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2 Available online at Remote Sensing of Environment 111 (2007) Identification of atmospheric influences on the estimation of snow water equivalent from AMSR-E measurements J.R. Wang a,, M. Tedesco b a NASA Goddard Space Flight Center, Greenbelt, MD 20771, United States b GEST, University of Maryland at Baltimore County, Baltimore, MD 21228, United States Received 10 July 2006; received in revised form 11 October 2006; accepted 14 October 2006 Abstract Radiometric measurements near 19 and 37 GHz have been used for estimation of snow water equivalent (SWE) for many years. Most conventional SWE retrieval algorithms depend on the difference between the brightness temperatures (T b 's) at these frequencies. The effect of atmospheric absorption is generally assumed to be insignificant, and thus often not taken into account in such estimation. In this paper this effect is closely examined with the aid of AMSR-E and radiosonde data sets over two widely separated regions in the continental U.S.A. Results of the analysis show that even under a clear sky the atmospheric absorption could account for as much as 25 50% to the estimation of SWE. For example, the AMSR-E estimated SWE of 10 cm would become about 13.6 cm when measured at the ground level under the same atmospheric condition; the estimation based on surface emission alone (i.e., no atmosphere) would be about 15.2 cm. There is some regional dependence of this atmospheric absorption effect, but the effect of seasonal variation is negligibly small. Under cloudy conditions, the impact of liquid cloud absorption is significant and it appears necessary to perform either cloud screening or quantify the cloud effects on SWE estimation from 19 to 37 GHz radiometric measurements at ground level or satellite altitudes. Published by Elsevier Inc. Keywords: Microwave remote sensing; Snow water equivalent; Atmospheric correction 1. Introduction Snow is an important component in studying the hydrological, meteorological and climatological cycles because of its effects on land surface albedo, the net radiation balance, and boundary layer stability. In many high-latitude and mountainous regions of the Earth snowfall accounts for a substantial portion of total annual precipitation. Many rivers originate from melting snow, which represents a major source of fresh water in many regions. Additionally, glaciers could form from accumulated snow packs in the cold regions. Thus, reliable global remote sensing of snow parameters (e.g., Snow Water Equivalent, SWE) is crucial to understand the evolution of the cryosphere for quantifying the water resources and improving the global climate and hydrological models. SWE is generally preferred to snow depth as it contains information on the amount of water within the snow pack Corresponding author. address: james.r.wang@nasa.gov (J.R. Wang). (e.g., for each snow layer SWE can be approximated as the snow density times snow depth). Microwave radiometric measurements near 19 GHz and 37 GHz have been used for estimation of snow water equivalent (SWE) for more than two decades at ground level (Chang & Shiue, 1980; Matzler, 1994), as well as aircraft and satellite altitudes (Armstrong & Brodzik, 1995; Chang et al., 1985, 1987; Hallikainen & Jolma, 1992; Foster et al., 1997, 2005; Kelly et al., 2003; Derksen et al., 2003; Pulliainen & Hallikainen, 2001; Tedesco et al., 2004). The satellite radiometric measurements, such as those from the Special Sensor Microwave/Imager (SSM/I) and the Advanced Scanning Microwave Radiometer E (ASMR-E), provide global coverage for SWE estimation. The measurements at ground level and aircraft altitudes are suitable for more intense studies at local and regional scales, as well as validation/calibration of satellite instruments. All of these measurements at different spatial scales are important and necessary in bringing about reliable SWE products. The past radiometric measurements and subsequent retrievals of SWE seldom dealt with the impacts of atmospheric /$ - see front matter. Published by Elsevier Inc. doi: /j.rse

