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2 Available online at Remote Sensing of Environment 111 (2007) Observations and statistical analysis of combined active passive microwave space-borne data and snow depth at large spatial scales M. Tedesco a,b,, J. Miller b,c a University of Maryland Baltimore County Baltimore, MD, USA b NASA Goddard Space Flight Center, Greenbelt, MD, USA c RSIS, 1651 Old Meadow Rd, McLean, VA, 22102, USA Received 14 October 2006; received in revised form 12 April 2007; accepted 14 April 2007 Abstract Remote sensing based on active and passive microwave data represents a useful tool for studying the state of the cryosphere at high temporal resolution and large spatial scale. In particular, retrieving snow parameters from space-borne data can benefit hydrological, meteorological, and climatological applications. In this paper, we analyze the trend of Ku band backscatter coefficients measured by the NASA's Quick Scatterometer (QuikSCAT) and K and Ka band brightness temperatures measured by the Special Sensor Microwave Imager (SSM/I) with respect to snow depth values at different locations in the Northern hemisphere during the period We also quantify, for the first time, the dynamic range of space-borne Ku band scatterometer data over snow covered areas at very large spatial scale in comparison to the range in passive microwave brightness temperatures. Also for the first time, we quantify the improvement on the snow depth retrieval related to the combined use of active and passive data and compare the results with those obtained using either only active or passive data. Finally, we report first results regarding an analysis involving X-band brightness temperatures, collected by the Advanced Microwave Scanning Radiometer for EOS (AMSR-E), aiming at understanding whether the improvements derived from using a combination of active and passive data are related to the use of a low frequency or to the different techniques used (e.g., active or passive) Elsevier Inc. All rights reserved. Keywords: Microwave remote sensing; Active and passive; Snow; Snow depth 1. Introduction Estimating snowpack properties over large geographic regions is a crucial task for multiple reasons. In many high altitude and latitude areas snow melt runoff represents an important source of water to rivers: for example in California and Colorado snow melt represents, respectively, 80% and 70% of all surface water ( Hydro/intro.html). Monitoring of snow from space may help in flood forecasting and reduce the risks to people living in those areas prone to floods: in the USA only, eight of the top twenty floods of the 20th century were related to snowmelt (Perry, 2000). The high albedo of snow makes it a dominant factor in the climate system. For example, if temperature decreases then Corresponding author. NASA Goddard Space Flight Center, Greenbelt, MD, USA. address: mtedesco@umbc.edu (M. Tedesco). the amount of snow will generally increase or last for longer periods annually, leading to an increase of the planetary albedo and to a further decrease of the temperature (because of the more solar radiation reflected and less energy available to heat the atmosphere). On the other hand, if the snow extent decreases then less solar radiation will be reflected and the temperature will increase, with further decrease of the snow cover (Peixoto & Oort, 1992). Space-borne remote sensing instruments provide data across remote areas at very large spatial scales. Optical data have the advantage of a high spatial resolution but they are limited in temporal coverage by sun illumination and cloud coverage. Besides, they can provide information only on the upper part of the snowpack (e.g. snow covered area (SCA), or surface temperature) because of the small penetration depth at the wavelengths of interest. In contrast, microwave data offer a coarser spatial resolution but they are not limited by the presence of sun and clouds. The resolution of microwave /$ - see front matter 2007 Elsevier Inc. All rights reserved. doi: /j.rse

3 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) sensors is a limiting factor for those applications where the scale of spatial variability of snow parameters is much smaller of the spatial resolution of microwave data (e.g., in mountain areas). In addition, the presence of forests masks the radiation emitted by the snowpack underlying the trees, with a consequent reduced sensitivity to snow parameters. In view of the high penetration depth, microwave data can also provide information on the internal structure of the snowpack and related parameters, such as snow depth and snow water equivalent (SWE). There are two distinct modes for collecting microwave data: active and passive. In the active case, the sensor (e.g. scatterometer) illuminates the object by emitting radiation in its direction and then it detects and measures the radiation that is reflected or backscattered from the target. Passive sensors (e.g. radiometers) detect natural energy (radiation) that is emitted by the object or scene being observed. Recent studies have proven that the combination of active and passive data can be very helpful for improving the retrieval of the parameters of interest. For example, studies conducted within the framework of the AQUARIUS (funded and scheduled for launch on 2009) and the HYDROS 1 (canceled) satellite missions show that the combination of active and passive data is very useful in improving the retrieval performance of the parameter under study (e.g., Entekhabi et al., 2004). The NASA Cold Land Processes Working Group (one of three Future Hydrologic Missions Working Groups sponsored by the NASA Land Surface Hydrology Program, LSHP) also has identified a high potential in the combination of active and passive microwave data for improving the retrieval of snow parameters with respect to passive data alone. Other studies reported promising benefits of combining active and passive microwave data for monitoring soil and vegetation (e.g., Macelloni et al., 2003; Wigneron et al., 1999). There are several practical advantages in combining Quik- SCAT and SSM/I data: first, the resolution is similar ( km); second, the incidence angle is constant and nearly the same with QuikSCAT collecting data at 46 for the horizontal polarization and 54 for the vertical polarization and SSM/I measuring brightness temperatures with a fixed