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A revision to the Holland parametric approach to modeling the radial profile of winds in hurricanes is presented. The approach adopted uses information readily available from hurricane archives or in hurricane warning information and the profile can be readily incorporated into existing parametric models of the hurricane surface wind field. The original model utilized central and environmental surface pressures, maximum winds, and radius of maximum winds. In the revision a capacity to incorporate additional wind observations at some radius within the hurricane circulation was included. If surface observations are used, then a surface wind profile will result, obviating the need for deriving a boundary layer reduction from the gradient wind level. The model has considerably less sensitivity to data errors compared to the original and is shown to reproduce hurricane reconnaissance and surface wind profiles with high accuracy.

Potential intensity (PI) is an analytical bound on steady, inviscid, axisymmetric hurricane wind speed. Studies have shown that simulated hurricane azimuthal wind speed can greatly exceed a PI bound on the maximum gradient wind. This disparity is called superintensity (SI) and has been attributed to the contribution of the unbalanced flow to the azimuthal wind. The goals of this study are 1) to introduce a new surface wind PI (PI s ), based on a differential Carnot cycle and bounding the magnitude of the surface winds; 2) to evaluate SI in numerical simulations with respect to diagnostic PI bounds on gradient wind (PI g ), azimuthal wind (PI a ), and surface wind (PI s ); and 3) to evaluate the validity of each PI bound based on the SI computations. Here, we define superintensity as the normalized amount by which each version of PI is exceeded by the quantity it bounds. Axisymmetric tropical cyclone simulations are performed while varying the parameterized turbulent mixing as a way of estimating SI in the inviscid limit. As the mixing length decreases, all three bounded wind speeds increase similarly from a sub-PI state to a marginally superintense state. This shows that all three forms of PI evaluated here are good approximations to their respective metrics in numerical simulations.

Hazard studies based on thousands of synthetic tropical cyclone (TC) events require a validated model representation of the surface wind field. Here, we assess three different TC parametric vortex models with input from four along-track parameter studies of the TC size and shape, based on statistical formulation of the relationships to observed TC intensity, geographic location, and forward transition speed. The 12 model combinations are compared to in situ 10-min observed surface mean wind speeds for 10 TCs that made landfall over Queensland, Australia, which occurred over the period 2006–17. Empirical wind reduction factors to reduce gradient winds to the surface are recalculated for the more recent TCs at both offshore (ocean, small islands, reefs, and moorings) and onshore (land) locations. To improve the wind comparisons over ocean and land, a secondary reduction factor was developed based on an inland decay function. Pearson correlations for the unadjusted modeled peak wind speed from 118 instances of a TC passing a weather station sit between a range of 0.57 and 0.65 for the 12 model combinations. Using the secondary reduction factor based on the inland decay function increases the range of correlation to 0.74–0.81. Based on the assessment of the instances of peak surface wind speed correlations, bias, and root-mean-square error, along with the correlation 48 h around the peak, the top-ranked performing model combination for the region was an along-track parameter study with a double-vortex model, both previously tested for the South Pacific basin.

Variations of global wind are important in changing the atmospheric structure and circulation, in coupling of atmospheric layers, and in influencing the wave propagations. Due to the difficulty of directly measuring zonal wind from the stratosphere to the lower thermosphere, we derived a global balance wind (BU) dataset from 50∘ S to 50∘ N and during 2002–2019 using the gradient wind theory and SABER temperatures and modified by meteor radar observations at the Equator. The dataset captures the main feature of global monthly mean zonal wind and can be used to study the variations (i.e., annual, semi-annual, ter-annual, and linear) of zonal wind and the responses of zonal wind to quasi-biennial oscillation (QBO), El Niño–Southern Oscillation (ENSO), and solar activity (F10.7). The same procedure is performed on the MERRA-2 zonal wind (MerU) to validate BU and its responses below 70 km. The annual, semi-annual, and ter-annual oscillations of BU and MerU have similar amplitudes and phases. The semi-annual oscillation of BU has peaks around 80 km, which are stronger in the southern tropical region and coincide with previous satellite observations. As the increasing of the values representing QBO wind, both values of representing BU and MerU (short for BU and MerU) change from increasing to decreasing with the increasing height and extend from the Equator to higher latitudes. Both BU and MerU increase with the increasing of the values of multivariate ENSO index (MEI) and decrease with increasing F10.7​​​​​​​ in the southern stratospheric polar jet region below 70 km. The responses of winds to ENSO and F10.7 exhibit hemispheric asymmetry and are more significant in the southern polar jet region. While above 70 km, BU increases with the increasing of MEI and F10.7. The negative linear changes of BU at 50∘ N are absent in MerU during October–January. The discussions on the possible influences of the temporal intervals and sudden stratospheric warmings (SSWs) on the variations and responses of BU illustrate the following: (1) the seasonal variations and the responses to QBO are almost independent on the temporal intervals selected; (2) the responses to ENSO and F10.7 are robust but slightly depend on the temporal intervals; (3) the linear changes of both BU and MerU depend strongly on the temporal intervals; (4) SSWs affect the magnitudes but do not affect the hemispheric asymmetry of the variations and responses of BU at least in the monthly mean sense. The variations and responses of global zonal wind to various factors are based on BU, which is derived from observations, and thus provide a good complement to model studies and ground-based observations.

