation (m). Black lines outline major ecoregions of northern Alaska, based on work by Nowacki et al. [2001]: (1) Arctic Coastal Plain, (2) Arctic Foothills, (3) Brooks Range, (4) Davidson Mountains, (5) Kobuk Ridges and Valleys, (6) Ray Mountains, (7) North Oqilvie Mountains, and (8) Yukon-Old Crow Basin. Ecoregions 1 and 2 constitute the Alaska North Slope. Ecoregions 4–7 are described in the text as Interior Highlands. The map also shows locations of the active layer monitoring (CALM) sites and the outline of the Kuparuk River region.

[19] The three spatial active layer data sets compared in this study differ in spatial resolution. The UAF-GIPL fields are available at 0.5° × 0.5° latitude/longitude resolution while the NSIDC and SHI models produce output at 25 km × 25 km resolution, projected to the NSIDC EASE grid. This discrepancy complicates comparison of modeling results. To provide a basis for comparison, output from the three models was standardized to the coarsest resolution. For EASE grid output the procedure involved averaging values of active layer thickness in a series of 625 km2 cells contained in each 0.5° × 0.5° grid box. If the EASE grid cell falls on the boundary between 0.5° × 0.5° boxes the portions of 625 km2 cell is contained in several 0.5° × 0.5° boxes. In this case the value of 625 km2 cell was weighted according to the proportion of its area contained in a specific 0.5° × 0.5° box. The conceptual idea behind standardizing model output to the coarser resolution is that the finer the scale the patchier the active layer pattern while the ensemble mean should remains consistent at all scales.

[20] The initial evaluation of three spatial active layer fields was conducted using active layer data from 23 Circumpolar Active Layer Monitoring (CALM) sites distributed over northern Alaska (Figure 1). The CALM program is a network of sites at which data about ALT and its dynamics are collected in standardized fashion [Brown et al., 2000]. The CALM observations provide an independent data set which was not used for the development and adjustment of models used in the analysis. In Alaska, 17 CALM sites include 1 km2 or 1 ha grids established to represent spatially heterogeneous active layer conditions within characteristic landscape units. At these sites periodic active layer measurements are conducted at regular spatial intervals (100 m for 1 km2 grids, 10 m for 1 ha grids) at the end of the thawing season by mechanical probing. At the remaining six sites active layer estimates are obtained from ground temperature measurements at regular vertical intervals. To evaluate spatial active layer fields produced by the three permafrost models, values for grid cells corresponding to the locations of CALM sites were extracted and compared to the mean value of ALT observed at CALM sites.

[21] To evaluate model-produced ALT fields in the explicitly spatial context we developed a multiscale hierarchical scheme. This scheme includes empirical data from observational plots provided by CALM, regional characterization of permafrost conditions, and output from continental- and circumpolar-scale models. Spatial characterization of permafrost conditions at regional scales and at high resolution is a key element of the multiscale structure, and provides a scale transition between observational plots and model grid cells. The location and size of the region is determined by (1) observations being sufficient in number and density to determine the spatial/temporal structure of the ground thermal regime over the area; (2) observations being representative of the dominant environmental conditions in the area; (3) having a sufficient amount of spatially distributed information to characterize environmental conditions in the area; (4) the region incorporating climatic and ecological gradients; and (5) the region being large enough to contain at least several small-scale model grid cells. The first two criteria were evaluated by analysis of empirical data, and are aimed at identifying dominant processes and environmental controls influencing permafrost conditions at different spatial and temporal scales within the region. The third criterion guides the selection of appropriate modeling techniques to high-resolution regional characterization of permafrost parameters. The last two criteria are necessary to provide representative samples large enough to facilitate evaluation of results from models operating at the continental and circumpolar scales.

[22] In northern Alaska the 27,000 km2 Kuparuk River region (Figure 1) meets these criteria. The region includes portions of two dominant physiographic provinces (Arctic Coastal Plain and Arctic Foothills) and its major axis extends along the primary climatic gradient. Since the early 1990s, the entire Kuparuk River basin has been the subject of extensive climatic, hydrologic, and ecological research. To address the problem of spatial and temporal active layer variability, extensive spatial sampling strategies were developed over a wide spectrum of scale, within 100 m2 to 1 km2 areas with representative soil and vegetation characteristics. To provide a consistent basis for extrapolation of field observations to the entire region, measurements were conducted at locations with various combinations of climatic, surface, and subsurface conditions, and supplemented by air and soil temperature observations. Extensive analysis of empirical data [Nelson et al., 1998; Klene et al., 2001b; Shiklomanov and Nelson, 2003; Walker et al., 2003] led to the development of a series of approaches for high-resolution active layer mapping [Nelson et al., 1997; Klene et al., 2001a; Anisimov et al., 2002]. Results from these procedures have been summarized in a series of annual regional gridded active layer fields at 1 km2 resolution, and validated with data from an extensive helicopter-based survey [Muller et al., 1998; Shiklomanov and Nelson, 2002]. In this study we use the high-resolution Kuparuk data sets to evaluate the ability of continental and circumpolar fields to represent spatial and temporal characteristics of ALT.

