### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[1] This paper describes research conducted to develop an integrated snow monitoring algorithm at global and regional scales for the Special Sensor Microwave Imager (SSM/I) and the planned Advanced Microwave Scanning Radiometer-EOS. Methods to detect global snow cover are well advanced and have been applied routinely at local, regional, and global scales. Current snow cover retrieval methods tend to underestimate snow volume because important fractional forest cover and snowpack physical properties are not well parameterized in simple snow parameter retrieval schemes. Building on a static approach to snow depth retrieval, a spatially dynamic algorithm is described that incorporates information about fractional forest cover and snowpack physical development. SSM/I brightness temperatures of land surfaces are calibrated with ground measurements of snow depth through empirical statistical and geostatistical models to produce globally distributed snow depth estimates. The calibration is based on a 4-year and a one winter season record of daily snow depth and SSM/I observations. The biasing effect of forest cover on microwave estimates is quantified and short-term fluctuations of microwave-estimated snow depth (caused by physical changes in the pack) are reduced by time smoothing daily estimated snow depth values. For the data sets used the estimated snow depth from the new algorithm gives global seasonal errors of 13.7 and 22.1 cm for the two data sets. Further major improvements in snow depth retrieval methods will only be achieved through enhancements to forest and snow metamorphism parameterizations.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[2] Global snow cover has an important influence on climate through its effect on the global water cycle and energy budgets at the surface and lower atmospheric levels [*Cohen*, 1994]. Instantaneous snow cover and temporal variations in snow cover must be represented accurately in climate models that are used to predict global climate change [*Foster et al.*, 1996]. It is known that large spatial and temporal variations exist in global and local snow cover extent and volume [*Frei and Robinson*, 1999] and characterization of these variations is of vital importance for effective climate prediction. In addition, water resource managers of snow covered river catchments need timely information about snowpack extent, volume and state. While the methods of estimation of snow area extent are beginning to mature, especially with the use of visible/infra-red radiometers such as MODIS [e.g., *Hall et al.*, 2001], there is a pressing need to estimate snow volume at regional and global scales to effectively constrain climate models. Furthermore, for many applications it is not sufficient to provide estimates only of snow depth or snow water equivalent; it is often necessary to calculate the errors associated with these estimates.

[3] The development of a snow depth retrieval algorithm for the Advanced Microwave Scanning Radiometer-EOS (AMSR-E) has proceeded from current applications of snow depth retrievals from the Special Sensor Microwave Imager (SSM/I). While the SSM/I is not identical in spatial and wave band configuration to the planned AMSR-E, it is sufficiently comparable over its four frequencies to be a useful instrument with which to develop a globally applicable snow retrieval algorithm based on the microwave emission properties of snow. The approach adopted here addresses the spatial and temporal variability in snowpack properties that can directly affect the microwave response from snow. AMSR-E will have an improved spatial resolution and expanded wave band range compared with the SSM/I and it is expected therefore that algorithm refinement will continue after the launch of Aqua.

[4] Two important elements are identified for snow cover retrieval from space using passive microwave radiometers. First, the snowpack must be detected and second it must be quantified in terms of its snow depth or volume. Compared with snow-free surfaces, a snowpack can have a distinctive electromagnetic signature at frequencies above 25 GHz. Dry snow is a scatterer of high frequency, naturally upwelling microwave radiation from the underlying ground. The microwave absorption by the snow is minimal. Therefore the extinction coefficient (sum of scattering and absorption coefficient) is dominated by scattering [*Ulaby et al.*, 1981]. When viewed using passive microwave radiometers from above the snowpack, the scattering of upwelling radiation depresses the brightness temperature of the snow at high frequencies. This scattering behavior can be exploited to detect the presence of snow on the ground and thickness of the pack.

