An Optimal Interpolation–Based Snow Data Assimilation for NOAA’s Unified Forecast System (UFS)

Tseganeh Z. Gichamo aCooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado
bNational Oceanic and Atmospheric Administration/Earth System Research Laboratories/Physical Sciences Laboratory, Boulder, Colorado

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https://orcid.org/0000-0001-5377-9482
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Clara S. Draper bNational Oceanic and Atmospheric Administration/Earth System Research Laboratories/Physical Sciences Laboratory, Boulder, Colorado

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Abstract

Within the National Weather Service’s Unified Forecast System (UFS), snow depth and snow cover observations are assimilated once daily using a rule-based method designed to correct for gross errors. While this approach improved the forecasts over its predecessors, it is now quite outdated and is likely to result in suboptimal analysis. We have then implemented and evaluated a snow data assimilation using the 2D optimal interpolation (OI) method, which accounts for model and observation errors and their spatial correlations as a function of distances between the observations and model grid cells. The performance of the OI was evaluated by assimilating daily snow depth observations from the Global Historical Climatology Network (GHCN) and the Interactive Multisensor Snow and Ice Mapping System (IMS) snow cover data into the UFS, from October 2019 to March 2020. Compared to the control analysis, which is very similar to the method currently in operational use, the OI improves the forecast snow depth and snow cover. For instance, the unbiased snow depth root-mean-squared error (ubRMSE) was reduced by 45 mm and the snow cover hit rate increased by 4%. This leads to modest improvements to globally averaged near-surface temperature (an average reduction of 0.23 K in temperature bias), with significant local improvements in some regions (much of Asia, the central United States). The reduction in near-surface temperature error was primarily caused by improved snow cover fraction from the data assimilation. Based on these results, the OI DA is currently being transitioned into operational use for the UFS.

Significance Statement

Weather and climate forecasting systems rely on accurate modeling of the evolution of atmospheric, oceanic, and land processes. In addition, model forecasts are substantially improved by continuous incorporation of observations to models, through a process called data assimilation. In this work, we upgraded the snow data assimilation used in the U.S. National Weather Service (NWS) global weather prediction system. Compared to the method currently in operational use, the new snow data assimilation improves both the forecasted snow quantity and near-surface air temperatures over snowy regions. Based on the positive results obtained in the experiments presented here, the new snow data assimilation method is being implemented in the NWS operational forecast system.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tseganeh Z. Gichamo, zacctsega@gmail.com

Abstract

Within the National Weather Service’s Unified Forecast System (UFS), snow depth and snow cover observations are assimilated once daily using a rule-based method designed to correct for gross errors. While this approach improved the forecasts over its predecessors, it is now quite outdated and is likely to result in suboptimal analysis. We have then implemented and evaluated a snow data assimilation using the 2D optimal interpolation (OI) method, which accounts for model and observation errors and their spatial correlations as a function of distances between the observations and model grid cells. The performance of the OI was evaluated by assimilating daily snow depth observations from the Global Historical Climatology Network (GHCN) and the Interactive Multisensor Snow and Ice Mapping System (IMS) snow cover data into the UFS, from October 2019 to March 2020. Compared to the control analysis, which is very similar to the method currently in operational use, the OI improves the forecast snow depth and snow cover. For instance, the unbiased snow depth root-mean-squared error (ubRMSE) was reduced by 45 mm and the snow cover hit rate increased by 4%. This leads to modest improvements to globally averaged near-surface temperature (an average reduction of 0.23 K in temperature bias), with significant local improvements in some regions (much of Asia, the central United States). The reduction in near-surface temperature error was primarily caused by improved snow cover fraction from the data assimilation. Based on these results, the OI DA is currently being transitioned into operational use for the UFS.

Significance Statement

Weather and climate forecasting systems rely on accurate modeling of the evolution of atmospheric, oceanic, and land processes. In addition, model forecasts are substantially improved by continuous incorporation of observations to models, through a process called data assimilation. In this work, we upgraded the snow data assimilation used in the U.S. National Weather Service (NWS) global weather prediction system. Compared to the method currently in operational use, the new snow data assimilation improves both the forecasted snow quantity and near-surface air temperatures over snowy regions. Based on the positive results obtained in the experiments presented here, the new snow data assimilation method is being implemented in the NWS operational forecast system.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Tseganeh Z. Gichamo, zacctsega@gmail.com

1. Introduction

In addition to being an important water storage in winter and spring for a significant portion of the Northern Hemisphere, the presence and quantity of snow cover influences the atmosphere through energy and mass flux partitioning at the surface, e.g., through increased albedo, with snow acting as a thermal insulator over the ground, through the impact of frozen soil on evaporation, through reduced turbulent exchange roughness length, etc. (Davies 1994; Henderson et al. 2018; Zhang et al. 2021). In numerical weather prediction (NWP) models, snowpack dynamics are modeled by the land surface models (LSMs) that provide the lower boundary conditions for the atmosphere above. Errors are introduced into LSMs in global NWP systems due to errors in atmospheric forcing, imperfect representation of subgrid variabilities over the often-coarser grid resolutions (e.g., compared to hydrologic models in research), and inadequate parameters (Pomeroy et al. 1998; Prihodko et al. 2008; Wang et al. 2020). Data assimilation (DA) is used to reduce the impacts of these model errors, by combining model forecast states and observations to generate more accurate estimates of the model initial conditions for each forecast.

