1. Introduction
The inclusion of surface momentum fluxes in idealized, “research-driven” convective storm simulations (i.e., simulations not done in the interest of numerical weather prediction, but rather controlled simulations designed to study physical processes within storms) is becoming increasingly common, owing to the increased model resolution and interest in boosting the realism of the simulations as computing power increases (Adlerman et al. 1999; Adlerman and Droegemeier 2002; Schenkman et al. 2012, 2014, 2016; Markowski 2016; Mashiko 2016; Roberts et al. 2016; Orf et al. 2017; Coffer and Parker 2017, 2018; Yokota et al. 2018). Several investigators have found that the inclusion of surface drag can alter the evolution and even the dynamics of storms in important ways (Schenkman et al. 2012, 2014; Markowski 2016; Roberts et al. 2016). Some research-driven simulations of convective storms also have included surface heat and moisture fluxes (Frame and Markowski 2010, 2013; Schenkman et al. 2012, 2014; Oberthaler and Markowski 2013; Nowotarski et al. 2014, 2015; Nowotarski and Markowski 2016). Although this has been less common, it is safe to assume the inclusion of surface heat and moisture fluxes will become more commonplace in the future. In operational simulations (i.e., those performed for numerical weather prediction), surface fluxes have always been included. However, as resolution increases and convection-allowing models are increasingly relied upon (e.g., “Warn-on-Forecast”; Stensrud et al. 2009; Lawson et al. 2018), it will likely become increasingly important to consider whether surface flux parameterizations are up to the task, especially given the well-known sensitivity of convective storms to the near-surface thermodynamic and vertical wind profiles (e.g., Markowski and Richardson 2014; Coffer and Parker 2015, 2017, 2018; Coffer et al. 2017).
The Monin–Obukhov similarity theory (MOST) of the atmospheric surface layer (Monin and Obukhov 1954) has been the standard framework by which surface fluxes of momentum, heat, and moisture are parameterized in numerical simulations (Foken 2006; Wilson 2008). MOST relates the vertical profiles of nondimensional mean flow and turbulence properties to a dimensionless height parameter z/L, where z is the height above the surface and L is the Obukhov length, which itself depends on the surface heat and momentum fluxes. Steadiness and horizontal homogeneity, which are the assumptions underpinning MOST, are unlikely to be satisfied within the downdrafts and outflow of convective storms, especially in strongly curved flow such as near an intensifying vortex, or in the vicinity of a gust front. These assumptions may not even be met within the near-storm environment, especially within boundary layers in which winds are rapidly accelerating toward a storm updraft or in boundary layers within complex terrain.
This article is about the characteristics of vertical wind profiles within the surface layer, both near and within convective storms, and their departures from MOST. We analyze data obtained from a Doppler lidar and instrumented towers deployed during the Verification of the Origins of Rotation in Tornadoes Experiment–Southeast (VORTEX-SE) field campaign during the spring of 2017. We are in desperate need of near-surface wind observations—and knowledge of their departures from MOST—in order to assess the credibility of present-day convective storm simulations and to develop/evaluate new formulations for the lower boundary condition in future simulations. Despite the fact that MOST has been the “industry standard” for over half a century, deviations from it are still not well understood, especially within convective storms. A priori, one might expect potentially large departures at times when surface winds are unsteady and/or being subjected to large horizontal pressure-gradient forces. Documenting departures from MOST is a necessary first step toward improving the lower boundary condition and parameterization of near-surface turbulence (“wall models”).
In section 2, additional details are provided about the data that are analyzed, as well as the analysis methods. Sections 3 and 4 contain, respectively, the results and discussion. Concluding remarks are provided in section 5.
2. Data and methodology
a. Vertical wind profile observations from CLAMPS
The Collaborative Lower Atmospheric Mobile Profiling System (CLAMPS; Wagner et al. 2019), which includes a Halo Streamline Doppler lidar (Pearson et al. 2009), was deployed at the Scottsboro Airport in north-central Alabama in March and April 2017 in support of the VORTEX-SE field campaign (Fig. 1; Turner 2017). The Doppler lidar measured radial winds at a 60° elevation angle and at 8 evenly spaced azimuths (at 1-s integration times per angle), followed by a series of 1-s vertical stares. The plan position indicator (PPI) scans were analyzed using the velocity–azimuth display (VAD) technique to derive the horizontal winds. Vertical profiles of horizontal winds were retrieved from the lidar at 182-s intervals and every 26 m AGL, starting at 13 m AGL.1 Data from the lowest two levels (13 and 39 m AGL) were excluded from analysis owing to poor data quality. An anemometer was collocated with CLAMPS, measuring wind every 5 s at a height of approximately 5.7 m AGL (Turner 2018). The airport is situated in a region characterized by hills, deciduous woodlands, and some fields used for agriculture (the area in the immediate vicinity of the airport is largely devoid of trees).
