Modelling and mapping permafrost at high spatial ...

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Modelling and mapping permafrost at high spatial resolution in Wapusk National Park, Hudson Bay Lowlands1,2 Yu Zhang, Junhua Li, Xiping Wang, Wenjun Chen, Wendy Sladen, Larry Dyke, Lynda Dredge, Jean Poitevin, Donald McLennan, Heather Stewart, Sheldon Kowalchuk, Wanli Wu, G. Peter Kershaw, and Ryan K. Brook

Abstract: Most spatial modelling of permafrost distribution and dynamics has been conducted at half-degree latitude/longitude or coarser resolution. Such coarse results are difficult to use for land managers and ecologists. Here we mapped permafrost distribution at 30 m × 30 m resolution for a region in the northwest Hudson Bay Lowlands using a process-based model. Land-cover types and leaf area indices were derived from Landsat imagery; peat thickness was estimated from elevation based on field measurements; and climate data were interpolated from station observations. The modelled active-layer thickness and permafrost extent compared well with field observations, demonstrating that modelling and mapping permafrost at a high spatial resolution is practical for terrains such as these lowlands. The map portrayed large variations in active-layer thickness, with land-cover type and peat thickness being the most important controlling variables. The modelled active-layer thickness on average increased by 37% during the twentieth century due to increases in air temperature and precipitation, and permafrost disappeared in some southern areas. The spatial scale of the permafrost maps developed in this study is close to that of the ecosystem and landscape features; therefore, the results are useful for land management and ecosystem assessment. Résumé : La plus grande partie de la modélisation de la distribution et de la dynamique du pergélisol a été effectuée à des résolutions d’un demi-degré de longitude/latitude ou à une résolution encore plus grossière. Les spécialistes en gestion des terres et les écologistes trouvent de tels résultats à faible résolution difficiles à utiliser. Dans le présent article, nous avons cartographié la distribution du pergélisol d’une région dans les basses-terres du nord-ouest de la baie d’Hudson à une résolution de 30 m × 30 m; nous avons utilisé un modèle basé sur les processus. Les divers types de couverture végétale et les indices de surface foliaire ont été déterminés à partir d’imagerie Landsat; l’épaisseur de la tourbe a été estimée à partir de l’élévation en se basant sur des mesures prises sur le terrain et les données climatiques ont été interpolées à partir des observations aux stations météorologiques. L’épaisseur de la couche active et l’étendue modélisées du pergélisol concordaient bien avec les observations sur le terrain, démontrant que la modélisation et la cartographie du pergélisol à une résolution spatiale élevée est pratique pour des terrains tels que ces basses-terres. La cartographie illustrait d’importantes variations dans l’épaisseur de la couche active : le type de couverture végétale et l’épaisseur de la tourbe étant les variables qui exerçaient le plus de contrôle. L’épaisseur modélisée de la couche active avait augmenté de 37 % au cours du 20e siècle en raison de l’augmentation de la température de l’air et des précipitations; le pergélisol avait disparu dans certains secteurs plus au sud. L’échelle spatiale des cartes de pergélisol développées dans la présente étude se rapproche de celle des caractéristiques des écosystèmes et du paysage; les résultats sont donc utiles à l’évaluation de la gestion du territoire et des écosystèmes. [Traduit par la Rédaction]

Received 24 June 2011. Accepted 16 May 2012. Published at www.nrcresearchpress.com/cjes on 9 July 2012. Paper handled by Associate Editor Chris R. Burn. Y. Zhang, J. Li, X. Wang, and W. Chen. Canada Centre for Remote Sensing, Natural Resources Canada, 588 Booth Street, Ottawa, ON K1A 0Y7, Canada. W. Sladen, L. Dyke, and L. Dredge. Geological Survey of Canada, Natural Resources Canada, Ottawa, ON K1A 0E8, Canada. J. Poitevin and D. McLennan. Parks Canada Agency, Hull, QC K1A 0M5, Canada. H. Stewart and S. Kowalchuk. Wapusk National Park and Manitoba North National Historic Sites, Parks Canada Agency, Churchill, MB R0B 0E0, Canada. W. Wu. Western and Northern Service Centre, Parks Canada Agency, Winnipeg, MB R3B 0R9, Canada. G.P. Kershaw. Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB T6G 2H1, Canada. R.K. Brook. Indigenous Land Management Institute, College of Agriculture and Bioresources, University of Saskatchewan, Saskatoon, SK S7N 5A8, Canada. Corresponding author: Yu Zhang (e-mail: [email protected]). 1This

article is one of a series of papers published in this CJES Special Issue on the theme of Fundamental and applied research on permafrost in Canada. 2Earth Science Sector Contribution 20110058. Can. J. Earth Sci. 49: 925–937 (2012)

