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    WRF-DART analysis of (left) 850-hPa geopotential height (contours; m), 0–1-km vector wind (vectors; m s−1), and 0–1-km equivalent potential temperature (colored shading, scale on x axis) valid at (a) 0000 (c) 1200, and (e) 1800 UTC 19 May 2013. (right) The 315-K PV (colored shading; PVU) and 500-hPa winds (vectors; m s−1), valid at (b),(d),(f) time as in (a),(c),(e); the thick gray line denotes the 30 m s−1 isotach on the 300-hPa surface.

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    (a) WSR-88D reflectivity (dBZ) at 2200 UTC 19 May 2013. The 22-h simulated radar reflectivity forecast for ensemble members (c) 6 and (e) 24 initialized at 0000 UTC 19 May 2013. (b),(d),(f) As in (a),(c),(e), but valid at 0000 UTC 20 May 2013. The asterisk in (a) and (b) denotes the location of the Norman, OK, ASOS station while the box in panels (c)–(f) denotes the forecast metric region used in the sensitivity calculations.

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    (a) Area-average 1-h precipitation over the box in Fig. 2c for each ensemble member as a function of lead time initialized at 0000 UTC 19 May 2013 (lines). The red (blue) lines denote the wet (dry) members, which are described in the text. (b) Histogram of the area-average precipitation between 2200 UTC 19 May and 0100 UTC 20 May 2013 (22–25-h forecast) for each ensemble member. (c),(d) As in (a),(b), but for the precipitation averaged over the box in Fig. 13c for the forecast initialized at 0000 UTC 31 May 2013.

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    Vertical profile of the normalized difference in the 21-h (a) equivalent potential temperature and (b) water vapor mixing ratio averaged over the COKP box shown in Fig. 2e between the wet and dry members as a function of pressure (red line) initialized at 0000 UTC 19 May 2013. The shaded layers indicate vertical levels where the difference is statistically significant at the 95% confidence level. The black line gives the ensemble-mean profile [K and kg kg−1 in (a),(b), respectively]. (c) As in (a), but for the COKP box in Fig. 13c initialized at 0000 UTC 31 May 2013.

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    Sensitivity of the 22–25-h accumulated precipitation averaged over the box shown in Fig. 2c to the (a) 0-, (b) 6-, (c) 12-, and (d) 18-h 315-K potential vorticity (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV at the appropriate time (PVU). The black line in (c) labeled A–A′ denotes the location of the cross section for Fig. 6.

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    Sensitivity of the 22–25-h precipitation averaged over the box shown in Fig. 2c to the 12-h 315-K PV along the cross section shown in Fig. 5c (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV (PVU).

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    Normalized difference in the 18-h 600-hPa vertical motion between the wet and dry members (color shading; m s−1). Black stippled regions indicate where the difference is statistically significant at the 95% confidence level. The thick gray contours denote the difference in the 600-hPa relative vorticity while the thin black contours give the ensemble-mean 600-hPa relative vorticity (10−5 s−1). Vectors indicate the 600-hPa thermal wind with the reference vector located at the bottom-right corner (m s−1 Pa−1).

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    Sensitivity of the 2200 UTC 19 May–0100 UTC 20 May precipitation averaged over the box shown in Fig. 2c to the 1200 UTC 315-K PV (shading; mm) initialized at (a) 1200 UTC 18 May and (b) 1200 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV (PVU).

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    Sensitivity of the 22–25-h precipitation averaged over the box shown in Fig. 2c to the (a) 6-, (c) 12-, and (e) 18-h forecast of the 0–1-km meridional wind (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The vectors are the ensemble-mean winds with the reference vector in the lower-right corners of each panel. (b),(d),(f) As in (a),(c),(e) but for the 0–1-km water vapor mixing ratio; contours are the ensemble mean (g kg−1).

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    (a) Difference in the 12-h 315-K PV between the wet and dry members for the forecast initialized at 0000 UTC 19 May 2013 (shading; PVU). The vectors denote the 800-hPa winds (m s−1) obtained by inverting the 315-K PV field within the thin contour using the statistical technique outlined in the text. The thick contours are the 800-hPa equivalent potential temperature at the corresponding time. (b) As in (a), but for the 12-h 312-K PV initialized at 0000 UTC 31 May 2013.

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    Sensitivity of the 21-h 0–1-km water vapor mixing ratio averaged over the box shown in Fig. 2c to the 12-h (a) 315-K potential vorticity and (b) 0–1-km water vapor mixing ratio (shading; mm) initialized at 0000 UTC 19 May 2013. Contours are the ensemble mean [in (a),(b) PVU and g kg−1, respectively].

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    WRF-DART analysis of (left) 850-hPa geopotential height (contours; m), average 0–1-km vector wind (vectors; m s−1), and 0–1-km equivalent potential temperature (colored shading: K) valid at (a) 0000, (c) 1200, and (e) 1800 UTC 31 May 2013. (b),(d),(f) The 312-K PV (shading; PVU) and 500-hPa winds (vectors; m s−1) valid as in (a),(c),(e). The thick gray line denotes the 30 m s−1 isotach on the 300-hPa surface.

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    As in Fig. 2, but for (a) 2200 UTC 31 May 2013 and for ensemble members (c) 26 and (e) 13 initialized at 0000 UTC 31 May 2013. (b),(d),(f), As in (a),(c),(e), but valid at 2300 UTC 31 May 2013.

  • View in gallery

    Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the (a) 0-, (b) 6-, (c) 12-, and (d) 18-h 312-K potential vorticity (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV. The black line in (b) labeled A–A′ denotes the location of the cross section for Fig. 15.

  • View in gallery

    Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the 12-h 312-K PV along the cross section shown in Fig. 14b (shading; mm) initialized at 0000 UTC 31 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean potential vorticity.

  • View in gallery

    Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the (a) 6-, (c) 12-, and (e) 18-h forecast of the 0–1-km meridional wind (shading; mm) initialized at 0000 UTC 31 May 2013. Dotted regions indicate where the sensitivity is statistically significant at the 95% confidence level. The vectors are the ensemble-mean winds, with the reference vector in the lower-right corner. (b),(d),(f) As in (a),(c),(e), but for the 800-hPa equivalent potential temperature; contours are the ensemble mean (K).

  • View in gallery

    Sensitivity of the 21-h forecast of the 0–1-km averaged box shown in Fig. 13c to the (a) 0-, (b) 6-, and (c) 12-h 312-K PV (shading; mm) initialized at 0000 UTC 31 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. Contours are the ensemble-mean PV ( PVU).

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Sensitivity of Central Oklahoma Convection Forecasts to Upstream Potential Vorticity Anomalies during Two Strongly Forced Cases during MPEX

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  • 1 Department of Atmospheric and Environmental Sciences, University at Albany, State University of New York, Albany, New York
  • | 2 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

The role of upstream subsynoptic forecast errors on forecasts of two different central Oklahoma severe convection events (19 and 31 May 2013) characterized by strong synoptic forcing during the Mesoscale Predictability Experiment (MPEX) are evaluated by applying the ensemble-based sensitivity technique to WRF ensemble forecasts with explicit convection. During both cases, the forecast of the timing and intensity of convection over central Oklahoma is modulated by the southward extent of upstream midtropospheric potential vorticity anomalies that are moving through the base of a larger-scale upstream trough but pass by central Oklahoma prior to convective initiation. In addition, the convection forecasts are also sensitive to the position of lower-tropospheric boundaries, such that moving the boundaries in a manner that would lead to increased equivalent potential temperature over central Oklahoma prior to convective initiation leads to more precipitation. Statistical PV inversion and correlation calculations suggest that the midtropospheric PV and near-surface boundary sensitivities are not independent; the winds associated with the PV error can modulate the position of the lower-tropospheric boundary through advection in a manner consistent with the implied sensitivity. As a consequence, it appears that reducing the uncertainty in specific upstream subsynoptic features prior to convective initiation could improve subsequent forecasts of severe convection.

