Sensitivity study of constant and variable snow density schemes in diagnosing and calculating snow depth
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摘要: 海冰上积雪的分布是影响海冰与大气能量交换以及气候变化的重要因素。当前的CMIP6气候模式（如CESM2和NESM3）采用定常的积雪密度，而专注于模拟雪厚度和密度变化的模式（如SnowModel-LG）则采用经验的变化雪密度公式。对比CryoSat-2卫星观测的积雪厚度发现，从积雪厚度的空间分布与平均值难以判断出变化雪密度对北冰洋积雪厚度模拟产生何种影响，对于变化雪密度模拟积雪厚度的改进及机制有待进一步研究。本文采用随气温、风速等因子变化的雪密度经验公式模型，并利用SNOTEL单站的长时间序列观测资料，对不同影响因子设计如下敏感性实验：A. 考虑所有气象因子的变化雪密度模型；B. 常数雪密度模型；C. 在A中不考虑风对密实化的影响；D. 在A中不考虑气温对密实化的影响。实验A、B、C和D诊断计算的2018年11月1日至2019年5月10日积雪厚度的均方根误差分别为4.2 cm、4.8 cm、25.9 cm和4.2 cm。结果表明，变化雪密度方案A模拟的积雪密度、厚度在平均值上与常数雪密度的结果接近，但其模拟的积雪厚度均方根误差最小，并且能够模拟出积雪厚度在几天到十几天时间尺度上的高频变化，同时减小了这种高频变化对应时段雪厚模拟结果的相对误差，二者具有一定的相关性。此外，还发现气温变化对积雪密实化的影响远小于风。Abstract: Current CMIP6 climate models (such as CESM2 and NESM3) use constant snow density, while those models that focus on snow depth and density changes (such as SnowModel-LG) use empirical snow density formulas. Comparing the modeled snow depth with those observed by the CryoSat-2 satellite, it is found that from the perspective of the spatial distribution and average value of the snow depth, it is difficult to detect the effects of varying snow density on the simulation of snow depth in the Arctic Ocean. The model improvement and its mechanism from varying snow depth is still to be further studied. Here an empirical snow density model considering meteorological factors such as air temperature, wind etc., is applied to the SNOTEL observational site to carry out the following sensitivity experiments for different factors: A. snow density model considering all meteorological factors; B. constant snow density model; C. same as A but the influence of wind on the densification is not considered and D. same as A but the influence of temperature on the densification is not considered. The root mean square error of snow depth simulated by experiments A, B, C and D from November 1, 2018 to May 10, 2019 are 4.2 cm, 4.8 cm, 25.9 cm, and 4.2 cm, respectively. The results show that the mean snow density and depth simulated by the varying snow density model are close to the results using constant snow density, but the root mean square error of the simulated snow depth from Case A is the smallest, and the Case A simulation can reproduce the high frequency variations of snow depth on the time scale of several days to ten days. In the meantime, the relative errors in the period with high-frequency snow depth variations are also reduced as they are found to be related. In addition, it is also found that the influence of temperature on snow densification is much smaller than that of wind.
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Key words:
- climate model /
- Arctic /
- snow depth /
- snow density
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图 2 CryoSat-2卫星观测的（a−d）与采用不同积雪密度的模式（CESM2（e−h）、NESM3（i−l）和SnowModel-LG（m−p））模拟的北冰洋2015年10月至2018年4月的3年平均的10月、12月、2月和4月积雪厚度
Fig. 2 October, December, February and April snow depth averaged between October 2015 to April 2018 observed by CryoSat-2 (a−d) and modeled by CESM2 (e−h), NESM3 (i−l) and SnowModel-LG (m−p) over the Arctic
图 3 CryoSat-2卫星观测的（a−d）与采用不同雪密度的模式（CESM2（e−h）、NESM3（i−l）和SnowModel-LG（m−p））模拟的北冰洋2015年10月、12月与2016年2月、4月平均积雪厚度
Fig. 3 Snow depth of October, December in 2015 and Febraury, April in 2016 between observed by CryoSat-2 (a−d) and modeled by CESM2 (e−h), NESM3 (i−l) and SnowModel-LG (m−p) over the Arctic
图 4 实验A、B、C和D模拟的普拉德霍湾站积雪厚度和观测值的比较
Fig. 4 Modeled snow depth in cases A, B, C and D at Prudhoe Bay Station, and comparison with observation
图 5 实验A、B和C模拟的普拉德霍湾站2018年11月至2019年5月积雪密度
实验D的积雪密度几乎与实验A的相同，故未展示
Fig. 5 Modeled snow density from November 2018 to May 2019 in cases A, B, C and D at Prudhoe Bay Station
The snow density in Case D is almost the same as that in Case A, so it is not shown in the figure
图 6 实验A和B模拟的普拉德霍湾站积雪厚度的相对误差
由于实验C的积雪厚度相对误差远大于其余三者，且实验D的结果与实验A的一致，故不展示
Fig. 6 Relative errors of modeled snow depth in cases A and B at Prudhoe Bay Station
Since the relative error of snow depth in Case C is more than three times as much as the other three and the result of Case D is almost consistent with that of Case A, it is not shown in the figure
表 1 CESM2、NESM3和SnowModel-LG的分量模式比较
Tab. 1 Comparison of component models among CESM2, NESM3 and SnowModel-LG
模式分量 CESM2 NESM3 SnowModel-LG 大气 CAM6 ECHAM v6.3 ERA5; MERRA2;
自动气象站数据海洋 POP2 NEMO v3.4 − 陆地 CLM5 JSBACH v3.1 − 海洋生物化学 MARBL − − 气溶胶 MAM4 − − 大气化学 MAM4 − − 海冰 CICE5.1 CICE4.1 海冰地形、海冰位置和
海冰密集度数据陆地冰 CISM4.1 − − 注：−代表模式不包含该分量。 
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表 2 实验A、B、C和D模拟的普拉德霍湾站积雪厚度的均方根误差与相关系数
Tab. 2 Root mean square errors and correlation coefficients of snow depth in cases A, B, C and D at Prudhoe Bay Station
方案 均方根误差/cm 总体相关系数 2018年10月（4−31日） 2018年11月 2018年12月 2019年1月 2019年2月 2019年3月 2019年4月 2019年5月（1−10日） 总体 A 2.4 4.8 5.8 4.5 2.2 1.8 2.9 7.5 4.2 0.82 B 2.7 4.5 9.4 2.8 1.4 2.8 4.3 1.4 4.8 0.80 C 6.1 18.5 25.6 35.2 27.4 25.3 23.5 15.8 25.9 0.67 D 2.4 4.8 5.8 4.6 2.2 1.8 2.9 7.4 4.2 0.82
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