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    (a)–(c) NARR (Mesinger et al. 2006) at 1200 UTC 25 May 2013, and (d) skew T–logp diagram showing sounding from Corpus Christi, TX (KCRP, denoted by cyan dot in Fig. 2), at 1200 UTC 25 May 2013. (a) Absolute vorticity at 500 hPa (×10−5 s−1), shaded every 3 × 10−5 s−1 above −9 × 10−5 s−1), 500-hPa geopotential height (contoured every 60 m), and 500-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt; 1 kt = 0.5144 m s−1). (b) 850-hPa geopotential height (contoured every 25 m), 850-hPa wind barbs, and 850-hPa temperature (shaded every 5°C from −20° to 35°C). (c) Precipitable water (shaded contours every 5 mm for values from 10 to 50 mm), 10-m wind barbs (kt), and MSLP (contoured every 3 hPa). The dashed black line in (d) shows the temperature of a lifted parcel with the mean characteristics of the lowest 500 m. Reproduced from Fig. 5 of Nielsen et al. (2016).

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    NCEP stage-IV precipitation analysis accumulation for the 12-h period ending at 1800 UTC 25 May 2013. Location labels correspond to cities (specifically airports) located on or near the Balcones Escarpment to identify its approximate location in central Texas (KDRT is Del Rio, TX; KSAT is San Antonio, TX; KAUS is Austin, TX; KCRP is Corpus Christi, TX; and KTPL is Temple, TX). Plot depicts the spatial coverage of the ARW domain used for each member of the convection-allowing ensembles run. Cyan dot for Corpus Christi, TX, marks location of the sounding shown in Fig. 1d.

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    Hovmöller (hourly averaged precipitation, time–longitude) diagrams (Hovmöller 1949) for the stage-IV precipitation analysis averaged over the (a) MCV and (b) MCS subregions depicted in Fig. 9 valid for the 23-h period ending at 2300 UTC 25 May 2013.

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    TX_control contoured accumulated precipitation valid for the 12-h period ending at 1800 UTC 25 May 2013 for each member of the ensemble, including the control. (a)–(j) Members 1–10 of the ensemble, respectively. (k) Control member of the ensemble, and (l) stage-IV gridded analysis valid over the same period.

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    (a)–(c) TX_control ensemble “paintball plot” of 3-h accumulated precipitation contoured only at 25.0 mm for each member of the ensemble. Each fill color represents a different ensemble member’s accumulation. (d)–(f) Stage-IV 3-h precipitation accumulation (mm) with fill contours beginning at 25.0 mm. Precipitation accumulations are valid for the 3 h ending at (a),(d) 1200; (b),(e) 1500; and (c),(f) 1800 UTC 25 May 2013.

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    (a)–(c) Downscaled (i.e., on 4-km grid) absolute vorticity at 500 hPa (×10−5 s−1), shaded every 3 × 10−5 s−1 (above −9 × 10−5 s−1), 500-hPa geopotential height (contoured every 60 m), and 500-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt) valid at 0000 UTC 25 May 2013 for members 2, 8, and 9 of TX_control, respectively. (d) As in (a)–(c), but valid at 0000 UTC 25 May 2013 from the NARR ( 32-km grid spacing).

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    Simulated radar reflectivity at 1 km AGL from members (a),(c) 8 and (b),(d) 9 of TX_control valid at (a),(b) 0600 and (c),(d) 1800 UTC 25 May 2013. KSAT denotes the location of San Antonio International Airport, and the figure depicts the coverage of the ARW domain.

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    Time series of the domain-averaged RMDTE highlighting the ensemble simulations for the 25 May 2013 case. Colored lines correspond to TX_control (orange), TX_half (yellow), TX_third (brown), TX_2km (black), TX_10th (purple), TX_20th (blue), TX_100th (green), and RMDTE from native Reforecast-2 resolution (dashed orange). Solid (dashed) gray lines represent the RMDTE time series for all of the other downscaled WRF ensemble simulations (native Reforecast-2 ensemble) in this study for comparison listed in appendix A. Dot–dashed orange line on bottom graph corresponds to percentage of ensemble average grid points that exceed 1 m s−1 of vertical velocity (w) at 700 hPa in TX_control to denote convectively active times.

  • View in gallery

    (a),(b) TX_control, (c),(d) TX_half, and (e),(f) TX_third contoured accumulated precipitation from members (b),(d),(f) 8 and (a),(c),(e) 9 valid for the 12-h period ending at 1800 UTC 25 May 2013. (g) The accumulated precipitation for the control member of the ensemble over the same time period. Boxes indicate regions of equal area associated with the “MCV” vortex (centered in Texas), the baroclinic zones called “MCS” (centered on Nebraska), and a region devoid of convection called “NOCON” (centered along the Alabama–Mississippi border) over which the AS metric (solid boxes) and regional RMDTE (dashed boxes) are calculated.

  • View in gallery

    (a) Regional RMDTE time series for TX_control run of the 25 May 2013 case for the full ensemble domain (black line), the area devoid of convection (i.e., “NOCON” region in green), the region bounding the Texas MCV vortex (i.e., “MCV” region in red), and the associated baroclinic zone (i.e., “MCS” region in blue) defined in Fig. 9. (b) RMDTE ratio time series for TX_100th over TX_control for the full domain (black line), MCV region (red line), MCS region (blue line), and NOCON region (green line). (c) Normalized RMDTE (N_RMDTE) time series as described in appendix B for TX_control the MCV region (red line), MCS region (blue line), and NOCON region (green line).

  • View in gallery

    Most unstable CAPE (MUCAPE; shaded at 100 J kg−1 and every 500 J kg−1 above 500 J kg−1), 900-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt), and 900-hPa isotachs in blue (contoured every 4 m s−1 above 12 m s−1) from the Rapid Refresh (RAP) analysis for the 25 May 2013 extreme precipitation case valid at (a) 0600, (b) 0900, and (c) 1500 UTC.

  • View in gallery

    Precipitation accumulation “paintball plot” contoured only at (a) 25.0 and (b) 50.0 mm for the members of TX_control valid for the 12 h ending at 1800 UTC 25 May 2013. Each fill color represents a different ensemble member’s accumulation. The area spread (AS) values for each threshold and region are plotted in the bottom right of the plots.

  • View in gallery

    RMDTE time series for TX_control (solid line), TX_half (dot–dashed lines), TX_third (dotted line), TX_10th (uneven dashed line), TX_20th (solid line), and TX_100th (dashed line) for the (a) full domain, (b) MCV region, (c) MCS region, and (d) NOCON region as defined by dashed boxed regions centered in the Mississippi–Alabama border, Texas, and Nebraska, respectively, in Fig. 9. The individual time series are also labeled corresponding to the matching ensemble run. Additionally, annotations indicating the ensemble spread originating from synoptic-scale processes and convective processes are indicated in each panel; a more detailed explanation of the separation is given in section 4b(2).

  • View in gallery

    Conceptual diagram of the theoretical limit of (a)–(c) practical and (d)–(f) intrinsic predictability. The blue oval in each pane represents the spread of ensemble initial conditions, the red oval represents the spread of ensemble solutions at some arbitrary end of the numerical simulations, black dots within blue/red circles represent each ensemble member, and black lines represent the ensemble spread envelop through the numerical simulation (which is increasing from blue to red ovals). The initial ensemble spread is reduced incrementally from (a),(d) to (b),(e) to (c),(f) in approximate equal amounts.

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Using Convection-Allowing Ensembles to Understand the Predictability of an Extreme Rainfall Event

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
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Abstract

This research uses convection-allowing ensemble forecasts to address aspects of the predictability of an extreme rainfall event that occurred in south-central Texas on 25 May 2013, which was poorly predicted by operational and experimental numerical models and caused a flash flood in San Antonio that resulted in three fatalities. Most members of the ensemble had large errors in the location and magnitude of the heavy rainfall, but one member approximately reproduced the observed rainfall distribution. On a regional scale a flow-dependent diurnal cycle in ensemble spread growth is observed with large growth associated with afternoon convection, but the growth rate then reduced after convection dissipates the next morning rather than continuing to grow. Experiments that vary the magnitude of the perturbations to the initial and lateral boundary conditions reveal flow dependencies on the scales responsible for the ensemble growth and the degree to which practical (i.e., deficiencies in observing systems and numerical models) and intrinsic predictability limits (i.e., moist convective dynamic error growth) affect a particular convective event. Specifically, it was found that large-scale atmospheric forcing tends to dominate the ensemble spread evolution, but small-scale error growth can be of near-equal importance in certain convective scenarios where interaction across scales is prevalent and essential to the local precipitation processes. In a similar manner, aspects of the “upscale error growth” and “downscale error cascade” conceptual models are seen in the experiments, but neither completely explains the spread characteristics seen in the simulations.

