Abstract

Surface pressure observations are assimilated into a Weather Research and Forecast ensemble using an ensemble Kalman filter (EnKF) approach and the results are compared with observations for two severe weather events. Several EnKF experiments are performed to evaluate the relative impacts of two very different pressure observations: altimeter setting (a total pressure field) and 1-h surface pressure tendency. The primary objective of this study is to determine the surface pressure observation that is most successful in producing realistic mesoscale features, such as convectively driven cold pools, which often play an important role in future convective development. Results show that ensemble-mean pressure analyses produced from the assimilation of surface temperature, moisture, and winds possess significant errors in regard to mesohigh strength and location. The addition of surface pressure tendency observations within the assimilation yields limited ability to constrain such errors, while the assimilation of altimeter setting yields accurate depictions of the mesoscale pressure patterns associated with mesoscale convective systems. The mesoscale temperature patterns produced by all the ensembles are quite similar and tend to reproduce the observed features. Results suggest that even though surface pressure observations can have large cross covariances with temperature and the wind components, the resulting analyses fail to improve upon the EnKF temperature and wind analyses that exclude the surface pressure observations. Ensemble forecasts following the assimilation period show the potential to improve short-range forecasting of surface pressure.

1. Introduction

Surface pressure observations provide significant information on atmospheric features across a broad range of scales. On the synoptic scale, surface pressure observations define the location and intensity of cyclones and anticyclones, while on the mesoscale these observations define the location and intensity of convectively induced mesohighs and mesolows (Fujita 1955). Temporal changes in surface pressure provide guidance on the movement and evolution of these large-scale and mesoscale features, and an analysis of surface pressure tendency is often more valuable than a surface pressure analysis (Sanders 1955; Hess 1959). Thus, surface pressure observations are important to creating a realistic three-dimensional depiction of the atmosphere.

While the current surface observation network is sufficient to capture large-scale atmospheric features, the average station spacing of approximately 100 km is insufficient to capture many mesoscale features. In such cases, relatively high-resolution numerical weather prediction (NWP) products can serve as a proxy for the real atmosphere, but the initial conditions of NWP models are often devoid of important mesoscale features, a potential source of forecast error. Mesoscale surface data assimilation is one approach for improving model initialization/spinup and subsequently derived products. The present study emphasizes the potential role of including surface pressure observations in mesoscale ensemble data assimilation.

To meld data and model dynamics, the ensemble Kalman filter (EnKF; Evensen 1994; Houtekamer and Mitchell 1998) is being increasingly utilized in conjunction with atmospheric models, such as the Weather Research and Forecasting (WRF; Skamarock et al. 2005) model, at increasingly smaller scales. An appealing aspect of the EnKF is that it uses an ensemble of nonlinear forecasts to estimate the flow-dependent covariances for the assimilation. In theory, surface data assimilation using an EnKF approach should produce more realistic estimates of the local atmospheric state than current statistical methods, such as three-dimensional variational data assimilation (3DVAR), which use fixed covariances for the assimilation.

Recent studies have demonstrated the potential benefits of standard surface observations (temperature, moisture, and winds only) assimilated via the EnKF. Hacker and Snyder (2005), using a parameterized one-dimensional planetary boundary layer (PBL) model, showed the effectiveness of simulated surface observations for reducing error throughout the vertical extent of the PBL. This influence is most pronounced in the well-mixed PBL of late afternoon, when land–atmosphere coupling strength is highest, but is significant even during the overnight hours. Fujita et al. (2007) performed EnKF simulations of two warm-season days, and showed that the assimilation of hourly surface observations in the first 6 h of a 24-h (ensemble) forecast improved the location and intensity of the dryline, frontal boundaries, as well as PBL height and structure. In light of the latter study, a similarly configured WRF mesoscale ensemble system was run during the spring of 2007, and produced realistic mesoscale temperature patterns associated with several mesoscale convective systems (MCSs), as well as attendant circulations (Stensrud et al. 2009). While the results of these studies are encouraging, further inclusion of surface pressure observations into the EnKF system may produce even more realistic mesoscale structures (and attendant circulations) in the ensemble mean fields.

At larger scales, several studies have demonstrated the impact of assimilating surface pressure observations using an EnKF approach (Whitaker et al. 2004; Anderson et al. 2005; Dirren et al. 2007). In particular, Whitaker et al. (2004) and Dirren et al. (2007) found assimilating total surface pressure effective at constraining errors from the surface through the midtroposphere. [Notably, the latter provided the groundwork for the University of Washington pseudo-operational EnKF, which makes continued use of surface pressure/altimeter setting assimilation (Torn and Hakim 2008).] However, these data assimilation studies focused mainly on improving depictions of the planetary to synoptic scale. It is unclear whether their approaches would produce similar results at the mesoscale.

For mesoscale applications, surface pressure assimilation is confronted with at least two other challenges, which as noted above have been more thoroughly considered for other surface observations (with reasonable success). First, a relatively high assimilation frequency (e.g., every hour) is required for short-range mesoscale ensemble prediction. It is possible that this type of assimilation procedure could saturate the domain with numerous, large-amplitude gravity waves, given no appropriate balance constraint(s) exist at these smaller scales of interest. Second, at least one previous mesoscale surface data assimilation study (Fujita et al. 2007) neglected surface pressure observations to avoid errors of representation caused by a mismatch between model and actual terrain heights. One approach that reduces this error of representation is the assimilation of surface pressure tendency fields. As mentioned earlier, these fields at times depict more coherent mesoscale structure than total surface pressure fields (e.g., Figs. 1a–f). In such cases, the tendency fields—at least in a local sense—may covary more strongly with the total surface pressure fields, as well as the surface temperature and wind fields.

Fig. 1.

Barnes objectively analyzed observations of altimeter setting and 1-h surface pressure tendency at (a),(b) 1500 UTC 4 Jul 2003; (c),(d) 0200 UTC 5 Jul 2003; and (e),(f) 0600 UTC 20 Jun 2007. Negative shading is enclosed by dashed contours.

Fig. 1.

