Abstract

Operational hydrology and meteorology requires timely information about the distribution of snow cover for input into forecasting models. Optical (visible and near-infrared) remote sensing techniques have been used operationally for many years to provide snow cover information. However, at any given time, large portions of the mapping domain may be obscured by cloud cover. A method is required to infer the presence or absence of snow cover beneath obscuring clouds.

We have developed a new data assimilation strategy that uses a snow energy and mass balance model as a basis for inference of snow cover when it is obscured to remote sensing by cloud cover. The model accounts for snow surface and internal snow pack energy exchanges, and mass exchanges including snow accumulation, sublimation, rainfall, and melt water outflux. The snow energy and mass exchanges are modeled hourly on a 4 km grid. Inputs to the model include analysis products from the Eta model, satellite-derived insolation products from NESDIS, and all available ground observations of precipitation. The modeled snow water equivalence (SWE) is classified into a binary map of snow/no snow using maximum likelihood logistic estimation, where the modeled SWE is a continuous independent variable, and the binary dependent variable consists of all available ground and airborne observations of snow depth and water equivalence, and of samples of snow cover randomly selected from cloud-free areas of a satellite snow cover product.

1. snow cover directly observed by remote sensing,
2. snow cover inferred under cloud cover,
3. snow-free directly observed by remote sensing,
4. snow-free inferred under cloud cover, and
5. not mapped.

We demonstrate this approach for the northwest quadrant of the GCIP NC-LSA (504,000 km²) comprising most of Minnesota and the eastern Dakotas for a four week period during March and April, 1997. Using the same modeled SWE as an independent variable, tests of different data configurations in the logistic estimation yielded overall classification accuracies ranging from 67-96% when compared to ground snow observations and to remotely sensed snow cover. On average, accuracies were highest (86-96%) during the first nine days of the study period, prior to the passage of a major storm system that lasted several days and included significant rainfall and snow accumulation. The lowest accuracies (67-81%) were observed during the storm period.

1. Objective

Infer presence or absence of snow cover beneath obscuring clouds, using information operationally available in near-real time, to augment traditional remote sensing classification of snow cover.

2. Background: Traditional Method

Cloud cover contamination represents a significant constraint on traditional approaches of mapping the areal extent of snow cover using optical (visible/near-infrared) remote sensing data . In recent years there have been marked improvements in algorithms designed to differentiate clouds from snow; however, no operational method yet exists to reliably map snow cover beneath clouds at high spatial resolution under a wide variety of snow pack conditions. Hence, snow cover maps produced by traditional classification methods necessarily include a map category for clouds (Figure 1).

Figure 1. Flowchart illustrating traditional supervised classification of snow cover using remotely sensed data in the visible and near-infrared regions of the electromagnetic spectrum. Since clouds are opaque in these regions, the presence or absence of snow cover beneath clouds is unknown.

3. Overview of New Approach

We present an innovative new modeling approach to estimate the spatial distribution of the presence or absence of snow cover. This new approach can be used operationally to augment traditional snow cover mapping where clouds are present. This approach consists of two steps (Figure 2). First, a spatially distributed snow energy and mass balance model is driven by various hydrometeorological data to estimate  the snow water equivalence (SWE) at any given time. The model should be expected to provide an approximate representation of where there is and is not snow, but for various reasons it is unlikely that it is exactly correct. In particular, nonlinear processes involved in snow melt become much more significant as the snow pack becomes very shallow; errors in the model at this stage could substantially impact the modeled position of the snow line. This problem is addressed by relating the modeled SWE back to observed snow cover. The SWE estimated by the model  is used in conjunction with snow cover observations to estimate the probability of the presence of snow cover.

Figure 2. Flowchart illustrating the two major steps of the new modeling approach: 1)  snow energy and mass balance modeling to estimate the spatial distribution of SWE, and 2) maximum likelihood logistic estimation to relate modeled SWE and observed snow cover in order to estimate the probability of snow cover.

