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Abstract
The parametric behavior of an axially symmetric circulation induced by heat and momentum sources is analyzed in the context of a simple Boussinesq model. Implications for the Venus atmosphere are examined in the light of recent data.
For nearly inviscid flows in a stably stratified atmosphere, this work extends the analysis of Held and Hou to large thermal Rossby numbers (slowly rotating atmospheres). For parametric values appropriate to the Venus atmosphere, heat flux by the Hadley circulation leads to a temperature distribution nearly uniform with latitude, close to the asymptotic limit for a nonrotating atmosphere, while the zonal wind shows a strong polar jet but does not superrotate at the equator, contrary to what is observed on Venus.
For the Venus atmosphere to superrotate above the cloud base, where most of the solar radiation is deposited, momentum sources and sinks must be provided by asymmetric motions to offset transports by the mean meridional circulation. Diagnostically, the eddy momentum source/sink pattern required by a given meridional cell depends upon both the sign of the vertical zonal wind shear and the direction of the meridional flow. For a realistic vertical zonal wind profile, the implication is that the observed superrotation on Venus can be supported by alternating layers of sources and sinks.
Abstract
The parametric behavior of an axially symmetric circulation induced by heat and momentum sources is analyzed in the context of a simple Boussinesq model. Implications for the Venus atmosphere are examined in the light of recent data.
For nearly inviscid flows in a stably stratified atmosphere, this work extends the analysis of Held and Hou to large thermal Rossby numbers (slowly rotating atmospheres). For parametric values appropriate to the Venus atmosphere, heat flux by the Hadley circulation leads to a temperature distribution nearly uniform with latitude, close to the asymptotic limit for a nonrotating atmosphere, while the zonal wind shows a strong polar jet but does not superrotate at the equator, contrary to what is observed on Venus.
For the Venus atmosphere to superrotate above the cloud base, where most of the solar radiation is deposited, momentum sources and sinks must be provided by asymmetric motions to offset transports by the mean meridional circulation. Diagnostically, the eddy momentum source/sink pattern required by a given meridional cell depends upon both the sign of the vertical zonal wind shear and the direction of the meridional flow. For a realistic vertical zonal wind profile, the implication is that the observed superrotation on Venus can be supported by alternating layers of sources and sinks.
Abstract
Studies based on GCM ensemble forecasts have shown that an intensification of the cross-equatorial Hadley circulation associated with a latitudinal displacement of the zonally averaged convective heating in the Tropics can lead to remote warming in the winter high latitudes. This work further investigates this tropical–extratropical connection in a perpetual winter experiment using an idealized GCM without orography to focus on the role of transient eddies, and tests against observations using a multiyear reanalysis produced by the Goddard Earth Observing System-Version 1 (GEOS-1) Data Assimilation System.
The GCM results show that the intensification and poleward expansion of the cross-equatorial Hadley cell induced by a tropical heating shift can lead to westerly acceleration in the winter subtropics and enhanced vertical shear of the zonal wind in the subtropics and midlatitudes. The increased baroclinicity outside the Tropics is accompanied by reduced meridional temperature and potential vorticity (PV) gradients, consistent with enhanced PV mixing and increased poleward heat transport by baroclinic eddies. But if the changes in the Hadley cell are such that they produce a deceleration of the zonal wind in the winter subtropics, stronger temperature and PV gradients result in the winter extratropics. The midlatitude response to Hadley acceleration of the subtropical jet is dominated by enhanced power in low-frequency planetary-scale waves that peaks at zonal wavenumber 2 with a period of 40 days.
The extent to which this tropical–extratropical connection may be present in nature is tested using the GEOS-1 reanalysis for five austral winters from 1985 to 1989. Results show that the year-to-year variation in the zonally averaged extratropical temperature gradient in austral winters is correlated with the variation in the acceleration of the subtropical zonal wind by the winter Hadley cell. The anomaly correlation coefficients range from 0.80 to 0.92, depending on the statistical test. The positive Hadley acceleration anomaly in the subtropics during the 1988 austral winter is accompanied by stronger than normal zonal wind shears in the subtropics and midlatitudes, a colder troposphere in the midlatitudes, and a warmer pole. The extratropical temperature anomalies are associated with a reduced PV gradient, and the midlatitude geopotential height anomaly shows a spectral peak at wavenumbers 2–3 with periods between 40 and 60 days, similar to the idealized GCM results. The implication of this study is that the Hadley circulation may play a role in modulating the temperature difference between middle and high latitudes by modifying the zonal wind shear in the subtropics and midlatitudes.