Barnes objectively analyzed observations of altimeter setting and 1-h surface pressure tendency at (a),(b) 1500 UTC 4 Jul 2003; (c),(d) 0200 UTC 5 Jul 2003; and (e),(f) 0600 UTC 20 Jun 2007. Negative shading is enclosed by dashed contours.

The two candidate cases for pressure data assimilation using an EnKF approach are the mesoscale convective events of 4–5 July 2003 and 19–20 June 2007. A series of three mesoscale convective systems moved across the upper Great Plains and Midwest regions of the United States on 4–5 July 2003, creating significant heterogeneity in the pressure and temperature patterns over these regions. This heterogeneity was poorly depicted in operational model initial conditions, and a real-time WRF forecast and subsequent research simulations were unable to develop the later convective systems at the proper times and places. In contrast, isolated convection over the Texas Panhandle and north-central Oklahoma grew upscale into a double-bowing convective system that propagated southward over Texas on 19–20 June 2007. Both of these cases have complex mesoscale structures that allow us to evaluate the advantages and disadvantages of the two surface pressure observations in mesoscale EnKF data assimilation. Thus, through analysis of EnKF simulations of two MCS events, the objective of this research is to determine the surface pressure observation that is most successful in producing realistic mesoscale structures by assessing the impact of surface pressure assimilation on important mesoscale features, such as cold pools, and attendant circulations depicted in the ensemble-mean fields.

Sections 2 and 3 provide a discussion of the ensemble design and EnKF formulation employed in this study. Sections 4 and 5 include detailed overviews of the 4–5 July 2003 and 19–20 June 2007 bow-echo events, respectively, and examine EnKF analyses and forecasts of these events. In section 6, the results of this study are summarized, their implications are discussed, and suggestions for future research on this topic are offered.

2. Ensemble design

This data assimilation research employs the fully compressible, nonhydrostatic Advanced Research WRF (WRF-ARW; Skamarock et al. 2005), version 2. Model computations are performed on a continental U.S. domain with a horizontal gridpoint spacing of 30 km (Fig. 2). The vertical grid has 35 levels that are spaced less than 100 m apart near the surface to over 1 km apart at the model top (i.e., the 50-hPa pressure surface). In the WRF model, prognostic model fields include the three wind components, perturbation potential temperature, perturbation geopotential, and perturbation surface pressure of dry air. The 10-m wind fields, 2-m temperature and moisture fields, and total surface pressure are diagnosed by the surface and boundary layer schemes using prognostic variables on the model grid. This set of prognostic and diagnostic variables is updated by the assimilation scheme described below.

Fig. 2.

Domain used for the data assimilation experiments and the distribution of surface observation sites at 1200 UTC 4 Jul 2003. Open circles represent sites where the difference between the model and actual terrain height exceeds 300 m.

Fig. 2.

Domain used for the data assimilation experiments and the distribution of surface observation sites at 1200 UTC 4 Jul 2003. Open circles represent sites where the difference between the model and actual terrain height exceeds 300 m.

The ensemble is populated with 30 members, which are created from the initial and boundary conditions provided by the Eta (North American Mesoscale) forecast cycle at 1200 UTC 4 July 2003 (19 June 2007). The perturbation technique of Torn et al. (2006) is used to account for uncertainties in initial and boundary conditions. As such, each member is constructed by adding random samples of background error covariances from the WRF variational data assimilation (WRF-Var) algorithm to the reference analysis. The horizontal scale of the perturbations is from several tens to several hundreds of kilometers, with magnitudes of 5–10 m s−1, 2–4 g kg−1, and 2–4 K for the horizontal components of wind, water vapor mixing ratio, and temperature, respectively (e.g., Fig. 3).

Fig. 3.

Example of (a) temperature and (b) water vapor mixing ratio perturbations produced with WRF-Var.

Fig. 3.

Example of (a) temperature and (b) water vapor mixing ratio perturbations produced with WRF-Var.

To further account for uncertainties in model physics, combinations of the available physical parameterizations are varied among the ensemble members (e.g., Stensrud et al. 2000; Fujita et al. 2007). Physics diversity is introduced in the ensemble as follows: microphysics parameterizations include Thompson (Thompson et al. 2004) and WRF Single-Moment 5-Class Microphysics scheme (WSM5; Hong et al. 2004); convection parameterizations include Kain–Fritsch (KF; Kain and Fritsch 1993), Betts–Miller–Janjic (BMJ; Betts and Miller 1986; Janjic 1994), and Grell–Devenyi (Grell and Devenyi 2002); planetary boundary layer parameterizations include Medium-Range Forecast model (MRF; Hong and Pan 1996), Yonsei University (YSU; Hong et al. 2006), and Mellor–Yamada–Janjic (MYJ; Janjic 1990, 1996, 2002); and radiation parameterizations include fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) shortwave (Dudhia 1989) and the Goddard shortwave (Chou and Suarez 1994). The complete makeup of the ensemble is summarized in Table 1.

Table 1.

Multiphysics options for the WRF mesoscale ensemble system employed in this study. Here SW, LW, and RRTM stand for shortwave, longwave, and rapid radiative transfer model, respectively.

Multiphysics options for the WRF mesoscale ensemble system employed in this study. Here SW, LW, and RRTM stand for shortwave, longwave, and rapid radiative transfer model, respectively.
Multiphysics options for the WRF mesoscale ensemble system employed in this study. Here SW, LW, and RRTM stand for shortwave, longwave, and rapid radiative transfer model, respectively.

3. EnKF formulation

Surface observations only are assimilated using an EnKF at hourly intervals starting at 1300 UTC and ending at 0600 UTC the following day. The procedure begins with the forecast step, whereby a 1-h forecast is made from each ensemble member and then averaged to form an ensemble-mean forecast. The surface observations are then assimilated in an analysis step using the parallel implementation of the Data Assimilation Research Test bed (DART) software (Anderson and Collins 2007), which is based upon the ensemble adjustment Kalman filter described in Anderson (2001) [a variant of the ensemble square root filter (Whitaker and Hamill 2002)]. At each analysis step, the available observations are processed serially (i.e., one at a time) until all available observations have been assimilated. This process yields the EnKF update of the ensemble-mean forecast. The difference between the ensemble-mean fields before and after this analysis step is called an increment and is used to examine how various observations influence the analysis. The filter algorithm also updates each ensemble member from its prior forecast. The updated ensemble members are then integrated forward for 1 h until the time of next available surface observation and the above procedure is repeated.

