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  • View in gallery

    Domains used for the 2003–05 4-km real-time WRF-ARW forecasts.

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    (a) Observed NOWRAD composite reflectivity at 0400 UTC 4 Jun 2005 compared to (b) 4-h forecast maximum column reflectivity from WRF-ARW at 0400 UTC, starting from an initial state with zero precipitation.

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    Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 10 Jun 2003 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 9 Jun 2003.

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    (a) Maximum column reflectivity, (b) surface flow field, (c) surface equivalent potential temperature, and (d) northwest–southeast vertical cross section, as located in (a), of reflectivity and ground-relative flow from the 30-h WRF-ARW forecast, valid at 0600 UTC 10 Jun 2003.

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    The 0000–0600 UTC accumulated precipitation (mm) for 10 Jun 2003 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

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    Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 12 Jun 2003 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 11 Jun 2003.

  • View in gallery

    The 0000–0600 UTC accumulated precipitation (mm) for 12 Jun 2003 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

  • View in gallery

    Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 30 May 2004 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 29 May 2004. Arrows in (a) and (b) point to locations of isolated tornadic supercells.

  • View in gallery

    The 0000–0600 UTC accumulated precipitation (mm) for 30 May 2004 from (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

  • View in gallery

    Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC for 5 Jun 2005 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 4 Jun 2005.

  • View in gallery

    The 0000–0600 UTC accumulated precipitation (mm) for 5 Jun 2005 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

  • View in gallery

    (a) Observed NOWRAD composite reflectivity at 0300 UTC for 10 Jun 2005 compared to (b) 27-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 9 Jun 2005. The 0000–0600 UTC accumulated precipitation (mm) for 10 Jun 2005 from the (c) Eta and (d) WRF-ARW 24–30-h forecasts.

  • View in gallery

    (a) Observed NOWRAD composite reflectivity valid at 0300 UTC 5 Jun 2005, and 27-h WRF-ARW forecast maximum column reflectivity, valid at the same time, from simulations using (b) YSU PBL and HRLDAS land surface, (c) MYJ PBL without HRLDAS, (d) YSU PBL without HRLDAS, (e) MYJ PBL and Thompson microphysics, and (f) YSU PBL with RUC vs Eta initial conditions, as described in the text.

  • View in gallery

    CAPE analysis and Springfield, MO (SGF), skew T, valid at 0000 UTC 5 Jun 2005: (a) CAPE analysis from the Eta Model; (b) observed SGF sounding; (c),(d) 24-h forecast CAPE and SGF sounding from the WRF-ARW model using the YSU PBL scheme; and (e),(f) 24-h forecast CAPE and SGF sounding from the WRF-ARW model using the MYJ PBL scheme.

  • View in gallery

    The 24-h WRF-ARW biases for (a) surface potential temperature (K) and (b) surface mixing ratio (g kg−1), averaged from 1 May to 10 Jun 2005, using the YSU PBL scheme.

  • View in gallery

    Maximum column reflectivity from 2-km WRF-ARW forecasts for (a) 30-h forecast valid 0600 UTC 10 Jun 2003 and (b) 24-h forecast valid 0000 UTC 5 Jun 2005. The 2-km WRF-ARW forecast for the 5 Jun 2005 case was contributed by CAPS, as part of the 2005 SPC/NSSL Spring Program.

  • View in gallery

    Hovmöller diagrams of hourly precipitation, extending from 105° to 85°W and averaged from 30° to 48°N for 10–31 May 2004, for the (a) NCEP ST4 analysis and (b) WRF-ARW 12–36-h forecasts.

  • View in gallery

    ETS (red line) and bias (blue line) for the 24-h WRF-ARW precipitation forecasts for the 2005 season. The pink and green lines represent the percentage of total accumulated precipitation beneath a given precipitation threshold, for the observed (ST4) and forecast (ARW) precipitation, respectively.

  • View in gallery

    Diurnally averaged Hovmöller frequency diagrams, extending from 105° to 85°W and averaged from 30° to 48°N, for 10 May–31 Jul 2004: using hourly precipitation data and a precipitation threshold of 0.02 mm, for (a) NCEP ST4 analysis and (b) WRF-ARW forecasts, and using 3-hourly precipitation data and a precipitation threshold of 0.05 mm for (c) ST4, (d) WRF-ARW, and (e) Eta Model forecasts. For (a),(b) dotted and dashed lines approximate the minimum and maximum phase lines for the propagating diurnal frequency signal, respectively, as discussed in the text.

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Experiences with 0–36-h Explicit Convective Forecasts with the WRF-ARW Model

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  • 1 National Center for Atmospheric Research, * Boulder, Colorado
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Abstract

Herein, a summary of the authors’ experiences with 36-h real-time explicit (4 km) convective forecasts with the Advanced Research Weather Research and Forecasting Model (WRF-ARW) during the 2003–05 spring and summer seasons is presented. These forecasts are compared to guidance obtained from the 12-km operational Eta Model, which employed convective parameterization (e.g., Betts–Miller–Janjić). The results suggest significant value added for the high-resolution forecasts in representing the convective system mode (e.g., for squall lines, bow echoes, mesoscale convective vortices) as well as in representing the diurnal convective cycle. However, no improvement could be documented in the overall guidance as to the timing and location of significant convective outbreaks. Perhaps the most notable result is the overall strong correspondence between the Eta and WRF-ARW guidance, for both good and bad forecasts, suggesting the overriding influence of larger scales of forcing on convective development in the 24–36-h time frame. Sensitivities to PBL, land surface, microphysics, and resolution failed to account for the more significant forecast errors (e.g., completely missing or erroneous convective systems), suggesting that further research is needed to document the source of such errors at these time scales. A systematic bias is also noted with the Yonsei University (YSU) PBL scheme, emphasizing the continuing need to refine and improve physics packages for application to these forecast problems.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Morris L. Weisman, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: weisman@ncar.ucar.edu

Abstract

Herein, a summary of the authors’ experiences with 36-h real-time explicit (4 km) convective forecasts with the Advanced Research Weather Research and Forecasting Model (WRF-ARW) during the 2003–05 spring and summer seasons is presented. These forecasts are compared to guidance obtained from the 12-km operational Eta Model, which employed convective parameterization (e.g., Betts–Miller–Janjić). The results suggest significant value added for the high-resolution forecasts in representing the convective system mode (e.g., for squall lines, bow echoes, mesoscale convective vortices) as well as in representing the diurnal convective cycle. However, no improvement could be documented in the overall guidance as to the timing and location of significant convective outbreaks. Perhaps the most notable result is the overall strong correspondence between the Eta and WRF-ARW guidance, for both good and bad forecasts, suggesting the overriding influence of larger scales of forcing on convective development in the 24–36-h time frame. Sensitivities to PBL, land surface, microphysics, and resolution failed to account for the more significant forecast errors (e.g., completely missing or erroneous convective systems), suggesting that further research is needed to document the source of such errors at these time scales. A systematic bias is also noted with the Yonsei University (YSU) PBL scheme, emphasizing the continuing need to refine and improve physics packages for application to these forecast problems.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation

Corresponding author address: Morris L. Weisman, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: weisman@ncar.ucar.edu

1. Introduction

Convective weather remains a significant challenge for numerical weather prediction systems, and is recognized as a major contributor to poor warm season quantitative precipitation forecasting (QPF). During the 2003 Bow Echo and Mesoscale Convective Vortex (MCV) Experiment (BAMEX; Davis et al. 2004; Done et al. 2004), and again for 2004 and 2005, 36-h real-time forecasts were conducted daily with the Advanced Research Weather Research and Forecasting Model (WRF-ARW, or simply ARW; Skamarock et al. 2005) using a 4-km horizontal grid resolution over increasingly large domains centered on the central United States (Fig. 1). The overall goal of these exercises was to determine if there is any increased skill in such convective-system-resolving forecasts during the warm season, measured objectively or subjectively, as compared to coarser-resolution simulations using convective parameterizations [e.g., operational 12-km North American Mesoscale Model (NAM, formerly the Eta Model)]. A more generic goal was simply to establish a better sense of the predictability of significant convective outbreaks over the next diurnal cycle (18–36-h period), and to better understand the factors that might be limiting this predictability within current numerical forecast models. Certainly, the potential applications of such convective-resolving forecasts can go well beyond regional QPF, including explicit prediction of severe surface winds, hail, localized flash flooding, and even perhaps tornadoes. In this regard, it is also important to consider whether there is sufficient value added to such higher-resolution guidance to warrant running such computationally expensive forecasts operationally. This latter question cannot be answered by this initial study, but hopefully this study will help build a foundation that will contribute to such discourse.