Abstract
Studies based on GCM ensemble forecasts have shown that an intensification of the cross-equatorial Hadley circulation associated with a latitudinal displacement of the zonally averaged convective heating in the Tropics can lead to remote warming in the winter high latitudes. This work further investigates this tropical–extratropical connection in a perpetual winter experiment using an idealized GCM without orography to focus on the role of transient eddies, and tests against observations using a multiyear reanalysis produced by the Goddard Earth Observing System-Version 1 (GEOS-1) Data Assimilation System.
The GCM results show that the intensification and poleward expansion of the cross-equatorial Hadley cell induced by a tropical heating shift can lead to westerly acceleration in the winter subtropics and enhanced vertical shear of the zonal wind in the subtropics and midlatitudes. The increased baroclinicity outside the Tropics is accompanied by reduced meridional temperature and potential vorticity (PV) gradients, consistent with enhanced PV mixing and increased poleward heat transport by baroclinic eddies. But if the changes in the Hadley cell are such that they produce a deceleration of the zonal wind in the winter subtropics, stronger temperature and PV gradients result in the winter extratropics. The midlatitude response to Hadley acceleration of the subtropical jet is dominated by enhanced power in low-frequency planetary-scale waves that peaks at zonal wavenumber 2 with a period of 40 days.
The extent to which this tropical–extratropical connection may be present in nature is tested using the GEOS-1 reanalysis for five austral winters from 1985 to 1989. Results show that the year-to-year variation in the zonally averaged extratropical temperature gradient in austral winters is correlated with the variation in the acceleration of the subtropical zonal wind by the winter Hadley cell. The anomaly correlation coefficients range from 0.80 to 0.92, depending on the statistical test. The positive Hadley acceleration anomaly in the subtropics during the 1988 austral winter is accompanied by stronger than normal zonal wind shears in the subtropics and midlatitudes, a colder troposphere in the midlatitudes, and a warmer pole. The extratropical temperature anomalies are associated with a reduced PV gradient, and the midlatitude geopotential height anomaly shows a spectral peak at wavenumbers 2–3 with periods between 40 and 60 days, similar to the idealized GCM results. The implication of this study is that the Hadley circulation may play a role in modulating the temperature difference between middle and high latitudes by modifying the zonal wind shear in the subtropics and midlatitudes.
Abstract
The hypothesis is advanced that a latitudinal shift in the tropical convective heating pattern can significantly alter temperatures in the extratropics. Results of a simplified GCM show that the shift of a prescribed tropical heating toward the summer pole, on time scales longer than a few weeks, leads to a more intense cross-equatorial “winter” Hadley circulation, enhanced upper-level tropical easterlies, and a slightly stronger subtropical winter jet, accompanied by warming at the winter middle and high latitudes as a result of increased dynamical heating. The indications are that there is a robust connection between the net dynamic heating in the extratropics and the implied changes in the subtropical wind shear resulting from adjustments in the Hadley circulation associated with convective heating displacements in the tropics. The implications are that (i) the low-frequency temporal variability in the Hadley circulation may play an important role in modulating wave transport in the winter extratropics, (ii) the global climate may be sensitive to those processes that control deep cumulus convection in the tropics, and (iii) systematic temperature biases in GCMs may be reduced by improving the tropical rainfall simulation.
Abstract
The hypothesis is advanced that a latitudinal shift in the tropical convective heating pattern can significantly alter temperatures in the extratropics. Results of a simplified GCM show that the shift of a prescribed tropical heating toward the summer pole, on time scales longer than a few weeks, leads to a more intense cross-equatorial “winter” Hadley circulation, enhanced upper-level tropical easterlies, and a slightly stronger subtropical winter jet, accompanied by warming at the winter middle and high latitudes as a result of increased dynamical heating. The indications are that there is a robust connection between the net dynamic heating in the extratropics and the implied changes in the subtropical wind shear resulting from adjustments in the Hadley circulation associated with convective heating displacements in the tropics. The implications are that (i) the low-frequency temporal variability in the Hadley circulation may play an important role in modulating wave transport in the winter extratropics, (ii) the global climate may be sensitive to those processes that control deep cumulus convection in the tropics, and (iii) systematic temperature biases in GCMs may be reduced by improving the tropical rainfall simulation.