doi:10.1139/E2012-031

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Introduction Climate warming at high latitudes during the twentieth century was about twice the global average (ACIA 2005). Associated increases in near-surface ground temperature and activelayer thickness (ALT) and, in places, permafrost disappearance have been observed (e.g., Vitt et al. 2000; Smith et al. 2010). Changes in permafrost conditions affect infrastructure, ecosystems, and wildlife habitats, and can have strong feedbacks on the climate system (ACIA 2005). Spatial information about permafrost conditions and their dynamics are essential for land use and land management, ecological impact assessment, and providing the lower boundary conditions for climate models. Spatial modelling is a major approach for understanding the distribution of permafrost and its changes with climate (Riseborough et al. 2008). Most regional and hemispherical permafrost modelling and mapping studies have been conducted using half-degree latitude/longitude or even coarser spatial resolution (e.g., Anisimov and Reneva 2006; Zhang et al. 2006, 2008a). A grid size of half-degree latitude/longitude at 60 °N is about 28 km × 55 km. These coarse results provide general patterns of permafrost distribution and their responses to climate change, but are difficult to use for land-use planning and management and for ecological monitoring and assessment. Furthermore, the results at this scale are difficult to test against field observations, which are usually site specific, and can vary significantly due to soil, vegetation, hydrologic, and topographic conditions (e.g., Nelson et al. 1998). Modelling and mapping permafrost at a high spatial resolution requires detailed input data, efficient computation schemes, and robust models. Such an approach has been implemented successfully by Duchesne et al. (2008) for the Mackenzie River valley at 30 m × 30 m resolution based on a process-based heat conduction model. The model used seasonal n-factors to estimate the near surface ground temperature from air temperature. In our study, we used an energy balance approach to determine the upper boundary conditions. This approach is more generic in time and space and can integrate ground thermal processes with the dynamics of snow and soil moisture. The study area for the research reported in this paper is Wapusk National Park (WNP) in the northwest Hudson Bay Lowlands (Fig. 1). The park covers 11 475 km2 and straddles the boundary between continuous and discontinuous permafrost zones and the tree line. WNP contains one of the most concentrated polar bear denning areas in the world (Richardson et al. 2005). It is a concern that permafrost thaw may induce the collapse of peat banks, which could affect the bears’ denning habitat. Permafrost thaw may also affect hydrology and vegetation and release carbon dioxide and methane to the atmosphere from the carbon-rich soils in this region. Changes in permafrost and ALT are considered to be important factors affecting the park’s ecosystem integrity (Parks Canada Agency 2002, 2007). The objectives of this study are to develop a method to map permafrost and its changes at a high spatial resolution and to develop spatially detailed maps and understanding about permafrost conditions in WNP.

Methods and data Field observations Field conditions in WNP and its surroundings have been studied by several agencies since the 1970s, so there are

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considerable data available regarding soil and surficial geology, vegetation, land-cover type, summer thaw depth, ground temperature, and snow conditions. Soil conditions and summer thaw depth were measured at 117 sites in WNP and its proximity by the Geological Survey of Canada in 1977 (Fig. 2a). A diamond drill was used to penetrate about 2 m below the base of the peat layer. The observed peat thicknesses were used to develop relations with elevation to map peat distribution in the park. Ground temperatures have been measured at sites near Mary Lake (from 2004), Roberge Lake (from 2005), and Fletcher Lake (from 2007) (Fig. 2b; Dyke and Sladen 2010). Snow depth was also measured near Mary Lake. Ground temperatures were recorded every 4 or 8 h at several depths from the surface to 0.8 m near Mary and Roberge lakes and to 5 m depth near Fletcher Lake. Ground temperature and permafrost conditions were also measured at York Factory National Historic Site (Fig. 1b), just outside the southern limit of WNP (Sladen et al. 2009). Around the site, ground temperatures were measured in seven boreholes to 15 m depth with different ground surface conditions (Sladen et al. 2009). Since the ground temperatures were measured at specific sites, these observations were used to test the performance of the model under local vegetation and ground conditions rather than the mapped spatial results. A detailed description of the site conditions and model tests is lengthy and is not presented in this paper. Fieldwork was conducted in 2007 along several coast–inland transects in WNP (Fig. 2b). Plant species composition, coverage, height, leaf area indices (LAI), and aboveground biomass were measured at 31 sites, and summer thaw depth was determined by probing at 34 sites. Field sampling sites were chosen in homogenous patches that were larger than 3 × 3 Landsat pixels — 90 m × 90 m, using a Landsat-7/ ETM+ mosaic image and aerial survey from a helicopter. Five 1 m × 1 m plots within each site were established to represent the site. Aboveground biomass and LAI were measured by harvesting all plants in each plot (Chen et al. 2009). Similar vegetation data (coverage of major plant species and plant heights) and summer thaw depths were collected by Brook (2001) and Brook and Kenkel (2002) at more than 300 other sites in WNP and its surroundings. The vegetation data were used for land-cover classification, and the summer thaw depths were used to validate the model. Kershaw and McCulloch (2007) monitored snow conditions at five sites in the northern part of WNP from 2002 to 2004. These data were used to estimate snow drifting factors for different land-cover types. Model and improvement The Northern Ecosystem Soil Temperature (NEST) model was used to model and map permafrost in WNP. NEST is a process-based model developed to simulate transient responses of the ground thermal regime to climate change (Zhang et al. 2003). Soil temperature dynamics are simulated by solving the one-dimensional heat conduction equation. The upper boundary condition (the ground surface or snow surface when snow is present) is determined by the surface energy balance, and the lower boundary condition (at a depth of 120 m) is defined by the geothermal heat flux. Changes in the amount of snow on the ground (water equivalent) and Published by NRC Research Press