angle of 53, both polarizations; third, both sensors have a wide swath (QuikSCAT 1800 km, SSM/I 1400 km) allowing data acquisition for northern regions twice per day; fourth, their overpasses are close in time. In this paper we a) investigate trends of active (QuikSCAT) and passive (SSM/I) space-borne data at different locations as the snow season evolves to improve our understanding of the relationships between snow depth and microwave data, b) study the sensitivity of passive and active data to snow depth by quantifying, for the first time, the dynamic range of active data over a large spatial scale; c) compare the results of the retrieval of snow depth from either the active or passive data alone with the combination of the two in order to understand whether a combined approach can benefit the snow depth retrieval. To achieve our task we select several World Meterological Organization (WMO) stations distributed over the Northern Hemisphere, reporting air temperature and snow depth and compare the 1 Although the HYDROS mission has been cancelled the studies and the research done in preparation of the potential mission still provides a valid reference. temporal trends of backscatter coefficients, brightness temperatures, snow depth and air temperature for five snow seasons ( ). We point out here that the comparison of point measurements with satellite derived snow estimates are affected by error and uncertainties deriving from the different spatial scales at which data are acquired. The number of samples required to accurately represent SWE or snow depth depends on both the spatial variability of the parameter of interest within the large field and the accuracy requirements (Snedecor & Cochran, 1967). For example, we will need 16 gauges within a satellite pixel that measure SWE variations of 20 mm accurate to +/ 10 mm. With four measurements the accuracy becomes +/ 20 mm. Unfortunately, only one point measurement per pixel was available for the data set used here, resulting in an increased uncertainty in the comparison between ground-based and satellite-derived snow depth values. The correlation between microwave data (both active and passive, as well as their combination) and snow depth is also studied. An analysis of the root mean square error (RMSE), the coefficient of determination and the regression coefficient for several combinations of active and passive data is performed to quantify the observed changes. We also report preliminary results aimed at understanding whether a combined use of microwave active and passive sensors will benefit from factors such as different and complementary observation characteristics, different frequencies and fundamental physical processes involved. To understand if the benefits observed with the combination of the active and passive data can be also obtained by using passive data collected at a frequency similar to that of active data, we compare the results obtained with the combination of K- and Ka-band brightness temperatures and Ku-band scatterometer data with those obtained from the combination of the K- and Ka-band data with data from AMSR-E at X band. 2. Background Space-borne passive microwave instruments have been measuring brightness temperatures from the Earth for about 30 years, starting with the Scanning Multichannel Microwave Radiometer (SMMR, ), continuing with the Special Sensor Microwave Imager (SSM/I, 1987 present) and with the most recent Advanced Microwave Scanning Radiometer (AMSR-E, 2002 present). The relationships between microwave brightness temperatures and snow parameters have been studied from both theoretical and practical points of view. The intensity of radiation emitted through and from a snowpack depends on several factors such as physical temperature, snow water equivalent (SWE, e.g. the amount of liquid water stored in the snowpack), grain size, and underlying surface conditions. For dry snow, the dominant mechanism is volumetric scattering, with brightness temperatures decreasing as snow accumulates (e.g., Chang et al., 1987). With the launch of space-borne scatterometers (originally designed to measure oceanic surface winds), active microwave data at Ku band (13.4 GHz) have become available, providing daily measurements for 90% of the Earth for nearly a decade (Seasat A scatterometer 1978, NSCAT August 1996 June 1997 and Seawinds on QuikSCAT June 1999 today). Ku-band backscatter coefficients are also sensitive to snow properties allowing the

4 384 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) development of techniques for the retrieval of onset of snowmelt and snow accumulation as well as for detecting and mapping the extent of ice layer formation. Several algorithms have been proposed in the literature for the retrieval of SWE and snow depth (SD) at large scale from passive microwave data, e.g. Aschbacher (1989), Chang et al. (1987) reviewed and updated for forested areas by Foster et al. (1997), Hallikainen and Jolma (1992) and Tait (1998), to name a few. Subsequently, further studies were conducted by Goita et al. (2003), Goodison and Walker (1995), Grippa et al. (2004). Also, Tedesco et al. (2004) show that a non-linear approach based on artificial neural networks (ANN) can considerably improve the retrieval of SD and SWE. In addition, Derksen et al. (2003) describe a regional approach to estimate SWE in western Canada using satellite passive microwave observations from SSM/I. The sensitivity of Ku-band space-borne scatterometer data to snow parameters has been investigated only in the past few years (Hallikainen et al., 2004; Hillard et al., 2003; Kimball et al., 2001; Nghiem & Tsai, 2001). The potential of the NSCAT data for applications to remote sensing of snow at global scale has been studied in the literature (Nghiem & Tsai, 2001; Wang et al., 2005) showing that Ku-band backscatter is sensitive to snow properties. They also show that onset of snowmelt can be detected effectively using NSCAT data. More recently, Nghiem et al. (2005) demonstrated that QuikSCAT backscatter signatures can be used to detect and map the extent of ice layer formation in Greenland and that snow accumulation derived from QuikSCAT data well compares with snow height data at the NASA-SE station of the Greenland Climate Network. Few studies report results regarding the combination of active and passive microwave data for remote sensing of snow. Hallikainen et al. (2003) show that QuikSCAT and SSM/I data provide useful diurnal and seasonal information on snow and that the application of a combined active/passive data set to retrieve snow water equivalent improved the results from those obtained by using solely passive microwave radiometry. They also investigated the sensitivity of scatterometer data to snow parameters. Results were obtained for 21 test sites distributed over Finland. As we pointed out, existing analyses deal only with local or regional scale and, to our knowledge, no study has been made concerning the application of QuikSCAT and SSM/I (or AMSR-E) data for remote sensing of snow at large geographic scales. 