Corresponding author address: Erik Nielsen, Department of Atmospheric Science, Colorado State University, 1371 Campus Delivery, Fort Collins, CO 80523. E-mail: erik.nielsen@colostate.edu

Abstract

This research uses convection-allowing ensemble forecasts to address aspects of the predictability of an extreme rainfall event that occurred in south-central Texas on 25 May 2013, which was poorly predicted by operational and experimental numerical models and caused a flash flood in San Antonio that resulted in three fatalities. Most members of the ensemble had large errors in the location and magnitude of the heavy rainfall, but one member approximately reproduced the observed rainfall distribution. On a regional scale a flow-dependent diurnal cycle in ensemble spread growth is observed with large growth associated with afternoon convection, but the growth rate then reduced after convection dissipates the next morning rather than continuing to grow. Experiments that vary the magnitude of the perturbations to the initial and lateral boundary conditions reveal flow dependencies on the scales responsible for the ensemble growth and the degree to which practical (i.e., deficiencies in observing systems and numerical models) and intrinsic predictability limits (i.e., moist convective dynamic error growth) affect a particular convective event. Specifically, it was found that large-scale atmospheric forcing tends to dominate the ensemble spread evolution, but small-scale error growth can be of near-equal importance in certain convective scenarios where interaction across scales is prevalent and essential to the local precipitation processes. In a similar manner, aspects of the “upscale error growth” and “downscale error cascade” conceptual models are seen in the experiments, but neither completely explains the spread characteristics seen in the simulations.

Corresponding author address: Erik Nielsen, Department of Atmospheric Science, Colorado State University, 1371 Campus Delivery, Fort Collins, CO 80523. E-mail: erik.nielsen@colostate.edu

1. Introduction

Throughout the United States, extreme rainfall and the often associated flash flood danger continue to threaten many facets of everyday life (e.g., Ashley and Ashley 2008), including the infrastructure of the built environment, individual livelihood, and personal safety. Forecasting both the occurrence and magnitude of flash flood events is critical to gauge the range of possible impacts (e.g., Doswell et al. 1996). However, this is made challenging because of complicated interacting hydrologic and meteorological dependencies that are unique to each flash flood event. The accurate prediction of these extreme rainfall events remains a significant challenge for the weather forecast community. Since their advent in the early to mid-1990s, the meteorological forecast community has established the usefulness of ensemble-based numerical weather prediction (NWP) for improving precipitation forecasting (e.g., Murphy 1988; Du et al. 1997; Zhang et al. 2006; Schumacher et al. 2013). The reliance of operational forecasters on these systems for precipitation guidance has led to an increasing need to determine the most effective use of ensemble prediction systems (EPS) in high-impact, extreme precipitation events.

The accuracy of the NWP forecast is tied to how well the initial atmospheric state, often referred to as the model initial conditions (ICs), is represented. Generally, the more accurate the initial representation of the atmosphere, in principle, the more accurate the resulting forecast will be at longer lead times. However, because of the chaotic nature of the atmospheric system, theoretical limits of the predictability of different atmospheric scales of motion, first examined by Thompson (1957) and Lorenz (1963, 1969), exist. More specifically, Lorenz (1969) presented the notion that forecast errors stem from unobservable small-scale atmospheric circulations. Any error in these small-scale atmospheric motions can rapidly grow upscale and reduce the lead time over which a deterministic forecast is valid. Further, this implies that as smaller atmospheric scales are resolved by an NWP model, the faster the forecast errors propagate upscale. The notion of upscale error growth creating a limit on atmospheric predictability has since been more precisely investigated (e.g., Leith 1971; Leith and Kraichnan 1972; Métais and Lesieur 1986; Rotunno and Snyder 2008) and gained wide acceptance in the meteorology community.

It has been noted that the results of Lorenz (1969) could also imply that error growth from very small scales can be masked by downscale error growth from larger scales and not have any substantial impact on the limit of predictability (e.g., Bei and Zhang 2007; Durran et al. 2013; Durran and Gingrich 2014; Durran and Weyn 2016). Using similar models as Lorenz (1969) and Rotunno and Snyder (2008), Durran and Gingrich (2014) found that small errors () in resolving larger-scale motions (400 km) could have the same effect on model predictability as 100% error at mesoscales (10 km). Simulations of thunderstorms and squall lines have shown similar impact on the event predictability from the small errors at scales of 100 km and much larger errors at meso- to convective scales (Durran and Weyn 2016). The large scales exert the most control on the smaller scales, but also introduce potentially serious errors to the smaller scales. These errors can then propagate back upscale, which can muddle the ability to identify the scale from where the errors originated (Durran and Weyn 2016).

Predictability as applied to NWP can be broken down into two distinct, but instructive, parts: practical predictability and intrinsic predictability. Practical predictability can be thought of as how well a model can predict future atmospheric states based upon the procedures currently available in NWP. Intrinsic predictability is defined as “the extent to which prediction is possible if an optimum procedure is used” (e.g., Lorenz 1969; Zhang et al. 2006; Melhauser and Zhang 2012). Practical predictability is limited by errors and uncertainties, for example, in model numerics, physics, and data assimilation procedures in the creation of the atmospheric ICs and NWP model architecture that are usually identifiable (Lorenz 1996). On the other hand, intrinsic predictability is the limit of predictability that is reached with an almost perfect knowledge of the atmospheric ICs and nearly perfect NWP model. The intrinsic predictability limit cannot be overcome due to the chaotic nature of the atmosphere described in Lorenz (1969), and, more specifically, is largely due to the chaotic nature of moist convective processes (e.g., Melhauser and Zhang 2012). Additionally, the practical and intrinsic predictability of the atmosphere are dependent on the scale of the motion and the specific atmospheric flow patterns that are in place (e.g., Lorenz 1996; Zhang et al. 2006).

Most processes of interest that govern extreme rainfall, especially in the warm season, reside in the storm-scale and mesoscale motions of the atmosphere. Studies conducted on upscale model spread growth in both the cold and warm season found that small-scale, nonlinear errors grow quickly upscale due to moist convective processes. This error growth limits the mesoscale predictability and potential forecast accuracy of deterministic NWP models in intense precipitation events (e.g., Zhang et al. 2002, 2003, 2006, 2007). Given that deterministic forecasts have limited predictability and skill for mesoscale features, convection, and, accordingly, precipitation accumulations (e.g., Zhang et al. 2003), trusting the output of one possible atmospheric state from a deterministic model can, in some cases, lead to particularly bad forecasts. However, NWP ensembles can be used to overcome some of these predictability problems and increase precipitation forecast accuracy, but coarse NWP ensembles do not perform well for warm season mesoscale dominated events (e.g., Du et al. 1997; Mullen and Buizza 2001; Hamill et al. 2008; Schumacher and Davis 2010). Increases in modern computing power have fortunately allowed NWP models to decrease grid spacing quite substantially, in some cases below 5 km. It has been shown, for instance in Bryan et al. (2003), that grid spacing near 4 km sufficiently resolves convective systems, but not the characteristics and motions of individual convective cells. For these reasons, NWP model configurations are often referred to as “convection allowing” instead of “convection resolving” when the horizontal grid spacing ranges from 1 to 5 km.

Many studies have shown that convection-allowing ensembles can serve as a viable forecast tool (e.g., Gebhardt et al. 2008; Schwartz et al. 2010) and have value over coarser ensembles in convectively active flow regimes (e.g., Kain et al. 2013). For example, small (5 member) convection-allowing ensembles can often produce more accurate forecasts of extreme precipitation than larger (15 member) ensembles that do not explicitly allow convection (20 km) (e.g., Clark et al. 2009). Convection-allowing ensembles are now used in research and semioperational predictions, such as the Center for Analysis and Prediction of Storms (CAPS) ensemble from the University of Oklahoma (e.g., Xue et al. 2007) and the experimental NCAR convection-allowing ensemble (e.g., Schwartz et al. 2015). However, the best way to design, implement, and interpret the output from convective-allowing ensembles is still a topic of active research.

While the increased resolution of ensembles to explicitly represent convection has shown to potentially produce more accurate rainfall forecasts in cases of extreme precipitation, the smaller resolved scales of motion can lead to forecast issues relating to practical and intrinsic predictability. For a bowing mesoscale convective system on 9–10 June 2003, Melhauser and Zhang (2012) found, despite the realistic ICs for a convection-allowing ensemble, members diverged into two different storm modes, regardless of the ensemble IC spread, since the “true” solution in this case existed along a bifurcation point between two near-equally likely outcomes. It has been theorized that in some, but not all, cases the use of convection-allowing ensembles may approach the limit of intrinsic predictability, due to chaotic nature of moist convection (Melhauser and Zhang 2012).