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

Corresponding author address: Ryan Torn, University at Albany, State University of New York, ES 351, 1400 Washington Ave., Albany, NY 12222. E-mail: rtorn@albany.edu

Abstract

The role of upstream subsynoptic forecast errors on forecasts of two different central Oklahoma severe convection events (19 and 31 May 2013) characterized by strong synoptic forcing during the Mesoscale Predictability Experiment (MPEX) are evaluated by applying the ensemble-based sensitivity technique to WRF ensemble forecasts with explicit convection. During both cases, the forecast of the timing and intensity of convection over central Oklahoma is modulated by the southward extent of upstream midtropospheric potential vorticity anomalies that are moving through the base of a larger-scale upstream trough but pass by central Oklahoma prior to convective initiation. In addition, the convection forecasts are also sensitive to the position of lower-tropospheric boundaries, such that moving the boundaries in a manner that would lead to increased equivalent potential temperature over central Oklahoma prior to convective initiation leads to more precipitation. Statistical PV inversion and correlation calculations suggest that the midtropospheric PV and near-surface boundary sensitivities are not independent; the winds associated with the PV error can modulate the position of the lower-tropospheric boundary through advection in a manner consistent with the implied sensitivity. As a consequence, it appears that reducing the uncertainty in specific upstream subsynoptic features prior to convective initiation could improve subsequent forecasts of severe convection.

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

Corresponding author address: Ryan Torn, University at Albany, State University of New York, ES 351, 1400 Washington Ave., Albany, NY 12222. E-mail: rtorn@albany.edu

1. Introduction

Increasing computer power has led to the proliferation of deterministic (e.g., Droegemeier 1997; Xue and Martin 2006; Kain et al. 2006; Done et al. 2004; Lean et al. 2008; Rotach et al. 2009; Seity et al. 2011; Weisman et al. 2008) and ensemble (e.g., Clark et al. 2010a,b, 2012; Kain et al. 2013; Schwartz et al. 2015; Hohenegger et al. 2008; Vie et al. 2011) numerical weather prediction systems that have sufficient grid spacing (≤4 km) to explicitly forecast convective storms. While these models can often realistically represent the structure and evolution of these phenomena, there are many cases characterized by significant errors in both the timing and location of convection (e.g., Done et al. 2004; Weisman et al. 2008). There are several potential reasons for these forecast failures, including physics parameterizations (e.g., Kain et al. 2006; Coniglio et al. 2013; Romine et al. 2013), grid spacing (e.g., Kain et al. 2008; Schwartz et al. 2009; Vandenberg et al. 2014), and errors in model analysis fields that are critical to the initiation and evolution of convection (e.g., Weisman et al. 2008; Clark et al. 2010a,b; Coniglio et al. 2010; Duda and Gallus 2013; Schumacher et al. 2013). Although the relative importance of any of these error sources could vary greatly from one case to another, the focus of this study is on the role of errors in forecast fields prior to convective initiation.

The role of uncertainty in the preconvective environment has been documented in a number of studies both in idealized and actual cases. It has long been known that convective initiation, mode, updraft strength, and propagation are sensitive to the profile of vertical wind shear (e.g., Weisman and Klemp 1982; Coniglio et al. 2006; Richardson et al. 2007) and thermodynamic fields (e.g., McCaul et al. 2005; Hohenegger and Schar 2007; Kirkpatrick et al. 2009, 2011; Wandishin et al. 2008, 2010) in idealized environments. These results suggest that accurate convection forecasts require good estimates of the mesoscale environment prior to convective initiation. Indeed, mesoscale data assimilation studies suggest that reducing mesoscale environmental errors generally leads to better convection forecasts (e.g., Wheatley et al. 2012; Stensrud et al. 2013).

The evolution of the mesoscale environment is often modulated by characteristics of larger-scale phenomena (e.g., motion, structure, location, orientation, etc.), such as troughs and near-surface boundaries. In these circumstances, the larger-scale phenomena tend to produce convection in specific locations, thus producing more skillful forecasts (e.g., Doswell 1987; Weisman et al. 2008) than might be expected from a theoretical perspective (e.g., Lorenz 1969; Lilly 1990; Hohenegger and Schar 2007). Various forms of sensitivity analysis, which involves perturbing some aspect of the model state vector that is believed to impact convection and measuring the impact on the forecast, indicate that variability in the structure and position of these larger-scale features can impact subsequent convection forecasts. One method of performing such a sensitivity analysis is to apply potential vorticity “surgery” to remove a synoptic feature believed to be important to the forecast and observe the impact on the forecast (e.g., Roebber et al. 2002; Nielsen-Gammon and Gold 2008; Gold and Nielsen-Gammon 2008a,b). Removing or doubling the amplitude of specific PV anomalies was found to impact the vertical wind shear, CAPE, and ascent, thereby changing the location and mode of convection. In addition, ensemble-based methods, which provide a more objective method of measuring sensitivity, also confirm the importance of upstream synoptic features. Although some studies indicate that convection is modulated by the timing of upper-level features and surface boundaries that are directly involved in the triggering of local convection (e.g., Melhauser and Zhang 2012; Li et al. 2014; Bednarczyk and Ancell 2015), errors in seemingly remote PV features can also influence the timing of convection (e.g., Hanley et al. 2013). As with PV surgery, the location of upper-level features is associated with differences in the CAPE, shear, and so on.

The goal of this study is to determine how upstream forecast uncertainty impacts subsequent convection forecasts for two cases (19 May and 31 May 2013) during the Mesoscale Predictability Experiment (MPEX; Weisman et al. 2015) that were characterized by the typical synoptic setup for severe convection over the southern Great Plains region [i.e., deep trough over the Rocky Mountains and lower-tropospheric moist southerly flow (Johns and Doswell 1992; McNulty 1995)]. One of the primary goals of MPEX was to evaluate the hypothesis that enhanced synoptic and subsynoptic observations over the Rocky Mountain region during the early morning will improve convection forecasts during the afternoon over the high plains. In particular, this study employs the ensemble-based sensitivity technique (e.g., Ancell and Hakim 2007) and convection-permitting ensemble forecasts to evaluate the sensitivity of convection forecasts to upstream forecast fields, such as the position and structure of near-surface wind and thermodynamic boundaries that could trigger convection, and to upstream synoptic and subsynoptic features. Moreover, this work evaluates the dynamical mechanisms that give rise to the regions of sensitivity and forecast differences that arise later in the afternoon, with emphasis on how the upstream upper-level forecast errors impact near-surface boundaries and preconvective thermodynamic state.

The remainder of the paper proceeds as follows. Section 2 describes the WRF forecasts and provides a brief summary of ensemble sensitivity analysis. Sections 3 and 4 describe a synoptic overview and forecast sensitivities for the 19 May and 31 May cases, respectively. A summary and conclusions are given in section 5.

2. Forecast description

Convective forecast sensitivity is evaluated using ensemble analyses and forecasts that allow for explicit convection that were produced in real time during the MPEX field phase. This forecasting system is similar to what is described in Schwartz et al. (2015) and is summarized here; the interested reader is directed to this paper for further details on the system outlined below. The ensemble data assimilation system generated 50-member ensemble analyses every 6 h from 1 May 2013 through 15 June 2013 by incorporating observations with 6-h ensemble forecasts valid at the analysis time on a 15-km horizontal grid-spacing domain that includes the continental United States and upstream areas [see Fig. 1 of Schwartz et al. (2015) for the exact dimensions].

