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

Figures & data

Table 1. FLake and HIGHTSI experiments setup

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:α 1=0.5 (0.6); α 2=0.3 (0.1) snow:α 1=0.87 (0.6); α 2=0.77 (0.1) (numbers in brackets are values used in reference version)	k i=2.29 W m^−1 K^−1 T 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^–1 T 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

T _f: freezing temperature; F _w: heat flux from water to ice; t: time.

Fig. 1.  Surface elevation [m] of the HIRLAM Alaska domain. In the south-east of Alaska the location of the Bear Lake is indicated in white.

Fig. 2.  Snow and ice depth and snow density measured on Bear Lake during the 2003/2004 ice season.

Fig. 3.  The forcing data from HIRLAM model; (a) wind speed; (b) air temperature; (c) relative humidity; (d) original snow precipitation from HIRLAM (blue) and snow precipitation for T2m < 0.1 °C (red); (e) downwelling short-wave radiation; and (f) downwelling long-wave radiation.

Fig. 4.  Observed and FLake-simulated snow and ice depth Hs and Hi. (a) Reference FLake run and sensitivity experiment S1; (b–d) sensitivity experiments S2–S4.

Fig. 5.  Observed and HIGHTSI-simulated snow and ice depth. (a–d) model experiments H1–H4.

Table 2. Bias, root mean square error (RMSE) and correlation coefficient of simulated snow and ice depths compared to observations. For the bias negative values indicate an underestimation by the models and positive values an overestimation

		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

Table 3. Comparison between simulated and measured surface temperatures (°C) for all model runs. The comparisons match the specific date and time of measurement (local noon). Bias, root mean square error (RMSE) and correlation coefficient are also given

		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

Table 4. Comparisons between simulated and measured temperature (°C) at the snow − ice interface for all model runs. The comparisons match the specific date and time of measurement (local noon). Bias and root mean square error (RMSE) are also given. Note that the experiment H1 is excluded because snow is not considered

		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

Table 5. Monthly mean of simulated ice depth and ice growth rate by FLake (S4) and HIGHTSI (H4)

	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

Fig. 6.  Snow-ice and superimposed ice simulated by HIGHTSI.

Fig. 7.  The time series of observed (black points) and simulated surface temperature (T _sfc), snow–ice interface temperature (T _si) from S4 (blue line) and H4 (red line).