Abstract
The possibility of empirically correcting a nonlinear dynamical model is examined. The empirical correction is constructed by fitting a first-order Markov model to the forecast errors using initial conditions as predictors. The dynamical operator of the Markov model can then be subtracted from the original forecast model to correct the forecast. The procedure is based on an earlier work by Leith, suitably modified for practical applications. The effects of analysis errors and finite difference approximations are analyzed. It is shown that uncorrelated analysis errors produce spurious terms in the empirical correction operator that act to damp eddy variance at a rate inversely proportional to the lead time used to estimate the Markov model. The finite difference approximation is appropriate as long as the forecast errors grow linearly with lead time. These restrictions can be interpreted as setting lower and upper limits on the lead time, respectively, and can be checked without knowing the true state exactly. The procedure is sensitive to sampling errors, but this problem was not explored.
These formal conclusions are tested on a nonlinear quasigeostrophic model in which model error is created by changing the model parameters. A “systematic error” correction, which does not depend on state and is held constant throughout the integration, does not improve the forecast skill of the model because the contrived error is primarily state dependent. However, an empirical correction, which depends on instantaneous state, improves the forecast skill of the model by 10 days, and further iterations extend the skill to the limit imposed by observation error (about 20 days in this example).
Abstract
The possibility of empirically correcting a nonlinear dynamical model is examined. The empirical correction is constructed by fitting a first-order Markov model to the forecast errors using initial conditions as predictors. The dynamical operator of the Markov model can then be subtracted from the original forecast model to correct the forecast. The procedure is based on an earlier work by Leith, suitably modified for practical applications. The effects of analysis errors and finite difference approximations are analyzed. It is shown that uncorrelated analysis errors produce spurious terms in the empirical correction operator that act to damp eddy variance at a rate inversely proportional to the lead time used to estimate the Markov model. The finite difference approximation is appropriate as long as the forecast errors grow linearly with lead time. These restrictions can be interpreted as setting lower and upper limits on the lead time, respectively, and can be checked without knowing the true state exactly. The procedure is sensitive to sampling errors, but this problem was not explored.
These formal conclusions are tested on a nonlinear quasigeostrophic model in which model error is created by changing the model parameters. A “systematic error” correction, which does not depend on state and is held constant throughout the integration, does not improve the forecast skill of the model because the contrived error is primarily state dependent. However, an empirical correction, which depends on instantaneous state, improves the forecast skill of the model by 10 days, and further iterations extend the skill to the limit imposed by observation error (about 20 days in this example).
Abstract
Currently, operational weather forecasting systems use observations to optimize the initial state of a forecast without considering possible model deficiencies. For precipitation assimilation, this could be an issue since precipitation observations, unlike conventional data, do not directly provide information on the atmospheric state but are related to the state variables through parameterized moist physics with simplifying assumptions. Precipitation observation operators are comparatively less accurate than those for conventional data or observables in clear-sky regions, which can limit data usage not because of issues with observations, but with the model. The challenge lies in exploring new ways to make effective use of precipitation data in the presence of model errors.
This study continues the investigation of variational algorithms for precipitation assimilation using column model physics as a weak constraint. The strategy is to develop techniques to make online estimation and correction of model errors to improve the precipitation observation operator during the assimilation cycle. Earlier studies have shown that variational continuous assimilation (VCA) of tropical rainfall using moisture tendency correction can improve Goddard Earth Observing System 3 (GEOS-3) global analyses and forecasts. Here results are presented from a 4-yr GEOS-3 reanalysis assimilating Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Special Sensor Microwave Imager (SSM/I) tropical rainfall using the VCA scheme. Comparisons with NCEP operational analysis and the 40-yr ECMWF Re-Analysis (ERA-40) show that the GEOS-3 reanalysis is significantly better at replicating the intensity and variability of tropical precipitation systems ranging from a few days to interannual time scales. As a further refinement of rainfall assimilation using the VCA scheme, a variational algorithm for assimilating TMI latent heating retrievals using semiempirical parameters in the model moist physics as control variables is described and initial test results are presented.
Abstract
Currently, operational weather forecasting systems use observations to optimize the initial state of a forecast without considering possible model deficiencies. For precipitation assimilation, this could be an issue since precipitation observations, unlike conventional data, do not directly provide information on the atmospheric state but are related to the state variables through parameterized moist physics with simplifying assumptions. Precipitation observation operators are comparatively less accurate than those for conventional data or observables in clear-sky regions, which can limit data usage not because of issues with observations, but with the model. The challenge lies in exploring new ways to make effective use of precipitation data in the presence of model errors.
