1. Introduction
Accurate numerical weather prediction (NWP) with convection-allowing models over continent-scale or larger domains requires initial conditions (ICs) that accurately represent the atmospheric state containing scales ranging from the planetary through synoptic and mesoscale to the convective scales. Therefore, a well-performing data assimilation (DA) system should be able to accurately analyze flow features and corresponding uncertainty across multiple scales. The current operational High-Resolution Rapid Refresh (HRRR; Alexander 2021; Dowell et al. 2022; Weygandt et al. 2022) forecast system of the U.S. National Weather Service (NWS) has a 3-km grid spacing and covers the contiguous United States (CONUS). The next-generation regional forecasting system of the NWS, the Rapid Refresh Forecast System (RRFS; Alexander 2021; Banos et al. 2022), based on the Finite-Volume Cubed-Sphere Dynamical Core (FV3; Putman and Lin 2007), will cover a much larger North American domain at a 3-km grid spacing. The larger domain of RRFS means that an even wider range of scales can be represented by the model, and all these scales need to be properly initialized in the IC.
The Gridpoint Statistical Interpolation analysis system (GSI; Kleist et al. 2009) DA system is currently used by all operational forecast models at the National Centers for Environmental Prediction (NCEP). Variants of the ensemble Kalman filter (EnKF; Evensen 1994) are used to produce ICs for ensemble forecasting systems such as the Global Ensemble Forecast System (GEFS; Toth and Kalnay 1997) and to provide ensemble perturbations for the hybrid ensemble–variational (EnVar) algorithm within the GSI framework. The latter provides ICs for deterministic forecasts, including the Global Forecast System (GFS) and HRRR. The GSI DA system, including its EnKF and hybrid EnVar algorithms, will also be used by the first operational implementation of RRFS. For large-domain convection-allowing forecasting systems like RRFS, observations representing a wide range of scales, including upper-air soundings (sampling mostly synoptic scales), surface observations (sampling mostly mesoscales), and radar observations (sampling mostly convective scales), will be assimilated together.
Multiscale DA has been the subject of a number of studies, mostly in the variational frameworks (Buehner 2012; Li et al. 2015). Li et al. (2015) formulated a multiscale DA scheme in a three-dimensional variational data assimilation (3DVar) framework that aims at high-resolution models. The scheme decomposes the original cost function into two or more components for different scales of analysis increments; the total analysis increment is the sum of increments obtained by minimizing these individual cost functions. A key aspect of the scheme is the partitioning of the background error covariance (BEC) into components estimated separately for distinct spatial scales incorporating multiple decorrelation scales. Such multiscale BEC enhances the spreading of sparse observations and prevents fine-scale structures in high-resolution observations from being overly smoothed.
In ensemble-based DA methods such as the ensemble Kalman filter, flow-dependent BECs derived from limited-size ensembles are rank deficient, resulting in spurious correlations between grid points at large distances; covariance localization is commonly used to alleviate this problem. Various treatments have been proposed to include some consideration of the multiscale nature of either observations or background correlations. Zhang et al. (2009) proposed a successive covariance localization method which uses different localization radii for several batches of observations grouped by random sampling. They initially tested it with EnKF assimilation of radar radial velocity for hurricanes by using three localization radii that, respectively, represent the large-scale background flow, mesoscale flow, and small-scale phenomena. A similar idea was used by Snook et al. (2015), who employed observation-dependent covariance localization in EnKF, assuming that different data types contain information at different scales. However, none of these approaches address the problem of excessive noise present in long-distance correlations derived from high-resolution ensembles with large localization radii applied for sparsely distributed observations (e.g., soundings).
Buehner (2012) proposed a spatial/spectral localization approach that enables the use of different spatial localization functions for the covariances associated with each set of overlapping horizontal wavelengths. The scheme effectively decomposed the ensemble background into multiple wavelength bands by applying bandpass filters. It was shown that the use of such scale-dependent localization (generally with more severe localization for small horizontal scales) reduced the error in spatial correlation estimates as compared to using the same localization for all scales. The benefit was further demonstrated by the improved analysis and forecast with either idealized experiments (Buehner and Shlyaeva 2015, which employed a related approach called scale-dependent localization) or real-case applications (Caron and Buehner 2018), both using EnVar DA systems with global models. In a later study of Caron et al. (2019), the relative performances of spectral and scale-dependent localizations in reducing sampling noise in the ensemble-derived BECs were compared in the context of regional NWP models.
Inspired by Buehner (2012), Miyoshi and Kondo (2013) proposed a dual-localization (DL) method for high-resolution models that separates scales of the analysis increment through multiple applications of a local ensemble transform Kalman filter (LETKF; Hunt et al. 2007) with different localization length scales. With observing system simulation experiments (OSSEs), they showed that the DL method produced improved analyses that contain both fine-scale structures near the observation locations and longer-range increments free of high-frequency noise. Yang et al. (2017) applied the DL method to real-case heavy rainfall forecasts; distant radiosonde observations were found critical to the analysis of moisture transport when the unreliable noisy correlations were removed from the large-scale BECs. Most recently, Wang et al. (2021) introduced multiscale capabilities into the local gain-form ensemble transform Kalman filter (LGETKF) following the general idea of Buehner (2012). The ensemble perturbations are decomposed into several scale bands, and the decomposition enables the use of different localization lengths for different scale bands. In their algorithm, all observations are assimilated at the same time to update the ensemble at multiple scales. Their experiments with simulated surface observations using a simple quasigeostrophic model showed that the multiscale LGETKF produced better forecasts than the single-scale LGETKF.
In this paper, we develop a multiscale EnKF (MEnKF) algorithm and implement and test it within the GSI EnKF system, which is based on the sequential ensemble square root filter (EnSRF; Whitaker and Hamill 2002). With this MEnKF algorithm, the background ensemble perturbations are subject to different bandpass filters so that the derived ensemble BECs from the filtered perturbations contain spatial covariances of different scales. The observations are also grouped into different batches that are considered to sample structures of different scales. For example, sounding and surface observation networks are considered mostly to sample synoptic- to mesoscale structures of the atmosphere because of the typical spacing from tens to hundreds of kilometers. Radar observations, on the other hand, are usually limited to precipitation regions and have spatial resolutions from subkilometer to several kilometers; therefore, they are considered to represent mostly small-scale structures of the atmosphere.
With our MEnKF algorithm, the batches of observations are assimilated in separate passes using the correspondingly filtered BECs and different localization scales, starting from the largest scale. Such an order of observations assimilated is chosen deliberately to ensure that small-scale analyses benefit from the improved large-scale background environment and the imposed BECs updated by conventional data. Given that the EnSRF algorithm is sequential, the main implementation effort is with the creation and use of the scale-dependent filtered ensemble BECs. Our MEnKF algorithm shares some of the design ideas of the spatial/spectral localization of Buehner (2012), which enables the use of different localization radii for different spectral bands of ensemble BECs. In their EnVar system, however, all observations are used simultaneously; therefore, the different localization radii are not tied to observation types. The multiscale LGETKF algorithm of Wang et al. (2021) also assimilates all observations at the same time. This is the key difference between their multiscale algorithms and ours. Herein, radar data sampling the small scales does not update the synoptic scales, for example.
