Enhanced algorithm for estimating snow depth from geostationary satellites

Remote Sensing of Environment 108 (2007) 97 – 110 www.elsevier.com/locate/rse

Enhanced algorithm for estimating snow depth from geostationary satellites Peter Romanov a,b,⁎, Dan Tarpley b a

Cooperative Institute for Climate Studies, University of Maryland, USA b Office of Research and Applications, NOAA/NESDIS, USA

Received 2 August 2005; received in revised form 2 November 2006; accepted 4 November 2006

Abstract Observations in the visible and infrared spectral bands from the Imager instrument onboard Geostationary Operational Environmental Satellite (GOES) have been used to derive snow depth. The technique makes use of correlation between depth of the snow pack and satellite-derived subpixel fractional snow cover. Previous efforts to infer snow depth from satellite data with this technique were focused on grasslands and croplands, where the snow depth/snow fraction relationship is most pronounced. In this paper we improve the retrieval algorithm to extend snow depth estimates to forested areas. The enhanced algorithm accounts for the tree cover fraction and for the type of forest, deciduous or coniferous. The developed technique was used to derive maps of snow depth over mid-latitude areas of North America during winter seasons of 2003– 2004 and 2004–2005. Satellite-based snow depth maps were produced daily at 4 km spatial resolution. To validate the retrievals we compared them with surface observations of snow depth and with the snow depth analysis prepared at the NOAA National Operational Hydrological Remote Sensing Center (NOHRSC). The estimated retrieval error was about 30% for snow depths below 30 cm and increased to 50% for snow depths ranging from 30 to 50 cm. Snow depth retrievals were limited to scenes with less than 80% deciduous forest cover fraction and less than 50% needle leaf forest cover. © 2006 Elsevier Inc. All rights reserved. Keywords: Snow depth; Satellite remote sensing

1. Introduction Information on the snow cover is needed in hydrological, numerical weather prediction, climate models and in a large number of other environmental applications. In-situ observation is a traditional source of this information, however they do not fully satisfy the needs of the modeling community. The distribution of surface meteorological stations is highly uneven, stations are sparse in remote polar areas and their reports are often unavailable in real time. Moreover, in recent years the number of stations conducting observations of snow cover has been steadily decreasing. For over three decades satellites have been actively used for monitoring snow cover from regional to global scales. Owing to frequent scene revisit and wide-area coverage satellite observa⁎ Corresponding author. Postal address: 5200 Auth Rd., World Weather Building, Room 712, Camp Springs, MD 20746, USA. Tel.: +1 301 763 8042x202; fax: +1 301 763 8108. E-mail address: [email protected] (P. Romanov). 0034-4257/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2006.11.013

tions can effectively supplement ground-based measurements and provide near-real time spatially-detailed information on the snow cover distribution. Since 1966 NOAA has generated snow cover charts over the Northern Hemisphere based on interactive interpretation of satellite imagery (Ramsay, 1998). These charts present one of the principle inputs to operational numerical weather prediction models run by NOAA National Centers for Environmental Prediction (NCEP) and are extensively used in climate change and climate modeling studies, (e.g. Frei et al., 2003; Groisman et al., 1994). A large number of automated snow mapping algorithms have been developed to infer snow cover and snow extent from satellite observations in the visible/ infrared and in microwave spectral bands. Maps of snow cover distribution have been derived from observations of NOAA Advanced Very High Resolution Radiometer, AVHRR (Simpson et al., 1998), Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua (Hall et al., 2002), Landsat TM (Dozier & Painter, 2004), Special Sensor Microwave Imager (SSM/I) onboard Defense Meteorological Satellite Platform, DMSP (Grody & Basist, 1996), and from a

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number of other instruments onboard research and operational satellites (e.g., Xiao et al., 2004). It is important that besides the snow cover extent, satellite observations are also sensitive to and thus can be used to obtain quantitative information on other physical properties of the snow pack, for example on its depth and the snow water equivalent (SWE). This ability, although limited, makes satellites even more attractive for the global snow cover monitoring and broadens the scope of possible environmental applications of snow remote sensing data. Earlier efforts to estimate the depth of snow or its SWE from satellites involved solely passive microwave measurements. Simple algorithms linearly relating the difference of brightness temperatures at 18 GHz and 37 GHz to the snow depth were proposed by Kunzi et al. (1982), Chang et al. (1987) and Goodison and Walker (1995). These algorithms were applied to infer snow depth from measurements of the Scanning Multichannel Microwave Radiometer (SMMR) onboard Nimbus-7 satellite and of the Special Sensor Microwave/Imager (SSM/I) on the Defense Meteorological Satellite Platform (DMSP). Forest cover attenuates the spectral signal coming from snow and complicates estimates of the snow depth or the SWE. In order to account for the masking effect of the forest cover, Foster et al. (1997) introduced a corrective factor dependent on the forest cover fraction to the slope of the snow depth/brightness temperature gradient relationship of Chang et al. (1987). Goita et al. (2003) employed different relationships for different land cover types (deciduous, coniferous forest, sparse woodland and open areas). More complicated algorithms involving a combination of multiple spectral gradients of microwave brightness temperature were applied by Tait (1998) to SSM/I data and by Kongoli et al. (2004) to the data from the Advanced Microwave Sounding Unit (AMSU) onboard NOAA satellites. The reported accuracy of microwave-based retrievals of the snow water equivalent ranges within 5 mm to 45 mm over nonforested areas and increases by 5–10 mm over forests (e.g., Derksen et al., 2003; Pulliainen et al., 1999; Singh & Gan, 2000; Tait, 1998). This corresponds to 40–100% if the error is expressed as a percentage error of the total SWE. Kelly et al. (2003) put an estimate of the accuracy of microwave snow depth retrievals to 50%–70% for mostly forested locations. Much of uncertainty associated with SWE and snow depth retrievals from satellite observations in the microwave results from a strong dependence of the surface-emitted microwave radiation on other physical properties of the snow pack, besides its depth, particularly on the snow grain size, density and stratification (Rosenfeld & Grody, 2000). Other deficiencies of the microwave technique include difficulty or inability to identify shallow, wet, melting snow and difficulty in distinguishing between snow and cold snow-free rocky surfaces. It is also important, that the spatial resolution of current satellite measurements in the microwave and hence the resolution of derived products ranges within 25–50 km. This spatial resolution is too coarse for many environmental applications including in particular, regional numerical weather prediction and hydrological models. Contrary to the microwave spectral range, in the visible part of spectrum the photon penetration into the snow pack does not