Attempts at using coarser-resolution models of order 10 km with parameterized convection to guide convective weather forecasting have generally not fared very well, providing one of the primary motivations for this work. Wilson and Roberts (2006) found that the 10-km Rapid Update Cycle (RUC10) 3-h forecasts of precipitation initiation were correct only 44% of the time during the International H2O Project (IHOP), allowing a tolerance of 250 km in space and about 3 h in time. They also found that the RUC10 was generally not successful in forecasting the evolution and motion of the larger, more intense storm systems, presumably because of the lack of gust fronts. Gallus et al. (2005) similarly document the inability of 10-km versions of the Eta Model, ARW, and the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) with a variety of physics and initializations to forecast a well-documented derecho event 12–24 h in advance. Coarse-resolution models with parameterized convection also have known deficiencies in their representation of the diurnal cycle of convection as well as the related precipitation episodes over the United States (e.g., Davis et al. 2003; Carbone et al. 2002).

Lilly (1990) offers an insightful review of the opportunities and challenges associated with explicit convective forecasting, with respect to the inherent predictability of convection as well as the proper representation of convective processes and the potential uses of radar assimilation within numerical models. In particular, he noted “Weather prediction is the principal reason for the support we are given by our fellow citizens. . . . I believe it is time for convective-storm scientists to apply our knowledge to this purpose and to subject our products to its discipline. . . . The task is not trivial. . . .” Indeed, this review helped motivate and guide the development of the Center for the Analysis and Prediction of Storms (CAPS; e.g., Droegemeier 1990, 1997), whose formal mission was to “demonstrate the practicability of storm scale numerical weather prediction and to develop, test, and validate a regional forecast system appropriate for operational, commercial, and research applications.”

Progress along these lines has indeed been notable over the past decade. For example, using a 6-km grid with explicit convection over Lake Michigan, Fowle and Roebber (2003) demonstrated enhanced skill at forecasting convective occurrence, coverage, and overall convective mode (e.g., linear, multicellular, and isolated) out to 2 days as compared to coarser-resolution forecasts with parameterized convection. Xue et al. (2001, 2003) describe a successful 8–18-h simulation of a line of tornadic storms in Arkansas on 21 January 1999 using 32-, 6-, and 2-km nested grids, starting at 1200 UTC. They found generally good agreement as to the number of storms, the rotational characteristics of the storms, the speed and direction of storm movement, the upscale organization from isolated cells into lines, and, subsequently, a bow-shaped pattern. They did note up to 2-h delays in storm initiation in some regions and position errors of up to 40 km. The 6-km grid correctly predicted the general characteristics of the storms in the late afternoon and evening, but with a timing delay of as much as 4 h, and with less accuracy for cell details and rotational characteristics. They also observed that “the 32-km grid played a key role in reproducing accurately the large-scale environment that fed the convective storms in this region but by itself it was incapable of providing specific, detailed guidance on the timing and location of precipitation or the type and characteristics of the systems that produced the precipitation.”

Xue et al. (2003) further describe a successful 2–3-h prediction of tornadic cells observed over Fort Worth, Texas, on 28–29 March 2000, using the Advanced Regional Prediction System (ARPS) with a 3-km grid resolution embedded within a larger 9-km domain, and by employing various radar assimilation strategies. Kong et al. (2006) considered the use of ensembles to predict this same tornadic thunderstorm complex, using nested grids of 24, 6, and 3 km. The ensembles showed both qualitative and quantitative improvements relative to the deterministic control forecasts. However, the evolutions of convection at 24 and 6 km were vastly different from and inferior to those at 3 km. For the 3-km grid forecasts, Kong et al. (2007) found that both the assimilation of Doppler radar data and shorter (1–2 h) forecast lead times improved the ensemble precipitation forecasts. Similarly Xue and Martin (2006a, b) successfully simulated convective initiation along the dryline 2–3 h in advance on 24 May 2002 during IHOP, using ARPS at 1-km grid resolution nested within a 3-km domain. Finally, Roebber et al. (2002) were able to reproduce many of the supercellular characteristics of the 3 May 1999 tornado outbreak in Oklahoma several hours in advance by initiating a nested 2-km grid 18 h into a coarser-resolution model forecast initialized at 0000 UTC the night before.

These previous studies clearly show the potential to explicitly forecast even the details of convection several hours in advance. In the present study, we build upon these experiences by extending the time frame of the forecast period to consider one and a half diurnal cycles of convective activity (18–36 h), and also by employing much larger forecast domains, thus emphasizing more of the regional convective forecasting issues. In addition, we consider a much larger sample size (232 cases over 3 yr), which represents a broader spectrum of convective scenarios. In contrast, no radar assimilation techniques are applied.

We present here only a representative sample of our forecast experiences to date, as more detailed analyses are still on going. Even at this early stage, however, valuable lessons have been learned that will hopefully guide other similar efforts. We begin in section 2 with a brief discussion of the model specifics for this exercise, followed in section 3 by comparisons between forecast-derived radar reflectivities and observed radar composites to establish the capabilities of the model at reproducing the range of observed convective phenomena critical for such forecast applications. We also compare this guidance to that offered by the 12-km Eta during this time period. In section 4 we present some preliminary subjective verifications of the overall capability of the explicit convective forecasts relative to the coarser-resolution Eta guidance, followed in section 5 by a discussion of forecast sensitivities to various physics options, such as PBL and microphysical representation, as well as resolution. In section 6, we discuss the improved ability of such resolutions to reproduce observed precipitation episodes and diurnal tendencies. In section 7, we discuss the forecaster feedback we received during these exercises. Finally, in section 8, we offer some summary comments and directions for future work.

2. Simulation design

The ARW model specifications for each year of these exercises are summarized in Table 1. The choice of 4 km for the horizontal grid resolution was based both on the practical constraints of completing the simulations overnight as well as recent studies that suggest that 4 km is nominally sufficient to represent mesoscale convective systems explicitly without the need for parameterization (e.g., Weisman et al. 1997). Such grid resolutions, however, are still insufficient for representing individual convective cells and their attendant severe weather (e.g., Bryan et al. 2003). Thus, in evaluating the present model capabilities, we are interested in the ability to forecast the location and timing of regions of convection and the structure and evolution of mesoscale convective systems as opposed to the characteristics of individual convective elements. Use of a 4-km grid over a single large domain, rather than using selective embedded high-resolution windows, avoids the problem of having to choose appropriate windows on a day-to-day basis and also avoids the potential problems associated with mismatched model physics across nested-domain boundaries [e.g., explicit convection on the inner grid versus parameterized convection on the outer grid; e.g., Warner et al. (1997); Warner and Hsu (2000)]. The lack of a convective trigger function for a 4-km grid resolution was initially a point of concern in designing these experiments. Our experiences, however, suggest that explicit convective triggering at such grid resolutions is sufficient in most cases, if not actually a bit overdone at times.

The model was initialized at 0000 UTC using the 40-km NAM/Eta (hereafter Eta) analysis, with the boundary conditions updated on a 3-hourly interval using the Eta Model forecasts. The ARW output was generally available by 1400 UTC (0800 local time), so that the forecast guidance would be available to National Weather Service (NWS) forecasters in time to address the afternoon/evening convective forecast problem. The choice to move the western boundary of the forecast domain from the Continental Divide in 2003 to Nevada for the 2004 and 2005 seasons (Fig. 1) was based on a noticeably weaker than observed diurnal maximum in convective activity over the highest terrain in 2003 (e.g., see section 6). We speculate that this deficiency was related to the inability of the model to properly reproduce the large-scale orographic circulation associated with the Rocky Mountains, but a more detailed discussion of this result is beyond the intended scope of the present study.

Another design factor that we were concerned about was the use of a cold-start initialization at 0000 UTC, when active convection was often already occurring. As shown in Fig. 2, however, observed convective systems and other precipitation features were often reasonably reproduced by the model within 3–5 h of initialization. Indeed, we may have been aided in this regard by our choice of initializing at 0000 UTC, when surface-based convective potential was at its greatest, making it easier to generate convection in regions of resolved low-level convergence. This result is also consistent with the kinetic energy spectral analyses of Skamarock (2004), who showed more generally that small-scale structures in such simulations are effectively spun up over the initial 6–12 h. This provides some confidence that our results for the ⩾12 h forecast periods were not unduly influenced by our simple cold-start procedure.

The basic physics packages included the Yonsei University (YSU) boundary layer scheme (Hong et al. 2006), the Oregon State University (OSU) land surface model (Chen and Dudhia 2001), and the Lin microphysics scheme [derived from the original scheme described in Lin et al. (1983)]. For 2005, the Lin scheme was replaced by the WRF single-moment six-class microphysics scheme (WSM6; Hong and Lim 2006) based on sensitivity testing that suggested the WSM6 reproduced stratiform precipitation somewhat better while also slightly reducing a known high precipitation bias. Also for 2005, we employed the National Center for Atmospheric Research (NCAR) High-Resolution Land Data Assimilation System (HRLDAS; Chen et al. 2007) to help improve the representation of soil moisture in the initial state. Although these variations represent potentially significant changes in the model configuration over the 3 yr considered herein, retesting of a representative set of cases has confirmed that they resulted in only relatively small changes in overall forecast accuracy, and thus we feel confident in discussing the results of all 3 yr together.

