### 2.8.7.1. Combination[¶](#combination "Permalink to this headline")

If a snow layer has nearly melted or if its thickness \\(\\Delta z\_{i}\\) is less than the prescribed minimum thickness \\(\\Delta z\_{\\min }\\) ([Table 2.8.2](#table-snow-layer-thickness)), the layer is combined with a neighboring layer. The overlying or underlying layer is selected as the neighboring layer according to the following rules

1.  If the top layer is being removed, it is combined with the underlying layer
    
2.  If the underlying layer is not snow (i.e., it is the top soil layer), the layer is combined with the overlying layer
    
3.  If the layer is nearly completely melted, the layer is combined with the underlying layer
    
4.  If none of the above rules apply, the layer is combined with the thinnest neighboring layer.
    

A first pass is made through all snow layers to determine if any layer is nearly melted (\\(w\_{ice,\\, i} \\le 0.1\\)). If so, the remaining liquid water and ice content of layer \\(i\\) is combined with the underlying neighbor \\(i+1\\) as

(2.8.44)[¶](#equation-8-51 "Permalink to this equation")\\\[w\_{liq,\\, i+1} =w\_{liq,\\, i+1} +w\_{liq,\\, i}\\\]

(2.8.45)[¶](#equation-8-52 "Permalink to this equation")\\\[w\_{ice,\\, i+1} =w\_{ice,\\, i+1} +w\_{ice,\\, i} .\\\]

This includes the snow layer directly above the top soil layer. In this case, the liquid water and ice content of the melted snow layer is added to the contents of the top soil layer. The layer properties, \\(T\_{i}\\), \\(w\_{ice,\\, i}\\), \\(w\_{liq,\\, i}\\), \\(\\Delta z\_{i}\\), are then re-indexed so that the layers above the eliminated layer are shifted down by one and the number of snow layers is decremented accordingly.

At this point, if there are no explicit snow layers remaining (\\(snl=0\\)), the snow water equivalent \\(W\_{sno}\\) and snow depth \\(z\_{sno}\\) are set to zero, otherwise, \\(W\_{sno}\\) and \\(z\_{sno}\\) are re-calculated as

(2.8.46)[¶](#equation-8-53 "Permalink to this equation")\\\[W\_{sno} =\\sum \_{i=snl+1}^{i=0}\\left(w\_{ice,\\, i} +w\_{liq,\\, i} \\right)\\\]

(2.8.47)[¶](#equation-8-54 "Permalink to this equation")\\\[z\_{sno} =\\sum \_{i=snl+1}^{i=0}\\Delta z\_{i} .\\\]

If the snow depth \\(0<z\_{sno} <0.01\\) m or the snow density \\(\\frac{W\_{sno} }{f\_{sno} z\_{sno} } <50\\) kg/m3, the number of snow layers is set to zero, the total ice content of the snowpack \\(\\sum \_{i=snl+1}^{i=0}w\_{ice,\\; i}\\) is assigned to \\(W\_{sno}\\), and the total liquid water \\(\\sum \_{i=snl+1}^{i=0}w\_{liq,\\; i}\\) is assigned to the top soil layer. Otherwise, the layers are combined according to the rules above.

When two snow layers are combined (denoted here as 1 and 2), their thickness combination (\\(c\\)) is

(2.8.48)[¶](#equation-8-55 "Permalink to this equation")\\\[\\Delta z\_{c} =\\Delta z\_{1} +\\Delta z\_{2} ,\\\]

their mass combination is

(2.8.49)[¶](#equation-8-56 "Permalink to this equation")\\\[w\_{liq,\\, c} =w\_{liq,\\, 1} +w\_{liq,\\, 2}\\\]