Both the data assimilation system and ensemble forecasts employ version 3.3.1 of the Advanced Research version of the Weather Research and Forecasting (ARW; Skamarock et al. 2008) Model with the following physics packages: Thompson microphysics (Thompson et al. 2008), the Mellor–Yamada–Janjić (MYJ) planetary boundary layer (Mellor and Yamada 1982; Janjić 1994, 2001), the Noah land surface model (Ek et al. 2003), Rapid Radiative Transfer Model (RRTM) longwave and shortwave radiation (Mlawer et al. 1997; Iacono et al. 2008) with ozone and aerosol climatologies (Tegen et al. 1997), and the Tiedtke cumulus parameterization (Tiedtke 1989; Zhang et al. 2011) and positive definite moisture advection (Skamarock and Weisman 2009). Ensemble lateral boundary conditions are taken from 6-h Global Forecast System (GFS) forecasts valid at the appropriate time, with perturbations taken from the WRF three-dimensional variational data assimilation (WRFDA-3DVAR; Barker et al. 2012) system via the fixed covariance perturbation technique of Torn et al. (2006).

Observations from rawinsondes, METAR, marine, Aircraft Meteorological Data Relay (AMDAR), atmospheric motion vectors (AMV; Velden et al. 2005), and global positioning system radio occultation observations (Kursinski et al. 1997) are assimilated using the Data Assimilation Research Testbed (DART; Anderson et al. 2009), which is an implementation of the ensemble adjustment Kalman filter (EAKF; Anderson 2001). The interested reader is directed to Table 3 of Romine et al. (2013) for a list of observation types that were assimilated from each platform and the observation error sources.

At any analysis time, two-way nested ensemble forecasts can be generated for a 15-km horizontal grid-spacing outer domain and a 3-km horizontal grid-spacing inner domain [exact location shown in Fig. 1 of Schwartz et al. (2015)]. The 3-km domain is initialized by downscaling from the 15-km analysis domain and uses the same physics packages as the 15-km domain, except that the 3-km domain does not employ a cumulus parameterization. Lateral boundary conditions are obtained from the corresponding-time GFS forecast, with lateral boundary condition perturbations generated using the same procedure as is used in the data assimilation system. For brevity, this study mainly focuses on forecasts initialized at 0000 UTC on the day of the case (i.e., roughly 21 h prior to convective initiation); however, a similar analysis was performed on forecasts initialized 12 h before and after for comparison.

The role of upstream forecast errors on subsequent convective forecasts is evaluated by applying the ensemble-based sensitivity technique to the ensemble forecasts. Specifically, the sensitivity of a forecast metric J to a model state variable at some earlier lead time is computed from the M member ensemble via
e1
where and are 1 × M ensemble estimates of the respective quantities computed from the forecast ensemble, i is the state variable index, cov denotes the covariance, and var denotes the variance. For most sensitivity calculations, the values of are normalized by its ensemble standard deviation. This choice allows for the comparison between fields that are characterized by varied intrinsic variability and units. By dividing by the ensemble standard deviation, all sensitivities have units of the metric per standard deviation of the state variable. Moreover, the statistical significance of the sensitivity values is tested using the method outlined in Torn and Hakim (2008). A sensitivity is deemed statistically significant if the null hypothesis of no relationship between the metric and analysis state variable can be rejected [i.e., if the absolute value of the regression coefficient is greater than its 95% confidence bounds computed from ensemble data (e.g., Wilks 2005, section 6.2.5)].

In general, J could be any combination of state variables or model outputs; however, the method is most applicable when there is a smooth range of forecast outcomes as opposed to clustering of metric values. For most of this study, J is the 3-h precipitation averaged over a geographic area, which is being used as a proxy for convection. This metric is chosen because of its ease in computing from model output and could be directly compared to observations. Other forecast metrics, such as the maximum vertical kinetic energy and simulated radar reflectivity, were also considered but often gave qualitatively similar results (not shown). This is consistent with the results of Bednarczyk and Ancell (2015), who found little sensitivity to the chosen metric. Although the total precipitation contains both convective and stratiform contributions, the time periods studied here are close to convective initiation; thus, the stratiform regions are not extensive. Moreover, the relatively long accumulation period is employed to remove variability in J related to small differences in the timing of convective initiation, while the area calculation is meant to remove variability related to small differences in position.

3. 19 May 2013

a. Overview

The synoptic setup during 19 May 2013 was similar to many past severe convective outbreaks over the southern Great Plains. At 0000 UTC, much of the southern plains is characterized by southerly winds in excess of 15 m s−1 through the lowest 1 km of the atmosphere,1 which is acting to advect higher equivalent potential temperature () air poleward (Fig. 1a). The significant gradient in through western Texas, Oklahoma, and Kansas represents the position of the dryline; to the west of this boundary, the winds are mainly from the west. In the midtroposphere, the winds indicate a broad 500-hPa trough axis centered on Utah and Arizona, with a shorter-wavelength ridge axis through Missouri and Iowa (Fig. 1b). In addition, the 315-K Ertel PV2 is asymmetric about the trough, with values generally >1 PVU (1 PVU = 10−6 K kg−1 m2 s−1) on the western side and <0.75 PVU on the eastern side. The increased PV on the western side is associated with an equatorward-moving jet streak.

Fig. 1.
Fig. 1.

WRF-DART analysis of (left) 850-hPa geopotential height (contours; m), 0–1-km vector wind (vectors; m s−1), and 0–1-km equivalent potential temperature (colored shading, scale on x axis) valid at (a) 0000 (c) 1200, and (e) 1800 UTC 19 May 2013. (right) The 315-K PV (colored shading; PVU) and 500-hPa winds (vectors; m s−1), valid at (b),(d),(f) time as in (a),(c),(e); the thick gray line denotes the 30 m s−1 isotach on the 300-hPa surface.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

At 1200 UTC, the lower-tropospheric increased by 4–6 K throughout much of the southern plains because of the deepening of the moist boundary layer by persistent southerly flow (Fig. 1c). The highest values (>344 K) were located just to the east of the nearly stationary dryline, with the >15 m s−1 southerly winds acting to maintain these values through advection. To the west of the dryline in western Texas, Oklahoma, and Kansas, a prominent lee trough in the winds had formed in response to downsloping related to the increasing westerly winds associated with the approaching jet streak that was rounding the base of the trough (Fig. 1d). At the same time, the area of >1 PVU air had also reached the base of the trough in northern New Mexico. As might be expected with this synoptic setup, the 1200 UTC Norman, Oklahoma (OK), sounding was characterized by significant veering of the wind with height and was unstable but capped, with 1965 J kg−1 of surface-based CAPE but also 389 J kg−1 of convective inhibition (CIN), which was at least partially caused by the 5-K temperature inversion between 840 and 870 hPa (not shown).

By 1800 UTC, the dryline begins to move to the east because of a number of factors and will become the focus of convection later in the day (Fig. 1e). In addition to the normal diurnal movement of the dryline, this boundary moved farther east over western Oklahoma because of the stronger cyclonic winds associated with a deeper surface cyclone over western Kansas that formed in response to the approaching midtropospheric PV anomaly (Fig. 1f). A special 1800 UTC Norman sounding indicated that the CIN decreased by 50% over the previous 6 h because of the boundary layer heating and mixing; however, the capping inversion changed little in strength (not shown), suggesting that additional forcing was necessary for convective initiation to take place. Convection initiates on this day along the dryline as a result of the strong near-surface confluence and proximity to the upstream midtropospheric PV anomaly, which act to produce deep-tropospheric lift that helps to erode the temperature inversion at the top of the boundary layer via adiabatic cooling over this layer (Trier et al. 2015).