3. Description of microwave and snow data In the following, for reader's convenience, we report a brief description of the microwave and snow data used in our analysis Passive microwave data Passive microwave data consist of brightness temperatures at K and Ka bands collected by the Special Sensor Microwave Imager (SSM/I) radiometer, flying on board of the Defense Meteorological Satellite Program (DMSP) F13 satellite as well as brightness temperatures collected at X, K and Ka bands by the Advanced Microwave Scanning Radiometer EOS (AMSR-E) flying on the AQUA satellite. The SSM/I is a seven-channel, four-frequency (19.35, , 37 and 85.5 GHz) microwave radiometric sensor. All channels operate in dual vertical (V) and horizontal (H) polarizations, except for the one at 22 GHz, which operates at a fixed V polarization. Detailed documentation about the SSM/I instrument is available in electronic format at In this study, we make use of the NOAA/NASA Pathfinder Program Special Sensor Microwave/Imager (SSM/I) Level 3 Equal-Area Scalable Earth Grid (EASE-Grid) Brightness Temperatures. Coverage is global and begins 9 July Gridded resolution is 25 km for all channels. The data gridding technique maximizes the radiometric integrity of the original brightness temperature values, maintains high spatial and temporal precision, and involves no averaging of original swath data. More information can be obtained at The AMSR-E is a conically scanning total power passive microwave radiometer measuring brightness temperatures at 6.925, 10.65, 18.7, 23.5, 36.5 and 89 GHz, using both vertical and horizontal polarizations, launched on May 2002 on the AQUA satellite. The mean spatial resolution is improved with respect to SSM/I and ranges between 56 km at GHz and 5.4 km at 89 GHz. In this study, we use the AMSR-E/Aqua L2A Global Swath Spatially-Resampled Brightness Temperatures (AE_L2A, Ashcroft & Wentz, 2002), containing brightness temperatures resampled to be spatially consistent. Further information about the L2A brightness temperatures can be found at As more than one pass can occur per day, depending on the latitude, the data collected during descending passes are averaged. The L2A brightness temperatures are then re-projected on the EASE-Grid with 25 km resolution Active microwave data Active data consist of backscatter coefficients measured by the Seawinds NASA's Quick Scatterometer (QuikScat), launched on June 1999 from Space Launch Complex 4 West at California's Vandenberg Air Force Base. Since then, the instrument has been collecting values of backscatter coefficient at 13.4 GHz continuously, covering approximately 90% of Earth's surface in one day. QuikSCAT operates at both vertical and horizontal polarizations with an incidence angle of, respectively, 46 (H polarization) and 54 (V polarization). Scatterometer data used in this study were obtained from the Physical Oceanography DAAC ( jpl.nasa.gov/products/product121.html) and consist of averaged daily values of backscatter coefficient, standard deviation and number of counts used to derive the average values. Further information on QuikSCAT can be found at gov/. As done for the AMSR-E data, QuikSCAT data were reprojected on the EASE-Grid with a resolution of 25 km (from the original resolution of 22.5 km/pixel at the equator) Description of snow data and test sites Daily snow depth and air temperature were measured from stations of the World Meteorological Organization (WMO) and obtained through the NOAA National Climate Data Center

5 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Fig. 1. Location of the test sites selected for this study and map of Sturm's snow classes. The numbers refer to Table 1. website ( In order to have a significant number of samples for analysis, only those stations having at least 20 measurements of snow depth per month were selected. The geographical distribution of the selected stations is reported Fig. 1., with their characteristics summarized in Table 1. Here the WMO station number, name, country or state (within the US), latitude, longitude and Sturm's snow class (Sturm et al.) of the EASE-grid pixel corresponding to the location of the station is reported. The distribution of the snow classes according to is also reported in Fig. 1. Among the 49 stations, 15 belong to the Tundra class, 26 to the Taiga class, 3 to the Alpine class, 2 to the Prairie class and 1 each to the Maritime, Water and Ice classes. To minimize the number of days when wet snow is present, 2 we consider only data collected between October 1st and March 2 As observed, the SWE/snow depth retrieval at the frequencies of interest fails in case of wet snow because of the high absorption coefficient of wet snow induced by the presence of liquid water. 1st of each year and when air temperature is less than or equal to 5 C. This is not assuring that wet snow is completely excluded from our analysis (as snow can melt below 0 C or because of the geothermal heat) but it helps in reducing the number of days when wet snow is present. It is also important to point out that ground measurements are performed at point scale where satellite data are collected at the scale of tens of kilometers. The number of ground measurements needed to fully represent the area under study depends on the required accuracy. Unfortunately, there is no satellite pixel where there is more than one point measurement and this, of course, is a source of error and uncertainty. 4. Analysis of the temporal trend of active and passive microwave data with snow depth evolution In this section, we compare the temporal trends of microwave and snow data for two selected test sites. Results and observations for these two sites can be considered valid for the remaining ones.