3 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) absorption explicitly, although the effect has previously been discussed and treated by Aschbacher (1989), Pulliainen et al. (1993), and Pulliainen and Hallikainen (2001). Pulliainen and Hallikainen (2001) included the atmospheric effects in their SWE retrievals with the SSM/I data; but such atmospheric effects were not explicitly quantified. This is perhaps due to the general perception that the effect of the clear-sky atmospheric absorption near 19 GHz and 37 GHz is not as significant for SWE estimation when compared to other factors such as vegetation cover and the evolution of grain size of snow crystals. As the retrieval techniques for SWE are refined with better handling of error sources, more accurate radiometric measurements are required and the effect of atmospheric absorption may need to be accounted for more explicitly. For example, Chang et al. (1997) observed significant differences in brightness temperatures (T b ) measured by the SSM/I and lowelevation airborne radiometers at several frequencies during the BOREAS winter field campaign in Canada. Wang and Manning (2003) analyzed and reported the differences of the 19 GHz and 37 GHz T b 's measured at ground level and satellite altitudes, and their implication on the retrievals of snow parameters based on these two frequencies. More recently, Tedesco and Wang (2006) reported an improved correspondence between the Moderate-Resolution Imaging Spectroradiometer (MODIS) and AMSR-E estimated areas of snow cover, when the AMSR-E data at 19 and 37 GHz were corrected for atmospheric absorption. These recent studies point to the need of examining the effect of atmospheric absorption quantitatively. In this paper, we attempt to quantify the effect of atmospheric absorption on SWE estimation by examining the AMSR-E measurements at 18.7 and 36.5 GHz during a 5-month period between November 2003 and March 2004 over two different regions in continental U.S.A. Radiosonde data from the National Weather Stations (NWS) in these two regions were used to derive the atmospheric absorption parameters. First, in Section 2 below, the radiative transfer equations relevant to satellite and ground level measurements are examined, and the atmospheric absorption parameters quantified. Next, these atmospheric absorption parameters are applied to the AMSR-E data to estimate the effect of atmospheric absorption on SWE retrievals under clear-sky condition in Section 3. The regional and seasonal variations of these parameters are briefly discussed in Section 4. The effect of liquid cloud absorption is analyzed in Section 5. Finally, the results and concluding remarks are given in Section Atmospheric radiative transfer and parameters In the frequency region covered by the AMSR-E, the radiative transfer equations can be simplified in the following manner with negligible error (Wang & Manning, 2003). The brightness temperature T bp_sat (ν,θ) measured from satellite altitudes at frequency ν and observational angle θ is given by: T bp sat ðm; hþ ¼T a ðm; hþd ð1 Cðm; hþþ þ T CB d ð1 e p ðm; hþþ d ðcðm; hþþ 2 þ½e p ðm; hþd T s þð1 e p ðm; h; ÞÞ d T a ðm; hþd ð1 Cðm; hþþšd Cðm; hþ ð1þ and that measured at surface at the same ν and θ, T bps_m (ν), is given by: T bps m ðm; hþ ¼e p ðm; hþd T s þð1 e p ðm; hþþd T a ðm; hþ d ð1 Cðm; hþþ þ ð1 e p ðm; hþþd T CB d Cðm; hþ ð2þ where e p (ν) is the surface emissivity, T CB is the cosmic background radiation, T s is the surface temperature, and the subscript p specifies the polarization state of radiation. The absorption factor of the atmosphere Γ(ν,θ) and the effective atmospheric temperature T a (ν) are given by: Cðm; hþ ¼eZ sðm;hþ l and T a ðm; hþ ¼ 0 e sð0;z;m;hþ d TðzÞd gðm; zþd sechd dz Z l e sð0;z;m;hþ d gðm; zþd sechd dz 0 Here τ(ν,θ)andγ(ν,z) are the optical depth and the absorption coefficient at altitude z, respectively. Clearly, one has to deal with three different brightness temperatures, T bp_sat (ν,θ), T bps_m (ν,θ), and the surface intrinsic brightness T bps (ν,θ)=e p (ν,θ) T s ; these brightness entities are inter-related through e p (ν,θ), T a (ν,θ), and Γ(ν,θ). It is noted that, at the frequencies near 19 and 37 GHz, both T a (ν,θ)andγ(ν,θ) mainly depend on oxygen gas absorption under clear-sky conditions; the variations of atmospheric moisture can be shown to be small compared to the standard deviations of the calculated T a (ν,θ) andγ(ν,θ) (Fig. 2 below). Furthermore, Wang and Manning (2003) showed that the brightness differences between these two frequencies, which are proportional to the SWE's, depend only weakly on atmospheric moisture when the total precipitable water is 1.5 cm. Therefore, the effect of atmospheric water vapor is omitted in the following discussion, and T a (ν,θ)and Γ(ν,θ) are assumed to depend only on the pressure level or elevation. The atmospheric absorption model of Rosenkranz (1998) is used in the calculations of T a (ν,θ) andγ(ν,θ). Two regions mainly in the continental U.S.A., as displayed in Fig. 1, are selected for this study. The first one