Within the National Weather Service (NWS), National Centers for Environmental Prediction (NCEP)’s NWP model, the Unified Forecast System (UFS), snow processes are simulated by the Noah LSM (Ek et al. 2003) and a snow depth analysis is performed once daily. The snow depth analysis (Meng et al. 2012) uses a simple rule-based process to assimilate the Air Force Weather Agency’s gridded snow depth (SNODEP) product (Kopp and Kiess 1996) and snow cover data from the National Oceanic and Atmospheric Administration (NOAA)’s National Environmental Satellite, Data, and Information Service, Interactive Multisensor Snow and Ice Mapping System (IMS; Helfrich et al. 2007).

The above snow data assimilation scheme is now quite outdated and is likely to result in suboptimal snow analysis, and most other major NWP centers have adopted more advanced snow data assimilation approaches. In particular, the more advanced approaches directly assimilate station snow depth observations (which tend to be of higher quality at a point compared to model simulations) rather than relying on externally produced gridded products that have ingested those station observations, such as the SNODEP product used at NCEP. Directly assimilating the station observations avoids introducing non-observed information (from the SNODEP analysis forecast model) into the Noah model, while also avoiding the unnecessary regridding and loss of spatial and temporal details of the station observations. It also allows for simpler observation error structures (specifically horizontal error covariances), and the ability to control the processing of the input observations. Most NWP centers use either optimal interpolation (OI) or Cressman interpolation schemes (Helmert et al. 2018). Notably, the European Centre for Medium-Range Weather Forecasts (ECMWF; de Rosnay et al. 2015), the Canadian Meteorological Centre (Brown et al. 2003), and the U.K. Met Office (Renshaw et al. 2018) all use the two dimensional (2D) OI scheme as formulated by Brasnett (1999) to assimilate station snow depth observations and remotely sensed snow cover. While both the OI and Cressman interpolation use weighting functions in terms of the horizontal and vertical distances between observations and model grid cells, the OI accounts for model background and observations errors, and has been shown to result in smoother snow fields than the Cressman approach (de Rosnay et al. 2014).

Compared to the data assimilation methods applied to the snow updates within NWP, the data assimilation methods applied to the atmospheric component of NWP models are more sophisticated, with most NWP centers now using one of a range of hybrid methods combining Variational and Ensemble-based methods (Bonavita et al. 2016; Houtekamer and Zhang 2016; Huang et al. 2021; Kleist and Ide 2015; Lorenc et al. 2015). Likewise, offline (land-only) LSMs and hydrologic systems also tend to use more sophisticated methods. In particular, Monte Carlo–based methods, such as the ensemble Kalman filter (EnKF), are generally preferred (Abbaszadeh et al. 2020; Draper et al. 2012; Reichle et al. 2021), including for snow DA (e.g., Clark et al. 2006; Franz et al. 2014; Gichamo and Tarboton 2019; Kumar et al. 2020; Li et al. 2017; Liu et al. 2013; Micheletty et al. 2021). Within the offline land modeling community, these methods are favored because they provide flexibility in representing the background error covariances, are comparatively robust to the nonlinearities inherent in land surface processes, and result in satisfactory, albeit usually suboptimal, DA outcomes (Draper and Reichle 2019; Zhou et al. 2006). However, the EnKF-type approaches have not yet been adopted for snow data assimilation in NWP systems, due at least in part to the difficulty of adequately representing the model errors within an NWP system.

This paper details recent work to modernize the UFS snow data assimilation scheme. The first stage of this work, which is reported here, is to implement a 2D OI snow depth analysis for the assimilation of station snow depth and satellite snow cover observations. This is currently state-of-the-art in NWP systems, and is a significant advance over the existing snow DA at NCEP. The second stage, to be investigated in future work, is to implement an EnKF-type snow depth analysis. The OI implemented here will provide a benchmark against which to evaluate the EnKF-type snow depth assimilation as an alternative approach to assimilating the same observations.

Here, the OI has been tested by assimilating daily snow depth observations from the Global Historial Climatology Network (GHCN, https://www.ncei.noaa.gov/products/land-based-station/global-historical-climatology-network-daily) and the IMS (U.S. National Ice Center 2008, updated daily) snow cover data into the global UFS model. Our OI design is based on Brasnett (1999), which is the state-of-the-art snow DA method used for NWP as stated above. The objective of this paper is to show that the new OI scheme improves the initial snow states used in the UFS, compared to the current assimilation scheme, and to demonstrate that this leads to the expected improvements in UFS forecasts of near surface atmospheric variables. In section 2, we introduce the model, the current and proposed OI-based data assimilation methods, and the assimilated observations. In section 3, we provide the experimental setup and the evaluation metrics. Results and discussion are presented in section 4, followed by summary and conclusions in section 5.