6 386 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Table 1 Summary of WMO stations used for this study: station number, name, country/state within the US, latitude, longitude and, finally, Sturm's snow class Test site WMO # Name Country/ state Lat. Lon. Snow class Test site WMO # Name Country/ state Lat. Lon. Snow class BETTLES FIELD AK Tundra KEVO FI Tundra SKWENTNA AK Prairie KUOPIO FI Maritime HEALY RIVER AIRPORT AK Tundra TAZOVSKOE RA Tundra SUTTON AK Prairie DUDINKA RA Tundra WAINWRIGHT AAF AK Taiga TURUHANSK RA Taiga FAIRBANKS/EIELSON A AK Taiga UZUR RA Tundra NORTHWAY AIRPORT AK Ice BOR RA Taiga FORT SIMPSON ARPT CN Taiga JARCEVO RA Taiga FORT ST. JOHN ARPT CN Alpine AGATA RA Tundra GRANDE PRAIRE ARPT CN Alpine TURA RA Taiga PEACE RIVER AIRPORT CN Taiga CHERNISHEVSKIJ RA Taiga HIGH LEVEL AIRPORT CN Tundra OLENEK RA Taiga HAY RIVER AIRPORT CN Taiga SELAGONCY RA Taiga YELLOWKNIFE AIRPORT CN Water LENSK RA Tundra FORT SMITH AIRPORT CN Taiga SUNTAR RA Taiga STONY RAPIDS ARPT CN Taiga NJURBA RA Taiga LYNN LAKE AIRPORT CN Taiga OLEKMINSK RA Taiga KARESUANDO SN Tundra VILJUJSK RA Tundra KAUTOKEINO NO Tundra ZHIGANSK RA Taiga PAJALA SN Taiga ISIT RA Taiga SIHCAJAVRI NO Tundra SANGARY RA Tundra MUONIO FI Taiga POKROVSKAJA RA Taiga PELLO FI Alpine JAKUTSK RA Tundra ROVANIEMI FI Taiga VERHOJANSK RA Taiga SODANKYLA FI Taiga A quantitative analysis regarding the dynamic of the active and passive microwave data during the snow seasons for all selected stations is reported in the next section. Fig. 2 shows the temporal trend of air temperature (upper plot), snow depth (second plot from the top) recorded by the WMO station, QuikSCAT backscatter coefficients at vertical and horizontal polarizations (third plot from the top), SSM/I brightness temperatures, vertical polarization (second plot from the bottom) and horizontal polarization (bottom plot) for the two stations of Njurba (Fig. 2 (a), WMO # , Lat N, Lon E) and Yellowknife Airport (Fig. 2 (b), WMO # , Lat N, Lon E). As pointed out by Nghiem and Tsai (2001), four distinct trends can be identified during the year: 1) the backscatter coefficient decreases before snow falls as a consequence of the freezing soil and consequent reduction of the permittivity of soil and vegetation; 2) the backscatter increases when snow accumulates because of the volumetric scattering introduced by the snowpack; 3) the backscatter strongly decreases when snow starts melting as a consequence of insurgence of liquid water in the snow; 4) finally, the backscatter coefficient increases again as the soil thaws and the permittivity of other elements in the scene, such as trees, leaves, increases. As expected, brightness temperatures at ~19 GHz show a weak sensitivity to the snow depth variation where the decrease of the brightness temperatures at 37 GHz is more pronounced. The sensitivity to melting snow is also evident in the active case (Nghiem & Tsai, 2001); measured backscatter suddenly decreases as snow starts melting because of the presence of liquid water within the snowpack. The passive measurements also show sensitivity to the melting snow, although their sensitivity appears to be smaller than the active data. A more detailed analysis of the variation of QuikSCAT data with snow depth reveals that backscatter coefficients can either increase or decrease when snow depth increases. Backscatter coefficients measured at the Yellowknife test site (Fig. 2 (a)) increase as snow depth increases for almost the entire season. On the other hand, backscatter at the Njurba test site (Fig. 2 (b)) increases with snow depth until the middle of the snow season, and then it decreases even if snow continues accumulating. Both trends are observed for several stations. An analysis aiming at understanding the relationships between the observed trends and factors such as forest cover fraction, Sturm's classes and land cover type is under progress. In the meantime, we propose a possible physical explanation in which vertical layers within the snowpack and coarse grains size are identified as possible sources of the observed trends. What happens at the beginning of the snow season is that the accumulation of snow on bare soil increases the radiation backscattered toward the receiving antenna, because snow crystals scatters part of the electromagnetic signal transmitted by the scatterometer. As the season goes on, layers with different snow properties accumulate one on the top of each other. Usually, bottom layers have grain size and density values greater than the upper layers, although this aspect is strongly affected by local variability of parameters such as air temperature, precipitation, solar radiation and wind redistribution. When a layer of new snow (consisting of small scatterers) is accumulating on an old snowpack (consisting of large scatterers), the backscatter contribution from the different layers becomes weaker because of the twoway attenuation in the snow and the measured backscatter coefficient decreases as snow depth increases. This hypothesis is supported by the trend of the passive data at 19 GHz. Indeed,

7 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) as we observe from Fig. 2 (a), the brightness temperature at 19 GHz does not change drastically during the season for the Njurba test site (when the backscatter increases with the snow depth for the whole snow season). On the contrary, for the Yellowknife test site, the 19 GHz brightness temperature strongly decreases during the snow season ( 30 K), presumably because of the coarsening of grain size. 5. Dynamic range of active and passive data Here we quantify the dynamic range (e.g. the difference between the maximum and minimum values) of the active and passive microwave data measured during the snow season. In order, to present our results the different stations are grouped in four groups based on geographic areas named Eurasia, Alaska, North America/Canada and Scandinavia. The dynamic range of passive microwave brightness temperatures to snow depth evolution has been reported in the literature (e.g., Chang et al., 1987; Kelly et al., 2003; Tedesco, 