exceed several centimeters (Li et al., 2001). Therefore, there is practically no direct physical relationship between the snow depth and reflectivity of the snow pack. However because of the vegetation cover and certain terrain roughness inherent to most natural land surfaces, changing snow depth causes a gradual change of the fraction of the land surface masked by snow (e.g., Baker et al., 1991). As a result, the reflectance of the land surface also increases with the increasing snow depth up to some depth where the underlying land surface is completely masked by snow. This relationship between the snow depth and the surface reflectance or the fractional snow cover is quite pronounced for thin to medium thick snow packs and thus provides means for estimating snow depth from satellite observations in the visible spectral band. Without the tree canopy, which masks and shadows the snow cover, the relationship between the snow depth and the snow fraction is the strongest. In our earlier work (Romanov & Tarpley, 2004) we have demonstrated that this relationship can be employed to estimate the snow depth over plain non-forested areas. The developed retrieval technique was successfully applied to observations of the Imager instrument onboard Geostationary Operational Environmental Satellite (GOES) to derive the snow depth over the North America prairie region. In this study we seek to improve the algorithm and evaluate potentials for snow depth retrievals within an expanded domain, which includes forested and alpine areas. The paper starts with an overview of the data and the existing algorithm for snow depth retrieval over prairies. Following the overview, we assess sensitivity of satellite observations to the snow depth with a special focus on forested areas and introduce improvements to the existing retrieval algorithm. The performance of the enhanced algorithm is evaluated by comparing snow depth retrievals with available in-situ data and with results of operational snow depth analysis. 2. Satellite data and snow depth retrieval algorithm for prairies For over three decades operational meteorological geostationary satellites have been providing valuable information on the global weather and climate. The ability of geostationary satellites to make observations at frequent time intervals is extensively used in monitoring diurnal variations of the atmospheric boundary layer and the land surface as well as cloud systems and precipitation. Monitoring snow cover is another important application of geostationary satellite data: since the middle of 1980s they have been utilized by analysts at the National Environmental Satellite Data and Information Service (NESDIS) of NOAA to interactively generate snow cover charts for the Northern Hemisphere (Ramsay, 1998). The GOES satellite system operated by NOAA consists of two geostationary satellites, GOES-East (GOES-8, and GOES-12 since April 2003) and GOES-West (GOES-10), which are positioned over the equator respectively at 75°W and 135°W. The Imager instrument onboard GOES provides observations which completely cover low and mid-latitude portions (up to 60°–70° latitude) of North and South America at a spatial

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resolution of 1 to 4 km. Images are available at a 30-minute interval. Three of the five spectral channels of Imager are centered in the visible (0.63 μm), middle infrared (3.9 μm) and infrared (10.7 μm) spectral bands. With this combination of spectral channels snow in GOES Imagery can be identified in an automated fashion using an unsupervised image classification technique. Detection of snow in satellite imagery is possible primarily due to its specific spectral feature: snow reflectance drops from up to 80–90% in the visible to less than 20% in the shortwave infrared and in the middle-infrared spectral range (Wiscombe & Warren, 1980). In image classification algorithms this feature is typically utilized through the use of spectral indices, such as Snow Index (SI) representing a simple ratio of the visible (RVIS) and shortwave-infrared (RSIR) or middleinfrared reflectance (RMIR) (e.g. Bunting & D'entremont, 1982; Dozier, 1989) or a Normalized Difference Snow Index (NDSI), characterizing the relative difference between reflectance in the visible and in the shortwave infrared (NDSI = (RVIS − RSIR) / (RVIS + RSIR)) (Hall et al., 2002). An automated snow mapping system currently implemented at NOAA/NESDIS uses GOES-Imager observations to routinely generate daily maps of snow cover over a mid-latitude portion of North America (25°N to 66°N) at a spatial resolution of 4 km. Snow fraction is estimated for snow-covered pixels from satellite observations in the visible spectral band following the technique described in Romanov et al. (2003). The relationship between the snow fraction and the snow depth as established over plain non-forested areas in Romanov and Tarpley (2004) is applied to derive the snow depth over U.S. Great Plains and Canadian Prairies. A detailed description of algorithms involved in estimating and mapping snow cover properties is given in our two papers cited above. In this work we provide only a brief overview of the data processing routine before discussing potentials for extending the snow depth retrieval technique to forested regions. Within the developed algorithm daily snow maps derived from GOES data utilize all available daytime satellite images. At the preprocessing stage half-hourly images in three spectral channels centered in the visible, middle infrared and infrared are calibrated, navigated and brought to a latitude–longitude projection with a 0.04°, or about 4 km, grid cell size. In order to achieve consistency in snow cover retrievals from all satellites (GOES-8, -10 and -12) we perform cross-calibration of the visible sensor of GOES-West and GOES-East Imager instruments by routinely collecting and comparing collocated synchronous observations from the two platforms taken at the same viewing-illumination geometry. Available daytime halfhourly images are then composited to retain the least cloud contaminated observation for every grid cell of the map. All pixels in the daily composited image are classified into “snowcovered”, “snow free” and “cloudy” categories. Image classification is performed with a threshold-based decision-tree algorithm which utilizes both the spectral response of the scene (including its reflectance in the visible and mid-infrared bands, infrared brightness temperature and the ratio of the visible and mid-infrared reflectance) and variability of its temperature and reflectance during the day. The reflectance in the middle infrared

