What's albedo and why should you care?

1. Snow: What’s albedo and why
should you care?
Jeff Dozier, UCSB
@ UCLA, 2017-04-10
(photo Tom Painter)

2. Albedo: the definition
• Nuances
• Incoming solar radiation can be direct and diffuse
• Albedo generally increases when the sun is closer to the
horizon (when the solar zenith angle is greater)
• “reflected” means reflected at all angles
2

3. (photo Ned Bair)
(photo Timbo Stillinger)

4. Effect of sun angle
4
𝑆0 × cos 𝑍0

5. Why should you care?
• Earth’s climate, the seasons, and snowmelt are driven by
absorbed solar radiation
5

6. You care because a small change in albedo causes a bigger
relative change in (1–albedo)
6
albedo
Fraction absorbed
(1–albedo)
Start with
0.8 0.2
Lower it by 20%,
you get 0.64 0.36
An increase of
80%

7. 7
Measurement of snowpack net solar radiation at Mammoth Mountain

8. 8

9. 9

10. 10

11. 11

12. Side note: this year
snow in the Sierra
Nevada on pace
with WY 1983 until
March
http://cdec.water.ca.gov/cgi-progs/products/PLOT_SWC.pdf

13. People who live in
the mountains think
how great it would
be to have a big
winter . . . until they
get one
13

14. Imagery courtesy GlacierWorks
Cho Oyu
East Rongbuk
1921 2009
1921
2011

15. What causes snow albedo to change?
• To answer this, we first need to define spectral
albedo
15
• because snow is made of ice crystals, and ice has different properties
at different wavelengths
• and impurities like dust or soot also affect albedo differently at
different wavelengths

16. Incoming solar radiation (“irradiance”) varies with wavelength
16

17. The point?
• The spectral albedo 𝑅 𝜆 is a fundamental property of the material
• Varies with wavelength
• Varies with illumination angle, and physical properties
• The broadband albedo 𝛼 is the convolution of the spectral albedo
and the spectral distribution of the incoming radiation 𝑆 𝜆
(irradiance)
𝛼 = 0
∞
𝑅 𝜆 𝑆 𝜆 𝑑𝜆
0
∞
𝑆 𝜆 𝑑𝜆
17

18. Albedo of clean snow varies with the grain size
18

19. Why? Answer lies in optical properties of ice
0 sin
sin


  i
r
c
n
c
i
r
I0 I
dx
4
0
4





 

kx
dI k
I
dx
I
e
I
19index of refraction
absorption coefficient, k

20. 20
𝑒
−
4𝜋𝑘𝑥
𝜆 = 1
2
𝑥 =
ln 2
4𝜋
𝜆
𝑘

21. Snow spectral albedo and absorption coefficient of ice
21

22. [Erbe et al., 2003] [Rosenthal et al., 2007]

23. Dust
(McKenzie Skiles)
algae

24. Spectral reflectance of dirty snow and snow with red algae
(Chlamydomonas nivalis)

25. 25

26. Snow is one of nature’s most colorful materials
(e.g., Landsat snow & cloud)
Bands 3 2 1 (red, green, blue) Bands 5 4 2 (swir, nir, green)

27. Planck equation for Sun and Earth
27
visible
near-infrared
shortwave-
infrared
mid-infrared
thermal
infrared
ultraviolet

28. What forces glacier melt?
[Kaspari et al, 2014]

29. Problem & heritage: Measure the snow-covered fraction of a pixel,
and the albedo of that snow
• Multiple endmember spectral mixture analysis (MESMA)
• Mapping chaparral vegetation in the Santa Monica Mountains [Roberts et al.,
Remote Sens Environ 1998]
• Snow grain size of 100% snow-covered pixels from spectrum around ice
absorption feature at 1030 nm
• Model albedo of clean snow over whole spectrum once grain size is known [Nolin
& Dozier, Remote Sens Environ 2000]
• Multiple endmember snow-covered area and grain size (MEMSCAG)
• Consider snow endmembers of different grain size, combine with multiple
vegetation and soil endmembers [Painter et al., Remote Sens Environ 2003]
• Adapted to 7 spectral bands of MODIS (MODSCAG)
• [Painter et al., Remote Sens Environ 2009; Sirguey et al. Remote Sens Environ 2009]
• Quantifying effect of light-absorbing impurities from spectroscopy and
multispectral remote sensing (MODDRFS)
• [Painter et al., Geophys Res Lett 2012, J Geophys Res 2013] 30

30. Comparison of MODIS (500m) and Landsat (30m) snow fraction, in the Sierra Nevada
200 scenes with
coincident MODIS and
Landsat images
Average RMSE = 7.8%
Range from 2% to 12%

31. Remotely sensed albedo of fractional snow (too high along the boundary)

32. Dirty snow albedo has a similar spectral shape to fine-grain clean snow

33. Results, with no noise or bias in the signal
34

34. Results, with noise and bias in the signal
35

35. fSCA and albedo, pale brown silty + grass
37

36. 38
Restrict albedo calculation to pixels with fSCA>0.3, grass+pale brown silty

37. 39
Restrict albedo calculation to MODIS pixels with fSCA>0.3, grass+pale brown silty