2. Data and methods

a. The snow model in the UFS LSM

The operational land surface model in NCEP’s UFS is the Noah LSM (Ek et al. 2003) which simulates snow water equivalent (SWE) and snow depth (SND) in a single bulk snow layer, accounting for snowfall, snow–atmosphere and snow–soil interface heat exchanges, sublimation, snowmelt, and compaction (Chen and Dudhia 2001; Ek et al. 2003; Wang et al. 2010). The snowpack and frozen ground simulations are based on the simple parameterizations of Koren et al. (1999). Snowpack density, which influences the thermal conductivity of snow and the calculation of SND from SWE, is simulated as a time-varying function of snow compaction and new snowfall. Snow cover is a model diagnostic, calculated as a function of SWE and vegetation type. The diagnosed snow cover is primarily used as input into the model radiation physics, to determine the energy flux in the grid cell as a function of the contributions from non-snow and snow-covered ground.

b. Current snow analysis

The current snow depth analysis at NCEP relies on an externally produced gridded snow depth analysis, SNODEP, and the IMS snow cover product (Meng et al. 2012). First, the SNODEP product is quality controlled with IMS snow cover to produce an intermediate snow depth product. If IMS indicates no snow, then the snow depth is set to 0.0 cm; if IMS indicates snow, then the snow depth is set to the greatest of the SNODEP depth or 2.5 cm. Next, this quality controlled SNODEP snow depth product is merged with the model snow depth. The model snow depth forecast is retained unchanged if it is between half and 2 times the SNODEP snow depth; if the model forecast snow depth is less than half the SNODEP snow depth, then it is set to half the SNODEP snow depth; and if the model forecast snow depth is more than 2 times the SNODEP snow depth, then it is set to 2 times the SNODEP value. Once the SND analysis is obtained as above, the SWE is recomputed using an assumed snow density, described in Meng et al. (2012) as being the snow density in the model forecast.

Note that as currently implemented, the operational snow analysis at NCEP uses a constant snow density, rather than the model forecast density to calculate SWE from SND (Dawson et al. 2016). As shown by Dawson et al. (2017) and Draper et al. (2021), the snowpack analysis is improved by using the snow density from the model forecasts in place of this constant density. Hence, the Control experiment against which the OI was compared in this study is the experiment of Draper et al. (2021), in which the model forecast snow density is used (while for snow added where none was present in the forecast, the density of falling snow is used). Other than this change, the Control snow analysis in this work is the same as is used operationally.

c. Optimal interpolation snow DA

The proposed framework for the new OI based DA is shown in Fig. 1. The OI is implemented as a univariate analysis, performed on the snow depth, and is based on the snow analyses used at other NWP centers (Brasnett 1999; de Rosnay et al. 2015). The OI spatially propagates information from observation points to model grid cells by accounting for spatial error correlations and model and observation error covariances.

Fig. 1.
Fig. 1.

Framework for the new OI based DA for Noah LSM in UFS.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

The background snow depth, in each model grid cell i, is updated using the observations that fall within the radius of influence (i.e., observation points in close enough proximity of the model grid cell, with the radius of influence determined empirically by the likelihood of the snow depth at a point to be correlated to that at a distant location). Specifically, the analysis increment (dX) at each grid cell is computed as the weighted sum of the innovations, where the innovations are the difference between observed and model states at the observation locations (Xo and Xb, respectively):
Xa=Xb+dX,
dX=W(XoXb),
where Xa is the analysis, and W contains the optimal weights, computed from the background error covariances (b and B), and observation error covariances (O):
W=b(B+O)1,
B=σb2ρjk,
b=σb2ρij,
O=σo2I,
where σb is the background error standard deviation, σo is the observation error standard deviation, ρjk is the background error correlation between observation points j and k, ρij is the background error correlation between model grid i and observation point j, and I is the identity matrix.
The observation errors at different locations are assumed uncorrelated. The background error covariances account for spatial correlations, which have horizontal [α(rjk)] and vertical [β(zjk)] components (Brasnett 1999; de Rosnay et al. 2015):
ρjk=α(rjk)β(zjk),
α(rjk)=(1+rjkL)exp(rjkL),
β(zjk)=exp[(zjkh)2],
where rjk is the horizontal distance between points j and k, zjk is the elevation difference between points j and k, L is the specified horizontal error correlation length scale, and h is the specified vertical error correlation length scale.

The error correlation lengths L and h, the background and observation error standard deviations (σb and σo), the radius of influence, and the background state search radius were adopted from well-established values used elsewhere (Brasnett 1999; de Rosnay et al. 2015) and are shown in Table 1. Note that, in Table 1, the 30-mm background error standard deviation is smaller than the error standard deviations of both observations (40 mm for GHCN and 80 mm for IMS). The relatively large observation errors were chosen for pragmatic reasons, to prevent too large increments given that there is a discrepancy in support scales of the point observations and the gridded model states. The observed snow depth at a point is likely more reliable than the model simulated snow depth at that point, but the station snow depth is used to update the average snow depth over a coarser grid cell. For the IMS observation, the conversion of snow cover to corresponding snow depth using the depletion curve adds to the uncertainty in the assimilated values.

Table 1

OI DA parameters, including QC parameters.

