IMPACT OF VERTICAL RESOLUTION, MODEL TOP AND DATA ASSIMILATION ON WEATHER FORECASTING-A CASE STUDY

In the early 20th century, many studies (e. g., Baldwin and Dunkerton ^[1], ^[2]; Baldwin et al. ^[3]) suggested that by including the stratospheric state in numerical weather prediction (NWP) systems, certain prediction skills could be gained in the troposphere. Later, in the early 2000s, Charlton et al. tested the impacts of the stratospheric state on tropospheric forecasts and found that a small amount of extra skill (~5%) could be obtained by including stratospheric information in a simple statistical forecasting model of the troposphere. At the same time, based on three cases, they also found that the tropospheric flow and tropospheric synoptic-scale systems could be statistically significantly influenced by including the stratospheric initial conditions ^[4]. Recently, owing to significant theoretical improvements in data assimilation fields and the application of ensemble methods in NWP systems, operational data assimilation systems have begun not only to assimilate traditional meteorological data, but also multiple atmospheric constituents extending from ozone to aerosols, particulate matter (e. g., PM_2.5), greenhouse gases, etc. With a better representation of the atmosphere, including valuable stratospheric information, Gerber et al. found that an improvement in short-range forecasts could be achieved; and at the same time, stratospheric information can provide additional skill to seasonal-timescale forecasts ^[5].

Apart from the dynamical impacts from the stratosphere to the troposphere by better representing the stratosphere in short-term weather forecasts, the selection in terms of both the horizontal and the vertical resolution of the model can also affect the resulting forecasts. The selection of horizontal resolution has been extensively tested, which is strongly related to the scale of the event being studied (e.g., hurricane, precipitation, etc.) (Torn ^[6]; Duvivier and Cassano ^[7]; Pieri et al. ^[8]). Further research has shown that both atmospheric and oceanic models are also sensitive to the vertical resolution of the model (Adamec ^[9]; Weaver and Sarachik ^[10]; Roeckner et al. ^[11]; Zhang et al. ^[12]). For regional NWP models, such as the Weather Research and Forecasting (WRF) system, the selection of vertical resolution is especially important owing to the errors caused by the interpolation of global products, data usage in data assimilation, and the different scales of the weather events being predicted (Chou ^[13]). Large reductions in biases over the tropopause (a result of the large gradient of lapse rate), as well as for surface pressure and geopotential height, can be obtained when a high vertical resolution is applied (Chou ^[13]). Furthermore, increasing the vertical resolution over typical levels, such as the melting level and surface layers, can also enhance rainfall forecasting skill. However, only weakly forced cases that are governed by thermodynamic forcing and are sensitive to the vertical profiles of temperature and moisture are more likely to be improved by a refined vertical resolution. In terms of the interaction between lower-atmosphere processes and microphysical processes above the melting level, applying a refined vertical resolution usually leads to negative impacts (Aligo et al. ^[14]).

To address the impacts of stratospheric vertical resolution on tropospheric weather forecasts, the non-hydrostatic Advanced Research version of the WRF system (hereafter simply referred to as WRF) was used in this study. The initial and boundary conditions were provided by the Global Forecast System (GFS). The model top of WRF was then raised, step-by-step, to include the whole stratosphere. Three experiments with different model tops and different vertical resolutions were conducted. Additionally, a three-dimensional variational (3D-Var) - based ensemble variational hybrid data assimilation scheme (hereafter simply referred to as Hybrid) was also applied to these three experiments, using operationally available observations from the National Oceanic and Atmospheric Administration (NOAA), bringing the total number of experiments presented here to six. Research methodology is described in section 2. The quantitative results are presented in section 3, followed by a case study. Section 4 summarizes the key findings of our work.

The WRF model (Skamarock et al. ^[15]; Wang et al. ^[16]) is a non-hydrostatic, fully compressible, primitive equation model. In this study, the WRF model was run with a 0.25° domain over the continental U. S. (Fig. 1). The physics schemes used in the model were as follows: the WRF Single-Moment 3-class scheme for microphysics; the RRTM scheme for longwave radiation and the Goddard shortwave scheme for shortwave radiation; the Noah Land Surface Model for the land surface; the Yonsei University scheme for the planetary boundary layer; and the Grell-Devenyi ensemble scheme for cumulus parameterization.