Our MEnKF algorithm is tested over a CONUS domain at a 3-km grid spacing, coupled with the full physics FV3 limited-area model (FV3-LAM). For assimilating conventional data, initially, we experimented with two low-pass (in terms of wavenumber) filters so that the filtered background fields retain, respectively, 1) the synoptic scales and up and 2) all scales down to mesoscale. These background plus the unfiltered fields are used to produce BECs for the assimilation of data sampling different scales. We later decided to apply a single low-pass filter whose filtering scale varies with height, increasing from shorter wavelengths at the surface through the boundary layer to larger wavelengths at higher levels. This way, the filtered BEC retains mesoscale structures at the lower levels but only synoptic-scale structures at higher levels where soundings are the main source of observations. Surface and sounding data together with other large-scale observations are assimilated using the same height-dependent localization radii, while radar data are assimilated using the unfiltered BECs with small localization radii. The MEnKF algorithm is then evaluated with six convective storm cases from May 2021, with cycled assimilation of either conventional data only or with additional radar reflectivity. Ensemble forecasts of 24-h length are launched from the final ensemble analyses. The forecasts are evaluated using various metrics, and the performance of MEnKF is compared with that of regular EnKF.
The rest of the paper is organized as follows. In section 2, the methodology and optimization of the proposed MEnKF algorithm are introduced. The design of cycled single-scale and multiscale EnKF DA experiments and an overview of the six convective storm cases are provided in section 3. Section 4 presents the experiment results, including discussions on both analysis and forecast performances. A summary and conclusions are given in section 5, along with thoughts for potential future work.
2. The multiscale EnKF algorithm
a. Multiscale EnKF formulation
The MEnKF algorithm developed is based on the GSI EnSRF. The key concept is to ensure low-noise analysis increments for convection-allowing resolution domains when assimilating sparse observations sampling the large scales (e.g., soundings) using an ensemble DA method. In practice, this is achieved by performing low-pass filtering on the ensemble forecasts to remove ensemble perturbations smaller than a specified length scale.1 For this study, a Fourier-based Lanczos filter (Lanczos 1956) is adopted. Through the use of a series of “sigma factors,” the Lanczos filter is able to perform effective scale separation while significantly reducing the amplitude of the Gibbs oscillation near the lateral boundaries, which is known as a major issue when applying spatial filters for limited-area domains (Duchon 1979).
Overall, when assimilating the large-scale observations, the MEnKF algorithm is very similar to the original EnSRF, except that filtered background perturbations are used to calculate the covariances and are also updated by the filter. For the second step that assimilates radar data, the relatively smooth analysis increments for all members are extracted and added to the unfiltered original ensemble backgrounds, which are used to calculate the covariances including all scales, and to produce the final ensemble analyses. Typically, different localization radii are used for different types of observations. With the above procedure, dense radar observations are assimilated using native-resolution covariances that have been updated by conventional data, and convective-scale structures sampled by the radar network can properly be analyzed. For simplicity, the large- and small-scale background forecast errors are assumed uncorrelated in this procedure.
b. Height-dependent background filter scales
As mentioned earlier, the filtered covariance is the key of the MEnKF when assimilating conventional observations to capture flow features at larger scales and is the main difference from single-scale EnKF (SEnKF). Therefore, the selection of proper filtering length scales is critical. Considering that the horizontal spatial correlation scale of atmospheric states tends to increase with height, background filtering length scales l as a function of model vertical level (a proxy for height above ground) is proposed for assimilating surface and upper-air conventional observations.
In our implementation, the l is a hyperbolic tangent function of the model level following Eq. (8) in Liu et al. (2019). As presented in Fig. 1, the l profile, in the unit of horizontal grid intervals, is confined between lmin = 20 and lmax = 40, corresponding to ∼60 km at the first model level and ∼120 km at the 21st model level from the surface, respectively. A constant l of 40 (i.e., ∼120 km) is applied for model levels 22 and above.
Filtering length scale (lower axis) and localization radius (upper axis) as hyperbolic tangent functions of model level. The dashed line denotes the model level 21 where the filtering length scale and localization radius reach maxima.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
A series of sensitivity experiments assimilating conventional data were conducted to determine the optimal filtering length. Based on the test results (not shown), the profile shown in Fig. 1 is chosen for this study. With such a filter-scale profile, the surface observations as well as boundary layer sounding data are effectively assimilated using covariances containing intermediate scales, while upper-level observations are assimilated using larger filter scales. The height-dependent filtering enables the assimilation of different types of conventional observations with a single set of filtered background ensembles, saving computational costs.
Expanding upon the detailed methodology described above, we want to emphasize that the design philosophy of our multiscale algorithm is different from the multiscale algorithm of Buehner (2012) implemented in EnVar or the multiscale LGETKF algorithm of Wang et al. (2021) based on the same design principle. With their algorithms, the ensemble covariances are decomposed into different scale bands to facilitate the application of scale-dependent localization radii, while all observations are assimilated simultaneously so that all observations are used to update all scales. In our case, observations from different networks that predominantly sample different scales of the atmosphere are used to update the corresponding scales, with appropriate filtering applied to the ensemble covariances to improve their reliability. Scale-dependent covariance localization is also applied in the process. Comparison of the two strategies or even the combination of the two may be worth exploring in future studies.
3. Experiment design
a. Prediction model and model configurations
The FV3, originally developed by the Geophysical Fluid Dynamics Laboratory (GFDL; https://www.gfdl.noaa.gov/fv3/) and recently elected as the dynamical core for the Unified Forecast System, is used as the prediction model in this study. The FV3-LAM used in this study was specifically developed for convection-allowing applications, including the planned ∼3-km RRFS.
The prognostic model state variables predicted by FV3 include three wind velocity components u, υ, and w; temperature T; pressure p (in the form of “delp,” the thickness between adjacent model levels); specific humidity qυ; and microphysical variables connected to the specific scheme used. This study uses the Thompson microphysics scheme (Thompson et al. 2004, 2008), which predicts mixing ratios of cloud water qc, cloud ice qi, rainwater qr, snow qs, graupel qg, and total number concentrations of rainwater NTr and cloud ice NTi. Other physics parameterizations utilized include the Mellor–Yamada–Nakanishi–Niino (MYNN; Nakanishi and Niino 2009) eddy diffusivity mass flux PBL scheme, the GFS Rapid Radiative Transfer Model for Global Circulation Models (RRTMG; Mlawer et al. 1997), the GFS surface layer scheme (Miyakoda and Sirutis 1986), and the GFS Noah multiphysics (Noah-MP) land surface model (LSM; Niu et al. 2011). The above combination is consistent with the RRFS_v1alpha physics suite, based on the Common Community Physics Package (CCPP; https://dtcenter.org/community-code/common-community-physics-package-ccpp), the initial choices for experimental RRFS (Banos et al. 2022).
For this study, the simulation model domain is configured to cover and center on the entire contiguous United States (Fig. 2), consisting of 1920 × 1296 grid cells in the horizontal with approximately 3-km grid spacing. In the vertical, a 64-level hybrid coordinate that transforms from a terrain-following bottom to isobaric upper levels is adopted, with a model top set at 40 Pa.
The computational domain (the outer black rectangle) and the subdomain for storm forecast verification (the inner blue rectangle).