2003). However, in the following we report the results obtained with the data at hand. Table 2 shows values of dynamic range averaged over the stations belonging to each of the four geographic areas, the relative standard deviation and maximum values of brightness temperature gradient (19 37 GHz). The maximum average dynamic range is obtained for the Scandinavian area (32.10 K), closely followed by the Eurasia area (29 K). The Alaska and North America/Canada areas show an average dynamic range 10 K smaller than the previous two areas ( 23 K). The maximum dynamic range in the case of passive data published in Kelly et al. (2003) ranges between 60 K and 35 K (see Fig. 4 in Kelly et al., 2003). This is for the period over a station in Russia and from SSM/I Fig. 2. Temporal trend of air temperature (upper plot), snow depth (second plot from the top) recorded by the WMO station, QuikSCAT backscatter coefficient (third plot), SSM/I brightness temperatures with vertical polarization plotted in the fourth plot from the top and horizontal polarization in the bottom plot.

8 388 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Fig. 2 (continued ). data. Note that the maximum dynamic range observed for the Eurasia geographic area in this study is 44 K. When comparing the two values, we must consider that data from different periods were used and that the results reported in this study are averaged over a large area where those reported by Kelly et al. (2003) concerns only one station. Also, the passive dynamic range of the data reported by Tedesco et al. (2004) in Fig. 2 show that, for the test site in object, the dynamic range is between 30 and 40 K, being higher in the case of vertical polarizationthaninthecaseofhorizontal polarization. Again, also in this case these values well agree with the results reported in this study. Table 2 Dynamic range of temperature gradient (19 GHz 37 GHz) for snow covered area at the four identified geographic areas in which the ground stations are located Average dynamic range Average standard deviation Maximum range AK CN/USA Fi/No/Sw Eurasia AK CN/USA Fi/No/Sw Eurasia AK CN/USA Fi/No/Sw Eurasia Temporal average Average values and average standard deviations for the temperature gradients are reported for each year, together with the maximum values.

9 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Table 3 Dynamic range of QuikSCAT backscatter coefficients for snow covered area at the four identified geographic areas in which the ground stations are located Average dynamic range Average standard deviation Maximum range AK CN/USA Fi/No/Sw Eurasia AK CN/USA Fi/No/Sw Eurasia AK CN/USA Fi/No/Sw Eurasia Average Average values and average standard deviations are reported for each year, together with the maximum values. In the case of scatterometer data (Table 3), the geographic area showing the highest average dynamic range is still the Scandinavia (3.36 db). The maximum dynamic range occurs in the case of the Scandinavian Peninsula with a value of 5.48 db, although it is very similar to the maximum range obtained in the case of the North America/Canada area (5.45 db). In contrast to the passive case, the second highest average dynamic range is obtained in the North America/Canada area, which is the area showing the lowest value in the passive case. The Eurasia and Alaska areas are, in that order, those showing the smallest values of average dynamic range. The standard deviation is similar for all areas and it is around 1 db. We point out here that the values of average dynamic range in the case of active data for the Scandinavia area well agree with those reported in Hallikainen et al. (2003) in Table 2. In order, to compare the dynamic range of the active and passive data sets to snow depth, we define the Normalized Dynamic Range (NDR), dividing the dynamic range by snow depth. Table 4 reports the average and maximum snow depth values for the four geographic areas obtained from averaging the values collected from the single stations and used to derive the NDR. Fig. 3 plots the NDR in the passive case (NDR passive, x-axis) versus the NDR in the active case (NDR active, y-axis). The NDR active ranges between 0.06 and 0.18 db/cm where the NDR passive ranges between 0.55 and 1.13 K/cm. A visual analysis of the figure suggests that the NDR passive and NDR active are well-correlated. If we fit NDR active vs. NDR passive then we obtain the following expression NDR active = NDR passive with R 2 =0.93. This result shows that the two NDR are strongly correlated with the fraction of variability in the active case that can be explained by the variability in passive one. 6. Combination of active and passive microwave data In the following we report the results of an analysis aimed at quantifying the potential improvements deriving from combining active and passive microwave data for snow depth retrieval. To this aim, for each station we divide the whole data set at our disposal (consisting of a total of 40,000 samples) into two sets, with the first one used to train (or fit) a relationship between microwave data and snow depth and the second one to extract the statistical parameters, consisting of Root Mean Square Error (RMSE) between retrieved and measured snow depth, the coefficient of determination R 2 and the regression coefficient r. The values of the training and validating sub-sets were derived by extracting randomly the values from the original data set. Several tests were made to evaluate the sensitivity of the results to the trainingsetbutnosignificant difference was observed. The relationship between microwave data and snow depth can be written in a general form as follows: SD ¼ f ðmwþþcost We use both a linear and a non-linear form of the function f to investigate if the benefits of the combination of active and ð1þ Table 4 Average and maximum values of snow depth (cm) for each of the four selected areas for the five considered snow seasons Average snow depth [cm] Maximum snow depth [cm] AK CN/ USA Fi/No/ Sw Eurasia AK CN/ USA Fi/No/ Sw Eurasia Average Fig. 3. Normalized passive vs. active dynamic ranges and relative fitting.

