1. Evaluation of Fractional Snow Cover Algorithms for an Enterprise Algorithm

2. Outline Algorithms background
GOESRACAG (GOES-R snow cover and grain size) Algorithm
Algorithm Heritage
Retrieval Strategy, Flow chart, and Retrieval Steps
Past, Ongoing and Proposed Testing/Validations
Single-Channel Reflectance-Based Algorithm
Mathematical Description and Retrieval Strategy
Verification and Accuracy
Practical Consideration
Approach to evaluate/validate these two algorithms

3. GOES-R snow cover and grain size (GOESRSCAG) Algorithm
Yinghui Liu and Jeff Key

4. Motivation 2 km snow veg 2 km rock AVIRIS
The pixel radiance from the surface that reaches the sensor is a mixture of contributions of radiances from snow, vegetation, soils, lake ice, etc.
snow
rock
veg
2 km
This scene is from the Sierra Nevada with 17 m imaging spectrometer data with the vast majority of radiances within a single pixel coming from a single surface.
AVIRIS

5. Motivation 2 km Single pixel snow veg 2 km rock GOES-R
In this case, a single GOES-R ABI pixel is presented showing the underlying mixture of radiances from snow, vegetation, and exposed rock
snow
rock
veg
Single pixel
2 km
With GOES-R ABI rich spectral information in the visible and near-visible portion of the energy spectrum, this algorithm is to retrieve sub-pixel fractional snow cover and grain size estimates via computationally efficient spectral mixture modeling.
GOES-R

6. Fractional Snow Cover Definition
Fractional Snow Cover Product
Fractional Snow Cover (FSC) reports the fractional area covered by snow in each reported product pixel. This is the viewable snow fraction.*
CONUS, Hemispheric, Mesoscale for Geostationary Satellites
Global for Polar-Orbiting Satellites
Measurement range
*To convert the viewable snow fraction into the true snow fraction on the ground you need to know the properties of the forest cover within a pixel (at least its extent and masking efficiency) and assume that in the forest the snow fraction is the same as in the open portion of the pixel. A more comprehensive approach to converting the viewable snow fraction into the snow fraction on the ground should requires the satellite zenith angle and information on the 3-d structure of the forest canopy. This is not done in the GOESRSCAG algorithm.

7. Algorithm Heritage
GOESRSCAG (GOES-R snow cover and grain size) Algorithm
Description: Retrieves sub-pixel fractional snow cover and grain size estimates via spectral mixture modeling
Heritage:
MEMSCAG (Multiple Endmember Snow Covered Area and Grain size) was original model - benchmark algorithm for imaging spectrometers (AVIRIS, Hyperion, HYDICE, ARTEMIS) - Painter et al., 2003, RSE
MODSCAG (MODIS-based fractional snow cover and grain size) algorithm. Painter et al, 2009, RSE.
TMSCAG model for Landsat Thematic Mapper (accounts for frequent saturation over snow in visible bands).
GOESRSCAG derives from MODSCAG accounting for differences between the MODIS and GOES-R ABI band passes, geometry, etc.

8. Retrieval Strategy
The GOES-R ABI Snow Cover algorithm consists of the following general steps:
Determine pixel non-snow endmember (based on preprocessing of ABI data)
From solar and view geometry, select spectral library per pixel
Given pixel non-snow endmember, unmix pixel spectral reflectance into snow fraction and non-snow fraction
In unmix step, determine grain size of snow fraction
Use ABI cloud map and Snow Cover grain size to determine pixel cloud cover
Shade-normalize snow fraction to pixel fractional snow covered area

9. Basic Flowchart for Fractional Snow Cover
Start Procedures
Initialize Variables
Manage Segments
Manage Memory
Loop Through Pixels
If cloud based on mask
If water based on reflectance
Read Input Data
Calculate solar angles
Select endmember spectral library
based on solar angle
Input Data
Surface Reflectance
Cloud Mask
View Angles
Endmember Libraries
Output Data
Snow Fraction
Snow Grain Size
Snow Albedo
RMS Error
Shade Fraction
Non-Snow Endmember
Loop Through Spectral
Endmember Models
Spectral Unmixing
Calculate snow, non-snow,
and shade fractions.
Grain size and RMS error
Current model not better fit
Save best model fit
End Loop Through Models
End Loop Through Pixels