Spatial localization is used to mitigate the impact of small, spurious correlations far from an observation, and improve filter performance. The localization function—the fifth-order piecewise rational function of Gaspari and Cohn [1999; see their Eq. (4.10)]—resembles a Gaussian distribution; however, its takes a value of zero for separation distances of greater than 2 times the half-radius. The horizontal half-radius is set to 150 km, consistent with this study’s focus on system–environment interactions at the mesoscale, while the vertical half-radius extends upward through 5 km above mean sea level.

Three EnKF assimilation experiments are run on each case and results compared with observations. In the control experiment (CNTRL), observations of 2-m potential temperature θ, 2-m dewpoint temperature Td, and the 10-m u and υ components of wind are assimilated hourly from 1300 to 0600 UTC on the following day [see Fujita et al. (2007) for a discussion on the use of θ and Td in place of temperature T and water-vapor mixing ratio qυ, respectively]. The observations are from National Weather Service (NWS)-maintained automated data sites (see, e.g., Fig. 2). At the suggestion of Zapotocny et al. (2000), the magnitudes of error standard deviations for wind and thermodynamics observations are set to 2 m s−1 and 2 K, respectively.

In this study, the CNTRL is compared with EnKF experiments that assimilate either altimeter setting (ALTM) or 1-h surface pressure tendency (PTND). Altimeter setting is the surface pressure reduced to sea level using the standard atmosphere temperature profile, and is merely a function of surface pressure and terrain height. The magnitude of error standard deviation for altimeter setting and 1-h surface pressure tendency is 1 hPa and 1 hPa h−1, respectively. Regardless of observation type, surface observations are not assimilated if the difference between the model and actual terrain height exceeds 300 m.

All assimilation runs are verified against single-pass Barnes analyses of surface data fields, as Rapid Update Cycle (RUC) analyses are unavailable for the period 4–6 July 2003. Furthermore, objective analyses of data for the 19–20 June 2007 MCS event show a more significant mesoscale structure than the available RUC analyses.

4. 4–5 July 2003 MCS event

Three MCSs moved across the upper Great Plains and Midwest regions of the United States during 4–5 July 2003. The first of the systems (hereafter, MCS1; Fig. 4a) formed by the merger of two smaller-scale convective systems over southern Minnesota. The trajectory of MCS1 followed the northern periphery of a low-level subtropical high, manifested as a stationary boundary across the upper Midwest, and then turned southeastward over Ohio. MCS1 was followed by another nocturnal MCS (hereafter, MCS2; Fig. 4a) that formed over the Dakotas during the overnight hours of 3–4 July 2003, and then dissipated as it moved over southern Minnesota and northwest Iowa. Complex mesoscale interactions between the cold pools of MCS1 and MCS2 and their surrounding environments were important to the initiation and subsequent evolution of MCS3, which formed over northern Indiana at 2000 UTC 4 July and then moved south-southeastward over southwest Ohio (Fig. 4b). The following section examines the ability of the EnKF to reproduce the mesoscale pressure and temperature patterns associated with these systems.

Fig. 4.

Radar images of the severe weather events of interest to this study, including (a) MCS1 and MCS2 at 1500 UTC 4 Jul 2003, (b) MCS3 at 0200 UTC 5 Jul 2003, and (c) the 5–6 Jun 2007 MCS at 0600 UTC 6 Jun 2007.

Fig. 4.

Radar images of the severe weather events of interest to this study, including (a) MCS1 and MCS2 at 1500 UTC 4 Jul 2003, (b) MCS3 at 0200 UTC 5 Jul 2003, and (c) the 5–6 Jun 2007 MCS at 0600 UTC 6 Jun 2007.

a. Assimilation impact on cold-pool structure: 1500 UTC 4 July 2003

1) Analysis of three-dimensional cold-pool structure

The associated convective activity of MCS2 decayed gradually as it moved east-southeast from the northern Plains over southern Minnesota and northwest Iowa, leaving an expansive cold pool and its associated mesohigh in place over the region. At 1500 UTC, a mean sea level pressure (MSLP) maximum of 1016 hPa was located over northwest Iowa, with a closed contour of 1012 hPa encircling the northwest quadrant of Iowa and extreme southern Minnesota (Fig. 5a). Temperatures at the cold-pool center were less than 18°C (Fig. 5e).

Fig. 5.

Barnes objective analysis of (a) MSLP (see color bar) and horizontal winds at 1500 UTC 4 Jul 2003, as compared with the same fields derived from (b) CNTRL, (c) ALTM, and (d) PTND. In (b)–(d), the ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1012-hPa MSLP from each ensemble member. Also shown is an objective analysis of (e) 2-m temperature (T2; see color bar) and horizontal winds at 1500 UTC 4 Jul 2003 (see color bar), as compared with the same fields derived from (f) CNTRL, (g) ALTM, and (h) PTND. In (f)–(h), the ensemble mean 2-m temperature is shown in solid black lines (every 4°C), as well as isolines of 20°C from each ensemble member. (i)–(l) The ensemble-mean horizontal wind and convergence(warm colors)/divergence (cool colors) fields for control and experimental ensembles. The black dots in (a) and (e) show the locations of the observed dropsondes in Figs. 10a–f.

Fig. 5.

Barnes objective analysis of (a) MSLP (see color bar) and horizontal winds at 1500 UTC 4 Jul 2003, as compared with the same fields derived from (b) CNTRL, (c) ALTM, and (d) PTND. In (b)–(d), the ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1012-hPa MSLP from each ensemble member. Also shown is an objective analysis of (e) 2-m temperature (T2; see color bar) and horizontal winds at 1500 UTC 4 Jul 2003 (see color bar), as compared with the same fields derived from (f) CNTRL, (g) ALTM, and (h) PTND. In (f)–(h), the ensemble mean 2-m temperature is shown in solid black lines (every 4°C), as well as isolines of 20°C from each ensemble member. (i)–(l) The ensemble-mean horizontal wind and convergence(warm colors)/divergence (cool colors) fields for control and experimental ensembles. The black dots in (a) and (e) show the locations of the observed dropsondes in Figs. 10a–f.