Table 1

d. Observations

1) Station-based snow depth observations

In the current study, we assimilated GHCN-Daily snow depth observations (https://www.ncei.noaa.gov/products/land-based-station/global-historical-climatology-network-daily). GHCN-Daily is a global station-based dataset that is updated daily and is subjected to extensive quality control. GHCN incorporates observations that are carried out automatically as well as manually (with human operators). The time of the day at which the observations are taken varies, and the observation times are not consistently reported. Hence, we assimilate the observations once daily at 1800 UTC, irrespective of the actual measurement time. While the number of daily observations varies (e.g., human operators may not record measurements when there is no snow on the ground), the average number of daily GHCN observations is in the order of 10 000. The GHCN snow observations have good coverage over the United States, but are sparser going northward to Canada, and across Europe, as shown by the map of GHCN observations for 15 December 2019 in Fig. 2.

Fig. 2.
Fig. 2.

GHCN observations on 15 Dec 2019.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

For operational NWP, station snow depth data would be obtained in real time through the Global Telecommunication System (GTS). However, at the time of writing, station snow depth was not downloaded from the GTS at NCEP, so GHCN data were used as a proxy for the GTS station observations. At ECMWF, snow depth observations from nearly 4000 stations from the GTS are assimilated 4 times daily (map on page 3 of de Rosnay et al. 2015). Also, de Rosnay et al. (2015) show the very limited GTS coverage over the United States, while GHCN has extensive U.S. coverage (Fig. 2) due to the inclusion of several U.S. national networks. The GTS observations have denser coverage across Europe due to the inclusion of various national observation networks not included in GHCN. NCEP is developing the infrastructure to download the GTS snow observations for future use, and also to add the available near real-time U.S. national snow depth observing networks to the GTS (J. Ator 2021, personal communication).

2) Snow cover observations

For snow cover, we use the same 4-km IMS (https://nsidc.org/data/g02156) snow cover data (Helfrich et al. 2007) as is used in NCEP’s current snow DA scheme. IMS snow cover is produced by analysts at U.S. National Ice Center (USNIC, and by NOAA/NESDIS before 2008) by merging a variety of input data sources including optical remote sensing and station-based snow analysis products.

As implemented, the OI is a univariate analysis, and the data assimilation is performed in terms of SND followed by an update of the SWE from the SND update and snow density. To assimilate the IMS snow cover observations, we convert the snow cover data to an equivalent SND following the steps in Fig. 3a. First the IMS observations are mapped to the UFS model grid cells. Then, for each model grid cell, we compute the snow cover fraction (SCF) as the ratio of the number of snow-covered IMS grid cells to the total number of IMS grid cells, based on all of the IMS (4 km) grid cells within that model grid cell. Note that the precision of the resulting SCF is dependent on the model grid size: at C768 grid (∼13 km), there are approximately 9 IMS grid cells in each UFS model grid cell, giving a SCF precision of about 10%.

Fig. 3.
Fig. 3.

Obtaining snow water equivalent (SWE) from IMS snow cover data. (a) Steps to generate model gridcell SWE from IMS binary snow/nonsnow observations; (b) Noah model snow areal depletion curve, relating gridcell-average SWE to SCF for two SWEt values; and (c) inverse of the snow depletion curve for the ratio of SWE to SWEt, calculated numerically using the full exponential equation (orange), and analytically with the truncated equation (blue).

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

Next, to obtain snow depth from the SCF, we use an inversion of the snow areal depletion curve (Koren et al. 1999; Livneh et al. 2010) that is used in the Noah model to diagnose SCF from SWE. Figure 3b shows an example snow depletion curve, in which the SCF is calculated from the ratio between the gridcell average SWE and the threshold SWE (SWEt) defined for the given vegetation type. The threshold SWE is the value of SWE beyond which the grid cell is fully covered by snow (SCF = 100%), and depends on the characteristics of the grid cell such as the land cover/vegetation type (Ek et al. 2003; Koren et al. 1999).

Curves for two vegetation types, based on the International Geosphere–Biosphere Programme (IGBP) Land Classification (https://climatedataguide.ucar.edu/climate-data/ceres-igbp-land-classification) are shown in Fig. 3b, with forest cover such as evergreen needleleaf land cover having a SWEt of 80 mm and Grasslands having SWEt of 20 mm. The smoother surfaces such as those with grass or bare land reach 100% snow cover faster and have lower threshold SWE than forests (Livneh et al. 2010). We use an approximate inverse of the exponential equation for the depletion curve, shown in Fig. 3c, to map the IMS SCF to the equivalent SWE value. The rightmost term of the exponential equation was truncated to obtain an analytically invertible approximation to the snow depletion curve. Figure 3c shows two curves, one for the full exponential function and another one with the rightmost term truncated. Truncating the right most term has a limited impact. Finally, the IMS-derived SWE is then converted to an IMS-derived SND using the ratio of density of water (ρw) to that of snow (ρs), calculated from the model forecast SND and SWE:
ρwρs=SNDSWE.