(2.8.50)[¶](#equation-8-57 "Permalink to this equation")\\\[w\_{ice,\\, c} =w\_{ice,\\, 1} +w\_{ice,\\, 2} ,\\\]

and their temperatures are combined as

(2.8.51)[¶](#equation-8-58 "Permalink to this equation")\\\[T\_{c} =T\_{f} +\\frac{h\_{c} -L\_{f} w\_{liq,\\, c} }{C\_{ice} w\_{ice,\\, c} +C\_{liq} w\_{liq,\\, c} }\\\]

where \\(h\_{c} =h\_{1} +h\_{2}\\) is the combined enthalpy \\(h\_{i}\\) of the two layers where

(2.8.52)[¶](#equation-8-59 "Permalink to this equation")\\\[h\_{i} =\\left(C\_{ice} w\_{ice,\\, i} +C\_{liq} w\_{liq,\\, i} \\right)\\left(T\_{i} -T\_{f} \\right)+L\_{f} w\_{liq,\\, i} .\\\]

In these equations, \\(L\_{f}\\) is the latent heat of fusion (J kg\-1) and \\(C\_{liq}\\) and \\(C\_{ice}\\) are the specific heat capacities (J kg\-1 K\-1) of liquid water and ice, respectively ([Table 2.2.7](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Ecosystem/CLM50_Tech_Note_Ecosystem.html#table-physical-constants)). After layer combination, the node depths and layer interfaces ([Figure 2.8.1](#figure-three-layer-snow-pack)) are recalculated from

(2.8.53)[¶](#equation-8-60 "Permalink to this equation")\\\[z\_{i} =z\_{h,\\, i} -0.5\\Delta z\_{i} \\qquad i=0,\\ldots ,snl+1\\\]

(2.8.54)[¶](#equation-8-61 "Permalink to this equation")\\\[z\_{h,\\, i-1} =z\_{h,\\, i} -\\Delta z\_{i} \\qquad i=0,\\ldots ,snl+1\\\]

where \\(\\Delta z\_{i}\\) is the layer thickness.

Table 2.8.2 Minimum and maximum thickness of snow layers (m)[¶](#id16 "Permalink to this table")      
| Layer
 | \\(\\Delta z\_{\\min }\\)

 | \\(N\_{l}\\)

 | \\(N\_{u}\\)

 | \\(\\left(\\Delta z\_{\\max } \\right)\_{l}\\)

 | \\(\\left(\\Delta z\_{\\max } \\right)\_{u}\\)

 |
| --- | --- | --- | --- | --- | --- |
| 1 (top)

 | 0.010

 | 1

 | \\(>\\)1

 | 0.03

 | 0.02

 |
| 2

 | 0.015

 | 2

 | \\(>\\)2

 | 0.07

 | 0.05

 |
| 3

 | 0.025

 | 3

 | \\(>\\)3

 | 0.18

 | 0.11

 |
| 4

 | 0.055

 | 4

 | \\(>\\)4

 | 0.41

 | 0.23

 |
| 5

 | 0.115

 | 5

 | \\(>\\)5

 | 0.88

 | 0.47

 |
| 6

 | 0.235

 | 6

 | \\(>\\)6

 | 1.83

 | 0.95

 |
| 7

 | 0.475

 | 7

 | \\(>\\)7

 | 3.74

 | 1.91

 |
| 8

 | 0.955

 | 8

 | \\(>\\)8

 | 7.57

 | 3.83

 |
| 9

 | 1.915

 | 9

 | \\(>\\)9

 | 15.24

 | 7.67

 |
| 10

 | 3.835

 | 10

 | \\(>\\)10

 | 30.59

 | 15.35

 |
| 11

 | 7.675

 | 11

 | \\(>\\)11

 | 61.30

 | 30.71

 |
| 12 (bottom)

 | 15.355

 | 12

 | 

 | 

 | 

 |

The maximum snow layer thickness, \\(\\Delta z\_{\\max }\\), depends on the number of layers, \\(N\_{l}\\) and \\(N\_{u}\\) (section [2.8.7.2](#subdivision)).

