Browse
Abstract
Wind and turbulence effects on raindrop fall speeds were elucidated using field observations over a 2-yr time period. Motivations for this study include the recent observations of raindrop fall speed deviations from the terminal fall speed predictions (Vt ) based upon laboratory studies and the utilizations of these predictions in various important meteorological and hydrological applications. Fall speed (Vf ) and other characteristics of raindrops were observed using a high-speed optical disdrometer (HOD), and various rainfall and wind characteristics were observed using a 3D ultrasonic anemometer, a laser-type disdrometer, and rain gauges. A total of 26 951 raindrops were observed during 17 different rainfall events, and of these observed raindrops, 18.5% had a subterminal fall speed (i.e., 0.85Vt ≥ Vf ) and 9.5% had a superterminal fall speed (i.e., 1.15Vt ≤ Vf ). Our observations showed that distributions of sub- and superterminal raindrops in the raindrop size spectrum are distinct, and different physical processes are responsible for the occurrence of each. Vertical wind speed, wind shear, and turbulence were identified as the important factors, the latter two being the dominant ones, for the observed fall speed deviations. Turbulence and wind shear had competing effects on raindrop fall. Raindrops of different sizes showed different responses to turbulence, indicating multiscale interactions between raindrop fall and turbulence. With increasing turbulence levels, while the raindrops in the smaller end of the size spectrum showed fall speed enhancements, those in the larger end of the size spectrum showed fall speed reductions. The effect of wind shear was to enhance the raindrop fall speed toward a superterminal fall.
Abstract
Wind and turbulence effects on raindrop fall speeds were elucidated using field observations over a 2-yr time period. Motivations for this study include the recent observations of raindrop fall speed deviations from the terminal fall speed predictions (Vt ) based upon laboratory studies and the utilizations of these predictions in various important meteorological and hydrological applications. Fall speed (Vf ) and other characteristics of raindrops were observed using a high-speed optical disdrometer (HOD), and various rainfall and wind characteristics were observed using a 3D ultrasonic anemometer, a laser-type disdrometer, and rain gauges. A total of 26 951 raindrops were observed during 17 different rainfall events, and of these observed raindrops, 18.5% had a subterminal fall speed (i.e., 0.85Vt ≥ Vf ) and 9.5% had a superterminal fall speed (i.e., 1.15Vt ≤ Vf ). Our observations showed that distributions of sub- and superterminal raindrops in the raindrop size spectrum are distinct, and different physical processes are responsible for the occurrence of each. Vertical wind speed, wind shear, and turbulence were identified as the important factors, the latter two being the dominant ones, for the observed fall speed deviations. Turbulence and wind shear had competing effects on raindrop fall. Raindrops of different sizes showed different responses to turbulence, indicating multiscale interactions between raindrop fall and turbulence. With increasing turbulence levels, while the raindrops in the smaller end of the size spectrum showed fall speed enhancements, those in the larger end of the size spectrum showed fall speed reductions. The effect of wind shear was to enhance the raindrop fall speed toward a superterminal fall.
Abstract
The position and strength of the Hadley cell circulation determine the habitable zones in the tropics, yet our understanding of and ability to predict changes in the circulation is limited. One potentially important source of uncertainty is the dependence of the Hadley cell on turbulent drag. Here, the sensitivity of the Hadley cell and associated features such as the intertropical convergence zone to variations in the magnitude of the turbulent drag is explored with an atmospheric general circulation model in aquaplanet configuration. The tropical circulation and precipitation, and extratropical features such as the polar jet stream, displayed a strong sensitivity to the strength of the parameterized turbulent drag, with distinct low- or high-drag regimes. However, the response of the meridional heat transport produced a surprising departure from previous expectations: with greater drag, simulations exhibited less heat transport than low-drag simulations, which is in the opposite sense to that from Held and Hou. This may be due to the energetic constraints in the present model framework. When exposed to a uniform global warming, the response of the ITCZ precipitation depends strongly on the choice of drag, whereas most simulations exhibit a poleward expansion of the subtropics.