Although there were several distinct areas of convection throughout the Great Plains during the afternoon of 19 May, the focus of this study is on the WRF ensemble’s prediction of the convection over central Oklahoma. This area was characterized by variability in the extent of convection within the WRF Model forecasts and was the focus of ground operations by MPEX crews. On this day, severe convection developed along the dryline in central Oklahoma, with several significant tornadoes accompanying supercells that passed near the Oklahoma City, OK, metropolitan area, including two fatalities and 14 injuries (National Climatic Data Center 2015). Figure 2 shows snapshots of simulated reflectivity for two members of the WRF ensemble (members 6 and 24) initialized at 0000 UTC 19 May and the corresponding-time observed reflectivity. At 2200 UTC, there were three distinct supercells oriented north–south along the dryline from Norman, OK, northward (Fig. 2a). Whereas member 6 has a line of discrete north–south-oriented cells from just west of Norman up to the Oklahoma–Kansas border (Fig. 2c), member 24 is characterized by a single supercell to the northwest of Norman, with two additional cells initiating farther north (Fig. 2e). Two hours later, there was a single supercell to the northeast of Norman (Fig. 2b) that was similar to member 24 (Fig. 2f), while the line of convection in member 6 had moved east through central Oklahoma (Fig. 2d).

Fig. 2.
Fig. 2.

(a) WSR-88D reflectivity (dBZ) at 2200 UTC 19 May 2013. The 22-h simulated radar reflectivity forecast for ensemble members (c) 6 and (e) 24 initialized at 0000 UTC 19 May 2013. (b),(d),(f) As in (a),(c),(e), but valid at 0000 UTC 20 May 2013. The asterisk in (a) and (b) denotes the location of the Norman, OK, ASOS station while the box in panels (c)–(f) denotes the forecast metric region used in the sensitivity calculations.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Given the variety of convective evolutions within the ensemble over central Oklahoma, the focus of this study turns toward understanding the processes that give rise to the precipitation forecast differences over the 165 km × 165 km box shown in Figs. 2c–f [herein denoted the central Oklahoma precipitation (COKP)], which is characterized by the largest ensemble standard deviation in 3-h accumulated precipitation over Oklahoma for this forecast. The variability in COKP is best illustrated by the time series of 1-h accumulated precipitation for each ensemble member as a function of forecast hour (Fig. 3a). As suggested by Fig. 2, there are large differences in both the amount and timing of precipitation, such that some members have precipitation rates exceeding 2 mm h−1 between 2200 and 2300 UTC, while others remain below 0.5 mm h−1 throughout the forecast. Given the large variability of precipitation amounts and the desire to focus on convective initiation prior to the period where cold pool propagation dominates convective evolution, the focus of this study is on COKP between 2200–0100 UTC. The accumulated precipitation over this time period has a Gaussian appearance, with a peak between 3 and 4 mm and a standard deviation of 1.7 mm (Fig. 3b).

Fig. 3.
Fig. 3.

(a) Area-average 1-h precipitation over the box in Fig. 2c for each ensemble member as a function of lead time initialized at 0000 UTC 19 May 2013 (lines). The red (blue) lines denote the wet (dry) members, which are described in the text. (b) Histogram of the area-average precipitation between 2200 UTC 19 May and 0100 UTC 20 May 2013 (22–25-h forecast) for each ensemble member. (c),(d) As in (a),(b), but for the precipitation averaged over the box in Fig. 13c for the forecast initialized at 0000 UTC 31 May 2013.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

b. Forecast sensitivities

Prior to evaluating the role of upstream forecast errors on modulating the convection over COKP, it is instructive to evaluate the difference in the thermodynamic profile averaged over the COKP region at 2100 UTC (i.e., preconvective initiation) between the members that produced the most precipitation and the members that produced the least precipitation. The normalized difference between the 10 members that predict the largest J (wet members) and the 10 members that predict the lowest J (dry members) is computed via
e2
where () denotes the mean of ith state variable for the wet (dry) ensemble members, and is the ensemble standard deviation of computed from all members. Dividing by the ensemble spread normalizes the difference between the two subsets of ensemble members, which makes it quantitatively possible to compare various levels, fields, and so on. The statistical significance of the composite differences is assessed by employing bootstrap resampling without replacement. In particular, two subsets of ensemble members, equal in size to the wet and dry members, are randomly selected from the full 50-member ensemble; then the ensemble mean of the two subsets is computed. This process is repeated 2000 times to obtain the 95% confidence bounds on the composite difference. The benefit of this particular method is that the statistical significance can be evaluated without assuming a Gaussian distribution for .

Figure 4a shows the difference in the 2100 UTC over the forecast metric box. The largest differences between the wet and dry members are concentrated in two layers: between the surface and 850 hPa (up to 1.4 standard deviations difference or 5.9 K) and between 500 and 700 hPa (up to 1.6 standard deviations or 3.6 K). Below 850 hPa, the difference is mainly caused by the wet members having a 1.4 standard deviations greater water vapor mixing ratio (Fig. 4b); the temperature in this layer is actually slightly colder in the wet members compared to the dry (not shown). In turn, these differences lead to 700 J kg−1 more CAPE for the wet members relative to the dry members (difference statistically significant at 99% confidence). In addition, the wet members are characterized by >1.2 standard deviations more water vapor mixing ratio from 500 to 700 hPa, which corresponds to the same layer over which the static stability is 1.0 standard deviation lower and the vertical motion is >1.0 standard deviation greater in the wet members (not shown). The layer of perturbation upward vertical motion is located directly above the layer of ensemble-mean upward vertical motion that is associated with convergence along the dryline. As a consequence, this suggests that the wet members are characterized by deeper vertical motion, which would be expected to cool, moisten, and destabilize a relatively deep column, thereby making it easier to erode the capping inversion in this region.

Fig. 4.
Fig. 4.

Vertical profile of the normalized difference in the 21-h (a) equivalent potential temperature and (b) water vapor mixing ratio averaged over the COKP box shown in Fig. 2e between the wet and dry members as a function of pressure (red line) initialized at 0000 UTC 19 May 2013. The shaded layers indicate vertical levels where the difference is statistically significant at the 95% confidence level. The black line gives the ensemble-mean profile [K and kg kg−1 in (a),(b), respectively]. (c) As in (a), but for the COKP box in Fig. 13c initialized at 0000 UTC 31 May 2013.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Given the differences in the preconvective environments described above, the remainder of this subsection shifts toward determining the sensitivity of the precipitation forecasts to upstream features and how this sensitivity relates to the preconvective initiation thermodynamic differences. In particular, the midtropospheric moisture and vertical motion differences noted above suggest that the thermodynamic environment could have been modulated by a midtropospheric synoptic feature; thus, it is of interest to determine the sensitivity of the precipitation forecasts to midtropospheric features. Ertel PV offers one of the best methods of tracking features, as it is conserved under adiabatic and frictionless conditions; thus, it can act as a forecast error “tracer” (e.g., Davies and Didone 2013).