After assimilating surface observations from 1300–1500 UTC, the mesohigh region in CNTRL is displaced ∼140 km too far south and the mesohigh possesses a 4-hPa deficit from observations (Fig. 5b), with little agreement among the various ensemble members as to the placement and intensity of this surface feature. Thus, the assimilation of temperature, moisture, and winds only will not fully reproduce mesohigh properties in ensemble-mean fields, and may lead to imbalances in the model.

The addition of ALTM or PTND observations produces significant horizontal and vertical modifications to the local atmospheric pressure fields (Figs. 5c,d and 6a–c). In ALTM, the size and strength of the analyzed mesohigh is very consistent with observations, with strong agreement among the various ensemble members (Fig. 5c), but a location error of ∼60 km persists between the observed and analyzed mesohigh centers. The salient features of the PTND analysis are similar to those depicted in the ALTM analysis (Figs. 5c,d). However, the PTND overstates the geographical extent of the cold-pool region. These structural differences also are manifest in ensemble error statistics. Over the assimilation period, the ALTM and PTND runs yield smaller rms differences between the ensemble mean and the assimilated pressure observations than CNTRL (Figs. 6a,b). For both pressure variables, the consistency ratio of ensemble variance to the sum of squared ensemble rms difference and observational error variance generally fall between 1 and 1.5 (not shown), which indicates that the ensemble spread is reasonable (in a few instances, the consistency ratio for PTND approaches 2.0). As a pseudoindependent evaluation, it is shown the ALTM run yields the smallest rms differences between the ensemble mean and total surface pressure observations (not assimilated; Fig. 6c), although PTND generally improves upon the CNTRL. The outcome of these analyses can be understood in the context of covariances between the respective pressure variables and the model pressure field, and is discussed in section 4a(2).

Fig. 6.

The rms difference between the ensemble mean and observations of (a) altimeter setting and (b) 1-h surface pressure tendency, averaged over the upper Midwest for the 4–5 Jul 2003 event. (c) Total surface pressure (not part of the assimilation) is evaluated for the control and experimental ensembles. (d)–(f) For the same event, verification statistics for a 6-h pure ensemble forecast that follows a 12-h assimilation period ending at 0000 UTC 5 Jul 2003. (g)–(l) The same differences for the 19–20 Jun 2007 event, with the statistics averaged over the southern Great Plains.

Fig. 6.

The rms difference between the ensemble mean and observations of (a) altimeter setting and (b) 1-h surface pressure tendency, averaged over the upper Midwest for the 4–5 Jul 2003 event. (c) Total surface pressure (not part of the assimilation) is evaluated for the control and experimental ensembles. (d)–(f) For the same event, verification statistics for a 6-h pure ensemble forecast that follows a 12-h assimilation period ending at 0000 UTC 5 Jul 2003. (g)–(l) The same differences for the 19–20 Jun 2007 event, with the statistics averaged over the southern Great Plains.

The impact of assimilating surface pressure observations on nonpressure fields is less discernible for this event. The 2-m ensemble-mean temperature analyses derived from ALTM and PTND provide little additional guidance on the temperature characteristics of the cold pool, although the pressure observation assimilations yield larger increments in temperature above the surface (Fig. 7). The control and experimental ensembles agree on cold-pool location, placing the coldest surface temperatures ∼60 km northeast of the observed location, but there is some surface warming of the cold pool in ALTM and PTND (Figs. 5f–h). Thus, it appears that the temperature characteristics of the cold pool above the surface are most influenced by the pressure observations. The relatively small impact of surface pressure observations on 2-m temperature and the other assimilated variables also is revealed through ensemble error statistics, where there are few significant differences between the time sequences for the control and experimental ensembles (Figs. 8a–d). As with the pressure variables, consistency ratio values between 0.6 and 1.5 for these observation types indicate that ensemble spread is reasonable.

Fig. 7.

Pressure (hPa) and temperature (K) increments along a west–east vertical cross section through Spencer, IA (SPW; shown as a filled circle in Figs. 9a,d), after the first analysis step. Pressure increments are shown by the color bar (with negative shading enclosed by dashed contours), while temperature increment isolines are shown every 0.5 K, with the zero value neglected and negative values dashed.

Fig. 7.

Pressure (hPa) and temperature (K) increments along a west–east vertical cross section through Spencer, IA (SPW; shown as a filled circle in Figs. 9a,d), after the first analysis step. Pressure increments are shown by the color bar (with negative shading enclosed by dashed contours), while temperature increment isolines are shown every 0.5 K, with the zero value neglected and negative values dashed.

Fig. 8.

The rms difference between the ensemble mean and observations of (a) 10-m u, (b) 10-m υ, (c) 2-m θ, and (d) 2-m Td, averaged over the upper Midwest for the 4–5 Jul 2003 event. (e)–(h) For the same event, verification statistics for a 6-h pure ensemble forecast that follows a 12-h assimilation period ending at 0000 UTC 5 Jul 2003. (i)–(p) The same differences for the 19–20 Jun 2007 event, with the statistics averaged over the southern Great Plains.

Fig. 8.

The rms difference between the ensemble mean and observations of (a) 10-m u, (b) 10-m υ, (c) 2-m θ, and (d) 2-m Td, averaged over the upper Midwest for the 4–5 Jul 2003 event. (e)–(h) For the same event, verification statistics for a 6-h pure ensemble forecast that follows a 12-h assimilation period ending at 0000 UTC 5 Jul 2003. (i)–(p) The same differences for the 19–20 Jun 2007 event, with the statistics averaged over the southern Great Plains.

The impact of surface pressure observations on the horizontal wind field also appears secondary to the direct assimilation of winds, but is still significant. While pressure–wind covariance calculations produce coherent structures at this time (Figs. 9a,d), the control and experimental ensembles show the same general divergent wind flow emanating from the cold-pool center over northwest Iowa (Figs. 5i–l). The experimental ensembles, though, are characterized by stronger flow away from the cold-pool center. The resultant 25%–50% increases in the maximum ensemble-mean divergence can be important to establishing realistic three-dimensional cold-pool circulations.