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
b. Cycled EnKF experiments
To evaluate the performance of the MEnKF algorithm, two pairs of experiments are designed. In the first pair, conventional observations only are assimilated hourly in a 12-h period (from 1200 to 0000 UTC; Fig. 3) using either single-scale or multiscale EnKF (hereafter referred to as SDA and MDA experiments, respectively). The second pair assimilates additional radar reflectivity from the Multi-Radar Multi-Sensor (MRMS) system (Zhang et al. 2005, 2016) every 15 min in the last hour of the DA period (named SDA_Z and MDA_Z experiments2). The 3-h forecasts (valid at 0900 UTC) of the first 40 members of the operational EnKF Global Data Assimilation System (GDAS) are used to initialize the ensemble forecasts, with the ensemble initial and lateral boundary conditions (LBCs) interpolated from the 0.25° GDAS ensemble forecasts. The ensemble spinup forecasts are run for 3 h to 1200 UTC when the DA cycles start. After the finish of all DA cycles, 24-h ensemble forecasts (of 40 members) are launched from the final ensemble analyses at 0000 UTC for each experiment. Hourly 0.5° GFS forecasts from the 0000 UTC GFS cycle are used to provide the LBCs for the ensemble forecasts. The implementation of the same LBCs for different ensemble members during the free forecasting stage facilitates the focus of investigation on the impact arising solely from different ICs attributed to different DA algorithms (i.e., SEnKF vs MEnKF).
Flowchart of the cycled DA experiment configuration, illustrating the timeline for daily experiments with 3-h spinup ensemble forecasts followed by 12-h cycled DA. Twenty-four-hour ensemble forecasts are launched from the final ensemble analyses at 0000 UTC.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
Three types of conventional observations in PREPBUFR format used by the operational 13-km Rapid Refresh model (Benjamin et al. 2016) are assimilated: 1) upper-air observations that include rawinsonde (raob) and radar VAD wind profiles; 2) surface observations including synoptic (SYNOP), aviation routine weather report (METAR), and marine stations; and 3) commercial aircraft observations provided by the Meteorological Data Collection and Reporting System (MDCRS) and Aircraft Communications Addressing and Reporting System (ACARS). Observed variables assimilated include surface pressure ps, temperature T, horizontal wind components u and υ, humidity qυ, and precipitable water pw, and the model state variables updated by conventional observations are ps, u, υ, T, and qυ. For both SDA and MDA, a height-dependent horizontal covariance localization strategy is adopted (Pan et al. 2014). As shown in Fig. 1, the localization radius rc begins with a minimum of 500 km at the first model level, increases with height using the same hyperbolic tangent function as the filter scale, and reaches a maximum of 1000 km at model level 21. An exception is with the MDCRS/ACARS observations above air pressure level 300 hPa (i.e., the common cruising altitude) that use a relatively short rc of 300 km, given the higher observation density there. For vertical localization, GSI applies scale heights in the unit of natural logarithmic pressure, which is set to 0.4 for ps and 0.2 for other observations.
For SDA_Z and MDA_Z, direct radar reflectivity assimilation capabilities developed by the Center for Analysis and Prediction of Storms (Chen et al. 2021; Liu et al. 2022; Tong et al. 2020) are employed. In addition to those state variables updated by conventional observations, vertical velocity w and all microphysics variables are also updated by reflectivity observations. For covariance localization, a horizontal rc of 12 km and a vertical scale height of 0.4 are selected based on Labriola et al. (2021). To prevent filter divergence, a relaxation-to-prior-spread (RTPS) procedure (Whitaker and Hamill 2012) is used to restore the spread of the analysis to 95% of the original background spread.
c. Overview of the test cases
Six cases with active convective storms of a variety of types over the CONUS in late May 2021 are chosen for the 12-h cycled EnKF experiments. A brief overview of the six cases, including the regions impacted, the number of hazardous event reports (tornado, hail, and wind) issued by the Storm Prediction Center (SPC), and general descriptions of the main storms, are provided in Table 1. All cases caused a significant number of hazards, in spite of the diverse modes of convective organization. In addition, prominent precipitation in each of the cases occurred mostly in the later 12 h of the 24-h forecast range. Particularly, all six cases have the most hazardous events between 2100 and 2300 UTC. To provide an insight into the storm systems studied, the MRMS observed composite reflectivity for each event is shown in Fig. 4.
List of six test cases. Remarks are provided according to the Mesoscale Discussions issued by the NWS SPC.
MRMS observed composite reflectivity (dBZ) of six test cases in the verification domain. The time presented for each case, as denoted in the lower left corner, is the hour of the day within which most hazardous events were reported (as denoted by the red dashed rectangles; see Table 1). The gray-shaded areas are outside the observing range of the radar network.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
4. Results
a. Single-sounding DA experiments
The SEnKF and MEnKF impacts on analyses are first demonstrated through experiments assimilating single-sounding observations. Observations collected at 1200 UTC 25 May 2011 at two sounding sites are chosen: 1) Fort Worth, Texas (FWD), at the leading edge of storms and 2) Lake Charles, Louisiana (LCH), in a clear-air area. The analysis increments of temperature at model level 25 (∼500 hPa) obtained with single- and multiscale EnKF are shown in Fig. 5. Note that at this level, a filter length scale of 120 km is applied to the ensemble background, and a 1000-km horizontal localization radius is used. An overall underestimated temperature field prevails in the background forecasts as the observations from both sounding sites produce analysis with positive corrections. It is shown that MEnKF produces a smoother increment pattern with generally smaller magnitudes than SEnKF, especially near the storm area (Figs. 5a,b). The smoother MEnKF increments contain fewer small-scale structures, and the analysis is expected to be more balanced at the larger scales.
Temperature analysis increments (K) of the first ensemble member at the 25th model level above ground from assimilating single-sounding observations at (top) FWD or (bottom) LCH at 1200 UTC 25 May 2021, using (left) SEnKF and (right) MEnKF; the increment maxima and minima are denoted at the lower right corner of each panel. The sounding stations are marked by blue triangles, and the 20-dBZ observed composite reflectivity by MRMS is overlaid in black contours.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
In the remaining sections, the impact of MEnKF on storm analysis and forecast is first examined in greater detail for a high-impact supercell case over the Great Central Plains on 26 May 2021. Subsequently, statistical evaluations aggregated across all six cases are provided.
b. Results for the 26 May 2021 supercell case
For the 26 May supercell case, we focus on comparing MDA_Z with SDA_Z given their generally better performance over the experiments assimilating conventional data only. Figure 6 shows the temperature analysis increments at the first model level above ground of the first ensemble member from the final analysis cycle (other members and state variables have similar behaviors). Overall, both experiments have broadly similar increment patterns in terms of sign; however, the increment field of MDA_Z is much smoother and free of small-scale structures. Such a favorable analysis of MDA_Z aligns with our expectations given the filtered ensemble perturbations and smooth ensemble spatial covariance utilized when assimilating conventional data.
Temperature analysis increments (K) at the first model level above ground from conventional and reflectivity DAs for the first ensemble member of (a) SDA_Z and (b) MDA_Z in the last cycle (0000 UTC) of 26 May 2021. The increment maxima and minima are denoted at the lower left corner of each panel.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
To illustrate the effect of height-dependent ensemble background filtering in MEnKF, the power spectra3 of T analysis increments at different model levels in the final DA cycle from different analysis passes for SDA_Z and MDA_Z are shown in Fig. 7. Regardless of model levels, power of analysis increments from MDA_Z shows abrupt drops in the first pass with conventional DA, indicating the scales at which the analysis increments are diminished. Specifically, the wavelength where the power spectrum drops in MDA_Z increases from ∼40 km at the first model level to ∼80 km at the 21st model level (as denoted by the dashed line), corresponding to the 60- and 120-km length scales utilized for background filtering at the respective levels; this is illustrated by the response functions (Figs. 7a,i) where the wavelengths of the completely eliminated signals fall at tens of kilometers below the selected filtering lengths (as denoted by the dashed lines). In addition, the power magnitudes in the first pass for both experiments decrease with increasing height because of the smoother atmosphere as well as fewer observations available at higher levels.
