### 2.3.2.1. Snow Albedo[¶](#snow-albedo "Permalink to this headline")

Snow albedo and solar absorption within each snow layer are simulated with the Snow, Ice, and Aerosol Radiative Model (SNICAR), which incorporates a two-stream radiative transfer solution from [Toon et al. (1989)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#toonetal1989). Albedo and the vertical absorption profile depend on solar zenith angle, albedo of the substrate underlying snow, mass concentrations of atmospheric-deposited aerosols (black carbon, mineral dust, and organic carbon), and ice effective grain size (\\(r\_{e}\\)), which is simulated with a snow aging routine described in section [2.3.2.3](#snow-aging). Representation of impurity mass concentrations within the snowpack is described in section [2.8.4](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Snow_Hydrology/CLM50_Tech_Note_Snow_Hydrology.html#black-and-organic-carbon-and-mineral-dust-within-snow). Implementation of SNICAR in CLM is also described somewhat by [Flanner and Zender (2005)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#flannerzender2005) and [Flanner et al. (2007)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#flanneretal2007).

The two-stream solution requires the following bulk optical properties for each snow layer and spectral band: extinction optical depth (\\(\\tau\\)), single-scatter albedo (\\(\\omega\\)), and scattering asymmetry parameter (_g_). The snow layers used for radiative calculations are identical to snow layers applied elsewhere in CLM, except for the case when snow mass is greater than zero but no snow layers exist. When this occurs, a single radiative layer is specified to have the column snow mass and an effective grain size of freshly-fallen snow (section [2.3.2.3](#snow-aging)). The bulk optical properties are weighted functions of each constituent _k_, computed for each snow layer and spectral band as

(2.3.62)[¶](#equation-3-62 "Permalink to this equation")\\\[\\tau =\\sum \_{1}^{k}\\tau \_{k}\\\]

(2.3.63)[¶](#equation-3-63 "Permalink to this equation")\\\[\\omega =\\frac{\\sum \_{1}^{k}\\omega \_{k} \\tau \_{k} }{\\sum \_{1}^{k}\\tau \_{k} }\\\]

(2.3.64)[¶](#equation-3-64 "Permalink to this equation")\\\[g=\\frac{\\sum \_{1}^{k}g\_{k} \\omega \_{k} \\tau \_{k} }{\\sum \_{1}^{k}\\omega \_{k} \\tau \_{k} }\\\]

For each constituent (ice, two black carbon species, two organic carbon species, and four dust species), \\(\\omega\\), _g_, and the mass extinction cross-section \\(\\psi\\) (m2 kg\-1) are computed offline with Mie Theory, e.g., applying the computational technique from [Bohren and Huffman (1983)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#bohrenhuffman1983). The extinction optical depth for each constituent depends on its mass extinction cross-section and layer mass, \\(w \_{k}\\) (kgm\-1) as

(2.3.65)[¶](#equation-3-65 "Permalink to this equation")\\\[\\tau \_{k} =\\psi \_{k} w\_{k}\\\]

The two-stream solution ([Toon et al. (1989)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#toonetal1989)) applies a tri-diagonal matrix solution to produce upward and downward radiative fluxes at each layer interface, from which net radiation, layer absorption, and surface albedo are easily derived. Solar fluxes are computed in five spectral bands, listed in [Table 2.3.4](#table-spectral-bands-and-weights-used-for-snow-radiative-transfer). Because snow albedo varies strongly across the solar spectrum, it was determined that four bands were needed to accurately represent the near-infrared (NIR) characteristics of snow, whereas only one band was needed for the visible spectrum. Boundaries of the NIR bands were selected to capture broad radiative features and maximize accuracy and computational efficiency. We partition NIR (0.7-5.0 \\(\\mu\\) m) surface downwelling flux from CLM according to the weights listed in [Table 2.3.4](#table-spectral-bands-and-weights-used-for-snow-radiative-transfer), which are unique for diffuse and direct incident flux. These fixed weights were determined with offline hyperspectral radiative transfer calculations for an atmosphere typical of mid-latitude winter ([Flanner et al. (2007)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#flanneretal2007)). The tri-diagonal solution includes intermediate terms that allow for easy interchange of two-stream techniques. We apply the Eddington solution for the visible band (following [Wiscombe and Warren 1980](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#wiscombewarren1980)) and the hemispheric mean solution (([Toon et al. (1989)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#toonetal1989)) for NIR bands. These choices were made because the Eddington scheme works well for highly scattering media, but can produce negative albedo for absorptive NIR bands with diffuse incident flux. Delta scalings are applied to \\(\\tau\\), \\(\\omega\\), and \\(g\\) ([Wiscombe and Warren 1980](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#wiscombewarren1980)) in all spectral bands, producing effective values (denoted with \\(\*\\)) that are applied in the two-stream solution

