1. Introduction
Convective parameterization has been used in the atmospheric models since the early days of numerical weather prediction. For model grid sizes greater than 10 km, such schemes have been conventionally applied in order to simulate the effect of unresolved convection in the atmosphere, and these schemes have been shown to be crucial in reproducing atmospheric phenomena such as tropical storms (e.g., Bassill 2015), mesoscale convective complexes (e.g., Zhang et al. 1989), and various other types of convection (e.g., Kuo et al. 1996; Bechtold et al. 2008). In recent years, the resolution of the numerical weather prediction models has increased significantly, and many global models have been run routinely at equivalent grid sizes of less than 10 km. At these resolutions, the assumption inherent in convective parameterizations that the convection occupies only a small percentage area of a grid box, and their application at grid sizes much less than 10 km has been called into question (e.g., Arakawa and Wu, 2013). Moreover, a new category of global and regional models that employ variable mesh sizes (e.g., Yeh et al. 2002; Fox-Rabinovitz et al. 2005; Zarzycki et al. 2014; Skamarock et al. 2012) has emerged in the last 10 years, and these models require a single convective parameterization that properly represents convection across the full range of the variable mesh.
At the other end of the spectrum, uniform mesh numerical weather prediction models at grid sizes 1–4 km without using a convective parameterization have been popular over the last 20 years (Done et al. 2004; Xue and Martin 2006; Weisman et al. 2008; Schwartz et al. 2015). While the forecasts from these models have shown great success, some issues have been reported. These include a slower onset of the convection, underestimation of weak convection, and overprediction of heavy rainfall (e.g., Schwartz et al. 2015). Recent works by Zheng et al. (2016); and Kwon and Hong (2017) have explored applying modified convective parameterizations that are scale-aware to convective cases at 3- and 1-km grid sizes and reported improved prediction of convection and surface rainfall. In their simulated 6–7 July 2010 case, Zheng et al. (2016) showed the scale-aware Kain–Fritsch scheme applied in a 3-km nest helped to reduce the widespread light precipitation, and focus more organized convection in northeastern Oklahoma (their Fig. 13). Using a modified simple Arakawa–Schubert scheme at 3 and 1 km, Kwon and Hong (2017) illustrated how the heavy rainfall center was shifted closer to the observed location from offshore to onshore of the Korean Peninsula in the 27 July 2011 case.
In addition to the abovementioned scale-aware convective parameterization schemes (CPS), Grell and Freitas (2014) is another widely used CPS that considers the grid-size dependency. All three schemes are available in the WRF Model, and the scale-aware Kain–Fritsch [also known as the multi-scale Kain–Fritsch (MSKF)] and Grell–Freitas options have also been applied in MPAS (Fowler et al. 2016, 2020). The main objectives of this study are to propose a scale-aware modification to the Tiedtke CPS, to evaluate its performance in predicting surface rainfall in a few convective cases using model grid sizes of 1.5–4.5 km, and to demonstrate the modified scheme can be applied in a variable mesh model. An earlier version of this scale-aware Tiedtke scheme was employed in a 40 days, 3.8-km quasi-uniform mesh MPAS simulation for the DYAMOND project. The model produced reasonable mean surface precipitation (Stevens et al. 2019), as well as tropical storm activity during the period (Judt et al. 2021). The IBM Global High-Resolution Atmospheric Forecasting System (GRAF) has adapted a version of this scheme for its global 15–3-km operational forecasts (Wilt and Wang 2020). Upon examination of 50 reforecasts and compilation of verification statistics for surface temperature, wind, and precipitation over CONUS, they showed that a tuned version of the scale-aware Tiedtke scheme performed well. In particular, the scale-aware aspect of the scheme produced smooth transitions across the variable resolution mesh regions for Hurricane Irma reforecasts as they tested different high-resolution mesh placements across the storm track.
The paper is organized in the following way: The scale-aware CPS as well as the testing strategy are presented in section 2, the results of the evaluation are discussed in section 3, and the work is summarized in section 4.