[5] The detection of snow is achieved using a combination of the methods of *Chang et al.* [1987] and *Grody and Basist* [1996]. *Armstrong and Brodzik* [2001] note that the *Chang et al.* [1987] approach generally agrees well with visible/infrared snow cover area maps produced on a weekly basis by NOAA [*Ramsay*, 1998]. We also use the decision-tree snow mapping approach developed by *Grody and Basist* [1996] that accounts for nonsnow surfaces that exhibit microwave scattering behavior (e.g., precipitation, cold desert, frozen ground). Wet snow, which can confound snow cover retrievals by depressing the scattering behavior of the snow, is detected using a combination of information about the surface temperature [*Sun et al.*, 1996], polarization difference at 37 GHz [*Walker and Goodison*, 1993] and immediate snow cover history. Any remaining nonscattering objects are classed as “no snow”. This study also incorporates subsidiary geographical information that identifies features such as water and ocean bodies and regions where the occurrence of snow climatologically is not possible by virtue of its low latitude location [*Dewey and Heim*, 1981, 1983]. Finally, ice sheets and complex mountainous terrains are screened from the algorithm since these terrains are dominated often by complex microwave signals. Mountainous terrain is important in many parts of the world from a water resource perspective. However, the approach taken here is a conservative approach. Snow cover in mountainous terrain is highly variable over many spatial scales due to the effects that mountains exert on snowfall patterns (topographic effects such as slope and aspect) and snow redistribution. The resulting spatial variations in snow depth/SWE caused by these terrain effects certainly are evident at scale lengths far less than the spatial resolution of currently available passive microwave radiometers such as the SSM/I. Consequently, because of this exceptionally large spatial heterogeneity in snow depth in these regions, coupled with the large spatial variability of land cover type often found in mountains, we do not estimate snow depth in these regions to prevent extremely erroneous estimates of snow depth. With the future availability of AMSR-E imagery, this problem will be partly resolved because the AMSR-E scattering channels have double the spatial resolution of the SSM/I channels.

[6] Various methods have been reported to retrieve snow depth or water equivalent using spaceborne passive microwave radiometers [e.g., *Kunzi et al.*, 1982; *Tait*, 1997]. *Chang et al.* [1987] estimated the snow depth of a dry, homogeneous, single layer snowpack using radiative transfer theory and the difference between two horizontally-polarized brightness temperature channels at high and low frequencies such that:

where *b* is generally regarded as zero and *a* = 1.59 cm K^{−1} and the assumption is made that the snow grain radius is 0.3 mm and snow density is 300 kg m^{−3}. The Δ*TB* term is the difference in brightness temperature between 19 GHz and 37 GHz channels (horizontal polarization) or Tb19H and Tb37H respectively. The 37 GHz channel is sensitive to scattering by the snowpack while the 19 GHz channel is relatively unaffected by the snow and is responsive to the subnivean surface. This model works well under the noncomplex snow conditions (flat terrain, no significant forest cover, single layer dry snow) and has been the basis for several snow depth or snow water equivalent (SWE) retrieval algorithms [e.g., *Goodison and Walker*, 1994; *Foster et al.*, 1997]. However, for global applications, there are additional factors that need to be incorporated into a retrieval scheme for successful snow depth estimation.

[7] Equation (1) above indicates a spatially static parameterization of *a* and *b* based on radiative transfer properties of a snowpack of specific character. While this might apply in some regions at certain times in the winter season [*Josberger et al.*, 1995], the nature of snow is temporally and spatially dynamic in evolution and physical properties [*Sturm et al.*, 1995]. *Foster et al.* [1997] made progress to spatially enhance the relationship at broad continental scales but further refinement is necessary given the regional variability of snowpack properties [*Sturm et al.*, 1995]. This paper therefore seeks to vary the *a* and *b* coefficients spatially using seasonally averaged SSM/I and snow depth data that represent “average” regional snow conditions. Additional problems that are addressed are the effects of forest cover on microwave scattering, and of temporally varying snowpack properties on microwave emission.