(2.3.66)[¶](#equation-3-66 "Permalink to this equation")\\\[\\tau ^{\*} =\\left(1-\\omega g^{2} \\right)\\tau\\\]

(2.3.67)[¶](#equation-3-67 "Permalink to this equation")\\\[\\omega ^{\*} =\\frac{\\left(1-g^{2} \\right)\\omega }{1-g^{2} \\omega }\\\]

(2.3.68)[¶](#equation-3-68 "Permalink to this equation")\\\[g^{\*} =\\frac{g}{1+g}\\\]

Table 2.3.4 Spectral bands and weights used for snow radiative transfer[¶](#id10 "Permalink to this table")   
| Spectral band
 | Direct-beam weight

 | Diffuse weight

 |
| --- | --- | --- |
| Band 1: 0.3-0.7\\(\\mu\\)m (visible)

 | (1.0)

 | (1.0)

 |
| Band 2: 0.7-1.0\\(\\mu\\)m (near-IR)

 | 0.494

 | 0.586

 |
| Band 3: 1.0-1.2\\(\\mu\\)m (near-IR)

 | 0.181

 | 0.202

 |
| Band 4: 1.2-1.5\\(\\mu\\)m (near-IR)

 | 0.121

 | 0.109

 |
| Band 5: 1.5-5.0\\(\\mu\\)m (near-IR)

 | 0.204

 | 0.103

 |

Under direct-beam conditions, singularities in the radiative approximation are occasionally approached in spectral bands 4 and 5 that produce unrealistic conditions (negative energy absorption in a layer, negative albedo, or total absorbed flux greater than incident flux). When any of these three conditions occur, the Eddington approximation is attempted instead, and if both approximations fail, the cosine of the solar zenith angle is adjusted by 0.02 (conserving incident flux) and a warning message is produced. This situation occurs in only about 1 in 10 6 computations of snow albedo. After looping over the five spectral bands, absorption fluxes and albedo are averaged back into the bulk NIR band used by the rest of CLM.

Soil albedo (or underlying substrate albedo), which is defined for visible and NIR bands, is a required boundary condition for the snow radiative transfer calculation. Currently, the bulk NIR soil albedo is applied to all four NIR snow bands. With ground albedo as a lower boundary condition, SNICAR simulates solar absorption in all snow layers as well as the underlying soil or ground. With a thin snowpack, penetrating solar radiation to the underlying soil can be quite large and heat cannot be released from the soil to the atmosphere in this situation. Thus, if the snowpack has total snow depth less than 0.1 m (\\(z\_{sno} < 0.1\\)) and there are no explicit snow layers, the solar radiation is absorbed by the top soil layer. If there is a single snow layer, the solar radiation is absorbed in that layer. If there is more than a single snow layer, 75% of the solar radiation is absorbed in the top snow layer, and 25% is absorbed in the next lowest snow layer. This prevents unrealistic soil warming within a single timestep.

The radiative transfer calculation is performed twice for each column containing a mass of snow greater than \\(1 \\times 10^{-30}\\) kgm\-2 (excluding lake and urban columns); once each for direct-beam and diffuse incident flux. Absorption in each layer \\(i\\) of pure snow is initially recorded as absorbed flux per unit incident flux on the ground (\\(S\_{sno,\\, i}\\) ), as albedos must be calculated for the next timestep with unknown incident flux. The snow absorption fluxes that are used for column temperature calculations are

(2.3.69)[¶](#equation-3-69 "Permalink to this equation")\\\[S\_{g,\\, i} =S\_{sno,\\, i} \\left(1-\\alpha \_{sno} \\right)\\\]

This weighting is performed for direct-beam and diffuse, visible and NIR fluxes. After the ground-incident fluxes (transmitted through the vegetation canopy) have been calculated for the current time step (sections [2.3.1](#canopy-radiative-transfer) and [2.4.1](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Radiative_Fluxes/CLM50_Tech_Note_Radiative_Fluxes.html#solar-fluxes)), the layer absorption factors (\\(S\_{g,\\, i}\\)) are multiplied by the ground-incident fluxes to produce solar absorption (W m\-2) in each snow layer and the underlying ground.