Further sensitivity testing on specific cases also considered the use of the Miller–Yamada–Janjić (MYJ) PBL scheme (Janjić 2001), the Thompson microphysical scheme (Thompson et al. 2006), and initialization using the analysis from the 25-km resolution RUC-native coordinate data (e.g., sigma–theta in the vertical) as obtained from the National Centers for Environmental Prediction (NCEP) operational site. Some of the more significant sensitivities will be discussed further in section 5.

3. Overall results

The primary goal of this study is to document the ability of 4-km grid resolution simulations to represent and forecast the characteristics of convective weather systems. As such, it is most appropriate to compare the model output directly to Next-Generation Doppler (NEXRAD) radar observations, which represents the method most readily available to forecasters for documenting convective weather. For this purpose, we found it most convenient to compare the maximum column reflectivity as derived from model variables to the observed maximum reflectivity obtained from WSI Corporation National Operational Weather Radar (NOWRAD) mosaics. Radar reflectivity for the model output was derived based on the mixing ratios of hydrometeor species (e.g., rain, snow, graupel), as described by Koch et al. (2005).

Another goal is to consider whether there is any value added in the present high-resolution simulations as compared to coarser-resolution simulations using convective parameterization. For this purpose, we chose to compare the 4-km ARW results primarily to the 12-km operational Eta, which was used to specify the initial state as well as the boundary conditions for the present ARW runs, and which was also readily available in real time and quite familiar to forecasters. In addition, 12-km versions of ARW were run for the select cases described in section 3 [using the Betts–Miller–Janjić (BMJ) convective parameterization scheme, as is also used by the Eta], though, to help clarify which differences may be specific to the differing model formulations versus resolution. For instance, we have noted that ARW generally produces finer-scale details in the precipitation fields compared to the Eta at a given grid resolution, primarily due to the differing numerical techniques employed (e.g., Skamarock 2004). However, we have found that such differences are small compared to the generic differences between the 12-km parameterized and 4-km explicit approaches, reflecting the enhanced ability of 4-km resolutions to begin to represent the convective phenomena of interest (e.g., Done et al. 2004). More specific comparisons between ARW and Eta, run at 10-km horizontal resolution for a variety of model physics and initial condition configurations, can be found in Gallus et al. (2005).

In comparing the 4-km ARW (explicit) versus 12-km Eta and ARW (parameterized) convective forecasts, we must accept that, in many respects, we are comparing apples and oranges. For the 4-km ARW model, we emphasize the comparison between the observed and model-derived reflectivities. For the 12-km Eta and ARW, the only related output readily available in real time was 6-h total precipitation (reflectivity could be calculated for the explicit portion of the precipitation, but not for the parameterized portion, which is where our primary interest lies). However, for the present purposes, such a comparison between reflectivity and total rainfall helps to highlight the different characteristics of the guidance available from the differing model configurations. Equivalent 6-h precipitation totals from the 4-km ARW, however, will also be included for ease of comparison with the Eta results and the observed 6-h NCEP stage IV (ST4) precipitation analyses. The 3-hourly precipitation totals were acquired for the Eta for some of the post-real-time analyses and are discussed in section 6 below in addressing convective climatologies.

All in all, we were surprised at the ability of these explicit forecasts not only to predict the timing and location of many significant convective outbreaks out to 36 h, but also to provide realistic guidance as to the mode of convective organization, such as squall lines, bow echoes, and mesoscale convective vortices (e.g., Done et al. 2004), information that has generally not been previously available to forecasters. An example of one of the better forecasts is presented in Fig. 3, which depicts an intense bow-echo system over Iowa and Nebraska predicted 24–30 h in advance on 10 June 2003. In addition to reproducing a bow-shaped system propagating southeastward, the 4-km forecasts were also able to generate a realistic surface outflow (Fig. 4b) and associated cold pool (Fig. 4c), along with a rear-inflow jet (Fig. 4d), as was indeed observed with this system (e.g., Davis et al. 2004). Such convectively generated mesoscale features are largely absent in coarser-resolution simulations that employ convective parameterization. Still, the upscale growth of convective cells into an organized convective system is several hours earlier than observed, and is off in location by about 100 km. Also, rather than one large bow segment evolving as in the simulation, the actual event was characterized by two smaller bow systems linked together.

The 24–30-h forecasts from the 12-km Eta and ARW models for this case were quite similar to each other (Figs. 5a and 5b), highlighting eastern Nebraska and western Iowa and Minnesota for heavy precipitation (with a bit more structure evident in the ARW forecast, as discussed previously), but no guidance is offered as to the probable mode of convective organization (unless such information could be inferred indirectly from the larger-scale parameters such as CAPE and vertical wind shear). The equivalent 6-h precipitation totals from the 4-km ARW forecast (Fig. 5d) depict a similarly broad area of heavy precipitation (although significantly overforecast), but additionally depict individual precipitation streaks embedded within the larger pattern, which represents the propagation of the smaller-scale convective elements that are beginning to be resolved at the 4-km grid resolution. The observed precipitation for this case (Fig. 5c), however, depicts several distinct swaths of precipitation from Kansas through the Dakotas, with two primary swaths in Nebraska, associated with the two bowing segments depicted in Fig. 3b.

An example from 12 June 2003 (Fig. 6) demonstrates the ability of such forecasts to capture a variety of convective scenarios in the same forecast period, from the regeneration of convection in association with an MCV over southern Illinois and Kentucky, to a bow-shaped system propagating southward through Arkansas, to convection developing in the plains from the Dakotas extending down to Colorado. One major failure for this case, however, was the lack of any convection forecast in central Oklahoma and Texas, where, in reality, a large, organized squall line occurred. Subsequent analysis of this case suggests that the triggering for this squall line originated from a subtropical upper-tropospheric wave that was poorly represented in the ARW simulation. The guidance from the 12-km Eta and ARW models for this case (Figs. 7a and 7b) were also somewhat mixed, generally capturing the region of widespread precipitation associated with the MCV as well as the convection over the plains, but generally misrepresenting the characteristics of the two distinct convective systems in Oklahoma and Arkansas. Indeed, the convective system in Arkansas turned out to be the primary precipitation producer on this day (Fig. 7c), although the 4-km ARW again significantly overforecast the amount of precipitation for this and other corresponding events on this day (Fig. 7d).

One of the concerns in using a 4-km grid resolution is whether such resolutions would be sufficient to distinguish between outbreaks of more isolated severe convective storms versus organized convective systems. A case from 30 May 2004 (Fig. 8) highlights such concerns. By 0000 UTC, a fairly widespread outbreak of severe convection has developed in Nebraska extending northward into the Dakotas, with more isolated (tornadic) supercells (highlighted by arrows) extending southward along the dryline in central Oklahoma (Fig. 8a). By 0600 UTC, the northern convection organizes into one dominant squall line extending from southeastern Nebraska into central Kansas, with one isolated supercell remaining in northeast Oklahoma (Fig. 8b). The 4-km ARW forecast for this event (Figs. 8c and 8d) largely captures the convective outbreak from Nebraska northward, but misses the isolated tornadic cells along the dryline in Kansas and Oklahoma. Instead, strong convection is forecast in southeastern Kansas and spreading into southern Missouri. Interestingly, the 6-h accumulated precipitation from the 12-km Eta and ARW model forecasts valid at 0600 UTC (Figs. 9a and 9b) similarly depict widespread heavy precipitation from Nebraska extending northeastward into Minnesota, with an additional area of significant precipitation in southeastern Kansas extending into southwestern Missouri, again largely missing the tornadic cells farther west in Kansas and Oklahoma. However, these more isolated cells did not produce widespread precipitation (Fig. 9c) and, thus, might not be considered to be a significant error when using verification schemes based merely on precipitation accumulations.

Finally, we present an example from 5 June 2005 (Fig. 10) in which an intense squall line develops along the dryline of central Oklahoma and Kansas by 0000 UTC, and proceeds eastward over the next 6 h, resulting in two primary bow-shaped systems over western Illinois and southeastern Oklahoma by 0600 UTC. The 4-km ARW captures the early convection quite well (Fig. 10c), but then fails to maintain the southern end of the squall line as it propagates into southeastern Oklahoma (Fig. 10d). As in the previous examples, the 4-km ARW forecast again parallels the 12-km Eta and ARW guidance quite closely (Figs. 11a and 11b), forecasting the heaviest precipitation for the northern portions of the squall line, with much lighter precipitation forecast for southeastern Oklahoma. This case will be examined further in section 5, where we consider forecast sensitivities to the PBL, land surface, microphysical, and initial state specifications.