Response functions of the (first column) low-pass Lanczos filters utilized and the resultant power spectra of analysis increments of T at the (top) 1st, (middle) 11th, and (bottom) 21st model level above ground as a function of wavelength (km) from the (second column) first pass, (third column) second pass, and (fourth column) entire cycle for the first ensemble member of SDA_Z (black) and MDA_Z (blue) in the last cycle (0000 UTC) of 26 May 2021. The subjectively drawn dashed line in the second column denotes where the power of MDA_Z shows abrupt drops.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
In contrast to the first pass, the power of increments from the second pass for radar DA is similar between SDA_Z and MDA_Z throughout the wavelengths. The MDA_Z increment from the second pass has a bit higher power than that of SDA_Z, which is seen mostly for short wavelengths at lower levels and extends to all wavelengths at model level 21. This suggests more corrections are made in MDA_Z with radar data, likely due to somewhat larger observation innovations. It is also noted the power gains from radar DA stay relatively constant with height in orders of magnitude smaller than those from conventional DA, mainly due to the limited regions that radar data cover (only in precipitation regions) and influence (within much smaller localization radii). For this reason, the total increments of the analysis cycle (Figs. 7d,h,l) come mostly from contributions of the first pass, with the most differences in the power spectra between SDA_Z and MDA_Z seen below the, respectively, truncated wavelengths.
In Fig. 8, the ensemble storm analyses and forecasts from SDA_Z and MDA_Z are first evaluated subjectively based on localized probability-matched mean (LPM) composite reflectivity. The LPMs are calculated following a patch-based algorithm (Snook et al. 2019) applying local patches with dimensions of 5 × 5 grid points, LPM domains of 60 × 60 grid points, and a Gaussian smoother with a 3-km decorrelation scale. In the final DA cycle (i.e., at 0000 UTC), both SDA_Z (Fig. 8b) and MDA_Z (Fig. 8c) show comparable storm reflectivity analyses mostly consistent with the MRMS observations (Fig. 8a). During the 9–12 h into the forecast, scattered storms form into a solid convection line while moving eastward. Meanwhile, MDA_Z is able to predict the major storm activity at the Arkansas/Louisiana border (Fig. 8f) that is mostly missed by SDA_Z (Fig. 8e) although the predicted intensity is too high. The better storm development in the MDA_Z forecast is likely due to a stronger temperature gradient ahead of storm and a significantly more moist low-level prestorm environment in the final analysis (not shown), which is likely owing to the improved BEC utilized for assimilating conventional data. Later in the 15–18 forecast hours, MDA_Z still outperforms SDA_Z in predicting the storm track around the western Tennessee border. Besides, for the storm activity in northern Louisiana, MDA_Z also shows less displacement error. Both experiments predict stronger reflectivity cores than observations though, which is a known tendency of the FV3 model.
MRMS observed composite reflectivity (dBZ) at (a) 0000 UTC 26 May 2021 and its swaths for the periods (d) 0900–1200 and (g) 1500–1800 UTC. The LPM of ensemble (top) analyses and (middle and bottom) forecasts at (during) the corresponding time (periods) are presented for experiments (b),(e),(h) SDA_Z and (c),(f),(i) MDA_Z, respectively, with the observed 20-dBZ areas overlaid in black contours for location referencing.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
To investigate the impact of MEnKF on precipitation forecasts, the LPMs of 0–12 and 12–24 h accumulated precipitation forecasts of SDA_Z and MDA_Z are compared with the stage IV precipitation in Fig. 9. Rainfall is better predicted in general by MDA_Z than by SDA_Z within the 24-h verification period; the difference between experiments gradually diminishes as forecast hours increase. Specifically, MDA_Z better captures the precipitation in Michigan and southern Arkansas in the first 12 h as well as near the Indiana–Kentucky border in 12–24 h, which are underpredicted by SDA_Z. Nevertheless, both experiments miss the heavy rain (above 80 mm within 12 h) associated with the supercell storm in central Kansas in the later 12-h forecasts. MEnKF also shows some advantages in predicting storm locations; the forecast precipitation displacement for the observed rainfall in northern Louisiana between 12 and 24 h (Fig. 9d) is smaller in MDA_Z as compared to SDA_Z.
LPMs of precipitation forecasts (mm) of (middle) SDA_Z and (right) MDA_Z, as compared to (left) stage IV observations, accumulated over (top) 0000–1200 UTC 26 May and (bottom)1200 UTC 26–0000 UTC 27 May.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
The performance of MEnKF is further evaluated for the prediction of severe weather events. Figure 10 shows the neighborhood maximum ensemble probability (NMEP) of 2–5-km updraft helicity (UH) exceeding 75 m2 s−2 and composite reflectivity above 60 dBZ predicted by SDA_Z and MDA_Z alongside the observed composite reflectivity swath and the neighborhood probability (NP) of Z ≥ 60 dBZ during the last half of 26 May 2021 (standard time), a time frame where the most vigorous supercell storms occurred. The probability fields at specified thresholds are generated following Schwartz and Sobash (2017) with a 42-km neighborhood radius and smoothed with a 42-km Gaussian kernel σ. The selected thresholds for the 2–5-km UH and column maximum Z are common indicators of midlevel rotation and hail events (e.g., Kain et al. 2008), respectively. Compared to SDA_Z, the ensemble forecasts of MDA_Z have higher NMEP of large 2–5-km UH (up to 40%) and intense reflectivity (50%) in northwest to central Kansas. Besides, MDA_Z also shows more expanded Z ≥ 60 dBZ NMEP of 80% northwestward to the observed hail events near the Wyoming–South Dakota border. In summary, MDA_Z provides higher confidence in predicting reported tornadoes, hail, and strong winds in corresponding regions.
(a) MRMS composite reflectivity swath (shading) between 1200 UTC 26 May and 0000 UTC 27 May 2021 and NP of the observed reflectivity exceeding 60 dBZ (contours in a 30% interval, starting from 20%). NMEP of 2–5 km AGL UH exceeding 75 m2 s−2 (shading) and NMEP of reflectivity exceeding 60 dBZ (contours) during the same period (12–24 h) of forecasts of experiments (b) SDA_Z and (c) MDA_Z. The SPC storm reports are overlaid in capitalized letters.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
c. Statistical results for six storm cases
In addition to the 26 May 2021 supercell thunderstorm case presented above, the relative performance of multiscale and single-scale EnKF is further examined for another 5 days during May 2021 that have significant convective weather (see section 3c). Aggregated results based on all six cases are assessed for more robust conclusions.
1) Prediction of atmospheric conditions
The ensemble forecasts of different DA experiments are first evaluated against surface observations (SYNOP and METAR) of various meteorological variables within the entire CONUS domain in terms of root-mean-square innovations (RMSIs; i.e., root-mean-square differences from observations) for up to 24 h (Fig. 11). The results presented are based on the hourly ensemble averages aggregated across six cases, which in practice are calculated by first aggregating over all six cases to calculate the RMSIs for each ensemble member and then averaging the RMSIs over the 40 ensemble members.
