Corresponding author: R. N. Brooks, Water and Climate Impacts Research Centre, University of Victoria, Victoria, BC V8W 3R4, Canada. (firstname.lastname@example.org)
 The areal extent and volume of peak freshwater (river and lake) ice are quantified across the Northern Hemisphere for the period 1957–2002. Quantification is conducted using a degree-day ice growth model and ice growth coefficients defined for 14 ice-specific hydroclimatic regions. The model is driven by ERA-40 gridded daily air temperature data, and the Global Lakes and Wetlands Database is employed to spatially define rivers and lakes. Results indicate that the total area covered by freshwater ice, at peak thickness, north of the January 0°C isotherm (excluding the Greenland ice sheet) is 1.7 × 106 km2 and the total freshwater ice volume is 1.6 × 103 km3. This area is approximately equal to that of the Greenland ice sheet and the volume to snow on land (Northern Hemisphere). Such values now permit a more complete quantification of the cryosphere (evaluations already having been completed for other components, such as snow, glaciers, and sea ice) and provide a reference data set for assessing future climate-related changes.
 Through their influence on surface energy budgets, gas exchanges, and the hydrologic cycle, components of the cryosphere are influenced by, and feedback to, climatic conditions across a wide range of spatial-temporal scales [Fitzharris, 1996]. Moreover, detecting and modeling climate variations in such components provides a visible analysis of the changing climate [Lemke et al., 2007], particularly in higher latitudes affected by polar amplification of climate change [e.g., Serreze et al., 2000; Kattsov and Källén, 2005]. To date, attempts have been made to quantify all components of the cryosphere across the Northern Hemisphere, except that of freshwater ice [Lemke et al., 2007]. This is surprising considering the increasing recognition of the broad environmental significance of freshwater ice to biogeochemical and socioeconomic systems [e.g., Prowse, 2001a,2001b; Walsh et al., 2005; Wrona et al., 2006; Prowse et al., 2011]. Given the above, the goal of this research was to provide the first quantification of the areal extent and volume of peak (maximum winter) freshwater ice across the Northern Hemisphere.
2 Data and Methodology
 Peak freshwater ice was estimated using a degree-day ice growth model [Michel, 1971] based on the Stefan equation,
where hi is peak winter ice thickness (mm), Df is the sum of accumulated freezing degree days (°C) over the hydrologic year (1 August to 31 July), and α is an ice growth coefficient (mm °C−1/2 d−1/2). Although more complex physically based models exist [e.g., Riley and Stefan, 1988; Vavrus et al. 1996; Duguay et al., 2003], they are more computationally demanding for large-scale applications as addressed in this study, and the requisite suite of meteorological variables has not been validated to the same degree as air temperature. Moreover, simplified degree-day models have been shown to produce reliable results, except in the very early stages of ice growth [Ashton, 1986] and hence are considered appropriate for estimating peak ice thicknesses in this study.
 Until recently, the only values for α were the very generalized ones first defined by Michel , which were formulated to explicitly account for variations in controlling factors, such as water body type/size, exposure, surface snow insulation, subsurface heat flux, and implicitly for white (snow) ice growth. New α values have been defined for this assessment that consider variations in ice growth conditions by ice-specific hydroclimatic regions and water body type for the Northern Hemisphere. The specific area selected for study was north of the January 0°C isotherm, which represents the most southern extent of appreciable freshwater ice cover [Bennett and Prowse, 2010], and excluded areas of large permanent ice coverage (e.g., Greenland).
 Air temperature, precipitation, elevation, and latitude data obtained from the Climate Research Unit Climatology data set (CRU CL 2.0) [New et al., 2002] were employed as the source of global land surface climate information (1961–1990) for defining hydroclimatic regions using a two-step clustering method [SPSS, 2001], primarily because these variables have a dominant role in determining maximum winter ice thickness [Huntington et al., 2003; Williams and Stefan, 2006]. For air temperature and precipitation, mean January values were used, as they capture climatic conditions during the coldest month of the year and are considered to best reflect overall winter ice growth conditions. The use of January precipitation values in deriving regional coefficients was to also account for the role that snow could play in augmenting overall ice growth through surface white ice formation. The formation of white ice was not explicitly modeled; however, as the net effect of snow on ice thickness (i.e., via reductions in growth via snow insulation and enhancements of ice growth via white ice formation) equalizes over the winter, peak ice thickness is attained [e.g., Adams and Prowse, 1981].
 Ice growth coefficients were defined for each hydroclimatic region and water body type using observational ice data, where water body type is defined as river or lake. Spatial data for all water bodies were obtained from the Global Lake and Wetlands Database (GLWD) [Lehner and Doll, 2004]. Recognizing that heat storage in large water bodies can significantly affect seasonal ice growth [Dereki, 1976], separate α values were defined for large lakes and reservoirs. Unfortunately, lake depth and volume data are not available on a hemispheric scale. Instead, water bodies with a surface area of >500 km2 were considered to be “large” [Herdendorf, 1982] for this application. This resulted in the definition of three water body categories: large lake and reservoir, small to medium lake and reservoir, and river.