The above examples were chosen both to be representative of the most common forecast successes and failures experienced with the 4-km ARW model as well as to highlight the differing types of guidance provided by the high-resolution ARW as compared to the coarser-resolution Eta and ARW forecasts. In this latter regard, it seems clear that potentially useful new information is offered by the higher-resolution forecasts, especially regarding convective system mode and structure. Still, significant errors in location and timing arise in many cases along with significant high precipitation forecast biases, especially for the higher precipitation categories. More will be said about this in section 6 below. Perhaps the most noteworthy observation from these examples, though, is the strong correspondence between the 4- and 12-km forecasts, for both good and bad forecasts. This suggests a dominating influence of the larger scales (as resolved by the Eta initial and boundary conditions) in controlling the overall timing, location, and extent of the convective outbreaks in the 24–36-h time frame in the higher-resolution ARW simulations. In the next section, we attempt to get a better sense of the overall quality and relative merits of these differing types of guidance for the full experimental period.

4. Subjective verification

Verifying small, intense, time- and location-specific events such as convective storms offers unique challenges that cannot be addressed using standard verification techniques such as the equitable threat score (ETS, e.g., Wilks 1995; Baldwin et al. 2001). In addition to point-specific verification measures, we are also now interested in other potential measures of value added, such as convective mode and evolution. Eventually, as model resolutions continue to increase, verifying actual severe weather events such as high winds, hail, and tornadoes, will become feasible. Among the promising approaches being considered are the so-called object-based techniques (e.g., Ebert and McBride 2000, Baldwin et al. 2001, 2005, Davis et al. 2006a), which attempt to identify various regions or patterns of precipitation or reflectivity; identify specific attributes that characterize those patterns, such as size, orientation, lifetime, and propagation; and then measure the degree of correspondence between the forecast and observed attributes. For example, Done et al. (2004) applied a simple version of such an approach for the 2003 ARW simulations during BAMEX by measuring the degree of correspondence between the individual observed and simulated convective systems, based on a range of specified minimal distance and timing errors for the system centroids during the mesoscale convective system (MCS) lifetime. This approach tended to verify our more subjective impressions that the 4-km ARW simulations reasonably forecast the majority of the significant convective systems during this time period. A more formal application of object-based approaches for nearly the same time period by Davis et al. (2006b) further identified a positive bias for the number, size, intensity, longevity, and timing of the significant convective systems in the model forecasts.

These more formal verification efforts are on going, but for the present purposes, we take a simpler, subjective approach, aimed merely at getting an overall sense of the capabilities of the high-resolution ARW forecasts relative to the coarser-resolution Eta guidance. One of the reasons for this choice is that specific objects are difficult to compare between the ARW and Eta forecasts, with, for instance, the 4-km ARW producing realistic reflectivity features while the Eta presents only the accumulated precipitation over a prescribed time period. Additionally, it is difficult to incorporate certain measures of forecast quality, such as convective system mode and evolution, which we feel are critical for interpreting the potential value added of the high-resolution forecasts, into such object-based schemes. The value of such subjective verifications in establishing a useful link between the research and operational forecast communities has recently been discussed by Kain et al. (2003). Still, in light of the inherent uncertainties associated with such techniques, we only emphasize here those results that we confidently feel could be deduced by a reasonable range of verification approaches.

We first present a very simple rating technique, aimed at documenting the ability of the models to broadly distinguish between days with significant convection from those with only weak, disorganized convection. For this purpose, significant convective outbreak days were defined as those that exhibited clusters of strong convective cells (e.g., reflectivities greater than 50 dBZ) or well-organized squall lines or bow echoes that lasted more than 3 h, as evident from radar or equivalent 4-km ARW reflectivity between 0000 and 0600 UTC. Days with only scattered, short-lived cells or with no appreciable larger-scale organization, were rated as “weak” convective outbreak days. All others were classified in the “moderate” category. Only the maximum-rated convective region was considered on a given day. Observationally, the “significant” convective outbreak days also were generally characterized by large outbreaks of severe weather, as documented by the Storm Prediction Center (SPC). The criteria for distinguishing between significant, moderate, and weak convective outbreak days from the Eta was based on a subjective judgment as to the potential degree of organization depicted by the 6-h precipitation field (e.g., size and orientation) as well as the maximum 6-h precipitation accumulation within the given precipitation region between 0000 and 0600 UTC. More specifically, regions of precipitation of at least 300-km horizontal extent with maximum precipitation greater than 25 mm were considered significant, likely composed of organized convective systems such as squall lines or bow echoes (at least within nominally convective environments, as primarily considered here). In contrast, regions producing less than 6 mm of precipitation over the 6 h were categorized as weak, probably not being composed of organized convective systems. Again, all others were classified in the moderate category. As examples, the 10 June 2003 (Fig. 3), 12 June 2003 (Fig. 6), 30 May 2004 (Fig. 8), and 5 June 2005 (Fig. 10) cases were classified as significant convective outbreak days from both the observational and model forecast perspectives (for both 4-km ARW and Eta).

Statistics were compiled for the number of events in each category as well as to whether the models underforecast, agreed with, or overforecast the observed convective outbreak intensity, based on the assigned intensity ratings described above. For this specification, a reasonable level of correspondence between the simulated and observed convective systems was also required, with simulated systems having to occur within roughly 3–4 h and 300–400 km of the observed systems to be considered a match. For this process, the ARW, Eta, and radar composites were categorized independently of each other to minimize any biases. Additionally, each group was categorized multiple times to help ensure reasonable internal consistency in how the ratings were assigned, as well as to access the level of uncertainty due to the subjective nature of the classifications. A 5%–10% variation in the statistics was noted when comparing among these multiple verification attempts. All of the subjective ratings were assigned by the first author alone.

The results of this analysis are summarized in Table 2. Based on the observed radar characteristics between 0000 and 0600 UTC, of the 232 case days considered, 54 were considered significant days, 106 were considered moderate days, and 72 were considered weak days (Table 2a). Both the 4-km ARW and Eta reproduced the overall climatology reasonably well. However, ARW seemed to underpredict the number of significant days a bit more, while the Eta seemed to underpredict the number of weak convective days a bit more. Based on the direct case by case comparison (Table 2b), both ARW and the Eta successfully predicted the observed category the majority of the time (63% and 59%, respectively).

One of the hoped for capabilities of such high-resolution forecasts is a more accurate prediction of the significant convective outbreak days. If we consider only such days (as defined above), the results can be presented in the form of a standard contingency table (Table 3), with standard statistical measures of forecast accuracy readily applied. From this perspective, the probability of detection (POD) for significant outbreak days was higher for the Eta Model (0.55 versus 0.42), while the false alarm ratio (FAR) was lower for the ARW forecasts (0.41 versus 0.47). All in all, though, the ETSs were comparable (0.23 for ARW versus 0.25 for Eta).

The above statistics clearly could be modified by changing the calibration of what might be considered significant or weak for the 4-km ARW versus Eta forecasts. However, the fact that a reasonable choice for this calibration resulted in similar climatologies for the two model configurations, and only small differences in guidance for the most significant convective outbreak days, suggests that similar overall forecast guidance for convective outbreak intensity could have been obtained from either the 4-km ARW or Eta output; for example, the 4-km ARW output did not demonstrate any value added in this regard.

For a second subjective verification approach, the goal was to document the more general, domain-wide correspondence in space, time, and organization of all of the convective events observed during the verification period. Implicit within this rating was, for example, the ability to represent the wide variety of convective regimes that often occur within a single forecast period (e.g., a squall line in one portion of the forecast domain versus more disorganized convection in another). For this purpose, the correspondence for specific regions of convection was more strict than used above, and was confirmed for the 4-km ARW model if the forecast convection was now within 200 km and 2–3 h of the observed convection, and was also characterized with the same intensity rating as the observed convection (e.g., significant, moderate, weak), as described above. The correspondence for the Eta was confirmed if there was both spatial overlap between the 6-h accumulated precipitation region and observed convection between 0000 and 0600 UTC, and, again, a match with the assigned intensity rating. An overall forecast was classified as “good” if all of the convective events/regions matched the above correspondence criteria, “okay” if the majority of the events displayed reasonable correspondence and significant events were not missed completely, and “bad” if significant events were missed completely. For example, for both the 4-km ARW and Eta forecasts, the 10 June 2003 case (Figs. 3 and 5) was classified as a good forecast, while the 12 June 2003 (Figs. 6 and 7), 30 May 2004 (Figs. 8 and 9), and 5 June 2005 (Figs. 10 and 11) cases were classified as okay forecasts. An example of a bad forecast for the 4-km ARW is presented in Fig. 12 from 10 June 2005, wherein a squall line from Oklahoma through Kansas was missed completely. This forecast was classified as okay for the Eta Model, however, because the Eta did suggest strong convection in southwestern Oklahoma (Fig. 12c), although it still missed the convection in Kansas.

The results of this verification for the full 3 yr (232 total cases) are presented in Table 4. Indeed, as was also noted above, the most significant result was the overall similarity in the forecast accuracy between the 4-km ARW and Eta for a 24–30-h forecast time period. Both models produced roughly the same number of good forecasts (86 for ARW versus 88 for the Eta), with the only possibly significant difference being the tendency for ARW to produce a few more bad forecasts (29 for ARW versus 19 for the Eta; Table 4a). Many of these additional bad forecasts, however, could be traced to the 2003 season (12 bad forecasts for ARW versus 5 for the Eta), when the ARW domain was at its smallest. On a head-to-head basis, the models again generally agreed with each other, with the 4-km ARW producing a subjectively better forecast than the Eta on 49 days and a worse one on 57 days (Table 4b). Again, much of this difference could be traced to the 2003 season (16 worse forecasts for ARW versus 8 better).