is in the west coast that contains the Sierra-Nevada, and is bounded by latitudes of 36 N and 40 N, and by longitudes of 115 W and 120 W. The second region is in the Midwest centered approximately at Fargo, North Dakota, and is bounded by latitudes of 44 N and 50 N, and by longitudes of 90 W and 104 W. While the Midwest region is relatively flat, the Sierra-Nevada region is characterized by large variation in elevation. There are two NWS stations in the Sierra-Nevada region, located at [39.57 N, W], and [36.62 N, W]. In the Midwest region, there are five NWS stations located at [44.83 N, W], [45.45 N, W], [44.07 N, W], [48.57 N, W], and [46.77 N, W]. The locations of these stations are indicated by crosses in Fig. 1. The radiosonde data over the 5-month period of a typical snow season between November 2003 and March 2004 from these stations are used in the calculations for T a (ν,θ) and Γ(ν,θ). Because the AMSR-E data from the night-time passes ( 0955 UTC, or 1:55 am local time, over Sierra-Nevada and 0817 UTC, or 1:17 am local

4 400 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Fig. 1. A sketch showing the two regions in the continental U.S.A. from which the AMSR-E and radiosonde data are used in this analysis. The crosses in each region give the locations of the NWS stations; the Sierra-Nevada region in the lower-left contains stations, while the larger Midwest region in the upper-right, five NWS stations. time, over the Midwest region) are selected for the analysis presented below, only the corresponding radiosonde data acquired around 1200 UTC are used in these calculations. It is assumed that the night-time surface and atmospheric conditions remain relatively constant between the AMSR-E and radiosonde observations. The calculations for the Midwest are made for 11 Fig. 2. The elevation dependence of the effective atmospheric temperature and absorption factor for both Sierra-Nevada and Midwest regions. The data points and their standard deviations in the figure are evaluated from the radiosonde data over the period between November 2003 and March 2004 from the NWS stations displayed in Fig. 1.

5 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) different altitudes in the range of 0 4 km in 0.4 km steps; those for Sierra-Nevada are made in the range of 1 5 km in the same steps because of the elevation of these stations. Fig. 2 shows the results from these calculations. Here the calculated 5-month averages of both T a (ν,θ)'s and Γ(ν,θ)'s at θ=55, the observational angle of the AMSR-E, are plotted as a function of elevation h; plots (a) and (b) denote T a (ν,θ), while plots (c) and (d) give Γ(ν,θ), at 18.7 GHz and 36.5 GHz, respectively. For all four plots, calculated results from both Sierra-Nevada and Midwest regions are shown. The plots give calculated values and their standard deviations for each NWS station at each h for Sierra-Nevada; for the Midwest region, the calculated values and their standard deviations are averages of all five NWS stations. A linear regression applied to the data points for each group gives the equation in each plot. Notice that the Vegas Reno data points for T a (ν,θ) ath 2 km show slight flattening of the h dependence. Examination of AMSR-E and NWS data over the period of study indicates that snow cover mainly occurs between the altitudes of 2 and 4 km; thus the application of the linear regression results displayed in these plots for the atmospheric corrections to SWE estimation should not introduce much error. Additional features from these plots are the large differences of up to 15 K for T a (ν,θ) and up to for Γ(ν,θ) between Sierra-Nevada and the Midwest regions; the standard deviations associated with these parameters and differences in Γ(ν,θ) values between the two NWS stations in Sierra-Nevada region are not small. These factors definitely will contribute to the errors in the estimation of atmospheric corrections, to be discussed in the next section. The symbol θ will be omitted from all expressions from here on because the calculations and discussions below refer only to the AMSR-E θ = 55. At this observational angle the results of calculations are irrelevant to Lambert or specular surface emission (Matzler, 2005). Fig. 3. Pseudo color maps of SWE's estimated from AMSR-E measurements (plots A and D), simulated measurements at the ground level (plots B and E), and simulated surface emission without contribution from atmospheric absorption (plots C and F); plots A, B, and C from March 24, 2004 over Sierra-Nevada region and plots D, E, and F from March 8, 2004 over the Midwest region.