This study continues the investigation of variational algorithms for precipitation assimilation using column model physics as a weak constraint. The strategy is to develop techniques to make online estimation and correction of model errors to improve the precipitation observation operator during the assimilation cycle. Earlier studies have shown that variational continuous assimilation (VCA) of tropical rainfall using moisture tendency correction can improve Goddard Earth Observing System 3 (GEOS-3) global analyses and forecasts. Here results are presented from a 4-yr GEOS-3 reanalysis assimilating Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Special Sensor Microwave Imager (SSM/I) tropical rainfall using the VCA scheme. Comparisons with NCEP operational analysis and the 40-yr ECMWF Re-Analysis (ERA-40) show that the GEOS-3 reanalysis is significantly better at replicating the intensity and variability of tropical precipitation systems ranging from a few days to interannual time scales. As a further refinement of rainfall assimilation using the VCA scheme, a variational algorithm for assimilating TMI latent heating retrievals using semiempirical parameters in the model moist physics as control variables is described and initial test results are presented.
Abstract
A high-resolution surface rainfall product is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating or nonprecipitating sample, statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented. Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors’ detection capabilities.
It is found that statistics of rain characteristics have large seasonal and geographical variations across the continental United States. Although heavy rain events (>10 mm h−1) only occupy 2.6% of total rain occurrence, they may contribute to 27% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%) than heavy rain events, can also make important contributions (15%) to the total rain volume.
For minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and future spaceborne precipitation radars, there are about 43% and 11% of total rain occurrence below these thresholds, and they respectively represent 7% and 0.8% of total rain volume. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rates around 1 mm h−1, the missed light rain events may account for 70% of rain occurrence and 16% of rain volume.
Statistics of rain characteristics are also examined on domains with different temporal and spatial resolutions. Current issues in estimates of rain characteristics from satellite measurements and model outputs are discussed.
Abstract
A high-resolution surface rainfall product is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating or nonprecipitating sample, statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented. Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors’ detection capabilities.
It is found that statistics of rain characteristics have large seasonal and geographical variations across the continental United States. Although heavy rain events (>10 mm h−1) only occupy 2.6% of total rain occurrence, they may contribute to 27% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%) than heavy rain events, can also make important contributions (15%) to the total rain volume.
For minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and future spaceborne precipitation radars, there are about 43% and 11% of total rain occurrence below these thresholds, and they respectively represent 7% and 0.8% of total rain volume. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rates around 1 mm h−1, the missed light rain events may account for 70% of rain occurrence and 16% of rain volume.
Statistics of rain characteristics are also examined on domains with different temporal and spatial resolutions. Current issues in estimates of rain characteristics from satellite measurements and model outputs are discussed.
Abstract
Critical-level absorption of a continuous spectrum of vertically propagating gravity waves is proposed as the mechanism for supporting the superrotation in the deep Venus atmosphere (below the cloud deck). It is shown that the observed westerly zonal wind effectively separates regions where waves of opposite phase speeds are absorbed, leading to westerly mean-flow acceleration below the clouds and easterly above. Using the diagnostic results of Hou and Goody, we obtain a quantitative assessment of the required wave spectrum and fluxes of energy and momentum, and show that they are compatible with observational constraints.
Abstract
Critical-level absorption of a continuous spectrum of vertically propagating gravity waves is proposed as the mechanism for supporting the superrotation in the deep Venus atmosphere (below the cloud deck). It is shown that the observed westerly zonal wind effectively separates regions where waves of opposite phase speeds are absorbed, leading to westerly mean-flow acceleration below the clouds and easterly above. Using the diagnostic results of Hou and Goody, we obtain a quantitative assessment of the required wave spectrum and fluxes of energy and momentum, and show that they are compatible with observational constraints.
Abstract
For the solar heating and zonal wind profiles observed in the Venus atmosphere (below 80 km) we have calculated the eddy source pattern required to maintain the zonally averaged circulation.