Hourly ensemble-averaged RMSIs of 24-h forecasts against conventional surface observations of (a) RH, (b) Tυ, (c) ps, and (d) u and υ wind components, aggregated over six cases for experiments SDA, MDA, SDA_Z, and MDA_Z.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
Among all variables examined, MEnKF shows the largest impact on humidity forecasts (Fig. 11a); a possible inference is that low-level moisture, compared to other fields, has higher spatial variability that generally results in more noisy analysis increments with SEnKF that tend to be unreliable at the small scales. This can be greatly alleviated by MEnKF. Considerably smaller forecast errors in relative humidity (RH) are produced by MDA and MDA_Z consistently over time; the advantage diminishes with forecast lead time and becomes negligible after 15 h. The benefit of including additional reflectivity DA to humidity forecasts is also prominent when comparing SDA (MDA) and SDA_Z (MDA_Z), but the difference is mostly limited to the first 12 h of the forecast. The improved RH forecast with the aid of reflectivity data is not surprising considering the intimate correlation between the low-level humidity and in-storm hydrometeors that are primarily updated by Z. It is interesting to note that a larger improvement in near-surface humidity forecast can be achieved by MEnKF with conventional data only (i.e., in MDA) than by SEnKF with additional Z DA (i.e., in SDA_Z).
The prominent impact of MEnKF is also found on temperature and surface pressure predictions. For temperature (Fig. 11b), MDA (MDA_Z) has a smaller forecast error than SDA (SDA_Z) in the first 14 forecast hours, but the error becomes larger afterward. As for the effect of additional Z DA, the general positive impact is evident throughout 24-h forecast in terms of smaller RMSIs. The forecast error reduction by assimilating Z is less significant in later forecast hours; this is consistent with prior findings that the impact of convective-scale DA with radar observations is usually limited to relatively short forecast ranges (Kain et al. 2010; Sun et al. 2014).
For surface pressure (Fig. 11c), smaller forecast errors are produced by MEnKF experiments throughout the 24-h forecast. When comparing experiments with and without Z DA, the relative forecast performance varies at different forecast ranges. Before ∼15 h, experiments assimilating only conventional data have smaller errors; the relative outperformances of SDA (MDA) over SDA_Z (MDA_Z) are reversed afterward although with much smaller differences. Since ps is a measure of column-integrated mass and its tendencies are commonly assessed for model balance, the results above suggest greater model shock caused by additional Z DA, initially in the form of small-scale/amplitude errors that can grow upscale; it takes hours of model integration to mitigate the “shock” before the benefit of assimilating reflectivity data is revealed.
Compared to other variables discussed above, different EnKF algorithms or assimilated observations show the least effect on wind prediction, with fairly minor forecast error differences among individual experiments at most forecast hours (Fig. 11d). Within the first three forecast hours where the most differences are seen, the smallest RMSI is produced by MDA_Z, followed by SDA_Z and MDA with errors of nearly identical magnitude.
For humidity and temperature that are affected significantly by MEnKF, their mean forecast innovations (i.e., mean bias) are further examined (Fig. 12). Innovations are calculated by subtracting forecasts from observations; therefore, positive (negative) values indicate underprediction (overprediction). For the prediction of surface RH (Fig. 12a), all experiments show a general dry bias with a similar trend of increasing (decreasing) mean innovation before (after) 12 h. The same diurnal variability is also present in RMSIs (Fig. 11a) for each of the six cases studied (not shown). Among the experiments, forecasts with MEnKF show smaller dry biases, which is consistent with the smaller RMSIs shown above. For surface temperature forecasts (Fig. 12b), diurnal variability is shown with an overall cold bias and a trend generally opposite to RH. MDA experiments predict smaller biases before 14 h, consistent with their smaller RMSIs; after then, cold biases in MDA/MDA_Z forecasts become larger than in SDA/SDA_Z, hence larger RMSIs (Fig. 11b). The larger cold bias is likely due to stronger evaporative cooling associated with the storm intensity overforecast in Fig. 8. The continuously increasing difference of bias between SDAs and MDAs in the later forecast hours is related to the reduced advantage of MEnKF in RH forecast in the corresponding period.
As in Fig. 11, but for mean innovations (observation minus forecast) against conventional surface observations of (a) RH and (b) Tυ.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
A few factors can be attributed to the overall underprediction tendency of surface temperature (i.e., cold bias) shown in all experiments. When considering the seemingly direct influence of evaporative cooling, the microphysics scheme utilized is of great relevance, as discussed in detail by Dawson et al. (2010). On the other hand, the Noah LSM applied in this study is reported by Niu et al. (2011) to show significant forecast cold biases in skin temperature during the summer daytime. Similar negatively biased surface temperature and its diurnal variability are evidently supported by the surface observation verification of the prototype RRFS ensemble forecasts for the 2021 Hazardous Weather Testbed (HWT) performed by Dong et al. (2022) with the same application of Noah LSM.
The ensemble forecasts of different experiments at 12- and 24-h lead times are further verified against rawinsonde observations (Fig. 13). The ensemble-averaged RMSIs are calculated as a function of pressure level and aggregated over six cases for each experiment. For 12-h forecast, the largest RMSI difference among individual experiments is seen in RH (Fig. 13a) with overall smaller errors provided by MEnKF experiments; the advantage of MEnKF is particularly significant at the middle levels between 850 and 300 hPa and somewhat appreciable near the surface (consistent with surface verification presented earlier). As for temperature forecast (Fig. 13c), the outperformance of MEnKF experiments is relatively limited and barely noticeable at low levels between 1000 and 850 hPa. The forecast error reduction by MDAs, on the other hand, is prominent over a wider vertical range between 850 and 150 hPa for wind prediction (Fig. 13e).
Ensemble-averaged RMSI profiles of (left) 12- and (right) 24-h forecasts against radiosonde observations of (top) RH, (middle) Tυ, and (bottom) u and υ wind components, aggregated over six cases for experiments SDA, MDA, SDA_Z, and MDA_Z. Mandatory constant-pressure levels of 925, 850, 700, 500, 300, and 200 hPa are denoted by dashed lines.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
At 24 h of the forecast, the RMSI profiles become comparable in general. Out of all variables verified, u and υ forecasts show the most advantage of MDAs (Fig. 13f), in contrast to the surface evaluations where MEnKF had the least impact on wind throughout 24 h. The diminishing advantage of MDAs in the later hours is consistent with the reduced effect of initial conditions in time on forecasts (e.g., Hohenegger et al. 2008; Vié et al. 2011) and increased effects of lateral boundary conditions (Johnson et al. 2011).