As previously noted, this approach is similar to the snow data assimilation schemes used in other NWP centers that convert snow cover observations into a model prognostic state (i.e., snow depth) before they are assimilated (de Rosnay et al. 2015). One distinction here from the scheme at ECMWF (de Rosnay et al. 2015) is that we compute the SCF from all IMS observations falling within model grid cell, which is then translated into a single, model gridcell specific snow depth.

3) Observation quality control

At each grid cell, the GHCN-Daily snow depth observations within the radius of influence and a single IMS snow depth corresponding to the gridcell snow cover are assimilated, after applying the following quality control (QC):

  • Exclude snow depth observations with too large a deviation from the model background state, based on the following criteria:

|dX|>γσb2+σo2.

The observation tolerance γ = 5 is adopted from de Rosnay et al. (2015):

  • A maximum of 50 station snow depth observations is used per grid cell.

  • Exclude IMS observations at model grid cells with elevations greater than 1500 m (de Rosnay et al. 2014).

  • Exclude IMS observations where both the forecast and observations indicate that the grid cell is fully snow-covered, i.e., when both the IMS and model SCF is 100%. This criterion is necessary since the snow cover observations cannot detect changes in SWE once the 100% threshold has been exceeded.

3. Experimental setup and evaluation metrics

In this section, we introduce the DA experiments and the error statistics and skill scores we used to evaluate them.

a. Cycling DA in the Global Unified Forecast System (Global UFS)

The OI was used to assimilate GHCN-Daily snow depth and IMS snow cover observations into NCEP’s cycling UFS system, to test the impact of the OI snow DA on the snow forecasts and low-level atmospheric forecasts. This experiment was run from 1 October 2019 to 31 March 2020 on the C128 (∼1°) model grid with 64 vertical levels, using an experimental setup designed to mimic the GEFSv12 Reanalysis (FV3-UFSv15, with EnKF assimilation of the standard suite of atmospheric observations; Hamill et al. 2022).

As the primary goal of this study is to test the impact of the snow DA for NWP, we opted to assimilate all available GHCN-Daily and IMS data (rather than to exclude some observations for later use in evaluation) so as to be able to measure the full impact of the assimilation on the atmosphere. We evaluated the resulting snow depth and snow cover by examining the impact of each DA method on the 24-h snow forecast using the observed minus forecast (OF) assimilation statistics (or the equivalent, calculated for the Control forecasts). While this is not a fully independent evaluation, the OF statistics provide a measure of the extent to which each assimilation improves the consistency between the model forecasts and the assimilated observations. Note that the control analysis ingests IMS snow cover and SNODEP, with the latter calculated from input station-based snow depth observations. While the stations included in SNODEP are not well documented, it is likely that there is considerable overlap with the GHCN datasets, hence the OF statistics are unlikely to be independent for the Control experiment either.

To evaluate the 2-m temperature (T2m) and specific humidity (q2m) outputs from this experiment, we compare them to the T2m and q2m from the ECMWF Reanalysis v5 (ERA5) over snow affected land, where “snow affected land” is defined as land (non-glacier, non-water) grid cells that have snow at least once during the modeling period, as detected by the IMS observations. We use the ERA5 6-hourly analysis output only, in which the 2-m fields are the output from a 2D OI assimilation of 2-m temperature and relative humidity (Hersbach et al. 2020). While the 2-m analysis includes model information from the background fields, it remains a good option for this evaluation as it is a uniquely high-quality observation-based gridded dataset.

b. Evaluation metrics

When comparing model snow depths to station-based observed snow depths, we compute error metrics bias, mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), root-mean-squared error (RMSE), and the unbiased RMSE (ubRMSE). For the T2m and q2m comparison to the ERA5 reanalysis, we compute the bias, RMSE, and ubRMSE for each DA method. Bias, MAE, RMSE are widely reported over hydrometeorological (and other) literature; the NSE and ubRMSE are defined as follows:
NSE=1iN(OiMi)2iN(OiO¯)2,
ubRMSE=1NiN[(MiM¯)(OiO¯)]2,
where M and O refer to model and observed snow depths, and the overbars are the averages, over N observation locations.
For snow cover evaluation, the skill scores for accuracy, hit rate, miss rate, false alarm ratio, and correct rejection rate are computed against the IMS SCF. We compute the analysis skill scores as defined in Eqs. (14)(18) (Wilks 2011). The hits (A), misses (C), false alarms (B), and correction rejections (D) in these equations are determined by classifying each model grid cell into one of the four cells in the contingency Table 2. A grid cell is classified as snow-covered or not snow-covered based on a 50% SCF threshold:
accuracy=(A+D)/(A+B+C+D),
hitrate=A/(A+C),
missrate=C/(A+C),
falsealarmratio=B/(A+B),
correctrejectionrate=D/(B+D).
Table 2

Contingency table for computation of skill scores against IMS snow cover observation.

Table 2

Because the overwhelming area of the globe is either waterbody or snow-free land, a global evaluation would be dominated by the “correct rejection” category. To avoid this, the skill scores were calculated using only model grid cells where IMS has detected snow at least once during the experiment period.

