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Following Geldsetzer & Jamieson (2000), snow density can be estimated using Equation (1). The results from our reference dataset are shown in Figure 1(a) and the corresponding regression coefficients are listed in Table 1(a). As can be seen, all lines except one have a positive slope and are closely grouped to each other. Figure 1(b) and Table 1(b) show the corresponding results for snow density using Equation (2). As can be seen for snow layer hardness R4–R5 (hard snow layers), the snow density is increasing with increasing snow particle size index, and for snow layer hardness R0–R3 (softer snow layers), the snow density is decreasing with increasing snow particle size index.
Table 1

Regression coefficient (k and m), correlation coefficient (R2), standard deviation of regression coefficients (σk and σm’ (determined at the centre of the distribution)), significance level (p) of regression constants, and number observations for calculating snow density with (a) Equation (1) and (b) Equation (2); see Figure 1(a) and 1(b), respectively

Snow particle size (E)kEmER2σkEσmE′p level of kE (%)p of mE (%)Number of observations
(a)                 
EN – – – –     
EP 0.0098 0.3580 0.49 0.0071 0.0136 80 99.9 
ER 0.0073 0.2944 0.01 0.0152 0.0168  99.9 31 
ESR −0.0056 0.2047 0.06 0.0157 0.0131  99.9 
ES 0.0294 0.2119 0.11 0.0132 0.0169 95 99.9 44 
EFS 0.1512 −0.3998 0.01 0.0467 0.0202 99 99.9 
EF 0.1196 −0.1382 0.83 0.0180 0.0247 99.9 99.9 
EFlake – 0.1700 – – 0.0126  70 
Snow layer hardness (R)kRmRR2σkRσmR′p level of kR (%)p level of mR (%)Number of observations
(b)                 
 R0 −0.0639 0.4678 0.08 0.2165 0.1021  99.9 
 R1 −0.0533 0.4877 0.40 0.0136 0.0164 99.9 99.9 25 
 R2 −0.0879 0.6016 0.08 0.0283 0.0158 99 99.9 30 
 R3 −0.0482 0.5002 0.08 0.0389 0.0253 70 99.9 19 
 R4 0.1189 −0.1318 0.45 0.0363 0.0234 99 99.9 15 
 R5 0.0503 0.2502 0.09 0.0706 0.0588 50 99.9 
Snow particle size (E)kEmER2σkEσmE′p level of kE (%)p of mE (%)Number of observations
(a)                 
EN – – – –     
EP 0.0098 0.3580 0.49 0.0071 0.0136 80 99.9 
ER 0.0073 0.2944 0.01 0.0152 0.0168  99.9 31 
ESR −0.0056 0.2047 0.06 0.0157 0.0131  99.9 
ES 0.0294 0.2119 0.11 0.0132 0.0169 95 99.9 44 
EFS 0.1512 −0.3998 0.01 0.0467 0.0202 99 99.9 
EF 0.1196 −0.1382 0.83 0.0180 0.0247 99.9 99.9 
EFlake – 0.1700 – – 0.0126  70 
Snow layer hardness (R)kRmRR2σkRσmR′p level of kR (%)p level of mR (%)Number of observations
(b)                 
 R0 −0.0639 0.4678 0.08 0.2165 0.1021  99.9 
 R1 −0.0533 0.4877 0.40 0.0136 0.0164 99.9 99.9 25 
 R2 −0.0879 0.6016 0.08 0.0283 0.0158 99 99.9 30 
 R3 −0.0482 0.5002 0.08 0.0389 0.0253 70 99.9 19 
 R4 0.1189 −0.1318 0.45 0.0363 0.0234 99 99.9 15 
 R5 0.0503 0.2502 0.09 0.0706 0.0588 50 99.9 

When modelling snow layer density the regressions will be applied for all index values except for snow layer hardness class R4 in Equation (2). There, the regression line is not applied for snow particle size index 1 and 2 (corresponding to EN and EP).

Figure 1

Result from the reference dataset. (a) Snow layer density (ρsnow) plotted against snow layer hardness index (Ri) for each snow particle size class (E) (see figure legend). Each line represents a linear regression for each E class. The regression coefficients for line EPEFlake are listed in Table 1(a). (b) Snow layer density plotted against snow particle size index (Ei) for each snow layer hardness class (R) (see figure legend). Each line represents a linear regression for each R class. The regression coefficients for lines R0–R5 are listed in Table 1(b).

Figure 1

Result from the reference dataset. (a) Snow layer density (ρsnow) plotted against snow layer hardness index (Ri) for each snow particle size class (E) (see figure legend). Each line represents a linear regression for each E class. The regression coefficients for line EPEFlake are listed in Table 1(a). (b) Snow layer density plotted against snow particle size index (Ei) for each snow layer hardness class (R) (see figure legend). Each line represents a linear regression for each R class. The regression coefficients for lines R0–R5 are listed in Table 1(b).

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Figure 2

Result from the reference dataset: (a) modelled snow density using Equation (1) with regression coefficients from Table 1(a), and (b) using Equation (2) with regression coefficients from Table 1(b) compared with the observed snow layer density. The solid lines show the linear regression lines. The regression constants are all determined with p-values ≥99.9%. (c) Distributions of modelled and measured snow layer density modelled using Equation (1) and (d) using Equation (2).

Figure 2

Result from the reference dataset: (a) modelled snow density using Equation (1) with regression coefficients from Table 1(a), and (b) using Equation (2) with regression coefficients from Table 1(b) compared with the observed snow layer density. The solid lines show the linear regression lines. The regression constants are all determined with p-values ≥99.9%. (c) Distributions of modelled and measured snow layer density modelled using Equation (1) and (d) using Equation (2).

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