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Fig. 1. The location of the study area: (a) Wapusk National Park (WNP) is in the northwest of the Hudson Bay Lowlands shown in dark grey; (b) the boundary of WNP and the locations of the climate stations and the York Factory National Historic Site. The curves indicated by numbers 1–4, respectively, are the southern boundaries of the continuous, extensive discontinuous, sporadic discontinuous, and isolated patches of permafrost mapped by Heginbottom et al. (1995). The boundary of the Hudson Bay Lowlands is based on the Terrestrial Ecozones of Canada (Wiken 1986).

snow density are included in the model. The simulation of soil water dynamics includes water input from rainfall and snowmelt, evaporation and transpiration, and distribution among soil layers. Soil thawing and freezing, and associated changes in proportions of ice and liquid water, are determined based on energy conservation. The model has been validated against measurements of energy fluxes, snow depth, soil temperature, thaw depth, and spatial distributions of permafrost and ground thermal conditions across Canada (Zhang et al. 2003, 2005, 2006, 2008b). The NEST model is one-dimensional for heat and water exchange, except outflow of water, which is estimated using the ground slope. Although WNP has a very low topographic gradient, drainage and snow conditions vary significantly among different land-cover types. To consider the drainage differences, we parameterized lateral water exchanges based on Zhang et al. (2002): ½1

Wis ¼ Fis X (

½2

Wos ¼ (

½3

Wog ¼

Fos ðWTos  WTÞ

ðWT < WTos Þ

0

ðWT  WTos Þ

Fog ðWTog  WTÞ

ðWT < WTog Þ

0

ðWT  WTog Þ

where Wis is the daily surface water inflow from the surroundings (mm/day). Fis is an input parameter for the rate of the surface water inflow (no unit); X is daily rainfall when

there is no snow on the ground or simulated daily snowmelt (millimetres of water per day). Wos and Wog are daily surface and ground lateral water outflows (cm/day), respectively. Fos and Fog are input parameters for the rates of surface and ground lateral water outflows, respectively (1/day). WT is water table depth (in centimetres relative to the ground surface). WT is positive when the water table is below the ground surface and negative when it is above the ground surface. WTos and WTog are the lowest water tables for the lateral surface and ground water outflows, respectively. The parameters are mainly determined by local topography and soil conditions. Tests showed that this approach is capable of capturing water table dynamics at different drainage conditions (Zhang et al. 2002, 2012). Snow has significant impacts on ground thermal conditions, and wind can redistribute snow by drifting, depending on vegetation conditions and local topography. Since fresh snow is easily redistributed, we estimated snow drifting based on snowfall: ½4

Psnow ¼ Psnow0 ð1  fsnow Þ

where Psnow0 is snowfall before considering local snow drifting, and Psnow is the effective snowfall at the site after drifting (in millimetres of water per day). fsnow is the snow drifting factor representing the fraction of snowfall drifted away from the site (no unit). It is an input parameter of the model for a site. Since Psnow cannot be negative, fsnow should be equal to or less than one; 0 < fsnow ≤ 1 means that snow is drifted away from the site, while fsnow < 0 means that the site captures extra snow from the surroundings. Published by NRC Research Press

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Fig. 2. The distribution of the field observation sites in and near Wapusk National Park. Observation sites for (a) peat thickness, mineral soil conditions, and thaw depth in 1977, and (b) land-cover types, plant species, leaf area indices, summer thaw depth in 2007 (dots), and ground temperature (three squares: site A is near Mary Lake, site B is near Fletcher Lake, and site C is near Roberge Lake).