The goal of the ensemble predictability experiments presented in this study will be to expand the scientific knowledge of the characteristics on how the spread of a convection-allowing ensemble evolves over time for an extreme precipitation event in the United States. Specifically, ensemble simulations of an extreme precipitation event will be used to examine the relative importance of small- and large-scale atmospheric motions on the ensemble spread growth and the level to which the event approaches the limits of intrinsic and practical predictability in a convection-allowing ensemble framework. Further, the ensemble spread characteristics will be examined over the full model domain and on regional scales that contain various convective forcing. These characteristics will speak to the viability of using convection-allowing ensembles for prediction of extreme rainfall events and characterize the types of events that present the largest predictive challenges. It will also address the completeness of both the upscale error growth model and the thinking that small large-scale errors are of more practical importance. While these predictive characteristics are of importance to NWP in general, they are of particular importance for quantitative precipitation forecasts in potentially life threatening extreme rainfall events. Section 2 gives a synoptic overview of the extreme precipitation event that is the focus of this study. Section 3 provides a summary of the methods, while the experiment results, discussion, and conclusions are presented in sections 4, 5, and 6, respectively.

2. Description of 25 May 2013 extreme rainfall event

On 25 May 2013, convection associated with a quasi-stationary, preexisting mesoscale convective vortex (MCV) (Fig. 1a) (Bartels and Maddox 1991; Trier et al. 2000a,b) led to large precipitation accumulation totals in the San Antonio, Texas (KSAT), metro area and other nearby regions of south-central Texas (Fig. 2). This region is hydrologically prone to flash flooding, due to the presence of a terrain feature known as the Balcones Escarpment (e.g., Baker 1975; Caran and Baker 1986; Costa 1987; O’Connor and Costa 2004), which is a limestone feature that separates the Texas coastal plain from the Edwards Plateau (i.e., the Texas Hill Country). A local maximum of flood fatalities within Texas is collocated with the Balcones Escarpment in central Texas, which also produces some of the highest flood-related injury and fatality rates in the United States (e.g., Smith et al. 2000; Ashley and Ashley 2008; Sharif et al. 2010, 2015). The heaviest precipitation for the 25 May 2013 event fell between 0800 and 1700 UTC (CDT = UTC − 5 h) near the southeastern edge of the Balcones Escarpment, but the heaviest rainfall rates were observed near 1200 UTC. The San Antonio International Airport recorded 250 mm (9.87 in.) of precipitation during this period, while a U.S. Geological Survey rain gauge near downtown San Antonio recorded a 1-h rainfall accumulation of 156 mm (6.13 in.) and a total of 432 mm (17.0 in.) in 24 hours. This extreme precipitation event caused flash flooding in local rivers, creeks, and drainage systems that swept vehicles and pedestrians off of roadways, leading to three reported fatalities and many road closures (NOAA 2015a). Nielsen et al. (2016) showed that the Balcones Escarpment had only subtle influences on the extreme rainfall in this case, although such changes could have important impacts on the hydrologic flood response.

Fig. 1.
Fig. 1.

(a)–(c) NARR (Mesinger et al. 2006) at 1200 UTC 25 May 2013, and (d) skew T–logp diagram showing sounding from Corpus Christi, TX (KCRP, denoted by cyan dot in Fig. 2), at 1200 UTC 25 May 2013. (a) Absolute vorticity at 500 hPa (×10−5 s−1), shaded every 3 × 10−5 s−1 above −9 × 10−5 s−1), 500-hPa geopotential height (contoured every 60 m), and 500-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt; 1 kt = 0.5144 m s−1). (b) 850-hPa geopotential height (contoured every 25 m), 850-hPa wind barbs, and 850-hPa temperature (shaded every 5°C from −20° to 35°C). (c) Precipitable water (shaded contours every 5 mm for values from 10 to 50 mm), 10-m wind barbs (kt), and MSLP (contoured every 3 hPa). The dashed black line in (d) shows the temperature of a lifted parcel with the mean characteristics of the lowest 500 m. Reproduced from Fig. 5 of Nielsen et al. (2016).

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

Fig. 2.
Fig. 2.

NCEP stage-IV precipitation analysis accumulation for the 12-h period ending at 1800 UTC 25 May 2013. Location labels correspond to cities (specifically airports) located on or near the Balcones Escarpment to identify its approximate location in central Texas (KDRT is Del Rio, TX; KSAT is San Antonio, TX; KAUS is Austin, TX; KCRP is Corpus Christi, TX; and KTPL is Temple, TX). Plot depicts the spatial coverage of the ARW domain used for each member of the convection-allowing ensembles run. Cyan dot for Corpus Christi, TX, marks location of the sounding shown in Fig. 1d.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The MCV was originally formed from convection in the Texas Panhandle in the early to late afternoon hours on 23 May 2013. The convection initiated near Lubbock, Texas, along the intersection of a remnant outflow boundary associated with a decaying MCS on the Texas–Oklahoma border, which originally formed along a diffuse stationary baroclinic zone corresponding to a weak surface low pressure center in the northern Texas Panhandle, and a north–south-oriented dryline in west Texas. These cells grew upscale into an MCS that moved southward throughout the day on 24 May 2013 and lead to the development of the MCV in question (Fig. 1a). Rain began to fall near KSAT around 0600 UTC 25 May as the MCV moved south into the region, and continued until 1800 UTC, at which point convection ceased at the center of the midlevel vortex, consistent with the usual diurnal cycle of MCVs (e.g., Trier et al. 2000b). Warm, moist southeasterly flow off the Gulf of Mexico provided a sustained moisture supply during this period (Figs. 1b,c) where the MCV was relatively stationary (Fig. 3a) (e.g., see, Schumacher and Johnson 2008, 2009). The southeasterly return flow associated with high pressure over the eastern United States (Figs. 1b,c) extended over a deep layer, from the surface to about 600 hPa with local maximums of over 50 mm of precipitable water (PWAT; Figs. 1c,d). Additionally, the 1200 UTC 25 May 2013 Corpus Christi, Texas, rawindsonde observation (Fig. 1d) measured precipitable water values (48.69 mm) over the 90th climatological percentile (45.72 mm) for that day (NOAA 2015b).

Fig. 3.
Fig. 3.

Hovmöller (hourly averaged precipitation, time–longitude) diagrams (Hovmöller 1949) for the stage-IV precipitation analysis averaged over the (a) MCV and (b) MCS subregions depicted in Fig. 9 valid for the 23-h period ending at 2300 UTC 25 May 2013.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

In addition to the precipitation associated with the MCV in central Texas, a broad region of rainfall associated with a fast-moving quasi-linear MCS occurred in Nebraska and Iowa during the same period (Fig. 2). A developing surface cyclone in the lee of the Rocky Mountains centered on the northeast corner of Colorado (Fig. 1c) had begun to establish a baroclinic zone (see wind shift at surface and at 850 hPa in Figs. 1b and 1c) and a moisture gradient (Fig. 1c) along the Nebraska–South Dakota border by 1200 UTC 25 May 2013. Convection initiated in the western part of Nebraska just before 0000 UTC 25 May and grew upscale into an identifiable MCS by 0500 UTC 25 May (not shown). The storm system then moved quickly to the east (Fig. 3b) and eventually dissipated by 0600 UTC 26 May 2013 in northern Kentucky. While this storm system did not produce flash flooding, it does provide a second region of organized convective activity with maximum precipitation accumulations over 100 mm, in addition to the MCV in central Texas, over which to investigate the evolution and characteristics of the ensemble spread.

3. Methods

a. Numerical model architecture

To test the spread characteristics of a convection-allowing ensemble, version 3.6, of the Advanced Research core of the Weather Research and Forecasting (WRF) Model (ARW; Skamarock et al. 2008) was used to create a 11-member ensemble, which corresponds to the number of members in the ensemble reforecast dataset (discussed in the next section) used for the initial and lateral boundary conditions (LBCs), at 4-km grid spacing. Many studies have found that 4-km grid spacing can generally resolve the location and timing of convective systems (e.g., Kain et al. 2008; Weisman et al. 2008; Clark et al. 2012; Hanley et al. 2013). Thus, a 4-km grid spacing should be sufficient in this experiment, given the often mesoscale nature of extreme rainfall and the large computational cost of multiple ensemble simulations. Each ensemble member is created with only varied initial conditions, and all members used the same physics packages (Table 1). The single-model domain encompasses the vast majority of the central part of the United States, Mexico, and the Gulf of Mexico (Fig. 2). In addition to the 4-km ensemble runs described above, one 2-km horizontal grid spacing ensemble run was created in the same configuration (i.e., same domain extent and model physics), with the exception of number of compute nodes, to test the effects of grid spacing (e.g., Kain et al. 2008; Schwartz et al. 2009) (Table 1). Through the course of the research, several cases of extreme precipitation in addition to the 25 May 2013 event have been simulated using the exact same numerical model configuration (see full list in appendix A). However, for the purposes of this study, only the 25 May 2013 event will be discussed in detail.