Abstract
The position and strength of the Hadley cell circulation determine the habitable zones in the tropics, yet our understanding of and ability to predict changes in the circulation is limited. One potentially important source of uncertainty is the dependence of the Hadley cell on turbulent drag. Here, the sensitivity of the Hadley cell and associated features such as the intertropical convergence zone to variations in the magnitude of the turbulent drag is explored with an atmospheric general circulation model in aquaplanet configuration. The tropical circulation and precipitation, and extratropical features such as the polar jet stream, displayed a strong sensitivity to the strength of the parameterized turbulent drag, with distinct low- or high-drag regimes. However, the response of the meridional heat transport produced a surprising departure from previous expectations: with greater drag, simulations exhibited less heat transport than low-drag simulations, which is in the opposite sense to that from Held and Hou. This may be due to the energetic constraints in the present model framework. When exposed to a uniform global warming, the response of the ITCZ precipitation depends strongly on the choice of drag, whereas most simulations exhibit a poleward expansion of the subtropics.
Abstract
Aerosol effects on micro/macrophysical properties of marine stratocumulus clouds over the western North Atlantic Ocean (WNAO) are investigated using in situ measurements and large-eddy simulations (LES) for two cold-air outbreak (CAO) cases (28 February and 1 March 2020) during the Aerosol Cloud Meteorology Interactions over the Western Atlantic Experiment (ACTIVATE). The LES is able to reproduce the vertical profiles of liquid water content (LWC), effective radius r
eff and cloud droplet number concentration Nc
from fast cloud droplet probe (FCDP) in situ measurements for both cases. Furthermore, we show that aerosols affect cloud properties (Nc
, r
eff, and LWC) via the prescribed bulk hygroscopicity of aerosols (
Abstract
Aerosol effects on micro/macrophysical properties of marine stratocumulus clouds over the western North Atlantic Ocean (WNAO) are investigated using in situ measurements and large-eddy simulations (LES) for two cold-air outbreak (CAO) cases (28 February and 1 March 2020) during the Aerosol Cloud Meteorology Interactions over the Western Atlantic Experiment (ACTIVATE). The LES is able to reproduce the vertical profiles of liquid water content (LWC), effective radius r
eff and cloud droplet number concentration Nc
from fast cloud droplet probe (FCDP) in situ measurements for both cases. Furthermore, we show that aerosols affect cloud properties (Nc
, r
eff, and LWC) via the prescribed bulk hygroscopicity of aerosols (
Abstract
For modern Earth, the annual-mean equatorial winds in the upper troposphere are flowing from east to west (i.e., easterly winds). This is mainly due to the deceleration effect of the seasonal cross-equatorial Hadley cells, against the relatively weaker acceleration effect of coupled Rossby and Kelvin waves excited from tropical convection and latent heat release. In this work, we examine the evolution of equatorial winds during the past 250 million years using one global Earth system model, the Community Earth System Model version 1.2.2 (CESM1.2.2). Three climatic factors different from the modern Earth—solar constant, atmospheric CO2 concentration, and land–sea configuration—are considered in the simulations. We find that the upper-tropospheric equatorial winds change sign to westerly flows (called equatorial superrotation) in certain eras, such as 250–230 and 150–50 Ma. The strength of the superrotation is below 4 m s−1, comparable to the magnitude of the present-day easterly winds. In general, this phenomenon occurs in a warmer climate within which the tropical atmospheric circulation shifts upward in altitude, stationary and/or transient eddies are relatively stronger, and/or the Hadley cells are relatively weaker, which in turn are due to the changes of the three factors, especially CO2 concentration and land–sea configuration.