Finally, we also considered the degree to which the 4-km ARW and Eta forecasts were similar to each other (using the same correspondence criteria described above), independent of the verifying weather. This produced perhaps the most significant result, in that the forecasts were in strong agreement on 131 days, with strong disagreement on only 11 of the 232 days considered (Table 4c). This suggests that the convection in the 4-km ARW model was strongly tied to the forcing features resolved in the Eta Model. An example of such strong correspondence was previously presented in Figs. 8 and 9, where both ARW and Eta correctly forecast convection in Nebraska but incorrectly forecast convection in southwest Oklahoma and Missouri. Similarly, the 10 June 2003 (Figs. 3 and 5) and 5 June 2005 cases (Figs. 10 and 11) were considered to have strong correspondence, while the 12 June 2003 (Figs. 6 and 7) and 10 June 2005 (Figs. 10 and 11) cases were considered to have only moderate correspondence. Such a strong general correspondence between the models should, perhaps, not be too much of a surprise, since the ARW model was initialized with and forced on the boundaries using the Eta analysis–forecast. These results also suggest that the addition of explicit convection does not necessarily have a large impact on such resolved-scale mesoscale forcing features over a 36-h period. Considering the intrinsic unpredictability of individual convective elements over a 24–36-h time period (e.g., Lilly 1990), such a strong dependence on more predictable synoptic-scale and larger mesoscale forcing features offers hope that useful convective forecast guidance can be realized over such forecast periods. But this also emphasizes the critical dependence on properly representing such large-scale forcing features in the initial state and lateral boundaries for making accurate forecasts at such time and space scales.

Although we are emphasizing the similarity here between the 4-km ARW’s and Eta’s “general” guidance, this is not meant to minimize what we still feel is true value added from the higher-resolution forecasts, namely, a more realistic representation of the convective system mode and evolution. Such information could only be “roughly inferred” from the Eta output, for example, through experience, an accurate forecast of the preconvective environment, and knowledge of how that environment might be related to convective mode, propagation characteristics, etc.

5. Forecast sensitivities

Most of the physical parameterizations being used in the 4-km ARW were originally designed for and tested in coarser-resolution forecast applications. As such, an important question is whether these parameterizations are still appropriate for the finer-resolution simulations being considered herein, or whether a certain degree of “tuning” is necessary. Even if a given parameterization nominally scales well with resolution, the implications of previously identified biases may not. For instance, a small bias in a PBL scheme could result in spurious explicit convective triggering in a high-resolution simulation, while such biases may not have resulted in triggering in a coarser-resolution simulation using a convective parameterization scheme. While the scope of the present paper is too limited to address all such issues, it is still useful to consider the sensitivities of the present results to a reasonable range of choices from the preferred group of physics schemes. As a start, we have run a limited set of sensitivities to the microphysics, land surface specification, initial state, and resolution for select cases over the past 3 yr. As a representative example, we present results from 5 June 2005 (Fig. 10), for which the 4-km ARW captures the initial development of a squall line in central Oklahoma and Kansas quite well, but then fails to maintain the squall line as it continues to propagate toward southeastern Oklahoma.

a. PBL and land surface sensitivities

Some of the bigger sensitivities that we documented resulted from the choice among two very different PBL schemes. For instance, the YSU scheme, which served as the default for these experiments, operates by diagnosing an expected boundary layer depth, and then mixing instantaneously through the entire boundary layer. Entrainment across the top of the boundary layer into the free atmosphere is achieved as a separate step. In contrast, the MYJ scheme builds the boundary layer via direct mixing between adjacent model levels, based on turbulence energy calculations. These distinct approaches have also resulted in fairly well recognized biases for each scheme (e.g., Kain et al. 2005). For instance, the YSU scheme tends to create boundary layers that are deeper and drier, and is also very aggressive in eliminating capping inversions. On the other hand, the MYJ scheme tends to deepen the boundary layer more slowly, resulting in PBL conditions that are characteristically cooler, moister, and more strongly capped.

The specification of land surface conditions, especially soil moisture, has also been shown to be critical at times for properly representing the evolution of the boundary layer as well as the initiation and evolution of any subsequent convection (e.g., Trier et al. 2004). During 2005, we employed the new HRLDAS system (Chen et al. 2007) to generate the initial conditions for the land surface model. We tested whether the improved representation of soil moisture processes afforded by HRLDAS significantly affected the resulting convective forecast by rerunning a few select cases using the YSU scheme without HRLDAS.

The forecast sensitivities to PBL and land surface specification for the 5 June 2005 case are presented in Fig. 13. By 0300 UTC, the squall line had continued to propagate eastward, forming two primary bow-shaped segments: one in southeast Oklahoma and one farther north into western Illinois (Fig. 13a). The convection farther south into Texas, however, had all but decayed. All of the simulations maintained a strong squall line at the northern end of the system, but all failed to maintain the appropriate extent of convection in southeastern Oklahoma. The MYJ simulation (Fig. 13c) did somewhat better in maintaining at least some convection in southeast Oklahoma through 0300 UTC, but by 0600 UTC, this convection had also decayed (not shown). The omission of HRLDAS (Fig. 13d) did affect the details of the convective forecast, but the sensitivities were not large enough to correct the bigger errors. All in all, the various simulations (Figs. 13b–d) appear to be more like each other than the observed event.

In an attempt to better understand the source of the forecast failure in this case, we examined the mesoscale environments produced by the variety of PBL schemes. For instance, using the Eta analysis as representative of the observed state at 0000 UTC, all three PBL combinations failed to replicate the magnitude of the observed CAPE (most unstable) in the Oklahoma region (Figs. 14a–e). The existence of far more CAPE in the Eta analysis was confirmed by viewing 0000 UTC soundings for the region, which depicted significantly greater boundary layer moisture values over much of Texas, Oklahoma, and Kansas than forecast (not shown). The forecast soundings for Springfield, Missouri (SGF; Figs. 14d and 14f), also exhibit some of the characteristic biases between the YSU and MYJ schemes, with the YSU sounding displaying a deeper, drier boundary layer and the MYJ scheme producing a cooler, more moist boundary layer.

This low bias for the 24-h forecasts of CAPE with the YSU scheme was quite systematic over the course of the 3-yr experiment. To consider this further, difference fields between the 24-h ARW forecast valid at 0000 UTC the next evening and the 0000 UTC Eta analysis valid at that same time were generated for the 40-day period from 1 May through 10 June 2005 (Fig. 15). This analysis clearly suggests a dry bias of order 2 g kg−1 in the surface moisture field over much of the central and southern United States, with a slight cold bias over most of the United States, and a slight warm bias evident over parts of Texas and Oklahoma. As noted above, this was consistent with a point-by-point comparison of sounding data in this region. At 850 mb (not shown), the moist bias becomes more limited to the high plains of west Texas, Oklahoma, and Kansas and is now coincident with a warm bias of order 0.5 K. In contrast, no significant biases are evident at 500 mb in these regions (not shown). Research is continuing to better understand the source of these biases with the YSU scheme. The handful of cases run with the MYJ scheme show that it was consistently better at maintaining the boundary layer moisture, but an insufficient number of cases have been considered as of yet to assess the relative merits of the two schemes. Still, based on the concerns with the YSU scheme, a choice was made to use the MYJ scheme for the 2006 season, the analysis of which is on going.

b. Microphysics sensitivities

Many studies have documented the potentially large sensitivities to the assumptions used in the variety of microphysical schemes available to the ARW community (e.g., Gilmore et al. 2004a, b). Some of the biases apparently common to all schemes at 4-km resolution are the overprediction of convective rainfall as well as an inability to properly represent the extent of stratiform regions of squall lines. The intensity and coverage of rainfall directly impacts the potential strength of the convectively produced cold pools, which have been shown to be one of the critical controlling components of MCS structure and evolution.