Model input data Climate data The climate data needed to drive the model include daily minimum and maximum air temperatures, precipitation, solar radiation, water vapour pressure, and wind speed. Although the model runs at a time step of 30 min, daily climate data are sufficient to capture permafrost conditions and ALT (Chen et al. 2003; Zhang et al. 2003). No widespread field observations of ground temperatures and soil water were available to initialize the model. Therefore, the model was spun up to an equilibrium condition with an initial climate. Recent climate warming began around the middle of the nineteenth century after the end of the Little Ice Age (e.g., Overpeck et al. 1997; Beltrami et al. 2003; Majorowicz et al. 2004). Observations in Alaska and modelling studies in Canada show that the current ground thermal regime is in strong disequilibrium with the atmospheric climate (Osterkamp 2005; Zhang et al. 2006, 2008a). Therefore, we initialized the model using the atmospheric climate in the 1850s. Monthly air temperature and precipitation data from 1901 to 2007 at 10 km × 10 km resolution were from McKenney et al. (2006). Air temperature is about 1.5 °C higher in the south than in the north of the park, and annual precipitation in the southern inland region is about 50 mm more than in the northern coastal region (Fig. 3). The monthly climate during 1850–1900 was estimated by linearly extrapolating the data for each month for each grid cell. We also extrapolated the data to 2010 based on observations at the Churchill climate station. The monthly data were downscaled to daily frequency using the daily observations at the Churchill climate station (from 1943 to 2010) and at the Marine climate station (1932–1943), about 8 km east of the Churchill station (Fig. 1). The technique for estimating daily climate variables is presented in Appendix A.

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Land-cover types and LAI The land-cover map for WNP was developed using an object-based unsupervised classification method, integrating Landsat-5 (acquired on 27 August 2006) and ALOS/PALSAR (acquired on 29 July 2007) images, and digital elevation models (DEM; Fig. 3d). The Landsat (red, near infrared, and short-wave infrared bands) and the ALOS/PALSAR (HH (horizontal transmit and horizontal receive) and HV (horizontal transmit and vertical receive) polarizations) images were segmented to generate image objects. The image objects were then classified into over 100 clusters using the Fuzzy K-means unsupervised clustering method. The DEM was used to constrain potential wetland areas in the clustered image. Finally, the clusters were merged and labelled as landcover types based on the legend used by Brook (2001) and Brook and Kenkel (2002). The final product included 14 land-cover types at a 30 m resolution (Fig. 3e): four types of fens (sedge fens, shrub–sedge fens, shrub fens, and sedge larch fens); four types of bogs (lichen bogs, lichen melt bogs, lichen spruce bogs, and sphagnum spruce bogs); two types of burned areas (recently burned areas and regenerated areas); two types of nonvegetated areas (beach ridges and tidal zones); salt marshes; and water bodies. The overall accuracy was 85% as determined by comparing the results with ground data collected at 293 sites. The best regression model for estimating LAI was obtained by linear regression using field-measured LAI and colocated Landsat spectral reflectance and their derived vegetation indices, including normalized difference vegetation index, shortwave vegetation index, and simple ratio vegetation index (SRVI; band-4/band-3). SRVI had the strongest linear relation with LAI: ½5

L ¼ 0:146ðSRVIÞ  0:36

ðR ¼ 0:91; N ¼ 31Þ

where L is the estimated LAI. Using eq. [5], we generated a 30 m resolution LAI map for WNP (Fig. 3f). Soil and ground conditions Except for beach ridges, peat thickness generally increases with elevation from coast to inland, corresponding to the time elapsed since the land emerged from Hudson Bay (Dredge and Mott 2003; Martini 2006). Using field observed peat thickness across the park, we developed two linear relations between peat thickness and elevation for bogs and fens, respectively: (

½6

D¼

0:0266H þ 0:1326 ðBog sites; R ¼ 0:74; N ¼ 48Þ 0:0141H þ 0:1029 ðFen sites; R ¼ 0:69; N ¼ 36Þ

where H is elevation above sea level (m), and D is the estimated peat thickness (m). In the field, we noticed that burned areas were usually bogs before they were burned. We assumed that peat thickness in burned areas was 0.2 m less than the nonburned area due to fire consumption and reduced accumulation. The burned year of the fires was estimated by Brook (2005). There is no peat accumulation on beach ridges due to their sandy and rapid drainage conditions. Thus, we can map peat thickness based on elevation and land-cover types. The bulk density of the peat increases from 0.4 g/cm3 at depth (Martini 2006; Kuhry 2008). Published by NRC Research Press

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Fig. 3. The distribution of (a) mean annual air temperature, (b) mean annual precipitation, (c) mineral soil conditions, (d) elevation, (e) landcover types, and (f) leaf area indices in Wapusk National Park. The air temperature and precipitation are averages from 1991 to 2000. The climate data are from McKenney et al. (2006). The types of the mineral soil conditions are shown in Table 1. The elevation data are from Natural Resources Canada (2007).