Figure 5 shows the sensitivity of COKP to the 315-K PV at various lead times3. This isentropic level is characterized by the largest normalized sensitivity values at nearly all lead times (not shown). For the 0-h forecast, the sensitivity is maximized over southwestern New Mexico at the southeast end of the strip of higher PV that is moving southeast along the western side of the larger-scale trough (Fig. 5a). The negative sensitivity values, which are on the order of 0.7 mm per standard deviation, suggest that shifting the PV maximum back toward the northwest is associated with greater COKP. Six hours later, the region of negative sensitivity remains along the southeastern edge of this area of higher PV, which has shifted to the east, such that the maximum sensitivity is now on the Texas–New Mexico border (0.9 mm per standard deviation; Fig. 5b). At 1200 UTC, the main region of sensitivity moves into the panhandle of Texas and is oriented along the ensemble-mean PV gradient (Fig. 5c). Taking a southwest-to-northeast cross section of the PV through the region of maximum sensitivity and computing the sensitivity of COKP to PV at various pressure levels along the cross section indicates that the sensitive region is maximized between 450 and 700 hPa and is mainly confined to the lower portion of a southwest-to-northeast-tilted PV anomaly, such that having a shallower anomaly is associated with more precipitation (Fig. 6). Moreover, this region of maximum sensitivity mainly follows the slope of the 315-K isentrope along the cross section, which justifies the use of this particular isentropic level (not shown).

Fig. 5.
Fig. 5.

Sensitivity of the 22–25-h accumulated precipitation averaged over the box shown in Fig. 2c to the (a) 0-, (b) 6-, (c) 12-, and (d) 18-h 315-K potential vorticity (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV at the appropriate time (PVU). The black line in (c) labeled A–A′ denotes the location of the cross section for Fig. 6.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Fig. 6.
Fig. 6.

Sensitivity of the 22–25-h precipitation averaged over the box shown in Fig. 2c to the 12-h 315-K PV along the cross section shown in Fig. 5c (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV (PVU).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Although isentropic potential vorticity is not the only field to which the precipitation forecast exhibits sensitivity, the sensitivity of COKP is most easily traced on isentropic surfaces relative to isobaric surfaces. For example, the sensitivity of COKP to the 1200 UTC 600-hPa vorticity is maximized in the same geographical location as the 315-K PV (i.e., the Texas Panhandle) and has comparable magnitude (1.1 mm per standard deviation); however, it is difficult to trace this region of maximum sensitivity to the 600-hPa vorticity backward in time (not shown). One possible reason for this result is the slope of the 315-K surface. At 0 h, the 315-K surface at the location of the sensitivity maximum is near 500 hPa; however, at 12 h, the 315-K surface is closer to 600 hPa at the location of the sensitivity maximum. As a consequence, the sensitivity to the 0-h 500-hPa (12 h 600 hPa) vorticity is greater than the sensitivity to the 600-hPa vorticity (500 hPa) vorticity in the vicinity of the 0-h (12 h) 315-K PV sensitivity maxima (not shown).

Returning to the sensitivity to the 315-K PV, the location of the sensitivity maximum and the orientation of the synoptic flow suggest that changes in the sensitive region could be directly responsible for convective initiation and, therefore, the variability in COKP; however, the region of largest sensitivity passes to the north of central Oklahoma at 1800 UTC along with the leading edge of the PV maximum (Fig. 5d). Even though this sensitive region passes by the COKP box, it can still influence the central Oklahoma forecast metric box by modifying the forcing for vertical motion. Figure 7 shows the difference in 600-hPa vorticity and vertical motion between the wet and dry members. The 600-hPa vorticity difference is maximized in nearly the same location as the 315-K PV sensitivity, such that the wet members are characterized by less vorticity, or a shortwave ridge, in north-central Oklahoma and southeast Kansas, which is in between two vorticity lobes located in the Texas Panhandle and northeast Kansas. In turn, this can produce a larger vorticity gradient in the direction of the thermal wind and, hence, forcing for upward (downward) vertical motion upstream (downstream) of the vorticity differences. Indeed, the wet members are characterized by anomalous upward (downward) motion upwind (downwind) of the anomalous vorticity. This region of upward motion over southwestern Oklahoma moves northeast over the next 3 h and coincides with the COKP box, which is likely responsible for the aforementioned higher midtropospheric moisture, vertical motion, and reduced cap strength in the wet members.

Fig. 7.
Fig. 7.

Normalized difference in the 18-h 600-hPa vertical motion between the wet and dry members (color shading; m s−1). Black stippled regions indicate where the difference is statistically significant at the 95% confidence level. The thick gray contours denote the difference in the 600-hPa relative vorticity while the thin black contours give the ensemble-mean 600-hPa relative vorticity (10−5 s−1). Vectors indicate the 600-hPa thermal wind with the reference vector located at the bottom-right corner (m s−1 Pa−1).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

While it is possible that the sensitivity of the COKP to the upstream 315-K PV is unique to this particular initialization time, COKP precipitation forecasts initialized 12 h before and after 0000 UTC 19 May exhibit similar sensitivity to the 1200 UTC 315-K PV. Figure 8 shows the sensitivity of COKP to the 1200 UTC 19 May 315-K PV using ensemble forecasts initialized at 1200 UTC 18 May and 1200 UTC 19 May; this figure is directly comparable to Fig. 5c. Although the details of the ensemble-mean PV change from one initialization time to another because of the nature of the ensemble mean (i.e., smooths out large gradients for longer-range forecasts), all three forecast initialization times are characterized by negative sensitivity to the 315-K PV in the Texas Panhandle, suggesting that decreasing the PV in that location, or shifting the PV anomaly to the northwest, is associated with greater precipitation. Moreover, it appears that the areal coverage of maximum sensitivity shrinks as the difference between the initialization time and forecast metric time decreases. Nonetheless, this result suggests that the sensitivity to the 315-K PV over the Texas Panhandle is robust among several initialization times.

Fig. 8.
Fig. 8.

Sensitivity of the 2200 UTC 19 May–0100 UTC 20 May precipitation averaged over the box shown in Fig. 2c to the 1200 UTC 315-K PV (shading; mm) initialized at (a) 1200 UTC 18 May and (b) 1200 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV (PVU).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Although the COKP exhibits large sensitivity to the midtropospheric PV, this forecast metric is also sensitive to near-surface wind and moisture fields at earlier lead times. Figure 9 shows the sensitivity of COKP to the near-surface meridional wind component and water vapor mixing ratio at various lead times. While there is no coherent region of sensitivity to either of these fields at 0000 UTC (not shown), the sensitivity of COKP to the 0600 UTC meridional wind and water vapor mixing ratio over west Texas is nearly equal, such that increasing (decreasing) either quantity by 1 standard deviation along the dryline is associated with up to 0.7 mm higher (lower) COKP (Figs. 9a,b). In essence, this pattern suggests that the COKP is sensitive to the position of the dryline, such that shifting it to the west during this particular lead time is associated with increased convection later on. By 1200 UTC, the regions of maximum sensitivity have shifted north along the dryline and expanded in area, such that the maximum sensitivity now exceeds 1.1 mm per standard deviation in both quantities (Figs. 9c,d). The same pattern is present at 1800 UTC; however, the region of maximum sensitivity, particularly for the water vapor mixing ratio, has shifted poleward along the dryline and reaches central Oklahoma (Figs. 9e,f). As a consequence, this set of figures suggests that COKP is modulated by perturbations to the position of the dryline to the south of the metric region. This sensitive region moves poleward with increasing lead time, likely because of advection, and could be responsible for the increased lower-tropospheric water vapor in the metric region just prior to convective initiation; this idea is explored later in this section.

Fig. 9.
Fig. 9.