Figure 1.  Study domain over the continental U.S. The shading indicates land (grey) and water (blue). The domain has a horizontal resolution of 0.25°.

The GFS whole atmospheric product set with a horizontal resolution of 0.5° × 0.5° and 47 unevenly distributed vertical levels with a top at 1 mb was used to provide the initial and boundary conditions for the WRF model. The GFS whole atmospheric data product has a vertical grid spacing of 25 mb below 100 mb, and another 10 levels between 100 mb and 1 mb (at 70, 50, 30, 20, 10, 7, 5, 3, 2 and 1 mb respectively).

The community gridpoint statistical interpolation (GSI) system was used as the data assimilation system in this study. The latest GSI version features the application of surface analysis, basic 3D-Var, an ensemble Kalman filter (EnKF), a Hybrid scheme, and 4D-Var if coupled with an adjoint GSI model-supported forecast system (Kleist ^[17]; Wang et al. ^[18]; Hu et al. ^[19]). With the help of the Community Radiative Transfer Model, GSI can assimilate both conventional and satellite radiance datasets. Detailed information can be found on the Developmental Testbed Center website (http://www.dtcenter.org/).

The GSI Hybrid scheme was used in this study. This scheme uses the background error covariance matrix, which is completely static or only slightly coupled to the dynamics of the forecast, and at the same time involves the fully flow-dependent background error covariance estimated from a set of ensembles of short-range forecasts with the WRF forecast model (Wang et al. ^[18]). The cost function for this hybrid data assimilation can be described as follows:

where x, x_b and yo are vectors of the analysis, background fields and observations, respectively; B_f and B_ens are the model static background error covariance and background error covariance estimated from a set of ensemble forecasts, respectively; R is the observational error covariance; H is the observation forward operator, which converts the model state to the observational state; and β₁ and β₂ are two factors whose inversions define the weights placed on the static covariance and the ensemble covariance, where these two factors satisfy the relation $\frac{1}{\beta_{1}}+\frac{1}{\beta_{2}}=1 $.

Two outer loops were used, and the maximum number of iteration steps for both loops was set to 50. Forty ensemble members were used in the Hybrid scheme, and a 20% weight was applied to the static covariance and an 80% weight to the ensemble covariance (Benjamin et al. ^[20]). The ensemble members were 6-hour WRF model forecasts of 40 initial conditions with random perturbations. The covariance localization scale (1000 km) was also applied to the ensemble covariance, to remove long-range spurious ensemble covariance through the removal of long-range spurious correlations and increase the effective ensemble size (Wang ^[21]).

The operationally available observations used in the GFS system, including conventional and satellite data, were used in the data assimilation system. The observations are constructed in BUFR format (binary universal form for the representation of meteorological data) and can be downloaded from the NCEP products website (http://www.nco.ncep.noaa.gov/pmb/products/gfs/). The conventional observations varied from in-situ observations covering both land and ocean, radiosondes, aircraft reports, to satellite retrievals, chemical compositions, etc. The satellite radiance/brightness temperature observations (level 1b) used in the data assimilation system included both infrared and microwave satellite instruments. The microwave instruments used here included: the AMSU-A (the Advanced Microwave Sounding Unit-A) onboard NOAA-15, NOAA-18, NOAA-19, MetOp-A, MetOp-B, and Aqua; the MHS (Microwave Humidity Sounder) onboard NOAA-18, NOAA-19, MetOp-A, and MetOp-B; the SSMI/S (Special Sensor Microwave Imager/Sounder) onboard the DMSP (Defense Meteorological Satellite Program)-f16, -f17, -f18, - f19 and - f20 satellites; and the ATMS (Advanced Technology Microwave Sounder) onboard the S-NPP (Suomi-NPOESS Preparatory Project) satellite. The infrared satellite instruments included: the HIRS/4 (High-resolution Infrared Radiation Sounder) onboard NOAA-19, MetOp-A, and MetOp-B (https://poes.gsfc.nasa.gov/hirs4.html); the AIRS (Atmospheric Infrared Sounder) launched in 2002 on Aqua (http://disc.sci.gsfc.nasa.gov/AIRS/documentation/airs_instrument_guide.shtml); the IASI (Infrared Atmospheric Sounding Interferometer) onboard MetOp-A and MetOp-B (https://wdc.dlr.de/sensors/iasi/); and the CrIS (Cross-track Infrared Sounder) launched along with the ATMS on S-NPP (https://jointmission.gsfc.nasa.gov/cris.html). A typical distribution of the conventional and satellite radiance observations at 1800 UTC 1 January 2015 is shown in Fig. 2.