38. Directions
• Test with airborne spectrometer data
• Especially where coincident independent comparison data are available
• Especially in the mountains, where the snow matters
• Identify two vegetation/soil endmembers for each pixel
1. Covered by snow
2. Sticking up above the snow
• Extend to multispectral sensors, and compare with spectrometer
data and also fine-resolution imagery
• Explore the consequences of uncertainty in the illumination angle
40

39. Radiative forcing with a
spectrometer
41

40. Surface wetness from an imaging spectrometer, Mt Rainier, June 1996
42
AVIRIS image, 409,
1324, 2269 nm
precipitable
water, 1-8 mm
liquid water,
0-5 mm path
absorption
vapor, liquid,
ice (BGR)

41. Details

42. Angular distribution of the reflected radiation depends on the snow
grains themselves and the surface geometry
44

43. The multiple endmember approach
• 𝑓𝑘: fraction of pixel covered by endmember k, where k can represent
snow-covered area (SCA), veg, or soil
• 𝑅 𝜆,𝑘: reflectance of endmember k at wavelength 𝜆 (or in
multispectral band corresponding to a wavelength interval)
• Integrated reflectance of a pixel at wavelength (or band pass) 𝜆 is
𝑅 𝜆 = 𝜖 𝜆 +
𝑘=1
𝑁
𝑓𝑘 𝑅 𝜆,𝑘
• For multiple wavelengths 𝜆1, … 𝜆 𝑀, where 𝑀 > 𝑁 (overdetermined)
solve for 𝑓𝑘 to minimize 𝜖 𝜆
2
• Choose the combination of endmembers of snow (grain size and
contamination), veg, and soil with the smallest 𝜖 𝜆
2
45

44. A new continuum approach with nonlinear least squares
• Multiple endmembers an important contribution to snow hydrology and
remote sensing science, but . . .
• Lots of combinations to consider: 𝑁𝑠𝑛𝑜𝑤 × 𝑁𝑣𝑒𝑔 × 𝑁𝑠𝑜𝑖𝑙 is a big number
• Efficient ways to search so don’t consider all, but still . . .
• Instead . . .
• Treat the snow as a single endmember at illumination angle 𝜃 with variable
grain size r and contaminant concentration c, so 𝑅𝜆,𝑠𝑛𝑜𝑤 = F cos 𝜃 , 𝑟, 𝑐 , with
estimated optical properties of dust or soot that could vary regionally
• Use snow-free imagery to estimate the background reflectance 𝑅 𝜆,𝑏𝑎𝑐𝑘
𝑅 𝜆,𝑚𝑜𝑑𝑒𝑙 = 𝑓𝑆𝐶𝐴 𝑅 𝜆,𝑠𝑛𝑜𝑤 + 1 − 𝑓𝑆𝐶𝐴 𝑅 𝜆,𝑏𝑎𝑐𝑘
• Minimize, over 3 unknowns 𝑓𝑆𝐶𝐴, 𝑟, 𝑐, at multiple 𝜆 weighted by 𝑤𝜆
𝜆
𝑤𝜆 𝑅 𝜆,𝑚𝑒𝑎𝑠 − 𝑅 𝜆,𝑚𝑜𝑑𝑒𝑙
2
or?
𝜆
𝑤𝜆
𝑅 𝜆,𝑚𝑒𝑎𝑠 − 𝑅 𝜆,𝑚𝑜𝑑𝑒𝑙
𝑅 𝜆,𝑚𝑒𝑎𝑠 + 𝑅 𝜆,𝑚𝑜𝑑𝑒𝑙
2
46

45. Choose weights based on snow, background, and atmosphere
47

46. Calculations
• Mie scattering
• For small Mie parameter
2𝜋𝑟
𝜆
< ~20 Bohren-Huffman code
• Available from MATLAB File Exchange as MatScat, by J-P Schäfer
• Else, Nussenzveig-Wiscombe complex angular momentum approximation
• I’ve coded this in MATLAB, runs only a little faster than the Fortran version
• Adjusted for dirty or sooty snow according to the absorption and scattering
cross-sections
• Sizes rdust=1µm, rsoot=10nm, complex refractive indices from a presentation
by Charlie Zender
• Radiative transfer
• For directional-hemispherical reflectance, two-stream approximation based
on the Meador-Weaver formulation
• For BRDF, use DISORT 48

47. Calculations, cont.
• Minimizing least squares
• Usually the MATLAB lsqnonlin
function
• Alternatives (always require
more function calls)
• Nonlinear programming —
fmincon
• Optimization — fminsearch
(unconstrained, w/o derivatives)
49

48. Evaluation of results
• 1000 snow spectra mixed with vegetation and soil endmembers
• Grass+PaleBrownSilty, NPV+DarkBrownSilty
• Range of snow properties
• fSCA 0 to 1, evenly spaced
• Grain size 30 to 1500 µm, evenly spaced in square root
• Dust 1 to 1000 ppmw, evenly spaced in log10
• (randomly shuffle each vector to get 1000×3 table)
• 4 error conditions
• None (neither noise nor bias)
• Noise, normally distributed with values of 0.05 and 0.1
• Bias, ±0.05
• Noise & bias
• Retrieve fSCA, grain size, and contaminant concentration
• Calculate broadband albedo (0.28 to 4.0 µm) 50