### 2. Data Sets Used in the Study

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[8] Two data sets were used for calibration. The first data set consisted of 100 distributed Northern Hemisphere meteorological stations obtained from the World Meteorological Organization (WMO)/Global Telecommunication System (GTS) archive [*Chang and Koike*, 2000]. The data span a four-year period (January 1992 to December 1995 inclusive) of daily observations (early morning) and were quality controlled to remove 29 anomalous stations or stations containing obvious erroneous readings. Anomalous stations were stations that are subject to large subfootprint emissivity variations (e.g., close to a large water body) or where the station elevation was unrepresentative of local terrain (e.g., on top of a mountain). Figure 1 shows the location of the 71 meteorological stations comprising the four-year record. A second set of daily snow depth measurements (October 2000 to May 2001 inclusive) from the WMO global data archive was also used (http://lwf.ncdc.noaa.gov/ (last visited 12 April 2001)). 8000 stations comprise this data set although less than 1000 stations record snow depth with any regularity. For both data sets, the snow depth measurements were converted from inches to centimeters and reprojected to the 25 km Equal Area Scaleable Earth Grid (EASE-grid) [*Armstrong and Brodzik*, 1995]. SSM/I brightness temperature swath data were reprojected to the EASE-grid projection and for each day, the geographically closest suite of SSM/I brightness temperature samples were paired with spatially coincident snow depth observations.

[9] In the absence of spatially intensive snow depth measurements, these data are often the only globally consistent data available. Problems exist with the WMO data since snow depth is not the prime measured variable; snow depth records are present but sometimes on a very irregular basis (especially during the early and late times in the winter season). In addition and in some cases, snow depth measurement sites will be unrepresentative of snow depth conditions at microscale distances (less than 10 m) and, therefore overestimation or underestimation of snow depth at this scale is expected. Furthermore, in the absence of spatially intensive measurements, an assumption is made that station measurements of snow depth were representative of the average 25 × 25 km EASE-grid cell snow depth. However, in many regions, terrain and vegetation are heterogeneous [e.g., *Yang and Woo*, 1999] and can produce large spatial variations in snow depth within an EASE-grid cell. *Brasnett* [1999] has shown quantitatively how WMO meteorological station elevation is not always representative of surrounding elevation suggesting therefore that snow depth measurements will not always be representative of the local conditions. This scaling issue is the focus for current research. Nevertheless, these WMO data were used, as they constituted the only independent means of quantifying snow depth on the ground.

### 3. Algorithm Recalibration

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[10] The approach for algorithm recalibration used the 1992–1995 data set of snow depth observations to compute new *a* and *b* coefficients in equation (1). This data set was chosen initially since it covers four different snow seasons in the Northern Hemisphere. Before recalibration could proceed, further quality control was required. Figure 2 shows two plots of paired Δ*TB* (Tb19V–Tb37V) for “cold” SSM/I passes in the early morning (when snowpack liquid water content is minimal) against snow depth for a GTS station in northern Sweden. The data represented span the winter seasons 1992/1993 and 1993/1994 with different symbols representing different time groupings for each season (October and November, December, January, etc.). It is interesting to note that for the 1992/1993, a hysteresis loop is evident in the data. An increase in snow depth through the early to mid season is accompanied by an increase in Δ*TB*. However, once maximum snow depths are reached and the pack starts to melt, the Δ*TB* values decrease more rapidly than the decline of measured snow depth. This is due to the presence of water in the snowpack (which suppresses scattering from the pack) and the effect is enough to suggest that for the whole season, the relationship between snow depth and SSM/I scattering indices is ambiguous with more than one snow depth value possible for any given Δ*TB*. For the 1993/1994 season, the situation is similar in the early part to the 1992/1993 mid season. However, as the snowpack begins to thaw and the depth declines, several melt-refreeze events cause the Δ*TB* to fluctuate significantly. Consequently, for robust relationships to be derived between snow depth and Δ*TB*, the late season data (April and May) are removed from the analysis.

[11] For all 71 stations, snow depth observations were linearly regressed against the Δ*TB* (Tb19V–Tb37V) for the “cold” SSM/I passes (early morning). For all the station data examined, only 52 stations had significant correlations between snow depth and Δ*TB* at the 95% significance level. In all regression cases, the *b* coefficient in equation (1) was computed and for the 52 stations, the maximum coefficient of determination (R^{2}) was 0.73 with a mean value of 0.32 and standard deviation of 0.20. Thus, although statistical significance could be assigned to the relationships, not all regression models were ideal. This is to be expected when comparing point snow depth measurements with areal brightness temperature values at the 25 × 25 km scale. Nevertheless, as a methodology on which to build, inclusion of future similar data sets would be expected to improve regression model fits.