Figure 2.  Typical coverage of conventional and satellite observations at 1800 UTC 1 January 2015.

Data used for the verification included the conventional data used in the data assimilation system and the 3-hourly accumulated precipitation product from the Global Land Data Assimilation System (GLDAS) with a horizontal resolution of 0.125°. GLDAS is a global, high-resolution terrestrial modeling system that uses both ground and satellite-based observations to optimize the products at land surface states (Rodell et al. ^[22]; Gottschalck et al. ^[23]).

Three sets of WRF and data assimilation (hereafter referred to as Hybrid) experiments with different model tops and vertical resolutions were conducted during January and February in 2015. Each run of the WRF experiment made a 72-hour forecast, and the operationally available observations, including conventional and satellite data, were assimilated every 6 hours; thus, over 100 samples for each experiment. The model top was raised from 50 mb to 10 mb, and then to 1 mb to include more stratospheric information, step-by-step. Detailed information on the vertical resolution and domain configuration of all experiments is listed in Table 1. In the first set of experiments including both WRF and data assimilation runs, there were 30 atmospheric vertical levels, among which 10 were located in the stratosphere. To evaluate the sensitivity of stratospheric initial conditions and the assimilation of stratospheric observations, 51 and 63 levels were selected in the second and third sets of experiments, in which 20 and 40 levels were located in the stratosphere, respectively.

The performance from raising the model top and assimilating extra stratospheric observations was evaluated through comparison with conventional observations. First, statistical results of wind speed and temperature in the initial conditions and the predictions were produced using the averaged bias and root-mean-square deviation (RMSD) calculated against the conventional observations during the study period. The differences in initial temperature RMSDs indicated the differences in performance skill when the model top was raised or data assimilation was applied. The differences in predicted temperature RMSD profiles indicated the differences in forecast skill (Wang et al.^[18]). Also, a snowstorm that occurred during 2 January to 4 January 2015 was used as a case study to demonstrate the importance of the inclusion of the entire stratosphere with data assimilation in severe weather predictions.

First guesses with different model tops and vertical levels were firstly generated with a 6-hour run of WRF. The impact of the assimilated observations in GFS products was assumed to be limited after the 6-hour integration of WRF. The analysis was produced by assimilating all operational available observations into the first guesses generated in the last step. Both first guesses and the analysis were used as the initial conditions for subsequent predictions. We began by calculating the bias and RMSD of all six sets of initial conditions against conventional observations.

The bias and RMSD differences of wind and temperature first guess profiles using WRF-50 as the baseline are plotted in Fig. 3. The bias and RMSD shown in Fig. 3 can be treated as systematic differences caused by raising the model top alone. Negative values indicate that raising the model top had positive impacts on the initial conditions, and vice versa for positive values. Raising the model top from 50 mb to 10 and 1 mb led to generally positive impacts on the biases of the initial conditions. The biases of near-surface wind were enlarged, and slightly larger wind and temperature biases were also observed at the tropopause layers in the WRF-10 experiment. Much smaller biases were obtained over the mid-troposphere and lower stratosphere. However, the RMSD of the initial wind and temperature profiles showed a general decline in performance skill in the troposphere. Better performances were obtained over the tropopause. WRF-10 and WRF-1 showed 9% and 12.5% lower wind-speed RMSDs over the tropopause, respectively, but in excess of 30% higher wind-speed RMSDs in the lower troposphere, compared to WRF-50. The initial temperature RMSD profiles also showed increased (~30%) RMSDs over the lower troposphere and decreased (8% and 13% for WRF-10 and WRF-1, respectively) RMSDs over the tropopause and lower stratosphere. However, the initial surface-layer temperature benefitted greatly from the raised model top and increased vertical resolution, with obviously reduced (> 13% and 20% for WRF-10 and WRF-1, respectively) temperature RMSDs. The extra vertical stratospheric layers in WRF-10 and WRF-1 particularly benefitted the tropopause and lower stratospheric layers compared to the WRF-50 experiment, which had fewer vertical layers and a lower model top. As mentioned in Chou ^[13], errors stemming from interpolation of the tropopause and lower stratosphere can be largely reduced by using high vertical resolutions. On the other hand, a raised model top shows negative impacts on the initial surface wind but positive impacts on the initial surface temperature.