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is estimated from brightness temperatures in the middle infrared and in the infrared spectral bands following Allen et al. (1990). Image classification results are tested for compliance with climatic data on the land surface temperature and the snow cover. Every satellite image pixel classified as snow-covered in the GOES snow map is further processed to estimate the fractional snow cover. The fractional snow cover, as we define it here, represents the portion of the terrain covered with snow as seen from the satellite. In other words, it does not include snow cover masked by the canopy. To calculate the snow fraction (F) we have employed a linear mixture technique with two endmembers representing the visible reflectance of a completely snow-covered and completely snow-free land surface, Rland and Rsnow, respectively: F ¼ ð R−Rland Þ=ðRsnow −Rland Þ;

ð1Þ

where R is the observed visible reflectance of the scene. The reflectance of the snow-free land surface in every grid cell of the snow map was established from satellite observations made in late fall before the beginning of the snow season. Snow reflectance was considered independent of location and was determined empirically from winter-time GOES measurements over several target areas representing flat terrain with no trees. To account for the change in snow reflective properties during its aging we have used the model of Melloh et al. (2002) where the snow albedo decreases proportionally to the square route of the grain size. Following Kelly et al. (2003), the snow grain size was assumed to exponentially grow throughout the winter season from 0.1 mm inherent to fresh snow (e.g. Lefebre et al., 2003; Wiscombe & Warren, 1980) to a maximum value of 1.0 mm in late spring. This grain size growth results in a 4% decrease in the visible reflectance of the snow pack. Rland and Rsnow in Eq. (1) were brought to the viewing and illumination geometry of a satellite observation using a kernel-driven model of Roujean et al. (1992) with empirically determined kernel loadings (see Romanov et al., 2003). The relationship between the snow depth (D) and the snow fraction (F) was established from matched satellite and in-situ observations collected during three winter seasons (2000–2003) over non-forested areas of US Great Plains and Canadian Prairies. It was found to closely follow an exponential law: D ¼ exp ðaF Þ−1;

ð2Þ

with a = 0.0333 and F expressed in percent. Application of this algorithm to satellite observations of the snow fraction over mostly shallow and moderate snow packs provided snow depth retrievals of 3–10 cm accuracy for snow depths up to 30 cm. In forests masking and shadowing of snow by trees, snow littering by tree debris and interception of snow by the tree canopy increases variability of the scene visible reflectance and thus weakens the correspondence between the snow fraction observed from satellites and the snow depth as compared to prairies. The use of a physical model to establish the snow fraction/snow depth relationship in forests is not feasible because of two reasons. First, physical models (e.g. Chen & Leblanc, 1997) require detailed information on the canopy

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structure, which is often unavailable. Second, available models produce unreliable results at high, exceeding 60°–70°, solar zenith and viewing zenith angles. The latter limitation is serious since low-solar-elevation conditions are typical for observations of snow-covered areas in winter. Therefore, we chose to follow an empirical approach adopted in Romanov and Tarpley (2004) where the relationship between the snow depth and the snow fraction was established from the statistics of matched satellite and in-situ observations. 3. Snow depth algorithm for forested areas The focus of this study was on the area in the central part of North America limited to 32°N–55°N latitude and 80°W– 120°W longitude. Grasslands and croplands of U.S. Great Plains and Canadian prairies occupy a large part of this region and appear as land surface with little or no forest cover in the map in Fig. 1a. In the east of the study area, the forest type changes from mostly deciduous in the south to coniferous in the north. In the west, predominantly coniferous forests are confined to alpine areas (see Fig. 1b,c). Forests were defined as predominantly deciduous or coniferous if over half of the forest stand was correspondingly deciduous or coniferous. Information on the tree cover distribution and type was obtained from the percent tree cover dataset prepared at the University of Maryland (DeFries et al., 2000). An important feature of the selected area is a dense network of meteorological stations including first-order, US Cooperative and Canadian climate stations, which provide routine snow depth observations. Availability of extensive ground-truth information is a critical factor both for the development of a snow depth algorithm and for its validation. The area is com-

pletely covered with observations from both GOES-East and GOES-West satellites. In this we have studied we have used daily observations from GOES Imager acquired during five winter seasons, from 2000– 2001 to 2004–2005. Maps of snow cover and snow fraction distribution were produced with the technique described above. In order to establish a statistical relationship between satellitederived snow fraction and snow depth we collected daily ground-based measurements of snow depth and matched them with observations from GOES-East and GOES-West. Since no snow fraction retrievals were available in cloudy conditions, matched pairs of observations were collected only for cloudclear scenes. Our analysis of satellite imagery has shown that image navigation and registration errors may reach 4–6 km. To reduce the effect of these errors on the statistics of matched satellite and surface data, satellite-derived snow fraction was averaged within the area of 3 × 3 grid cells of the snow map (or approximately 12 × 12 km) centered at the station location. Stations located in the vicinity of urbanized areas were excluded from the dataset because snow removal in big cities changes the satellite-observed snow fraction and hence affects the snow depth-snow fraction relationship. Overall more than 70,000 matched satellite and surface observations were accumulated during five winter seasons. The size of the statistics for each location ranged from several to several hundred cases, depending upon the length of the snow season in a particular location, the number of issued snow depth reports and the number of available cloud-clear satellite observations. About 40,000 pairs collected in the first three winter seasons (2000– 2001 to 2002–2003) were used to develop and refine the snow depth retrieval algorithm, whereas the rest match-ups were used as an independent dataset for validation of snow depth estimates.

