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- Author or Editor: Kuan-Man Xu x
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Abstract
A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance.
The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.
Abstract
A new method is proposed to compare statistical differences between summary histograms, which are the histograms summed over a large ensemble of individual histograms. It consists of choosing a distance statistic for measuring the difference between summary histograms and using a bootstrap procedure to calculate the statistical significance level. Bootstrapping is an approach to statistical inference that makes few assumptions about the underlying probability distribution that describes the data. Three distance statistics are compared in this study. They are the Euclidean distance, the Jeffries–Matusita distance, and the Kuiper distance.
The data used in testing the bootstrap method are satellite measurements of cloud systems called “cloud objects.” Each cloud object is defined as a contiguous region/patch composed of individual footprints or fields of view. A histogram of measured values over footprints is generated for each parameter of each cloud object, and then summary histograms are accumulated over all individual histograms in a given cloud-object size category. The results of statistical hypothesis tests using all three distances as test statistics are generally similar, indicating the validity of the proposed method. The Euclidean distance is determined to be most suitable after comparing the statistical tests of several parameters with distinct probability distributions among three cloud-object size categories. Impacts on the statistical significance levels resulting from differences in the total lengths of satellite footprint data between two size categories are also discussed.
Abstract
This study presents an approach that converts the vertical profiles of grid-averaged cloud properties from large-scale models to probability density functions (pdfs) of subgrid-cell cloud physical properties measured at satellite footprints. Cloud physical and radiative properties, rather than just cloud and precipitation occurrences, of assimilated cloud systems by the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis (EOA) and 40-yr ECMWF Re-Analysis (ERA-40) are validated against those obtained from Earth Observing System satellite cloud object data for the January–August 1998 and March 2000 periods. These properties include the ice water path (IWP), cloud-top height and temperature, cloud optical depth, and solar and infrared radiative fluxes. Each cloud object, a contiguous region with similar cloud physical properties, is temporally and spatially matched with EOA and ERA-40 data. Results indicate that most pdfs of EOA and ERA-40 cloud physical and radiative properties agree with those of satellite observations of the tropical deep convective cloud object type for the January–August 1998 period. There are, however, significant discrepancies in selected ranges of the cloud property pdfs such as the upper range of EOA cloud-top height. A major discrepancy is that the dependence of the pdfs on the cloud object size for both EOA and ERA-40 is not as strong as in the observations. Modifications to the cloud parameterization in ECMWF that occurred in October 1999 eliminate the clouds near the tropopause but shift power of the pdf to lower cloud-top heights and greatly reduce the ranges of IWP and cloud optical depth pdfs. These features persist in ERA-40 due to the use of the same cloud parameterizations. The less sophisticated data assimilation technique and the lack of snow water content information in ERA-40, not the larger horizontal grid spacing, are also responsible for the disagreements with observed pdfs of cloud physical properties, although the detection rates of cloud object occurrence are improved for small-size categories. A possible improvement to the convective parameterization is to introduce a stronger dependence of updraft penetration heights on grid-cell dynamics.
Abstract
This study presents an approach that converts the vertical profiles of grid-averaged cloud properties from large-scale models to probability density functions (pdfs) of subgrid-cell cloud physical properties measured at satellite footprints. Cloud physical and radiative properties, rather than just cloud and precipitation occurrences, of assimilated cloud systems by the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis (EOA) and 40-yr ECMWF Re-Analysis (ERA-40) are validated against those obtained from Earth Observing System satellite cloud object data for the January–August 1998 and March 2000 periods. These properties include the ice water path (IWP), cloud-top height and temperature, cloud optical depth, and solar and infrared radiative fluxes. Each cloud object, a contiguous region with similar cloud physical properties, is temporally and spatially matched with EOA and ERA-40 data. Results indicate that most pdfs of EOA and ERA-40 cloud physical and radiative properties agree with those of satellite observations of the tropical deep convective cloud object type for the January–August 1998 period. There are, however, significant discrepancies in selected ranges of the cloud property pdfs such as the upper range of EOA cloud-top height. A major discrepancy is that the dependence of the pdfs on the cloud object size for both EOA and ERA-40 is not as strong as in the observations. Modifications to the cloud parameterization in ECMWF that occurred in October 1999 eliminate the clouds near the tropopause but shift power of the pdf to lower cloud-top heights and greatly reduce the ranges of IWP and cloud optical depth pdfs. These features persist in ERA-40 due to the use of the same cloud parameterizations. The less sophisticated data assimilation technique and the lack of snow water content information in ERA-40, not the larger horizontal grid spacing, are also responsible for the disagreements with observed pdfs of cloud physical properties, although the detection rates of cloud object occurrence are improved for small-size categories. A possible improvement to the convective parameterization is to introduce a stronger dependence of updraft penetration heights on grid-cell dynamics.
