2.1. Active Layer and Freeze Depth Interpolation
 The data used in this study include soil temperature, observed freeze/thaw depth, air temperature, and snow depth. Soil temperature data are available for 242 stations located throughout Russia (Figure 1) [Barry et al., 2001; International Permafrost Association Standing Committee on Data Information and Communication, 2003] and can be obtained from the Frozen Ground Data Center (http://nsidc.org/fgdc/). Detailed descriptions of soil temperature measurements in the former Soviet Union were provided by Gilichinsky et al. , Zhang et al. [2001a], and in the instruction manuals of the State Committee of the U.S.S.R. for Hydrometeorology and Environmental Control  and earlier issues from 1946 to 1969 [State Committee of the U.S.S.R. for Hydrometeorology and Environmental Control, 1960–1964, 1964–1972, 1966–1990, 1970–1978]. A brief review follows.
Figure 1. Map showing the geographic locations of the 242 Russian stations with available data. Grey diamonds represent stations with both soil temperature and freeze/thaw depth data, and black circles represent those stations with soil temperature data only. Expanding the database of active layer and freeze depth stations from 208 to 242 adds many sites throughout Siberia, especially in central and northeastern Siberia (black circles). Denoted also are those 31 stations that are characterized as permafrost (black open circles and grey open diamonds) and those 211 that are on seasonally frozen ground (black closed circles and grey closed diamonds).
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 Mean monthly soil temperature was measured by extraction thermometers enclosed in ebonite pipes and installed at a depth of 0.20 m and deeper under natural surface cover such as grass, periodically cut during the warm season, and undisturbed snow cover during the cold season [Gilichinsky et al., 1998]. During the 1960s and 1970s, the soil temperature measurements were performed using electrical resistance thermometers at some stations. It must be noted, however, that taking these soil temperature observations unavoidably causes some site disturbance, which, over time, may cause increased thaw propagation. Therefore any long-term trends in active layer thickness potentially include this nonclimatic component. However, in the former Soviet Union hydrometeorological observation system, these measurements were conducted by well-trained technicians and professionals with established and uniform guidelines. Therefore site disturbance was reduced to minimum [Gilichinsky et al., 1998]. Observations were generally made at standard depths; however, as some of these stations span a century of observations, the standard depths changed several times. The measurements at 0.2 m, 0.4 m, 0.6 m, 0.8 m, 1.2 m, 1.6 m, 2.0 m, 2.4 m, and 3.2 m used here represent those depths that did not change throughout the observational period across all stations. The time period covered by these data varies by location: At some stations, the soil temperature record spans from the late 1800s to 1990, while at others only a few years of measurements are available. However, for many of the stations, data for the 1930–1990 period are available, and therefore this study focuses on this portion of the record. Similarly, observed freeze/thaw depth data, i.e., the monthly maximum depths of penetration of the 0°C isotherm during freezing/thawing, are generally consistently available beginning in 1930, but only until 1985. These freeze/thaw depths are based on daily observations of soil temperature, from which a daily freeze/thaw depth is interpolated. The maximum daily depth was selected from all daily depths for each month to represent that month's thaw or freeze depth. Of the 242 Russian stations, 208 also have these freeze/thaw depth observations (Figure 1).
 To expand the number of stations with freeze/thaw depth data from 208 to 242 and to expand the time series from 1985 to 1990 for all stations, thereby obtaining a larger and longer database of observations characterizing freeze/thaw depth in the permafrost and seasonally frozen ground regions throughout Russia, we linearly interpolated the depth of the 0°C isotherm throughout the 0.2–3.2 m temperature profile. It should be noted, however, that although the depth of the 0°C isotherm can be used as an estimate of the freeze/thaw depth it is not necessarily the same as the “true” freeze/thaw depth. For wet/ice-rich soils latent heat can play an important role which could lead to errors in estimating the freeze/thaw depth using the propagation of the 0°C isotherm. The stations were first classified as either permafrost or seasonally frozen ground, depending on soil temperature at the 3.2 m depth. If, for the entire record, a station's soil temperature at 3.2 m was negative, that station was classified as permafrost. The remaining stations were considered to be characterized as seasonally frozen ground. Soil temperature time series at 3.2 m depth were also plotted and analyzed visually, to ensure proper classification. The two subsets of stations were then analyzed separately. Active layer depths were interpolated in the permafrost region, where the temperature from one depth to the next switched from being positive to negative. Similarly, in the seasonally frozen ground regions, the freeze depth was interpolated between those layers where the temperature switched from negative to positive.
 In the best-case scenario, the 0°C isotherm falls between a positive and an adjacent negative value. However, because of missing values, this interpolation is often not possible. Therefore interpolations were performed between multiple layers, depending on data availability across the 0.2–3.2 m profile. There is a trade-off between sample-size and interpolation accuracy, though, such that the most restrictive interpolation (where the depth of the 0°C isotherm is interpolated between available adjacent values only) results in the smallest sample-size. Conversely, if the freeze/thaw depth is interpolated between any and all available depths, the interpolation skill decreases, since the temperature profile between, for example, the 0.2 m depth and the 3.2 m depth is not linear. Therefore our interpolation was limited to between any four standard soil depths only (i.e., allowing soil temperature at two depths to be missing), providing an optimal sample size and interpolation skill.