10. Algorithm Inputs Start Procedures Loop Through Pixels
Initialize Variables
Manage Segments
Manage Memory
Loop Through Pixels
If cloud based on mask
If water based on reflectance
Read Input Data
Calculate solar angles
Select endmember spectral library
based on solar angle
Input Data
Surface Reflectance
Cloud Mask
View Angles
Endmember Libraries
Output Data
Snow Fraction
Snow Grain Size
Snow Albedo
RMS Error
Shade Fraction
Non-Snow Endmember
Loop Through Spectral
Endmember Models
Spectral Unmixing
Calculate snow, non-snow,
and shade fractions.
Grain size and RMS error
Current model not better fit
Save best model fit
End Loop Through Models
End Loop Through Pixels

11. Playa/Snow Discrimination
Algorithm Inputs
Future
GOES
Imager
(ABI)
Band
Nominal
Wavelength
Range
(μm)
Nominal Central
Wavenumber
(cm-1)
sub-satellite
IGFOV
(km)
Purpose 1
0.47
21277
Snow Cover 2
0.64
15625
0.5 3
0.865
11561 4
1.378
7257 5
1.61
6211 6
2.25
4444 7
3.90
2564
Playa/Snow Discrimination 8
6.19
1616 9
6.95
1439 10
7.34
1362 11
8.5
1176 12
9.61
1041 13
10.35
966 14
11.2
893 15
12.3
813 16
13.3
752
Current Input
Expected Added Input

12. Algorithm Inputs Visible/Near-Infrared/SWIR
Bands 1, 2, 3, 5, 6
Makes use of the dramatic improvement in spectral sampling in the solar spectrum by the ABI
Spectral mixture analysis relies on relative orthogonality of surface reflectances (endmembers)
These bands cover the high reflectance of snow in the visible and the low reflectance of snow in the SWIR; likewise, they cover the low reflectance of vegetation in the visible and moderately high reflectance of vegetation in the SWIR
Spectral reflectance of snow (blue) and vegetation (red)
Short-wave IR (3.9um and um)
Facilitates discrimination of erroneous snow cover mapping in areas of playa and shallow water
Playa and shallow water have spectral reflectances similar to snow under relatively poor illumination
However, they have higher temperatures than snow covered areas
(Note: this is an expected band inclusion)

13. Algorithm Inputs Three types of ancillary data needed: ABI Data:
Clear sky (cloud) mask
Surface reflectance (Not at the TOA)
Non-ABI Dynamic Data: N/A
Non-ABI Static Data:
Spectral libraries
Snow grain size lookup table
Previous FSC
Previous snow grain size

14. Algorithm Inputs Start Procedures Loop Through Pixels
Initialize Variables
Manage Segments
Manage Memory
Loop Through Pixels
If cloud based on mask
If water based on reflectance
Read Input Data
Calculate solar angles
Select endmember spectral library
based on solar angle
Input Data
Surface Reflectance
Cloud Mask
View Angles
Endmember Libraries
Output Data
Snow Fraction
Snow Grain Size
Snow Albedo
RMS Error
Shade Fraction
Non-Snow Endmember
Loop Through Spectral
Endmember Models
Spectral Unmixing
Calculate snow, non-snow,
and shade fractions.
Grain size and RMS error
Current model not better fit
Save best model fit
End Loop Through Models
End Loop Through Pixels

15. Endmember Spectral Library
Collection of endmembers that spans snow grain size, solar zenith angle, view azimuth angle, vegetation type, soil type
Snow endmembers vary by solar zenith and view zenith and azimuth angles