4. Results and discussion

a. Evaluation of snow depth and cover

Figure 4 plots the snow depth observed minus forecast (OF) statistics, comparing the model background to the observations prior to assimilation, in terms of MAE, NSE, RMSE, and the ubRMSE. The temporally averaged error statistics are summarized in Table 3, including confidence intervals calculated using the bootstrap resampling method. The OI has improved the OF statistics for the 24-h forecast snow after assimilation, which indicates that the assimilation is bringing the model forecasts closer to subsequent observations and is improving the model snow depth states.

Fig. 4.
Fig. 4.

MAE, NSE, RMSE, and ubRMSE of the 24-h forecast snow depth compared to the GHCN observations for the cycling DA on C128 grid.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

Table 3

Time average of OF statistics for the 24-h forecast snow depth compared to the GHCN observations for the cycling DA on C128 grid. Values in brackets below each statistic are the 95% confidence intervals, computed by using bootstrap resampling. The best experiment for each statistic is in bold.

Table 3

From Fig. 4 and Table 3, the OI DA has drawn the forecasts closer to the GHCN observations than the Control, with significant improvement in all of the statistics in Table 3. Specifically, the bias (6.3 mm), MAE (26.5 mm), NSE (0.68), and ubRMSE (85.1 mm) of the OF are all significantly improved, compared to the Control OF (18.7, 49.9, 0.25, and 130.4 mm, respectively). This suggests the OI DA, that directly assimilates observations while accounting for the spatial correlations between observation and background errors, makes better use of the available observation information than the Control method (SNODEP analysis plus rule-based merging into model). Maps of snow depth forecast, analysis and analysis increments (not shown) also indicate that the spatial structures/patterns of the OI analysis snow depths appear smooth, with few obvious discontinuities, even in places like the mountainous western United States where the complex terrain results in mixture of positive and negative innovations in close proximity with each other.

Likewise, the snow cover skill scores for each experiment calculated against the IMS SCF, are shown in Fig. 5 and Table 4. Forecasts from the OI DA experiments have accuracy, hit rate, and miss rate of 92.3%, 90.7%, and 9.3%, respectively, improving on the Control (91.6%, 86.8%, and 13.2% respectively). Meanwhile, the false alarm ratio and correct rejection rate are 7.3% and 91.2% for the OI, both a degradation from the Control (6.0% and 93.7%, respectively). Overall, the 24-h forecasts from the OI DA are closer to the IMS observations when the observations indicate snow, while the Control forecasts are closer to IMS when the observations indicate no snow. This difference can be traced to the assimilation algorithms. The first result likely occurs because the Control DA method only corrects the snow when the errors are relatively large. Meanwhile the second result occurs because the Control DA method corrects the forecast snow depth to the SNODEP snow depth if the forecast snow depth is more than double the SNODEP value. If the SNODEP snow depth is 0 mm (because IMS indicated no snow), the Control analysis output will be 0 mm, regardless of the forecast value. By contrast, for a 0-mm IMS snow depth, the OI analysis would adjust the model snow depth toward 0 mm, by an amount determined by the OI’s model and observation errors.

Fig. 5.
Fig. 5.

Forecast snow-cover skill scores against IMS snow-cover observations for cycling DA on C128 grid.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

Table 4

Time average of skill scores of forecast snow cover against IMS snow cover observations for cycling DA on C128 grid. Values in brackets below each score are the 95% confidence intervals, computed by using bootstrap resampling. The best experiment for each statistic is in bold.

Table 4

In summary, the OI DA results in forecasts with a better match to GHCN observations compared to the Control, while the comparison in terms of snow cover fraction is mixed—the new OI DA draws the 24-h forecast closer to the subsequent IMS observations than the Control does in situations where the background underestimates snow cover, while the Control draws the forecasts closer when the background snow cover is overestimated.

b. Evaluation of 2-m temperature

Figure 6 shows plots of bias, RMSE and the ubRMSE for the T2m over snow affected land for the Control and the OI DA forecasts, with each statistic compared to the ERA5 outputs. These statistics are summarized in Table 5. These plots and the statistics were calculated using data at 0000, 0600, 1200, and 1800 UTC for each day of the experiment period, to average out the diurnal cycle (although the sign of the differences was relatively consistent throughout the diurnal cycle). Figure 6 shows that the OI DA results in a significant reduction in the T2m bias. In general, the control has a warm temperature bias, compared to the ERA T2m, which was reduced in the OI analysis. While the spatially averaged reductions in the 2-m temperature RMSE and ubRMSE by the OI DA were modest, there are some relatively large local improvements (up to by 0.3 K, shown in Fig. 7). The error statistics of 2-m specific humidity (q2m) were similar for both the Control and OI, likely because the main impact of snow on the atmosphere is via the radiation and thermal properties of the surface, rather than on moisture transport such as snow sublimation.

Fig. 6.
Fig. 6.

T2m bias, RMSE, and ubRMSE over snow-affected land, compared to the ERA5 reanalysis.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

Table 5

Global 2-m temperature (T2m) error statistics for snow covered land. Values in brackets below each statistic are the 95% confidence intervals, computed by using bootstrap resampling. The best experiment for each statistic is in bold.

Table 5
Fig. 7.
Fig. 7.

