The NCEP of the United States developed, optimized, and improved the Noah land surface model. The Noah model depicts the exchange of water in the snow–vegetation–soil mixing layer and simulates the snow accumulation, sublimation, melting, and associated heat transfer, in which aging, freezing, compacting, and dynamic SD, as well as density change processes, are considered. The model can output snow water equivalent (SWE), SD, and snow density and can be used to calculate snow cover fraction based on the region’s empirical ablation curve. Noah versions 3.3–3.6 adopt a snow cover fraction parameterization scheme (Koren et al., 1999) that emphasizes the relationship between the snow coverage rate and SWE. Many scholars have further studied and evaluated this model (e.g., Zhang et al., 2016). The relationships between the snow cover fraction, SWE, and SD were calculated by using Eqs. (1) and (2):
where SNCOVR is snow cover, SNEQV is SWE, SNUP is the SD threshold when the snow cover fraction equals 1, RSNOW is the ratio of SNEQV to SNUP, and SALP is an adjustable coefficient.
The Noah 3.6 land surface model is taken as the mo-del operator for snow cover fraction assimilation, and SD and SWE are state variables of the land surface model. EnKF is used to assimilate the FY-3 snow cover fraction products into the Noah land surface model, and the state variables of the model are updated. The snow cover ablation curve describes the relationship between snow cover and SD in Noah 3.3–3.6, and is used as an observation operator in the snow cover fraction assimilation by use of Eqs. (1) and (2).
In the present study, the Noah 3.6 model was driven by CLDAS-2.0 forcing, and the EnKF (Evensen, 2003) method was used to assimilate the FY-3 snow cover fraction product. Downward shortwave radiation (SW) and precipitation (PRCP) are subject to multiplicative perturbations with a mean of 1 and standard deviations of 0.1 (SW) and 0.5 (PRCP), respectively. Zero-mean additive perturbations are applied to air temperature (T) and longwave radiation (LW) with standard deviations of 0.5 K (T) and 15 W m–2 (LW), respectively. The Noah model prognostic variables for SWE and SD are subject to multiplicative perturbations with mean = 1 and standard deviation = 0.01. A total of 25 members and the perturbation method in Table 1 were used for the EnKF runs following the methods of De Lannoy et al. (2012), with an assumption that the disturbance of these variables obeys the normal distribution. The standard deviation of the snow cover fraction in snow cover fraction assimilation was set to 0.1, which was identified according to Su et al. (2008) and Andreadis and Lettenmaier (2006).
Variable Perturbation method Standard deviation Model states SWE Multiplicative 0.01 (–) SD Multiplicative 0.01 (–) Forcing SW Multiplicative 0.1 (–) LW Additive 15 W m–2 PRCP Multiplicative 0.5 (–) T Additive 0.5 K Observation SCF Multiplicative 0.1
Table 1. Ensemble perturbation method used in the snow cover assimilation. SCF denotes snow cover fraction
Without quality control on the snow cover products, erroneous observations may be assimilated, and erroneous results would be produced. Therefore, quality control of snow cover products is very important. The scatter plots of averaged monthly snow cover fraction and SD, based on the FY-3 0.05° daily snow cover fraction and 0.25° SD data from November 2013 to April 2014, are shown in Figs. 2a, c, which reveal some problems as follows: (1) in some grid cells, the snow cover fraction was small (nearly 0), but the SD was very large; and (2) the SD was 0 in some grid cells, but the snow cover fraction was 1.
Figure 2. Scatter plots of snow cover fraction (SCF) and snow depth (SD) from the FY-3 0.05° daily SCF and 0.25° SD (cm) products (a, b) for November 2013–April 2014 and (c, d) in February 2014. (a, c) SCFDA and (b, d) SCFDA_WSD.