2) Prediction of storms
The efficacy of the MEnKF algorithm is assessed in terms of storm prediction. Contingency table-based verification indices including bias, false alarm ratio (FAR), probability of detection (POD), and critical success index (CSI) are calculated with a 42-km neighborhood radius for quantitatively evaluating the composite reflectivity forecasts of SDA_Z and MDA_Z. Clark et al. (2010) provide a detailed description of how the four key contingency table elements (i.e., hit, miss, false alarm, and correct negative) are defined on a neighborhood basis. The ensemble average results of six individual cases are presented in performance diagrams (Roebber 2009) for forecasts at 1-, 3-, and 12-h lead times for thresholds of 20 and 35 dBZ (Fig. 14). The statistics averaged over all six cases are also shown in the plots. For the 20 dBZ threshold that denotes primarily the areal coverage of storms, MDA_Z has consistently lower biases in 1-h forecasts for all six cases compared to SDA_Z (Fig. 14a). The relative performance of two experiments in the 3-h forecast is rather indistinct, with generally larger success ratios provided by MDA_Z (Fig. 14b). Later, in the 12-h forecast, the MDA_Z outperforms SDA_Z with moderately smaller biases and higher PODs for most cases (Fig. 14c). As for the 35 dBZ threshold corresponding to moderate rain, MDA_Z again shows lower biases than SDA_Z in the first hour (Fig. 14d). In the 3-h forecasts of most cases, MDA_Z has both higher PODs and success ratios (SRs), except for 22 May (Fig. 14e). The advantage of MDA_Z over SDA_Z in terms of lower biases and higher PODs persists in the 12-h forecast (Fig. 14f). Overall, the above evaluation suggests better performance of MEnKF in predicting precipitating storms at least up to 12 h, with the differences generally decreasing in time.
Performance diagrams for (a),(d) 1-, (b),(e) 3-, and (c),(f) 12-h composite reflectivity forecasts of experiments SDA_Z (red) and MDA_Z (green) with (top) 20- and (bottom) 35-dBZ thresholds. The ensemble-averaged results of individual studied cases are denoted by different solid symbols, and the six-case averaged results are denoted by hollow pentagrams. Dashed lines and shading contours represent constant bias and CSI, respectively. The six-case averaged POD, SR, and bias are denoted at the lower right corner of each panel.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
In Fig. 15, MEnKF performance is further evaluated for hourly precipitation forecasts in terms of neighborhood (42-km) bias and ETS aggregated over six cases and averaged among all ensemble members. The statistical significance of the relative performances of different experiments is denoted by the 95% confidence intervals calculated using 1000 bootstrap samples. For the 2.54 mm h−1 threshold, MDA_Z has the lowest mean bias (highest mean ETS scores) within the first 13 h (15 h) of forecast (Figs. 15a,c), while for the 12.7 mm h−1 threshold, the advantage of MDA_Z over SDA_Z is limited approximately to the first 10 h (Figs. 15b,d). For MDA and SDA that do not assimilate reflectivity, the advantage of MDA appears to last longer, especially for the lower threshold where the higher mean ETS scores of MDA can last consistently to the end of 24-h forecasts. Moreover, the benefit of assimilating reflectivity data in precipitation forecasts (particularly within the first 9 h) is quite evident when comparing experiments with and without Z DA. On the other hand, it is worth noting that all experiments show tendencies to overpredict heavy rain (i.e., ≥12.7 mm h−1) after 10-h forecast (Fig. 15b), which matches the beginning time of the increasing cold bias seen in Fig. 12b. Meanwhile, even though noticeable differences are evident in the mean biases and mean ETS scores, their 95% confidence intervals overlap most times beyond 6 h, suggesting statistically insignificant differences. The statistical difference is expected to increase with a larger sample than the six cases. It is worth noting that the scores are rather consistent among the individual cases (not shown) and with the aggregated scores shown here, suggesting that the observed improvements are systematic.
(a) Six-case aggregated, (b) frequency biases, and (c),(d) ETSs of ensemble-averaged hourly precipitation forecasts for experiments SDA, MDA, SDA_Z, and MDA_Z, calculated with a neighborhood radius of 42 km at thresholds of (left) 2.54 and (right) 12.7 mm h−1. The solid lines are the averages, while the shaded areas in matching colors represent the 95% confidence ranges calculated with bootstrap resampling.
Citation: Monthly Weather Review 152, 8; 10.1175/MWR-D-23-0235.1
5. Summary and conclusions
A new multiscale EnKF (MEnKF) DA scheme is developed and implemented within the GSI EnSRF framework to effectively assimilate synoptic- through convective-scale observations, aiming at more balanced initial conditions for NWP on large continent-sized grids at resolutions that explicitly represent convection. The algorithm incorporates ensemble background error covariances with structures matching the scales reflected by the assimilated observations; this is achieved by applying scale-selective filters to the ensemble perturbation fields that are used to calculate ensemble covariance, i.e., by performing scale decomposition of the background error covariance. When assimilating observations from conventional networks that sample mostly the atmospheric state at relatively large scales (e.g., synoptic scale and mesoscale), structures smaller than specified length scales in the background ensemble perturbations are excluded to provide smoother spatial covariances for the ensemble analysis. This results in analysis increments free of unreliable small-scale structures linked to the noisy ensemble background error covariances derived from undersized high-resolution, convection-allowing ensemble. Given the sequential nature of the EnSRF, the unfiltered original background updated with smoother analysis increments from conventional DA can then be used for assimilating higher-resolution observations (e.g., radar).
The MEnKF algorithm is optimized through a series of sensitivity tests coupled with the FV3-LAM. Height-dependent background filtering is introduced and utilized for assimilating conventional data, considering the general decreasing horizontal variability of atmospheric states with increasing altitude. This enables the assimilation of different types of conventional observations in the same step while retaining the spatial scales in the covariances represented by corresponding observations. Besides the background filtering, the horizontal radius of covariance localization is also height dependent, with the same functional form as the profile of horizontal filtering scale length.
Experiments are conducted using a 12-h cycled DA configuration assimilating either standard conventional observations (hourly) alone or in conjunction with radar reflectivity (at 15-min intervals in the final hour); ensemble free forecasts of 24 h are launched from the end of the DA cycling. A total of six active convection cases from May 2021 are examined to provide a more robust assessment of the MEnKF.
According to the aggregated statistics over the six storm cases verified against conventional surface observations, MEnKF tends to outperform SEnKF in forecasting most surface variables at forecast ranges up to a day, with the largest positive impact on humidity and the least on winds. Nevertheless, a larger surface cold bias is found for MEnKF forecasts after 14 h into the forecast, which is likely responsible for the degraded humidity forecast in the later hours; this is consistent with the qualitative diagnosis of the 26 May supercell storm case examined in a greater depth. For the upper-air forecasts against soundings, the advantage of MEnKF is limited to the initial 12 h for humidity but can last up to 24 h for wind; the least impact is seen with temperature forecasts.
The impact of multiscale EnKF on storm prediction is assessed through contingency table-based scores for both composite reflectivity and rainfall. Relative outperformance of experiments with MEnKF is evident in terms of reduced bias and increased probability of detection in reflectivity forecast at various forecast ranges. For rainfall, MEnKF also produces more skillful forecasts with generally smaller biases and higher ETSs; the positive impact of MEnKF becomes less significant with increasing forecast lead time. Specifically, the advantage of MEnKF over SEnKF lasts longer in the forecasts of light rain than heavy rain. Moreover, the benefit of MEnKF in precipitation forecast appears to last longer when only conventional data are assimilated, suggesting the critical role of the larger-scale storm environment in the development of precipitation systems. In summary, whether assimilating reflectivity or not, MEnKF generally outperforms SEnKF in intraday storm-scale forecasts over the 3-km CONUS domain, as demonstrated consistently across all six tested cases.