16. Endmember Spectral Library: Non-Snow Spectral Libraries
Soil and vegetation directional reflectance spectra have been measured with spectrometer in the laboratory and field.
They span the ranges of vegetation directional reflectances and soil/rock directional reflectances. 16

17. Endmember Spectral Library: Snow Spectral Library
Spectral reflectance for different angles
View azimuth
0 = 30
Forward Side Backward
Solar zenith
0 = 60
Forward Side Backward

18. Basic Flowchart for Fractional Snow Cover
Start Procedures
Initialize Variables
Manage Segments
Manage Memory
Loop Through Pixels
If cloud based on mask
If water based on reflectance
Read Input Data
Calculate solar angles
Select endmember spectral library
based on solar angle
Input Data
Surface Reflectance
Cloud Mask
View Angles
Endmember Libraries
Output Data
Snow Fraction
Snow Grain Size
Snow Albedo
RMS Error
Shade Fraction
Non-Snow Endmember
Loop Through Spectral
Endmember Models
Spectral Unmixing
Calculate snow, non-snow,
and shade fractions.
Grain size and RMS error
Current model not better fit
Save best model fit
End Loop Through Models
End Loop Through Pixels 18

19. This step includes looking up the pixel’s non-snow endmember (the vegetation or soil that is always there) and 11 snow endmembers of varying grain size specific to the given solar geometry and view geometry }
Snow endmembers specific to solar and view geometry; vary by grain size
Vegetation endmember specific to pixel

20. Basic Flowchart for Fractional Snow Cover
Start Procedures
Initialize Variables
Manage Segments
Manage Memory
Loop Through Pixels
If cloud based on mask
If water based on reflectance
Read Input Data
Calculate solar angles
Select endmember spectral library
based on solar angle
Input Data
Surface Reflectance
Cloud Mask
View Angles
Endmember Libraries
Output Data
Snow Fraction
Snow Grain Size
Snow Albedo
RMS Error
Shade Fraction
Non-Snow Endmember
Loop Through Spectral
Endmember Models
Spectral Unmixing
Calculate snow, non-snow,
and shade fractions.
Grain size and RMS error
Current model not better fit
Save best model fit
End Loop Through Models
End Loop Through Pixels 20

21. Spectral Mixture Step ABI Band MODIS Proxy
Spectral reflectance of snow (blue) and vegetation (red)
ABI Band
MODIS Proxy 1 2 3 4 5 6 7
GOESRSCAG spectrally unmixes allowing the endmembers themselves to vary on a pixel by pixel basis.
R is surface reflectance, R is the ABI spectral reflectance
N is the number of endmembers, M is the number of spectral bands,
 is the residual for the fit of N endmembers
Fi is the coefficient (fraction) determined from the Modified Gram-Schmidt Orthogonalization.

22. Algorithm Flow Output Data
Snow cover fraction
Non-snow fraction
Snow grain size
Snow albedo
Quality flags
RMSE 22

23. Testing and Validation
Practical Considerations:
There are no in situ measurements of fractional snow cover available for algorithm validation
Can validate against very high resolution binary snow cover retrievals convolved into GOES-R scale fractional snow cover estimates
Can validate the GOES-R FSC algorithm against another version of the algorithm that has already been vigorously validated
Current inputs to the GOESRSCAG is reflectance at TOA, not the surface reflectane 23

24. Past Testing and Validation
Can validate against very high resolution binary snow cover retrievals
convolved into GOES-R scale fractional snow cover estimates
snow
rock
veg
Single GOES-R Pixel
Binary
Classifier
AVIRIS for GOES-R IFOV
~65% Binary Snow Cover
(Target GOES-R FCS value for this pixel)

25. Past Testing and Validation
Use the results from a vigorously validated 7-band MODIS version of the FSC algorithm as validation for the 5-band GOES-R version
A heritage version of the FSC algorithm using 7 bands of MODIS data was validated against LANDSAT TM data for a broad range of snow regimes
Use the results of this version to test and validate the GOES-R version of the FSC algorithm
RMSE =7.8%,
31 TM scenes (Himal, Sierra, CLPX, Rio Grande) 25