6 402 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Estimation of snow water equivalent under clear sky The estimation of SWE from the AMSR-E measurements is based on the work of Foster et al. (1997) and is given by: SWE x ðcmþ ¼0:48d ½T bv ð18:7þ T bv ð36:5þš Here the vertically polarized components of the AMSR-E are used throughout this paper. The expression T bv (ν) stands for any one of the three brightness entities, T bv_sat (ν), T bvs_m (ν), and T bvs (ν), with corresponding SWE subscript x=sat, sm, and s; i.e., the estimated SWE will be written as SWE sm if T bvs_m (ν)'s are used in the estimation. Only the night-time passes of the AMSR-E data are used in the present analysis. Given the AMSR-E T bv_sat (ν) and assuming two different T s values of 250 K and 270 K, T bvs_m (ν), and T bvs (ν)are evaluated from Eqs. (1) and (2) above with the calculated results of T a (ν) andγ(ν) infig. 2. To account for the variations of elevation in Sierra-Nevada, the AMSR-E pixels at 18.7 GHz resolution over that entire region are co-located with a digital elevation model (DEM) with an original resolution of 1 km (GTOPO30 DEM downloaded from the U.S. Geological Survey's EROS Data Center). The terrain in the Midwest region is relatively flat; thus, a median value of h=0.5 km is assumed in the calculations. After T bvs_m (ν), and T bvs (ν) are calculated, SWE sm and SWE s are estimated from Eq. (3), and a typical result is shown in Fig. 3 for the AMSR-E passes over Sierra-Nevada on March 24, 2004 and over the Midwest on March 8, 2004; T s =250 K in this case. In this figure, the three plots from top to bottom on the left column show the SWE distributions in Sierra-Nevada region: plots (A), (B), and (C) for SWE sat, SWE sm, and SWE s, respectively. The three plots on the right column give the corresponding SWE results for the Midwest region. The color scales are set differently for the two regions to bring about better contrast for each. In the Sierra-Nevada region, the snow cover on March 24, 2004 is generally limited to the high-elevation areas (elevation map not shown); in the Midwest region, the snow cover is more wide spread, and the SWE x values are generally higher too. Among the three different SWE x 's in each region, values of SWE sat are the lowest and those of SWE s are the highest. Figs. 4 and 5, for Sierra-Nevada and Midwest regions respectively, show the scatter plots between SWE sat and SWE sm (A), and between SWE sat and SWE s (B), with 1:1 dashed reference lines. In each plot, results based on the calculations of T bvs_m (ν)andt bvs (ν)witht s =250KandT s =270 K are included for comparison. Clearly, from plot (A) of each figure, the T s values do not have impact on the end results of SWE sm ; the effect of T s on SWE s appears to be fairly small too, based on the regression results. Thus, unless the effective T s for snow packs is significantly different at ν=18.7 GHz and at ν=36.5 GHz, T s variations should not affect greatly the SWE x estimation based on Eq. (3). These two figures also show that SWE sat is smaller than either SWE sm or SWE s ; i.e., when the effect of atmospheric absorption is accounted for, the same snow packs on the ground will assume largest SWE s, then SWE sm, and smallest SWE sat. ð3þ For example, if SWE sat =10 cm, the regression results in Fig. 4 (Sierra-Nevada) will give SWE sm 13.5 cm and SWE s 15.0 cm; the corresponding results from Fig. 5 (Midwest region) will be SWE sm 13.7 cm and SWE s 15.3 cm. The slightly smaller SWE sm and SWE s values in Sierra-Nevada region are due to the fact that proportionally there are more pixels in the high-elevation areas where there is less atmospheric burden. Another feature common to all these plots is that, when SWE sat =0, both SWE sm and SWE s remain positive and have values on the order of 2 3cm. This implies that, if the snow packs are thin and yet measurable by a ground based radiometer operating at ν near 19 and 37 GHz, they may not be detected by the same radiometer at satellite altitudes. This could also explain the improvements in the correspondence between the MODIS and AMSR-E estimated areas of snow cover reported by Tedesco and Wang (2006). 4. Regional and seasonal dependence of atmospheric parameters The values of T a (ν) and Γ(ν) displayed in Fig. 2 are quite different for Sierra-Nevada and Midwest regions; at a given h, T a (ν) and Γ(ν) values differ by about K and , respectively, between the two regions. Examination of these parameters on monthly basis also reveals some seasonal variations. Thus, one would expect a certain impact of these variations on the relations among SWE sat, SWE sm, and SWE s. Fig. 4. Scatter plots of SWE's derived from AMSR-E measurements over Sierra- Nevada on March 24, 2004: (A) regression between SWE estimated from AMSR-E measurements and that from simulated ground-level measurements, and (B) regression between SWE estimated from AMSR-E measurements and that from simulated surface emission. Calculations of ground-level measurements and surface emission were made at surface temperatures of 250 K and 270 K.