Our results presented in this paper show that the proposed MEnKF scheme is promising and has the potential to improve the initial condition of NWP models on large high-resolution grids when assimilating a variety of observations sampling many scales. Due to high computational costs associated with running the cycled DA experiments and ensemble forecasts over the CONUS domain, only six cases are included, which represent a relatively small sample. More systematic evaluations over many more cases should be performed in the future for statistically more robust conclusions. We want to point out that the relative verification scores comparing MEnKF and SEnKF are consistent among individual cases and with the aggregated scores for all six cases, giving us more confidence that the observed performance improvement with MEnKF is systematic. We also point out that the multiscale EnSRF algorithm is more computationally expensive. The main increase is associated with the cost of filtering the background ensemble. This cost can be reduced by using computationally faster filters such as that of Yang et al. (2017). Another added cost is the extra memory storage needed to keep a second copy of the filtered background ensemble. This will not affect the throughput of the DA as long as sufficient memory is available on the compute nodes. Last, we want to point out that a similar strategy can be taken in ensemble–variational (EnVar) systems where filtered perturbations are used to calculate the ensemble background error covariance. However, because EnVar algorithms typically assimilate all observations simultaneously, to use the current multiscale strategy, multiple analysis passes will have to be taken (Pan et al. 2014).
Periodic boundaries are assumed and implemented using a mirroring approach, which enables the use of discrete cosine transform (DCT) in the fast Fourier transform (FFT) utilized by the Lanczos filter.
The term “Z” is used to represent both observed and simulated radar reflectivity.
The power spectra were calculated using FFT.
Acknowledgments.
This research was primarily supported by the NOAA Grant NA19OAR4590236 of the Joint Technology Transfer Initiative (JTTI) program. Additional support for this project was provided by the Development Testbed Center (DTC) Visitor Program, which is funded by the NOAA, the NCAR, and the NSF. Special notes of appreciation are extended to Will Mayfield of NCAR/RAL for his host for the DTC Visitor Program and help on data collection, Drs. Ming Hu and Guoqing Ge of NOAA/GSL, and Ivette Hernández Baños of NCAR/MMM for invaluable discussions. Computational resources were provided by the XSEDE Stampede2 and Frontera supercomputers at the University of Texas Advanced Computing Center (TACC).
Data availability statement.
The implementation of the multiscale EnKF capabilities presented in this study is based upon the community GSI available at https://github.com/NOAA-EMC/GSI (gfsda.v16.0.0). The FV3 model employed in this study can be accessed at the GitHub repository: https://github.com/NOAA-GSL/ufs-weather-model (gfs_v16.0.1). Due to the regular data size limit for cloud-based storage, the data for the results presented in this paper are archived on local disks and should be made available upon request by emailing the author at cctong@ou.edu.
REFERENCES
Alexander, C. R., 2021: Overview of regional modeling development at NOAA/GSL. Special Symp. on Global and Mesoscale Models: Updates and Center Overviews, Online, Amer. Meteor. Soc., 12.7, https://ams.confex.com/ams/101ANNUAL/meetingapp.cgi/Paper/382970.
Banos, I. H., W. D. Mayfield, G. Ge, L. F. Sapucci, J. R. Carley, and L. Nance, 2022: Assessment of the data assimilation framework for the Rapid Refresh Forecast System v0.1 and impacts on forecasts of a convective storm case study. Geosci. Model Dev., 15, 6891–6917, https://doi.org/10.5194/gmd-15-6891-2022.
Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 1669–1694, https://doi.org/10.1175/MWR-D-15-0242.1.
Buehner, M., 2012: Evaluation of a spatial/spectral covariance localization approach for atmospheric data assimilation. Mon. Wea. Rev., 140, 617–636, https://doi.org/10.1175/MWR-D-10-05052.1.
Buehner, M., and A. Shlyaeva, 2015: Scale-dependent background-error covariance localisation. Tellus, 67A, 28027, https://doi.org/10.3402/tellusa.v67.28027.
Caron, J.-F., and M. Buehner, 2018: Scale-dependent background error covariance localization: Evaluation in a global deterministic weather forecasting system. Mon. Wea. Rev., 146, 1367–1381, https://doi.org/10.1175/MWR-D-17-0369.1.
Caron, J.-F., Y. Michel, T. Montmerle, and É. Arbogast, 2019: Improving background error covariances in a 3D ensemble-variational data assimilation system for regional NWP. Mon. Wea. Rev., 147, 135–151, https://doi.org/10.1175/MWR-D-18-0248.1.
Chen, L., C. Liu, M. Xue, G. Zhao, R. Kong, and Y. Jung, 2021: Use of power transform mixing ratios as hydrometeor control variables for direct assimilation of radar reflectivity in GSI En3DVar and tests with five convective storm cases. Mon. Wea. Rev., 149, 645–659, https://doi.org/10.1175/MWR-D-20-0149.1.
Clark, A. J., W. A. Gallus Jr., and M. L. Weisman, 2010: Neighborhood-based verification of precipitation forecasts from convection-allowing NCAR WRF model simulations and the operational NAM. Wea. Forecasting, 25, 1495–1509, https://doi.org/10.1175/2010WAF2222404.1.
Dawson, D. T., II, M. Xue, J. A. Milbrandt, and M. K. Yau, 2010: Comparison of evaporation and cold pool development between single-moment and multimoment bulk microphysics schemes in idealized simulations of tornadic thunderstorms. Mon. Wea. Rev., 138, 1152–1171, https://doi.org/10.1175/2009MWR2956.1.
Dong, J., and Coauthors, 2022: Evaluation of the prototype Rapid Refresh Forecast System (RRFS) ensemble forecasts with cloud High Performance Computing (HPC) at NOAA testbeds. 12th Conf. on Transition of Research to Operations, Houston, TX, Amer. Meteor. Soc., 11B.3, https://ams.confex.com/ams/102ANNUAL/meetingapp.cgi/Paper/397401.
Dowell, D. C., and Coauthors, 2022: The High-Resolution Rapid Refresh (HRRR): An hourly updating convection-allowing forecast model. Part I: Motivation and system description. Wea. Forecasting, 37, 1371–1395, https://doi.org/10.1175/WAF-D-21-0151.1.
Duchon, C. E., 1979: Lanczos filtering in one and two dimensions. J. Appl. Meteor., 18, 1016–1022, https://doi.org/10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.
Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 143–10 162, https://doi.org/10.1029/94JC00572.
Hohenegger, C., A. Walser, W. Langhans, and C. Schär, 2008: Cloud-resolving ensemble simulations of the August 2005 Alpine flood. Quart. J. Roy. Meteor. Soc., 134, 889–904, https://doi.org/10.1002/qj.252.
Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112–126, https://doi.org/10.1016/j.physd.2006.11.008.
Johnson, A., X. Wang, M. Xue, and F. Kong, 2011: Hierarchical cluster analysis of a convection-allowing ensemble during the Hazardous Weather Testbed 2009 spring experiment. Part II: Ensemble clustering over the whole experiment period. Mon. Wea. Rev., 139, 3694–3710, https://doi.org/10.1175/MWR-D-11-00016.1.
Kain, J. S., and Coauthors, 2008: Severe-weather forecast guidance from the first generation of large-domain convection-allowing models: Challenges and opportunities. 24th Conf. on Severe Local Storms, Savannah, GA, Amer. Meteor. Soc., 12.1, https://ams.confex.com/ams/pdfpapers/141723.pdf.
Kain, J. S., and Coauthors, 2010: Assessing advances in the assimilation of radar data and other mesoscale observations within a collaborative forecasting–research environment. Wea. Forecasting, 25, 1510–1521, https://doi.org/10.1175/2010WAF2222405.1.