The above situations in Figs. 2a, c are unreasonable. Therefore, it is necessary to use SD data to control the quality of remote sensing snow cover products. Figure 3 is a flow chart of the process used for FY-3 snow cover fraction quality control. The following unreasonable snow cover fractions must be assigned default values (−9999.0) to avoid assimilating these unreasonable values into the model: (1) when the snow cover fraction of the grid is 100% but the SD is less than 1 cm, and (2) when the snow cover fraction of the grid is less than 30% but the SD is greater than 10 cm. In Fig. 3, SCF is the original FY-3 snow cover fraction, SCF′ is the processed (quality controlled) FY-3 snow cover fraction, SD is the FY-3 SD, and undef stands for missing value, which is set to −9999.0 in this study.
To illustrate the effects of the quality control on the snow cover fraction assimilation, a series of experiments were carried out by using the FY-3 snow cover fraction, which was assimilated into the Noah model. The CLDAS-V2.0 (CMA Land Data Assimilation System version 2) forcing data were obtained from the National Meteorological Information Center of China, and the Noah 3.6 model was run from arbitrary initial conditions for 21 yr by cycling the CLDAS forcing data from 1 January 2008 to 31 December 2014, with three repetitions for the spin-up. The meteorological forcing analyses with hourly products covering the region of Asia (0°–65°N, 60°–160°E) have a spatial resolution of 0.0625° × 0.0625°, and these forcing data have a good effect on snow simulation in winter (Shi et al., 2018). The Noah 3.6 land surface model was run from 1 January 2008, and began to carry out the FY-3 snow cover fraction assimilation experiments from 1 November 2011. Model runs were carried out at 6.25 km and hourly resolutions. The grid data were processed at the model resolution (0.0625°).
In the FY-3 snow cover assimilation experiment, the surface parameters were first input into the land surface model, and the Noah model was driven by CLDAS-2.0 forcing data to obtain stable initial conditions; then, the snow cover simulation was started. Snow cover fraction products were assimilated at a daily frequency. The snow cover fraction product was assimilated at 1330 local solar time to be close to the overpass time of FY-3B. The snow cover fraction was quality controlled from a microwave radiation imager SD product before assimilation, and then EnKF was used to assimilate snow cover products to update the SD and water equivalent in the Noah model, and the assimilation results of snow variables were then examined. Figure 4 shows a flow chart of FY-3 snow cover fraction assimilation.
The FY-3 snow cover fraction assimilation was carried out, and the improved effects of the assimilation were verified against the MODIS remote-sensing satellite products. The SD results were compared with the SD station observations. This paper used the BIAS, root mean square error (RMSE), and correlation coefficient (R) as evaluation indices as follows:
where Xo represents the observation, Xm represents the model value, and N is the total number of observations.
Scatter plots of monthly average snow cover fraction and snow depth are drawn based on the FY-3 0.05° daily snow cover fraction and 0.25° daily SD products from November 2013 to April 2014 (Figs. 2b, d). The number of irrational points was greatly reduced compared to that before quality control (snow cover fraction is 0, so SD is high). Before quality control, because the snow cover fraction of many points equaled 0, the monthly average snow cover fraction was small (basically below 0.5), which led to an average monthly snow cover fraction of 0 and an average monthly SD above 50 cm. After quality control, such points were reduced, with a less “thick” graphic showing reduced points of SCF = 0 and large SD; these points accounted for only 0.3% of all grid points. Because of the quality control, fewer irrational snow grids were taken into the assimilation.
Figures 5a and 5b show the BIAS histogram of the SD from November 2013 to April 2014 before and after quality control. Clearly, the BIAS in Fig. 5a is mainly concentrated between −0.06 and 0.02 m, whereas the BIAS in Fig. 5b is mainly concentrated between −0.02 and 0.02 m; the large BIAS values are reduced, and the histogram distribution in Fig. 5b is closer to the normal distribution. It is believed that considerable erroneous snow data points with snow cover fraction of 0 and SD of large values were eliminated during the quality control process.
The FY-3 snow cover fraction assimilation results were evaluated and analyzed by using the MODIS snow cover fraction product. The FY-3 snow cover fraction assimilations with and without quality control (proposed in this paper) are denoted here as SCFDA_WSD and SCFDA, respectively.