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI + . The formula, PI +2 = EPI 2 + αr m w m η m , where EPI is the maximum potential intensity of the gradient wind and αr m w m η m represents the supergradient winds. The latter term is the product of the radius r m , the vertical velocity w m , the azimuthal vorticity η m at the radius and height of the maximum tangential wind ( r m , z m ), and the (nearly constant) α . Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI + as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical cyclone boundary layer dynamics. It is found that , where − u min is the maximum boundary layer radial inflow velocity and l υ ( z ) is the vertical mixing length.

Global long-term stable 3D wind fields provide valuable information for climate-oriented analyses of the dynamics of the atmosphere. Their monitoring remains a challenging task given the shortcomings of available observations. One promising option for progress is the use of radio occultation (RO) satellite data, which enable deriving dynamics based on thermodynamic data. In this study we focus on three main goals, explored through the fifth version of the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA5) and RO datasets, using monthly-mean January and July data over 2007–2020. Our focus is on a 2.5° × 2.5° spatial synoptic scale over the free troposphere to the mid-stratosphere (i.e. 800–10 hPa). First, by comparing ERA5-derived geostrophic and gradient wind speeds to the original ERA5 ones, we examine the regions of validity of the studied approximations at a given synoptic-scale resolution. Second, to assess the possible added value of the RO-derived climatic winds in terms of their long-term stability, we test their consistency with the corresponding ERA5-derived winds. Third, by comparing the RO climatic winds to the original ERA5 winds, we evaluate the potential benefit of RO as an additional dataset for wind analyses and climate monitoring. With this three-step analysis, we decompose the total wind speed bias into the contributions from the approximation and the systematic difference between the RO and ERA5 datasets. We find that the geostrophic approximation is a valid method to estimate winds in the free troposphere, while the gradient wind approximation works better in the lower stratosphere. Both approximations generally work well over the mentioned altitudes, within an accuracy of 2 m s−1 for the latitudes 5–82.5°. Exceptions are found in winter in the monsoonal area and above larger mountain ranges in the free troposphere, as well as above the northern polar regions in the mid-stratosphere. RO- and ERA5-derived geostrophic winds mostly showed good agreement (within 2 m s−1). However, temporal change in the systematic difference higher than 0.5 m s−1 per decade was found. This points to a possible impact of changes in the source of the assimilated data in ERA5. The overall high accuracy of the monthly-mean wind fields, backed by the long-term stability and fine vertical resolution of the underlying RO data, highlights the added value and potential benefit of RO-derived climatic winds for climate monitoring and analyses.

The validity of the gradient wind balance in a tropical cyclone (TC) remains controversial, especially for the boundary layer and the upper outflow layer, even though this balance is assumed in the derivation of the Sawyer–Eliassen (SE) equation. This study derives an extended SE equation with the relaxation of the gradient wind and hydrostatic balance in cylindrical r – z coordinates, and then we diagnose the secondary circulation using this unbalanced SE equation and the azimuthally averaged tangential wind and thermodynamical fields from a three-dimensional numerical simulation of an intensifying TC. The gradient wind and hydrostatic imbalance produce two additional time-dependent forcing terms on the right-hand side (rhs) of SE equation, which are proved to be negligible for diagnosing the secondary circulation, even as the storm evolves rapidly. The use of the unbalanced basic state deforms the fields of coefficients that appear in the SE equation, and thus the forced secondary flows. The results indicate that the unbalanced solution captures the boundary layer inflow better than the balanced solution described by Bui et al. and the pseudobalanced solution described by Heng et al. The unbalanced solution is closer to the simulation because more unbalanced components are included. Many previous studies always employ the thermal wind balance relation to simplify the SE equation, which is invalid in an unbalanced vortex and result in an overestimation of the boundary layer inflow. These unbalanced dynamics could provide a reliable diagnosis of the secondary flow near the boundary layer.