[12] Figure 3 shows the variation in regression coefficient (*a*) and standard error of the regression as a function of latitude. It shows that the standard error of regression is unrelated to geographical latitude suggesting that there is no geographical bias or trend to the standard errors. Seven stations with unusually high standard errors of regression are shown with shaded circles. Further investigation could not provide any evidence for the abnormally high errors (the sites are not close to large water bodies nor at unrepresentative terrain locations) and so these data were retained in the data set. It is useful to note, however, that these anomalous sites are not geographically clustered (Quebec, central north Siberia, central Siberia, central Europe, Alaska, Sweden, British Columbia). This lends confidence to the approach as a global method.

[13] With respect to the regression coefficient (*a*) from equation (1), the coefficient increases with latitude to approximately 60°N before generally decreasing at higher latitudes. The increase in coefficient between 55 and 63°N is probably caused by vegetation effects (especially forest cover) in this latitude band which can suppress the microwave signal significantly. At latitudes greater than 63°N, the coefficient declines, probably as a result of the occurrence of depth hoar that can strongly enhance microwave scattering at frequencies greater than 25 GHz and can result in significant snow depth overestimation. It is useful to note that the station data and passive microwave data appear to compensate for such behavior. In general the error bars, representing the confidence intervals for each *a* coefficient, show an increase with increased coefficient. At higher latitudes, snowpacks tend to be seasonally stable and persistent in nature with changes in their physical properties related more to slowly varying internal processes. At low latitudes, snow cover is dominated by often hydrologically similar short-lived events that can have stable snowpack characteristics. At middle latitudes (55–63°N) persistent seasonal snowpacks can be subjected to aggressively changing external meteorological forcing (especially dynamic thermal regimes) which can produce highly variable and complex snowpacks both in terms of microwave emissivity and the spatial variability of snow depth at different spatial scales. These factors together explain the observed latitudinal pattern in Figure 3 of coefficient and confidence intervals.

[14] Having characterized the relationship between snow depth and Δ*TB* at the discrete station scale, it was necessary to integrate these relationships to a global scale. This integration was achieved using geostatistical interpolation. The spatial dependence of a variable is expressed by the semi-variogram (hereafter referred to as the variogram). In statistics, observations of a selected property are often modeled by a random variable (RV) and the spatial set of RVs covering the region of interest is known as a random function, RF [*Isaaks and Srivastava*, 1989]. In geostatistics, a sample of a spatially varying property is commonly represented as a regionalized variable, that is, as a realization of a random function, RF. The semi-variance (γ) may be defined as half the expected squared difference between the RFs *Z*(**x**) and *Z*(**x** + **h**) at a particular lag **h**. The variogram, defined as a parameter of the RF model, is then the function that relates semi-variance to lag:

The sample variogram γ(h) can be estimated for *p*(**h**) pairs of observations or realizations, {*z*(*x*_{l} + h), *l* = 1,2,...., *p*(h)} by:

[15] In this paper all variograms were computed using the GSTAT software [*Pebesma and Wesseling*, 1998]. Variograms were calculated for the *a* and *b* regression coefficients in all directions with a 260 km lag spacing (this represents the minimum spacing of snow depth measurement sites). This spacing was chosen because the SSM/I data are projected to the 25 km EASE-grid. The semivariance was estimated to a maximum lag of 200 lags (5000 km), variograms were computed and spherical models were fitted using a weighted least squares criterion (WLS). Figure 4 shows the variograms of the Northern Hemisphere for both coefficients and gives the variogram model statistics for both regression parameters. For the variogram of the *b* coefficient, a nugget model was computed as suggested by the experimental variogram. However, for the *a* coefficient, the justification for a nugget model was not obvious and so a nugget model was not used. The nugget variance represents unresolved variation (including measurement error) while the range represents the spatial limit to spatial correlation. The form of the variograms (in particular, that a bounded model provided a good fit in both cases) suggests that a stationary RF model provides an adequate model of the variation in this case. In particular, a trend model was not necessary. These model parameters were then used to interpolate globally both coefficients using kriging. Figure 5 shows the *a* and *b* linear regression coefficient maps.