2. Method
a. The scale-aware scheme
The Tiedtke convective parameterization scheme (Tiedtke 1989) considered in this study is based on the document for the Integrated Forecasting System (IFS) Cy40r1, European Centre for Medium-Range Weather Forecasts (ECMWF 2014), and implemented in the WRF Model by Zhang and Wang (2017). The scheme considers three types of convection: deep, shallow, and midlevel. The midlevel convection is considered only if the scheme fails to trigger deep or shallow convection, and represents convection that does not originate from the boundary layer. A cloud model with simple microphysics is used in the scheme. Both entrainment and detrainment are considered in the cloud model, and they are function of height. The scheme employs a new convective available potential energy (CAPE) closure (Bechtold et al. 2014) that relaxes to a value produced by the boundary layer processes, rather than to zero. This allows the scheme to better simulate diurnal precipitation over land. The convective adjustment time scale used in the scheme is a function of cloud depth and averaged updraft velocity in the cloud layer, as well as a scaling factor αx. The scaling factor prior to the November 2016 implementation has only a weak dependency on the model’s grid size. In addition to provide changes to temperature and water vapor on the grid scale, the scheme also adds detrained cloud water and ice to the model microphysics variables. Momentum transport is also considered. For the intricate details of the scheme, readers are referred to ECMWF physics document.
Recent works by Zhang et al. (2015) and Malardel and Bechtold (2019) have established that the basic mass flux equations are valid even when the model grid sizes fall below 10 km. At these resolutions, the dynamics of the model begins to resolve more convective motions and mass fluxes required to stabilize atmosphere must decrease, and reduce to zero in the limit of grid size approaching to zero. For a practical approach, we follow the idea that increasing the convective adjustment time scale will lead to slower consumption of CAPE and hence reduce the parameterized convective activity. This idea has been reported in many studies. For example, Done et al. (2006) used this time scale in the Gregory and Rowntree (1990) convective parameterization to control the partition between parameterized and explicit convection. Zheng et al. (2016) used this idea to develop the scale-aware Kain–Fritsch scheme (KF; Kain 2004), which uses a closure that depends on CAPE removal. The Tiedtke scheme used in this study also employs a CAPE closure. Hence, using a scaling that increases the convective adjustment time with decreasing grid size appears to be a reasonable approach. Since the version of IFS Cy43r1 (ECMWF 2016), this scaling parameter has also been made more grid-size dependent when the grid size falls below 8 km.
b. Testing strategy
Several cases are selected to test the modified scheme in the WRF Model version 4.1 (Skamarock et al. 2019) and the MPAS version 7.0 (Skamarock et al. 2012). The objective is to evaluate how the scale-aware scheme behaves in a variety of convective environments and how the surface rainfall prediction may change at model grid sizes less than 4.5 km when compared to simulations in which only a microphysics scheme is used without the SAT.
The first case is a springtime convective event that occurred over the continental United States on 20 May 2017. A line of convection developed in the west-central Texas early in the day and moved northeastward into central Oklahoma (OK). Aided by a strong low-level jet and a deep moist layer, the convective system produced heavy rainfall over eastern OK between 0000 and 1200 UTC. Over 50 mm of rain fell during the two consecutive 6-h periods over a large swath of the state, and rainfall exceeding 120 mm in 6 h was observed locally. The WRF Model is used for this case with a single 3-km mesh, and the model was initialized at 0000 UTC 20 May 2017 and run for 24 h.
A tropical convective event on 26 January 2016 in the vicinity of Singapore and Sumatra is selected as a second test case for evaluating the scheme. On this day, isolated showers developed over the sea east of Singapore and moved west-southwest throughout the day (0000–1100 UTC), as revealed by the radar estimated rainfall. Occasionally very localized hourly rainfall exceeding 9 mm h−1 was observed. For this case, the WRF Model uses 4.5- and 1.5-km 1-way interactive nested grids and is run for 24 h starting from 0000 UTC 26 January 2016.