7 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Fig. 5. Scatter plots of SWE's derived from AMSR-E measurements over the Midwest region on March 8, 2004: (A) regression between SWE estimated from AMSR-E measurements and that from simulated ground-level measurements, and (B) regression between SWE estimated from AMSR-E measurements and that from simulated surface emission. Calculations of ground-level measurements and surface emission were made at surface temperatures of 250 K and 270 K. the differences SWE s SWE sat from plots (A) and (B). A few data points with low values between days in plots (A) and (B) are likely caused by cloudy conditions or precipitation during the AMSR-E passes; these are not of major concern in this paper. A comparison between plots (A) and (B) clearly indicates larger estimated SWE sm and SWE s when the T a (ν)andγ(ν)valuesfrom Sierra-Nevada region are used; plot (C) illustrates this particular observation even more clearly for the case of SWE s. This points to the need of using regional radiosonde data for a more accurate determination of atmospheric corrections to the SWE x 's. For the analysis of the seasonal dependence of the atmospheric effects, the monthly means of both T a (ν) andγ(ν) are evaluated and then used in the radiative transfer calculations for the derivation of the relations among SWE sat, SWE sm, and SWE s.for Sierra-Nevada the h dependence of both T a (ν) andγ(ν) isin effect, and for the Midwest region, h is again assumed to be 0.5 km in the calculations. The results are shown in Tables 1, 2A and 2B for the Midwest and Sierra-Nevada regions, respectively. In Table 1, valuesoft a (ν) andγ(ν) for both frequencies are estimated at h = 0.5 km, and the regression coefficients are derived from SWE sat =a+b SWE sm and SWE sat =a+b SWE s. Table 2A gives the regression coefficients for the functional dependence of T a (ν)andγ(ν)onh for both 18.7 and 36.5 GHz, and Table 2B,the resulting regression coefficients relating SWE sat to both SWE sm and SWE s. The last row in Tables 1 and 2B again gives the results from the average T a (ν) andγ(ν); some of the values are slightly For an illustration of such impact, the same AMSR-E data set from March 8, 2004 over the flat Midwest region is used for this analysis, and all the calculations are made with h=0.5 km and T s =260 K. For regional dependence of T a (ν) and Γ(ν), the results of 5-month averages displayed in Fig. 2 from both regions are used in the calculations. The calculated results of SWE sm and SWE s are displayed as scatter plots against SWE sat in Fig. 6: plot (A) gives the relation between SWE sat and SWE sm and plot (B), between SWE sat and SWE s. A linear regression applied to each of the four data group in the figure results in the regression equations displayed in the figure. It is clear from this figure that the errors introduced by using radiosonde data from a different region on the estimation of SWE sm and SWE s are not negligible. If SWE sat =10 cm, plot A (Fig. 6) gives SWE sm 13.5 cm or SWE sm 14.5 cm depending on whether T a (ν) and Γ(ν) values from the Midwest or Sierra-Nevada are used; the corresponding values for SWE s from plot B (Fig. 6) are 15.0 cm or 17.0 cm. The magnitude of the differences in SWE sm and SWE s resulting from different sets of T a (ν) and Γ(ν) increases with increasing SWE sat. This can also be seen clearly from the time variations of SWE sat, SWE sm, and SWE s for the whole season at a single location near Fargo, North Dakota as shown in Fig. 7. Here the plots (A) and (B) give the results for these three parameters based on Midwest and Sierra-Nevada radiosonde data, respectively; plot (C) shows Fig. 6. The impact of the regional dependence of atmospheric parameters on the SWE estimation: (A) SWE estimated from AMSR-E measurements against SWE estimated from simulated ground-level measurements, and (B) SWE estimated from AMSR-E measurements against SWE estimated from simulated surface emission.