Surficial mineral materials in WNP are mainly marine or glaciomarine deposits. These sediments form a seaward-thickening wedge, developed during progressive isostatic rebound of the Hudson Bay coast. Their distribution has been mapped and described by Dredge and Nixon (1986, 1992). A summary of the mineral soil texture and thickness is listed in Table 1. There are few observations of the depth to bedrock in the WNP region. We assumed that the total thickness of the unconsolidated mineral material is 20 m except for beach

ridges. Since beach ridges are usually several metres higher than the surrounding areas, we assumed the thickness of the mineral soil in beach ridges to be 23 m plus the thickness of the peat in the surrounding areas. The bedrock in WNP is Paleozoic dolomite and limestone several hundred metres thick (Dredge and Nixon 1992). The thermal conductivity (2.99 W/(m·°C)) and geothermal heat flux (0.054 W/m2) were estimated based on site observations compiled by Pollack et al. (1993) and Jessop et al. (1984). Published by NRC Research Press

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Can. J. Earth Sci., Vol. 49, 2012 Table 1. The estimated texture and thickness of the mineral soils above the till, based on Dredge and Nixon (1986, 1992). Type 1

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2 3 4 5 6 7

Deposit Undifferentiated marine offlap deposits Sand and gravel beach ridge complexes Littoral and sublittoral sand Intertidal silt Stony marine pelite

Texture Silt at the top and sand at the bottom Sand

Thickness Decreasing from 6 to 2 m from coast to inland 4m

Sand Silt Silty sand with 10% stones

Modern or older fluvial deposit Kame and esker sand, outwash deposits and till

Sand with 10% stones Sand with 10% stones

2m 2m 2 m (in north), 5 m (middle and south) 3m 6m

Table 2. Parameter values for snow drifting and lateral water outflows in eqs. [1]–[3] and [7]. Land-cover type Salt marsh Tidal zone Shrub–sedge fen Shrub fen Sedge larch fen Beach ridge Lichen spruce bog Sphagnum spruce bog Lichen melt bog Lichen bog Recent burn Regenerated

a 0.5 0.6 0.5 0.5 0.0 0.7 0.0 0.0 0.5 0.5 0.0 0.0

b 0.1 0.1 0.2 0.3 0.5 0.2 0.5 0.5 0.2 0.2 0.5 0.5

WTos (cm) –5 –5 0 0 0 0 0 0 0 0 0 0

Fos (1/day) 0.05 0.05 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

WTog (cm) 30 30 30 30 30 50 50 50 50 50 50 50

Fog (1/day) 0.0001 0.01 0.0005 0.001 0.002 0.02 0.02 0.03 0.04 0.05 0.05 0.05

Note: a and b are parameters in eq. [7] relating to land-cover types and vegetation conditions (no units). WTos and WTog are the lowest water tables for the lateral surface and ground water outflows, respectively. Fos and Fog are the rates of surface and ground lateral water outflows, respectively.

Hydrological parameters Although the overall surface gradient in WNP is low, the hydrological conditions vary significantly among land-cover types due to local topography and drainage conditions. We calibrated the lateral water flow parameters in eqs. [1]–[3] by comparing the simulated water table with general hydrological conditions observed in the field and in the literature (e.g., Dredge 1992; Dredge and Nixon 1992; Parks Canada Agency 2007). We assumed that there was no surface inflow (Fis = 0) due to the low gradient. For surface outflow, we used WTos = 0 cm and Fos = 0.1/day for all the land-cover types except for salt marshes and tidal zones, where we used WTos = –5 cm and Fos = 0.05/day because the water table is commonly above the surface. Beach ridges and bogs, including burned areas have a much lower water table, so we used WTog = 50 cm for these land types, and WTog = 30 cm for fens and salt marshes. Water usually flows away much faster from bogs than from fens because the bogs are commonly raised above the local surroundings. Vegetation types are also indicators of hydrological conditions, e.g., lichens dominate the driest peat plateau bogs, and very wet fens support sedge-dominated communities, while better drained fens permit the colonization of shrubs and larches. We estimated Fog based on these considerations (Table 2). The snow-drifting factor in eq. [4] was estimated considering land-cover type and vegetation conditions:

½7

fsnow ¼ a  bL

where a and b are parameters relating to land-cover type and vegetation conditions (no units), and L is the LAI estimated using remote sensing in summer months, which was used as a surrogate of vegetation conditions affecting snow drifting. We determined the parameters under different land-cover types by comparing the modelled snow depth with the observations from Kershaw and McCulloch (2007). The parameter a was small (a = 0) for land-cover types with trees, but larger for vegetated nontreed areas (a = 0.5), and maximal for nonvegetated areas (beach ridges and tidal zones). The parameter b was the largest for land-cover types with trees (b = 0.5) and diminished gradually (from 0.3 to 0.1) for land-cover types with shrubs, sedges, and sparse vegetation (Table 2). Procedures for modelling and mapping There are about 10 million 30 m × 30 m nonwater pixels in WNP. It is not practical to simulate each pixel due to the computation time required, given that one pixel needs about 1 min of computer time. On the other hand, climate does not vary significantly from pixel to pixel, and small variations in peat thickness and LAI do not significantly affect permafrost conditions as shown in model sensitivity tests. Therefore, we divided elevation and LAI into discrete classes and ran the Published by NRC Research Press

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Fig. 4. Modelled average active-layer thickness (a) in the 1900s (1900–1909), (b) in the 2000s (2000–2009), and (c) the relative changes from the 1900s to the 2000s in Wapusk National Park.

model only for the unique combinations of the input data rather than all the individual land pixels. Climate data were available at 10 km × 10 km resolution with 200 climate grid cells for the entire park, elevation was divided into 15 classes ranging from 0 to 80 m, and LAI was divided into 20 classes between 0 and 4. The steps between classes increased from 1 to 10 m for elevation and increased from 0.1 to 0.5 for LAI. In addition to the land-cover types and mineral soil types, the input data have 56 609 unique combinations for the entire park, which are about 0.5% of total land pixels in the park. Thus, the simulation can be completed in a month for a typical personal computer.