In the cloud-top region (45-75 km) the calculated residual meridional circulation corresponds to multiple direct and indirect cells in the vertical, whose depths are controlled by the scales of solar heating and eddy sources. For the amount of small-scale diffusion suggested by in situ measurements, the circulation is close to the nearly inviscid limit, and advections by the mean circulation must be balanced by eddy sources. In the presence of mean meridional transports, the observed zonal superrotation can be supported by alternating layers of eddy sources and sinks (i.e., Eliassen-Palm flux divergences or convergences), which may possibly be caused by thermal tides.
Below the cloud decks, the effect of meridional motions is small, and eddy sources are required to balance diffusion (if diffusion is as large as measurements indicate). Near the lower model boundary, differential solar heating forces a shallow Hadley cell which controls surface winds and ensures that the net surface torque vanishes in a steady state.
Abstract
For the solar heating and zonal wind profiles observed in the Venus atmosphere (below 80 km) we have calculated the eddy source pattern required to maintain the zonally averaged circulation.
In the cloud-top region (45-75 km) the calculated residual meridional circulation corresponds to multiple direct and indirect cells in the vertical, whose depths are controlled by the scales of solar heating and eddy sources. For the amount of small-scale diffusion suggested by in situ measurements, the circulation is close to the nearly inviscid limit, and advections by the mean circulation must be balanced by eddy sources. In the presence of mean meridional transports, the observed zonal superrotation can be supported by alternating layers of eddy sources and sinks (i.e., Eliassen-Palm flux divergences or convergences), which may possibly be caused by thermal tides.
Below the cloud decks, the effect of meridional motions is small, and eddy sources are required to balance diffusion (if diffusion is as large as measurements indicate). Near the lower model boundary, differential solar heating forces a shallow Hadley cell which controls surface winds and ensures that the net surface torque vanishes in a steady state.
Abstract
We have extended our previous calculations of zonally averaged temperature, circulation, and eddy source requirements for the Venus atmosphere to include the region from the surface to 95 km, using a Curtis matrix method for the radiation calculation. We conclude: (i) The cloud top circulation is not significantly changed from our previous calculations based on a radiative-relaxation method, but large differences occur in the lower atmosphere. (ii) The physical and dynamical states of the atmospheric regions above and below the cloud base are effectively independent and are equally important for accounting for the 4-day circulation at the cloud tops. (iii) Above the cloud base, the circulation is effectively inviscid and the eddy source requirements at the low latitudes are consistent with the mean-flow forcing by the semidiurnal tide. (iv) The circulation below the clouds is important compared to viscous dissipation above the lowest scale height. We discuss possible mechanisms for satisfying the tropical eddy source requirements in the lower atmosphere.
Abstract
We have extended our previous calculations of zonally averaged temperature, circulation, and eddy source requirements for the Venus atmosphere to include the region from the surface to 95 km, using a Curtis matrix method for the radiation calculation. We conclude: (i) The cloud top circulation is not significantly changed from our previous calculations based on a radiative-relaxation method, but large differences occur in the lower atmosphere. (ii) The physical and dynamical states of the atmospheric regions above and below the cloud base are effectively independent and are equally important for accounting for the 4-day circulation at the cloud tops. (iii) Above the cloud base, the circulation is effectively inviscid and the eddy source requirements at the low latitudes are consistent with the mean-flow forcing by the semidiurnal tide. (iv) The circulation below the clouds is important compared to viscous dissipation above the lowest scale height. We discuss possible mechanisms for satisfying the tropical eddy source requirements in the lower atmosphere.
Abstract
We obtain an exact nonlinear stationary solution for barotropic waves in a β-plane channel and show that it can be excited under a range of initial conditions. Results show that a finite-amplitude wave in a constant shear flow, given an initial phase tilt against the shear and a sufficient initial amplitude, interacts with the mean flow to produce a nearly steady state close to the exact stationery solution. This equilibration process involves nonlinear transients; in particular, as die flow equilibrates, the emergence of critical levels is accompanied by the neutralization of local mean vorticity gradients at these levels, thus allowing the solution to attain a nonsingular model structure.
Abstract
We obtain an exact nonlinear stationary solution for barotropic waves in a β-plane channel and show that it can be excited under a range of initial conditions. Results show that a finite-amplitude wave in a constant shear flow, given an initial phase tilt against the shear and a sufficient initial amplitude, interacts with the mean flow to produce a nearly steady state close to the exact stationery solution. This equilibration process involves nonlinear transients; in particular, as die flow equilibrates, the emergence of critical levels is accompanied by the neutralization of local mean vorticity gradients at these levels, thus allowing the solution to attain a nonsingular model structure.