The snow model is a spatially distributed energy and mass balance model for a single-layer snow pack. It is based in large part on the Utah Energy Balance Snow Accumulation and Melt Model (UEB) (Tarboton and Luce, 1995), and on the snow energy and mass balance model SNTHERM.89 (Jordan, 1991). The distributed model developed for this approach accounts for mass exchanges of snow fall, rain fall, sublimation, and snow melt outflux. It accounts for radiative and turbulent energy exchanges, and includes parameterizations for forest cover effects (Figure 3). Model state variables include the water equivalence of the snow pack and the internal energy of the snow pack.

The estimation of the probability of snow cover involves relating the SWE state variable of the model at time t to available observations of the presence or absence of snow cover (Figure 4). Snow cover observations may include ground-based or airborne-based observations of SWE, ground-based observations of snow depth, and/or satellite observations of snow cover where clouds do not obscure the surface. In the case of satellite data, random samples of snow and no snow are drawn from the image-derived snow cover map.

Figure 4. Flowchart illustrating inference of the presence or absence of -snow cover based on probability of snow cover.

A set of snow cover observations and modeled SWE at corresponding locations are input into a maximum likelihood logistic estimation (logit) model. The logit model in turn estimates for each grid cell the probability (0-1)  that snow cover exists. The probability map is then classified into snow or no snow by identifying a probability threshold that minimizes the number of incorrectly classified observations and maximizes the number of correctly classified observations. The final "cloud-free" snow cover map consists of remotely sensed observations of snow cover where clouds are not present, and the modeled snow cover beneath clouds.

4. Demonstration of New Approach

4.1 Methods

This approach was tested in a 504,000 km² area of the northwest quadrant of the GCIP NC-LSA, which includes most of Minnesota and the eastern Dakotas. This region is characterized by relatively minor topography, with extensive forest cover throughout northern Minnesota.

The model was run for a four-week period from March 26, 1997 through April 22, 1997, which includes the major flooding on the Red River of the North in the central part of the study area. This time period includes three major snow pack/weather situations. The first eight days (3/23 - 4/3) represents a "pre-storm period", during which no significant precipitation occurred. During this first eight days, active snow ablation was observed in the southern margins of the snow pack, with the snow line receding northward.  The second "storm period" occurred during the next nine days from 4/4 through 4/12, during which time a series of storm systems passed through the region. Significant precipitation resulted from these systems, with the most notable event being a blizzard which occurred while residents of the Grand Forks area were filling sand bags in preparation for the 1997 Red River flood. The storm systems began as a warm event, with widespread rainfall, which eventually turned to snow in the northern part of the study area. Successive precipitation events occurred during this period, with both snow pack ablation and accumulation observed. The final "post-storm period" followed, from 4/13 through 4/22. During this period, only scattered minor precipitation events were observed. Ablation of the snow pack was widespread, with nearly complete ablation observed throughout the study area by April 22.

Data to drive the snow model came from three major sources: 1)  3-hourly analysis products from the NOAA Eta atmospheric model , 2) hourly insolation products derived from the NOAA GOES 8/9 satellites (Tarpley, 1997; Pinker, 1997), and 3) all available ground precipitation observations within the study area from WFOs and cooperative observers (Figure 5). The model was run at hourly temporal resolution and 4 km spatial resolution. Gridded input data were interpolated from relatively coarse source grids to the 4 km grid, treating the source grids as a lattice of points. Similarly, the ground observations of precipitation were simply interpolated to a grid. Gridded forest cover and type information was derived from AVHRR data (Zhu and Evans, 1994). Since for this demonstration it was necessary to "cold-start" the model on 3/26/97, initial SWE conditions were estimated using all available ground and airborne observations of SWE, and all available snow depth observations. Co-located or neighboring SWE and snow depth observations were used to estimate snow density in order to relate snow depth observations to SWE.