Locations of CLAMPS and the NOAA/ARL/ATDD towers during the VORTEX-SE field campaign during the spring of 2017.
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
Vertical wind profiles were binned by weather regime. The weather regimes are as follows: 1) fair-weather, nonoperations days; 2) VORTEX-SE operations days, but before the arrival of cool outflow from convective storms (i.e., in what might be regarded as “fair weather,” but this regime differs from the first regime in that a strong horizontal pressure-gradient force and geostrophic vertical wind shear are frequently present on VORTEX-SE operations days, so there might be an a priori expectation that MOST would not be as applicable); and 3) VORTEX-SE operations days, within the outflow of convective storms (such regions are characterized by large horizontal heterogeneity and unsteadiness, especially in the vicinity of gust fronts). The VORTEX-SE operations days are listed in Table 1. In the “warm sector” regimes (i.e., regimes 1 and 2), vertical profiles of the magnitude of the mean horizontal wind vector, hereafter referred to as the mean wind speed
VORTEX-SE operations days in spring 2017.
(a) Mean wind speeds (
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
Calculations of
The sensitivity of the
b. Near-surface velocity and flux observations from the NOAA/ARL/ATDD towers
Two 10-m NOAA/ARL/ATDD (NOAA Air Resources Laboratory, Atmospheric Turbulence and Diffusion Division) micrometeorological towers (Lee et al. 2017, 2019) were installed during VORTEX-SE (Fig. 1). One tower was approximately 2 km north of Belle Mina at the Tennessee Valley Research and Extension Center. The other was installed near Cullman at the Auburn University North Alabama Horticulture Research Center. Both towers were situated in fairly flat terrain. The Belle Mina tower was surrounded by grazed pasture, whereas the Cullman tower was surrounded by ungrazed pasture. We refer the reader to Lee et al. (2019) and Lee and Buban (2019, manuscript submitted to J. Appl. Meteor. Climatol.) for additional details on the sites’ characteristics. Wind, temperature, and turbulent fluxes were measured at 3 m AGL and 10 m AGL. Turbulent fluxes were obtained from sonic anemometer data; mean winds were obtained from a propellor anemometer. As was the case for the CLAMPS Doppler lidar data, 30-min averaging periods were used in the fair-weather and prestorm weather regimes (regimes 1 and 2), and 15-min averaging periods were used within convective storm outflow (regime 3).
Friction velocity (m s−1) derived from NOAA/ARL/ATDD tower observations of vertical momentum fluxes at 3 m AGL (“measured
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
Histograms of (a),(c),(e) surface heat flux H and (b),(d),(f) Obukhov length L diagnosed for the various weather regimes from the NOAA/ARL/ATDD tower observations (3 and 10 m AGL measurements were averaged).
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
3. Results
a. Fair-weather days
On fair-weather, nonoperations days—that is, days generally characterized by weak synoptic-scale pressure gradients, baroclinicity, and geostrophic wind shear—vertical mean wind profiles retrieved from the CLAMPS Doppler lidar in the surface layer generally adhere to MOST expectations (Fig. 2). This is unsurprising, especially given that the roughness length was tuned in order to obtain good agreement between the wind profiles and MOST predictions on fair-weather days.
The surface layer can be assumed to be 100–150 m deep at the times corresponding to the wind profiles depicted in Fig. 2, based on boundary layer depths of 1000–1500 m evident from nearby observed or model soundings. In Figs. 2b and 2c, which display
Values of ϕm most often lie in the 0.5–1.0 range within the surface layer, also in general agreement with MOST predictions (Figs. 2c,d). More than 70% of the ϕm values computed at heights of 65 and 91 m (heights that can be safely assumed to be within the surface layer) fall in the ϕm = 0–1 bin in the histogram shown in Fig. 2d, and of the small fraction in the ϕm = 1–2 bin, 80% have ϕm in the 1.0–1.3 range (Fig. 2c). It is unrealistic to expect every wind profile to conform to MOST predictions, even on fair-weather days, given the local heterogeneity in the surface characteristics at the CLAMPS site, in addition to uncertainties in the most appropriate averaging period (Pan and Patton 2017) and occasionally large errors in computed
Last, the tower-based observations of ϕm at 6.5 m AGL are presented in Fig. 5a. Over 95% of ϕm values are in the 0.5–1.25 range. Given expected errors in the calculations of up to ~0.25 (see the appendix), the observations of near-surface vertical wind shear are also in good agreement with MOST predictions, which would be in the range of ≈0.6–1 at a height of 6.5 m AGL for L ranging from −10 m to −∞.