Results and analyses Spatial distribution and change of permafrost conditions in the park Figures 4a and 4b show the modelled distribution of the ALT in the 1900s (1900–1909) and the 2000s (2000–2009). The active layer increases in thickness towards the coast. The modelled ALT is more than 2 m in coastal areas, principally due to lack of organic layer on the top of the soil. The sandy mineral soils on beach ridges and the wet conditions in marshes and coastal fens also favour deep summer thaw. The modelled ALT is about 1–2 m some distance away from the coast due to the combined effects of relatively thin peat and wet conditions, mainly fens. In the inland areas, the modelled active layer is usually 1 due to the shading effects of the vegetation. ALT is not sensitive to LAI for bogs probably due to the dominant effects of the insulation effects of peat. In bogs, the active layer becomes thinner if the soil becomes drier, but in fens, the active layer is thinner when the lateral outflow rate is higher or smaller than a critical value, i.e., the soil becomes very wet or very dry. Sensitivity tests also show that ALT increases from the north to the south in WNP for the same ground conditions due to the climate gradient, especially for fens with shallow peat (Fig. 7c). The average ALT decreases from the north to the south in the northern part of the park (Fig. 6d), mainly due to the increase in bogs, which have thinner active layers. The slight increase in the average ALT from middle to the south in WNP is probably related to the climatic gradient, although changes in land-cover types may be important as well.

ners (Fig. 4). In terms of land-cover types, the areas without permafrost are mainly in treed or shrubby areas (Fig. 5c), probably because of greater snow accumulation in these land types. The model results also indicate that permafrost has been disappearing in the last century, mainly from spruce bogs. The land area without permafrost in the park increased from 2.8% in the 1900s to 5.6% in the 2000s, and about 0.5% of the land areas contain no near-surface permafrost (i.e., permafrost exists at depth, but the permafrost table is deeper than 4 m).

Validation analysis Figure 8 shows comparisons between the modelled and observed summer thaw depths, where “summer thaw depth” is the thaw depth on a specific date in summer, while “activelayer thickness” is the maximum thaw depth in a year. The modelled summer thaw depths are close to the observations in magnitude for most sites. However, the correlation coefficient is not very high (R = 0.49), mainly because the model significantly underestimated the summer thaw depth at five sites (sites 19, 24, 25, 27, and 30 shown in Fig. 8b). These five sites are in the middle of the park: one site is sedge fen, three sites are shrub fens, and the other site is sedge larch fen. The model used peat thickness of 0.6–0.9 m for these sites based on eq. [6]. We probably overestimated their peat thickness while underestimated their snow accumulation due

Major controls on the modelled spatial distribution of ALT in the park We calculated the variations of the ALT in the 2000s with varying input variables to understand the impacts of different

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Fig. 6. The distribution of the mean and the average absolute deviation of the active-layer thickness in the 2000s with different input data or input-related variables: (a) elevation, (b) leaf area index, (c) land-cover type, (d) distance from north to south in Wapusk National Park, and (e) mineral soil conditions. The distance from north to south is related to the climatic gradient, and elevation was related to peat thickness (eq. [6]). The mineral soil types are listed in Table 1. The mean and the absolute deviation of a type (or a class) (represented by a dot and the range bar across the dot, respectively) were calculated based on all the grid cells with that input variable type (or class). The grey bars represent the fraction of land area associated with each type (or class) of the input variables.

Table 3. The average interclass and intraclass variations of the active-layer thickness in the 2000s and their ratios for five inputs or input-related variables. Variables Land-cover types Elevation Mineral soil conditions Leaf area indices Distance from north to south

Average interclass variations (m)* 0.42 0.36 0.34 0.26 0.20

Average intraclass variations (m)* 0.36 0.40 0.46 0.32 0.56

Ratio* 1.17 0.92 0.75 0.50 0.35

*The average intraclass variation of the active-layer thickness (ALT) was calculated as the weighted mean of the average absolute deviations of all the classes for an input variable (i.e., the mean of the ranges of the deviation bars in each panel in Fig. 6). The weighting factor is the fraction of the land area of the class. The average interclass variation was calculated as the average absolute deviation of the average ALT of classes for an input variable (i.e., the variation of the averages of the classes represented by the dots in a panel in Fig. 6). The contribution of each class was weighted based on the fraction of the land area of the class as well. The last column presents the ratios of the average interclass and intraclass variations.

to local terrain and vegetation conditions, especially the shrub fen sites, where shrubs seem tall and dense according to the satellite images. If we exclude these five sites, the correlation coefficient increases significantly (R = 0.72). The model results show nonpermafrost areas in the southern parts of the park. These results are comparable with the permafrost maps of Heginbottom et al. (1995) and Dredge (1979, 1992), who both mapped the southern part of the park as discontinuous permafrost. Ground temperature observations show that permafrost is absent at the forested margin of a peat plateau near Fletcher Lake, mainly due to the accumulation of 1.5 m of drifting snow (Dyke and Sladen 2010).