Sensitivity of the 22–25-h precipitation averaged over the box shown in Fig. 2c to the (a) 6-, (c) 12-, and (e) 18-h forecast of the 0–1-km meridional wind (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The vectors are the ensemble-mean winds with the reference vector in the lower-right corners of each panel. (b),(d),(f) As in (a),(c),(e) but for the 0–1-km water vapor mixing ratio; contours are the ensemble mean (g kg−1).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Given that the two primary sensitivity regions are associated with the 315-K PV and the lower-tropospheric meridional wind and water vapor mixing ratio, it is possible that these two sensitive regions are dynamically related to each other. One possible hypothesis to explain these two sensitive regions is that the winds associated with the PV differences in the sensitive region modulate the position through advection. One method of evaluating this hypothesis is to apply statistical PV inversion (e.g., Hakim and Torn 2008) to derive the lower-tropospheric wind associated with the difference in the 1200 UTC 315-K PV between the wet and dry members over the Texas Panhandle. In essence, this technique involves computing the linear operator that maps from a particular PV field to the wind field using a singular value decomposition of the ensemble forecast fields. Although this method suffers from statistical artifacts caused by using a small ensemble relative to the number of degrees of freedom, it has the advantage that it does not require the specification of boundary conditions. The interested reader is directed to Hakim and Torn (2008) for a full description of the method.

Inverting the 315-K PV difference between the wet and dry members suggests that the PV and lower-tropospheric wind and water vapor sensitivities are dynamically related to each other. Figure 10a shows the 315-K PV anomaly, defined as the difference between the wet and dry members, and domain over which the inversion was applied. The inversion is applied over this relatively small region because of the ensemble size, which is half of what was used in Hakim and Torn (2008). Although the inversion was performed on several different pressure levels, only the 800-hPa surface is shown, because it is located relatively close to the surface and thus could influence the position of the dryline. A negative elliptical PV anomaly like this would be expected to have perturbation anticyclonic winds throughout the troposphere. It is likely that the small ensemble size and close proximity to the ground precludes the winds from looking more anticyclonic, though it is worth noting that the 600- and 700-hPa winds have a more anticyclonic character on all sides of the anomaly (not shown). To the south of this anomaly, the inverted winds are easterly, ranging from 2 to 5 m s−1, except right along the dryline, where they are southerly and closer to 5 m s−1. As a consequence, it appears that the perturbation winds are made up of two factors: (i) easterly winds associated directly with the PV difference and (ii) southerly winds, which are caused by the westward shift in the dryline position. The perturbation easterly winds act to slow the eastward progression of the dryline, which would account for the region of statistically significant positive differences in the near-surface in this region (not shown). The relationship between the 315-K PV and dryline position is further supported by the −0.69 correlation (r2) between the 1200 UTC 315-K PV averaged over the sensitive region in Fig. 5c and the 1200 UTC near-surface water vapor mixing ratio averaged over the sensitive region in Fig. 9d.

Fig. 10.
Fig. 10.

(a) Difference in the 12-h 315-K PV between the wet and dry members for the forecast initialized at 0000 UTC 19 May 2013 (shading; PVU). The vectors denote the 800-hPa winds (m s−1) obtained by inverting the 315-K PV field within the thin contour using the statistical technique outlined in the text. The thick contours are the 800-hPa equivalent potential temperature at the corresponding time. (b) As in (a), but for the 12-h 312-K PV initialized at 0000 UTC 31 May 2013.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Recall from Fig. 4b that the wet members are characterized by the greater water vapor mixing ratio below 850 hPa just prior to convective initiation, which could imply that this quantity modulates COKP. In turn, another way to validate the importance of the upstream 315-K PV on the COKP forecast is to compute the sensitivity of the 2100 UTC 0–1-km AGL water vapor mixing ratio averaged over the COKP box to the 315-K PV and near-surface water vapor mixing ratio at earlier times using Eq. (1). If the hypothesis that the winds associated with the 315-K PV difference modulate the position of the dryline and subsequent lower-tropospheric in central Oklahoma, then the 2100 UTC 0–1-km water vapor mixing ratio averaged over the COKP box should be sensitive to the 315-K PV in the same location as the COKP. Indeed, Fig. 11 indicates that the 2100 UTC 0–1-km AGL water vapor over the metric box is sensitive to the 1200 UTC 315-K PV and near-surface water vapor mixing ratio in almost identical locations to COKP (i.e., Texas Panhandle and along the dryline, respectively). In particular, decreasing the 315-K PV or increasing the 0–1-km water vapor mixing ratio by 1 standard deviation at 1200 UTC is associated with a 1.1 g kg−1 change in the 0–1-km water vapor mixing ratio in the COKP box by 2100 UTC. As a consequence, it is possible to conclude that the same upstream features that modulate COKP also modulate the lower-tropospheric thermodynamic state prior to convective initiation.

Fig. 11.
Fig. 11.

Sensitivity of the 21-h 0–1-km water vapor mixing ratio averaged over the box shown in Fig. 2c to the 12-h (a) 315-K potential vorticity and (b) 0–1-km water vapor mixing ratio (shading; mm) initialized at 0000 UTC 19 May 2013. Contours are the ensemble mean [in (a),(b) PVU and g kg−1, respectively].

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

4. 31 May 2013

a. Overview

In a broad sense, the synoptic evolution during 31 May was similar to what was observed during the 19 May case; however, there were notable differences in the location and evolution of lower-tropospheric boundaries and upstream troughs. At 0000 UTC 31 May, a vertically stacked cyclone was present over western South Dakota, with an associated cold front that extended southward through Nebraska and Kansas (Fig. 12a). Farther south, there was a robust dryline through western Oklahoma and Texas, as indicated by the strong gradient, with southerly winds out ahead of it and near-surface in excess of 356 K and southwesterly winds behind. At 500 hPa, there was a broad trough centered over far western South Dakota, which was associated with the cyclonic wrap up of 315-K PV (Fig. 12b). Similar to 19 May, the 315-K PV was generally higher on the western side of the larger-scale trough, with embedded PV maxima in excess of 2 PVU in northern Colorado, western Wyoming, and Idaho.

Fig. 12.
Fig. 12.

WRF-DART analysis of (left) 850-hPa geopotential height (contours; m), average 0–1-km vector wind (vectors; m s−1), and 0–1-km equivalent potential temperature (colored shading: K) valid at (a) 0000, (c) 1200, and (e) 1800 UTC 31 May 2013. (b),(d),(f) The 312-K PV (shading; PVU) and 500-hPa winds (vectors; m s−1) valid as in (a),(c),(e). The thick gray line denotes the 30 m s−1 isotach on the 300-hPa surface.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Over the next 18 h, the cold front pushed south through Kansas and into northwestern Oklahoma (Figs. 12c,e). To the east of this front, the near-surface exceeded 356 K over a broad swath of central Oklahoma, while the front itself was characterized by strong confluence from the southerly winds ahead of the front and northwesterly winds behind, which acted as a focal point for convection. The 1800 UTC Norman, OK, sounding was characterized by 3056 J kg−1 of CAPE and a nearly 90° of veering in the wind between the surface and 500 hPa; however, the atmosphere was capped by a 4-K temperature inversion at 800 hPa (not shown), so the CIN was 128 J kg−1. Beyond this time, the CIN was further reduced by cooling of the inversion at the top of the boundary layer because of large-scale vertical motion (not shown). At 500 hPa, the broad upper-level trough changed little over this period; however, the aforementioned 315-K PV maxima moved quickly from west to east along the northern edge of the jet through Nebraska and Iowa (Figs. 12d,f).