10 390 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Fig. 4. Values of (a) RMSE, (b) R 2 and (c) the regression coefficient r between measured and retrieved snow depth values for the different stations. White circles correspond to the use of passive data only (Eq. (3)), black squares to the use of active data only (Eq. (4)) and white triangles to the combination of the active and passive data (Eq. (2)). passive data can be improved by using a non-linear relationship. The expression considered in the linear approach is the following (Eq. (2)) in the case of both active and passive data: Instead, in the case of only passive or active data the following expressions are used: SD ¼ Ad ðtb 19V Tb 37V ÞþC Passive ð3þ SD ¼ Ad ðtb 19V Tb 37V ÞþBd ðr 13:4V ÞþC ð2þ SD ¼ Bd ðr 13:4V ÞþC Active ð4þ

11 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) In the non-linear approach we make use of artificial neural networks (ANN). ANN have been found to be very useful in dealing with several problems and have already been successfully applied to the retrieval of snow parameters (e.g., Tedesco et al., 2004). We use a multi-layer perceptron with the number of inputs given by the number of microwave data (e.g., 1 input if we are considering either active or passive, 2 inputs if we are considering their combination). The output is fixed to 1 (snow depth) and the number of hidden layers is found to be 2 with each layer having 5 neurons. The configuration of the ANN used here was obtained after testing different configurations and selecting the one providing the minimum RMSE on the validation data set. The transfer function is a sigmoid so that the ANN can be seen as a non-linear (sigmoidal) interpolator whose fitting coefficients are expressed through weights and inputs. In both linear and non-linear cases, the validation data set is used for evaluating the performance of the three different approaches (passive, active, passive and active). In the case of the linear approach, the values of the RMSE, R 2 and regression coefficient r are reported in Fig. 4. In more detail, Fig. 4 (a) shows the RMSE, (b) shows the R 2 and (c) the regression coefficient r for the different stations with white circles corresponding to the use of passive data only (Eq. (3)), black squares to the use of active data only (Eq. (4)) and white triangles to the combination of the active and passive data (Eq. (2)). Results show that the technique with poorest performance is the one using only active data. It has the highest values of RMSE, lowest values of coefficient of determination R 2, and values of regression coefficient considerably different from 1. Both the techniques based only on passive data and on the combination of active and passive data show a similar behavior, although the cases using both active and passive data are showing better performance. In Fig. 5 we plot the improvement due to the use of both active and passive data with respect to the case when only passive data are used (e.g., RMSE passive RMSE actþpass ) for (a) RMSE RMSE passive and (b) the coefficient of determination. The analysis on the regression coefficient can be performed directly on Fig. 4 (b), where we observe that the regression coefficient for the different stations are, generally, closer to 1 when the combined active and passive data are used. In the case of RMSE (Fig. 5 (a)), there are only four cases with negative values (the performance using both Fig. 5. Relative improvement (with respect to the use of the only passive) of (a) RMSE and (b) R 2 when the combination of active and passive data is used.

12 392 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) active and passive data is worse with respect to when only passive data are used), while all remaining values are positive. Therefore, in general, the use of an approach based on the combination of active and passive data reduce the RMSE between measured and retrieved values. The maximum and average values of RMSE improvement are, respectively, 24.65% and 7.6% (8.9% excluding the negative values). The number of negative values is also small in the case of the coefficient of determination R 2,with only five of them. In this case, the maximum and average values of improvement are, respectively, 42% and 6%. A trend similar to that obtained when using the linear approach is observed when ANN are used (non-linear Fig. 6. RMSE, R 2 and r for the linear and non-linear approaches when considering both active and passive data. Black squares represent the results obtained with the linear approach where white circles those obtained with the non-linear one.