Table 1.

ARW model configuration for ensemble predictability experiments.

Table 1.

b. Boundary and initial conditions

The ICs and LBCs (updated every 3 h) used to create the 11-member ensemble were taken from the National Oceanic and Atmospheric Administration (NOAA) Second-Generation Global Medium-Range Ensemble Reforecast Dataset (Reforecast-2; Hamill et al. 2013). The Reforecast-2 ensemble is a dataset of ensemble reforecasts based upon the 2012 update of the National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System (GEFS) that has once daily (at 0000 UTC) initializations from December 1984 to the present. Each run of the Reforecast-2 ensemble contains 11 members (10 perturbations and 1 control) that maintains the ensemble spread of the operational GEFS with fewer members. The first 8 days of the Reforecast-2 ensemble is run at T254L42 resolution, which is the equivalent of 40-km grid spacing at 40° latitude. The Reforecast-2 ensemble creates an easily accessible, operationally representative, and temporally expansive dataset from which to obtain the ICs and LBCs to create a downscaled, convection-allowing ensemble for almost any extreme rainfall event in the past 30 years. A similar process of using the Reforecast-2 members to initialize the ICs and LBCs of convection-allowing ensembles has been used previously in Galarneau and Hamill (2015) and Lawson and Horel (2015). Further, no additional simulation-scale LBC perturbations (e.g., Nutter et al. 2004) were added, which is consistent with some semioperational convection allowing ensembles [e.g., the NCAR ensemble; Schwartz et al. (2015)].

For the 25 May 2013 Texas MCV, the ICs and LBCs were taken from the Reforecast-2 ensemble for the control ensemble run and various convection-allowing ensemble experiments (discussed in section 3c). The numerical simulations for this case were run for 24 h beginning at 0000 UTC 25 May 2013. The midlevel vortex associated with the MCV was already present in the ensemble ICs and LBCs at initialization.

c. Ensemble spread evaluation

There are many ways to diagnose the evolution of a NWP ensemble’s spread characteristics. For the purposes of this study, the ensemble spread will be quantified using the difference total energy (DTE) as a basis for evaluation (e.g., Zhang et al. 2003; Zhang 2005; Zhang et al. 2006, 2007; Melhauser and Zhang 2012; Peters and Roebber 2014). The DTE is defined in Zhang et al. (2003) as
e1
where the , , and are the differences of the zonal wind, meridional wind, and temperature from the ensemble mean, respectively; and ( J kg−1 K−1 and K). The differences , , and are five-dimensional variables that are functions of grid points in the x (i) and y (j) directions, vertical level k, time t, and ensemble member m. DTE can be thought of as a representation of the energy difference from both thermodynamic and kinematic fields per unit mass between the ensemble mean and a specific ensemble member. Further, one can define the root mean difference total energy (RMDTE) by taking the square root of the average DTE summing across each ensemble member in either the horizontal or vertical (Melhauser and Zhang 2012). The horizontal RMDTE as a function of the horizontal grid points and time can be expressed as
e2
where is the number of ensemble members, is the number of vertical levels from the surface () to model top (), and p is pressure on the vertical levels. For this study the horizontal RMDTE [Eq. (2)] was calculated by summing the DTE from each ensemble in the vertical and taking a pressure-weighted average [Eq. (2)]. This creates a two-dimensional horizontal depiction of the ensemble spread growth and evolution. This, while good for diagnosing specific regions of evolving ensemble divergence, does not quantify the temporal evolution of the entire ensemble spread. To accomplish this, an area-averaged version of the RMDTE was calculated to arrive at a time series of RMDTE throughout the ensemble forecast, which can be described as
e3
where is the total number of grid points in the x direction, is the total number of grid points in the y direction, and is the solution to Eq. (2). The solutions resulting from Eq. (3) yield a time series of the domain-averaged RMDTE that is representative of the spread compared to the ensemble mean. This time series creates a simple metric that is used to compare the ensemble spread between different runs and evaluate the results of any ensemble predictability experiments. To test the effects of normalizing the RMDTE by the regional kinetic energy, a normalized RMDTE (N_RMDTE) was also calculated for the 25 May 2013 case. The specifics of the normalization are given in appendix B.

Several experiments were designed and performed to test the predictability of this extreme precipitation event in a convection-allowing ensemble. The presence of the control member in the Reforecast-2 ensemble allows for calculation of the atmospheric perturbation off the control associated with each member of the ensemble. Once calculated, the perturbation was scaled and added back to the control run to create a new set of ensemble ICs and LBCs still based on the original Reforecast-2 ensemble. For example, the atmospheric perturbation of the ICs and LBCs associated with each ensemble member off the control run were halved (this corresponds to the “half magnitude” ICs and LBCs in Table 2) to artificially narrow the initial spread of the ensemble. The newly created ICs and LBCs were used to rerun the ensemble and the resulting RMDTE calculated. Table 2 describes the ensemble predictability experiments and their associated ICs and LBCs performed for the Texas MCV described in the previous section. The last column of Table 2 depicts the abbreviations that are used throughout the rest of the manuscript when referring to each run of the ensemble predictability experiments.

Table 2.

Summary of ICs and LBCs used in ensemble experiments. “Half magnitude” or “one-third magnitude” specifically means that the IC or LBC perturbation off the control Reforecast-2 member for each ensemble member was cut in half or one-third, respectively. The TX_2km ensemble run uses the same IC and LBCs as TX_control except at 2-km grid spacing.

Table 2.

Last, an effort was made to quantify the spread of the precipitation forecasts for each experiment that would be depicted on a “spaghetti plot”—a single plot that overlays the precipitation accumulation contours for each member on the same chart. This is accomplished using the area spread (AS) metric as defined in Schumacher and Davis (2010), which is calculated by dividing the total area of predicted rainfall by all ensemble members over a specified threshold by the average area over that threshold predicted by each ensemble member. Mathematically this can be expressed as
e4
Here is the precipitation forecasts for a n-member ensemble at the jth of m grid points, which has been converted to a binary grid where if the forecasted precipitation reaches or exceeds the prescribed threshold and if it does not. The term is the minimum possible value and represents the case where all forecast contours exactly overlap. Conversely, , where n = number of ensemble members (11 in this case), is the maximum value possible and represents when none of the ensemble member’s forecasts overlap. In other words, higher values indicate more ensemble spread in the precipitation field. The AS metric was then compared to the RMDTE to see if overall ensemble spread is directly comparable to forecasted precipitation spread.

4. Results

a. Meteorological sensitivities

There were differences in the ensemble members precipitation forecasts in central Texas during the time of the observed extreme rainfall (Fig. 4). Most of the members in TX_control produce rainfall accumulations of similar magnitudes to those observed, but have large errors in the location of the heaviest rainfall (e.g., cf. Figs. 4a,b,h and Figs. 4l and 5). All of the forecasts have the local maximum of precipitation in central Texas too far to the north and/or west (e.g., Figs. 4a,f,j,k and Fig. 5), which is similar to the operational guidance for this event (not shown). Several of the members create two local precipitation maxima in central Texas directly north and south of one another (Figs. 4b,c,k). The timing of the precipitation in Texas was fairly well represented by the model, but the spatial coverage was more extensive compared to stage IV (Fig. 5). In contrast to the high variability in central Texas, the members in TX_control produced similar precipitation forecasts for the bowing MCS in Nebraska and Iowa (Figs. 4 and 5). The members of TX_control reproduced the precipitation for this Nebraska MCS well both spatially and in overall magnitude, but there were differences in the exact location of the precipitation shield (cf. Figs. 4a–k and Figs. 4l and 5).

Fig. 4.
Fig. 4.

TX_control contoured accumulated precipitation valid for the 12-h period ending at 1800 UTC 25 May 2013 for each member of the ensemble, including the control. (a)–(j) Members 1–10 of the ensemble, respectively. (k) Control member of the ensemble, and (l) stage-IV gridded analysis valid over the same period.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

Fig. 5.
Fig. 5.