[16] Once the spatial dependency of the *a* and *b* coefficients had been modelled and interpolated, it was necessary to quantify the effects of forest cover on the passive microwave retrievals. Studies have shown that forest cover can lead to significant underestimation of snow depth because a forest canopy often masks the scattering signal from the under-storey snowpack [*Chang et al.*, 1996]. In the boreal forests of the world, this effect is important and needs to be accounted for in a global snow depth retrieval algorithm. A major problem is that of obtaining representative data on forest cover (spatial percentage of forest fraction) at a scale that can be used with large-scale microwave observations. Forest fraction data were derived from the International Geosphere Biosphere Project product reported by *Loveland et al.* [2000]. The National Snow and Ice Data Center have reprojected these data to a 25 km EASE-grid product to produce seventeen files of percentage land cover class. For each 25 × 25 km pixel, a percentage value of the seventeen land cover types is assigned. We aggregated all forest classes to produce a total fractional forest cover map.

[17] Using the four-year 52 station snow depth data set, a statistical linear regression relationship between the *a* coefficient from (1) and forest fraction gave an R^{2} of 0.2 and standard error of 0.7 cm K^{−1}. Although the relationship was statistically significant, the regression did not model the relationship well. The reason for this is that the 52 meteorological station network does not cover a large enough range of forest fractions and so even though the SSM/I and snow depth data were temporally intensive they could not encapsulate the forest fraction effect. It should also be noted that the forest fraction data are not pure forest fraction data but a surrogate of forest fraction and that calculating a regression equation in this manner probably will not improve the accuracy of snow depth estimation. Therefore, to circumvent the problem, using the spatially intensive and geographically widespread 2000/2001 data, an alternative approach was devised to quantify the forest effect. For each day from December through March, the snow depth was estimated using the kriged coefficients described above. The difference between estimated and observed snow depth (hereafter referred to as bias) was calculated ({estimated-measured}*100%) and for each integer forest fraction percent, the average bias was computed. The result is shown in Figure 6a and reveals a weak inverse linear trend between these variables. Because the forest fraction data are not ideal and the snow depth measurements can have considerable errors, the bias data were aggregated further into larger classes of forest fraction at 10% increments. Figure 6b shows the result of this aggregation and reveals an improved relationship between bias and forest fraction:

The R^{2} was 0.6 with a standard error of regression 3.4%. It is expected that very little effect on snow depth retrieval bias will be observed for fractions greater than 70% since the microwave response is already dominated by the forest emission. Therefore fractions greater than 70% are reset to 70%. Furthermore, it is assumed that for forest fractions less than 30% (when the bias exceeds 100%) there is no underestimation by forest cover within the 25 × 25 km grid cell and the bias is set to 100%. The new estimated snow depth (*SD*′) is:

[18] A final component was required in the algorithm to account for short-term fluctuations in the scattering response of the SSM/I. Figure 7 shows the 1993/1994 season time series of measured snow depth at a north Sweden meteorological station. In addition, the estimated snow depth using the kriged *a* and *b* coefficients in (1) plus the forest bias effect is shown. The thin black line represents independent, daily SSM/I-derived estimates. For the majority of the time period the thin black line is coincident with the thicker black line. However, toward the end of the season on a day-to-day basis the microwave-estimated snow depth line becomes highly variable even though the measured snow depth changes only gradually. The reason for this fluctuation is because the pack undergoes melt-freeze processes that cause the microwave scattering behavior of the pack to fluctuate dramatically. By comparing the instantaneous estimate of snow depth from the SSM/I with the recent past snow depth history (five days), a smoothing mechanism can be applied to reduce the effects of the snowpack physical state which might cause significant under or over-estimation of snow depth. In the approach used here, if the instantaneous snow depth is not significantly different from the previous five-day average (less than 20 cm of snow depth change), then the instantaneous value is the estimate used. If there is a significant difference, then the value used is an average of the five days plus the instantaneous value. This has the effect of smoothing out large fluctuations and is shown by the thick line in Figure 7.