8 404 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Fig. 7. The impact of the regional dependence of atmospheric parameters on the SWE estimation for an entire season near Fargo, North Dakota: (A) when Midwest atmospheric parameters were used, (B) when Sierra-Nevada atmospheric parameters were used in the calculations, and (C) the differences SWEs SWEsat from (A) and (B). different from the ones displayed in Figs. 4 and 5 because the calculations are made at the median T s of 260 K. It is clear from both Tables 1 and 2A that the impacts of the seasonal of T a (ν) and Γ(ν) on both SWE sm and SWE s are small. The monthly variations of the regression coefficients between SWE sat and SWE sm, or between SWE sat and SWE s are negligible compared to the regional changes displayed in Fig. 6. For instance, the most significant changes in the regression coefficients between SWE sat and SWE s in Table 1 occur between January and March of 2004; SWE sat of 10 cm results in SWE s of 15.0 cm for January and 15.2 cm for March. On the other hand, the regression equations in Fig. 6B give SWE s values of about 14.8 cm and 16.7, respectively, if the T a (ν) and Γ(ν) data from Midwest and Sierra-Nevada regions are used in the calculations. Therefore, it is not crucial to consider the seasonal variations of the atmospheric parameters in the improvement of the estimation of SWE. It is emphasized that the atmospheric influence on the SWE retrievals discussed above (or below) is based on idealized modeling with assumptions of a few values of surface temperatures, and the surface emissivities, e p (ν,θ)'s, in Eqs. (1) and Table 1 Monthly regression coefficients between SWE sat and SWE sm, and between SWE sat and SWE s for the Midwest region Month/ year 18.7 GHz 36.5 GHz SWE sat and SWE sm SWE sat and SWE s T a (ν) Γ(ν) T a (ν) Γ(ν) a b a b 11/ / / / / Average

9 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Table 2A Monthly regression coefficients of T a (ν) and Γ(ν) in Sierra-Nevada Month/ year 18.7 GHz 36.5 GHz T a (ν)= a+b h (2) are a direct consequence of the AMSR-E measurements and the calculated T a (ν,θ) and Γ(ν,θ). Values of e p (ν,θ) strongly depend on other surface variables like the vegetation cover and the evolution of snow pack properties (e.g., density and crystal sizes) (Tedesco et al., 2006), the discussion of which is beyond the scope of this paper. Therefore, there is no attempt here to compare the estimated SWE s with the in-situ value, because such a comparison will undoubtedly require further analysis and lengthy discussion of these surface parameters. Studies of SWE s in relation to snow pack intrinsic properties and vegetation cover will be the subject of future endeavors. 5. The effect of clouds Γ(ν)= a+b h T a (ν)= a+b h Γ(ν)= a+b h a b a b a b a b 11/ / / / / Average The microwave absorption by cloud liquids in the atmosphere is approximately proportional to ν 2 (Staelin et al., 1976); thus, their presence is expected to have a significant impact on the observed T b (18.7) and T b (36.5). To estimate the effects of clouds on SWE sat,swe sm, and SWE s, the same AMSR-E data set from the March 8, 2004 pass over the relatively flat Midwest region is again used in the analysis. Assuming T s =260 K and the average T a (ν) andγ(ν) valuesath=0.5 km given by Fig. 2, thee v (18.7) and e v (36.5) values are readily calculated from the AMSR-E data set. Eqs. (1) and (2) are not adequate to include a cloud layer in the calculations of T bvs_m (ν)andt bv_sat (ν). A more complete radiative transfer equation to deal with multiple atmospheric absorption layers (e.g., Wang et al., 1995) is thus used here in the calculations. The average temperature and relative humidity profiles (100 layers between 0 and 20 km) are derived from the 5-month Midwest radiosonde data. These and the cloud profiles as well as the T s, e v (18.7), and e v (36.5) values are input to the radiative transfer equation (Wang et al., 1995) toestimatet bvs_m (ν) and T bv_sat (ν) under cloudy sky. The changes in T bvs_m (ν) andt bv_sat (ν) caused by the scattering of microwave radiation to cirrus clouds are known to be negligible near 19 and 37 GHz, and the convective clouds associated with storms are not dealt with in the present context. Thus, the calculations and results presented below pertain to a light to moderate liquid cloud layer between the altitudes of 2.5 and 3.5 km. Four values of total cloud liquid water (CLW) at 0.02, 0.04, 0.06, and 0.08 g/cm 2 are used in the calculations and the results are shown in Figs. 8 and 9, and summarized in Table 3. Fig. 8, (A) and (B) for CLW=0.02 g/cm 2 and CLW = 0.04 g/cm 2 respectively, shows the scatter plot between SWE sat and SWE sm,andbetweenswe sat and SWE s. The values along the horizontal axis of the figure represent either SWE sm or SWE s. Although the calculations include both clear-sky and cloud liquid absorption, it is quite clear from a comparison of this figure and Fig. 5 that liquid clouds have a significant impact on the estimation of SWE sat and SWE sm because of a strong frequency dependence of cloud liquid absorption. As an example, for a relatively small CLW=0.02 g/cm 2 in plot (A), the values of SWE sat and SWE sm are reduced to about 11.9 cm and 15.1 cm, respectively, when SWE s =20 cm. For the same SWE s but with CLW=0.04 g/cm 2 in plot (B), the values of SWE sat and SWE sm are further reduced to about 9.0 cm and 13.1 cm, respectively. Table 3 gives the regression coefficients for CLW= 0.02, 0.04, 0.06, and 0.08 g/cm 2, in the form of SWE sat = a + b SWE sm (or SWE s ). Table 2B Monthly regression coefficients between SWE sat and SWE sm, and between SWE sat and SWE s for Sierra-Nevada region Month/ year SWE sat =a+b SWE sm, cm SWE sat =a+b SWE s, cm 11/ / / / / Average Fig. 8. Scatter plots of SWE's estimated from three different entities under cloudy conditions: (A) CLW=0.2 g/cm 2, and (B) CLW=0.4 g/cm 2.