Temporally averaged bias, MAE, RMSE, and ubRMSE in T2m, computed against ERA-5 for the Control and OI DA, and their differences. These are computed from model and observations (ERA5) at 0000, 0600, 1200, and 1800 UTC for each day between 1 Oct 2019 and 31 Mar 2020.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

In Fig. 7, maps of the temporally averaged T2m bias, MAE, RMSE and ubRMSE, computed against ERA5, are shown. Also, the differences between these statistics for the OI and Control DA are included. For each statistic, the regions where the OI analysis performs better than the Control analysis (blue colors for the difference plots in Fig. 7 over much of Asia and the central United States) are generally larger than the regions where the Control analysis has better performance (red colors for the difference plots in northern Canada, northern Asia, and some isolated pockets of Asia). As in Fig. 6, the differences in the bias are larger than those in the ubRMSE. The OI improves the model T2m biases because the assimilation is adjusting the model mean toward the observed mean. Even though, the OI data assimilation algorithm is not optimized to improve the model mean values, changes to the mean will be beneficial in instances when the observed mean is more accurate than the modeled mean. In this study, a priori, our expectation was that the IMS snow cover observations are closer to the true mean snow cover fraction than the model is (since the UFS modeled SCF has not been carefully evaluated and has considerable uncertainty, while IMS is a very well established and fine-tuned product that is being used widely).

Figure 8 then shows maps of mean T2m and mean snow cover fraction for each experiment, and the differences between the two experiments. This figure shows the expected negative correlation between changes in the mean T2m and changes in the mean snow cover fraction (and snow depth), with increased snow cover associated with decreased temperatures (and vice versa). This is the cause of the strong spatial correlation between the change in T2m bias (OI analysis bias − Control analysis bias) in Fig. 7, and the change in snow cover (OI analysis SCF − Control analysis SCF) in Fig. 8 (average value of −0.85). Maps of the change in mean snow depth appear qualitatively similar, with a correlation of −0.53. The stronger correlation to the changes in mean T2m for snow cover suggests that it is primarily the change in the snow cover, rather than the change in snow depth, that has contributed to the reduction in the T2m biases in the OI DA. This is consistent with the findings of Draper et al. (2021), in which differences in snow depth but not snow cover had little impact on the 2-m temperature. Note that, while the largest reductions in the T2m bias follow an increase in snow cover (and cooling of temperatures), there are areas (especially in the center of the United States) where snow removal corresponds to reductions in MAE, RMSE and ubRMSE. The small improvements in T2m skill obtained here are consistent with the changes expected from assimilating new observations and/or updating the DA methods used in an NWP system, given the already very large number of observations that are assimilated. For example, similar magnitudes of improvements were obtained by Gómez et al. (2020) and de Rosnay et al. (2015) when upgrading the land DA used within their respective NWP systems.

Fig. 8.
Fig. 8.

Temporally averaged 2-m temperature (T2m) and snow cover fraction for the Control and OI analyses, and their difference. These are computed at 0000, 0600, 1200, and 1800 UTC for each day between 1 Oct 2019 and 31 Mar 2020.

Citation: Weather and Forecasting 37, 12; 10.1175/WAF-D-22-0061.1

Taken together, our a priori expectation that the mean IMS SCF is more accurate than the model, the strong correlations between change in mean SCF and change in mean T2m, and the improved mean T2m, strongly suggest that the OI has improved the representation of snow/atmosphere processes in the analysis.

5. Summary and conclusions

An optimal interpolation (OI)-based data assimilation scheme was developed to improve the snowpack and near surface atmospheric forecast in the NOAA’s Unified Forecasting System (UFS), as a first step toward improving the current snow analysis. In our experiments with the UFS over the 2019/20 boreal winter, the statistics for the observed minus forecast (OF), between the 24-h forecasts and the station snow depth observations before assimilation, were significantly improved by the OI, compared to the Control DA method (a slightly improved version of the current snow analysis method at NCEP). Comparison against the IMS observed snow cover data demonstrated that the OI based forecast had a significantly better fit to the assimilated observations for the hit rate and miss rate while the false alarm ratio and correct rejection rate are degraded in the OI compared to the Control, suggesting that the new data assimilation performs well in adding snow where the forecast fails to detect observed snow.

In addition, the OI reduced the magnitude of the T2m biases, compared to the Control DA. Overall, the model forecast has a warm T2m bias, and the OI reduced this better than the Control. Comparison of the spatial pattern of the T2m field and the change in snow cover/depth field by the OI DA shows that the reduction of the warm bias by the new OI DA follows the increase in snow cover/depth by the OI DA. In addition, the largest reductions in the T2m bias follow an increase in snow cover (and cooling of temperatures). However, the pattern was more complex for the other error stats such as the ubRMSE.