Fig. 1. a: Forest fraction (deciduous and coniferous). Triangles indicate the location of ground-based stations. Two large red triangles and a red rectangle show the location of two stations and the study area used in detailed analysis of matched snow depth and snow fraction (see Figs. 2 and 6 below). The insert in the upper right shows the location of the region. b: Dominant forest type, c: Alpine areas with elevation over 2000 m. Information on the tree cover distribution and type was taken from the percent tree cover dataset prepared at the University of Maryland (DeFries et al., 2000).

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Fig. 2. Matched observations of in-situ snow depth and satellite-based snow fraction for locations with different forest cover fraction. Left: tree cover fraction is 19%, fraction of coniferous forest is 3%. Right: tree cover fraction is 46%, fraction of coniferous forest is 35%. The fraction of coniferous forest is given relative to the entire pixel area.

Fig. 2 presents matched snow fraction and snow depth data extracted from the dataset for two sites in the north-eastern quarter of the area (see Fig. 1 for the location of the sites). The selected sites are characterized by moderate forest cover fraction (19% and 46%), with mostly deciduous stands at the first one and mostly coniferous stands at the second. Despite a substantial scatter both graphs in Fig. 2 exhibit a noticeable increase of the snow fraction with increasing snow depth for snow packs up to 40 to 50 cm thick. Because of larger stem density, the transmissivity of coniferous canopy cover for solar radiation is about two times less than the one of leafless deciduous trees (Link et al., 2004). This partially explains the slower growth of the snow fraction with the increase of the snow depth for the location with larger fraction of needle leaf trees in the forest stand. A similar effect has the increase of the tree cover fraction. Outliers with the snow fraction exceeding 70% in Fig. 2b most probably result from missed partial cloudiness or semitransparent clouds by the satellite image classification algorithm. At snow fraction below

30% stations sometimes report a ‘zero’ snow depth (or no snow on the ground), thus giving an indication of a patchy snow cover. Results of a broader analysis of matched satellite and surface observations presented in Fig. 3 confirm high sensitivity of the snow fraction/snow depth relationship both to the tree cover fraction and forest type. All matched observations collected in 2000–2003 over the study area were used in this analysis. Snow depth values were averaged over 10% snow fraction intervals. As it is seen from Fig. 3, increasing forest cover fraction reduces the snow fraction observed at the same snow depth, whereas the shape of the snow depth/snow fraction relationship depends on the type of the forest, deciduous or coniferous. The scatter of snow depth around its mean values (not shown in Fig. 3) generally ranges within 50%–100% with lower end values corresponding to higher snow fractions and larger depths. No sufficient statistics was accumulated for very dense coniferous forests with over 80% tree cover fraction because of the lack of appropriate in-situ observations.

Fig. 3. In-situ snow depth vs satellite-derived snow fraction. Snow depth is averaged within 10% snow fraction bins. Lines represent the model approximation (see text). Left: deciduous forest, right: coniferous forest.

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Table 1 Polynomial coefficients (ai and bi) used in Eq. (3) to approximate the snow fraction/snow depth relationship with respect to the forest cover fraction Deciduous

i=0 i=1 i=2 i=3

Coniferous

ai

bi

ai

bi

0.0333 − 0.420·10− 3 0.737·10− 6 − 0.359·10− 7

0 0.611·10− 1 − 0.585·10− 3 0.231·10− 5

0.0333 − 0.750·10− 3 0.111·10− 4 − 0.148·10− 7

0 0.115 − 0.208·10− 2 0.128·10− 4

To account for the effect of the forest cover when estimating the snow depth, we modified the original relationship between the snow depth and the snow fraction Eq. (2) developed for prairies to D ¼ expðaF þ bÞ−1;

ð3Þ

where coefficients a and b depend on the tree cover fraction and the forest type. A reasonable fit to matched observations was achieved with a and b represented with a third order polynomial of the tree cover fraction (f ), a = Σaif i , b = Σbif i. To ensure consistency with the earlier model (2) the values of a0 and b0 were set to 0.0333 and 0, respectively. Least square estimates of ai and bi, i = 0.3 for coniferous and deciduous forests are given in Table 1. The model approximation of the snow depth/snow fraction relationship for deciduous and coniferous forests is shown in Fig. 3. In prairies the principal factor that controls the snow fraction is protrusions of low-level vegetation through the snow pack. Once snow covers all of the low-level vegetation, the observed snow fraction becomes insensitive to further increase of the snow depth. For non-forested locations Formula (3) yields a 100% snow fraction for about 30 cm of snow depth. This value can be interpreted as an upper limit of the retrievable snow depth. Similar estimate for forests cannot be easily made since the maximum snow fraction depends on the tree cover fraction and the forest type. However it is clear that more snow is needed to cover tree debris on the forest floor along with shrubs and seedling layers vegetation inherent to most forests. Therefore