5. Results

5.1. Consistency

[23] The active layer fields produced by the three permafrost models are shown in Figure 2a. Although a general north-south trend toward increasing ALT is apparent in all fields, there are drastic differences in the magnitude of seasonal thaw in the central and southern portions of maps. Despite the similarities in methodological approaches, discrepancies are largest between fields produced by the UAF-GIPL and NSIDC models, reflecting differences in forcing data and parameterizations. On the southern fringes of the map the NSIDC model produced ALT values five to seven times greater than those produced by the UAF-GIPL model. Compared to the two dynamic approaches, the SHI model provides moderate ALT values.

Figure 2.

(a) Spatial fields of 1995–2000 mean ALT for northern Alaska (north of 65.5°N), produced by three permafrost models (NSIDC, SHI, and UAF-GIPL). (b) ALT latitudinal profile produced by the three models along the 150°W meridian (bold line in Figure 2a) and the dominant physiographic units of Alaska along the profile.

[24] Figure 2b shows a latitudinal profile of ALT produced by the three models along the 150°W meridian, and the dominant physiographic units of Alaska along the profile. The SHI and UAF-GIPL active layer fields show consistent latitudinal trends. The relatively high active layer values in the southern portion of the profile decrease gradually toward the north, in response to the general climatic gradient. The lowest values are associated with higher elevations in the Brooks Range. On the North Slope, ALT increases toward the north in response to a decrease in climatic continentality, the insulating properties of vegetation, and the thickness of the organic layer. The NSIDC field contains extremely high ALT values, associated with complex terrain in the Ray Mountains and Brooks Range. On the North Slope, the NSIDC ALT trend decreases gradually toward the Coastal Plain. A detailed evaluation of active layer fields on the North Slope is provided in sections 5.2 and 5.3.

[25] To analyze spatial inconsistencies in the modeled ALT fields, an index of similarity was calculated as the relative range of differences between SHI-, UAF-GIPL-, and NSIDC-produced ALT data sets [Fekete et al., 2004]

equation image

where max and min are, respectively, the highest and lowest values for a specified grid cell across the three data sets. Higher values of the similarity index (SI), expressed in percent, indicate higher similarity between fields. Figure 3 shows a map of the similarity index for northern Alaska. The highest similarity between model predictions is achieved primarily on the Coastal Plain of the Alaskan North Slope, while areas occupied by the Brooks Range and interior highlands show a high degree of uncertainty in model-produced ALT fields.

Figure 3.

Map of the similarity index (SI), expressed in percent, computed for ALT fields produced by the three permafrost models. Higher SI values indicate greater similarity between fields. The map also shows locations of CALM sites.

5.2. Evaluation of Model-Produced Active Layer Fields Using Observational Data

[26] Figure 4 shows plots of modeled vs. observed ALT at 23 CALM sites. The best agreement between predicted and observed values was produced by the UAF-GIPL model. The NSIDC model significantly overestimates ALT for several Arctic Foothills locations. To evaluate ALT fields further, the mean absolute error (MAE), root-mean-square error (RMSE), mean bias error (MBE) and mean percentage error (MPE), were calculated, as suggested by Willmott and Matsuura [2005]:

equation image
equation image
equation image
equation image

where Pi and Oi are, respectively, predicted and observed ALT values at site i, and n– is the total number of sites. A positive value of MBE shows an overestimate, while a negative value is an underestimate, indicating an average model bias. A drawback is that overestimation of an individual observation will cancel underestimation in a separate observation. The RMSE gives information on model performance on individual observations by allowing a term-by-term comparison of actual deviations between estimated and measured values. The MBE represent systematic errors or bias, while the RMSE are nonsystematic errors. In MPE, signs of errors are neglected and percentage errors are added up to obtain the mean. MAE gives the absolute value of the bias error and is a measure of the overall goodness of a correlation between modeled and observed values.

Figure 4.

Relations between 1995–2000 ALT estimates obtained by the three permafrost models and observed at CALM sites.