 Maximum observed, winter ice thickness data were compiled from five national archives: Canada [Lenormand et al., 2002]; Sweden (unpublished data, 2010), available from Swedish Meteorological and Hydrological Institute (www.smhi.se); Finland (unpublished data, 2010), available from Finnish Environmental Institute (www.environment.fi); Russia [Vuglinsky, 2000]; and USA-Alaska (unpublished data, 2010), available from National Oceanic and Atmospheric Administration/National Weather Service, Alaska-Pacific River Forecast Center (aprfc.arh.noaa.gov). Additional data for the Yukon (Water Survey of Canada, unpublished data), the British Columbia (Water Survey of Canada, unpublished data), and the Great Lakes [Sleator, 1995] were employed to augment the Canadian data set. The final compilation of sites and measurements (maximum winter ice thickness) included 46 large lakes and reservoirs with 548 measurements, 130 small to medium lakes and reservoirs with 2468 measurements, and 256 rivers with 5219 measurements. For each hydroclimatic region and water body type, α values were calibrated and validated using the maximum observed ice thickness data set, and a generalized α value was calculated for each water body type over the entire study area for use in regions lacking observational data.
 The gridded daily air temperature data employed to calculate Df were obtained from ERA-40, a gridded climatology data set (spatial resolution of 2.5°) covering the period September 1957 to August 2002 [Uppala et al., 2005]. Values of Df were calculated for each hydrologic year, during which a 31 day running mean was used to identify the crossing of the 0°C thresholds following Bonsal and Prowse  and averaged to produce a spatial grid of 44 year average Df values. These were used with regional α values in equation ((1)) to produce spatial grids of ice thickness for each water body category. The ice thickness data from these grids were applied to the respective spatial data from the GLWD to derive the total areal extent and volume for each water body category and summed for the study area.
3 Results and Discussion
 The two-step clustering method produced a 14 hydroclimatic region definition (Figure 1) in which there was a statistically significant difference (p < 0.05) for the mean values of at least three of the controlling variables (latitude, elevation, temperature, and precipitation) in each region compared to the respective means for all the other regions. This regional classification gave the best calibration results when compared to the other hydroclimatic region definitions and was found to broadly reflect the spatial patterns of standard climatic regions (e.g., arctic, subarctic, maritime, etc.). These regions also reflect winter conditions of air temperature and precipitation (Table 1), capturing regions with cold air temperature and low snowfall (e.g., region 1) to regions with warm air temperature and high snowfall (e.g., region 2). The regional values of α ranged from 18.0 to 26.4 with a mean of 20.1 for large lakes and reservoirs, 17.7–24.6 with a mean of 20.9 for small to medium lakes and reservoirs, and 14.0–27.5 with a mean of 20.0 for rivers, with corresponding adjusted r2 values obtained from validations of 0.45, 0.73, and 0.44 (all at p < 0.001). The generalized values of α used for regions lacking observational data were 19.4, 21.2, and 19.9, respectively.
Table 1. Cluster Means and Standard Deviations (in Parenthesis) for Mean January Precipitation and Mean January Air Temperature
Mean January Precipitation Cluster Mean (mm/month)
Mean January Temperature Cluster Mean (°C/month)
 The calculated total area and volume of peak winter freshwater ice are 1.71 × 106 and 1.56 × 103 km3, respectively (Figure 2 and Table 2). Compared to other cryospheric components, the areal extent is approximately equal to that of the Greenland ice sheet (1.7 × 106 km2) [Bamber and Layberry, 2001] and similar to that of Antarctica ice shelves (1.5 × 106 km2) [Lythe et al., 2001] and the mean August estimates (1966–2004) of snow on land across the Northern Hemisphere (1.9 × 106 km2) [Lemke et al., 2007]. In terms of volume, freshwater ice is within the range of mean estimates for snow on land across the Northern Hemisphere at 0.5 × 103 to 5 × 103 km3 [Lemke et al., 2007]. Notably, however, the calculated volume and extent of freshwater ice based on the GLWD spatial data are considered to be conservative estimates given that the GLWD does not capture very small rivers and lakes. For example, the GLWD estimates the global area of lakes to be 3.2 × 106 km2 [Lehner and Doll, 2004], whereas a more recent estimate, which includes a larger abundance of small ponds, puts this figure at 4.2 × 106 km2 [Downing et al., 2006].
Table 2. Area and Volume of Peak Freshwater Ice Across the Northern Hemisphere (NH) by Water Body Type
Error estimates were calculated based on ice thickness model validation residual standard error.
0.14 ± 0.03
Large lakes and reservoirs (NH)
0.56 ± 0.12
Small to medium lakes and reservoirs (NH)
0.86 ± 0.13
1.56 ± 0.28
 Using a degree-day ice growth model and ice growth coefficients defined for multiple hydroclimatic regions, the first estimates of the areal extent (1.71 × 106 km2) and volume (1.56 × 103 km3) of freshwater ice have been made for the Northern Hemisphere. The calculated quantities are comparable to those of other cryospheric components, including the volume of snow on land and the area of the Greenland ice sheet; now permit a more complete quantification of the total cryosphere; and provide benchmarks for assessing climate-related changes—those for freshwater ice being the focus of a subsequent paper.
 This research was completed as part of the Master's thesis of R. N. Brooks and supported in part by Environment Canada and the Natural Sciences and Engineering Research Council of Canada via Discovery and ArcticNet grants to T. D. Prowse.