Abstract
For modern Earth, the annual-mean equatorial winds in the upper troposphere are flowing from east to west (i.e., easterly winds). This is mainly due to the deceleration effect of the seasonal cross-equatorial Hadley cells, against the relatively weaker acceleration effect of coupled Rossby and Kelvin waves excited from tropical convection and latent heat release. In this work, we examine the evolution of equatorial winds during the past 250 million years using one global Earth system model, the Community Earth System Model version 1.2.2 (CESM1.2.2). Three climatic factors different from the modern Earth—solar constant, atmospheric CO2 concentration, and land–sea configuration—are considered in the simulations. We find that the upper-tropospheric equatorial winds change sign to westerly flows (called equatorial superrotation) in certain eras, such as 250–230 and 150–50 Ma. The strength of the superrotation is below 4 m s−1, comparable to the magnitude of the present-day easterly winds. In general, this phenomenon occurs in a warmer climate within which the tropical atmospheric circulation shifts upward in altitude, stationary and/or transient eddies are relatively stronger, and/or the Hadley cells are relatively weaker, which in turn are due to the changes of the three factors, especially CO2 concentration and land–sea configuration.
Abstract
Using detailed radar observation data for Typhoon Faxai, which made landfall in the Tokyo metropolitan area in 2019, a sensitivity test of the boundary layer (BL) schemes for a numerical weather prediction (NWP) model was conducted for gray-zone numerical simulations with a grid spacing of 250 m. We compared the results of our simulations using an NWP model with radar observations that captured the BL and the secondary circulation structures of Faxai. We used three BL schemes based on a Reynolds-averaged model, the gray-zone model, and a large-eddy simulation (LES) model: the Mellor–Yamada–Nakanishi–Niino level 3 (MYNN3) scheme, the Anisotropic Deardorff Model (ADM) scheme, and the Deardorff (DDF) scheme, respectively. The turbulence kinetic energy was the smallest, and the inflow near Earth’s surface the strongest, in the gray-zone simulation with the DDF scheme. This simulation also produced values for BL thickness and secondary circulation that were the closest to observation and reproduced horizontal roll structures whose scale was larger than the observation. Neither experiment using the MYNN3 scheme or the ADM scheme produced rolls, but the parameterized turbulence seemed to estimate the effects of the rolls. However, their BL heights were higher than observed, suggesting that the MYNN3 and ADM schemes are not appropriate for a 250 m grid simulation of the present case. These results are also confirmed against LES with 50 m grid spacing in which the DDF scheme is used. In summary, this study provides insights into the interpretation of the properties of BL schemes in the gray zone.
Abstract
Using detailed radar observation data for Typhoon Faxai, which made landfall in the Tokyo metropolitan area in 2019, a sensitivity test of the boundary layer (BL) schemes for a numerical weather prediction (NWP) model was conducted for gray-zone numerical simulations with a grid spacing of 250 m. We compared the results of our simulations using an NWP model with radar observations that captured the BL and the secondary circulation structures of Faxai. We used three BL schemes based on a Reynolds-averaged model, the gray-zone model, and a large-eddy simulation (LES) model: the Mellor–Yamada–Nakanishi–Niino level 3 (MYNN3) scheme, the Anisotropic Deardorff Model (ADM) scheme, and the Deardorff (DDF) scheme, respectively. The turbulence kinetic energy was the smallest, and the inflow near Earth’s surface the strongest, in the gray-zone simulation with the DDF scheme. This simulation also produced values for BL thickness and secondary circulation that were the closest to observation and reproduced horizontal roll structures whose scale was larger than the observation. Neither experiment using the MYNN3 scheme or the ADM scheme produced rolls, but the parameterized turbulence seemed to estimate the effects of the rolls. However, their BL heights were higher than observed, suggesting that the MYNN3 and ADM schemes are not appropriate for a 250 m grid simulation of the present case. These results are also confirmed against LES with 50 m grid spacing in which the DDF scheme is used. In summary, this study provides insights into the interpretation of the properties of BL schemes in the gray zone.