Histograms of ϕm values at 6.5 m AGL for the various weather regimes, as diagnosed from the NOAA/ARL/ATDD tower observations at 3 and 10 m AGL.
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
b. VORTEX-SE operations days in the prestorm and near-storm environments
The prestorm and near-storm environments (i.e., not within cool convective outflow) of VORTEX-SE operations days potentially differ from fair-weather days in that the former environments typically would be characterized by larger horizontal pressure-gradient forces and larger mean wind shear (the presence of larger mean shear is evident in Fig. 6a). On these days, the characteristics of the Doppler lidar–retrieved wind profiles exhibit significant departures from MOST with regularity. Considerably more shear is present than MOST would predict, as is evident in both the vertical profile of
As in Fig. 2, but for VORTEX-SE operations days before the arrival of convective storm outflow.
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
Although MOST predictions of the profiles of
The tower-based observations of vertical wind shear just above the surface in prestorm and near-storm environments also frequently exhibit departures from MOST expectations (Fig. 5b). Slightly more than 50% of the ϕm values measured in this weather regime exceed 1. Except in cases of strong surface-layer stabilization owing to cloud-shading effects, MOST predictions of ϕm would be in the 0.9–1.0 range (e.g., Businger et al. 1971).
c. VORTEX-SE operations days in the outflow of convective storms
The Doppler lidar-retrieved vertical wind profiles exhibit their largest departures from log-law behavior within convective outflow, where it seems that “almost anything goes” with respect to the characteristics of the wind profiles (Fig. 7). The variability is reminiscent of tower and radar observations of wind profiles within convective outflow made near Lubbock, Texas, by Lombardo et al. (2014) and Gunter and Schroeder (2015). At the lowest two lidar levels used (65 and 91 m AGL), ϕm values range from 0.5 to 6.8 (Figs. 7c,d). Admittedly, it is difficult to quantify the departures from MOST given the shortness of the averaging period (only 15-min averages are used within the outflow, as explained in section 2b), uncertainty in the depth of the surface layer, and uncertainty in the surface heat flux [negative surface heat fluxes are likely (Figs. 4e,f), for which ϕm > 1 would be expected]. It seems unlikely that MOST could account for such variability, nor would MOST be expected to, given the likelihood of extreme unsteadiness and large horizontal heterogeneity. Regarding the MOST predictions for L > 0 in Figs. 7b,c, some words of caution are warranted. The corrections for a stable surface layer made in prior studies may not be applicable to the outflow of convective storms. Moreover, a positive surface heat flux is occasionally observed within thunderstorm outflow (12% of the time at the NOAA/ARL/ATDD tower sites; Fig. 4e).
As in Fig. 2, but within the outflow of convective storms occurring on VORTEX-SE operations days.
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
The tower observations of vertical wind shear within convective outflow (Fig. 5c) also are more variable than in fair-weather regimes or in the prestorm/near-storm environment (Figs. 5a,b), though not as variable as at the higher altitudes measured by the CLAMPS Doppler lidar. This is unsurprising given that MOST predicts ϕm to depart from unity by a term proportional to z/L. Although little can be said about the magnitude of the departures from MOST for the reasons given in the preceding paragraph, a stability-corrected ϕm value would be larger than unity in the case of L > 0.
4. Discussion
In addition to the surface-layer vertical shear, the friction velocity also is of interest given that surface stress is proportional to
The frequently large differences between the observed vertical wind shear and MOST-based predictions of vertical wind shear within the surface layer imply that numerical simulations, which virtually always assume the applicability of MOST in the formulation of the lower boundary condition (at least those simulations not assuming a free-slip lower boundary), are likely to have errors in their lower boundary condition and near-surface vertical wind profiles. On one hand, given the common observations of stronger shear than MOST predicts near and within convective storms, it would be tempting to conclude that numerical simulations using a MOST-based lower boundary condition would tend to underpredict surface-layer wind shear. On the other hand, many numerical simulations of storms, specifically those run as large-eddy simulations (LES), might suffer from the problem exposed by Markowski and Bryan (2016, hereafter MB16).
MB16 found that unrealistically large vertical wind shear develops, at least in boundary layers that are approximately statistically steady and horizontally homogeneous (i.e., boundary layers for which MOST is applicable), if the LES lacks significant, resolvable, turbulent eddies—not merely as the surface is approached, but throughout the entire depth of the domain. The “eddyless LES” problem MB16 identified leads to even larger wind shear errors than the so-called log-layer-mismatch or law-of-the-wall problem in LES. The latter has been studied for decades (e.g., Mason and Thomson 1992; Sullivan et al. 1994; Brasseur and Wei 2010) and stems from inadequate resolution of turbulent eddies in the immediate vicinity of the surface (eddy size scales with distance above the surface).
