Snow and ice on Bear Lake (Alaska) – sensitivity experiments with two lake ice models

Flake Parameters HIGHTSI Parameters RF S1 Reference FLake RF setup, but ρ_s=320 kg m⁻³ (constant) ρ_s(initial) = 100 kg m⁻³ (unless specified differently) H1 Without snow ρ_s(initial)= 320 kg m⁻³ for existing snow ρ_s(t): Anderson (1976). S2 S1 setup, but k_s(t): eq. (3) k_s(t): eq. (2) (unless specified differently) H2 Snow added, but without snow-to-ice transformation.k_s(t): Sturm et al. (1997) S3 S2 setup, but modify albedo to ice:α₁=0.5 (0.6); α₂=0.3 (0.1) snow:α₁=0.87 (0.6); α₂=0.77 (0.1) (numbers in brackets are values used in reference version) k_i=2.29 W m⁻¹ K⁻¹T_f=0°C Initial lake water Temperature: 4 °C H3 Snow added, with insulation and snow- to-ice transformation. k_i=2.03 W m^–1 K^–1T_f= − 0.1°C F_w=0.5 W m⁻² S4 S3 setup, but prescribed snow density from ALISON (2011) observations Number of layers in the snow: 1 Number of layers in the ice: 1 H4 H3 setup, but prescribed snow density from ALISON (2011) observations Number of layers in the snow: 10 Number of layers in the ice: 20

RF S1 S2 S3 S4 H1 H2 H3 H4 Bias (m) Snow −0.01 −0.13 −0.10 −0.10 −0.06 – 0.06 −0.04 −0.01 Ice −0.44 −0.32 −0.16 −0.03 −0.09 0.04 −0.13 0.05 0.01 RMSE (m) Snow 0.21 0.20 0.20 0.18 0.15 – 0.15 0.14 0.13 Ice 0.48 0.40 0.31 0.12 0.14 0.14 0.18 0.08 0.07 Correlation coefficient Snow 0.23 0.23 0.23 0.28 0.42 – 0.17 0.23 0.36 Ice 0.21 0.06 0.1 0.74 0.74 0.54 0.67 0.92 0.90

Temperature difference at surface: (T_cal – T_ob) Date T_sfc (ob) RF S1 S2 S3 S4 H1 H2 H3 H4 18 December 2003 −4.3 −2.74 −1.26 0.01 −0.18 −0.73 0.31 −0.31 −0.22 −0.52 23 December 2003 −10.6 3.44 3.57 4.35 4.14 3.47 3.18 2.04 1.98 1.80 2 January 2004 −7.8 −18.03 −13.98 −7.91 −8.76 −8.25 −4.37 −6.39 −6.26 −6.49 7 January 2004 −9.0 −13.86 −12.81 −9.75 −11.06 −9.90 −3.72 −4.41 −5.15 −4.40 10 January 2004 −0.7 −0.09 0.08 −0.66 −1.20 −0.64 −1.75 −1.62 −1.39 −1.60 14 January 2004 −12.0 −1.72 −1.35 −0.89 −1.43 −1.44 1.82 −2.42 −2.31 −2.71 22 January 2004 −0.20 0.20 0.20 0.20 0.20 0.20 0.07 0.20 0.20 0.20 29 January 2004 −9.8 6.23 3.99 2.86 1.19 0.79 3.67 3.63 3.42 3.35 12 February 2004 −4.7 4.47 4.51 4.61 −1.09 −2.34 1.96 −0.45 0.26 −2.45 8 March 2004 −4.4 3.38 3.22 1.26 −4.84 −4.70 −0.39 −1.39 −0.28 −3.08 18 March 2004 −5.6 5.14 5.32 4.83 −4.98 −5.06 2.39 1.30 2.13 0.15 Bias −1.23 −0.77 −0.10 −2.55 −2.60 −0.03 −0.89 −0.69 −1.43 RMSE 7.61 6.40 4.59 4.96 4.62 2.57 2.86 2.91 3.04 Correlation coefficient 0.55 0.62 0.69 0.68 0.72 0.82 0.81 0.82 0.81

Temperature difference at snow–ice interface: (T_cal – T_ob) Date T_sin RF S1 S2 S3 S4 H2 H3 H4 18 December 2003 −1.29 0.56 −0.42 −2.17 −2.33 −1.37 −0.59 −0.61 −0.26 23 December 2003 −0.75 0.32 −0.63 −3.08 −3.23 −1.36 −1.40 −1.43 −0.95 2 January 2004 −2.12 1.35 −0.14 −3.70 −3.92 −8.44 −1.12 1.14 −0.83 7 January 2004 −5.41 3.73 0.20 −7.38 −8.21 −7.84 0.42 0.36 0.68 10 January 2004 −0.22 0.17 0.09 −0.57 −0.89 −0.22 −2.22 −2.26 −1.75 14 January 2004 −1.32 0.56 −1.15 −5.33 −5.59 −3.77 −1.70 −1.73 −1.02 22 January 2004 −0.03 0.03 0.03 0.03 0.03 0.03 −1.26 −1.31 −1.29 29 January 2004 −2.18 1.93 0.88 −2.02 −2.95 −2.54 0.06 0.02 0.46 12 February 2004 −0.15 – – – −3.42 −3.31 −0.03 −0.04 −0.03 8 March 2004 −1.01 – – – −7.57 −7.24 0.34 0.30 0.47 18 March 2004 0.00 – – – −8.46 −7.98 −0.44 −0.47 −0.35 Bias 1.08 −0.14 −3.03 −4.23 −4.00 −0.72 −0.76 −0.44 RMSE 1.36 0.50 3.24 5.04 5.08 1.10 1.13 0.88 Correlation coefficient 0.75 0.86 0.90 0.73 0.72 0.83 0.83 0.86

Simulated monthly mean snow depth (m) Simulated monthly mean ice depth (m) Simulated monthly mean ice growth rate (cm d⁻¹) S4 H4 S4 H4 S4 H4 November 0.06 0.02 0.12 0.21 1.0 1.3 December 0.14 0.11 0.36 0.42 0.5 0.4 January 0.16 0.19 0.58 0.58 0.6 0.4 February 0.17 0.23 0.69 0.69 0.2 0.3 March 0.09 0.24 0.76 0.81 0.4 0.2 April 0.03 0.11 0.56 0.81 −2.5 −0.7 May 0 0 0.03 0.31 0 −2.1