Abstract
This study uses semi-idealized simulations to investigate multiscale processes induced by the heterogeneity of soil moisture observed during the 2016 Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) field campaign. The semi-idealized simulations have realistic land heterogeneity, but large-scale winds are removed. Analysis on isentropic coordinates enables the tracking of circulation that transports energy vertically and facilitates the identification of the primary convective processes induced by realistic land heterogeneity. The isentropes associated with upward motion are found to connect the ground characterized by high latent heat flux to cloud bases directly over the ground with high sensible heat flux, while isentropes associated with downward motion connect precipitation to the ground characterized by high sensible heat fluxes. The mixing of dry, warm parcels ascending from the ground with high sensible heat fluxes and moist parcels from high latent heat regions leads to cloud formation. This new mechanism explains how soil moisture heterogeneity provides the key ingredients such as buoyancy and moisture for shallow cloud formation. We also found that the submesoscale dominates upward energy transport in the boundary layer, while mesoscale circulations contribute to vertical energy transport above the boundary layer. Our novel method better illustrates and elucidates the nature of land atmospheric interactions under irregular and realistic soil moisture patterns.
Significance Statement
Models that resolve boundary layer turbulence and clouds have been used extensively to understand processes controlling land–atmosphere interactions, but many of their configurations and computational expense limit the use of variable land properties. This study aims to understand how heterogeneous land properties over multiple spatial scales affect energy redistribution by moist convection. Using a more realistic land representation and isentropic analyses, we found that high sensible heat flux regions are associated with relatively higher vertical velocity near the surface, and the high latent heat flux regions are associated with relatively higher moist energy. The mixing of parcels rising from these two regions results in the formation of shallow clouds.
Abstract
This study uses semi-idealized simulations to investigate multiscale processes induced by the heterogeneity of soil moisture observed during the 2016 Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) field campaign. The semi-idealized simulations have realistic land heterogeneity, but large-scale winds are removed. Analysis on isentropic coordinates enables the tracking of circulation that transports energy vertically and facilitates the identification of the primary convective processes induced by realistic land heterogeneity. The isentropes associated with upward motion are found to connect the ground characterized by high latent heat flux to cloud bases directly over the ground with high sensible heat flux, while isentropes associated with downward motion connect precipitation to the ground characterized by high sensible heat fluxes. The mixing of dry, warm parcels ascending from the ground with high sensible heat fluxes and moist parcels from high latent heat regions leads to cloud formation. This new mechanism explains how soil moisture heterogeneity provides the key ingredients such as buoyancy and moisture for shallow cloud formation. We also found that the submesoscale dominates upward energy transport in the boundary layer, while mesoscale circulations contribute to vertical energy transport above the boundary layer. Our novel method better illustrates and elucidates the nature of land atmospheric interactions under irregular and realistic soil moisture patterns.
Significance Statement
Models that resolve boundary layer turbulence and clouds have been used extensively to understand processes controlling land–atmosphere interactions, but many of their configurations and computational expense limit the use of variable land properties. This study aims to understand how heterogeneous land properties over multiple spatial scales affect energy redistribution by moist convection. Using a more realistic land representation and isentropic analyses, we found that high sensible heat flux regions are associated with relatively higher vertical velocity near the surface, and the high latent heat flux regions are associated with relatively higher moist energy. The mixing of parcels rising from these two regions results in the formation of shallow clouds.
Abstract
Air–sea exchange in high winds is one of the most important but poorly represented processes in tropical cyclone (TC) prediction models. Effects of sea spray on air–sea heat fluxes in TCs are particularly difficult to model due to complex sea states and lack of observations in extreme wind and wave conditions. This study introduces a new sea-state-dependent air–sea heat flux parameterization with spray, which is developed using the Unified Wave Interface–Coupled Model (UWIN-CM). Impacts of spray on air–sea heat fluxes are investigated across a wide range of winds, waves, and atmospheric and ocean conditions in five TCs of various sizes and intensities. Spray generation with variable size distribution is explicitly represented by surface wave properties such as wave dissipation, significant wave height, and dominant phase speed, which may be uncorrelated with local winds. The sea-state-dependent spray mass flux is substantially different than a wind-dependent flux, especially when wave shoaling occurs with enhanced wave dissipation near the coast during TC landfall. Spray increases the air–sea enthalpy flux near the radius of maximum wind (RMW) by approximately 5%–20% when mean 10-m wind speed at the RMW reaches 40–50 m s−1. These values can be amplified significantly by coastal wave shoaling. Spray latent heat fluxes may be dampened in the eyewall due to high saturation ratio, and they consistently produce a moistening and cooling effect outside the eyewall. Spray strongly modifies the total sensible heat flux and can cause either a warming or cooling effect at the RMW depending on eyewall saturation ratio.