Figure 6 shows distributions of the average snow cover fraction in northeastern China during the snow accumulation period (NDJ: November, December, and January) and the snowmelt period (FMA: February, March, and April) from November 2013 to April 2014. The MODIS snow cover fraction (Figs. 6a, d) shows that the snow cover in northeastern China was mainly concentrated in the western part of the Greater Khingan Mountains in Inner Mongolia and the eastern part of Heilongjiang Province. The snow cover fraction values were mostly within 40%–60%. It was lower in the snowmelt period than in the snow accumulation period. SCFDA_WSD in Figs. 6c, f reduces the snow cover overestimations in Heilongjiang and Jilin provinces. The magnitude and spatial distribution of SCFDA_WSD were more consistent with the observations than those of SCFDA in Figs. 6b, e.
Figure 6. Distributions of the average snow cover fraction (%) during the (a, b, c) snow accumulation period (NDJ: November, December, and January) and (d, e, f) snowmelt period (FMA: February, March, and April) in northeastern China. (a, d) MODIS observations, (b, e) SCFDA, and (c, f) SCFDA_WSD.
The BIAS and RMSE of the SCFDA snow cover fraction were large in northeastern China, and the improvement achieved by SCFDA in northeastern China (BIAS in Figs. 7a, b and RMSE in Figs. 8a, d) was insignificant. It is believed that erroneous snow information was assimilated, resulting in too much snow. In addition, the SCFDA_WSD result was significantly improved in northeastern China (see BIAS in Figs. 7c, d and RMSE in Figs. 8b, e), with reduced snow cover fraction in the overestimated areas and significantly decreased BIAS and RMSE. Compared with SCFDA, the BIAS of snow cover in SCFDA_WSD decreased from 0.0905 to 0.0806 (a decrease by 9.3%) and the RMSE decreased from 0.1782 to 0.1692 (a decrease of 5%). Compared with the Open Loop simulation (Figs. 8c, f), the RMSE of SCFDA_WSD decreased by 23%. When assimilating the snow cover fraction with an SD constraint (SCFDA_WSD), snow cover fraction estimates showed a substantially larger improvement than those produced by assimilating the snow cover fraction without quality control (SCFDA). The erroneous snow information in the FY-3 snow cover fraction was reduced with the FY-3 SD constraint.
Figure 7. BIAS distributions of average snow cover fraction (%) during the (a, c) snow accumulation period and (b, d) snowmelt period in northeastern China. (a, b) SCFDA and (c, d) SCFDA_WSD.
Figure 8. RMSE distributions of average snow cover fraction during the (a, b, c) snow accumulation period and (d, e, f) snowmelt period in northeastern China. (a, d) SCFDA, (b, e) SCFDA_WSD, and (c, f) Open Loop (OL, simulation).
Figure 9 shows the time series of the correlation coefficient (R) in Northeast China from December to March 2011–14. Compared with SCFDA, the R values of SCFDA_WSD are significantly improved during these periods. Especially after February, the improvement in R is obvious. Figure 9 shows that SCFDA_WSD has a significantly larger improvement than SCFDA.
The SD simulation results were evaluated against the station SD data. Figure 10a shows the time series of the average SD of the selected in-situ SD measurements (117 points) in northeastern China from November 2013 to April 2014. In some grids, the assimilated snow cover fraction may be inconsistent with the actual fraction at some stations, resulting in an abnormal SD. The SD BIAS in SCFDA_WSD was reduced more significantly than that in SCFDA, and SCFDA_WSD successfully improved the monthly SD RMSE from 0.055 m for SCFDA to 0.043 m for SCFDA_WSD; the RMSE decreased by 21.8%, while the correlation coefficient (R) improved from 0.673 for SCFDA to 0.710 for SCFDA_WSD.
The data assimilation performance was evaluated against the SD observations for different stages, land cover types, elevations, and snow depths. The left y axis of Fig. 11 represents the RMSE, and the right y axis represents the number of stations.
Figure 11. Histograms of the SD RMSE (SCFDA and SCFDA_WSD) for (a) each individual month, (b) various types of land covers, (c) various elevations, and (d) various SDs. The left y axis represents the RMSE, and the right y axis represents the number of in-situ SD measurements.