MB16 did not investigate environments in which significant departures from MOST might be present. That is, their work did not address the ability of an LES using a MOST-based lower boundary condition to correctly represent near-surface wind profiles in situations in which MOST does not apply in the first place.2 However, this issue is raised here because both the MOST-based formulation of the lower boundary condition and the aforementioned problems with LES potentially can contribute to low-altitude wind shear errors in numerical simulations. From the analyses in section 3, we can say with confidence that a MOST-based lower boundary condition is likely to be a source of model error in convective storm simulations. However, it is difficult to say what the range of adverse effects might include, given that “adverse effects” would be measured relative to past storm simulations, and some past simulations also might be affected by the issue identified by MB16.
5. Summary and conclusions
The purpose of this article was to assess how closely surface-layer wind characteristics, vertical shear and surface shear stress in particular, agree with predictions by MOST near and within convective storms. Departures from MOST within convective storm outflow were detectable in the Doppler lidar–based wind profiles, as well as in the micrometeorological tower data. Specifically, on thunderstorm days the vertical wind shear within the surface layer tended to be stronger than MOST predicts, both within the warm-sector air mass and within the convective outflow. This should not be surprising, given that MOST is based on the assumption of horizontal homogeneity and steadiness within a constant-flux surface layer. The atmosphere ahead of and within convective storms is not generally horizontal homogeneous and steady, rather, it is frequently characterized by strong horizontal temperature and pressure gradients and unsteadiness, especially near thunderstorm gust fronts.
It seems safe to conclude that a lower boundary condition based on MOST would be a source of error in numerical simulations of convective storms, given that many convective storm hazards and their parent storms are well known to be sensitive to the low-altitude vertical wind shear. It is unlikely that the community’s “first-order” understanding would be changed by improving the wall models used in convective storm simulations (i.e., the lower boundary condition and parameterization of near-surface turbulence). However, improvements in wall models—specifically, migrating to models that do not rely on the applicability of MOST (Piomelli 2008)—are very likely to have a significant effect on the development of small-scale vortices (including tornadoes), vorticity budgets, low-altitude updrafts and downdrafts, and the transient momentum surges within the outflow that some have linked to tornado formation (Lee et al. 2004; Finley and Lee 2004; Marquis et al. 2008; Mashiko et al. 2009; Wurman et al. 2010; Kosiba et al. 2013; Schenkman et al. 2014, 2016). As numerical simulations continue moving toward higher and higher resolution (e.g., Orf et al. 2017), the near-surface flow will become better and better resolved, and surface interactions will need to be included in simulations in a better way.
Acknowledgments
We thank NOAA and all of the VORTEX-SE PIs, students, and other participants, without which the project would not have been possible. The analysis was supported by NOAA award NA17OAR4590189. Special thanks go to Ying Pan for extended discussions on this topic and her comments on the first draft of the manuscript. Marcelo Chamecki, Evgeni Fedorovich, Petra Klein, and Scott Salesky are also acknowledged for discussions related to this work. Lastly, we appreciate the constructive and thorough critiques provided by the reviewers.
APPENDIX
Error Analysis for Friction Velocity, Dimensionless Velocity, and Dimensionless Shear
This appendix contains estimates of the errors in
a.
Uncertainty in friction velocity,
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
b.
Using the expression for
Uncertainty in nondimensional velocity measured by the CLAMPS Doppler lidar,
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
c. ϕm errors
Figure A3 (blue dots) plots δϕm for each Doppler lidar wind profile using
Uncertainty in nondimensional shear δϕm as a function of ϕm. Blue dots are for the CLAMPS Doppler lidar. Red dots are for the NOAA/ARL/ATDD tower.
Citation: Monthly Weather Review 147, 10; 10.1175/MWR-D-19-0091.1
Figure A3 (red dots) also plots δϕm for the NOAA/ARL/ATDD tower using z = 6.5 m, Δz = 7 m (wind observations are at 3 and 10 m AGL),
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CLAMPS was also deployed in the spring of 2016, but data from 2016 were excluded from the analysis owing to the coarser vertical resolution of the 2016 wind profiles.
We cannot refute the possibility that a simulation using a MOST-based lower boundary condition, even though MOST might not be applicable, along with the simulation being run as an LES yet not resolving turbulent eddies—i.e., a model with two “wrongs”—could be better than a simulation with only one “wrong.” In the MB16 “eddyless LES,” a MOST-based lower boundary condition was justified, but the LES contained no eddies.