Two alternative snow cover data configurations were tested for the probability estimation component of this approach:

1. only ground-based observations of snow cover (e.g. WFO and cooperative observer observations of SWE or snow depth) were used in the maximum likelihood logistic estimation. This simulates a "worst case" scenario, where remotely sensed snow cover data are never available for an entire month (e.g. continuous overcast conditions).
   
2. randomly sampled remotely sensed snow cover observations are used when  they were available (i.e. not obscured by clouds). This simulates a more typical scenario, where a given location is temporarily obscured by periodic cloud cover. Remotely sensed snow cover observations were available for 17 of the 28 days of the study period form the National Operational Hydrologic Remote Sensing Center (NOHRSC).

4.2 Results

The model representation of SWE during the 28-day study period is shown in animation in Figure 6. In this figure, the hourly modeled data are sampled every six hours. The view here is from the southwest looking to the northeast.

Figure 6. Animation illustrating the modeled spatial distribution of SWE throughout the study period.

A particularly interesting two day period (April 4 and 5) is shown at full hourly resolution in Figure 7. This period marks the onset of the storm period. Relatively warm temperatures and widespread rainfall resulted in rapid snow melt; subsequently, temperatures cooled and the rain turned to snow, resulting in accumulation of the snow pack in some areas. The model representation of SWE during this complex situation is conceptually correct.

Figure 7. Hourly animation illustrating rapid snow melt resulting from warm air temperatures and rain-on-snow, followed by snow fall and accumulation of the snow pack.

The final "cloud-free" snow cover maps produced using this approach consist of remotely sensed snow cover observations where clouds are not present, and the modeled snow cover beneath clouds. The accuracy of the methods described here was evaluated using the raw modeled snow cover information optimally classified form the probability estimates, prior to combining the remotely sensed and modeled information into a single product.  Accuracy was evaluated in two ways: 1)  using information from the optimal classification of snow cover probability into presence or absence of snow cover (where the number of correctly and incorrectly classified sample observations are precisely known), and 2) by comparing remotely sensed snow cover to modeled snow cover, pixel-by-pixel, in cloud-free areas, using a standard KHAT statistic. The latter method does not indicate how well the model performs beneath cloud cover, but the large sample size in cloud-free areas allows inference of the overall accuracy of the model. The first method does include clouded as well as cloud-free areas, but involves a smaller sample size.

Overall, classification accuracies ranged from 67-96% agreement with observed snow cover, depending on the data configuration (worst-case or typical)  tested and the weather situations described previously (pre-storm, storm, and post-storm). The average accuracy of this approach for the worst case configuration (#1, 27 modeled products) was 76% agreement with observed snow cover. The average accuracy of the typical configuration (#2, 16  modeled products, corresponding to availability of remotely sensed snow cover) was 82% agreement with observed snow cover. The accuracy varied between the three snow pack/weather situations described above (pre-storm, storm, and post-storm) (Figure 8). In general, accuracies were highest during the pre-storm period, and lowest during the storm when only ground observations were used.

Figure 8. Mean accuracy of modeled snow cover for the three consecutive snow pack/weather situations observed during the study period. The "worst case" uses no remotely sensed data to develop the snow cover probability estimate, simulating continuous overcast conditions. The "typical case" uses a random sample of remotely sensed snow cover observations when they are available.

The new "cloud-free" assimilated (modeled under cloud, observed where cloud-free) snow cover map products generated for this demonstration are listed below in Table 1, together with the corresponding traditional NOHRSC snow cover products. These may be viewed and compared by selecting the appropriate date in the table. The percentage of the satellite image that was contaminated by cloud cover is shown in column two. The model accuracy for the typical case described above is shown in column three. This is the percentage of the snow cover observations, both ground-based and satellite based, that were correctly classified following the identification of the optimum probability threshold. The "Overall Agreement", "Commission Error", and "Omission Error" columns result from a pixel-to-pixel comparison of the model-estimated snow cover to satellite-observed snow cover wherever there are not clouds. The Overall Agreement in column four is the percentage of cloud-free pixels that were correctly classified by the model. The Commission Error is the percentage of pixels where no snow cover was observed by satellite but the model estimated to be snow-covered.  The Omission Error is the percentage of pixels where snow was observed by satellite but the model estimated to be snow-free. The assimilated products shown for each date only use modeled snow cover only under clouds, i.e. those areas which are not reflected in the overall agreement or the commission and omission errors. However, these values do provide some measure of how accurate the inferred snow cover under clouds may be.