[27] Evaluation statistics, presented in Table 1, indicate that all three models tend to overestimate the ALT values observed at CALM sites. MBE ranges from 0.14 m (for UAF-GIPL) to 0.55 m (for NSIDC). The corresponding values of MPE are 34% (for UAF-GIPL) and 126% (for NSIDC). Comparison of results from the NSIDC model with CALM observations yields the largest error values. The error statistics for the SHI and UAF-GIPL models are similar. The UAF-GIPL model performed slightly better, as indicated by lower values of MAE, RMSE, MPE, and MBE.

Table 1. Error Statistics Obtained by Comparing 1995–2000 Mean ALT Estimates Produced by the SHI, NSIDC, and UAF-GIPL Permafrost Models With ALT Observations at 23 Northern Alaska CALM Sitesa
  • a

    ALT values are given in m, and n = 23.

MPE, %4912634

5.3. Evaluation of Model-Produced Fields Using Regional ALT Maps

[28] Use of data obtained from observation sites for evaluation of model-produced gridded fields involves a large discrepancy between the size of observation plots (1 ha and 1 km2) and that of the model grid cells (25 km × 25 km and 0.5° × 0.5° latitude/longitude). Because of widely reported high spatial variability of ALT in northern Alaska [e.g., Nelson et al., 1998, Shiklomanov and Nelson, 2003], observational locations rarely represent generalized conditions prescribed for the model's grid cells; correspondence between the scale of observations and modeling resolution is necessary for effective comparison of observed and simulated patterns. To achieve geographic correspondence between the scales of observation and modeling we utilized a regional-scale active layer characterization based on observations obtained from representative locations. Active layer maps for the Kuparuk region, a 27,000 km2 area in north-central Alaska, provide a transitional scale between observations and models, and were used to evaluate model-produced ALT fields. The details on construction of active layer maps are provided by Shiklomanov and Nelson [2003]. The results of map validation using extensive helicopter-based ALT surveys indicate that the MAE does not exceed 0.05 m for all landscape categories represented in the Kuparuk region [Shiklomanov and Nelson, 2003].

[29] Figure 5 contains a map of mean active layer thickness in the Kuparuk region at 1 km2 resolution for the period 1995–2000, and the regional representations extracted from output derived from the three models. The regional high-resolution map (Figure 5a) shows differences in thaw depth corresponding to a regional climatic gradient, and local variability arising from variations in surface and subsurface conditions associated with the different landscape categories. The gentle topography and relatively homogeneous landscapes on the coastal plain result in an active layer pattern that isolates climatic effects throughout the area. The general pattern is punctuated by greater thaw depths in areas adjacent to water bodies. The higher elevations of the foothills show relatively thin active layers. This is a response to the thick insulating cover of vegetation and organic soil provided by the tussock tundra occupying many upland surfaces [Walker et al., 1998] and, to a smaller degree, by colder summer temperatures at higher elevations. The deepest thaw in the foothills occurs in wet areas along major streams. River valleys occupy lower elevations and, as a result, experience warmer summer temperatures. The shallow thaw depths of the southern foothills are attributed primarily to colder summer temperatures at high elevation.

Figure 5.

Spatial representation of the 1995–2000 mean ALT (m) in the Kuparuk region, obtained by regional semiempirical model (KUP, 1 km2 resolution) and three circumpolar spatial permafrost models: SHI, NSIDC (625 km2 resolution), and UAF-GIPL (0.5° latitude/longitude resolution). The boundary between Coastal Plain and Foothills physiographic provinces is shown by a gray line. Areas occupied by exposed bedrock and open water without ALT observations are shown in black.

[30] Visual analysis of regional representations from the three models indicates that the NSIDC model captures ALT accurately on the Coastal Plain. In the Foothills, the NSIDC model generally overestimates ALT (Figure 5c), producing values reaching 4 m.

[31] The SHI and UAF-GIPL models produce a spatial trend in the Kuparuk region opposite to that obtained from the NSIDC model. Higher ALT values occur on the Coastal Plain, where both models tend to overestimate ALT. The gradual decrease in ALT, apparent in the SHI active layer field (Figure 5b), is due primarily to the regional trend of summer air temperature, because the SHI model assumes a single soil type. Considering a course 0.5° × 0.5° resolution, the active layer boundary between the Coastal Plain and Foothills provinces is relatively well reproduced by UAF-GIPL model (Figure 5d).