Combined with the small improvements in the T2m ubRMSE and the (often significant) improvements to the snow OF statistics, this is an overall positive result, particularly since achieving improved land surface states through land DA has not consistently led to the expected improvements in atmospheric forecasts. In many cases, land DA has been shown to improve the land states, while degrading atmospheric and/or streamflow forecasts (Crow et al. 2020; Muñoz‐Sabater et al. 2019; Zsoter et al. 2019), to the extent that this has been a barrier to operational implementation of land DA within NWP (Belair et al. 2019). Based on these results, we are proceeding with implementing the snow depth OI in NCEP’s operational global NWP system. The OI has been converted into the Joint Center for Satellite Data Assimilation’s Joint Effort for Data Assimilation Integration (JEDI) software framework, and is being prepared for final testing for operational use in NCEP’s global NWP systems (Dong et al. 2022; Draper et al. 2022).

This work is intended as first step toward investigating the use of an EnKF for the UFS snow analysis, and the OI presented here will be used as a benchmark against which to compare the EnKF in the future. Note that the OI update equation has a similar form to the EnKF (and most Kalman filters). In both the OI and EnKF assimilation updates, the model states in each grid cells are updated using observations within the radius of influence. The major difference is that the error covariances in the EnKF are estimated from the background state ensembles, usually convoluted with a localization function, while in the OI a spatial background error correlation function is assumed. The results for the OI obtained here confirm that the spatial error correlations that were assumed were sufficient for a successful analysis, which is not surprising considering that topography is a significant determinant of snow spatial variability.

While the EnKF is a more sophisticated algorithm than OI, further tests are needed to determine whether it can improve snow depth analyses. In theory, we would expect an ensemble to be able to provide more accurate representation of the model errors (and in particular to be able to represent errors of the day); however, in practice it can be very difficult to generate and maintain ensembles with reasonable forecast error structures. Another potential advantage of the ensemble approach is that it can more easily handle different input variable types. Here, we relied on the current formulation of the snow areal depletion curve in the model to convert the observed snow cover into snow depth before assimilating it. Ensemble filters such as the EnKF, which compute these relationships from the ensemble covariances, could directly assimilate the SCF information by relying on the ensemble correlations between the SCF and snow depth.

Acknowledgments.

We thank Jeffrey S. Whitaker (NOAA/PSL) and Laura C. Slivinski (CIRES and NOAA/PSL) for their constructive feedback to the draft manuscript. We are very grateful to the anonymous reviewers whose constructive comments have helped to substantially improve the paper. This research was supported by NOAA cooperative agreements NA17OAR4320101.

Data availability statement.

Output from all experiments is currently archived at NOAA’s National Environmental Security Computing Center, and can be made available by contacting the authors. The GHCN daily snow depth observations were accessed from https://www.ncei.noaa.gov/pub/data/ghcn/daily/, and the IMS snow dover data are available at https://nsidc.org/data/g02156.

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  • Abbaszadeh, P., K. Gavahi, and H. Moradkhani, 2020: Multivariate remotely sensed and in-situ data assimilation for enhancing community WRF-Hydro model forecasting. Adv. Water Resour., 145, 103721, https://doi.org/10.1016/j.advwatres.2020.103721.

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    • Search Google Scholar
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    • Search Google Scholar
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  • Clark, M. P., A. G. Slater, A. P. Barrett, L. E. Hay, G. J. McCabe, B. Rajagopalan, and G. H. Leavesley, 2006: Assimilation of snow covered area information into hydrologic and land-surface models. Adv. Water Resour., 29, 12091221, https://doi.org/10.1016/j.advwatres.2005.10.001.

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    • Export Citation
  • Crow, W. T., and Coauthors, 2020: Soil moisture–evapotranspiration overcoupling and L-band brightness temperature assimilation: Sources and forecast implications. J. Hydrometeor., 21, 23592374, https://doi.org/10.1175/JHM-D-20-0088.1.

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  • Fig. 1.

    Framework for the new OI based DA for Noah LSM in UFS.

  • Fig. 2.

    GHCN observations on 15 Dec 2019.

  • Fig. 3.

    Obtaining snow water equivalent (SWE) from IMS snow cover data. (a) Steps to generate model gridcell SWE from IMS binary snow/nonsnow observations; (b) Noah model snow areal depletion curve, relating gridcell-average SWE to SCF for two SWEt values; and (c) inverse of the snow depletion curve for the ratio of SWE to SWEt, calculated numerically using the full exponential equation (orange), and analytically with the truncated equation (blue).

  • Fig. 4.

    MAE, NSE, RMSE, and ubRMSE of the 24-h forecast snow depth compared to the GHCN observations for the cycling DA on C128 grid.

  • Fig. 5.

    Forecast snow-cover skill scores against IMS snow-cover observations for cycling DA on C128 grid.

  • Fig. 6.

    T2m bias, RMSE, and ubRMSE over snow-affected land, compared to the ERA5 reanalysis.

  • Fig. 7.

    Temporally averaged bias, MAE, RMSE, and ubRMSE in T2m, computed against ERA-5 for the Control and OI DA, and their differences. These are computed from model and observations (ERA5) at 0000, 0600, 1200, and 1800 UTC for each day between 1 Oct 2019 and 31 Mar 2020.

  • Fig. 8.

    Temporally averaged 2-m temperature (T2m) and snow cover fraction for the Control and OI analyses, and their difference. These are computed at 0000, 0600, 1200, and 1800 UTC for each day between 1 Oct 2019 and 31 Mar 2020.

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