Significance Statement
Fluxes of heat and moisture from the ocean to the atmosphere are important for hurricane intensification, but the impact of sea spray generated by breaking waves on these fluxes is not well understood. We develop a new model for heat fluxes with spray that accounts for how waves control spray, and we apply this model to a set of five simulated hurricanes to better understand the broad range of ways that spray impacts heat fluxes in high wind conditions. We find that spray significantly affects heat fluxes in hurricanes and that impacts are strongly controlled by waves, which are not always correlated to winds. This research improves our understanding of how spray affects heat fluxes in hurricanes and provides a foundation for future studies investigating sea spray and its impacts on high-impact weather systems.
Abstract
Air–sea exchange in high winds is one of the most important but poorly represented processes in tropical cyclone (TC) prediction models. Effects of sea spray on air–sea heat fluxes in TCs are particularly difficult to model due to complex sea states and lack of observations in extreme wind and wave conditions. This study introduces a new sea-state-dependent air–sea heat flux parameterization with spray, which is developed using the Unified Wave Interface–Coupled Model (UWIN-CM). Impacts of spray on air–sea heat fluxes are investigated across a wide range of winds, waves, and atmospheric and ocean conditions in five TCs of various sizes and intensities. Spray generation with variable size distribution is explicitly represented by surface wave properties such as wave dissipation, significant wave height, and dominant phase speed, which may be uncorrelated with local winds. The sea-state-dependent spray mass flux is substantially different than a wind-dependent flux, especially when wave shoaling occurs with enhanced wave dissipation near the coast during TC landfall. Spray increases the air–sea enthalpy flux near the radius of maximum wind (RMW) by approximately 5%–20% when mean 10-m wind speed at the RMW reaches 40–50 m s−1. These values can be amplified significantly by coastal wave shoaling. Spray latent heat fluxes may be dampened in the eyewall due to high saturation ratio, and they consistently produce a moistening and cooling effect outside the eyewall. Spray strongly modifies the total sensible heat flux and can cause either a warming or cooling effect at the RMW depending on eyewall saturation ratio.
Significance Statement
Fluxes of heat and moisture from the ocean to the atmosphere are important for hurricane intensification, but the impact of sea spray generated by breaking waves on these fluxes is not well understood. We develop a new model for heat fluxes with spray that accounts for how waves control spray, and we apply this model to a set of five simulated hurricanes to better understand the broad range of ways that spray impacts heat fluxes in high wind conditions. We find that spray significantly affects heat fluxes in hurricanes and that impacts are strongly controlled by waves, which are not always correlated to winds. This research improves our understanding of how spray affects heat fluxes in hurricanes and provides a foundation for future studies investigating sea spray and its impacts on high-impact weather systems.