The third case is a forecast for Hurricane Harvey, which made landfall on the Texas coast on 26 August 2017. The storm became well organized during the day on 23 August, and then underwent rapid intensification over the next 2 days from a tropical depression at 1200 UTC 23 August to a category-1 hurricane at 0000 UTC 25 August, and attained category-4 strength a day later, just prior to landfall. In making landfall as a major hurricane, Harvey produced heavy rainfall along the coastal area. The WRF Model forecast is initialized at 0000 UTC 23 August and run for 84 h to cover the time of landfall. The model is configured with nested 27-, 9-, and 3-km, 1-way interactive grids, such that the 3-km domain covers the storm track for the entire period.
A simulation for Hurricane Irma was selected as the final case for this testing. Irma was first declared as a tropical depression near 16°N, 27°W on 30 August 2017. It became a major hurricane in just 2 days. The storm moved across Atlantic Ocean in the subsequent 10 days, affecting multiple islands along the way, and made its final landfall near Marco Island, Florida, at 1930 UTC 10 September. The long history of the storm makes it a good case to test the scale-aware Tiedtke scheme in the global MPAS as the storms traverse through its variable-resolution mesh. The MPAS model using a 15–3-km variable mesh is initialized at 0000 UTC 6 September and run for 5 days to include Irma’s landfall in Florida. At the model start time, Irma is a category-5 storm with minimum sea level pressure of 915 hPa, and maximum winds of 155 kt (1 kt ≈ 0.51 m s−1) from the best track data.
For all four test cases, the Global Forecast System (GFS) analyses and forecast data from the National Centers for Environmental Prediction at 0.25° resolution at 3-h intervals are used for initial and lateral boundary conditions, whenever appropriate. The forecast period, grid sizes and major physics options used are listed in Table 1. The physics set used for case 1 is the same as those used in the NCAR Ensemble Forecast Experiment ran from April 2015 to December 2017 (Schwartz et al. 2019). The model configuration from case 2 came from the Centre for Climate Research, Singapore, which ran real-time forecast using the WRF Model. The physics used in the two hurricane cases are those employed in the real-time MPAS forecast experiments from 2016 and 2017 seasons (Wang et al. 2018). The PBL option was switched to MYNN in the Irma case because it produced a slightly better track in the 5-day forecast. The model runs with microphysics only will be referred to as MP, while the runs with added scale-aware Tiedtke scheme will be called SAT. In some cases, the runs using the original Tiedtke scheme are also included to assist comparison, and these runs will be noted as “Original.”
Model start time, forecast length, grid size, and major physics used in the simulations. RRTMG: Long- and shortwave radiation (Iacono et al. 2008); Noah LSM: Land surface model (Chen and Dudhia 2001); MYJ PBL: Mellor–Yamada–Janjić planetary boundary layer scheme (Janjić 1994), YSU PBL: Yonsei University PBL scheme (Hong et al. 2006); MYNN PBL: Mellor–Yamada–Nakanishi–Niino PBL scheme (Nakanishi and Niino 2009); Thompson microphysics: Thompson et al. (2008); and WSM6 microphysics: Dudhia et al. (2008).
3. Results
Among many aspects of the convection that could be examined, we choose to focus mainly on the surface rainfall prediction with and without the modified CPS.
a. The midlatitude convection case
This case provides an opportunity to look at two types of convection. In the first type, strong and organized convection with heavy precipitation that evolved from a system that developed on the previous day and moved from central to east Oklahoma and then into Missouri and Arkansas. This period covers mainly from 19 May to the early morning of 20 May. As the system moved through Missouri and Arkansas, it began to dissipate. Ahead of this decaying system, scattered convection developed after the sunrise over Mississippi, Alabama, and Georgia. This convection was not well organized, but some cells were intense and produced significant rainfall at some locations.