Table 1. Traditional satellite-derived snow cover maps produced by the NOHRSC and the corresponding assimilated snow cover products.  All  products are for 1600 UTC of the date indicated.

For discussion purposes, we compare two particular series of traditional and assimilated snow cover products, with each series consisting of three consecutive days. The first series includes April 1, 2, and 3, during the pre-storm period (Figure 9). On April 1, 30% of the traditional  satellite-only snow cover map is contaminated by patchy cloud cover. Based on the optimal classification results,  the modeled 4/1 snow cover is 81% correct for the worst case and 92% correct for the typical case.  On April 2, 85% of the traditional satellite-only snow cover map is contaminated by cloud cover. The 4/2 assimilated product is therefore almost entirely dependent on the modeled snow cover. The areal extent of snow cover portrayed by the assimilated product is approximately consistent with the previous and following days. The worst-case accuracy for the assimilated 4/2 product is 87% when compared to ground observations.

The second series includes April 14, 15, and 16, just after the storm period has passed (Figure 10). Once again, almost complete (86%) overcast conditions were observed in the traditional satellite-only snow cover map for April 15. On April 14, snow cover was observed by satellite throughout central and southern South Dakota and northern Nebraska, with fairly extensive cloud cover throughout most of North Dakota.  The worst-case accuracy for 4/14 is 70%, and the typical-case accuracy is 77%. The assimilated product for 4/15 is again dependent almost entirely on modeled snow cover due to the extensive overcast conditions. The model indicates that the snow cover in central South Dakota and northern Nebraska present the previous day has ablated. The worst-case accuracy of the 4/15 assimilated product is 77%, and typical case accuracy is lower at 69%. However, the satellite-observed snow cover on the following day does reveal that the snow cover throughout most of central South Dakota and northern Nebraska has indeed ablated.  Although the exact timing of this widespread ablation cannot be determined from available observations, these results do suggest that the modeled snow cover is reasonable.

5. Conclusions

This approach to inferring the presence or absence of snow cover beneath clouds is promising. All data used to drive the snow model are available operationally in near-real time. The snow model includes the major physical processes involved in snow accumulation and melt, but remains a relatively simple, parsimonious model for snow energy and mass exchanges. Consequently, the model is computationally tractable at relatively high spatial resolutions over large areas.

The overall accuracies of the modeled snow cover information are comparable to accuracies typically attainable by traditional remote sensing classification of snow cover.  The assimilated snow cover products demonstrated here use remotely sensed snow cover where clouds are not present, and only employ the modeled snow cover beneath clouds.  The comparable accuracies of the two methods suggests that augmentation of operational satellite remote sensing of snow cover with this new approach in an automated framework would not result in a significant loss of accuracy. Moreover, this approach potentially permits more frequent (e.g. daily) production of snow cover maps that reaonably infer snow cover beneath clouds.

6. References

Jordan, R., 1991. A one-dimensional temperature model for a snow cover, Spec. Rep. 91-6, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, NH.

Pinker, R.T., and I. Laszlo, 1992. Modeling surface solar irradiance for satellite applications on a global scale, Journal of Applied Meteorology, 31, 194.

Tarboton, D., and C. Luce, 1996. "Utah Energy Balance Snow Accumulation and Melt Model (UEB)," Computer model technical description and users guide, Utah Water Research Laboratory and USDA Forest Service Intermountain Research Station.

Tarpley, D., 1998. Personal communication.

Zhu, Z., and D.L. Evans, 1994. U.S. forest types and predicted percent forest cover from AVHRR data, Photogrammetric Engineering and Remote Sensing, 60(5), 525-531.

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