### 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[19] Comparisons between estimated and measured snow depth values were undertaken for the 1992–1994 data set. For each “cold” pass, and for each station, the original snow depth algorithm coefficient (hereafter referred to as “Standard 1.59”), that assigns 1.59 cm K^{−1} to *a* (equation 1), was applied to the data set. The Δ*TB* term in (1) is the vertically polarized brightness temperature difference between 19 and 37 GHz. It includes a −5 k offset implicitly presented by *van der Veen and Jezek* [1993] and also noted by *Armstrong and Brodzik* [2001] for application to the horizontally polarized version of the algorithm in (1). *Van der Veen and Jezek* [1993] observed that the difference between summer maximum brightness temperatures for the Scanning Multichannel Microwave Radiometer (SMMR) at 18 and 37 GHz vertical polarization was −6.5 K while for the SSM/I, the difference was noted as −1.5 K. Consequently, when applying the expression in (1) using either vertical or horizontal polarization versions, a −5 K offset must be added to the Δ*TB* term. Although several authors have implemented this algorithm using horizontal polarized channels, similar results will be obtained using vertically polarized channels [*Chang and Koike*, 2000]. Over an SSM/I instantaneous field of view, the horizontally polarized channels are slightly more sensitive to surface scattering than the vertically polarized channels (especially at 37 GHz). However, these differences are rendered almost negligible when using the brightness temperature differences between 19 and 37 GHz at either like polarization combination. The slight discrepancies sometimes found are often caused by surface, or subsurface scattering effects (perhaps crustal features in the snow). Furthermore, although previous algorithms have estimated SWE and/or snow depth using horizontally polarized channels, *Hallikainen and Jolma* [1992] describe an extensive intercomparison of different passive microwave retrieval algorithms and found that the vertically polarized channels produced better results when tested against independent field data. Snow depth was also estimated using the recalibrated algorithm from section 3 above. It should be noted that for the algorithm testing, comparisons were omitted between estimated and measured snow depths in mountainous terrain (defined by the United States Geological Survey GTOPO30 data set) and over the ice sheets (Greenland and Antarctica) because the detection algorithm did not detect snow in these regions.

[20] Figure 8 shows a histogram of the standard errors for both methods applied to each station for the full four-year record. The histogram reveals that the best results are obtained using the newly recalibrated algorithm; the average standard error for all days over the four-year period is 11.7 cm (standard deviation of 5.2 cm) while the Standard 1.59 algorithm has an error of 19.4 cm with a standard deviation of 8.3 cm. These results are encouraging and demonstrate that the recalibrated method is an improvement (7.7 cm) on the original standard algorithm.