10 406 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) Table 4 Regression coefficients between cloudy- and clear-sky conditions CLW, g/cm 2 SWE sat, cm SWE sm,cm a b a b Fig. 9. Scatter plots between SWE estimated from measurements under cloudy sky and that estimated from measurements under clear sky: (A) CLW=0.2 g/ cm 2, and (B) CLW=0.4 g/cm 2. Another useful feature resulting from these calculations is the comparison between the SWE sat values, or between the SWE sm values, with and without the liquid cloud layer. Fig. 9 shows the calculated values of SWE sat and SWE sm with clouds plotted against those of the same parameters under clear-sky condition: plot (A) and plot (B) are for CLW values of 0.02 g/cm 2 and 0.04 g/cm 2, respectively. For CLW=0.02 g/cm 2 in plot (A), values of SWE sat and SWE sm are reduced to about 15.6 cm and 17.6 cm, respectively, in reference to their clear-sky value of 20 cm. When CLW is increased to 0.04 g/cm 2, the corresponding SWE sat and SWE sm become 12.1 cm and 15.5 cm, respectively. The regression coefficients, in the form of SWE sat (cloudy)= a + b SWE sat (clear-sky) or SWE sm (cloudy)= a + b SWE sm (clear-sky), are listed in Table 4 together with the cases of CLW=0.06 g/cm 2 andclw=0.08g/cm 2.Thedashed1:1 lines in both Figs. 8 and 9 provide a useful reference in the regression of these SWE parameters. Table 3 Regression coefficients between SWE sat and SWE sm (or SWE s ) CLW, g/cm 2 SWE sat =a+b SWE sm, cm SWE sat =a+b SWE s,cm a b a b The results presented in Figs. 8 and 9, and Tables 3 and 4 clearly indicate the need to account for the effects of liquid cloud cover in order to more reliably estimate SWE from satellite radiometric measurements near 19 and 37 GHz. Reliable microwave radiometric measurements of atmospheric parameters at these frequencies over land from satellites or highaltitude aircraft are generally difficult because of the lack of radiometric contrast and the variable surface emissivities. Thus, it may not be feasible to quantify the effects of cloud cover and simultaneously arrive at a reliable SWE estimation from the measurements by the sensors like AMSR-E. It may be necessary to use cloud screening techniques such as that developed for sea ice by Miao et al. (2000), or from the measurements of other sensors (e.g., MODIS) to exclude microwave data under cloudy conditions from SWE estimation. Similarly, radiometric measurements of snow packs near or at the ground level could end up with very different results depending on clear-sky or cloudy conditions. It may require monitoring and quantification of the effects of cloud cover to interpret the measurements correctly. 6. Discussion and conclusion Studies on the retrieval of snow depth or snow water equivalent (SWE) using microwave radiometric measurements near 19 and 37 GHz have been conducted for more than three decades. During all these years significant progress on the estimation of SWE has been made on many fronts but, to the best of our knowledge, the effects of atmospheric absorption on the retrieval results have not been explicitly discussed or quantified. The main reason for this lack of attention could be due to the fact that researchers need to fully understand a way of quantifying many crucial parameters in the retrieval algorithm, such as size of the snow crystals and fractional vegetation cover, to arrive at reliable retrievals of SWE. Another reason could be the general perception that the effects of atmospheric absorption are not serious enough to introduce significant errors in the SWE estimation. There have been continual improvements in the understanding of the snow pack radiometric signatures and the measurement techniques through the past research efforts, and it could be time now to closely examine the impact of this atmospheric effect on the SWE retrievals. Additionally, the effects of atmospheric absorption will have to be taken into account to correctly compare measurements and model calculations of the emissive properties of ice crystals of snow packs. The impact of such atmospheric influence could be extended to the case of snow cover over sea ice, because the

