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Abstract This study extends the linear theory of Shapiro et al. (S18) for the onset of horizontal convergence and ascent in nocturnal boundary layers in baroclinic environments such as the U.S. Great Plains. In S18, the sudden decay of turbulence in a surface-based warm tongue at sunset triggers a surge of convergent inflow/ascent as well as a Blackadar-like nocturnal low-level jet. For conditions typical of broad warm-season surface-based baroclinic zones over the Great Plains, the S18 theory predicts that air parcels can rise 500 m–1 km before the onset of a descent phase. Such displacements may help sustain or initiate convection and play a role in the well-known nocturnal maximum in rainfall over the region. In this study, the Cloud Model 1 is used to examine the S18 predictions in a more realistic setting in which the nonlinear terms in the governing equations are retained, and the sudden shutdown of turbulence at sunset is replaced by a more gradual evening transition. A warm tongue arises in the simulated boundary layer over a 5-day period through a prescribed deficit in surface moisture which causes the greatest daytime heating in the domain center. As in S18, the simulations depict a surge of convergent flow, descent of the zone of peak ascent, replacement of the ascent zone by subsidence, peak vertical motion decreasing with latitude and warm tongue width, and the generation of free-atmosphere inertia–gravity waves. The divergence and vorticity fields are found to oscillate at the inertial frequency. 

Abstract We introduce a quasi-analytical model of thermally induced flows in valleys with sloping floors, a feature absent from most theoretical valley wind studies. One of the main theories for valley winds—the valley volume effect—emerged from field studies in the European Alps in the 1930s and 1940s. According to that theory, along-valley variations in the heating rate arising from variations in valley geometry generated the pressure gradient that drove the valley wind. However, while those early studies were conducted in valleys with relatively flat (horizontal) floors, valleys with sloping floors are ubiquitous and presumably affected directly by slope buoyancy (Prandtl mechanism). Our model is developed for the Prandtl setting of steady flow of a stably stratified fluid over a heated planar slope, but with the slope replaced by a periodic system of sloping valleys. As the valley characteristics do not change along the valley, there is no valley volume effect. The 2D linearized Boussinesq governing equations are solved using Fourier methods. Examples are explored for symmetric (with respect to valley axis) valleys subject to symmetric and antisymmetric heating. The flows are 2D, but the trajectories are intrinsically 3D. For symmetric heating, trajectories are of two types: i) helical trajectories of parcels trapped within one of two counterrotating vortices straddling the valley axis and ii) trajectories of environmental parcels that approach the valley horizontally, move under and then over the helical trajectories, and then return to the environment. For antisymmetric heating, three types of trajectories are identified. 

Abstract Weak but persistent synoptic-scale ascent may play a role in the initiation or maintenance of nocturnal convection over the central United States. An analytical model is used to explore the nocturnal low-level jets (NLLJ) and ascent that develop in an idealized diurnally varying frictional (Ekman) boundary layer in a neutrally stratified barotropic environment when the flow aloft is a zonally propagating Rossby wave. Steady-periodic solutions are obtained of the linearized Reynolds-averaged Boussinesq-approximated equations of motion on a beta plane with an eddy viscosity that is specified to increase abruptly at sunrise and decrease abruptly at sunset. Rayleigh damping terms are used to parameterize momentum loss due to radiation of inertia–gravity waves. The model-predicted vertical velocity is (approximately) proportional to the wavenumber and wave amplitude. There are two main modes of ascent in midlatitudes, an afternoon mode and a nocturnal mode. The latter arises as a gentle but persistent surge induced by the decrease of turbulence at sunset, the same mechanism that triggers inertial oscillations in the Blackadar theory of NLLJs. If the Rayleigh damping terms are omitted, the boundary layer depth becomes infinite at three critical latitudes, and the vertical velocity becomes infinite far above the ground at two of those latitudes. With the damping terms retained, the solution is well behaved. Peak daytime ascent in the model occurs progressively later in the afternoon at more southern locations (in the Northern Hemisphere) until the first (most northern) critical latitude is reached; south of that latitude the nocturnal mode is dominant. 