WRF ensemble forecasts initialized at 0000 UTC (roughly 21 h prior to convective initiation) do a fairly good job capturing the convective mode along the front, with largest differences associated with the southward extent. In Oklahoma, convection began as discrete supercells at the intersection of the cold front and a dryline to the northwest of Oklahoma City between 2100 and 2200 UTC (Fig. 13a). This initial convection included large and destructive tornadoes (8 fatalities, 38 injuries) and evolved into a storm complex over the Oklahoma City metropolitan area during the evening (Fig. 13b) that lead to deadly flash flooding (14 fatalities) from central into east central Oklahoma (National Climatic Data Center 2015). While both ensemble forecasts are able to capture the transition from discrete cells during this time period, there is uncertainty regarding how far south the convection occurs within Oklahoma, with member 26 showing more discrete cells and the convection staying well north of Norman, while member 13 shows greater areal extent of convection farther south (Figs. 13c–f). Given the uncertainty in the amount of convection over central Oklahoma, the focus of this section is on understanding the sensitivity of the 2100–0000 UTC precipitation forecast over a new 120 km × 120 km box over central Oklahoma to forecast fields at earlier times. This box encompasses the uncertainty in the southern extent of the precipitation associated with the ensemble forecasts. Figure 3c shows that the hourly precipitation rate increases for most of the ensemble members during this period; however, there are differences in amount of precipitation, related mostly to the areal extent. Furthermore, there was a fairly broad range of precipitation amounts over this 3-h period, which had a standard deviation of 3.0 mm (Fig. 3d).

Fig. 13.
Fig. 13.

As in Fig. 2, but for (a) 2200 UTC 31 May 2013 and for ensemble members (c) 26 and (e) 13 initialized at 0000 UTC 31 May 2013. (b),(d),(f), As in (a),(c),(e), but valid at 2300 UTC 31 May 2013.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

b. Forecast sensitivities

Similar to 19 May, the wet members are characterized by distinct differences in the thermodynamic profile just prior to convective initiation (i.e., 2100 UTC). Figure 4c indicates that the in the wet members is at least 1.0 standard deviation (2.5 K) greater between the surface and 700 hPa in the wet members compared to the dry members. While the difference is attributable to both temperature and water vapor mixing ratio from the surface to 850 hPa, the 850–700 hPa difference is primarily caused by the water vapor mixing ratio (not shown). As a consequence, the CAPE in the wet members is 460 J kg−1 greater. In addition, the wet members are characterized by nearly 2.0 standard deviations greater convergence below 850 hPa. In turn, the wet members are associated with >1.0 standard deviation larger vertical motion between the surface and 700 hPa and 1.5 standard deviations more cooling at the level of the capping inversion (not shown), which helps to reduce the convective inhibition. As a consequence, the remainder of this section considers the sensitivity of the COKP forecasts to earlier forecast times, with emphasis on how this sensitivities could modify the lower-tropospheric and lower-tropospheric convergence.

The COKP forecasts during this case are also characterized by large sensitivity to upstream PV errors, though, unlike the 19 May case, the sensitive features are to the northwest, rather than southwest, of central Oklahoma. Figure 14a shows that COKP is sensitive to the 0-h 312-K PV through northern Colorado and Utah along the southern edge of one of the aforementioned PV maxima, such that decreasing (increasing) the PV by 1 standard deviation is associated with up to a 1.2 mm increase (decrease) COKP. This sensitivity is akin to shifting the 0-h position of this PV anomaly farther north. By 6 h, the sensitivity maxima remain on the southern side of the PV anomaly through northern Colorado but have increased in both spatial area and magnitude (Fig. 14b). Taking a north–south cross section through the sensitive region indicates that this region of negative sensitivity is present from 250 to 650 hPa on the southern side of the downward-extending PV anomaly that is along the Colorado–Wyoming border (Fig. 15), with the largest values near 450 hPa, which is roughly the pressure level of the 312-K surface at the horizontal location of the sensitivity maximum. Beyond 6 h, the sensitive region remains on the southern side of the PV anomaly, translating from eastern Colorado at 12 h (Fig. 14c) into northern Kansas, southeast Nebraska, and Iowa by 18 h (Fig. 14d); therefore, similar to the 19 May case, it appears that the most sensitive region moves past the forecast metric region prior to convective initiation taking place. Starting at 1200 UTC, the precipitation forecast exhibits positive (negative) sensitivity to the north (south) of the PV maximum associated with the aforementioned lower-tropospheric cold front and dryline through the Texas Panhandle and western Oklahoma, such that shifting the position of this front to the north is associated with greater precipitation (Figs. 14c,d). The mechanism by which these two sensitive regions impact the forecast will be discussed later in the section.

Fig. 14.
Fig. 14.

Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the (a) 0-, (b) 6-, (c) 12-, and (d) 18-h 312-K potential vorticity (shading; mm) initialized at 0000 UTC 19 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean PV. The black line in (b) labeled A–A′ denotes the location of the cross section for Fig. 15.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Fig. 15.
Fig. 15.

Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the 12-h 312-K PV along the cross section shown in Fig. 14b (shading; mm) initialized at 0000 UTC 31 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. The contours are the ensemble-mean potential vorticity.

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

In addition to the midtropospheric PV sensitivities, COKP is also sensitive to the lower-tropospheric wind and thermodynamic fields starting around 1200 UTC. While the sensitivity of COKP to the 6-h near-surface meridional wind is not coherent (Fig. 16a), by 1200 UTC, there is a large region of positive sensitivity stretching from the Texas Panhandle, northwestern Oklahoma, and southeastern Kansas, which indicates that increasing the meridional wind by 1 standard deviation is associated with a 1.1-mm increase in COKP (Fig. 16c). This sensitive region is centered on the ensemble-mean wind shift associated with the lower-tropospheric front, suggesting that shifting the position of the front to the north, which would lead to a larger meridional wind component, is associated with greater COKP. Moreover, the sensitivity of COKP to the 800-hPa is mainly confined to eastern Colorado at 6 h (1.0 mm per standard deviation; Fig. 16b) but expands in horizontal area and magnitude, such that the sensitivity to the 12-h is maximized along the northern side of the baroclinic zone (up to 1.2 mm per standard deviation; Fig. 16d), which also indicates that shifting this baroclinic zone to the north is associated with greater COKP. In turn, this is likely to influence the lower-tropospheric in the COKP box prior to convective initiation. It is worth pointing out that the sensitivity to slopes poleward with increasing height, though the largest values are in the lower troposphere (not shown). By 1800 UTC, the largest sensitivity to meridional wind (Fig. 16e) and (Fig. 16f) remains in northwestern Oklahoma near the intersection of the dryline and cold front, such that shifting the position of these boundaries away from the COKP box is associated with greater precipitation.

Fig. 16.
Fig. 16.

Sensitivity of the 21–24-h precipitation averaged over the box shown in Fig. 13c to the (a) 6-, (c) 12-, and (e) 18-h forecast of the 0–1-km meridional wind (shading; mm) initialized at 0000 UTC 31 May 2013. Dotted regions indicate where the sensitivity is statistically significant at the 95% confidence level. The vectors are the ensemble-mean winds, with the reference vector in the lower-right corner. (b),(d),(f) As in (a),(c),(e), but for the 800-hPa equivalent potential temperature; contours are the ensemble mean (K).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

Statistical inversion of the 1200 UTC 312-K PV difference between the wet and dry members over eastern Colorado and northwestern Kansas suggests that the PV and near-surface sensitivities are also not independent of each other. Figure 10b shows the 800-hPa vector wind associated with the inversion of the 312-K PV difference between the wet and dry members using the method outlined in the previous section. Similar to the results for the 19 May case, the winds are generally anticyclonic along the southern side of this negative PV anomaly, though the results are not uniformly anticyclonic, likely because of the proximity to the surface and small number of ensemble members. This PV anomaly is associated with 1–2 m s−1 southeasterly winds along the baroclinic zone through northern Oklahoma and Texas, which would act to move the front toward the northwest and away from central Oklahoma. In addition, the combination of the southeasterly perturbation winds associated with the PV difference and ensemble-mean northwesterly wind to the north of the baroclinic zone (cf. Fig. 12c) is associated with higher-amplitude lower-tropospheric convergence along the baroclinic zone, which likely explains the increased convergence within the COKP box described earlier, while the increased lower-tropospheric is a consequence of the more northern position of the front, which this calculation suggests is related to the negative PV difference between the wet and dry members. Finally, the correlation (r2) between the 312-K PV averaged over the sensitive region for this field and the 800-hPa averaged over the sensitive region for that field is −0.65, which further confirms that the evolution of the 312-K PV at this location and the 800-hPa baroclinic zone are linked.