13 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) approach). The values of RMSE, R 2 and r for the linear and non-linear approaches when considering both active and passive data are plotted in Fig. 6. Here, black squares represent the results obtained with the linear approach where white circles those obtained with the non-linear one. Results show that the performances of linear and non-linear approaches are comparable, though the ANN approach is showing slightly better results. A preliminary analysis aimed at understanding if land cover is affecting the correlation between microwave data and snow depth is also carried out. In Fig. 7 we show the correlation coefficient between the (a) passive and (b) active microwave data and snow depth for the different stations as a function of the forest cover fraction. The number of the stations is also reported as a reference. No particular trend is observed for the correlation as a function of the different forest cover fraction in both active and passive cases. This result suggests that the negative correlation between microwave and snow depth data might not be due to the presence of forest cover. We also studied the values of correlation coefficients at different stages of the snow season. To this aim, we divided the period of interest into three sub-periods: October December, January February and March of each year. In Fig. 8 we show the correlation coefficients between microwave and snow depth data for the different stations (x-axis) in the case of (a) passive and (b) active data when considering measurements performed each year between October December (dotted black line and black square), January February (gray line and open circle) and March (gray line with black diamond) for all years. In the passive case, we observe that, in general, the periods January February shows the highest values of correlation coefficient. This is consistent with the idea that for this period little or no melting should occur, snow depth values are high enough to be detected by the passive microwave sensors, and layering due to melting/ refreezing cycles is absent. The trend of correlation coefficients for the periods October December shows that for this period the lowest values are observed for stations 4 and For the remaining stations in this period and for the other period Fig. 7. Correlation coefficient between the (a) passive and (b) active data and snow depth for the different stations as a function of the forest cover fraction of each test site for the study period

14 394 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Fig. 8. Correlation coefficient between microwave data and snow depth for the different stations (x-axis) in the case of (a) passive and (b) active data for considering measurements performed each year between October December (dotted black line and black square), January February (gray line and open circle) and March (gray line with black diamond). (March) the values are generally similar. In the case of correlation coefficients between the active microwave and snow depth data, the values derived from the periods January February are, generally, the highest. However, we observe that for some stations correlation coefficient values for this period are the lowest ones, with some of them becoming also negative from a positive value for other periods as, for example stations # 17 and 18, 35 and 44. Also in this case no particular relationship is observed among these stations in terms of snow classes or forest cover fraction. Values of average (annual) correlation coefficients between microwave and snow depth data for the four geographic areas and the five seasons are reported in Tables 5 and 6. In order to investigate whether the improvement derived from the use of the combination of active and passive data depends on the frequency or on the different detection approach, we report the results of a preliminary analysis making use of AMSR-E brightness temperatures at K, Ka and X band. The values of Ku-band backscatter coefficients in Eq. (2) are substituted with the values of brightness temperatures at X band ( 10 GHz). The approach followed when using X-band brightness temperatures is the same as that one described in Table 5 Values of correlation coefficients between the horizontal and vertical spectral gradient (19 GHz 37 GHz) and snow depth for the four geographic areas and the five snow seasons under study Alaska Russia Scandinavia Canada H V H V H V H V Results obtained by using horizontal and vertical polarizations are reported, respectively, in the first and second columns of each area.

15 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Table 6 Values of correlation coefficients between the horizontal and vertical backscatter coefficients and snow depth for the four geographic areas and the five snow seasons under study Alaska Russia Scandinavia Canada H V H V H V H V Results obtained by using horizontal and vertical polarizations are reported, respectively, in the first and second columns of each area. the previous sections. We note that the use of 10 GHz AMSR-E data is currently a component of the NASA standard AMSR-E SWE algorithm, used to differentiate deep snow from shallow and that results showing the behaviour of snow covered ground at 10 GHz relative to 19 GHz were also presented in Derksen et al. (2006). Results are reported in Table 7, showing RMSE, R 2 and offset for selected stations when using a) the passive data at K and Ka bands, b) the passive data at K and Ka bands plus the active data at Ku band and c) the passive data at K, Ka and X bands for some selected stations. In Fig. 9, for reader's convenience, we report a graphical representation of the results reported in Table 7. We observe that the combination of active and passive data provides better results than using passive K and Ka band data alone. We also observe that in some cases the combined use of the X, K and Ka band passive data provides better results than the case when active and passive data are used in combination. Also, the use of brightness temperatures at X-band provides results highly comparable to those obtained when using the active data. As part of an ongoing investigation regarding the improvement related to the use of X-band brightness temperatures, we analyze the dynamic range of the difference between K and Ka band and X and Ka band brightness temperatures. In Table 8 we show the maximum differences (dynamic range) between 18.7 and 36.5 GHz and between 10.6 and 36.5 GHz