At a wet sphagnum spruce bog site in the southwest corner of the park, our field probing in 2007 showed no near-surface permafrost in the top 4 m. This is consistent with the model results. Ground temperature observations at York Factory just south of WNP also indicate that permafrost is absent in treed and dense shrubby areas (Sladen et al. 2009).

Discussion The high spatial resolution permafrost maps developed in this study show significant variation in ALT. Such strong spatial heterogeneity is consistent with field observations in Published by NRC Research Press

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Fig. 7. Sensitivity of the modelled active-layer thickness to the different input variables: (a) peat thickness; (b) leaf area index; (c) distance from north to south; (d), (e) lateral flow rate; (f) mineral soil texture. The tests were based on climate in the centre of Wapusk National Park (WNP) except for (c), which is based on climate from north to south in WNP. Leaf area indices were set as 0.2 for all except (b). Lateral flow parameters were based on the land-cover types given in Table 2 except for the outflow rates in (d) and (e).

which ALT ranges from 2 m under different vegetation and ground conditions. Our analysis shows that landcover type, peat thickness, and LAI are more important than the regional climatic gradient for the spatial distribution of ALT in WNP. Land-cover type is closely related with ALT and permafrost conditions because it integrates the information of peat thickness, vegetation types and status, and drainage conditions. Results from coarser spatial modelling not only have less spatial detail as the grid cells are large but also have smoother spatial distributions because climatic gradient is the major driver of the modelled spatial distribution. In our previous work (Zhang et al. 2006, 2008a), for example, the entire park was covered by about 10 grid cells, and the modelled ALT was quite similar among the cells. High spatial resolution maps of permafrost may reflect the large spatial variations in ALT due to variations in vegetation and ground conditions, and therefore are more useful for land users and ecologists. More importantly, at such a spatial resolution, the pixel size is similar to the land areas represented by field observations, allowing precise ground truthing for model testing and improvement. A robust model, detailed input data, and computation time are three major challenges for mapping permafrost and its dynamics at high spatial resolutions using process-based models. This study demonstrates that NEST can represent diverse hydrological, vegetation, and ground conditions. The work

also shows that computation in the data domain, rather than in the spatial domain (i.e., running the model for the individual pixels), may be an efficient approach for spatially detailed modelling. Changes in vegetation conditions could have significant effects on snow drifting and on energy exchanges between the surface and the atmosphere. In this study, we only considered the effects of fire on vegetation and peat thickness, including recent fires and regenerated areas after older fires. The effects of other disturbances (e.g., disturbances by migrating birds and erosion) and changes in land-cover type with time were not considered. Although we considered snow drifting and lateral water flows, the NEST model is still one dimensional, assuming each grid cell to be uniform and large enough that the lateral heat flux can be ignored. Therefore, the results do not represent transitional areas, especially sites very close to rivers, ponds, lakes, and Hudson Bay.

Conclusions In this study, we modelled and mapped ALT and permafrost distribution and their long-term changes at 30 m × 30 m resolution for WNP. The modelled ALT and permafrost distribution show large spatial variations, which are consistent with field observations and other studies. This work demonstrated that modelling and mapping permafrost at a Published by NRC Research Press

Zhang et al.

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Fig. 8. (a) The distribution of the summer thaw depth observation sites and their sequence numbers; (b), (c) comparison with the modelled results. The modelled summer thaw depths were on the exact dates corresponding to the observation dates. Panel (b) shows the modelled and observed summer thaw depths for each site, including the means and the standard deviations of the observations. Panel (c) is a scattergraph comparison for the modelled and observed thaw depths of the same sites. R is correlation coefficient.

high spatial resolution is possible in terms of the model’s broad applicability, data availability, and computation time. The results suggest that average ALT increased by 37% in the twentieth century due to climate change, and permafrost disappeared from some southern areas. Land-cover type and peat thickness appear to be the most important factors controlling the spatial distribution of ALT; LAI is a significant variable as well, while the regional climatic gradient is not as important. The results emphasize the importance of determining ground conditions for high resolution permafrost mapping. The scale of the maps developed in this study is close to the scale of landscape features and field observations; therefore, the results are useful for land-use management and ecosystem assessment.