 The resulting data set of interpolated monthly freeze/thaw depths, as well as the observed daily freeze/thaw depths, were then analyzed further: Annual maximum depth of penetration of the 0°C isotherm during both freezing and thawing was calculated, as it is the changes in this variable over time that provide insight into climate change in the Russian high latitudes. The maximum depth of freezing values were selected from the months of March, April, and May only, and the maximum depth of thawing was selected from the months of August, September, and October only. It is during these months that the maximum depths are expected to occur, and this restriction was necessary because of missing data. For instance, if the maximum freeze depth was always chosen from all months of the calendar year, but the winter and spring half of a year is missing, the maximum depth of freezing could be severely underestimated because it would be chosen from the warm season, when thawing has already begun.
 The accuracy of the interpolation is dependent on interpolation method, vertical spacing of measuring devices, as well as other factors, and we therefore carefully assess the accuracy of our interpolation: The monthly interpolated freeze/thaw depths were compared to the observed daily values for those stations where both variables are available. This was done via linear regression between the observed daily freeze/thaw depths and the monthly interpolated ones. It is this analysis that assesses the accuracy of our interpolation, where a perfect 1:1 relationship would be described by a regression R-value of 1 and a regression slope of 1.
 Given this new and expanded data set of monthly freeze/thaw depths, the long-term trends were then assessed for the Russian high latitudes. An average time series was generated for the annual active layer depth departures in the permafrost region, and an average time series was generated for the maximum annual freezing layer depth departures in the seasonally frozen ground regions. The permafrost region average was formed by averaging, for each year, all available stations' annual active layer depth departures from each station's mean for the available record, for those stations that are classified as permafrost. Similarly, the seasonally frozen ground average was formed by averaging all available stations' maximum annual freezing depth departures from each station's mean, for all seasonally frozen ground stations. Linear least squares regression was then applied to these two time series to quantify their long-term changes.
2.2. Forcing Variables
 To explore possible causes for potential long-term changes in the freeze/thaw depths, the averaged time series were related to a number of external forcing variables, such as air temperature, freezing index, thawing index, and snow depth. Air temperature was based on the CRU TS 1.0 (1901–1995) and CRU TS 1.1 (1996–1998) data [New et al., 2000], which are available as globally gridded monthly air temperature data on a 0.5° × 0.5° grid for 1901–1998. The air temperatures corresponding to the 242 Russian stations were extracted from that grid on the basis of which grid cell each station occupies, i.e., the closest grid cell center to each station, for 1930–1990. Mean annual air temperatures were calculated for January–December of each year from the monthly data. The freezing and thawing indices were also calculated from the New et al.  air temperature data. The freezing index is a measure of the combined duration and magnitude of below 0°C temperatures during any given freezing season, and is generally calculated as the sum of the average daily temperatures for all days with below-zero temperatures [Permafrost Subcommittee, 1988]. Similarly, the thawing index is a measure of the duration and magnitude of above-zero temperatures during the thawing season, and is generally calculated as the sum of the daily temperatures for all days with positive temperatures [Permafrost Subcommittee, 1988]. In this study, however, the freezing index was calculated on the basis of mean monthly air temperature. Zhang et al.  found that the use of mean monthly air temperature to estimate freezing and thawing indices is accurate to approximately 95% for northern Alaska. The freezing and thawing indices were calculated for July (year t-1)–June (year t) and January (year t)–December (year t), respectively, to ensure that the entire freeze/thaw season was captured.
 Snow depth data were obtained from the Historical Soviet Daily Snow Depth (HSDSD) data set [Armstrong, 2001]. The HSDSD data are based on observations from 284 World Meteorological Organization (WMO) stations located throughout the former Soviet Union for the period 1881–1995. Those WMO stations closest to the 242 Russian soil temperature stations were selected (Figure 2), and the daily snow depths were averaged into monthly snow depths for 1930–1990, as well as annual averages. Similarly, monthly maximum snow depth was acquired from the daily snow depths, as well as annual maximum snow depth. The annual averages and maxima were not calculated for the calendar year but rather for July (year t-1)–June (year t). Therefore, in establishing potential relationships between snow depth and freeze/thaw depth, we are linking the previous winter's snow depth with concurrent or subsequent freeze/thaw depth. It was possible to match 92 of the Russian soil temperature stations to the WMO snow depth stations, of which 9 were in the permafrost region and the remaining 83 in the seasonally frozen ground region. In some instances, it was possible to match a WMO snow station to two soil temperature stations; in this case, the same snow station data were used for both soil temperature stations.
Figure 2. Geographic location of the snow depth data stations and Russian soil temperature stations. The 92 matched-up snow and soil temperature stations are circled. Of these 92 sites with both snow and soil temperature data, 9 are located on permafrost and 83 are located on seasonally frozen ground.
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 Air temperature, freezing/thawing index, and snow depth corresponding to the 242 Russian soil temperature stations were then averaged for the permafrost and the seasonally frozen ground regions separately, and related to the changes in maximum annual freeze/thaw depth using both correlation and multiple regression analysis. For the permafrost region, active layer depth was correlated with air temperature, the thawing index, and both average and maximum snow depth, and a multiple regression model was also built to evaluate the combined effect of these variables on the active layer. The temporal trend of each variable is also determined for the permafrost region using linear regression. For the seasonally frozen ground region, freeze depth was correlated with air temperature, freezing index, and average as well as maximum snow depth, and multiple regression was again employed. The long-term trend of each variable was also assessed to determine the changes of those variables in the seasonally frozen ground region.