[32] To evaluate regional model representations quantitatively, mean ALT values were calculated for each grid cell (625 km2 for NSIDC and SHI; 0.5° × 0.5° for UAF-GIPL) of the high-resolution Kuparuk map and compared on a cell-by-cell basis with output from the three models. Error statistics for the two physiographic provinces and for the entire Kuparuk region are presented in Table 2. The largest error statistics for the entire region were produced by the NSIDC model, which overestimated the regional mean by 0.38 m, or 68% of the observed regional ALT mean (Table 2). However, the large errors associated with the NSIDC model are due to significant overestimation of ALT values at Foothills locations, while this model performed very well over the Coastal Plain. The UAF-GIPL model most accurately represents the regional ALT mean with a mean bias error of only 5 cm, which is compatible with errors of ALT measurements. Both the UAF-GIPL and SHI models overestimate ALT on the Coastal Plain by around 40% of the observed value. In the Foothills, the UAF-GIPL model shows a high degree of accuracy with respect to the geographic mean, while the SHI model overestimates the mean ALT value slightly.

Table 2. Error Statistics Obtained by Comparing 1995–2000 Mean ALT Estimates Produced by the Three Permafrost Models With the Results of High-Resolution ALT Mapping for the Kuparuk River Regiona
  • a

    Mean ALT values were calculated for each grid cell (25 × 25 km for NSIDC and SHI, 0.5° for UAF-GIPL) of the high-resolution Kuparuk map and were compared on a cell-by-cell basis with output from the three models. The error statistics were calculated separately for two dominant physiographic provinces (Coastal Plain and Foothills) and the entire 27,000 km2 Kuparuk region. ALT values are in m.

Coastal Plain
Entire Kuparuk Region

5.4. Interannual Dynamics of ALT

[33] To evaluate interannual variations in the spatial active layer estimates produced by the three models for the Kuparuk region, the regional annual active layer anomalies were calculated for the 1995–2000 period by subtracting the 6-year mean from annual values. Figure 6 shows a 6-year time series of annual ALT anomalies, averaged over the Kuparuk region for three modeled ALT fields and for high-resolution maps. Both dynamic models (NSIDC and UAF-GIPL) are able to reproduce interannual variability well, despite having been driven by different climatic fields. The large temporal variability produced by the SHI model is related to limitations inherent in the equilibrium approach.

Figure 6.

Six-year time series of annual ALT anomalies, averaged over the Kuparuk region for the three modeled ALT fields and for high-resolution maps (KUP). Regional annual active layer anomalies were calculated for the 1995–2000 period by subtracting the 6-year mean from annual values.

6. Discussion

[34] The comparisons of model-produced ALT estimates in the previous sections demonstrate that significant differences exist in the ALT fields produced by different models. Greater similarity between model predictions is achieved on the Coastal Plain of the Alaskan North Slope, where climatic, surface, and subsurface conditions are relatively homogeneous, than in the more complex terrain of the Brooks Range and interior Alaska. In upland regions NSIDC active layer values are significantly higher then those produced by the SHI and UAF-GIPL models.

[35] Quantitative accuracy assessments using observational sites indicated that the largest overall errors occur in the NSIDC model's predictions, while the UAF-GIPL model produced the most accurate results. The regional analysis revealed spatial patterns of errors in model-produced ALT fields associated with major physiographic features. Results from the regional analysis indicate that the NSIDC model performed very well on the Coastal Plain but significantly overestimated ALT in the areas near Brooks Range. In contrast, the UAF-GIPL and SHI models overestimated ALT on the Coastal Plain while providing accurate ALT estimates in the Foothills.

[36] Geographic discrepancies in model-produced ALT estimates can be attributed largely to the manner in which surface and subsurface conditions are parameterized in each model. In the Brooks Range and interior Alaska uplands, surfaces are underlain primarily by coarse mineral material, and large areas contain exposed bedrock. The geographically variable soil types, derived from the global soil database used in the NSIDC model, treat mountainous areas explicitly as exposed bedrock. Because of the high thermal conductivity of bedrock, lack of soil ice/water, vegetation, and organic layer, thaw can propagate to substantial depths, resulting in active layer thickness exceeding two meters. The SHI model's assumption of a single soil type in tundra environments resulted in an ALT trend corresponding closely to the general climatic gradient. The soil characterization used in the UAF-GIPL model is based on empirical observations, conducted in representative locations characteristic of major physiographic units of Alaska. Because observational sites in the interior uplands are located exclusively on low-lying accumulation surfaces with well-developed vegetation, soils, and cryogenic processes, the UAF-GIPL model produced relatively low ALT values for the Brooks Range and interior uplands.