Acknowledgements The authors would like to thank Drs. Fuqun Zhou and Ian Olthof for their critical internal review of the paper. Dr. Christopher Burn carefully reviewed and commented on the paper, which greatly improved its quality. Dan McKenney and colleagues kindly provided us with grid climate data for

this region. This study was supported by GRIP funding (ParkSPACE) from the Canadian Space Agency, the climate change program and the remote sensing science program of Natural Resources Canada, and Canada’s IPY funding (CiCAT). Churchill Northern Study Centre, Manitoba Conservation, and University of Manitoba also provided much support for the fieldwork.

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(MJ/m2), R0 is the daily total irradiance above the atmosphere (MJ/m2), estimated from latitude and Julian date. K is the daily average transmittance of the atmosphere to solar radiation, estimated based on Bristow and Campbell (1984): ½A4 and

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½A5

Appendix A: Estimating daily climate variables based on monthly spatial data and daily station observations Air temperature and precipitation We downscaled the monthly air temperature and precipitation grid data to daily data based on daily observations from Environment Canada (2011) at the Churchill climate station (from 1943 to 2010) and at the Marine climate station (from 1932 to 1943), about 8 km east of the Churchill station. The equations used were ½A1

Tg;y;d ¼ To;y;d þ DTg;y;d

½A2

Pg;y;d ¼ Po;y;d DPg;y;d

Solar radiation, water vapour pressure, and wind speed Environment Canada and the National Research Council of Canada (NRC 2007) calculated hourly solar radiation from 1953 to 2005 based on hourly weather data. From these data sets, we calculated the daily total solar radiation for the period. For other years during the simulation period, we estimated daily solar radiation based on irradiance above the atmosphere and atmospheric transmittance: ½A3

R ¼ R0 K

where R is the daily total irradiance on a horizontal surface

DTd ¼ TM;d  ðTm;d  Tm;dþ1 Þ=2

where DTd is the range of the daily air temperature on day d (°C), TM,d is the daily maximum air temperature on day d, and Tm,d and Tm,d+1 are daily minimum air temperatures on day d and day d + 1, respectively. V is the daily water vapour pressure (mbar; 1 mbar = 100 Pa), and a1, a2, a3, and a4 are empirical parameters, determined as 0.96, 0.06, 1.25, and 0.02, respectively, by comparing the estimated daily irradiance using eq. [A4] with the daily irradiance from Environment Canada and the National Research Council of Canada (NRC 2007). Daily water vapour pressure was estimated based on the saturated water vapour pressure corresponding to the daily minimum air temperature (Running et al. 1987): ½A6

where Tg,y,d and Pg,y,d, respectively, are estimated daily air temperature (daily minimum or maximum temperature) and precipitation in grid cell g in year y on day d. To,y,d and Po,y,d, respectively, are daily air temperature and precipitation observed at the Churchill or Marine climate stations on the same day. DTg,y,d is the difference of the air temperature between the grid cell and the Churchill (or Marine) station on that day, which is estimated from the difference between the monthly air temperatures (the month of the day d in the year y) of the grid data and climate station data. Similarly, DPg,y,d is the ratio of monthly precipitation between the grid data and the climate station data. For the period 1850–1931, daily air temperatures (maximum and minimum) were linearly extrapolated from the monthly means. Daily precipitation was estimated assuming that wet days (days with precipitation) were regularly distributed within a month and each wet day in a month has the same amount of precipitation. The monthly wet days (days with precipitation in a month) were from Mitchell and Jones (2005).

K ¼ a1 ½1  expða2 DTd a3 Þð1  a4 VÞ

V ¼ aVs;Tm

and ½A7

Vs;Tm ¼ 6:11 exp½17:27Tm =ðTm þ 237:3Þ

where Vs,Tm is the saturated water vapour pressure (mbar) at temperature Tm, which is the daily minimum air temperature (°C); the factor a was determined as 1.04 for the Churchill climate station by comparing the estimated with the observed daily average water vapour pressure from 1953 to 2005. Wind speed data are available from Environment Canada and the National Research Council of Canada (NRC 2007) from 1953 to 2005. An average daily wind speed was used for years without data. References Bristow, K.L., and Campbell, G.S. 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agricultural and Forest Meteorology, 31(2): 159– 166. doi:10.1016/0168-1923(84)90017-0. Environment Canada. 2011. Canadian daily climate data (CDCD). Available from ftp://arcdm20.tor.ec.gc.ca/pub/dist/CDCD/. Environment Canada and the National Research Council of Canada (NRC). 2007. Canadian Energy and Engineering Data sets (CWEEDS) and Canadian Weather for Energy Calculations (CWEC) (CD-ROM). Mitchell, T.D., and Jones, P.D. 2005. An improved method of constructing a database of monthly climate observations and associated high resolution grids. International Journal of Climate, 25(6): 693–712. doi:10.1002/joc.1181. Running, S.W., Nemani, R.R., and Hungerford, R.D. 1987. Extrapolation of synoptic meteorological data in mountainous terrain and its use for simulating forest evapotranspiration and photosynthesis. Canadian Journal of Forest Research, 17(6): 472–483. doi:10.1139/x87-081.

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