Abstract An analytical model is presented for the generation of a Blackadar-like nocturnal low-level jet in a broad baroclinic zone. The flow is forced from below (flat ground) by a surface buoyancy gradient and from above (free atmosphere) by a constant pressure gradient force. Diurnally varying mixing coefficients are specified to increase abruptly at sunrise and decrease abruptly at sunset. With attention restricted to a surface buoyancy that varies linearly with a horizontal coordinate, the Boussinesq-approximated equations of motion, thermal energy, and mass conservation reduce to a system of one-dimensional equations that can be solved analytically. Sensitivity tests with southerly jets suggest that (i) stronger jets are associated with larger decreases of the eddy viscosity at sunset (as in Blackadar theory); (ii) the nighttime surface buoyancy gradient has little impact on jet strength; and (iii) for pure baroclinic forcing (no free-atmosphere geostrophic wind), the nighttime eddy diffusivity has little impact on jet strength, but the daytime eddy diffusivity is very important and has a larger impact than the daytime eddy viscosity. The model was applied to a jet that developed in fair weather conditions over the Great Plains from southern Texas to northern South Dakota on 1 May 2020. The ECMWF Reanalysis v5 (ERA5) for the afternoon prior to jet formation showed that a broad north–south-oriented baroclinic zone covered much of the region. The peak model-predicted winds were in good agreement with ERA5 winds and lidar data from the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) central facility in north-central Oklahoma. 

Abstract Techniques to mitigate analysis errors arising from the nonsimultaneity of data collections typically use advection-correction procedures based on the hypothesis (frozen turbulence) that the analyzed field can be represented as a pattern of unchanging form in horizontal translation. It is more difficult to advection correct the radial velocity than the reflectivity because even if the vector velocity field satisfies this hypothesis, its radial component does not—but that component does satisfy a second-derivative condition. We treat the advection correction of the radial velocity ( υ r ) as a variational problem in which errors in that second-derivative condition are minimized subject to smoothness constraints on spatially variable pattern-translation components ( U , V ). The Euler–Lagrange equations are derived, and an iterative trajectory-based solution is developed in which U , V , and υ r are analyzed together. The analysis code is first verified using analytical data, and then tested using Atmospheric Imaging Radar (AIR) data from a band of heavy rainfall on 4 September 2018 near El Reno, Oklahoma, and a decaying tornado on 27 May 2015 near Canadian, Texas. In both cases, the analyzed υ r field has smaller root-mean-square errors and larger correlation coefficients than in analyses based on persistence, linear time interpolation, or advection correction using constant U and V . As some experimentation is needed to obtain appropriate parameter values, the procedure is more suitable for non-real-time applications than use in an operational setting. In particular, the degree of spatial variability in U and V , and the associated errors in the analyzed υ r field are strongly dependent on a smoothness parameter. 

Abstract Phased array radars (PARs) are a promising observing technology, at the cusp of being available to the broader meteorological community. PARs offer near-instantaneous sampling of the atmosphere with flexible beam forming, multifunctionality, and low operational and maintenance costs and without mechanical inertia limitations. These PAR features are transformative compared to those offered by our current reflector-based meteorological radars. The integration of PARs into meteorological research has the potential to revolutionize the way we observe the atmosphere. The rate of adoption of PARs in research will depend on many factors, including (i) the need to continue educating the scientific community on the full technical capabilities and trade-offs of PARs through an engaging dialogue with the science and engineering communities and (ii) the need to communicate the breadth of scientific bottlenecks that PARs can overcome in atmospheric measurements and the new research avenues that are now possible using PARs in concert with other measurement systems. The former is the subject of a companion article that focuses on PAR technology while the latter is the objective here. 

Abstract Observation system simulation experiments are used to evaluate different dual-Doppler analysis (DDA) methods for retrieving vertical velocity w at grid spacings on the order of 100 m within a simulated tornadic supercell. Variational approaches with and without a vertical vorticity equation constraint are tested, along with a typical (traditional) method involving vertical integration of the mass conservation equation. The analyses employ emulated radar data from dual-Doppler placements 15, 30, and 45 km east of the mesocyclone, with volume scan intervals ranging from 10 to 150 s. The effect of near-surface data loss is examined by denying observations below 1 km in some of the analyses. At the longer radar ranges and when no data denial is imposed, the “traditional” method produces results similar to those of the variational method and is much less expensive to implement. However, at close range and/or with data denial, the variational method is much more accurate, confirming results from previous studies. The vorticity constraint shows the potential to improve the variational analysis substantially, reducing errors in the w retrieval by up to 30% for rapid-scan observations (≤30 s) at close range when the local vorticity tendency is estimated using spatially variable advection correction. However, the vorticity constraint also degrades the analysis for longer scan intervals, and the impact diminishes with increased range. Furthermore, analyses using 30-s data also frequently outperform analyses using 10-s data, suggesting a limit to the benefit of increasing the radar scan rate for variational DDA employing the vorticity constraint.