11 J.R. Wang, M. Tedesco / Remote Sensing of Environment 111 (2007) retrievals of sea-ice concentration mainly rely on the measurements from these two frequencies (Markus & Cavalieri, 2000; Markus et al., 2006). In this paper, the AMSR-E measurements at the frequencies (ν) of 18.7 and 36.5 GHz over two regions in the continental U.S.A. are used to demonstrate the effects of atmospheric absorption on the SWE retrievals based on the radiometric differences at these two frequencies. One of these regions is in the west coast that contains Sierra-Nevada with large variations in surface elevation, and another is in the relatively flat Midwest centered about Fargo, North Dakota. Radiosonde data sets over a 5-month period from November 2003 to March 2004 from a number of NWS stations in these regions are used to calculate the effective atmospheric temperature T a (ν) and absorption factor Γ(ν), the two parameters determining the atmospheric absorption under clear conditions. At 18.7 and 36.5 GHz these two atmospheric parameters are found to depend on surface elevation. Thus, the AMSR-E measurements over Sierra-Nevada region are co-located with a digital elevation model at 1 km resolution before the radiative transfer calculations are made for individual pixels for the analysis of the atmospheric effects on SWE retrievals; a constant elevation of 0.5 km is assumed in similar calculations for the flat Midwest region. Two effective snow pack temperatures (T s )of250kand 270 K are assumed in the calculations. It is found that the impact of T s is negligible if the discussions are confined to SWE (or the difference between the two brightness temperatures at 18.7 and 36.5 GHz), which is the case throughout this paper. Under the clear conditions, the calculations show that the effects of atmospheric absorption to the SWE retrievals are not negligible. For example, if the SWE based on the AMSR-E measurements over the Midwest region is 10 cm, then the corresponding measurements conducted at the ground level under the same atmospheric condition will give a SWE of about 13.5 cm; the SWE based on surface emission alone (i.e., no atmosphere) will be about 15.1 cm. The similar estimation over Sierra-Nevada gives slightly less changes because the snow packs in this region occur in higher elevation (2 4 km altitudes) and thus less atmospheric absorption. A subtle feature is noted from these calculations that, when the snow pack is thin with the surface-measured or the surface emission based SWE on the order of 2 3 cm, it is unlikely to be detected by orbiting microwave radiometers like AMSR-E. This is mostly likely the reason for the improved correspondence between the MODIS and AMSR-E snow cover mapping, after the AMSR-E data are corrected for the effects of atmospheric absorption, as reported by Tedesco and Wang (2006). Additionally, there is a regional dependence of T a (ν) and Γ(ν), and this dependence translates into some difference in the estimation of atmospheric effects on the SWE retrievals. Therefore, it is necessary to derive these parameters from radiosonde stations in near proximity for more accurate calculations of the atmospheric absorption effects. The seasonable dependence of these parameters appears to be small, and its impact on the SWE retrievals can be considered as a second-order effect. The calculations of the effects of cloud liquid water (CLW) on SWE are made for the Midwest regions with CLW in the amount of 0.02, 0.04, 0.06, and 0.08 g/cm 2 uniformly distributed in an altitude layer of km, and the effects are found to be significant. As an example, if the SWE value is 10 cm based on AMSR-E measurements under cloudy condition with CLW=0.04 g/cm 2, the corresponding measurements at the ground level will give a SWE of about 14.4 cm, and the SWE value based on surface emission (no atmosphere) will be about 21.9 cm. These estimations include both CLW and clear-sky absorptions. Thus, additional calculations of the effects of cloud liquid water absorption are made in reference to the clear-sky condition. The results show that the same 10 cm SWE value based on AMSR-E measurements under cloudy sky with CLW of 0.04 g/cm 2 will become about 16.9 cm under the clear-sky condition. Similar calculations show that a SWE of 10 cm based on measurements conducted at the ground level under the same cloudy-sky condition will assume a value of about 13.2 cm under clear sky. 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