Although there is little doubt that microphysical sensitivities can have a significant impact on convective storm-scale structure and relatively short time-scale forecasting (e.g., several hours), we found that such sensitivities did not greatly impact the overall forecast guidance over the 24–30-h time period. Indeed, the microphysical sensitivities were well within the range of the other sensitivities discussed above. As an example, we employed the new Thompson microphysical scheme (Thompson et al. 2006) for the 5 June 2005 case (Fig. 13e), using the MYJ PBL scheme (chosen here as it seemed to produce a slightly better forecast), with other physics settings as described for the basic model configuration. As with the MYJ simulation discussed above (Fig. 13c), the Thompson scheme produces essentially the same squall line at 27 h, with the exception that the convective cores now appear smaller and the stratiform precipitation more extensive both forward and rearward of the convective line. Also, the convective line in Iowa and Missouri appears to propagate slightly faster. Precipitation totals are also slightly reduced compared to the WSM6 run (not shown). By 30 h, however, the squall line again decays (not shown), suggesting that the microphysical sensitivities were unable to account for the larger forecast errors.

c. Initial state sensitivities

Considering the apparently strong correspondence between the ARW and Eta forecast guidance out to 36 h, it is also important to document the potential sensitivities of the convective forecasts to the specification of the initial state. As a first step, several of the cases were rerun starting with the RUC initial-state analysis (using the 25-km resolution RUC-native coordinate data as obtained from the NCEP operational site). For the present purpose, we did not use the microphysics species in the data, nor land surface data. Also, the lateral boundaries continued to be forced by the Eta Model, since the RUC data are only available through 12 h. As shown for the 5 June 2005 case (Fig. 13f), the RUC forecast was perhaps the best of the bunch, with the convection still extending well down into Oklahoma at 0300 UTC. This relative success, however, was at the expense of about a 2-h delay in triggering the convection relative to the other forecasts, which were more correct in this regard. The RUC forecast out to 0600 UTC, though, continued to show some improvement over the other forecasts. This larger sensitivity of the forecasts to the initial state versus physics variations was also apparent in other cases rerun with the RUC data (not shown), sometimes producing better forecasts, sometimes producing worse forecasts. This suggests that much attention still needs to be addressed toward improved representation of the initial state, for both deterministic and ensemble approaches, for 18–36-h explicit convective forecasts.

d. Resolution sensitivities

One of the questions raised by these convective forecasts is whether there would be enhanced value by increasing the grid resolutions beyond 4 km. Such value added could result from both improved representation of the processes critical to convective initiation as well as a better representation of the dynamic processes of individual convective cells. For instance, higher resolutions could conceivably improve the representation of the triggering of more isolated convective cells along a dryline, as observed on 30 May 2004 (e.g., Fig. 8), or could also potentially allow for the explicit prediction of supercell storms, which are not sufficiently represented at 4-km grid resolutions. Indeed, explicit forecast guidance for all forms of severe convective weather, including tornadoes, high winds, hail, and flash flooding, could be significantly improved by employing higher resolutions.

During the 2005 experimental forecast season, a 2-km version of ARW was run by CAPS as a contribution to the SPC/National Severe Storms Laboratory (NSSL) Spring Program (e.g., Kain et al. 2005), in parallel to the standard 4-km runs. Additionally, several of the 2003 and 2004 simulations discussed herein have been rerun using a 2-km grid resolution. Although analyses of all these simulations are on going, preliminary results do suggest an improvement in the representation of the convective system structure, by, for instance, producing a more realistic leading-line–trailing-stratiform structure, as shown for the 10 June 2003 bow echo (Fig. 16a) described previously in section 3. However, the overall guidance as to the timing and location of the convective systems displayed in Fig. 16 did not seem to be significantly impacted by the higher resolution. Thus, it is not yet clear whether increasing resolutions beyond 4 km is warranted, considering the increased computational costs.

6. Convective climatology

One of the hopes for high-resolution forecasts is in their potential to more correctly represent the climatological characteristics of the convection. In this regard, we are more interested in the integrated behavior of the convection as opposed to detailed information concerning the timing and location of specific convective events. In essence, this perspective addresses the ability of the model to properly represent the transfer of convective energy among the critical meteorological scales. Questions abound as to the current ability of convective parameterizations to properly represent such interactions. One example of such concerns is the tendency for some coarse-resolution models with parameterized convection to produce overly strong grid-scale storms as a response to convective activity (e.g., Molinari and Dudek 1992). Another example is the apparent limitations of models with parameterized convection in representing the diurnal cycle of convective frequency across the United States (e.g., Davis et al. 2003). Simply turning convective parameterizations off at resolutions of order 10 km is problematic as well. For example, Weisman et al. (1997) demonstrated that such coarser resolutions with explicit treatment of convection result in a significant slowing of convective system evolution as well as a significant overestimation of the convective mass and momentum fluxes and precipitation.

The climatological character of the convection during our experimental period can be summarized via the use of Hovmöller diagrams (e.g., Carbone et al. 2002). These diagrams are produced by interpolating hourly precipitation totals from the model and stage IV gauge plus radar rain estimates onto a latitude–longitude grid, and then averaging these precipitation totals over the latitude band from 30° to 48°N. Only the 12–36-h forecast period was used for the model precipitation data to avoid spinup issues and overlapping model forecasts. The period from 11 to 31 May 2004 is shown here as representative of the full experimental dataset (Fig. 17).

Perhaps the most evident feature from this analysis is the abundance of precipitation episodes propagating from west to east across the analysis domain, both in the model and observations. From this perspective, the 4-km ARW forecasts did a good job of replicating the frequency, longevity, and propagational characteristics of the precipitation episodes. However, the latitudinally averaged precipitation within the ARW episodes is noticeably larger than that for ST4, offering further evidence of the previously noted positive precipitation bias in the ARW forecasts. This precipitation bias is further documented in Fig. 18 for the 2005 season, which shows that the positive biases were largely limited to the precipitation events greater than 10 mm. Indeed, 50% of the total precipitation from ARW was associated with precipitation events greater than 20 mm, as compared to about 30% from the ST4 estimates. These higher precipitation categories are also characterized by very low ETS scores, as is quite characteristic for convective precipitation events. The cause of this overprediction is still under investigation but, as discussed above, is likely related to several factors, including deficiencies in the current microphysics scheme being employed, a lack of sufficient resolution (e.g., Weisman et al. 1997; Bryan et al. 2003), or issues of nonconservation of water by the currently used advection scheme (e.g., Bryan et al. 2006).

To further document the climatological character of the forecast convection, diurnally averaged Hovmöller frequency diagrams for the entire 2004 season (10 May–31 July) are presented in Fig. 19. These diagrams were created by counting the number of times for a given hour and given longitude that the total precipitation averaged over latitude (from 30° to 48°N) exceeded a specified threshold, here chosen to be 0.02 mm. This number of occurrences is then plotted as a percentage of the maximum possible number of occurrences (i.e., number of days in sample) for a given hour and longitude. The ST4 observations (Fig. 19a) clearly depict a strong, stationary diurnal maximum in precipitation frequency near 0000 UTC over the Rockies, and from 95°W eastward. Additionally, the maximum in frequency in the Rocky Mountains near 0000 UTC appears to propagate to 90°–95°W by 0900 and 1200 UTC (e.g., Carbone et al. 2002). Likewise, the minimum in frequency evident at 1200 UTC over the Rockies also appears to propagate eastward. These “propagating” features in convective frequency have been hypothesized to contribute to the well-known nocturnal maximum in convective activity in the plains and Midwest, which is also evident between 90° and 95°W. The ARW 4-km forecasts (Fig. 19b) reasonably reproduce both of these observed features, offering further confidence that the model is capable of representing the basic character of convection over the central United States.

To compare the 4-km ARW results to the 12-km Eta, the ARW rainfall data had to be coarsened to a 3-h frequency to match the output readily available from the Eta. A comparison of the 3-h ARW versus 3-h Eta Hovmöller diagrams for 11–31 May 2004 is shown in Figs. 19c–e. Most evident is the lack of a well-defined diurnal frequency minima in the Eta results, with the frequency of precipitation spread more evenly throughout the day than for the observations and 4-km ARW forecasts. Also evident is a less clearly defined propagational signal emanating from the Rockies. The reasons for these less-defined diurnal tendencies in the Eta simulations are not known, but may be at least partly related to the inability of the convective parameterization to produce and maintain the circulations associated with cold pools, which have been shown to be critical for the maintenance and propagation of convective systems in simulations that employ nominally explicit grid resolutions (e.g., 4 km or higher). Propagation of convective systems can occur in mesoscale models that employ convective parameterizations (e.g., Bukovsky et al. 2006), but it is not as yet clear that these parameterized propagational mechanisms are sufficiently realistic. Further documentation and discussion of the limitations of coarser-resolution simulations using convective parameterization in producing observed propagating precipitation episodes and diurnal tendencies can be found in Davis et al. (2003) and Clark et al. (2007).

7. Forecaster feedback

For the 2004 and 2005 seasons, forecasters from NWS offices around the country were invited to view the 4-km ARW forecasts online (e.g., see appendix B), and make comments on their quality and usefulness. This feedback was critical for clarifying the aspects of the new, high-resolution information that were most useful to the forecasters, how they were using this new information, as well as helping to identify model deficiencies or biases. In 2004 and 2005, these ARW forecasts were similarly evaluated as part of the SPC/NSSL Spring Program, where forecasters and researchers from around the country compared the guidance from among various versions of the WRF model [e.g., ARW and the Nonhydrostatic Mesoscale Model (NMM)]. Results from these springtime exercises are discussed separately in Weiss et al. (2004) and Kain et al. (2005, 2006).