the upper limit of retrievable snow depth should be larger in forested than in non-forested areas. Graphs of the model approximation of the snow depth and snow fraction relationship in Fig. 3 demonstrate the importance of proper account for the forest cover and type when estimating the snow depth. Even when the forest is sparse, with less than 40% tree cover fraction, application of the prairie algorithm (2) results in underestimating the snow depth by up to 10 cm and up to 22 cm for deciduous and coniferous forests respectively. The bias gradually increases both with the increase of the tree cover fraction and the snow depth. There are a number of factors which tend to increase the scatter in the snow depth/snow fraction statistics and weaken the relationship between these two parameters. The list includes in particular, finite accuracy of snow fraction estimates, inaccuracy of satellite image navigation, high spatial variability of snow depth distribution, undetected semitransparent cloudiness, variable properties of the low-level vegetation and variable terrain roughness. This explains a rather low correlation between the snow fraction and the snow depth, which does not exceed 0.6 even over plain non-forested areas (see Fig. 4a). Correlation coefficients in Fig. 4a were calculated from the statistics of matched satellite and surface observations for the years 2000 to 2003. Increasing forest cover further reduces the impact of changing snow depth on the satellite-observed snow fraction and therefore increases the uncertainty in the estimate of the snow depth from remote sensing data. Over alpine areas the correspondence between the snow fraction and the snow depth observed on the ground further weakens due to highly inhomogeneous distribution of snow in the mountains, topographic shadowing and specular reflectance effects. In order to avoid unreliable estimates when generating maps of snow depth we limited snow depth retrievals to land covers where correlation between the snow fraction and the snow depth exceeded 0.35. As it follows from Fig. 4a, this criterion is satisfied over plains with less than 80% deciduous or less than 50% coniferous tree cover fraction and over mountains with less than 30% forest fraction. Even with these restrictions, extending snow retrievals from non-forested to lightly and moderately

Fig. 4. (a): Correlation between satellite-observed snow fraction and snow depth as a function of forest cover fraction, (b): Distribution of application areas of the old and the new GOES-Imager data based snow retrieval algorithm.

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forested locations implies a substantial, over 60%, increase in the effective area coverage (Fig. 4b). Since coefficients in Formula (3) relating the snow depth and the snow fraction were obtained only for pure deciduous and coniferous forests, the retrieval algorithm required a modification to account for mixed forests. In this case we defined the snow depth estimate (D) as a weighted average of two snow depth estimates: D ¼ ðDc fc þ Dd fd Þ=ð fc þ fd Þ;

ð4Þ

where Dc and Dd are snow depths derived from (3) assuming that the forest stand was pure coniferous and pure deciduous and fc and fd are fractions of coniferous and deciduous forest in the mixture. 4. Application of the enhanced algorithm To evaluate the performance of the enhanced snow depth retrieval algorithm (3) we applied it to the data from GOES-East and GOES-West Imager instrument acquired during two winter seasons of 2003–2004 and 2004–2005. Daily maps of snow depth were generated at 4 km spatial resolution. The analysis of snow depth maps derived from GOES-East and -West has

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revealed their close similarity. In over 90% of comparisons, the mean difference between estimated snow depth was below 2.5 cm and the mean absolute deviation was less than 5 cm and the correlation coefficient exceeded 0.7. Much of the disagreement was due to inaccuracy in the satellite image registration. Because of the similarity of products, below we present the results obtained only with observations from GOES-East satellite. An example of a GOES-based snow depth map shown in Fig. 5a illustrates the snow depth distribution after a series of strong snow falls that affected Midwestern and Great Plains states of U.S. and Southern Central Canada in the end of January 2004. Retrievals in the cloud-clear portion of the image on February 2, 2004 show snow cover reaching 35°N and substantial snow accumulation in the south of Canadian prairies and in Northern U.S. Great Plains (47°–51°N, 105°–110°W). Plain areas exhibit a fairy smooth snow depth distribution whereas alpine areas can be easily identified by a highly variable snow depth (see Fig. 5a). Enlarged portions of the snow depth map demonstrate a good correspondence of satellite retrievals to insitu observations (Fig. 5c and d). Quantitatively the agreement between satellite and surface observations is the best over areas with low or moderate snow accumulation, below 30–40 cm. Quantification of larger snow packs tends to be less accurate and the derived snow depth in these cases is often underestimated.

Fig. 5. (a) GOES-E-based snow depth map for February 2, 2004. The black oval shows snow depth retrievals in the mountainous area. (b) NOHRSC snow depth analysis. (c) and (d) are enlarged fragments of GOES-based snow depth map with surface observations overlaid.

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Some disagreement between satellite and surface snow depth may be caused by the time difference between the two observations. Snow depth measurements at most ground-based stations are performed in the early morning whereas satellite snow depth is derived from the “warmest” observation during a day which is most likely to occur in the afternoon. The effect of this factor becomes most pronounced when snow cover experiences fast changes due to snowfalls or active snow melting. For example, in the map on Fig. 5d, fast-melting snow and different time of observations explain the difference between satellite and in-situ snow depth estimates along the southern tip of the snowcovered area. Snow cover from 2 cm to 5 cm deep observed in situ in the morning may have melted by the end of the day and thus was not mapped in the satellite product. This conclusion is supported by synoptic records of ground-based meteorological stations located in this region which revealed maximum air temperatures for that day ranging from 5 °C to 9 °C.