Figure 11a shows histograms of the relative RMSE in SCFDA and SCFDA_WSD for each individual month, demonstrating that the SCFDA errors typically started small in November and gradually increased each month to a peak in April. The relative RMSE of SCFDA_WSD was relatively stable. Overall, the SCFDA_WSD achieved significant improvements over SCFDA in terms of SD values during both the snow accumulation and snowmelt periods. The reduced RMSE of the FY-3 snow cover fraction with quality control resulted in a large reduction in errors of simulated SD for all months.
The data assimilation performance was also evaluated against the SD observations for cropland, shrubland, grassland, woodland, mixed land, and forest regions. Figure 11b shows the RMSE histogram for northeastern China from November 2013 to April 2014 for different land cover types. It can be seen that the SCFDA_WSD produced an improvement in SD than the SCFDA for all land cover types. Among the various land cover types, the improvements in woodland and shrubland were the most obvious. The vegetation coverage is the main factor that influences the snow distribution, and the snow cover on woodland and shrubland is scattered. The ability of remote sensing snow products to monitor shredded snow is not sufficient; therefore, SCFDA_WSD plays an important role in areas with low vegetation cover.
Figure 11c shows a histogram of the SD RMSE for the study region from November 2013 to April 2014 for different elevations. For different altitudes, the effect of SCFDA_WSD was basically equivalent. The assimilation of SCFDA_WSD drastically reduced the SD overestimation for all elevations, and the SD RMSE was significantly reduced. The results needed to be further analyzed because samples from higher than 1000 m were limited in this study.
Figure 11d shows a histogram of the SD RMSE for northeastern China from November 2013 to April 2014 for different SD ranges. The SCFDA_WSD significantly reduced the RMSE and achieved significantly greater improvements in SD than the SCFDA for all SD ranges. The deeper the SD, the better the effect of the SCFDA_WSD.
Figure 12 shows an SD time series for northeastern China from November 2013 to April 2014 for different land cover types. The data assimilation performance was significantly improved for all land cover types. The SCFDA_WSD successfully reduced the SD RMSEs of SCFDA for cropland, forests, grassland, mixed land, shrubland, and woodland (see Table 2 for specific values), respectively. In shrubland (Fig. 12e), where the SD BIAS increased early in January 2014, the SCFDA_WSD also improved, especially after January. Simultaneously, in the end of February 2014, the SD predicted by the SCFDA suddenly increased in the woodland (Fig. 12f), which should have been caused by a sudden increase in the observed snow cover fraction. These SD results were improved by the SCFDA_WSD. Of all land cover types, the improvements in SD for woodland and shrubland were the most obvious throughout the study period, and the SD results in forests were improved in the snow accumulation period.
Figure 12. Time series of mean SD in northeastern China from November 2013 to April 2014 for various land cover types: (a) cropland, (b) forest, (c) grassland, (d) mixed land, (e) shrubland, and (f) woodland
Land cover BIAS RMSE SCFDA SCFDA_WSD SCFDA SCFDA_WSD Cropland −0.0011 −0.0141 0.05924 0.04748 Forests 0.0258 0.0318 0.08596 0.07427 Grassland −0.0052 −0.0034 0.03440 0.02953 Mixed 0.0107 −0.0162 0.08591 0.05723 Shrubland 0.0216 0.0080 0.04979 0.02498 Woodland 0.0310 0.0089 0.10760 0.07743
Table 2. Statistics of average SD (m) for different land cover types in northeastern China from November 2013 to April 2014
Figure 13 shows the SD time series of Huadian in Jilin Province of China during this period. The SCFDA tended to underestimate the SD, but the SCFDA_WSD effectively produced a snow accumulation curve that was in better agreement with the observations, and the SCFDA_WSD performed very well because of a reduction in the number of erroneous snow cover fraction observations. In addition, the assimilation of the FY-3 snow cover fraction with quality control resulted in a marginal improvement in the snow ablation processes. This case shows that sudden snowfall can be well reflected by the SCFDA_WSD.
|Variable||Perturbation method||Standard deviation|
|Model states||SWE||Multiplicative||0.01 (–)|
|LW||Additive||15 W m–2|