To offer some more specific insights into how the forecasters viewed this new information, a representative sample of the comments we received during the 2005 season is included in appendix A. One of the more common observations was how impressed the forecasters were with the perceived degree of realism afforded by the 4-km ARW simulations, especially with regard to the reflectivity field and its ability to replicate real convective system structure, such as squall lines, bow echoes, mesoscale convective vortices, and the like. On the other hand, with the far greater detail available to them for the first time, this realism could also result in a false sense of security concerning the potential forecast accuracy. As such, the frequent errors in the specific timing and location of convective events was initially viewed by many as disturbing. However, as forecasters became more familiar with both the capabilities and limitations of these new high-resolution forecasts, this new information was viewed more as general guidance on the most probable modes of convection to be expected on a given day within a given time frame and region, rather than for the specific details of timing and location. Given the apparent limitations in forecasting such specifics over a 36-h period with the current ARW modeling system, we feel that this is the most appropriate manner in which to use such high-resolution output.

8. Summary

The analyses of the 2003–05 ARW forecast exercises offer hope that significant improvements in convective forecast guidance out to 36 h can be achieved by increasing horizontal grid resolutions into the convectively explicit regime, thereby avoiding uncertainties inherent with convective parameterization schemes currently used in coarser-resolution operational models. Herein, we used a 4-km grid resolution, which is nominally sufficient to resolve convective systems explicitly, and found that such forecasts often realistically represent the structure and evolution of mesoscale convective phenomena, such as squall lines, bow echoes, and mesoscale convective vortices. A subjective comparison to the guidance offered by the operational 12-km Eta Model, however, did not suggest improvements in forecasting the broader characteristics of convective systems such as location, timing, and relative intensities. Still, the overall realism as well as the apparent improvements in forecasting convective mode and evolution were found to be extremely useful for BAMEX operations planning during 2003, and have also been highly valued by NWS forecasters across the country, who viewed the forecasts during 2004 and 2005.

The relative success in forecasting a seemingly unpredictable phenomenon such as convection out to 36 h seems most directly related to its strong connection to identifiable and more predictable synoptic or subsynoptic features, which establish the mesoscale environment favorable for the convection as well as serving as the primary triggering agents. The conclusion implied by this is that, in most cases, the feedback of the convection on the larger scales is not significantly impacting the predictability of the primary convective forcing features over a 1–2-day period. This seems consistent with Lilly (1990), who hypothesized that forecast improvements for small-scale phenomena such as convection may still be realized through increases in model resolution as long as the primary forcing for the convection is still at scales large enough that they reside within the k−3 range of the atmospheric spectrum (where k is wavenumber) (although there is still much debate over the lower limit of scales that resides within this potentially more predictable regime). The diurnal cycle may also help in this regard by providing a reasonably predictable cycle of convective enhancement and decay juxtaposed on the other forcing influences.

The increased realism in convective structure and dynamics using higher resolutions has also resulted in a demonstrable improvement in the representation of the diurnal cycle of convection over the United States, showing an ability to reproduce both the observed propagating maximum and minimum in convective frequency extending from the Rocky Mountains to the Mississippi River valley as well as the more stationary observed frequency maxima (minima) near 0000 (1200) UTC in the Southeast and East. This signal was less clear in the 12-km Eta, with the precipitation frequency spread more evenly throughout the day. These same limitations were also noted in coarser-resolution versions of the ARW model, as was established in an earlier study (e.g., Davis et al. 2003). We hypothesize that the improvements with the high-resolution ARW are directly related to a more accurate representation of convective processes, such as cold-pool circulations and the associated convective propagational mechanisms, as well as a better representation of the impact of the convection on the larger scales relative to the parameterized approaches. Indeed, Lilly (1990) further suggests that the true value of increasing resolution may ultimately not be in improving the predictability of small-scale events as much as in “removing damage due to inaccurate parameterizations.” This may have important implications for the ability to properly represent convective processes and feedbacks in longer-term simulations that employ convective parameterizations, as is being proposed for regional climate applications.

The ability of high-resolution simulations to properly represent the structure and evolution of the boundary layer remains a significant challenge since boundary layer structure is a key factor in convective storm initiation, structure, and evolution. Comparisons between two commonly used PBL schemes (YSU and MYJ) showed significant differences in boundary layer structure and evolution over a single diurnal cycle, sometimes producing significant differences in the convective forecast. A more detailed look at a 40-day period during 2005 further revealed a systematic negative bias in low-level moisture of up to 2 g kg−1 at 0000 UTC over much of the southern and western United States with the YSU scheme (which was the standard scheme applied during the 2003–05 seasons). It is clear that more careful analyses of both the abilities and limitations of existing PBL schemes at such resolutions is needed. Also, a significant positive bias is evident for the precipitation in convective systems, which needs to be remedied via improved microphysics, resolution, advection schemes, or some combination thereof.

Future studies must also consider more carefully the potential value of increasing grid resolutions beyond 4 km. Our preliminary results suggest that the use of 2-km grids does improve the structural features of some convective systems. However, such increases in the resolution do not seem to improve the overall forecast of the system timing and location. These latter attributes of the forecast, however, may be more sensitive to improving the model initial state, via four-dimensional variational data assimilation (4DVAR), ensemble Kalman filter techniques, etc.

Many challenges remain in addressing the predictability of convective events out to 36 h. Sometimes, the 4-km ARW forecasts were remarkably accurate, offering some hope that convective predictability is not as bad as theory might suggest. On the other hand, significant errors in the timing and location of significant convective events were also frequently encountered. It is unclear at this point how many of these forecast issues are related to the model physics, resolution, or representation of the features critical for convective triggering, etc. However, our sensitivity studies to date for model physics and resolution have been unable to explain the larger forecast errors. Larger forecast sensitivities arose, however, when varying the initial conditions for the forecasts (e.g., initializing with the RUC versus Eta). This result seems consistent with that of Gallus et al. (2005), who also noted the inability of a “poor man’s” ensemble of various model resolutions and physics configurations to forecast a severe derecho-producing convective system. They suggest that “It thus appears that useful forecasts of systems such as this one may require a much better observation network than now exists, or better methods of including additional information from radar and satellites.” Furthermore, a recent simulation study of the 3 May 1999 Oklahoma tornado outbreak by Roebber et al. (2002) suggests that 24-h forecast errors of order of several hundred kilometers and/or several hours (similar to the more significant forecast errors noted in the present experiment) can indeed be related to resolvable-scale observational errors in the initial upstream conditions. The fact that many of the significant errors in the ARW model also corresponded to similar errors in the Eta Model further supports the hypothesis that the source of at least some of these errors may be at scales that are nominally resolvable and, thus, hopefully could be remedied by better observational or assimilation techniques. In any event, more systematic studies are clearly needed to better characterize the nature of the model sensitivities and the modes of forecast failure for the full range of scales relevant to the convective forecast problem.

Acknowledgments

We have benefited greatly from discussions and reviews of this manuscript by Jack Kain, Steve Weiss, and several anonymous reviewers. We also thank the many NWS forecasters who contributed to this study via their comments and observations of the ARW real-time output. We especially thank Ron Przybylinski, Dan Smith, Dan Baumgardt, and Steve Zubrick, who allowed some of their comments to be included in this manuscript. We also acknowledge the support of the NCAR computing center, without whom such real-time forecasts would not have been possible.

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  • Xue, M., , Wang D. , , Gao J. , , Brewster K. , , and Droegemeier K. K. , 2003: The Advanced Regional Prediction System (ARPS), storm-scale numerical weather prediction and data assimilation. Meteor. Atmos. Phys., 82 , 139170.

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APPENDIX A

Forecaster Comments

The following represents a sample of the comments we received from NWS forecasters across the country, describing some of their experiences (both good and bad) using the 4-km ARW 36-h forecast output during the 2005 season. These comments were selected to offer a representative flavor of how the ARW output was viewed and used. The complete set of comments received during the 2004 and 2005 forecast seasons can be viewed online (see the following Web sites: http://catalog.eol.ucar.edu/wrf-2004/ and http://catalog.eol.ucar.edu/wrf-2005/.)

Sample forecaster comments from 2005

Dan Baumgardt, NWS forecaster, La Crosse, Wisconsin
20–21 July

“Unreal. This model and the reflectivity product is [sic] the largest single advancement in numerical modeling in my career thus far. The model is remarkable and a noticable [sic] improvement since the BAMEX experiment. This run initiated convection on the Nebraska/South Dakota border a bit further east than actual in its 24–30 hour time frame and then evolved the cellular convection into a N-S line across Iowa overnight. By its 36h forecast 12z July 21, reflectivity was produced in a line mode affecting the southern half of the forecast area. The line was a bit further north than the model indicated at 12Z but not too much. BUT, the bottom line is this model produced a solution of mode, propagation, and strength via reflectivity that the forecasters could monitor realtime conditions for and improve the forecasts accordingly.”