Snow depth distribution derived from GOES observations compares favorably to the snow depth analysis of the National Operational Hydrological Remote Sensing Center (NOHRSC) of the National Weather Service (NWS) (see an example of matched maps in Fig. 5a and b). The comparison of these datasets however is limited to the area south of 49°N latitude since the NOHRSC product covers only the territory of conterminous U.S. As it is seen from Fig. 5a and b, satellite-derived snow depth exhibits noticeably higher spatial variability than the snow depth distribution in the NOHRSC product. This may be due to small-scale variability of vegetation cover properties or surface features, e.g., surface roughness, subresolution lakes and built-up areas, which are not accounted for in the algorithm. On the other hand, it should be remembered that the NOHRSC snow depth map presents an output of a distributed energy-and-mass balance model, which relies on the analysis and forecast fields from a low resolution (∼20 km) mesoscale numerical weather

Fig. 6. Time series of satellite-derived and in-situ snow depth over 2° by 2° area centered at 47°N and 96°W for winter seasons of 2003–2004 and 2004–2005. Bar graphs on top present the cloud cover fraction over the area estimated from GOES data. In-situ snow depth is calculated using observations from 8 to 13 ground-based stations within the area. Grey bars in the snow depth graph show the range (minimum to maximum) of snow depths observed in situ. Satellite estimates are given for days when the cloud cover fraction was below 60%. The distribution of the forest cover fraction and location of stations within the area are shown in Fig. 7.

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Fig. 7. Forest fraction and location of meteorological stations (shown with blue triangles) within 2° by 2° test area used in the comparison of area-averaged estimates of the snow depth in Fig. 6. The insert in the upper right shows the location of this area.

prediction model. Therefore, despite high, 1 km, nominal spatial resolution of the land surface model used at NOHRSC, the effective spatial resolution of the NOHRSC analysis is lower. As a result, the NOHRSC snow map may not be able to reproduce small-scale peculiarities of the snow depth distribution seen in the higher spatial resolution satellite-based product. The analysis of time series of matched satellite and surface observations has shown that on the whole, GOES-based snow depth retrievals correctly capture the timing of snow accumulation and ablation periods and accurately reproduce major seasonal changes in the snow depth. As an example, in Fig. 6 we present time series of satellite and in-situ observations of snow depth over a small area in the north-eastern part of the U.S. Great Plains. The selected area is centered on 47°N and 96°W and has a size of 2° by 2°. It is characterized by predominantly deciduous forests with the fractional cover ranging from 0%– 10% in the south-east to over 80% in the north-west (see Fig. 7 for the distribution of the forest fraction and the location of ground-based stations within the area). The mean forest cover fraction was 28% with coniferous stands comprising about one third of the forest cover. To reduce the effect of satellite image navigation and registration errors, finite instrument field of view and high spatial variability of the snow depth on the correspondence between satellite and ground-based observations, instead of point-wise data in Fig. 6 we compared areaaveraged estimates of snow depth. In-situ estimates were obtained by averaging daily observations from 8 to 13 ground stations available within the area. Satellite estimates of the areaaverage snow depth were generated if at least 40% of the area was cloud-clear. With the selected threshold value 155 valid daily satellite estimates of the area-average snow depth were obtained during the two winter seasons of 2003–2004 and 2004–2005 and were compared to surface observations. Results presented in Fig. 6 demonstrate a good overall correspondence between the two datasets during both winter

seasons. The only exception concerns the first half of February 2004, when following a strong snowfall satellite retrievals indicated only about 10 cm increase in the snow depth instead of over 20 cm increase observed on the ground. The absolute deviation between satellite and surface snow depth estimates averaged over the two winter seasons was 3.3 cm. There is also much similarity between changes in the minimum and maximum values of the satellite-observed and in-situ snow depth, however the range of satellite-derived snow depths is larger than the range of snow depths reported from the ground. Part of the problem is the “noise” in the derived snow depth, however the fact that observations from only few ground stations may not adequately represent the snow depth variability within the area of approximately 40,000 km2 may also contribute to this difference. Quantitative evaluation of the statistics of matched satellite and surface observations grouped by station has shown that for most locations the mean absolute error of satellite snow depth retrievals remains within 10 cm (see Fig. 8). This is true for about 90% of locations in prairie, 84% and 80% of locations correspondingly in deciduous and in coniferous forest. Mean absolute errors were calculated for stations with over 10 matched satellite and surface observations accumulated during two winter seasons, 2003–2004 and 2004–2005. Of the total 2002 of such stations 988 are located in prairies, 857 in predominantly deciduous forest and the rest in predominantly coniferous forest. The number distribution of stations by the land cover type is given in Table 2. As it is evident from the map in Fig. 8 disagreements between satellite retrievals and surface observations exceeding 15 cm are mostly confined to areas with inhomogeneous snow cover and/or highly variable land surface features (i.e., mountains, gaps in dense forest). In the North of Great Lakes the lack of stations located outside dense forests does not allow for a thorough validation of the snow depth product. In winter seasons of 2003–2004 and 2004–2005 the

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Fig. 8. Left: mean absolute error of satellite snow depth retrievals at stations within the study area for two winter seasons of 2003–2004 and 2004–2005. Stations with more than 10 matched surface and satellite observations were only included. Right: frequency distribution of the mean absolute error of satellite snow depth retrievals for stations located in the prairies, in predominantly deciduous forest with less than 80% forest fraction and in predominantly coniferous forest with less than 50% forest fraction.