In this study, we examine the role of curvature in modifying frontal stability. We first evaluate the classical criterion that the Coriolis parameter f multiplied by the Ertel potential vorticity (PV) q is positive for stable flow and that instability is possible when this quantity is negative. The first portion of this statement can be deduced from Ertel’s PV theorem, assuming an initially positive fq . Moreover, the full statement is implicit in the governing equation for the mean geostrophic flow, as the discriminant, fq , changes sign. However, for curved fronts in cyclogeostrophic or gradient wind balance (GWB), an additional term enters the discriminant owing to conservation of absolute angular momentum L . The resulting expression, (1 + Cu) fq < 0 or Lq < 0, where Cu is a nondimensional number quantifying the curvature of the flow, simultaneously generalizes Rayleigh’s criterion by accounting for baroclinicity and Hoskins’s criterion by accounting for centrifugal effects. In particular, changes in the front’s vertical shear and stratification owing to curvature tilt the absolute vorticity vector away from its thermal wind state; in an effort to conserve the product of absolute angular momentum and Ertel PV, this modifies gradient Rossby and Richardson numbers permitted for stable flow. This forms the basis of a nondimensional expression that is valid for inviscid, curved fronts on the f plane, which can be used to classify frontal instabilities. In conclusion, the classical criterion fq < 0 should be replaced by the more general criterion for studies involving gravitational, centrifugal, and symmetric instabilities at curved density fronts. In Part II of the study, we examine interesting outcomes of the criterion applied to low-Richardson-number fronts and vortices in GWB.

Ground-based Doppler-lidar instrumentation provides atmospheric wind data at dramatically improved accuracies and spatial/temporal resolutions. These capabilities have provided new insights into atmospheric flow phenomena, but they also should have a strong role in NWP model improvement. Insight into the nature of model errors can be gained by studying recurrent atmospheric flows, here a regional summertime diurnal sea breeze and subsequent marine-air intrusion into the arid interior of Oregon–Washington, where these winds are an important wind-energy resource. These marine intrusions were sampled by three scanning Doppler lidars in the Columbia River basin as part of the Second Wind Forecast Improvement Project (WFIP2), using data from summer 2016. Lidar time–height cross sections of wind speed identified 8 days when the diurnal flow cycle (peak wind speeds at midnight, afternoon minima) was obvious and strong. The 8-day composite time–height cross sections of lidar wind speeds are used to validate those generated by the operational NCEP–HRRR model. HRRR simulated the diurnal wind cycle, but produced errors in the timing of onset and significant errors due to a premature nighttime demise of the intrusion flow, producing low-bias errors of 6 m s−1. Day-to-day and in the composite, whenever a marine intrusion occurred, HRRR made these same errors. The errors occurred under a range of gradient wind conditions indicating that they resulted from the misrepresentation of physical processes within a limited region around the measurement locations. Because of their generation within a limited geographical area, field measurement programs can be designed to find and address the sources of these NWP errors.

The efficacy of the boundary condition on ds/dM was verified by BR09. d. Response to comment on balance in the boundary layer We agree that assumptions relating the gradient wind to the surface winds are needed to simplify this formulation of PI. Azimuthal wind PI a. Response to comment on difference between boundary layer top and height of maximum winds Equation (8) in RE19 is stated to pertain to the level of maximum wind, not the top of the boundary layer and we make no assumption about the relationship between the two altitudes. [...]similar simulations in Rotunno and Bryan (2012, Figs. 3b,f) show that vertical diffusion terms in the radial and tangential momentum equations are small at and above the height of maximum winds. b. Response to comment on radius of maximum winds Once again, we are not trying to predict the radius of maximum winds and invite the authors of the comment to develop such a formulation. Once again, there is no evidence that the diffusive terms are very important near the altitude of maximum winds (e.g., Rotunno and Bryan 2012), nor do we think that the good agreement between the theory and observed peak wind speeds is an accident. c. Response to comment on a priori potential intensity Nowhere did we describe our analysis as an a priori theory for the potential intensity but rather as an analysis of the validity of potential intensity diagnostics at maximum intensity.