(a)–(c) TX_control ensemble “paintball plot” of 3-h accumulated precipitation contoured only at 25.0 mm for each member of the ensemble. Each fill color represents a different ensemble member’s accumulation. (d)–(f) Stage-IV 3-h precipitation accumulation (mm) with fill contours beginning at 25.0 mm. Precipitation accumulations are valid for the 3 h ending at (a),(d) 1200; (b),(e) 1500; and (c),(f) 1800 UTC 25 May 2013.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The nature of the midlevel vorticity anomaly associated with the Texas MCV seems to be the main cause of variability in the ensemble forecast precipitation in central Texas. The model was initialized, in almost all members, with a very elongated north–south local vorticity maximum at 500 hPa (e.g., Figs. 6a–c), which is similar to the NARR at the time of model initialization (Fig. 6d). However, the NARR did not reproduce the dual local vorticity maxima embedded within the larger feature seen in the TX_control members, though this could be due to resolution differences (cf. Figs. 6a–d). The initial representation of the vorticity structure in members of TX_control differs in finer scale details (Figs. 6a–c), but the initial differences do not intuitively correspond to the resulting precipitation forecasts. For instance, both members 8 (Fig. 6b) and 9 (Fig. 6c) of TX_control were initialized with strong central vortex signatures. However, member 8 goes on to produce less intense, scattered precipitation in north-central Texas (Fig. 4h), but member 9 produces the best subjectively determined precipitation forecast (Fig. 4i), compared to the observations (Fig. 4l), of any member in the ensemble. Model-simulated radar reflectivity shows much deeper convection developing by 0600 UTC 25 May 2013 in north-central Texas in member 9, compared to member 8 (cf. Figs. 7a and 7b). This convection then continues to exist throughout 1800 UTC in member 9, but becomes disorganized and dissipates in member 8 (cf. Figs. 7c and 7d). This illustrates the importance of the presence and location, or lack thereof, of convective initiation along the elongated vorticity maximum in strengthening the MCV and determining the location and breadth of each members precipitation forecast, even if the model initial conditions are similar. That is, the variation in the ensemble’s precipitation forecasts is largely due to differences in the location and strength of the initial convection. Thus, the forecast variability between members in TX_control is largely due to a combination between the unusual elongated vorticity signature and the low predictability of the initiation and evolution of deep moist convection.

Fig. 6.
Fig. 6.

(a)–(c) Downscaled (i.e., on 4-km grid) absolute vorticity at 500 hPa (×10−5 s−1), shaded every 3 × 10−5 s−1 (above −9 × 10−5 s−1), 500-hPa geopotential height (contoured every 60 m), and 500-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt) valid at 0000 UTC 25 May 2013 for members 2, 8, and 9 of TX_control, respectively. (d) As in (a)–(c), but valid at 0000 UTC 25 May 2013 from the NARR ( 32-km grid spacing).

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

Fig. 7.
Fig. 7.

Simulated radar reflectivity at 1 km AGL from members (a),(c) 8 and (b),(d) 9 of TX_control valid at (a),(b) 0600 and (c),(d) 1800 UTC 25 May 2013. KSAT denotes the location of San Antonio International Airport, and the figure depicts the coverage of the ARW domain.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

b. Ensemble predictability experiments

1) Full model domain results

In addition to TX_control, six ensemble simulations, were performed based upon Reforecast-2 IC and LBCs: TX_half, TX_third, TX_10th, TX_20th, and TX_100th where the IC and LBC perturbation off the control for each member was scaled by , , , , and , respectively and TX_2km, where TX_control was replicated except at a 2-km grid spacing. The domain-averaged RMDTE time series for all of these ensemble runs is presented in Fig. 8. A diurnal cycle of the ensemble spread growth rate, peaking during the convectively active hours, is seen across all downscaled ensemble runs for the 25 May 2013 case (colored solid lines Fig. 8). The spread growth minimum occurs from 1200 to 1800 UTC, and maximizes during the convectively active times (first 9 h, last 6 h, see bottom panel of Fig. 8). The smaller reduction in ensemble RMDTE after the first convective cycle, compared to other cases of extreme precipitation run in the same configuration (i.e., gray lines in Fig. 8), seen over the full domain for the 25 May 2013 case is likely due to convection continuing throughout the day near the MCV center. However, despite the constant source of convection associated with the MCV center (which can be thought of as a constant source of upscale error growth), the presence of even a slight diurnal cycle shows that the large-scale meteorological characteristics and features continue to affect and, to some extent, limit the evolution and ensemble spread growth from smaller-scale features. This speaks to the viability of using convection-allowing ensembles for prediction beyond the first convective cycle, since the upscale error growth associated with moist convection does not cause rapid divergence of the individual ensemble solutions. Additionally, the diurnal cycle is almost nonexistent in the ensemble spread evolution of the native Reforecast-2 ensemble (orange dashed line in Fig. 8). Spread growth rates between the TX_control run (orange line in Fig. 8) and the native Reforecast-2 ensemble (orange dashed line in Fig. 8) are similar, despite significant differences in resolution, except for a large increase in the first 6 hours and smaller increases during convective times, due to the 4-km runs spinning up to resolve smaller convective scales and explicitly allowing convection, respectively (Fig. 8) (e.g., Clark et al. 2009). This further implies that the large-scale atmospheric features, which are resolved by the individual members at the native Reforecast-2 resolution through the ICs and LBCs, provide a constraint on the overall ensemble spread evolution on the time scales considered here.

Fig. 8.
Fig. 8.

Time series of the domain-averaged RMDTE highlighting the ensemble simulations for the 25 May 2013 case. Colored lines correspond to TX_control (orange), TX_half (yellow), TX_third (brown), TX_2km (black), TX_10th (purple), TX_20th (blue), TX_100th (green), and RMDTE from native Reforecast-2 resolution (dashed orange). Solid (dashed) gray lines represent the RMDTE time series for all of the other downscaled WRF ensemble simulations (native Reforecast-2 ensemble) in this study for comparison listed in appendix A. Dot–dashed orange line on bottom graph corresponds to percentage of ensemble average grid points that exceed 1 m s−1 of vertical velocity (w) at 700 hPa in TX_control to denote convectively active times.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The precipitation forecasts associated with the MCV continue to converge as the perturbation off the control is reduced, but nonnegligible differences still remain. For instance, member 8, which produced the least precipitation in the central Texas region in TX_control, increases the forecasted accumulation as the perturbation is reduced (cf. Figs. 9b,d,f). Member 9, which produced the most representative precipitation compared to the observations, moves the forecast accumulations north and decreases the forecast accuracy (cf. Figs. 9a,c,e). These two members, as the perturbation of the control is reduced, create precipitation forecasts that look more like the control member of the ensemble (Fig. 9g). Given that in the scaled experiments the ensemble is artificially being made underdispersive, reduction of the ensemble spread is the expected behavior. This reduction in precipitation forecast spread is a depiction of the overall ensemble spread reduction shown in Fig. 8 from TX_control to TX_100th and discussed below. Further, the scaled ensemble runs for this case, specifically the TX_half and TX_third runs, produced continued consistency in the precipitation forecasts along the baroclinic zone in Nebraska and Iowa (Figs. 9c–f). In fact, almost no variability between ensemble runs in TX_half and, especially, TX_third are seen for this rainfall swath (cf. Figs. 9e and 9f). However, there was also little variation between the members for precipitation in Nebraska and Iowa in TX_control (Fig. 4).

Fig. 9.
Fig. 9.

(a),(b) TX_control, (c),(d) TX_half, and (e),(f) TX_third contoured accumulated precipitation from members (b),(d),(f) 8 and (a),(c),(e) 9 valid for the 12-h period ending at 1800 UTC 25 May 2013. (g) The accumulated precipitation for the control member of the ensemble over the same time period. Boxes indicate regions of equal area associated with the “MCV” vortex (centered in Texas), the baroclinic zones called “MCS” (centered on Nebraska), and a region devoid of convection called “NOCON” (centered along the Alabama–Mississippi border) over which the AS metric (solid boxes) and regional RMDTE (dashed boxes) are calculated.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The scaled ensemble experiments allow for the characterization of the linearity of the ensemble spread for a specific meteorological case. If the spread growth reduction was linear (i.e., corresponding to a case at the pure theoretical limit of practical predictability), the ratio of a scaled run (i.e., TX_100th) over the control (i.e., TX_control) should stay approximately at the factor by which the perturbations were reduced; if the case is purely limited by intrinsic predictability (i.e., the error growth is entirely driven by convection), then the ratios would immediately approach 1 during the first convective cycle; and, if the spread growth is not purely linear or governed totally by convection (i.e., both intrinsic and practical predictability are influencing the results), the ratio should increase somewhere between the two previous ends of the spectrum. Here the “pure theoretical limit of practical predictability” refers to an idealized bound to the predictability spectrum where only the limitations of the model can limit the ability to predict the future atmospheric state. Continued improvement of the forecast at this bound is solely due to improvements in the model. At this theoretical bound we assume that convection has no dominant influence on the ability for the ensemble to predict the future. This is clearly very idealized (hence the “pure theoretical” moniker), since we know moist convection is innately chaotic and almost always present, but it provides a theoretical scenario to compare to the real results (i.e., our ensemble runs).