26. Past Testing and Validation
Study Site
Number of MODIS Snow
Pixels
Mean FSC Difference Simulated ABI versus MODIS
RMSE
Simulated ABI
Omission Error
Simulated ABI Commission Error
Dukes
66774
-0.069
0.146
3.58%
2.43%
Hubbard Brooks
44418
-0.036
0.144
6.35%
8.80%
Fraser
228686
0.018
0.106
1.69%
1.96%
Weighted Mean
339878
0.006
0.119
2.67%
2.97%
Essentially no bias in FSC
Dukes
Hubbard
Brooks
Fraser 26

27. Ongoing Testing and Validation
We have developed an automated validation system for GOES-16 FSC.
Routinely acquires snow cover products from different sources:
National Ice Center’s Interactive Multisensor Snow and Ice Mapping System (IMS) Northern Hemisphere snow cover at 1 km
Snow cover derived from the NOAA National Weather Service's National Operational Hydrologic Remote Sensing Center (NOHRSC) SNOw Data Assimilation System (SNODAS) at 1 km over the Contiguous United States (CONUS) and southern Canada
Remap these snow cover data to the GOES-16 footprint, where IMS and SNODAS FSC calculated as the ratio of snow covered pixels to all pixels at each GOES-16 foot print.
Plots all FSC products that were acquired and performs some simple statistical comparisons with GOES-16 FSC.

28. Ongoing Testing and Validation
GOES-16 Fractional Snow Cover daily composite on February 6, 2017 with quality control (left), from IMS (middle), and MODIS false color image (right).

29. Ongoing Testing and Validation
GOES-16 Fractional Snow Cover daily composite on from February 7, 2018 to February 12, 2018 with quality control (left from top to bottom, then right from top to bottom)

30. Proposed Testing and Validation
We propose to add more validation data sets to the automated validation system, and expand the validation effort.
Expand the validation data sets to include very high resolution binary snow cover retrievals from Landsat-8 and other sensors convolved into GOES-R scale fractional snow cover estimates
Perform the validations of FSC products on different surface types and in different months
Implement more robust statistical tools for evaluation
Most importantly, we will work with Dr. Romanov to incorporate his VIIRS snow fraction algorithm into our validation system we can do a robust inter-comparison of the two algorithms.

31. Single-band Reflectance-based Fractional Snow Cover Algorithm
Peter Romanov

32. Reflectance-Based FSC: Basics
Algorithm uses satellite observations in one, visible spectral band and applies a linear unmixing technique to estimate the snow fraction within an image pixel.
The technique incorporates two end-members representing the reflectance of the snow-covered and of the snow-free land surface.
To perform retrievals the end-member reflectance and associated reflectance anisotropy has to be established.
Algorithm is applied to clear sky scenes where any amount of snow rhas been identified by the snow detection algorithm.
Heritage: Algorithm was used with GOES Imager data (Romanov & Tarpley, 2003) . It is currently used with AVHRR data as part of GMASI system and has been implemented with VIIRS data within NDE.

33. Mathematical Description
R = Rland (1-SCF) + R snow SCF
where R is TOA reflectance in the visible spectral band,
Rland is reflectance of snow-free land
Rsnow is reflectance of snow in VIIRS band 1
SCF is the snow cover fraction
Both end-memebrs Rland and Rsnow vary with the observation geometry.
In the VIIRS algorithm end-members are assumed independent of location and time of the year.
In the GOES Imager algorithm end-members are location-specific

34. SCF = (R -Rland)/(R snow- Rland)
Retrieval Strategy
Offline Preprocessing
Determine TOA reflectance snow-free land surface and completely snow-covered surface and associated reflectance anisotropy.
Retrieval
(1) Given solar and view geometry parameters predict endmember values
(2) Unmix the observed visible reflectance into the snow cover fraction and snow-free land fraction.
SCF = (R -Rland)/(R snow- Rland)