Kleist, D. T., D. F. Parrish, J. C. Derber, R. Treadon, W.-S. Wu, and S. Lord, 2009: Introduction of the GSI into the NCEP global data assimilation system. Wea. Forecasting, 24, 1691–1705, https://doi.org/10.1175/2009WAF2222201.1.
Labriola, J., Y. Jung, C. Liu, and M. Xue, 2021: Evaluating forecast performance and sensitivity to the GSI EnKF data assimilation configuration for the 28–29 May 2017 mesoscale convective system case. Wea. Forecasting, 36, 127–146, https://doi.org/10.1175/WAF-D-20-0071.1.
Lanczos, C., 1956: Applied Analysis. Prentice-Hall, 539 pp.
Li, Z., J. C. McWilliams, K. Ide, and J. D. Farrara, 2015: A multiscale variational data assimilation scheme: Formulation and illustration. Mon. Wea. Rev., 143, 3804–3822, https://doi.org/10.1175/MWR-D-14-00384.1.
Liu, C., M. Xue, and R. Kong, 2019: Direct assimilation of radar reflectivity data using 3DVAR: Treatment of hydrometeor background errors and OSSE tests. Mon. Wea. Rev., 147, 17–29, https://doi.org/10.1175/MWR-D-18-0033.1.
Liu, C., H. Li, M. Xue, Y. Jung, J. Park, L. Chen, R. Kong, and C.-C. Tong, 2022: Use of a reflectivity operator based on double-moment Thompson microphysics for direct assimilation of radar reflectivity in GSI-based hybrid En3DVar. Mon. Wea. Rev., 150, 907–926, https://doi.org/10.1175/MWR-D-21-0040.1.
Miyakoda, K., and J. Sirutis, 1986: Manual of the E-physics. Princeton University, 97 pp., https://www.gfdl.noaa.gov/bibliography/related_files/Manual_of_the_E-Physics.pdf.
Miyoshi, T., and K. Kondo, 2013: A multi-scale localization approach to an ensemble Kalman filter. SOLA, 9, 170–173, https://doi.org/10.2151/sola.2013-038.
Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 663–16 682, https://doi.org/10.1029/97JD00237.
Nakanishi, M., and H. Niino, 2009: Development of an improved turbulence closure model for the atmospheric boundary layer. J. Meteor. Soc. Japan, 87, 895–912, https://doi.org/10.2151/jmsj.87.895.
Niu, G.-Y., and Coauthors, 2011: The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J. Geophys. Res., 116, D12109, https://doi.org/10.1029/2010JD015139.
Pan, Y. J., K. Zhu, M. Xue, X. Wang, M. Hu, S. G. Benjamin, S. S. Weygandt, and J. S. Whitaker, 2014: A GSI-based coupled EnSRF-En3DVar hybrid data assimilation system for the operational rapid refresh model: Tests at a reduced resolution. Mon. Wea. Rev., 142, 3756–3780, https://doi.org/10.1175/MWR-D-13-00242.1.
Putman, W. M., and S.-J. Lin, 2007: Finite-volume transport on various cubed-sphere grids. J. Comput. Phys., 227, 55–78, https://doi.org/10.1016/j.jcp.2007.07.022.
Roebber, P. J., 2009: Visualizing multiple measures of forecast quality. Wea. Forecasting, 24, 601–608, https://doi.org/10.1175/2008WAF2222159.1.
Schwartz, C. S., and R. A. Sobash, 2017: Generating probabilistic forecasts from convection-allowing ensembles using neighborhood approaches: A review and recommendations. Mon. Wea. Rev., 145, 3397–3418, https://doi.org/10.1175/MWR-D-16-0400.1.
Snook, N., M. Xue, and Y. Jung, 2015: Multiscale EnKF assimilation of radar and conventional observations and ensemble forecasting for a tornadic mesoscale convective system. Mon. Wea. Rev., 143, 1035–1057, https://doi.org/10.1175/MWR-D-13-00262.1.
Snook, N., F. Kong, K. A. Brewster, M. Xue, K. W. Thomas, T. A. Supinie, S. Perfater, and B. Albright, 2019: Evaluation of convection-permitting precipitation forecast products using WRF, NMMB, and FV3 for the 2016–17 NOAA Hydrometeorology Testbed flash flood and intense rainfall experiments. Wea. Forecasting, 34, 781–804, https://doi.org/10.1175/WAF-D-18-0155.1.
Sun, J., and Coauthors, 2014: Use of NWP for nowcasting convective precipitation: Recent progress and challenges. Bull. Amer. Meteor. Soc., 95, 409–426, https://doi.org/10.1175/BAMS-D-11-00263.1.
Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Wea. Rev., 132, 519–542, https://doi.org/10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2.
Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095–5115, https://doi.org/10.1175/2008MWR2387.1.
Tong, C.-C., Y. Jung, M. Xue, and C. Liu, 2020: Direct assimilation of radar data with ensemble Kalman filter and hybrid ensemble-variational method in the National Weather Service operational data assimilation system GSI for the stand-alone regional FV3 model at a convection-allowing resolution. Geophys. Res. Lett., 47, e2020GL090179, https://doi.org/10.1029/2020GL090179.
Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 3297–3319, https://doi.org/10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2.
Vié, B., O. Nuissier, and V. Ducrocq, 2011: Cloud-resolving ensemble simulations of Mediterranean heavy precipitating events: Uncertainty on initial conditions and lateral boundary conditions. Mon. Wea. Rev., 139, 403–423, https://doi.org/10.1175/2010MWR3487.1.
Wang, X., H. G. Chipilski, C. H. Bishop, E. Satterfield, N. Baker, and J. S. Whitaker, 2021: A multiscale local gain form ensemble transform Kalman filter (MLGETKF). Mon. Wea. Rev., 149, 605–622, https://doi.org/10.1175/MWR-D-20-0290.1.
Weygandt, S. S., S. G. Benjamin, M. Hu, C. R. Alexandar, T. G. Smirnova, and E. P. James, 2022: Radar reflectivity-based model initialization using specified latent heating (radar-LHI) within a diabatic digital filter or pre-forecast integration. Wea. Forecasting, 37, 1419–1434, https://doi.org/10.1175/WAF-D-21-0142.1.
Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 1913–1924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.
Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 3078–3089, https://doi.org/10.1175/MWR-D-11-00276.1.
Yang, S.-C., S.-H. Chen, K. Kondo, T. Miyoshi, Y.-C. Liou, Y.-L. Teng, and H.-L. Chang, 2017: Multilocalization data assimilation for predicting heavy precipitation associated with a multiscale weather system. J. Adv. Model. Earth Syst., 9, 1684–1702, https://doi.org/10.1002/2017MS001009.
Zhang, F., Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 2105–2125, https://doi.org/10.1175/2009MWR2645.1.
Zhang, J., K. Howard, and J. J. Gourley, 2005: Constructing three-dimensional multiple-radar reflectivity mosaics: Examples of convective storms and stratiform rain echoes. J. Atmos. Oceanic Technol., 22, 30–42, https://doi.org/10.1175/JTECH-1689.1.
Zhang, J., and Coauthors, 2016: Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimation: Initial operating capabilities. Bull. Amer. Meteor. Soc., 97, 621–638, https://doi.org/10.1175/BAMS-D-14-00174.1.
