Snow: What’s albedo and why should you care? Jeff Dozier, UCSB

@ UCLA, 2017-04-10

(photo Tom Painter)

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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

𝑎𝑙𝑏𝑒𝑑𝑜=𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

(photo Ned Bair)

(photo Timbo Stillinger)

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Effect of sun angle

, Solar zenith angle

𝑆0

𝑆0× cos 𝑍0

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Why should you care?

• Earth’s climate, the seasons, and snowmelt are driven by absorbed solar radiation

𝑛𝑒𝑡 𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛=¿𝑛𝑒𝑡 𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛=¿

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You care because a small change in albedo causes a bigger relative change in (1–albedo)

albedoFraction absorbed(1–albedo)

Start with 0.8 0.2Lower it by 20%, you get 0.64 0.36 An increase

of 80%

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Measurement of snowpack net solar radiation at Mammoth Mountain

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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

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

Imagery courtesy GlacierWorks

Cho Oyu

East Rongbuk

1921 2009

1921

2011

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What causes snow albedo to change?

• To answer this, we first need to define spectral albedo

𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙𝑎𝑙𝑏𝑒𝑑𝑜 (𝑎𝑡 h𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡 𝜆 )= 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 (𝜆 )𝑖𝑛𝑐𝑜𝑚𝑖𝑛𝑔𝑠𝑜𝑙𝑎𝑟 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 (𝜆 )

• 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

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Incoming solar radiation (“irradiance”) varies with wavelength

O3

O2

Mostly scattering

H2Ovisib

le li

ght

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The point?

• The spectral albedo is a fundamental property of the material• Varies with wavelength• Varies with illumination angle, and physical properties

• The broadband albedo is the convolution of the spectral albedo and the spectral distribution of the incoming radiation (irradiance)

(for parts of the wavelength range between 0 and

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Albedo of clean snow varies with the grain size

Why? Answer lies in optical properties of ice

0 sinsin

i

r

cnc

ir

I0 I

dx

4

0

4

kx

dI k IdxI eI

19index of refraction

absorption coefficient, k

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absorption coefficient

½ decay distance

Setand solve𝑒− 4 𝜋𝑘𝑥𝜆 =1

2

𝑥=( ln 24𝜋 )( 𝜆𝑘 )

Snow spectral albedo and absorption coefficient of ice

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

Dust

(McKenzie Skiles)

algae

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

[Painter et al., 2001]

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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)

Planck equation for Sun and Earth

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10-1 100 101 102

100

102

104

106

108

Wavelength,mm

Rad

ianc

e, W

m-2mm

-1sr-1

Sun (5800K)Earth (288K)Scaled for Earth-Sun Distance

visib

le

near

-infra

red

shor

twav

e-in

frare

d

mid

-infra

red

ther

mal

in

frare

dultra

viol

et

What forces glacier melt?

[Kaspari et al, 2014]

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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]

Comparison of MODIS (500m) and Landsat (30m) snow fraction, in the Sierra Nevada

200 scenes with coincident MODIS and Landsat imagesAverage RMSE = 7.8%Range from 2% to 12%

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

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

[Warren, Rev Geophys, 1982]

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Results, with no noise or bias in the signal

fSCA =75%

fSCA = 25%

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Results, with noise and bias in the signal

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fSCA and albedo, pale brown silty + grass

RMSE = 1.2%RMSE w/o bias = 0.49%

RMSE = 5.0%RMSE w/o bias = 1.9%

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

RMSE = 1.4%

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

RMSE = 3.6%

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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 pixel1. Covered by snow2. 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

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Radiative forcing with a spectrometer

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Surface wetness from an imaging spectrometer, Mt Rainier, June 1996

AVIRIS image, 409, 1324, 2269

nm

precipitable water, 1-8

mm

liquid water, 0-5 mm

path absorption

vapor, liquid, ice

(BGR)

Details

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

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The multiple endmember approach• : fraction of pixel covered by endmember k, where k can

represent snow-covered area (SCA), veg, or soil• : reflectance of endmember k at wavelength (or in

multispectral band corresponding to a wavelength interval)• Integrated reflectance of a pixel at wavelength (or band

pass) is

• For multiple wavelengths , where (overdetermined) solve for to minimize

• Choose the combination of endmembers of snow (grain size and contamination), veg, and soil with the smallest

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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: 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 with

variable grain size r and contaminant concentration c, so , with estimated optical properties of dust or soot that could vary regionally

• Use snow-free imagery to estimate the background reflectance

• Minimize, over 3 unknowns , at multiple weighted by

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Choose weights based on snow, background, and atmospheresnow, grass, pale brown silty snow, NPV, dark brown silty

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Calculations• Mie scattering

• For small Mie parameter 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

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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)

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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)