The relative importance of the southward extent of the 312-K PV anomaly on the lower-tropospheric over the COKP region prior to convective initiation is confirmed by computing the sensitivity of the 2100 UTC 0–1-km to the 312-K PV at earlier lead times (Fig. 17). At 0 h, the near-surface COKP is mainly sensitive to the 312-K PV along the southern end of the aforementioned PV anomaly, such that decreasing the PV by 1 standard deviation (akin to shifting the PV anomaly to the north) is associated with a 0.9-K change in the near-surface . This region is nearly identical to the region of greatest sensitivity of COKP to the 0-h 312-K PV (cf. Fig. 14a). Beyond 0 h, the sensitive region translates along the southern end of the PV gradient through Colorado at 6 h (Fig. 17b) and then along the Kansas–Nebraska border at 12 h (Fig. 17c), which nearly corresponds to the sensitive region for COKP (cf. Figs. 14b,c). In addition, the sensitivity to the 1200 UTC PV is also maximized in a southwest–northeast-oriented region of ensemble-mean PV from west Texas through southeast Kansas that corresponds with the lower-tropospheric baroclinic zone. The positive (negative) sensitivity indicates that increasing (decreasing) the PV on the northwest (southeast) flank, akin to shifting the position of the front poleward, is associated with higher within the COKP box. It is worth pointing out that this sensitivity to the position of the front does not appear until 1200 UTC. Finally, the 2100 UTC surface-to-850-hPa convergence is also most sensitive to the southward extent of the aforementioned PV anomaly (not shown). As a consequence, these results suggest that errors associated with the southward extent of this PV anomaly modulate the position of the front and lower-tropospheric convergence along the baroclinic zone.

Fig. 17.
Fig. 17.

Sensitivity of the 21-h forecast of the 0–1-km averaged box shown in Fig. 13c to the (a) 0-, (b) 6-, and (c) 12-h 312-K PV (shading; mm) initialized at 0000 UTC 31 May 2013. Black stippled regions indicate where the sensitivity is statistically significant at the 95% confidence level. Contours are the ensemble-mean PV ( PVU).

Citation: Monthly Weather Review 143, 10; 10.1175/MWR-D-15-0085.1

5. Summary and conclusions

This study evaluates the role of upstream forecast errors on subsequent forecasts of severe convection in central Oklahoma for two cases during the MPEX field project that were characterized by strong synoptic forcing (19 May and 31 May). The role of the upstream precursors is diagnosed by computing the sensitivity of precipitation averaged over a central Oklahoma box that encompasses the area with large ensemble standard deviation in precipitation to forecast fields at earlier times using the ensemble sensitivity technique on a relatively large ensemble of convection-permitting WRF forecasts. Both cases were characterized by a relatively broad trough to the west of the Great Plains, with embedded smaller-scale PV anomalies rotating around the trough and strong lower-tropospheric temperature and water vapor mixing ratio gradients associated with the dryline on 19 May and southward-moving baroclinic zone on 31 May, respectively.

For both the 19 May and 31 May forecasts, precipitation forecast variability can be traced backward in time to uncertainty in the location of upstream midtropospheric PV anomalies. In both cases, larger forecast precipitation was obtained by shifting the position of the upstream PV anomalies to the north. These sensitive areas are most readily traced backward in time on isentropic surfaces, rather than on constant pressure surfaces. This result is most likely obtained because PV is conserved on isentropic surfaces, assuming adiabatic and frictionless conditions and the general downward slope of the isentropic surfaces as these upstream PV anomalies move equatorward around the larger-scale trough. Surprisingly, the PV anomalies and the sensitive regions pass by central Oklahoma prior to convective initiation; therefore, it suggests that these PV anomalies have an indirect impact on convective initiation.

While the a priori expectation might be that the PV errors are associated with differences in the convective triggering location; instead, the upstream PV errors act to modify the location of lower-tropospheric boundaries that act as focal points for convection. For 19 May, the forecast sensitivities suggest that the precipitation forecast is modulated by the position of the dryline in west Texas earlier in the day, which, in turn, is associated with the lower-tropospheric in central Oklahoma. The more western dryline position in the wet members relative to the dry members is consistent with having perturbation lower-tropospheric easterly winds on the southern side of the negative PV anomaly. In turn, these easterly winds can advect the dryline to the west, thus accounting for the large correlation between the PV and averaged over their sensitive regions. Similarly, the 31 May forecast is sensitive to the position of a southward-moving baroclinic zone, such that a northward shift in the baroclinic zone, which is associated with higher lower-tropospheric , leads to more precipitation in the forecast within the metric box. The easterly and northeasterly lower-tropospheric perturbation winds associated with the PV difference between the wet and dry members act to advect the baroclinic zone to the north and lead to more convergence along the baroclinic zone, making it easier to trigger convection. For both cases, the sensitivities to near-surface wind and do not appear until the PV-sensitive region comes into close proximity to the lower-tropospheric boundaries. This result suggests that the midtropospheric PV errors are the primary driver of the forecast variability in convection. This result appears to be consistent with the results of Roebber et al. (2002), Hanley et al. (2013), and Bednarczyk and Ancell (2015), who concluded that upper-tropospheric features appeared to modulate convection forecasts in their particular cases, and with Hanley et al. (2013) arguing that seemingly remote PV features could have an outsized impact on squall-line forecasts.

The results of this study suggest that errors associated with the upstream PV at subsynoptic scales can have a significant impact on convection forecasts in a number of ways; therefore, it is important to densely sample these features. For both cases, the sensitive region at both 0000 UTC and 1200 UTC is small enough that it would typically be sampled by no more than one rawinsonde over the Intermountain West, given the relatively coarse distance between stations in this part of the United States. Moreover, the sensitivity appears to be maximized in the midtroposphere; thus, commercial aircraft observations flying at a constant altitude (typically 200–250 hPa) would not sample these features, though aircraft taking off or landing could provide soundings. As noted earlier, these cases represented two of the missions flown by the National Science Foundation/NCAR Gulfstream-V during the MPEX field project; therefore, there are relatively dense upstream dropwindsonde data for these two cases. For the 19 May case, five dropwindsondes either partially or fully sampled the locations where the precipitation forecast is most sensitive to the 1200 UTC 315-K PV. By contrast, 7 dropwindsondes sampled the 1200 UTC lower-tropospheric sensitive region during 31 May, while the 312-K PV sensitive region was sampled by one dropwindsonde. Future work will involve validating the importance of these sensitive regions through a series of data denial experiments whereby dropwindsonde data are either assimilated or not, and the impact on subsequent convection forecasts is documented. Furthermore, sensitivity analysis will be extended to other MPEX cases with weaker synoptic forcing to determine how upstream forecast variability modulates convection for these cases.

Acknowledgments

Real-time observation data access was provided by MADIS, COSMIC, and SSEC. We would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. This work was supported by NSF Grant 1239787.

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1

The 0–1-km quantities are determined by computing the mass-weighted average within 1 km of the model surface height.

2

This isentropic level is chosen because it intersects the 500-hPa surface through the core of the maximum 500-hPa winds and, as will be shown later, is associated with large sensitivity.

3

The PV values at each grid point represent the average PV within 100 km of each grid point. This choice reduces the noise in the PV field and provides more robust sensitivity results. Locations with white shading denote where the 315-K surface is below ground at that particular time.

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