southern part of Great Plains, south of ∼37°N did not receive much snow, therefore the number of accumulated satellitesurface match-ups in this region was not sufficient to obtain a reliable estimate of the snow depth retrieval accuracy in this area. Similar to the station-based error statistics, the error statistics incorporating all satellite retrievals grouped by the land surface cover type (Fig. 9) reveals a decreasing accuracy of snow depth retrievals from prairies to forested areas. The portion of retrievals made with less than 10 cm error exceeds 80% in prairies and drops to 72.2% and 48.9% in deciduous and coniferous forests, respectively. As it is seen from graphs in the bottom row in Fig. 9, sites with different tree cover fraction are almost equally represented in the statistics of snow depth retrievals over coniferous forests. The statistics for deciduous forests includes a slightly larger portion of retrievals made over sparsely forested locations: about 50% of all matched data correspond to sites less than 30% tree cover fraction. The total number of matched satellite and surface observations used in the validation study ranged from over 2000 for mountainous areas to over 20,000 for locations in deciduous forest (see Table 3). The distribution of snow depth retrieval errors in prairies (upper row in Fig. 9) is almost symmetrical around zero and becomes skewed in forests due to more frequent large underestimates of the snow depth. This change in the error distribution is explained primarily by different properties of the snow pack in different environments, and, first, by different snow accumulation. The statistics of snow depth reported from ground-based stations presented in Fig. 9 (middle row) indicates that snow packs in deciduous and especially in coniferous forests are noticeably deeper than in prairies. Although the upper limit of retrievable snow depth in forests is higher than in

prairies, higher frequency of large underestimates of the snow depth indicates that snow depth in forests exceeds this limit more often. Graphs in Fig. 10 illustrate the change of snow depth retrieval errors with the depth of the snow pack in different environments. Over prairies the average error gradually increases from about 5 cm over thin, below 15 cm snow packs to ∼ 10 cm (or about 30%) and ∼ 26 cm (or about 50%) at 30 cm and 50 cm snow depth, respectively. Except of small, below 15 cm–20 cm, snow depths, a similar behavior with slightly higher values is evident in snow depth retrieval errors in forests. Higher errors inherent to snow depth estimates over forested locations are attributed primarily to inaccurate specification of forest cover properties, particularly of its fraction and type. Masking and shadowing of snow by the tree canopy have the strongest effect on the ability to identify and

Table 2 Distribution of ground-based stations according to the surface cover type and the tree cover fraction Surface type

Forest fraction, %

Number of stations

Prairies Predominantly deciduous forest

b5 5–25 25–50 50–80 5–25 25–50 50–80

988 424 208 225 64 74 19 2002

Predominantly coniferous forest

Total

Included are stations with over 10 matched satellite and surface observations accumulated during 2003–2004 and 2004–2005 winter seasons.

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Fig. 9. Frequency distribution of snow depth retrieval errors (upper row), frequency distribution of snow depth observed on the ground (middle row) and the number distribution of snow depth retrievals by the tree cover fraction. Results are presented for prairies (left column), predominantly deciduous forest with the forest fraction below 80% (center column) and predominantly coniferous forest with coniferous forest fraction below 50% (right column). See Table 3 for the number of matched satellite and surface observations collected over each surface type.

accurately quantify the depth of shallow snow packs. This causes an increase of errors with the decrease of the snow depth below ∼ 15 cm over coniferous forests and to a lesser extent, over deciduous forests. Retrieval errors in alpine areas closely follow the pattern seen in the error distribution in prairies but are several centimeters larger. Since snow depth estimates in alpine areas are limited to non-forested and sparsely forested areas with maximum tree cover fraction of 30%, snow depth retrieval errors exhibit only a very small increase when the snow depth drops below 10 cm. 5. Discussion The analysis of snow depth retrievals presented above clearly indicates that satellite observations in the visible and infrared spectral band can provide valuable information on the depth of the snow pack in a variety of environments. With its high spatial resolution this information may be helpful in the water resource management and in forecasting of floods. It can also be used to complement snow depth or SWE retrievals in the

microwave, particularly over shallow or melting snow where microwave-based techniques experience difficulties or fail. It is important however, that interpretation of satellite snow depth retrievals should be done with some caution. First, the distribution of snow depth may be highly uneven and during snowmelt the snow cover is often intermittent. Gaps in the snow cover start to appear when the snow depth drops below 20 cm (Romanov & Tarpley, 2004) and at 2 cm snow depth, there is a Table 3 Distribution of the number of matched surface and satellite observations by the surface type Surface type

Number of matched observations

Prairies Predominantly deciduous forest Predominantly coniferous forest Alpine areas Total

7647 21,232 4536 2208 35,623

These matched observations were colleted during two winter seasons of 2003– 2004 and 2004–2005 and were used in validation of satellite retrievals.

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Fig. 10. Snow depth retrieval errors in different environments vs in-situ snow depth. See Fig. 1b for the distribution of the dominant forest type and Fig. 1c for the location of alpine areas.

50% chance, that the snow cover is patchy. Inasmuch subpixel variations of snow cover properties cannot be resolved, the satellite-derived snow depth should be viewed as an effective or area-weighted estimate of snow depth within a satellite image pixel. Second, the maximum snow depth retrievable with the developed technique is limited and the limit depends on the type of the land surface cover. Over prairies, about 30 cm of snow is enough to mask most of the low-level vegetation thus a further increase of the snow depth does not substantially change the snow fraction observed from satellites. Over forests, the snow fraction remains sensitive to snow depth at least up to 40–50 cm. Clouds are the major factor affecting snow depth retrievals from satellite observations in the visible and infrared spectral band. They cause gaps in the derived snow depth distribution and prevent from timely detecting snow depth changes. The problem is most persistent during the snow advance in fall and in early winter because of frequent heavy cloudiness. Confusion of clouds with snow or failure to detect semitransparent clouds over snow typically results in an overestimation of the snow depth. The effect of this confusion is most serious over dense forests, where small inaccuracy in the estimate of the scene reflectance and hence the fractional snow cover causes large errors in the estimated snow depth. Cloud shadows also present a potential source for errors causing underestimation of the snow depth or even failure to properly identify the snow cover. For GOES-based snow products, however, the effect of cloud shadows is small. First, winter-time observations from geostationary satellites over middle and high latitudes are made solely in the backscatter (i.e. with the Sun behind the satellite), thus mostly sunlit surfaces are viewed. Second, “shadowed” observations are effectively removed by the image compositing procedure, which retains the “warmest” observation for a day. There are several other factors, besides clouds, that may affect the accuracy of snow depth retrievals and their correspondence to surface observations. First, there is an uncertainty of about 10% in the snow cover fraction, which is mostly due to variable reflective properties of snow (see Romanov et al. (2003) for a detailed discussion of errors in the snow fraction estimate). If Eq. (3) is adopted as a model relating the snow fraction to the snow depth, this uncertainty translates