The simulated 6-h rainfall (0000–0600 UTC 20 May) from three 3-km WRF runs is presented in Fig. 1 together with Multi-Radar Multi-Sensor (MRMS) system (Zhang et al. 2016) estimated rainfall for the same period when the severe and organized convection occurred. Compared to the MRMS analysis, the modeled rainfall generally captured the main features of the system even when the original Tiedtke scheme is used (Fig. 1f). The model reproduced the heavy rainfall exceeding 50 mm and even 100 mm in 6 h over the eastern Oklahoma (Figs. 1b and 1d). Adding the scale-aware CPS produced a similar outcome, with somewhat better positioning of the heavy rainfall center (>125 mm in 6 h). The light and contiguous precipitation east of the heavy rainfall area at the border of Oklahoma and Arkansas, and the break between the main system in Oklahoma and the convection in central Texas are also somewhat better represented in the SAT run. The convective portion of the total modeled precipitation for the SAT and Original runs are also shown in Figs. 1c and 1e. With the scaling, the percentage of rainfall produced by the CPS is reduced significantly, making the rainfall distribution more like the MP run. In the Original run, the CPS dominates the event, and did not capture the heaviest precipitation. Figure 2 shows the predicted 6-h rainfall in the southeastern United States from 1800 UTC 20 May to 0000 UTC 21 May, representing the period of less organized convective activity. Compared to the MRMS analysis, it is apparent that the original Tiedtke scheme is not adequate to simulate the surface rainfall during this period (Fig. 2f). This run produces too much widespread light precipitation and fails to generate any significant rainfall amount. On the other hand, both the MP and SAT runs are able to forecast localized surface rainfall exceeding 25 mm in 6 h. Precipitation in Louisiana and Georgia, and a few high rainfall centers in Alabama are overpredicted in the MP run (Fig. 2b), and some improvement can be seen in SAT (Fig. 2d). Though the precipitation near the coastal area is underpredicted in both the MP and SAT runs, light rain did extend to offshore in the SAT simulation.
(a) MRMS-estimated 6-h surface precipitation (mm) from 0000 to 0600 UTC 20 May 2017. Model simulated surface rainfall for the same period over a subarea of the simulation domain using the (b) Thompson microphysics only; (c),(d) microphysics plus scale-aware Tiedtke; and (e),(f) the original Tiedtke. The rainfall produced by the Tiedtke scheme in the respective runs is shown in (c) and (e).
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
As in Fig. 1, but for the 6-h period ending at 0000 UTC 21 May 2017.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The MRMS analysis and simulated 1-h surface rainfall valid at 1900 UTC 20 May are shown in Fig. 3. The observed rainfall shows a weakening line of convection along the eastern border of Arkansas, and newly developed rain cells in Louisiana, Mississippi, and Georgia. Compared to the observed rainfall (Fig. 3a), both WRF simulations reproduce the line of decaying convection and widespread convection ahead of it. The new convection in the model is less organized, and not as strong as it is in the observation. A closer look at the modeled rainfall shows that the orientation of the decaying system and separation between the old and new convection in Arkansas and Mississippi is better represented in the SAT run. The light surface rain is more widespread in the SAT run (<1 mm h−1), which may be considered as small improvement in areas of southeast of Mississippi and southwest of Alabama. The intensity of the rain cells is often weaker in SAT, which helps to reduce high rain biases in some places such as near the Arkansas and Louisiana border, and in northern Alabama where very little rain is observed.
The 1-h surface rainfall (mm) valid at 1900 UTC 21 May 2017 from (a) MRMS analysis, (b) MP, and (c) SAT.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
Figure 4 depicts the 24-h observed and simulated precipitation on 20 May. The previously discussed strengths and weaknesses of the simulations are also evident. Although the inclusion of the scale-aware CPS did not significantly alter the simulated rainfall, it did help remove some localized high rainfall cells in the south and reduced the rainfall in other parts of the domain. This can be due to the stabilizing effect of convective parameterization, especially in area where convection may not be well resolved by the model. The hourly time series for rainfall falling in the area depicted in the red box in Fig. 4a also provides some evidence of this improvement (Fig. 5). The hourly rainfall is slightly lower in the SAT run from forecast hour 8 to 20, and closer to the observed amounts. The SAT run also produced slightly higher hourly rainfall at forecast hour 1, indicating a small improvement in the slow start of model convection. The dashed lines shown in Fig. 5 are percentages of convective rainfall over the total rainfall for the SAT and Original runs. The scaling successfully reduces the widespread convective rain and does not inhibit microphysics to activate in strongly convective areas. Although the added SAT provides a small improvement over the MP run in some areas (such as along the coast), it generates too much drizzle [e.g., <1 mm (6 h)−1 and <2 mm (24 h)−1]. More research will be needed to improve this aspect of the CPS. In general, the strongly forced convection at midlatitudes in the spring is expected to be simulated reasonably well with explicit convection in numerical models having a 3-km grid size. However, this case demonstrates that there is some benefit in including a scale-aware CPS to reduce light precipitation bias and overprediction of localized rainfall in some areas, and to improve area rainfall totals.