Figure 3.  Bias (a, c) and RMSD (b, d) differences between model results with different model tops: (a, b) wind profiles (m s^-1); (c, d) temperature profiles (K).

The bias and RMSD differences of the wind and temperature analysis profiles after subtracting the systematic differences shown in Fig. 3 are plotted in Fig. 4. Thus, the bias and RMSD differences in Fig. 4 indicate the impact of data assimilation on the initial conditions alone. Negative values indicate that more improvements are made after the application of data assimilation than by raising the model top alone. Also, the smaller the score, the greater the improvement. Improvement was generally achieved in the troposphere. The biases of wind profiles differed from the temperature profiles. Positive impacts on analyzed wind profiles were found over the lower troposphere, whereas slightly negative impacts were observed over the lower troposphere in the analyzed temperature profiles and positive impacts were found in the tropopause layers. Overall, RMSDs showed improvement after data assimilation. Larger improvement for wind profiles was achieved in the lower troposphere, with an extra 15% performance skill. Smaller improvement was also observed at the tropopause. The improvements in the analyzed temperature profiles showed two peak values over the lower troposphere at the 900 - and 200-mb layers. An extra 40% and 50% performance skill was obtained at those two layers, respectively, in Hybrid-1 compared to Hybrid-50. By comparing the Hybrid-10 and Hybrid-1 experiments, no significant differences were observed in the bias patterns. The major improvements from a model top at 10 mb to one at 1 mb were located at the tropopause for both wind and temperature. No significant improvements were achieved in the analyzed wind profiles when the model top was raised from 10 mb to 1 mb, since no significant bias differences can be seen in Fig. 4a, and only slight improvements of RMSD are apparent in Fig. 4b. In contrast, further improvements (approximately 20%) in the analyzed tropospheric temperature, especially in the lower troposphere and tropopause, were obtained when the model top was raised from 10 mb to 1 mb.

Figure 4.  Bias (a, c) and RMSD (b, d) differences between model results with different model tops after data assimilation and systematic differences were subtracted: (a, b) wind profiles (m s^-1); (c, d) temperature profiles (K).

A 72-hour forecast was applied for each run, and the forecasts of wind and temperature profiles at 12 -, 24-, 36-, 48-, 60- and 72-hour forecast lead times were analyzed against conventional observations. The differences in the forecast performance skill for wind and temperature profiles caused by raising the model top and applying data assimilation are plotted in Fig. 5 and Fig. 6, respectively. The negative values (blue shaded areas) in Figs. 4, 5a and 5d indicate improvement was made by raising the model top alone. Blue shaded areas in Figs. 5, 6b and 6e indicate improvement was made by raising the model top and by assimilating added stratospheric information. Blue shaded areas in Figs. 5, 6c and 6f (produced by subtracting the systematic differences caused by raising the model top alone) indicate that further improvement was made by data assimilation alone.

Figure 5.  RMSD differences between predicted wind speed profiles (m s^-1) as a function of forecast lead time (h). Results from the model top at 50 mb were used as reference. (a, d) WRF-10/WRF-1 minus WRF-50; (b, e) Hybrid-10/Hybrid-1 minus Hybrid-50; (c, f) net improvements by data assimilation with a model top at 10 mb/1 mb, respectively.

Figure 6.  RMSD differences between predicted temperature profiles (K) as a function of forecast lead time (h). Results from the model top at 50 mb were used as reference. (a, d) WRF-10/WRF-1 minus WRF-50; (b, e) Hybrid-10/Hybrid-1 minus Hybrid-50; (c, f) net improvements by data assimilation with a model top at 10 mb/1 mb, respectively.