into ∼ 30–35% error in the derived snow depth. Second, the tree cover fraction and the tree type datasets which the retrieval algorithm relies on, may also contain errors. As follows from DeFries et al. (2000) and Hansen et al. (2003) the tree cover fraction can hardly be specified to better than 20% accuracy. Calculations performed using Eq. (3) have shown that this uncertainty causes an error of 2 to 10 cm in the derived snow depth over deciduous forest and a 4–15 cm error over coniferous forests. The effect of the tree cover fraction error on the accuracy of the snow depth estimate generally increases with the increase of the forest density. The difference in the spatial resolution of satellite and surface observations may also contribute to their disagreement on the estimated snow depth. Because of high spatial variability of the snow depth, point-wise ground measurements may not be representative of snowpack characteristics averaged over a 4 km satellite image pixel. Our earlier analysis of snow-course observations made at meteorological stations in the Former Soviet Union (FSU) has shown that in non-forested areas the scatter in the snow depth along a 2 km transect comprises about 50% of the value of the average snow depth (Romanov & Tarpley, 2004). It is reasonable to expect an even larger variability of the snow depth in forests and especially in alpine areas. A technique to derive the snow depth based on the relationship between the snow depth and the snow fraction can be modified for use with polar-orbiting satellite data. As compared to geostationary satellites, polar-orbiting satellites offer closer to nadir views and hence are better suit for detecting and quantitative characterization of snow cover in forests. They also provide complete global coverage, which is an obvious advantage before geostationary satellites covering the globe only up to 65°–70° latitude. In the same time, estimating snow depth from observations of polar-orbiting satellites appears more challenging since it needs an accurate model reproducing reflective properties of snow and snow-free land surface within a much broader angular range of viewing and illumination directions. Contrary to geostationary satellites, observations from polar-orbiting satellites are made both in the forward scatter and in the backscatter. Interpreting these observations may require the use of a more advanced bidirectional reflectance model than a simple kernel-driven model employed in the current algorithm. It is also important for snow cover and snow depth monitoring, that polar-orbiting satellites typically provide only one daytime observation over a given area per day. As a result, snow maps, as well as other daily land surface products derived from these data, are affected by clouds to a much larger extent than similar products based on multiple daily observations from geostationary satellites. Examination of GOES-based snow depth maps derived during the 2003–2004 winter season has shown that the average interval between two consecutive cloudclear retrievals over the same location makes less than 2 days (1.6–1.9 days in October and November, 2.0–2.1 days in December and January and 1.4–1.7 days in February, March and April). A similar estimate for MODIS snow cover maps (Hall et al., 2002) yielded 3.3 days (2.5–2.8 days in October and November, 3.7–4.4 days in December and January, 2.4–3.0 in

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February, March and April). Although part of this difference may be attributed to a more conservative approach to cloud identification in the MODIS image classification algorithm, we believe, that most of it is due to the use of half-hourly observations in the GOES snow mapping algorithm. 6. Conclusion A new enhanced algorithm for estimating snow depth from satellite observations in the visible spectral band is presented. As compared with the earlier algorithm developed solely for prairie environments, the new technique extends snow depth retrievals to partially forested areas. Estimating snow depth is possible owing to the fact that changing snow depth affects the fraction of the land surface masked by snow and as a result, changes the visible reflectance of the land surface. The relationship between the snow depth and snow fraction is mostly due to low-level vegetation protruding through the snow pack. It is the strongest over plain non-forested areas and decreases in forests and areas with heterogeneous topography. The developed algorithm estimates snow depth using observations of the Imager instrument onboard GOES satellites. In order to derive the snow depth over forests, the tree cover fraction and the tree type (deciduous and/or coniferous) should be specified. Reliable snow depth retrievals are possible in most environments except densely forested areas with over 80% of deciduous tree cover or over 50% of coniferous tree cover. Snow depth estimates are generally limited to snowpacks below 30–50 cm. At these depths, snow masks most of the low-level vegetation and further snow accumulation brings only minor change to the snow fraction. Application of the developed technique over a large study area in North America has shown its effectiveness and a good potential for routine monitoring of snow depth. Derived distributions of snow depth agree well to in-situ data and to results of snow depth analysis of NOAA NOHRSC. The accuracy of snow depth estimates ranges from 5 to 10 cm (or about 30%) for snow packs below 30 cm and increases to about 50% at 50 cm snow depth. A technique similar to the one presented in this paper can be developed for polar-orbiting satellites. Because of the different viewing-illumination geometry observations the existing algorithm for geostationary satellites cannot be directly applied to polar satellite data. Retrieving snow fraction and snow depth from polar satellites requires establishing appropriate (and probably more advanced) bidirectional reflectance models for snow and snow-free land surface. The use of observations from polar satellites in the visible/infrared spectral band at high spatial resolution may be beneficial for snow depth monitoring in forested regions and will allow for extending snow depth retrievals to polar areas if sufficient daylight is available. References Allen, R. C., Durker, P. A., & Wash, C. H. (1990). Snow/cloud discrimination with multispectral satellite measurements. Journal of Applied Meteorology, 29, 994−1004.

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