(a) MRMS 24-h surface precipitation (mm) from 0000 UTC 20 May to 0000 UTC 21 May 2017. Model simulated precipitation for the same period using the (b) original Tiedtke scheme, (c) Thompson microphysics only, and (d) with microphysics and scale-aware Tiedtke. The red box in (a) indicates the area over which Fig. 5 is calculated.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
Area-averaged hourly rainfall time series over the 24-h forecast period from the MRMS analysis (black line) and the three model runs: MP (skyblue), SAT (red), and original Tiedtke (orange). The percentages of convective rainfall from the SAT and original Tiedtke runs are also shown in dashed lines. The totals are computed over the area over 30°–45°N and 82°–103°W as shown by the red box in Fig. 4a.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
b. The tropical convection case
It is well known that convection and rainfall is harder to forecast in the tropics. Although many factors contribute to the challenge, an important one is that the scale of the convection is typically smaller than its counterpart at the midlatitudes. In a numerical model, this implies that a CPS may play a more significant role in model simulations of tropical convection even with a grid size of a few kilometers.
Figure 6 shows the radar estimated rainfall for the tropical convection case at two selected times, 0800 UTC [1600 local time (LT)] and 1800 UTC (0200 LT) 26 January 2016 (courtesy of Meteorological Service Singapore). The two time periods are selected to represent widespread afternoon showers and relatively calm situation at night. (It is noted that the rainfall map is estimated from a single radar located in Singapore. This means the lack of rain farther away from the domain center may be a result of lack of coverage.) Earlier in the day, showers developed over the sea east of Malaysia and moved across the region. Showers at 0800 UTC were present to the south of Singapore with an hourly accumulation exceeding 9 mm in a few places (Fig. 6a). The showers largely dissipated over land at night, as indicated by the radar estimated rainfall valid at 1800 UTC (Fig. 6b), with some lingering showers farther to the south. The WRF simulated surface rainfall in the 4.5-km domain is shown in Fig. 7 over a larger area than depicted in Fig. 6. It shows widespread showers over both Malaysia and Sumatra that persisted over land at night. Compared to the simulated rainfall using microphysics only (Figs. 7a,b), adding the scale-aware Tiedtke scheme shows some improvement (Figs. 7c,d). During the day, the showers are less widespread and with fewer intense cells. At night, the improvement is more noticeable. Over land in Malaysia and over the sea to the east, showers are largely absent, agreeing more with the radar estimated rainfall from Fig. 6. Showers over Sumatra becomes less intense in many locations, but light showers are more widespread to the west of Sumatra. Similar improvements including the SAT can be found in the 1.5-km domain (Fig. 8). Showers are less prevalent and weaker in intensity during the day (comparing Figs. 8a–c), and dissipated more over the domain at night (Figs. 8b,d). Improvement is also noted over the ocean in the east part of the domain with significant less shower activities in the SAT run.
Single radar estimated surface rainfall in mm at (a) 0800 UTC (1600 LT) and (b) 1800 UTC (0200 LT) 26 Jan 2016. The blue dot in the center of the domain indicates where Singapore is and where radar observation is made. (Courtesy of Centre for Climate Research, Singapore.)