brightness temperatures for both vertical and horizontal polarizations for the same stations reported in Table 7. Forest cover fraction for each test site is also reported for reader's convenience. We see that, as reported in other studies (e.g., Derksen et al., 2006), the highest value of maximum dynamic range is reached in the case of the difference between X and Ka band brightness temperatures, vertical polarization, with the only exceptions of the Bor and Yellow- Knife stations where the values obtained using either X or K band and Ka band are comparable. This is also a consequence of the reduced sensitivity of the X band data to grain size: as snow season evolves, grain size increase and the K band brightness temperatures are becoming more and more affected by the presence of bigger scatterers, decreasing concurrently with the K band data and, hence, reducing or making it insensitive the difference between the data collected at the two frequencies. On the contrary, at X band this effect does not occur and therefore the difference between X and Ka band data tends to increase when grain sizes increase (because the X band values are almost constant where the Ka band values tend to decrease). 7. Discussion and conclusions We analyzed the behavior of Ku band active and K and Ka band passive data with respect to the variation of snow depth along five seasons ( ) over different locations in the Northern Hemisphere. When we compared the temporal trend of the backscatter coefficient and the spectral gradient with the snow depth evolution, we observed three distinct behaviors: 1) both backscatter and spectral gradient increase as snow depth increases; 2) the spectral gradient starts decreasing in the middle of the snow season where the backscatter increases for the whole season; and 3) both backscatter and spectral gradient increase up to a certain time of the snow season and then they decrease, although snow depth is still increasing. This aspect is very important because many techniques for the retrieval of snow depth (or SWE) are based on the assumption that the spectral gradient increases with snow depth. More investigation is Table 7 RMSE, R 2 and offset for selected stations when using a) the sole passive data at K and Ka bands, b) the passive data at K and Ka bands and the active data at Ku band and c) the passive data at K, Ka and X band for some selected stations K, Ka K, Ka, Ku K, Ka, X K, Ka K, Ka, Ku K, Ka, X K, Ka K, Ka, Ku K, Ka, X RMSE R 2 Offset Olekminsk (RA) Dudinka (RA) Bor (RA) Skwentka (AK) Sutton (AK) Sodankyla (FI) Rovaniemi (NO) Kuopio (FI) Agata (RA) Jakutsk (RA) Pokrovskaja (RA) Yellowknife (CA) Fairbanks (AK)

16 396 M. Tedesco, J. Miller / Remote Sensing of Environment 111 (2007) Fig. 9. (a) RMSE, (b) R 2 and (c) offset values for the different stations reported along the x-axis when combining K and Ka (light gray), K, Ka and Ku band data (dark gray) and K, Ka and X band data (white). Please see Table 7 for numerical values. required and is already under progress. A preliminary explanation is that the behavior of the electromagnetic quantities relates to the stratigraphy of the snow pack and air temperature. The presence of multiple layers with coarse snow crystals reduces the values of the K band brightness temperature, hence reducing the spectral gradient. In the active case, the radiation backscattered by large scatterers is attenuated by the new snow on top of old layers with a decrease on the backscatter coefficient. We quantified, for the first time, the dynamic range of spaceborne Ku band scatterometer data with respect to the snow depth at very large spatial scale and compared it with that obtained in the passive case. Results show that dynamic ranges in active and passive cases are strongly correlated (R 2 =0.93), suggesting that QuikSCAT data have a sufficient dynamic range to monitor snow depth at large scale. In the active case the normalized dynamic range (NDR) was found to range between 0.06 and 0.18 db/cm where in the passive it was between 0.55 and 1.13 K/cm. The potential improvement on the snow depth retrieval related to the combined use of active and passive data was quantified by evaluating the root mean square error (RMSE), the regression coefficient and the coefficient of determination. In general, best results were obtained when both active and passive data were used, with respect to the use of the only passive or active data. The maximum and average values of RMSE improvement were, respectively, 24.65% and 7.6%. In the case of the coefficient of determination R 2, the maximum and average values of improvement were, respectively, 42% and 6%. Further investigation is required regarding the causes of the improvement related to the use of a combined active and passive data set for the retrieval of snow depth. A first step into this direction was to evaluate to compare the results of the approach involving the combination of active and passive with another one when the Ku-band backscatter coefficients are substituted with X-band brightness temperatures from AMSR-E. The combination of active and passive data provided better results than passive data alone at K and Ka bands although results obtained using the brightness temperatures at X-band were comparable to and sometimes better than those obtained when using the active data. Brightness temperatures at X band are available only since May 2002, measured by the AMSR-E flying on board of the AQUA satellite where QuikSCAT data are available since 1999 (NSCAT data also are available between 1997 and 1999). As a consequence, for the period the use of combined active and passive microwave data can offer an improvement on the retrieval of snow depth with respect to the use of passive data at K and Ka band. After May 2002, it might not be necessary to combine active and passive data because the use of X, K and Ka band data could provide similar results. An analysis of the performance of the two Table 8 Maximum differences (dynamic range) between 19 and 37 GHz and between 10 and 37 GHz brightness temperatures in the case of vertical and horizontal polarizations for the stations reported in Table Vertical Horizontal Vertical Maximum dynamic range [K] Horizontal Forest cover fraction [%] Olekminsk (RA) Dudinka (RA) b10 Bor (RA) Skwentka (AK) Sutton (AK) Sodankyla (FI) Rovaniemi (NO) Kuopio (FI) b10 Agata (RA) b10 Jakutsk (RA) Pokrovskaja (RA) b10 Yellowknife (CA) Fairbanks (AK) Forest cover fraction for each test site is also reported for reader's convenience.