Abstract
It has been demonstrated that there is a globally unified linear relationship between the interannual variations of the fall-to-spring polar ozone accumulation and the winter-mean poleward eddy heat flux on the 100 hPa pressure surface. The foundation of this relationship is investigated using time-slice experiments on a chemistry–climate model with two levels of ozone-depleting substances (ODSs). The features of the transport field are interpreted by decomposing the horizontal ozone flux caused by the residual circulation into contributing processes including the eddy heat flux with the aid of the transformed Eulerian-mean momentum equation followed by rearrangement of terms. The linear relationship between the interannual variations of the fall-to-spring ozone buildup integrated poleward and above a reference point P
ref on a meridional plane and the poleward eddy heat flux during the corresponding period at P
ref is realized for each hemisphere implying that the interhemispheric unification should be treated with caution. This relationship is interpreted using the fact that the interannual variation of poleward ozone transport in the upper stratosphere is captured well by the vertical convergence of the constituent-based Eliassen–Palm (EP) flux (
Abstract
It has been demonstrated that there is a globally unified linear relationship between the interannual variations of the fall-to-spring polar ozone accumulation and the winter-mean poleward eddy heat flux on the 100 hPa pressure surface. The foundation of this relationship is investigated using time-slice experiments on a chemistry–climate model with two levels of ozone-depleting substances (ODSs). The features of the transport field are interpreted by decomposing the horizontal ozone flux caused by the residual circulation into contributing processes including the eddy heat flux with the aid of the transformed Eulerian-mean momentum equation followed by rearrangement of terms. The linear relationship between the interannual variations of the fall-to-spring ozone buildup integrated poleward and above a reference point P
ref on a meridional plane and the poleward eddy heat flux during the corresponding period at P
ref is realized for each hemisphere implying that the interhemispheric unification should be treated with caution. This relationship is interpreted using the fact that the interannual variation of poleward ozone transport in the upper stratosphere is captured well by the vertical convergence of the constituent-based Eliassen–Palm (EP) flux (
Abstract
One source of uncertainty associated with vertical wind shear (VWS) on tropical cyclone (TC) intensity evolution arises when the VWS becomes sufficiently strong such that the TC vortex is unable to overcome the inhibiting effects of VWS (the critical shear regime), resulting in a transition from vortex realignment and eventual reintensification to persistent vortex misalignment and failure of reintensification. To uncover the initiation mechanism of the behavioral transition, this study examines the dynamical evolution of the vortex tilt and precession through a set of CM1 ensemble simulations in moderate shear (7.5 m s−1) that includes the behavioral transition by systematically enhancing the TC vorticity amplitude aloft (vortex resiliency) at a restart point. In this critical shear regime, all experiments exhibit a common precession hiatus behavior, during which the tilt magnitude increases and later leads to divergent outcomes in intensity and tilt evolutions. Volume-averaged horizontal vorticity budget reveals an anomalous differential vorticity flux that emerges in the downtilt-left quadrant during the hiatus period. This differential vorticity flux generates horizontal vorticity that points toward the downtilt-right direction, simultaneously increasing the vortex tilt and slowing down the precession rate. This downtilt-left differential vorticity flux is due to midlevel vortex stretching at the rainband terminus region, where there is a transition from convective to stratiform precipitation. Meanwhile, the downdraft associated with stratiform precipitation also causes vorticity compression at the low levels. These results indicate that the stratiform rainband region is important for increasing the vortex tilt and pausing the precession.
Abstract
One source of uncertainty associated with vertical wind shear (VWS) on tropical cyclone (TC) intensity evolution arises when the VWS becomes sufficiently strong such that the TC vortex is unable to overcome the inhibiting effects of VWS (the critical shear regime), resulting in a transition from vortex realignment and eventual reintensification to persistent vortex misalignment and failure of reintensification. To uncover the initiation mechanism of the behavioral transition, this study examines the dynamical evolution of the vortex tilt and precession through a set of CM1 ensemble simulations in moderate shear (7.5 m s−1) that includes the behavioral transition by systematically enhancing the TC vorticity amplitude aloft (vortex resiliency) at a restart point. In this critical shear regime, all experiments exhibit a common precession hiatus behavior, during which the tilt magnitude increases and later leads to divergent outcomes in intensity and tilt evolutions. Volume-averaged horizontal vorticity budget reveals an anomalous differential vorticity flux that emerges in the downtilt-left quadrant during the hiatus period. This differential vorticity flux generates horizontal vorticity that points toward the downtilt-right direction, simultaneously increasing the vortex tilt and slowing down the precession rate. This downtilt-left differential vorticity flux is due to midlevel vortex stretching at the rainband terminus region, where there is a transition from convective to stratiform precipitation. Meanwhile, the downdraft associated with stratiform precipitation also causes vorticity compression at the low levels. These results indicate that the stratiform rainband region is important for increasing the vortex tilt and pausing the precession.
Abstract
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.
Abstract
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.