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
Simulated hourly rainfall (mm) valid for (a),(c) 0800 and (b),(d) 1800 UTC 26 Jan 2016 at 4.5-km grid size. (top) With WSM6 microphysics only and (bottom) with WSM6 and scale-aware Tiedtke.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
Simulated hourly rainfall (mm) valid for (a),(c) 0900 and (b),(d) 1800 UTC 26 Jan 2016 at 1.5-km grid size. (top) WSM6 microphysics only and (bottom) WSM6 and scale-aware Tiedtke.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The overpredicted surface rainfall by using microphysics alone is better illustrated using time series of domain-averaged precipitation. Figure 9 shows the time series plots from both the 4.5- and 1.5-km domain, covering the area of the 1.5-km domain. In the 4.5-km domain, the hourly precipitation rate is reduced nearly by half during much of the simulation period when the scale-aware CPS is added. The averaged rain is also decreased in the 1.5-km domain by about 30%. The most dramatic differences are shown from 1800–0000 UTC (0200–0800 LT), where very little precipitation is simulated when the scale-aware CPS is included. Without the scale-aware CPS, the simulated showers continued overnight in the area. This overprediction of surface rain does not seem to be sensitive to domain sizes or choice of microphysics (three other schemes were tested). This issue does not appear to be unique to the WRF Model either. In an effort to develop a convective-scale NWP system for Singapore and surrounding area, Dipankar et al. (2020) documented a similar problem with the Met Office convective-permitting model over this region. Significant development has been carried out to improve the model performance over this area.
Model simulated time series of area-averaged rainfall from (a) 4.5-km domain covering the area of 1.5-km domain area and (b) 1.5-km domain. The black lines are from microphysics-only runs, and red lines are from the SAT run. The dashed red lines represent the percentage of convective rainfall in the scale-aware CPS.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The dashed lines in Fig. 9 depict the percentage of convective rainfall from the SAT run and it indicates the scaling of the CPS works as expected, decreasing when the grid size is reduced from 4.5 to 1.5 km.
In contrast to the midlatitude convective case, this case demonstrates that a CPS may be necessary to better predict tropical convection and improvement may be obtained even at a 1.5-km grid size. When the convection is not well resolved, without a CPS its formation may be delayed, but once it develops, its intensity can be oversimulated by the model, similar to the scenarios discussed in Weisman et al. (1997) and Bryan and Morrison (2012). In this case, it is likely the stabilizing effect of the Tiedtke scheme helps to reduce the widespread showers and contribute to the improvement.
c. Hurricane Harvey (2017)
The observed and simulated 24-h surface rainfall, from 84-h forecast in the 3-km domain, for Hurricane Harvey ending at 1200 UTC 26 August is presented in Fig. 10. The rainfall from the original Tiedtke run is plotted for comparison. Both the MP and SAT runs produced heavy rain in excess of 300 mm during the 24-h period near the location of landfall. A closer examination shows that the forecast heavy rainfall in the SAT run is better represented both near the storm center as well as in the secondary band to the northeast. The storm tracks from the observation and simulations are shown in Fig. 11a, while the intensity of the storm as measured by mean sea level pressure (SLP) is presented in Fig. 11b. Overall, the track simulated in the SAT run lines up better with the observed one, especially during the latter part of the run. Neither model runs capture the intensity of the storm well, and they especially miss the rapid intensification during the third day of the simulation. Initializing the model at a time (0000 UTC 23 August) when the storm was not even declared a tropical depression still presents a challenge. Compared to the MP run, the SAT run produces a deeper storm. As shown in Figs. 10 and 11, the original Tiedtke run fails to produce a reasonable forecast for this case.
The 24-h surface rainfall (mm) ending at 1200 UTC 26 Aug 2017. (a) MRMS analysis, (b) 3-km WRF run using the original Tiedtke, (c) with microphysics only, and (d) with microphysics and scale-aware CPS.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
(a) Observed (black) and simulated tracks from 0000 24 Aug to 0600 UTC 26 Aug 2017. (b) Observed (black) and simulated MSLP plotted from 0000 UTC 24 Aug to 1200 UTC 26 Aug 2017. Orange: from original Tiedtke, blue: MP run, and red: SAT run. The marks in (a) are storm positions at 6-h intervals. The position and intensity of the model storm are estimated using RIP4 (https://www2.mmm.ucar.edu/wrf/users/docs/ripug.htm).