Fig. 9.

Covariance values from ALTM between the forecast altimeter pressure and 10-m u (solid gray contours)/10-m υ (solid black contours) at (a) SPW, (b) Middletown, OH (MWO), and (c) Childress, TX (CDS). (d)–(f) The same covariances for PTND. In (a)–(c), the length scale shows the full horizontal extent of covariance localization, as centered about the observation location.

Fig. 9.

Covariance values from ALTM between the forecast altimeter pressure and 10-m u (solid gray contours)/10-m υ (solid black contours) at (a) SPW, (b) Middletown, OH (MWO), and (c) Childress, TX (CDS). (d)–(f) The same covariances for PTND. In (a)–(c), the length scale shows the full horizontal extent of covariance localization, as centered about the observation location.

The vertical structure of the remnant cold pool over northwest Iowa and southern Minnesota was sampled by a number of dropsondes during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX) field campaign. These data provide a unique opportunity to further evaluate the impact of assimilating surface pressure observations on fields above the surface. Dropsondes released at 1736 and 1742 UTC (see Figs. 5a,e for dropsonde locations) show onion soundings (Zipser 1982) within the cold-pool region (Figs. 10a,d). In general, the ensemble-mean temperature profiles derived from the ALTM and PTND at 1800 UTC (to account for drop time) show some improvement over those derived from CNTRL, particularly within the lowest 1 km AGL.

Fig. 10.

Comparison of dropsonde soundings (solid black line) at (a)–(c) 1736 UTC 4 Jul 2003, (d)–(f) 1742 UTC 4 Jul 2003, and (g)–(i) 0234 UTC 5 Jul 2003 with temperature and dewpoint profiles derived from the control and experimental mean-ensemble fields at the next nearest hour (to account for drop time).

Fig. 10.

Comparison of dropsonde soundings (solid black line) at (a)–(c) 1736 UTC 4 Jul 2003, (d)–(f) 1742 UTC 4 Jul 2003, and (g)–(i) 0234 UTC 5 Jul 2003 with temperature and dewpoint profiles derived from the control and experimental mean-ensemble fields at the next nearest hour (to account for drop time).

The dropsondes show that moisture can have large variation with height (Figs. 10a,d), making it a difficult variable to assimilate without precise covariance estimates (that represent these more complex variability patterns). With the exception of PTND at 1736 UTC, the ensemble-mean moisture profiles are too moist. Recent work has shown boundary layer moisture to be a relatively intractable problem for the EnKF, even in the absence of surface pressure assimilation. In this study, the aforementioned issue is most likely being exacerbated by very weak covariances between the respective pressure variables and moisture species in the model state vector. One possible remedy not afforded to the current study would be to increase the number of ensemble members in an effort to improve forecast covariance estimates.

2) Relation to covariance structures

Given the important role of forecast error covariances in the EnKF, it is prudent to consider the covariance structures produced in the ALTM and PTND experiments when assessing their relative performances. These calculations are made for surface observation locations across the upper Midwest at several analysis times. The following analysis begins by examining covariance structures at 1500 UTC using Spencer, Iowa (SPW) as the observation point.

By 1500 UTC 4 July 2003, a consistent pattern emerges in which the horizontal and vertical covariance structures associated with altimeter setting possess intrinsically longer horizontal and vertical length scales than those associated with surface pressure tendency (Fig. 11). Thus, in ALTM, a single pressure observation is able to constrain analysis errors over a greater portion of the three-dimensional pressure space. However, the pressure–temperature relationships calculated from ALTM and PTND are similar, consistent with the similar temperature analyses produced by the ALTM and PTND experiments (see Figs. 5g,h). Correlation values (i.e., “normalized covariance”) calculated at this time (and others) lead to the same conclusions as above, and clearly show the stronger relationship between altimeter setting and the total surface pressure field (e.g., see Fig. 12).

Fig. 11.

Covariances between the (a) forecast altimeter setting at SPW and the total surface pressure field, and (b) a west–east vertical cross section of the same field, taken through the surface observation site, shown as a filled circle at 1500 UTC 4 Jul 2003. Covariance values are contoured every 0.25 units (see color bar, with negative shading enclosed by dashed contours). (c),(d) The same covariances, except using the forecast 1-h surface pressure tendency at SPW. In (a)–(d), the covariance between the respective forecast pressure variable and the temperature field is contoured every 0.5 units, with no zero and negative dashed contours. In (a) and (c), the length scale shows the full horizontal extent of covariance localization, as centered about the observation location.

Fig. 11.

Covariances between the (a) forecast altimeter setting at SPW and the total surface pressure field, and (b) a west–east vertical cross section of the same field, taken through the surface observation site, shown as a filled circle at 1500 UTC 4 Jul 2003. Covariance values are contoured every 0.25 units (see color bar, with negative shading enclosed by dashed contours). (c),(d) The same covariances, except using the forecast 1-h surface pressure tendency at SPW. In (a)–(d), the covariance between the respective forecast pressure variable and the temperature field is contoured every 0.5 units, with no zero and negative dashed contours. In (a) and (c), the length scale shows the full horizontal extent of covariance localization, as centered about the observation location.

Fig. 12.

Correlation values between the (a) forecast altimeter setting at SPW (shown as a filled circle) and the total surface pressure field at 1500 UTC 4 Jul 2003. Correlation values are contoured every 0.2 units (see color bar, with negative shading enclosed by dashed contours). (b) The same correlation values, but using the forecast 1-h surface pressure tendency at SPW. In (a),(b), the correlation between the respective forecast pressure variable and the temperature field is contoured every 0.2 units, with no zero and negative dashed contours.

Fig. 12.

Correlation values between the (a) forecast altimeter setting at SPW (shown as a filled circle) and the total surface pressure field at 1500 UTC 4 Jul 2003. Correlation values are contoured every 0.2 units (see color bar, with negative shading enclosed by dashed contours). (b) The same correlation values, but using the forecast 1-h surface pressure tendency at SPW. In (a),(b), the correlation between the respective forecast pressure variable and the temperature field is contoured every 0.2 units, with no zero and negative dashed contours.