35. Algorithm Inputs Dynamic inputs
- Observed TOA reflectance in the visible spectral band (VIIRS band I1)
- Observation geometry angles
- Binary snow map with cloud mask
Static inputs
- Endmember BRDF model parameters
- Additional: Normalized snow-free land surface reflectance

36. BRDF Model Development for VIIRS
Used to determine snow BRDF
End-member values and angular anisotropy are established empirically from VIIRS observations over two regions
Used to determine snow-free land BRDF
BRDF model:
Rsnow, land = C0 + Σ i=1,7 Ci Fi,
Kernel functions (Fi) and kernel loads (Ci)
Kernel Functions
Kernel Loads
Kernel Load Values
Snow-free land
Snow 1. C0
19.02
63.45
Cos (θsol) C1
9.699
89.90
Cos (θsat) C2
-9.944
-16.33
Cos (θsol) Cos (θsat) C3
13.16
61.81
Cos2 (θsol) C4
-36.30
-140.9
Cos2 (θsat) C5
-6.289
-5.114
Cos4 (θsol) C6
20.18
51.62
Cos4 (θsat) C7
5.419
-2.623

37. BRDF Model for VIIRS Mean Land and Snow Reflectance
Model-simulated Land and Snow Reflectance

38. VIIRS SCF Product

39. VIIRS SCF Product, Cont’d

40. Theoretical Accuracy Estimate
SCF = (R –Rland)/(R snow- Rland)
Estimated accuracy of FSC is within
Calculated using error propagation formula
Assuming:
0.15 snow reflectance uncertainty due to snow properties change
0.15 snow reflectance uncertainty due to BRDF uncertainty
0.10 land reflectance uncertainty due to different land surface cover types
0.05 land reflectance uncertainty due to BRDF uncertainty
0.05 uncertainty due to aerosol effects on the observed reflectance
No error covariance

41. Algorithm and Product Verification
Independent quantitative assessment of the accuracy is impossible since snow fraction is not observed in situ
Therefore the general approach to verification includes
Consistency testing
Self-consistency:
Lack of abnormal spatial patterns
Day-to-day repeatability of spatial patterns
Consistency with the forest cover distribution
Consistency with in situ snow depth data over open flat areas.
Comparison with higher spatial resolution data (i.e. with “surrogate truth data”)

42. Repeatability of Spatial Pattern
VIIRS-derived snow fraction is compared on two consecutive days
No snow fall and no snow melt: the derived snow fraction should not change much
Mean: 36.8
Mean: 34.7
Reflectance-based
Reflectance -based
Map Type
Feb 14 to Feb 15, 2014
Mean Diff.
Correlation
Refl.-based
1.9%
0.80
Feb 14, 2014
Feb 15, 2014
Reflectance-based snow fraction retrievals demonstrate robust performance over space and time
2% day-to day variations
0.80 spatial correlation between FSC on consecutive days

43. Snow Fraction vs Tree Cover
Snow fraction vs forest fraction scatter plot
Forest cover fraction, Univ of MD
Snow cover fraction
Forest Cover vs Snow Fraction daily map correlation: : -0.8
Strong correlation indicates consistency of snow fraction retrievals

44. Snow Fraction vs In Situ Snow Depth
Over non-forested areas the snow cover fraction is determined primarily by the depth of the snow pack
VIIRS-derived snow fraction is consistent with the observed snow depth (positive daily correlation within )
Correlation between VIIRS snow fraction and in situ snow depth
Statistics collected over Great Plains
Jan-Feb 2014
Pixel-to-point match-ups
20 to 200 match-ups per day
Number of collocated observations per day used to calculate correlation

45. Verification with Landsat Data
Approach
(1) Generate binary snow mask for a Landsat scene at 30 m resolution
(2) Use Landsat binary snow to derive snow fraction within VIIRS pixels
(3) Compare with VIIRS snow fraction estimate
Landsat
VIIRS
Compare