A decrease in the initial RMDTE corresponding, roughly, to the perturbation scaling is seen when TX_control (orange line) is compared to any of the scaled perturbation ensembles (i.e., TX_third, TX_10th, etc.) (Fig. 8). However, specifically focusing on TX_100th and TX_control over the full domain, this linear scaling is not maintained throughout the ensemble simulations with the ratio of RMDTE between TX_100th and TX_control increasing through time (black line in Fig. 10b), which implies the RMDTE of TX_100th is increasing faster than TX_control and illustrates that there is some nonlinearity in the ensemble spread growth. There is a leveling in the ratio after the first convective cycle (black line in Fig. 10b), likely owing to the decrease in convection over the entire domain. This shows that the chaotic moist convective dynamics in TX_100th continues to increase the model spread through time over the exact linear scaling regime. This is also true when comparing any of the scaled perturbation ensemble runs to TX_control, not just TX_100th. The significant decrease in the overall RMDTE from TX_control to TX_third and on to TX_100th again shows the importance that the large-scale atmospheric forcing has on the magnitude of the ensemble spread (Fig. 8). However, the steadily increasing RMDTE ratio between TX_100th and TX_control shows that the upscale spread growth associated with small-scale motions is still present, but of lesser magnitude to the influences of large-scale atmospheric motions on the ensemble RMDTE. The ensemble spread evolution characteristics seen over the entire model domain are similar to those for other cases tested that were run out to 48 h (i.e., inland motion of Tropical Storm Erin in 2007, the Arkansas MCV in 2010, and the Iowa MCS in 2015).

Fig. 10.
Fig. 10.

(a) Regional RMDTE time series for TX_control run of the 25 May 2013 case for the full ensemble domain (black line), the area devoid of convection (i.e., “NOCON” region in green), the region bounding the Texas MCV vortex (i.e., “MCV” region in red), and the associated baroclinic zone (i.e., “MCS” region in blue) defined in Fig. 9. (b) RMDTE ratio time series for TX_100th over TX_control for the full domain (black line), MCV region (red line), MCS region (blue line), and NOCON region (green line). (c) Normalized RMDTE (N_RMDTE) time series as described in appendix B for TX_control the MCV region (red line), MCS region (blue line), and NOCON region (green line).

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

Reducing the grid spacing of the ensemble from 4 to 2 km in the TX_2km case did not increase the overall ensemble spread significantly by the end of the simulation (cf. black and orange lines in Fig. 8). This indicates that the additional small-scale motions resolved by halving the grid spacing did not, in this case, lead to a substantial increase in the spread of the ensemble (this was also found to be true on the regional scale). However, the model grid spacing is still only on the kilometer scale. It is possible that this conclusion would change for ensembles with subkilometer grid spacing, but conducting such simulations was beyond the scope of this study.

2) Regional results

The three different subregions chosen, outlined by the dashed boxes in Fig. 9, for the 25 May 2013 case include a region centered in Texas on the MCV (known as the “MCV subregion” for the rest of this study), the area of rainfall associated with the northern baroclinic zone centered in Nebraska (“MCS” subregion), and a region with little to no convection centered along the Alabama–Mississippi border (“NOCON” subregion). The results of the subsetted RMDTE show variance in the overall RMDTE magnitude, RMDTE growth rate, and strength of the regional diurnal cycle (Fig. 10a).

The MCV subset initializes with the highest RMDTE (red line in Fig. 10a) and the NOCON region, the lowest RMDTE (green line in Fig. 10a), likely due to the significant differences in the nature of the elongated vorticity structure near the MCV, and the lack of moist convection in the NOCON region, respectively. The lack of a clear diurnal cycle (i.e., a reduction in ensemble RMDTE between 1500 and 2100 UTC) in the RMDTE in the MCV region (red line Fig. 10a) is an important factor to note. As discussed above, the diurnal cycle in the ensemble spread shows the importance of the large-scale atmospheric forcing, including the daily solar forced diurnal cycle in convection, in not allowing the error growth associated with moist convection to cause rapid divergence of the ensemble members. It could also be thought of as how convective motions transfer energy across scales and, thus, increase the ensemble RMDTE (spread) until the governing large-scale atmospheric characteristics constrain the spread growth. In the MCV region of TX_control, convection occurs throughout the majority of the period with very little movement (Fig. 3a), which is one way to view the lack of a diurnal cycle. However, for convection to occur over a multiday period, large-scale to mesoscale forcing must be involved to maintain the ingredients needed for moist convection. In this case warm, moist, and unstable flow off the Gulf of Mexico (Figs. 11a–c), and a convectively reinforced MCV (Fig. 1) compose the needed forcing for multiday convection. An MCV is a very good example of how both the convective and large-scale forcing can interact to produce varying solutions within an ensemble. For instance, the strength, presence, and evolution of an MCV is tied to the initiation, strength, and maintenance of convection through vertical heating profiles (e.g., Raymond and Jiang 1990; Fritsch et al. 1994; Trier et al. 2000b)., and the MCV motion is largely determined by the large-scale atmospheric flow field. Thus, the lack of diurnal cycle and larger spread growth rates in the MCV subset are associated with increased energy interactions between the convective and synoptic scales, which here has been associated with multiday convective rainfall.

Fig. 11.
Fig. 11.

Most unstable CAPE (MUCAPE; shaded at 100 J kg−1 and every 500 J kg−1 above 500 J kg−1), 900-hPa wind barbs (half barb = 5, full barb = 10, pennant = 50 kt), and 900-hPa isotachs in blue (contoured every 4 m s−1 above 12 m s−1) from the Rapid Refresh (RAP) analysis for the 25 May 2013 extreme precipitation case valid at (a) 0600, (b) 0900, and (c) 1500 UTC.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The pronounced diurnal cycle (blue line in Fig. 10a) present in the MCS region of TX_control illustrates, unlike the MCV region, the greater importance of synoptic- to meso-α-scale constraint on the ensemble spread evolution in that region. A significant amount of convection occurs in this region from 0600 to 1500 UTC 25 May, which leads to a very large RMDTE growth rate and peak magnitude (blue line in Fig. 10a). However, despite this large increase, the ensemble spread is reduced by over 20% within 10 h (by 2100 UTC) in this region in TX_control. The MCS region is conducive for convective initiation and maintenance because of the environmental conditions established by the location and characteristics of the developing extratropical cyclone and presence of a lower-level jet (LLJ) (Fig. 11). Near the time of convection initiation in the MCS region (0600 UTC), over 2500 J kg−1 of MUCAPE combined with a 50 kt LLJ were oriented perpendicular to the developing baroclinic zone (Fig. 11a), which provided the needed ingredients for the bowing MCS to form. As the MCS matured (0900–1500 UTC), the LLJ and MUCAPE axis shifted to the east (Figs. 11b,c), aiding in the system maintenance, eastward motion (Fig. 3b), and eventual dissipation (not shown). Compared to the MCV region, which has little change in the large-scale forcing through time (see MCV region in Figs. 11a–c), the large-scale atmospheric forcing (i.e., LLJ, developing extratropical cyclone, steering flow) in the MCS region is controlling the evolution and characteristics of the bowing MCS. Thus, as the more predictable large-scale forcing changes, so does the nature of the convection and the regional RMDTE. In other words, the surface baroclinic zone and LLJ forcing that is responsible for the convective development and resulting precipitation accumulation is equally responsible for the reduction of RMDTE following the first convective cycle in this region (blue line in Fig. 10a), which is reflected in the pronounced diurnal cycle in the RMDTE. This could also be interpreted as a measure of how much the MCS modifies the local environment relative to the ensemble mean, insofar as those modifications are not advected away from the calculation region.

While the RMDTE reflects the spread in the ensemble from an energy perspective, it does not necessarily follow that it directly relates to the spread of the forecasted precipitation, especially on a regional scale. From an extreme rainfall event forecasting perspective, the relationship between the ensemble spread and the resulting precipitation uncertainty is of great importance for determining the confidence and forecasted magnitude of a specific event. The AS metric, which quantifies the spread of precipitation that would be depicted on a spaghetti plot, for these two regions follows a somewhat contradictory pattern to the regional RMDTE. The AS for the MCV subset was larger (i.e., more areal spread between members precipitation accumulation) than that of the MCS region at both the 25.0- and 50.0-mm thresholds (Fig. 12), which makes intuitive sense based upon the differences in the individual ensemble member precipitation accumulations in Figs. 4 and 12. While the larger AS was seen in the MCV region, the RMDTE during the time most intense precipitation (i.e.,0600–1800 UTC for both the MCS and MCV regions) is smaller in the MCV region than the MCS region (cf. Figs. 12 and 10a). This implies that the RMDTE, which here quantifies the regional spread from an energy perspective, in some cases, may not have a direct relationship to the spread seen in the precipitation forecasts. In other cases studied that are not discussed in depth in this manuscript, such as the inland phase of Tropical Storm Erin in 2007 and Iowa MCS in June of 2015, the region of highest RMDTE was also the region of largest AS, but this case shows that this does not always follow.

Fig. 12.
Fig. 12.