In PTND, another possible source of error may be the lack of information in surface pressure tendency fields away from regions of large pressure change. To demonstrate this potential, the covariance between the forecast 1-h surface pressure tendency at Columbia, Missouri (COU)—where the observed and simulated 1-h pressure tendencies are approximately zero—and the total surface pressure field is calculated. While weak covariance structure is apparent in this result, the same calculation using the forecast altimeter setting at COU yields stronger covariance structure that extends several hundred kilometers away from the surface observation location (Figs. 13a,b). A similar result is obtained for a number of observation points across the United States [including, e.g., Atlanta, Georgia (ATL); Figs. 13c,d] positioned away from any mesoscale variability.

Fig. 13.

Covariance between the forecast (a) altimeter pressure and (b) 1-h surface pressure tendency at Columbia, MO (COU), and the total surface pressure field at 1500 UTC 4 Jul 2003. (c),(d) The same covariances, but with Atlanta, GA (ATL), as the surface observation site. Covariance values are shaded every 0.25 units (see color bar). Negative shading is enclosed by dashed contours.

Fig. 13.

Covariance between the forecast (a) altimeter pressure and (b) 1-h surface pressure tendency at Columbia, MO (COU), and the total surface pressure field at 1500 UTC 4 Jul 2003. (c),(d) The same covariances, but with Atlanta, GA (ATL), as the surface observation site. Covariance values are shaded every 0.25 units (see color bar). Negative shading is enclosed by dashed contours.

The significance of this difference is twofold. First, for a model grid point within a simulated mesoscale structure, there is potential for a relatively larger number of altimeter setting observations (as compared with surface pressure tendency observations) to modify this location, including some observations away from the feature of interest. Second, as might be expected with an inherently synoptic dataset, altimeter setting observations are better able to constrain pressure analyses errors across the meso- to synoptic-scale spectrum. At 1500 UTC 4 July 2003, this effect is apparent across northern Missouri, where the 1012-hPa ensemble mean pressure isolines from ALTM shows the far northwest periphery of the subtropical high located over the southeastern United States (Figs. 5c,d). There is no clear delineation of this feature in the PTND analysis (Fig. 5d). In general, the PTND analyses undervalue the strength of this high pressure cell by approximately 1–2 hPa (not shown).

b. Assimilation impact on cold-pool structure: 0200 UTC 5 July 2003

The passage of MCS3 over southwest Ohio produced an approximately 4-hPa increase in the MSLP field at Dayton, Ohio (DAY), with the pressure rising from 1013.9 to 1018.0 hPa during the period 0000–0100 UTC (not shown). Over the next hour, as the system decayed, a similar increase in MSLP was observed over extreme northern Kentucky, at Covington, with the pressure rising from 1013.5 to 1018.3 hPa (Fig. 14a). At 0200 UTC, a region of cold air, with temperatures generally less than 20°C, covered extreme western Indiana and southwestern Ohio.

Fig. 14.

As in Fig. 5, but at 0200 UTC 5 Jul 2003. (b)–(d) The ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1016-hPa MSLP from each ensemble member. (f)–(h) The ensemble mean 2-m temperature is shown in solid black lines (every 2°C), as well as isolines of 22°C from each ensemble member. The black dot in (a) and (e) shows the location of the observed dropsonde in Figs. 10g–i.

Fig. 14.

As in Fig. 5, but at 0200 UTC 5 Jul 2003. (b)–(d) The ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1016-hPa MSLP from each ensemble member. (f)–(h) The ensemble mean 2-m temperature is shown in solid black lines (every 2°C), as well as isolines of 22°C from each ensemble member. The black dot in (a) and (e) shows the location of the observed dropsonde in Figs. 10g–i.

The mesoscale pressure pattern associated with the mesohigh of MCS3 is poorly depicted in CNTRL, manifested only as a local pressure maxima (∼1014 hPa) over extreme southwestern Ohio, as well as an undulation in the 1012-hPa ensemble mean pressure isolines (Fig. 14b). Furthermore, none of the ensemble members produce closed isolines of 1016 hPa, as suggested by observations. There are also significant errors in the synoptic-sale pressure distribution within which the mesohigh is embedded. The PTND analysis deviates little from the control ensemble, producing only small corrective modification to the larger-scale pressure distribution (Fig. 14d).

The ALTM analysis provides the most realistic depiction of the pressure characteristics associated with the mesohigh, although the mesohigh center has a 2-hPa deficit from observations (Fig. 14c). Similar to the earlier analysis, the impact of assimilating altimeter setting is not confined to the mesoscale, as evidenced by the significant agreement between the observed synoptic-scale pressure distribution and that of ALTM.

An analysis of covariance structures at 0200 UTC 5 July produces results similar to those from 1500 UTC 4 July. Based on covariance calculations using Middletown, Ohio (MWO) as the observation location, it is again found that horizontal and vertical covariance structures associated with altimeter setting possess intrinsically longer horizontal and vertical length scales than those associated with surface pressure tendency (Figs. 15a–d). Notably, the covariance structures present at 0200 UTC 5 July are spatially smaller than those present at 1500 UTC 4 July. It is curious that the covariance between pressure tendency and temperature is negative above the ground (Fig. 15d), a result not seen in the ALTM run.

Fig. 15.

As in Fig. 11, but with MWO as the surface observation site at 0200 5 Jul 2003. Pressure–pressure covariances are shaded every 0.25 units (see color bar), while pressure–temperature covariances are contoured every 0.25 units, with no zero and negative dashed contours.

Fig. 15.

As in Fig. 11, but with MWO as the surface observation site at 0200 5 Jul 2003. Pressure–pressure covariances are shaded every 0.25 units (see color bar), while pressure–temperature covariances are contoured every 0.25 units, with no zero and negative dashed contours.

The decrease in the spatial extent of the covariance structures from 1500 UTC 4 July to 0200 UTC 5 July is likely twofold. First, it is highly likely that the spatial extent of the earlier covariance structures is to some degree an artifact of ensemble construction. Ensemble initialization is an active area of research, of which there is no universally accepted or perfect approach. Second, small errors introduced by imperfect EnKF analyses can contaminate covariance calculations and slowly compound in subsequent analyses, especially for small ensemble sizes. Still, even at this later time, it is notable that the ALTM experiment is able to constrain pressure analysis errors across the meso- to synoptic scale.

