Climatology of snow cover and snow water equivalent based on satellite data

General remarks

Meteorological observations from space started more than 50 years ago with the launch of Tiros I in 1960. Satellite instruments and observation techniques have changed dramatically since then, making time series of satellite data very inhomogeneous and causing their availability to vary across different regions. Using various assimilation techniques, it is possible to compile regional and global climate datasets based on satellite data. However, before applying satellite data for climatological assessments it is important to reduce the number of gaps in the data and validate satellite data with ground measurements.

Cloud gap filling

One of the main shortcomings of satellite observations is that the Earth's surface is often obscured by clouds, and it interrupts the temporal continuity of surface observations. There are several different gap filling techniques to reduce the number of cloud-covered pixels, which can also be used for other data gaps. The most common techniques are: 1) combining observations from different satellites (Wang et al., 2009; Gafurov, Bárdossy, 2009); 2) spatial filtering (Parajka, Blöschl, 2008); and 3) temporal filtering (Hall et al. 2010; Foppa, Seiz, 2012). One simple temporal filtering technique is explained here.

The temporal gap filling approach is based on assigning a cloud-covered pixel its latest cloud-free value. There are two ways to assign values to cloudy pixels: forward and backward filling. In forward gap filling the pixel is assigned its value prior to the cloudy days, while in backward gap filling the pixel is assigned the value of the first cloud-free observation following a cloudy period (Fig 1). Even though the number of consecutive days with cloud cover could accumulate over time, the gaps are filled with the same value provided from the latest cloud-free pixel.

Figure 1: Temporal data gap filling of cloud-covered pixels.

Daily "cloud-free" composites are generated using forward and backward gap-filling. This allows calculating monthly and annual numbers of snow cover days (SCD). It is assumed that exactly opposite gap-filling techniques minimizes over- and underestimations (Foppa, Seiz, 2012). The total annual number of snow days is derived by calculating the average of backward and forward composites. It should be noted, however, that this temporal gap-filling procedure is usable for data re-processing only. It is performed with the intention of deriving the total number of snow days on a yearly time resolution.

Extracting data for a particular location

Once the gap filling is done, daily "cloud-free" satellite data composites can be used to extract time series of snow cover days. Finding the pixel whose center coordinates are closest to the geographical coordinates of a particular point on the Earth is required for extracting snow cover data for the point in question. Most commonly it is done by using nearest neighbor sampling (Fig. 2).

Figure 2: The easiest way to extract values for a particular location is to determine the value of the nearest pixel center.

Validation techniques

The accuracy of satellite-based snow cover data can be determined using in-situ data or high resolution satellite imagery as a reference. Statistical scores for data validation can be calculated using contingency table statistics. The contingency table shows the frequency of "yes" and "no" events (snow presence in satellite data) compared with in-situ data. The categories of the contingency table are:

• HIT — the snow was identified by satellite data and was observed in-situ;
• MISS — the snow was not identified in satellite data but was observed in-situ;
• FALSE_P — the snow was identified in satellite data but was not observed in-situ (false alarms);
• TRUE_N — the snow was not verified in satellite data and was not observed in-situ (correct negatives).

The contingency table is a useful way to show what type of errors occur when deriving snow cover days (SCD) from satellite measurements. A perfect snow product from a remote sensing system would produce only hits (HIT) and correct negatives (TRUE_N), and no misses (MISS) or false alarms (FALSE_P). The statistical scores for satellite products can be computed from contingency table values to describe the products' performance. A summary of different statistical scores is presented in Table 1.

Table 1: Statistical scores used for satellite data validation with in-situ measurements.

Statistical Score	Formula	Description
Accuracy		What fraction of satellite derived snow cover was correct? Range: 0 to 1. Perfect score: 1.
Bias		How satellite derived snow cover frequency compare with snow observed in-situ? Range: 0 to ∞. Perfect score: 1.
Probability of detection (POD)		What fraction of the in-situ snow events were determined by satellite data? Range: 0 to 1. Perfect score: 1.
False alarm ratio (FAR)		What fraction of the satellite derived snow cover was false (no snow was observed in-situ)? Range: 0 to 1. Perfect score: 0.
Probability of false detection (POFD)		What fraction of the observed "no snow" events were determined as snow in satellite data? Range: 0 to 1. Perfect score: 0.
6. Threat score (TS)(Critical success index)		How well did the satellite derived snow cover correspond to the observed snow cover in-situ. Range: 0 to 1. Perfect score: 1.

Additional statistical parameters can be calculated to show the different aspects of satellite data accuracy and performance:

1. the mean absolute difference (d)
2. standard deviation (SD)
3. correlation coefficient (c)
4. relative difference (d, %)
5. Climatological Skill Score (SSclim), which indicates whether satellite-based data was better than the in-situ station climatology:

	[1]
	[2]
	[3]

MSE - mean square error (satellite observations versus in-situ);
MSEclim - mean square error (climatological value versus satellite observations).

Contingency table statistics can be applied to evaluate snow cover presence, but it is not applicable for quantitative snow characteristics such as snow depth or SWE. Satellite-based SWE products can be evaluated using correlation coefficients, bias, and RMSE (Root-Mean-Square-Error).