[21] Snow depth estimates were then tested against the data set used to define the forest fraction adjustment for the period 1 October 2000 to 30 April 2001. The two algorithms were applied and global daily snow depth maps were produced. Figure 9 shows the time series of average global daily standard errors for both algorithms. The average error for the standard 1.59 algorithm and recalibrated algorithm is 26.1 cm and 22.1 cm respectively (with a standard deviation of 9.9 cm and 7.4 cm respectively). The recalibrated algorithm therefore produces better results. It is significant in Figure 9, however, that for both algorithms the errors gradually increase from early to late winter suggesting that perhaps a time dynamic aspect of the algorithm (for example, representation of the snowpack physical properties) requires further improvement. Although these statistics are useful for characterizing the entire winter season, they do not provide information on the spatial distribution of the errors of estimate; are the global errors evenly distributed or are a few localized errors significant enough to adversely affect the global averages? To address this issue, Figure 10a shows a map of seasonal average errors for each station for the recalibrated algorithm. The errors are scaled from −20 to +20 cm and the error at each meteorological station has been spatially dilated to 3 × 3 pixels to enhance the visual interpretation. The error map suggests that there is significant underestimation of snow depth in two main areas, south-east central Russia and north and east of the Great Lakes in Canada as shown by negatively shaded pixels in these regions. To determine whether these are random or systematic errors, Figures 10b, 10c, and 10d show a sequence of average errors on 15 December 2000, 31 January 2001, and 15 March 2001 for the recalibrated algorithm. Again, the points are dilated for visual interpretation. The two areas identified above are clearly visible for all three times during the year suggesting that the underestimation is systematic. The forest cover data set is shown in Figure 10e and comparison between the errors of underestimation in the algorithm estimates and the forest cover location reveals that the areas of large underestimation coincide with forest covered areas. The most probable cause of this underestimation therefore is the nature of the relationship between the estimate bias and the forest fraction described in section 3. While the methodology seems reasonable, the IGBP forest fraction data set is a surrogate of forest fraction and needs improvement. The most widespread underestimation occurs in the mid season (31 January, 2000) in the identified Russian and Canadian areas. In other areas, however, the algorithm errors are well below the 22 cm standard error (most stations are shaded within the −10 to +10 cm error range).

### 5. Conclusions and Future Developments

- Top of page
- Abstract
- 1. Introduction
- 2. Data Sets Used in the Study
- 3. Algorithm Recalibration
- 4. Comparison of Microwave Snow Depth Estimates With Ground Measurements
- 5. Conclusions and Future Developments
- Acknowledgments
- References

[22] An improved dynamic method to estimate snow depth using passive microwave observations has been presented. The results from the presented comparison are encouraging and indicate that for the 1992–1995 data set, the global snow depth estimates for 52 stations have an average error of 11.7 cm, which is 7.7 cm better than the *Chang et al.* [1987] estimates. For the more spatially intensive and globally widespread data set of 2000/2001, the error is 22.1 cm, which is 4.0 cm lower than the errors from the standard 1.59 algorithm. This spatially dynamic approach to estimating snow depth is an improvement on the original retrieval algorithm of *Chang et al.* [1987]; not only is the total average global seasonal error less for the new dynamic approach, but for the 2000–2001 season, daily global average snow depth errors generally are smaller (see Figure 9). Further analysis using different years of winter data should refine the spatially dynamic coefficients used in the improved algorithm. However, two issues require further attention before very significant improvements can be realized. First, a data set that better represents forest fraction is needed since the IGBP product is only a coarse surrogate of forest fraction. It is expected that in the future, more dynamic forest cover information will be available through 16-day MODIS land products. This will provide a better, more dynamic characterization of the forest cover plus it could provide information about stem volume (rather than percentage cover in a pixel) which is known to be a key effect on the microwave response of snow in forested areas [*Kurvonen et al.*, 1998]. Furthermore, it will be possible to investigate and quantify the important effect that vegetation (other than forest cover) heterogeneity has on snow emission from snowpacks within the passive microwave field of view. We have restricted ourselves to the effect that forest cover has on passive microwave emissions. However, it is known that different types of vegetation can affect the passive microwave response from snow. Using time dynamic MODIS land cover data, vegetation effects as a whole can be incorporated in our snow estimation methodology. Second, a means of estimating the changes in snowpack vertical grain size distribution is required to provide better parameterization of the retrieval algorithm. This is the reason why the errors increase globally through the winter season in Figure 9. Numerical models are available to assist in this respect but often they require high quality and frequent microclimatological data at local spatial scales; at the regional/global scale, these data may not always be available. Efforts need to be focused on these dynamic issues to further reduce the snow cover retrieval errors from passive microwave estimates.

[23] Finally, this work paves the way for developing a semi-empirical SWE/snow depth retrieval methodology for use with AMSR-E due for launch aboard Aqua. Compared with the SSM/I configuration, AMSR-E has twice the spatial resolution and two extra low frequency channels that will assist with subnivean state quantification (frozen/wet/dry soil). These two factors alone should help to improve both snowpack detection accuracy and snow depth/SWE retrieval accuracy.