The major improvements for the predicted wind profiles were achieved in the tropopause layers for both a model top at 10 mb and 1 mb (Fig. 5). On average, an extra 6.5% and 11.5% in prediction skill at the 12-hour forecast lead time was obtained by raising the model top to 10 mb and 1 mb alone, respectively. After the assimilation of operationally available observations, major improvements were also obtained in the tropopause layers, with an extra 7.7% and 15% in prediction skill, on average, at the 12-hour forecast lead time when the model top was raised to 10 mb and 1 mb, respectively. Both raising the model top alone and applying data assimilation showed less prediction skill over the near-surface level at all forecast lead times. From Figs. 5c and 5f, the major contributions of the assimilation of extra stratospheric measurements were also in the tropopause layers. The Hybrid-10 experiment showed less improvement in the lower stratosphere (100-150 mb) and lower troposphere. In contrast, Hybrid-1 showed more improvement over all layers at early forecast lead times. An extra 5% in performance skill was achieved over the tropopause layers after subtracting the systematic differences. Less improvement was obtained by data assimilation alone over the lower troposphere at longer forecast lead times (60 - and 72-hour forecast lead times) than raising the model top alone.

For the predicted temperature profiles (Fig. 6a and d), major improvements made by raising the model top alone were located mainly at higher levels and the near-surface level. By raising the model top to 10 mb alone, an extra 22%, 13% and 20% in performance skill, on average, was obtained at early forecast lead times in predicting temperature at the near-surface level, tropopause layers, and lower-stratospheric layers, respectively. However, at longer forecast lead times, negative impacts were found in the lower-tropospheric layers with an average decrease of 3% in performance skill. When the model top was further raised to 1 mb, improvement was found in all vertical layers. The layers with major improvement showed an extra 25.7%, 18.8% and 22.4% in performance skill, on average, which was slightly better than raising the model top to 10 mb.

Similar structures were obtained in the data assimilation experiments. As shown in Fig. 6b and 6e, slight improvements were obtained in the lower troposphere, while larger improvements were achieved in the tropopause layers. After subtraction of the systematic differences, the gross impacts of data assimilation alone are shown in Fig. 6c and 6f. Unlike the prediction of wind profiles, the assimilation of operationally available observations showed less of an impact in the lower stratospheric layers than by raising the model top alone. However, greater improvement over the tropopause layers was obtained in the prediction of both wind and temperature. On average, an extra 4.8% and 8% in prediction skill was obtained over the tropopause layers after subtracting the systematic differences for a model top at 10 - and 1 mb, respectively. Thus, the added information in the 10-1-mb layers had more of a positive impact on the prediction of tropopause temperature. However, for the near-surface and lower-tropospheric temperatures, the assimilated stratospheric information located in the 10-1-mb layers did not lead to greater improvement. In contrast, the Hybrid-10 experiment did show greater improvement (an extra 2.3% in performance skill) over the lower levels at early forecast lead times, as compared to the Hybrid-1 experiment (an extra 0.5% in performance skill). Thus, the extra stratospheric information in the 50-10-mb layers played a positive role in the prediction of lower-troposphere and near-surface temperatures.

The heavy precipitation event used for the verification of model tops and extra stratospheric information occurred during 2-4 January 2015. The observed precipitation distribution during this period is illustrated in Fig. 7. The GLDAS precipitation data were obtained from NOAA' s Advanced Hydrologic Prediction Service. As shown in Fig. 7, this precipitation event started east of Texas and moved eastwards. The main precipitation area is demarcated by the black box in Fig. 6.

Figure 7.  Observed precipitation distribution (inches) from 2 January to 4 January 2015, from NOAA. The black box indicates the main precipitation area.

As shown in Fig. 8, the experiments with a model top at 50 mb generally had better correlation coefficients and RMSDs. Only slight differences were observed when the model top was raised. When the model top was raised to 10 mb, with 20 vertical levels in the stratosphere, the scores dropped to the lowest among these three vertical resolutions. The scores increased slightly when the model top was further raised to 1 mb, with 40 vertical levels in the stratosphere. According to Aligo et al. ^[14], this drop in score level may be related to the uncertainties caused by the interaction between lower-atmospheric processes and microphysical processes above the melting level with a refined vertical resolution. The assimilation of operationally available observations, especially satellite measurements, in the stratosphere may bring more uncertainties into the system. Further studies of the impacts of assimilation of satellite measurements on the amount of precipitation are needed. Despite the drop in scores in the data assimilation experiments, we found that data assimilation did benefit the forecast at certain points. For instance, at 1200 UTC 2 January 2015, the WRF experiments underestimated the precipitation, while the data assimilation experiments better predicted the amount of precipitation. Also, between 1200 and 1500 UTC 3 January 2015, the WRF experiments largely overestimated the precipitation (bias exceeded 1500 mm), while the data assimilation experiments improved the total precipitation amount a lot (bias reduced to ~500 mm).