[37] The site-specific parameterizations of surface and subsurface conditions also caused the UAF-GIPL model to produce higher ALT values in the central portion of the coastal plain. The coastal plain contains a mixture of drained-lake basins and dry surfaces with drastically different ground thermal regimes [Hinkel and Nelson, 2003], resulting in high ALT variability over short lateral distances [Nelson et al., 1998]. Statistical analysis of ALT data obtained from coastal plain locations indicates that the distribution of ALT is highly skewed toward higher values [Shiklomanov and Nelson, 2003]. In such a situation the observation-based parameterizations tend to overestimate model-produced ALT. This effect is most prominent in the central portion of the coastal plain, where differences in ALT between landscape elements is greatest [Hinkel and Nelson, 2003]. The geographically variable soil properties, derived from the Soil Data System [Global Soil Data Task, 2000], and used in the NSIDC formulation, helped this model to achieve its good performance in the coastal plain province.

[38] Analysis of interannual variations in spatial active layer estimates produced by the three models revealed inherent limitations in the equilibrium approach used by the SHI model. The SHI model does not take into account the damping effect of the deeper, low-temperature permafrost layers that mitigate the summer heat wave propagating downward from the surface. The damping effect is particularly strong during years that are colder or warmer than the climatological norm because of a progressive imbalance developing between the thermal state of the upper layer of seasonal thawing and that of the deeper permafrost layers. This effect is clearly seen for the year 1998 (Figure 6), which was the warmest in the period under consideration. During that year, the SHI model produced an active layer field that was on average more than 30 cm deeper than observed values. Another limitation of the equilibrium modeling approach is that it does not consider the “thermal memory” of the ground, but instead assumes that equilibrium is established each year between the climate and the ground thermal regime. This results in abnormally large fluctuations between years.

7. Conclusions

[39] This study provides a comparison of gridded active layer fields derived from the NSIDC, SHI, and UAF-GIPL 2.0 spatial permafrost models for northern Alaska. Although the models used are based on algorithms that provide good results for simulating active layer thickness when driven with site-specific boundary conditions and forcing parameters [Zhang et al., 1996; Romanovsky et al., 1997; Zhang and Stamnes, 1998], comparison of model-produced ALT fields reveal substantial differences attributable to differences in representation of surface and subsurface conditions, and possibly to uncertainties associated with climatic forcing.

[40] The largest differences in modeled ALT occurred in the Alaskan interior. However, the spatial distribution of observational sites, which are predominantly located on the North Slope or in low-lying vegetated areas, precludes definitive conclusions about the accuracy of the models' predictions of active layer thickness in mountainous areas of Alaska. The distribution of CALM sites in northern Alaska (Figure 3) indicates that majority of sites are located in areas of high consistency in modeling predictions. These results emphasize the need to improve the sampling of active layer thickness and other permafrost parameters in the more heterogeneous areas of interior Alaska.

[41] Perhaps the most basic conclusion from this study is that there no simple answer to the question “which model-produced active layer field is better?” The NSIDC model is very accurate at predicting active layer over the extent of the coastal plain. Although its estimates are very high in mountain regions compared to other models and observations, they are probably more realistic and geographically representative. However, high ALT estimates associated with bedrock can be misleading for hydrological and biochemical assessments at continental and regional scales. In our analysis the UAF-GIPL model was able to reproduce regional and site-specific active layer values very well, which can be attributed to the Alaska-specific parameterizations used in the UAF-GIPL model. However, it significantly overestimates active layer thickness on relatively homogeneous Coastal Plain. The SHI model, based on a simple equilibrium approach, provided reasonable active layer estimates. The inherent limitation of this approach is in its inability to accurately reproduce interannual active layer dynamics.

[42] The large heterogeneity of surface (vegetation, snow) and subsurface (soil properties, soil moisture) conditions and limited availability of empirical information have resulted in development of simplified approaches for spatial characterization of edaphic parameters. Diversity in approaches used in permafrost models to prescribe surface and subsurface parameters led to great divergence of results. More detailed studies, including analysis of the effects of surface and subsurface characterization and climate forcing on the performance of spatial permafrost models over different regions, are needed to provide more definite conclusions about the accuracy and applicability of results from the three permafrost models. At present, a map of the similarity index (Figure 3) best represents our ability to assess and compare modeled patterns of active layer thickness for northern Alaska. The results presented in this study can be used as an indication of potential source of errors in spatial hydrologic and biochemical assessments that involve output from permafrost models.


[43] This research was sponsored by the U.S. National Science Foundation grants OPP-0352957 and OPP-0352958 to the University of Delaware and OPP-0352910 to the University of Colorado at Boulder. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. We are grateful to A. Etringer, and J. McCreig (National Snow and Ice Data Center, Boulder, Colorado) for assistance in providing data for this research and to three anonymous reviewers for valuable suggestions.