Precipitation accumulation “paintball plot” contoured only at (a) 25.0 and (b) 50.0 mm for the members of TX_control valid for the 12 h ending at 1800 UTC 25 May 2013. Each fill color represents a different ensemble member’s accumulation. The area spread (AS) values for each threshold and region are plotted in the bottom right of the plots.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

In a similar fashion as the RMDTE for TX_control (Fig. 10a), the N_RMDTE (Fig. 10c), the RMDTE normalized by the mean regional kinetic energy, was calculated for the three subregions (i.e., MCV, MCS, and NOCON regions). The time series of RMDTE and N_RMDTE for these regions show a similar pattern. There is, similar to the RMDTE trace, a pronounced diurnal cycle in the N_RMDTE for MCS region, and a muted diurnal cycle in the MCV and NOCON regions (Fig. 10c). However, the relative magnitudes of the N_RMDTE time series compared to one another are altered. The MCS time series does still peak during the most convectively active times above the MCV region in the N_RMDTE series; however, the magnitude of the difference is much less (cf. Figs. 10a and 10c), which tends to bring the N_RMDTE comparison closer to the AS differences for these two regions (Fig. 12). Further, the NOCON region N_RMDTE is significantly reduced in relative magnitude compared to the other two regions, compared to the RMDTE traces (cf. Figs. 10a and 10c). The lowered relative magnitude of the NOCON region in the N_RMDTE time series is more what one might expect a priori for this subset of the domain, since no moist convection takes place in this region over the ensemble simulations. In general, the results of the N_RMDTE and RMDTE traces for TX_control can be interpreted the same way, although the N_RMDTE values might present a comparative regional magnitude scaling closer to what might be expected based upon the local convective characteristics.

The above results of the AS and N_RMDTE comparison to RMDTE are both rooted in the interactions between the precipitation forcing mechanisms and the energy of the regional background flow. In the MCS region, uncertainty in the mesoscale specifics embedded within a region of relatively high momentum can lead to increased ensemble spread from an energy perspective (i.e., RMDTE) but not change the synoptic forcing in a substantial enough way to change the location of the precipitation (i.e., AS metric). In other words, large errors in the MCS region in speed will rapidly increase the RMDTE but are not necessarily going to lead to large precipitation position errors. Conversely, in the lower background energy MCV region, the mesoscale uncertainty and the precipitation forcing are dependent on one another. The differences at the mesoscale can feed back to the convective scale and vice versa, which can cause large differences in the precipitation position. This relationship between the RMDTE and the background environment is illustrated by the N_RMDTE traces, which normalizes the spread growth relative to the mean kinetic energy of the background flow and reduces the absolute magnitude of the MCS region, but maintains the relative differences from the specific precipitation forcing in each region (cf. Figs. 10c and 10a).

Overall, the decrease in the RMDTE across all times from TX_control to any of the scaled perturbation ensemble runs (e.g., TX_half, TX_10th, etc.) again shows that the large-scale atmospheric forcing is the main constraint on the overall magnitude of the ensemble spread in these three regions (and the full model domain, Fig. 13). The specific diurnal cycle characteristics for the full domain and each region persists as the perturbation of the control is reduced from TX_half to TX_100th (Figs. 13a–d), despite the overall magnitude being lessened. This shows that convective scale processes are determining the “shape” of the RMDTE time series, which fits within the idea presented earlier that the magnitude of the diurnal cycle is dependent on the convective-scale interactions with the large-scale atmospheric forcing. Additionally, the continued reduction of the magnitude of the ensemble member perturbations from TX_half to TX_100th leads to an eventual convergence of the final RMDTE values (cf. TX_10th, TX_20th, and TX_100th traces in Figs. 13a–d). The RMDTE value of the convergence highlights the component of the spread growth associated with convective processes, since further reduction in the magnitude of the synoptic-scale ensemble perturbations to the point of negligible IC and LBC spread (i.e., TX_100th) yields almost no change in the RMDTE. Furthermore, by the same logic, the difference in the RMDTE magnitude from TX_control to TX_100th highlights the component of the RMDTE magnitude that is associated with large-scale ensemble variability (see annotations “synoptic scale” and “convective scale” in Figs. 13a–d). Figures 13b–d also show there is large variability in the RMDTE value at which the different regions converge and appears to scale based upon the amount of moist convection present within the region. The MCV region, which has persistent convection over the period, has a larger component of the total RMDTE from convective-scale processes than the MCS and NOCON regions, which have less persistent and little to no convection, respectively. The regional RMDTE decomposition further shows that the synoptic-scale atmospheric forcing is, generally, the main control on the overall magnitude of the ensemble RMDTE over the full domain and on regional scales. However, the increased spread growth due to convective processes is present and in some cases of sustained convection (i.e., increased interaction between the convective and large scales), such as the MCV region here, can be nearly half of the total RMDTE (Fig. 13b).

Fig. 13.
Fig. 13.

RMDTE time series for TX_control (solid line), TX_half (dot–dashed lines), TX_third (dotted line), TX_10th (uneven dashed line), TX_20th (solid line), and TX_100th (dashed line) for the (a) full domain, (b) MCV region, (c) MCS region, and (d) NOCON region as defined by dashed boxed regions centered in the Mississippi–Alabama border, Texas, and Nebraska, respectively, in Fig. 9. The individual time series are also labeled corresponding to the matching ensemble run. Additionally, annotations indicating the ensemble spread originating from synoptic-scale processes and convective processes are indicated in each panel; a more detailed explanation of the separation is given in section 4b(2).

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

The regional ratios of RMDTE (Fig. 10b) between the TX_100th and TX_control can be used to look further into the predictability of specific regions in the 25 May 2013 case. In a perfectly theoretical sense, if a meteorological case is at the pure theoretical limit of practical predictability, a decrease in the spread of the ensemble perturbations should result in a proportionate decrease in the ensemble spread over time (i.e., the beginning and end RMDTE are scaled by the proportion of the perturbation scaling). This is not seen in the experiments performed for the 25 May 2013 case, since the ratio of RMDTE for TX_100th to TX_control do not remain constant (Fig. 10b) across the full domain or any of the subregions. This implies that this modeling system is not at the pure limit of practical predictability and could be improved by advancements in data assimilation, numerics, and parameterizations, among others. It does not mean that the forecast is not improved by reducing the initial uncertainty; it just means that model ICs, physics, and numerics can still be improved. However, the faster increase in RMDTE in TX_100th could also, in addition to practical predictability issues, be caused by approaching, to some degree, the intrinsic predictability limit. If an ensemble system and specific case of interest were limited completely by intrinsic predictability, a scaled decrease in the ICs and LBCs would result in a similar ensemble spread for both the scaled and control ensemble. This is also not seen in the 25 May 2013 case and the lack of convergence of RMDTE ratio to 1 between TX_100th and TX_control illustrates that this case and the subregions are also not purely limited by intrinsic predictability, at the lead times and over the spatial regions where RMDTE is calculated. The exact degree to which intrinsic predictability spread growth influences the RMDTE evolution of the full domain and subregions, in addition to the growth associated with practical predictability limits, is difficult to discern. However, it is highly dependent on the amount of convection present, and how much that convection can affect the future state of large-scale atmospheric features (cf. subregional differences in Fig. 10).

5. Discussion

The various ensemble experiments presented here for the 25 May 2013 flooding event illustrate the spread characteristics associated with extreme precipitation in an 11-member convection allowing ensemble. Several characteristics were generally seen in all regions and over the full model domain. The presence of a diurnal cycle in the spread, even in regions of significant convection (i.e., the MCS subset), was particularly intriguing because it illustrates the ability for the large-scale atmospheric characteristics to constrain convective spread growth, which can speak to the viability of using convection-allowing ensembles for prediction on multiday time scales. Additionally, the magnitude of the diurnal cycle also shows the relative importance of the interactions between the convective and synoptic scales for a particular region and precipitation forcing. The less pronounced the diurnal cycle is for a particular region, the increased dependence the spread evolution has on the location and evolution of convective-scale processes. These events, such as the MCV described here, usually reside in the mesoscale, occur in the warm season, are still present a significant forecast challenge (e.g., Fritsch and Carbone 2004), and represent, from a precipitation standpoint at least, low predictability scenarios. The presence of a diurnal cycle in the ensemble spread has been seen previously (e.g., Zhang et al. 2006; Clark et al. 2010; Johnson et al. 2014; Surcel et al. 2016), but the persistence across all of the cases tested (see gray lines in Fig. 8) and the flow regime dependence is particularly illustrative.