Figure 8.  Three-hourly accumulated precipitation (mm) from GLDAS and experiments with different model tops and vertical resolutions. The blue solid line indicates the GLDAS products; the black solid, dashed and dotted lines indicate the WRF-50, WRF-10 and WRF-1 experiments; and the red solid, dashed and dotted lines indicate the Hybrid-50, Hybrid-10 and Hybrid-1 experiments, respectively.

The precipitation Threat Scores (TSs) based on the contingency table shown in Fig. 9 were calculated to further analyze the impact of raising the model top and data assimilation. The TSs as a function of precipitation threshold calculated from all six sets of experiments are plotted in Fig. 10. As can be seen, there was hardly any difference when the precipitation threshold was less than 10 mm. The scores started to differ when the threshold was larger than 20 mm. By raising the model top alone, the TSs at precipitation thresholds larger than 20 mm decreased slightly. However, when data assimilation was applied, the best results were obtained from the Hybrid-1 experiment. Thus, the inclusion of the entire stratosphere and added information from assimilation in the extra layers benefitted the tropospheric predictions, despite the magnitude being relatively small.

Figure 9.  A 2 × 2 contingency table, where a represents the number of correctly forecast events "(hits"), b the number of false alarms, c the number of misses, and d the number of correctly forecast non-events.

Figure 10.  Threat Score (TS) as a function of precipitation threshold from different experiments.

The impacts of the model top and the assimilation of added stratospheric information on continental U. S. winter short-range weather forecasts were investigated in this study. The initial and predicted wind and temperature profiles were analyzed against conventional observations. A winter storm case was further studied to demonstrate the usage of more stratospheric layers and data in NWP.

Generally, the initial wind and temperature bias profiles were better adjusted when a higher model top and refined vertical resolution were used. Generally, positive impacts were observed over the tropopause and lower stratosphere, which were related to the interpolation with finer vertical resolution leading to a better representation of the tropopause and stratosphere. However, negative impacts were observed over the lower troposphere in both the initial wind and temperature profiles. The assimilation of operationally available observations then had even more of a positive impact on the initial tropospheric wind and temperature profiles, with lower RMSDs than raising the model top alone. A better representation of the stratosphere with high vertical resolution had more of a positive impact on the initial stratospheric wind profiles.

Predictions made with the stratospheric initial conditions and refined vertical resolution showed generally better forecast skill. The major improvements caused by raising the model top with refined vertical resolution, as well as by data assimilation, were in both cases located in the tropopause and lower stratosphere. Frequent negative impacts were also observed, in the predicted near-surface wind and lower-atmospheric temperature. These negative impacts may be due to the uncertainties related to more vertical layers and the assimilation of satellite measurements over high altitudes in the stratosphere. Also, these negative impacts may further affect the tropospheric weather forecast.

A winter snowstorm case was used to evaluate the stratospheric initial conditions and data assimilation. Predicted 3-hourly accumulated precipitation showed that both the raised model top and data assimilation had negative impacts on the predictions. The largest drop in scores was observed in the experiments with a model top at 10 mb, while the experiments with a model top at 1 mb showed only a slight drop in scores. The negative impacts are believed to have been caused by the uncertainties stemming from the interaction between the lower-atmospheric processes and the microphysical processes above melting levels, as mentioned by Aligo et al. ^[14], since the lower troposphere and near-surface state suffered in terms of quality in the initial conditions and predictions. However, the TS showed that raising the model top alone may bring some negative impacts, but the assimilation of the added stratospheric information up to 1 mb did have slightly positive impacts on the prediction of precipitation. Furthermore, the vertical layers used in this study may still be insufficient for a model top set as high as 1 mb. More experiments with finer vertical resolutions and carefully selected observations, especially remotely sensed observations from satellites, are needed. Also, just the one winter storm case used here may not be sufficient. More cases studies, including severe storms, hurricanes, convection-related local storms etc., are needed.