22–23 July

“Again, this model is amazing people at the NWS La Crosse WI office. Initiation of a longer-lived squall line with 60–80mph winds and widespread tree damage from mpx-Lake Michigan. . . . WRF reflectivity had the line track almost exact from 12–21Z July 23. This was a great confidence builder for short-term convective decisions and storm propagation into our forecast area. Timing in the model was excellent. The model no longer is ‘bow happy’ as versions in the past. It creates less bowing structures and verifies these better. Again, this model is providing excellent mission-related benefits that include better verified forecasts of sensible weather, office staffing guidance on both numbers needed and timing, and forecaster visualization of forcing mechanisms and outcomes.”

Dan Smith, NWS forecaster, Lincoln, Illinois
26 July

“Forecasted the convective mode well during this time period. The model picked up on the post frontal convection during the night with a pre-frontal trof [sic] or outflow boundary pushing across our northern forecast area during the morning. New convection developed along the eastern flank of the stratiform rain shield during the mid and late afternoon hours, which was forecast well by the model, although a bit too far southeast. Mulicellular [sic] convection edged southeast during the evening hours with a trend towards linear convection across the southeast portion of the forecast area with scattered reports of wind damage. Overall, the model did a very good job in depicting convective mode and evolution during the time frame and gave the forecasters some lead time with respect to additional development during the afternoon and evening hours. The model did seem to underforecast the instability ahead of the frontal boundary in the afternoon.”

Ron Przybylinski, Science Operations Officer, Saint Louis, Missouri (LSX)
13 June

“Concerning CAPE and surface winds . . . the WRF underforecast the magnitude of CAPE by as much as 1000–1500 J kg−1 between 2000 UTC 06/13 through 0200 UTC 06/14. Concerning reflectivity patterns . . . the WRF performed very well in capturing the reflectivity pattern during the severe weather event over eastern Missouri through southwest Illinois. We mainly had a mixture of scattered to broken severe storms west and southwest of St. Louis between 1900–2200 UTC then a convective line segment formed over southwest Illinois after 2300 UTC. The WRF captured the location of these features very well. The only problem is that the WRF timing of the severe convection was about 3 to 4 hours too slow. I was impressed with the structure of the precipitation field the WRF forecasted in this episode.”

Steve Zubrick, Science Operations Officer, Sterling, Virginia (LWX)
General comments

“I was struck by how real the WRF-modeled convective structures appeared. There were large MCSs, bowing line segments, linear structures of individual cells appearing in the simulated reflectivity images. While these structures all appeared real, they often failed to materialize in the real world. However, there were times when they did appear in ‘kind-of’ the right place and times. These times were unfortunately few, and there were many false alarms. But I understand how difficult this is to model . . . so I’m impressed overall that the model could capture at least some of the structures. But I think we have a ways to go before we can develop consistent and reliable forecasts that the forecasters can count on to be (mostly) correct.”

APPENDIX B

WRF-ARW Forecast Output

The 4-km ARW forecasts for the 2003, 2004, and 2005 seasons, along with radar images and Eta forecasts, can be found online (see the following Web sites: http://catalog.eol.ucar.edu/bamex/, http://catalog.eol.ucar.edu/wrf-2004/, and http://catalog.eol.ucar.edu/wrf-2005/).

Comparisons between the ARW 4-km simulations, a CAPS ARW simulation using an advanced data assimilation system (ADAS), and the NCEP WRF-NMM core are also available online for 2004 from roughly May 1 to 4 June (http://www.nssl.noaa.gov/etakf/compare/wrf/).

Comparisons between the ARW 4-km simulations, ARW 2-km simulations run by CAPS, and the WRF-NMM 4.5-km simulations for the 2005 season can be viewed online (http://www.spc.noaa.gov/exper/Spring-2005/).

Fig. 1.
Fig. 1.

Domains used for the 2003–05 4-km real-time WRF-ARW forecasts.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 2.
Fig. 2.

(a) Observed NOWRAD composite reflectivity at 0400 UTC 4 Jun 2005 compared to (b) 4-h forecast maximum column reflectivity from WRF-ARW at 0400 UTC, starting from an initial state with zero precipitation.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 3.
Fig. 3.

Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 10 Jun 2003 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 9 Jun 2003.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 4.
Fig. 4.

(a) Maximum column reflectivity, (b) surface flow field, (c) surface equivalent potential temperature, and (d) northwest–southeast vertical cross section, as located in (a), of reflectivity and ground-relative flow from the 30-h WRF-ARW forecast, valid at 0600 UTC 10 Jun 2003.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 5.
Fig. 5.

The 0000–0600 UTC accumulated precipitation (mm) for 10 Jun 2003 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 6.
Fig. 6.

Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 12 Jun 2003 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 11 Jun 2003.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 7.
Fig. 7.

The 0000–0600 UTC accumulated precipitation (mm) for 12 Jun 2003 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 8.
Fig. 8.

Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC 30 May 2004 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 29 May 2004. Arrows in (a) and (b) point to locations of isolated tornadic supercells.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 9.
Fig. 9.

The 0000–0600 UTC accumulated precipitation (mm) for 30 May 2004 from (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 10.
Fig. 10.

Observed NOWRAD composite reflectivity at (a) 0000 and (b) 0600 UTC for 5 Jun 2005 compared to (c) 24- and (d) 30-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 4 Jun 2005.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 11.
Fig. 11.

The 0000–0600 UTC accumulated precipitation (mm) for 5 Jun 2005 from the (a) 24–30-h Eta forecast, (b) 24–30-h 12-km ARW forecast, (c) NCEP ST4 analysis, and (d) 24–30-h 4-km ARW forecast.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 12.
Fig. 12.

(a) Observed NOWRAD composite reflectivity at 0300 UTC for 10 Jun 2005 compared to (b) 27-h forecast maximum column reflectivity from WRF-ARW, for forecasts initialized at 0000 UTC 9 Jun 2005. The 0000–0600 UTC accumulated precipitation (mm) for 10 Jun 2005 from the (c) Eta and (d) WRF-ARW 24–30-h forecasts.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 13.
Fig. 13.

(a) Observed NOWRAD composite reflectivity valid at 0300 UTC 5 Jun 2005, and 27-h WRF-ARW forecast maximum column reflectivity, valid at the same time, from simulations using (b) YSU PBL and HRLDAS land surface, (c) MYJ PBL without HRLDAS, (d) YSU PBL without HRLDAS, (e) MYJ PBL and Thompson microphysics, and (f) YSU PBL with RUC vs Eta initial conditions, as described in the text.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 14.
Fig. 14.

CAPE analysis and Springfield, MO (SGF), skew T, valid at 0000 UTC 5 Jun 2005: (a) CAPE analysis from the Eta Model; (b) observed SGF sounding; (c),(d) 24-h forecast CAPE and SGF sounding from the WRF-ARW model using the YSU PBL scheme; and (e),(f) 24-h forecast CAPE and SGF sounding from the WRF-ARW model using the MYJ PBL scheme.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 15.
Fig. 15.

The 24-h WRF-ARW biases for (a) surface potential temperature (K) and (b) surface mixing ratio (g kg−1), averaged from 1 May to 10 Jun 2005, using the YSU PBL scheme.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 16.
Fig. 16.

Maximum column reflectivity from 2-km WRF-ARW forecasts for (a) 30-h forecast valid 0600 UTC 10 Jun 2003 and (b) 24-h forecast valid 0000 UTC 5 Jun 2005. The 2-km WRF-ARW forecast for the 5 Jun 2005 case was contributed by CAPS, as part of the 2005 SPC/NSSL Spring Program.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 17.
Fig. 17.

Hovmöller diagrams of hourly precipitation, extending from 105° to 85°W and averaged from 30° to 48°N for 10–31 May 2004, for the (a) NCEP ST4 analysis and (b) WRF-ARW 12–36-h forecasts.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 18.
Fig. 18.

ETS (red line) and bias (blue line) for the 24-h WRF-ARW precipitation forecasts for the 2005 season. The pink and green lines represent the percentage of total accumulated precipitation beneath a given precipitation threshold, for the observed (ST4) and forecast (ARW) precipitation, respectively.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Fig. 19.
Fig. 19.

Diurnally averaged Hovmöller frequency diagrams, extending from 105° to 85°W and averaged from 30° to 48°N, for 10 May–31 Jul 2004: using hourly precipitation data and a precipitation threshold of 0.02 mm, for (a) NCEP ST4 analysis and (b) WRF-ARW forecasts, and using 3-hourly precipitation data and a precipitation threshold of 0.05 mm for (c) ST4, (d) WRF-ARW, and (e) Eta Model forecasts. For (a),(b) dotted and dashed lines approximate the minimum and maximum phase lines for the propagating diurnal frequency signal, respectively, as discussed in the text.

Citation: Weather and Forecasting 23, 3; 10.1175/2007WAF2007005.1

Table 1.

Model specifications.

Table 1.
Table 2.

Convective and forecast outbreak intensity.

Table 2.
Table 3.

Significant convective outbreaks.

Table 3.
Table 4.

Overall forecast accuracy.

Table 4.
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