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The simulation period starts with the redevelopment of Harvey in the Bay of Campeche at 0000 UTC 23 August. The convection in the model is not well organized during the first day, and convection mostly occurs on the east and northeast side of a broad surface low in the Bay because the air in the midlevels over the west side of the Bay and west of the Gulf of Mexico is relatively dry. Starting from the second day, the convection begins to increase and organize closer to the low center. This is illustrated well by the 3-h surface rainfall time series averaged over the 222 km × 222 km area following the storm center associated with each run for the entire 84-h forecast (Fig. 12). The result from the original Tiedtke run is included for comparison. Beginning on the second day, the rainfall rapidly increases in both MP and SAT runs, but it maintains a higher average in SAT over most of the times, which leads to a deeper storm. Several features from the SAT run are noted. In the first day and half, the SAT run produces wider-spread rain to the east of the developing surface low, and this leads to a broader low pressure area by forecast hour 36, even though the central pressure of the storm is not lower. The SAT run also suppresses some rain cells farther away from the storm and keeps convection somewhat stronger and closer to the low pressure center. The more vigorous convection around the storm seems to help prevent the midlevel dry air from entering the storm center. In contrast, the convection in the MP run takes longer to organize around the low center, partly due to the proximity of the midlevel drier air. In the last 24 h of the forecast, both the MP and SAT runs produced the second rainband to the northeast of the storm, but the location of the band is closer to the storm center in SAT. As shown by the dashed lines in Fig. 12, SAT only contributes a very small part to the total rain, decreasing its portion as the storm becomes well developed. The bit more activity of SAT during the first day may help set the stage for the better organized convection later as discussed above.
Time series of 3-hourly surface rainfall following the storm centers from the runs of MP, SAT, and original Tiedtke for the 84 forecast hours from 0000 UTC 23 Aug to 1200 UTC 26 Aug 2017. The area of average is about 222 km × 222 km.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
d. Hurricane Irma (2017)
One of the motivations for developing a scale-aware CPS is to be able to apply it in a model with variable resolutions, ranging from mesh sizes where a CPS is required to where it approaches to convection permitting scales out of necessity. For this test case, the MPAS model is configured with variable mesh sizes from 3 km centered over the continental United States to 15 km over the rest of the globe. Figure 13 shows the simulated 6-h rainfall from a 96-h forecast ending at 0000 UTC 10 September, overlaid with the contours of the variable mesh at approximately 3-km intervals. At this time, the simulated Hurricane Irma is located between Florida and Cuba, about 46 km east of the observed storm. When the case is initialized at 0000 UTC 6 September, Irma is located near 17.3°N and 60.6°W, roughly in the area where the mesh size is about 6 km. To its east is Hurricane Jose, which has been developing in the past 4 days from an area where the mesh size is about 13 km. Both storms move through the variable mesh region smoothly. As mesh sizes coarsen from 3 km outward, it is observed that the convective features become smoother, as the CPS gradually plays a larger role.
Simulated 6-h rainfall (mm) at forecast hour 96 ending at 0000 UTC 10 Sep 2017, overlaid with mesh contours from 3 to 15 km at roughly 3-km intervals.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The simulated tracks of Irma from the SAT and MP runs are obtained from the Geophysical Fluid Dynamics Laboratory (GFDL) tracker (https://dtcenter.org/community-code/gfdl-vortex-tracker) and presented in Fig. 14a, together with the observed track at 6-h intervals. The central pressure of the storm at every 6 h are extracted directly from the model runs and shown in Fig. 14b. The track of Irma is well simulated in the 5-day forecasts, with SAT producing a slightly better track by moving the storm farther west and landing the storm at about the observed location and time. The modeled intensity is underpredicted in both MP and SAT runs with averaged biases of 2.2 and 3.6 hPa in the first 3 days of the forecast. With the model cold starting at a time when Irma is classified as a category-5 storm, the model does reasonably well in reproducing the strength of the storm. The forecast intensity becomes more challenging in the last 2 days with both runs overdoing the intensity of the storm. Even though the MP run did well to simulate the storm intensity during the first 3 days, the storm becomes too intense in the last 2 days of the forecast. With a better track, the SAT run captures better the interaction between the storm and nearby land by reproducing the weakening and re-strengthening of the storm, as the storm approaches Cuba and then reenters the Straits of Florida. The overprediction of the storm strength is also reflected in the simulated 24-h surface rainfall as shown in Fig. 15. Compared to the MRMS analysis, the SAT run produces slightly better forecast. Overall, adding the scale-aware CPS in this case improves the storm track and surface rainfall as the storm moves through the variable mesh.