Little improvement in the ensemble-mean temperature fields is derived from ALTM or PTND when compared with CNTRL (Figs. 14e–h). In all three analyses, surface temperatures over western Indiana and southwest Ohio are 2°–4°C too warm, although a few members of the PTND ensemble show more significant cooling at the cold-pool center. Overall, these results are consistent with covariance estimates at this time. Covariances between the pressure and temperature fields are negligible at the surface (Fig. 15), and even more notably, temperature covariances are also negligible at other locations across the region (not shown).

The cold pool associated with MCS3 also was sampled by a number of dropsondes during the BAMEX field campaign. A dropsonde released at 0234 UTC (see Figs. 14a,e for dropsonde locations) show an onion sounding within the cold-pool region. Again it is found that surface–pressure assimilation produces little modification of the three-dimensional temperature distribution derived from the CNTRL (Figs. 10g–i). However, the next section will suggest that this result is case dependent.

Unlike the previous analysis, the impact of surface pressure observations on the horizontal wind field is negligible, with few significant differences between the control and experimental ensembles (Figs. 14i–k). Not surprisingly, the pressure–wind covariance calculations also are negligible at this time (Figs. 9b,e).

Finally, the control and pressure experiments were repeated but modified so that a 12-h assimilation period is followed by a pure ensemble forecast (with no data assimilation). In an operational setting, the resultant analyses and subsequent short-range forecasts could serve as improved initial and boundary conditions for real-time convection-permitting simulations. As compared with CNTRL, ALTM produces smaller rms differences between the ensemble mean and the assimilated pressure observations throughout the 6-h forecast period (Fig. 6d). PTND produces smaller rms differences than CNTRL for nearly 2 h after the last assimilation period (Fig. 6e). The rms differences derived from ALTM and PTND for other surface variables are very similar in magnitude to those derived from CNTRL (Figs. 8e–h).

5. 19–20 June 2007 MCS event

The large MCS on this day forms from the merger of two smaller-scale bowing MCSs over southwestern Oklahoma at 0600 UTC (Fig. 4c). This complex mesoscale circulation structure provides another useful case study in which to evaluate the ALTM and PTND experiments.

At 0600 UTC 20 June 2007, the single, larger MCS is associated with a mesoscale high pressure axis in excess of 1018 hPa across west-central Oklahoma and the Texas Panhandle (Fig. 16a). An embedded pressure maximum in excess of 1020 hPa over the Texas Panhandle is associated with the intersection of the two bowing convective systems. Two distinct temperature minima, associated with the two convective segments, can be identified in surface observations over west-central Oklahoma and over the Texas Panhandle (Fig. 16e).

Fig. 16.

As in Fig. 5, but at 0600 UTC 20 Jun 2007. (b)–(d) The ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1020-hPa MSLP from each ensemble member. (f)–(h) The ensemble mean 2-m temperature is shown in solid black lines (every 2°C), as well as isolines of 22°C from each ensemble member.

Fig. 16.

As in Fig. 5, but at 0600 UTC 20 Jun 2007. (b)–(d) The ensemble mean MSLP is shown in solid black lines (every 2 hPa), as well as isolines of 1020-hPa MSLP from each ensemble member. (f)–(h) The ensemble mean 2-m temperature is shown in solid black lines (every 2°C), as well as isolines of 22°C from each ensemble member.

Similar to ensemble-mean pressure analyses produced for the 4–5 July 2003 MCS event, the ALTM analysis best reproduces the mesoscale pressure distribution associated with this event, clearly depicting the high pressure axis across the mesohigh at 0600 UTC 20 June (Fig. 16c). Furthermore, there is relatively strong agreement among the various members of the ALTM ensemble. While examination shows that the ALTM analysis possesses a high bias of 1–2 hPa (see Figs. 16a,c), this difference results largely from smoothing of the raw observations (in Fig. 16a) by the objective analysis scheme. The CNTRL and PTND analyses each depict a local pressure maximum over west-central Oklahoma, but its periphery is ill defined by the respective members of each ensemble. Again, these structural differences are manifest in ensemble error statistics averaged over the southern Great Plains (Figs. 6g–i). Similar to the previous case, consistency ratio values for all observation types generally are between 0.6 and 1.5 (with some higher values for PTND), which indicate that ensemble spread is reasonable.

Covariance calculations are performed using Childress, Texas (CDS), as the surface observation location, given the city’s proximity to the most pronounced pressure and temperature patterns in the surface fields. As with previous calculations, a rather strong relationship exists between altimeter setting and total surface pressure at greater distances from CDS (as compared with the relationship between surface pressure tendency and total surface pressure; Figs. 17a–d), thus explaining the improvements seen in the ALTM analyses. Similar relationships are found at surface stations across the region.

Fig. 17.

As in Fig. 11, but with CDS as the surface observation site at 0600 20 Jun 2007. Covariance values are contoured every 0.5 units (see color bar). Pressure–pressure covariances are shaded every 0.5 units (see color bar), while pressure–temperature covariances are contoured every 1.0 unit, with no zero and negative dashed contours.

Fig. 17.

As in Fig. 11, but with CDS as the surface observation site at 0600 20 Jun 2007. Covariance values are contoured every 0.5 units (see color bar). Pressure–pressure covariances are shaded every 0.5 units (see color bar), while pressure–temperature covariances are contoured every 1.0 unit, with no zero and negative dashed contours.

For this event, temperature assimilation alone is not sufficient to reproduce the southwestern extent of the cold pool in ensemble-mean fields. In all three ensembles, undulations of the 22°C ensemble-mean temperature isoline emphasize two separate areas of cooling associated with each bowing convective segment, with strong agreement among their respective members (Figs. 16f–h). The PTND analysis marginally improves upon that of CNTRL by expanding the aerial coverage of the 20°C ensemble-mean temperature isoline to the southwest over the Texas Panhandle (Fig. 16h), where there is weak covariance between the surface pressure tendency and temperature fields (Figs. 17c,d). The ALTM analysis also improves the temperature estimates over the Texas Panhandle, where there is strong covariance between the altimeter setting and temperature fields, and reproduces the 20°C temperature minima observed over west-central Oklahoma. However, the aerial coverage of the cold-pool region associated with the eastern bowing segment in ALTM is significantly diminished. This feature is preserved in the PTND analysis, and the corresponding smaller error is reflected in ensemble statistics (Fig. 8k). In this case, vertical cold-pool structure is not analyzed owing to a lack of research-quality soundings at high time resolution for this event.