46. Verification Statistics with Landsat
Comparison Statistics of VIIRS and Landsat snow fraction
Statistics is provided for observations aggregated within 1 km and 5 km grid boxes.
Non-forested scenes are only used
The overall agreement of VIIRS and Landsat snow fraction is 12.1% for 1 km grid cells and about 8% for 5 km aggregation

47. Concluding Practical Considerations
The current VIIRS single-channel reflectance-based algorithm demonstrates robust performance, the estimated FSC retrieval accuracy is generally within 0.25.
The VIIRS algorithm is tuned for a particular sensor (VIIRS) and platform (polar).
Application of the algorithm to other sensors, e.g. ABI, will require a new BRDF model specific to sensor spectral characteristics and prevailing observation geometry
Introducing location-dependent end-members will improve the accuracy
Product performance is critically dependent on the accuracy of
- Snow identification
- Cloud identification
- Cloud and terrain shadow mapping
Other factors may adversely affect the accuracy (sub-resolution unfrozen water bodies, urban areas, heavily polluted snow, smoke, etc.)

48. Evaluating the Two Algorithms (1/3)
The proposed approach to evaluating the two algorithms is to use GOES-R ABI as the test bed because:
GOESRSCAG is difficult to adjust to VIIRS, because a new spectral model library is needed.
The single-band algorithm is easier to adjust to ABI. However, new BRDF models for ABI need to be developed.
The two algorithms will be compared using a variety of tests (next slide).

49. Evaluating the Two Algorithms (2/3)
Independent quantitative assessment of the accuracy is impossible since snow fraction is not observed in situ. We will perform evaluation of these two algorithms mainly through consistency tests.
Self-consistency test: Evaluates and compares short-term (intraday) variations in FSC. Variations should be minimal. Test indicates how well viewing-illumination geometry effects are taken care of in the FSC estimate. Test requires clear sky for most of the day, no snowfall and snowmelt. Test will be conducted both over open and forested areas.
Forest cover consistency test: Evaluates FSC correlation with the forest fraction. Correlation should be strongly negative. Ground surface should be fully snow-covered (midwinter conditions). Test will be conducted preferably over evergreen needle-leaf forest.
Snow depth consistency test: Evaluates FSC correlation with the in situ snow depth. Correlation should be positive. Test will be conducted over flat non-forested areas, not including urban areas and unfrozen lakes/rivers.
LST consistency test: Identifies cases when LST of over 273K corresponds to estimated FSC of 1.0 (full snow cover). Fraction of these cases should be very small. Test will be conducted both over all surface cover types and terrains. Observed IR brightness temperature may be used instead of the LST estimated.
Consistency with FSC from finer resolution satellite data (“surrogate truth”): Need to avoid fractional snow cover at the finer resolution as much as possible. Mountain areas/isolated glaciers will be used in the test. Finer resolution imagery: Landsat, Sentinel 2.

50. Evaluating the Two Algorithms (3/3)
Other factors to be considered
Clouds should be completely filtered out. Quality of the GOESR ABI cloud mask should be considered.
GOESRSCAG requires normalized atmospherically-corrected land surface reflectances. This product is not currently implemented but is expected soon. GOESRSCAG retrievals are performed with solar/satellite zenith angle cutoffs, thus may have smaller area coverage than the products from the single band algorithm.
GOESRSCAG identifies snow and determines snow fraction in one step. Single- band algorithm assumes that binary snow/no snow mask is already available. Ideally a binary snow identification routine in the ABI processing system is optimal. This way both FSC algorithms can be applied to snow covered pixels.
GOESRSCAG snow fractions may be larger than FSC derived with single-band algorithm since GOESRSCAG (apparently) tries to determine the shade fraction within a pixel and then subtracts it from the snow cover fraction. The single band algorithm does not consider shade as a separate category, therefore shaded fractions are likely to be incorporated as part of non-snow covered portion of the scene.