(a) Simulated 5-day tracks from two MPAS runs: microphysics only (blue) and SAT (red). The observed track is in black. The positions of the track are marked every 12 h. (b) Simulated mean sea level pressure from the model and best track. The model tracks are obtained from the GFDL tracker.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
The 5-day forecast of 24-h surface rainfall (mm) ending at 0000 UTC 11 Sep 2017. (a) MRMS analysis, (b) WRF run with microphysics only, and (c) WRF run with microphysics and scale-aware CPS.
Citation: Weather and Forecasting 37, 8; 10.1175/WAF-D-21-0179.1
4. Summary
In this study, a scale-aware Tiedtke scheme is developed and tested in the WRF and MPAS models for several convective environments that include midlatitude convection, less-organized tropical convection, and Hurricanes Harvey and Irma of 2017 at model grid sizes of 1.5–4.5 km. The results show that the modified scheme reduces the effect of the parameterized convection as designed, and in a few cases presented here, provides some improvement in several aspects of the precipitation forecasts. In the midlatitude convection case, which is simulated well by the microphysics-only run, the added scale-aware CPS produced a small improvement by reducing the low bias in light precipitation in some areas, suppressing convection in others, and bringing the area-averaged total rain closer to the observation. For the less-organized tropical convection case, the scale-aware Tiedtke scheme played a larger role. It reduced the area total rainfall by removing convective instability more effectively and suppressing spurious convection over the ocean. In the Hurricane Harvey’s case, when the model starts in the early phase of storm formation, SAT appears to aid the development by producing broader convection and better organizing it near the circulation center. The stronger convection also helps to prevent the drier midlevel air in the west part of the Gulf entering the storm center. When the scale-aware CPS is applied in the variable resolution MPAS model, the track of the Hurricanes Irma is improved and the intensity of the storm is better simulated compared to the MP run in the last 2 days of the forecast. The storms move through the variable resolution mesh smoothly. The convective features are sharper in the relatively high-resolution section of the mesh and smoother in the coarser mesh region where the effect of parameterized convection is more dominant.
The work presented here demonstrates that the scaling applied to the Tiedtke scheme works as expected with contribution from the convective parameterization decreasing as the grid size decreases. The modified scheme can be applied to models at a few kilometers resolution and may help improve certain aspects of surface rainfall forecast in some cases. Most importantly, as a scale-aware CPS is required in models with variable mesh sizes, this study, together with others already published, has shown this scheme works well across different mesh sizes.
Acknowledgments.
The author would like to thank Drs. Joseph Klemp and Jimy Dudhia for their review and discussion of the manuscript. The author would also like to thank Dr. Brett Wilt of The Weather Company, An IBM Business for continued evaluation of the scale-aware Tiedtke scheme in the GRAF system, and David Ahijevych for his assistance to use GFDL tracker to produce Fig. 14a. Critics and suggestions from two anonymous reviewers and Dr. Gary Lackmann, the Chief Editor for WAF, have helped to improve this manuscript. The data for Fig. 6 were kindly provided by Centre for Climate Research Singapore, Meteorological Service Singapore. This material is based upon work supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Computing resources were provided by NCAR’s Computational and Information Systems Laboratory (CISL).
Data availability statement.
Data supporting the findings of this work are available from the corresponding author. Specifically, the MRMS surface rainfall data are obtained from https://mtarchive.geol.iastate.edu, and the estimated surface rainfall data for Fig. 6 is provided by the Centre of Climate Research Singapore, Meteorological Service Singapore. The scale-aware Tiedtke scheme code and the WRF and MPAS model output data are available upon request.
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