The scaled ensemble perturbation experiments showed that the ensemble RMDTE growth is made up of both large- and small-scale atmospheric components that vary in magnitude based upon the specific flow regime and the amount of moist convection present (e.g., Surcel et al. 2016). Generally, the synoptic-scale component controls the magnitude of the ensemble RMDTE (i.e., spread) at both the regional scale and over the full ensemble domain, which was shown by the reduction in overall magnitude when the ICs and LBCs were scaled (Fig. 13). However, the convergence of the RMDTE traces to a value, when the synoptic perturbations associated with each member were very small (i.e., TX_100th), revealed that there is a component of the growth associated with convective-scale processes (Fig. 13). This was further corroborated by the constantly increasing RMDTE ratios between TX_100th and TX_control. In some cases, such as the MCV region for this event, the two components could approach one another in magnitude (Fig. 13b). These results show that both the “upscale error growth” model described by Lorenz (1969, and others) and the “downscale error cascade” (e.g., Durran et al. 2013; Durran and Gingrich 2014; Durran and Weyn 2016) perspectives are possibly incomplete. The relative importance of each component of the RMDTE, similar to the magnitude of the diurnal cycle, depends on the amount and type of moist convection that is occurring in the area of interest. The more moist convection is present and the more the convective evolution is dependent on interactions between the convective and synoptic scales (i.e., such as an MCV), the larger the small-scale error growth component will be of the ensemble spread growth. Similar results describing the varying importance of large- and small-scale errors have been found in recent experiments using idealized (e.g., Sun and Zhang 2016) and real-time (e.g., Vié et al. 2011; Johnson et al. 2014) NWP simulations.

All together the results illustrate the same basic idea: there is a dependence on the characteristics of the ensemble spread growth for cases of extreme precipitation in convection-allowing ensembles on the amount and specific forcing of convection that is present. Similarly, from an intrinsic versus practical predictability standpoint, the amount to which each one of these limits is affecting a particular case of precipitation is dependent upon these same factors (e.g., Melhauser and Zhang 2012). While the ensemble used in this study is not at the theoretical limit of practical predictability (characterized in Figs. 14a–c), it is also not at the theoretical limit of intrinsic predictability (characterized in Figs. 14d–f), based upon the RMDTE ratio analysis above. However, each case and region lay somewhere in between. In other words there is a nondiscrete continuum between the bounding theoretical limits of practical and intrinsic predictability where the ability for a particular ensemble system to converge to a solution is limited by varying degrees of deficiencies in model architecture (i.e., practical predictability limits) and varying degrees of error growth associated with chaotic moist convective processes (i.e., intrinsic predictability limits).

Fig. 14.
Fig. 14.

Conceptual diagram of the theoretical limit of (a)–(c) practical and (d)–(f) intrinsic predictability. The blue oval in each pane represents the spread of ensemble initial conditions, the red oval represents the spread of ensemble solutions at some arbitrary end of the numerical simulations, black dots within blue/red circles represent each ensemble member, and black lines represent the ensemble spread envelop through the numerical simulation (which is increasing from blue to red ovals). The initial ensemble spread is reduced incrementally from (a),(d) to (b),(e) to (c),(f) in approximate equal amounts.

Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0083.1

6. Conclusions

The ensemble predictability experiments illustrated the spread characteristics of a convection-allowing ensemble prediction system for extreme precipitation events in the contiguous United States over the full model domain and on regional scales. In general, the main constraint on the magnitude of the model spread was found to be associated with large-scale atmospheric features (e.g., Bei and Zhang 2007; Durran et al. 2013; Durran and Gingrich 2014; Durran and Weyn 2016). This was illustrated by several aspects of the ensemble experiments over the full model domain and subregions, including the diurnal cycle in the ensemble spread, similar spread growth rates in the convection-allowing ensemble compared to the native Reforecast-2 outside of model spin up and convectively active times, and the large decrease in the magnitude of the ensemble RMDTE when the ICs and LBCs were scaled. Additionally, the magnitude of the diurnal cycle appears to reflect the influence of the convective scales on the atmospheric evolution of a region.

Over the full model domain and regional subsets, it was found that the RMDTE of the scaled runs (i.e., TX_half, TX_10th, TX_100th, etc.) increased at a faster rate than the control simulation (i.e., TX_control), as denoted by the increasing RMDTE ratios in all cases. The faster rate of RMDTE increase in the scaled runs implies that upscale spread growth due to the resolution of convective scales is still present, but is, generally, of lesser influence than the large-scale forcing. This point was further corroborated by the convergence of the scaled perturbation ensemble runs to a final RMDTE value, which represented the component of the total spread growth from convective-scale processes. In the MCV region, where sustained convection is present and interactions between convective and synoptic scales are more prevalent (and the predictability is arguably lower), the large-scale component and convective-scale component of the RMDTE growth approached one another in magnitude.

Since the proportional scaling of the RMDTE between the scaled and control simulations is not maintained on both the full domain and regional scale, it shows that this ensemble system is not at the theoretical limit of practical predictability and can be improved by modeling system advancements. Additionally, no rapid convergence of the regional RMDTE ratio was seen between the scaled and control runs, implying that these regions are also not at the pure limit of intrinsic predictability. In regions of extreme precipitation, the increase in the RMDTE ratio is from a combination of intrinsic and practical predictability limits, since the RMDTE ratios increase faster than the nonconvective regions (Fig. 10b), and the scaled perturbation ensemble RMDTE traces converge to a larger RMDTE value (cf. Figs. 13b–d). The degree to which the limits of intrinsic and practical predictability affect the spread growth of a region is highly dependent on the specific forcing and amount of moist convection present in the simulations. In other words, there is a continuum between purely practical (Figs. 14a–c) and purely intrinsic (Figs. 14d–f) predictability-limited cases where both predictability limits could be influencing the ensemble spread growth characteristics in cases of extreme precipitation. Similarly, if you relate intrinsic and practical predictability to the atmospheric scales of motion that are the main cause of each predictability component (i.e., small and large scales for intrinsic and practical predictability, respectively), aspects of both the “upscale error growth” and “downscale cascade” theories are seen in the studied case(s) of extreme precipitation, but the observed behavior is not fully explained by either viewpoint.

Acknowledgments

The authors thank Gregory Herman, Robert Tournay, Stacey Hitchcock, John Peters, Matthew Igel, Editor Ryan Torn, and two anonymous reviewers for their helpful comments and discussion regarding this work. This research was supported by National Science Foundation Grant AGS-1157425, NASA Grant NNX15AD11G, and a National Science Foundation Graduate Research Fellowship Grant DGE-1321845, Amendment 3. Access to the full model output of NOAA’s Second-Generation Global Medium-Range Ensemble Reforecast Dataset (Reforcast-2) was provided by the Department of Energy (DOE). High-performance computing resources from Yellowstone (ark:/85065/d7wd3xhc) were provided by the National Center for Atmospheric Research (NCAR) Computational and Information Systems Laboratory, which is sponsored by the National Science Foundation. North American Regional Reanalyses (NARR) were obtained from the NOAA/Physical Sciences Division, and stage-IV analyses were provided by NCAR. Observational sounding data were provided by the University of Wyoming Department of Atmospheric Science. Flood damage estimates and reported fatalities for the extreme precipitation events examined were provided by the Storm Events Database of the National Climatic Data Center (NCDC).

APPENDIX A

List of All Ensemble Simulations Performed throughout this Study

For a list of all ensemble simulations performed throughout this study please see Table A1.

Table A1.

Precipitation events run in the same ensemble configuration as the 25 May 2013 event, which is not discussed in depth in this study. Many are plotted in the gray lines in Fig. 8. For more discussion on the predictability results of these cases see Nielsen (2016). For more discussion on previous research on these cases see mentioned references.

Table A1.

APPENDIX B

Description of Normalized Root Mean Difference Total Energy (N_RMDTE)

The specifics of the typical RMDTE calculation are given in the main body of the manuscript in section 3c. Here the process behind creating a RMDTE that is normalized by a specific region or the full domain’s mean kinetic energy (N_RMDTE) is discussed. As in the standard RMDTE calculation, the difference total energy (DTE; Zhang et al. 2003) is calculated for each ensemble member:
eb1
where the , , and are the differences of the zonal wind, meridional wind, and temperature from the ensemble mean, respectively; and ( J kg−1 K−1 and K). The differences , , and are five-dimensional variables that are functions of grid points in the x (i) and y (j) directions, vertical level k, time t, and ensemble member m.
Then, using the same framework, the total mean kinetic energy (TMKE) of a specific subregion (or full domain) can be calculated as
eb2
where and are the values from the ensemble mean [i.e., the mean had been subtracted from the DTE calculation in Eq. (B1)]. The temperature term [e.g., ] in Eq. (B1) is not included in the to allow the term to dominantly vary with the particular convective situation in question. The temperature term would be too large to allow anything more than a latitudinal dependence to be identified (i.e., the would constantly scale based upon the latitude of the subsetted region).
Since Eqs. (B1) and (B2) have slightly different dimensionality, a pressure-weighted average for both the and and an ensemble average for must be performed to arrive at comparable variables:
eb3
eb4
eb5
A normalized () can then be calculated as
eb6
The is at this point subsetted (or calculated over the full domain) and averaged over the region of interest to arrive at the :
eb7
eb8

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