At 0600 UTC, ensemble-mean vertical velocity fields produced from all three ensembles depict circulations typical of MCSs, whereby negative vertical velocities within the stratiform precipitation region trail a narrow band of positive vertical motion coincident with the leading-edge convection (Figs. 18a–c). The larger magnitude velocities, though, are depicted in ALTM and PTND. In particular, the greatest upward motion in both analyses is vertically collocated with the observed pressure maximum over extreme southwest Oklahoma, near the merger point of the two smaller-scale bowing convective lines (see Fig. 4c). This result is consistent with the circulations associated with MCSs. The enhanced convergence and resultant vertical motion at the merger point could support more intense convection and subsequently a stronger cold pool (which can also contribute to stronger vertical motion). The PTND analysis, in contrast to that of ALTM, also has a narrow band of positive vertical velocities along the entire extent of the observed convective line across Oklahoma and not just in association with the prominent zone of outflow collision implied by surface pressure observations. While physically consistent, it should be noted that confirmatory observations are needed to further support the above interpretation. Still, this analysis demonstrates the potential impact of surface pressure observations on different fields in the ensemble-mean pressure analyses.

Fig. 18.

Approximately 500-m AGL horizontal cross section of vertical motions depicted in the ensemble-mean fields of (a) CNTRL, (b) ALTM, and (c) PTND at 0600 UTC 20 Jun 2007.

Fig. 18.

Approximately 500-m AGL horizontal cross section of vertical motions depicted in the ensemble-mean fields of (a) CNTRL, (b) ALTM, and (c) PTND at 0600 UTC 20 Jun 2007.

Finally, the control and pressure experiments were repeated but modified so that a 12-h assimilation period is followed by a pure ensemble forecast (with no data assimilation). When compared with CNTRL, ALTM produces smaller rms differences between the ensemble mean and the assimilated pressure observations throughout the 6-h forecast period (Fig. 6j), and PTND produces smaller rms differences than CNTRL for 1–2 h after the last assimilation period (Fig. 6k). The rms differences derived from ALTM and PTND for other surface variables are very similar in magnitude to those derived from CNTRL (Figs. 8m–p).

6. Summary and discussion

A series of EnKF experiments are performed for the severe weather events of 4–5 July 2003 and 19–20 June 2007, with the primary objective of determining which surface pressure observations produce the most realistic mesoscale features during the assimilation period. For each case, surface observations of temperature, moisture, wind, and one of two pressure parameters—altimeter setting (a total pressure field) or 1-h surface pressure tendency—are assimilated into the ensemble. Results from the EnKF experiments are compared with the CNTRL that assimilates only surface observations of temperature, moisture, and winds.

Ensemble-mean pressure analyses produced from CNTRL possess significant errors in regards to cold-pool strength and location. For the two cases examined here, the assimilation of altimeter setting produces the most accurate depictions of the mesoscale pressure patterns associated with mesoscale convective systems, as gauged by ensemble statistics and cold-pool analyses. The altimeter setting observations also exhibit more potential for constraining pressure analysis errors at the synoptic scale. The assimilation of surface pressure tendency observations produces reasonable estimates of cold-pool location; however, these analyses are plagued by significant errors in magnitude and extent. The relative performance of two pressure parameters appears to be associated with the covariance structures realized in the experiments. Almost without exception the horizontal and vertical covariance structures associated with altimeter setting possess intrinsically longer horizontal and vertical length scales, and at times greater magnitudes, than those associated with surface pressure tendency.

Cross-covariance values between pressure parameters and the temperature fields are similar in the two experiments, and the mesoscale temperature patterns produced by all the ensembles are quite similar. While they tend to preserve the salient features of CNTRL, neither surface pressure assimilation experiment outperforms CNTRL, as gauged by ensemble statistics and cold-pool analyses. This result merely underscores the secondary role of surface pressure observations in the temperature update, and signals the impact of spurious covariance between pressure parameters and the temperature field. However, in several examples, the assimilation of surface pressure tendency observations produces better ensemble-mean temperature analyses than those produced by the assimilation of altimeter setting. One possible explanation for this difference is the inherently mesoscale nature of surface pressure tendency observations. The more compact spatial extent of cross covariances between surface pressure tendency and temperature may lend to improved temperature estimates within mesoscale features, such as cold pools.

The direct assimilation of horizontal winds is sufficient to reproduce the mesoscale (near surface) wind patterns associated with MCSs; however, the assimilation of surface pressure observations is important in accurately portraying the three-dimensional circulations typical of MCSs. For the 19–20 June 2007 MCS event, positive vertical motion coincident with the leading-edge convection is enhanced (cf. the control ensemble) over those parts of the outflow collision zone associated with local pressure maxima. This result is not confirmed observationally, but is physically consistent and underscores the potentially broad impact of surface pressure observations on different fields.

A logical next step in the development of the above type of mesoscale ensemble data assimilation system is the inclusion of other routine observations. In this study and others, surface data assimilation alone has been shown to be quite useful in improving estimates of those structures associated with MCSs, as well as the general structure of the boundary layer. Still, standard surface observations compose just a fraction of the available observation types. Other observations from standard upper-air soundings, wind profilers, aircraft, and satellites might further improve the realism of simulated mesoscale features and the larger-scale environment in which they are embedded. The current study indicates that these further experiments will require a larger ensemble size, to mitigate spurious cross covariances between weakly related fields.

Acknowledgments

The authors thank the three anonymous reviewers for their constructive comments. This work was completed while the first author was a National Research Council Postdoctoral Research Fellow.

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Footnotes

Corresponding author address: Dr. Dustan M. Wheatley, Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, OK 73072. Email: dustan.wheatley@noaa.gov