Abstract
Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble.
The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using “quick-look” and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.
Abstract
Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble.
The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using “quick-look” and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.
Abstract
Simulated data from the UCLA Cumulus Ensemble Model (CEM) are analyzed to partition mass, heat, and moisture budgets of cumulus ensembles into convective and stratiform components. A method based primarily on the horizontal distribution of maximum cloud draft strength below the melting level in a CEM grid column has been developed for this analysis. The stratiform region includes both precipitating and nonprecipitating anvils.
The convective and stratiform components of mass, heat, and moisture budgets are distinctly different, in qualitative agreement with previous observational and modeling studies. In the heat and moisture budgets, the difference is due mainly to that in the phase change processes. In general, condensation/deposition dominate evaporation/sublimation in the convective region. All of these processes are more or less equally important in the stratiform region. Freezing occurs only in the convective region. Sublimation from snow/graupel in the stratiform region is much more important than in the convective region. Radiative effects in the stratiform component of the heat budget are as important as effects of phase changes, while radiative effects in the convective component are far less significant.
The importance of the convergences of eddy fluxes, especially in the moisture budget, is confirmed. The convergences in the stratiform component are found to be parameterizable only if the vertical motions and the properties of both mesoscale updrafts and mesoscale downdrafts are known. The horizontal inhomogeneity within mesoscale updrafts/downdrafts is of secondary importance for parameterizing the convergences of eddy fluxes in the stratiform component.
Abstract
Simulated data from the UCLA Cumulus Ensemble Model (CEM) are analyzed to partition mass, heat, and moisture budgets of cumulus ensembles into convective and stratiform components. A method based primarily on the horizontal distribution of maximum cloud draft strength below the melting level in a CEM grid column has been developed for this analysis. The stratiform region includes both precipitating and nonprecipitating anvils.
The convective and stratiform components of mass, heat, and moisture budgets are distinctly different, in qualitative agreement with previous observational and modeling studies. In the heat and moisture budgets, the difference is due mainly to that in the phase change processes. In general, condensation/deposition dominate evaporation/sublimation in the convective region. All of these processes are more or less equally important in the stratiform region. Freezing occurs only in the convective region. Sublimation from snow/graupel in the stratiform region is much more important than in the convective region. Radiative effects in the stratiform component of the heat budget are as important as effects of phase changes, while radiative effects in the convective component are far less significant.
The importance of the convergences of eddy fluxes, especially in the moisture budget, is confirmed. The convergences in the stratiform component are found to be parameterizable only if the vertical motions and the properties of both mesoscale updrafts and mesoscale downdrafts are known. The horizontal inhomogeneity within mesoscale updrafts/downdrafts is of secondary importance for parameterizing the convergences of eddy fluxes in the stratiform component.
Abstract
This study examines the sensitivity of diagnosed radiative fluxes and heating rates to different treatments of cloud microphysics among cloud-resolving models (CRMs). The domain-averaged CRM outputs are used in this calculation. The impacts of the cloud overlap and uniform hydrometeor assumptions are examined using outputs having spatially varying cloud fields from a single CRM. It is found that the cloud overlap assumption impacts the diagnosis more significantly than the uniform hydrometeor assumption for all radiative fluxes. This is also the case for the longwave radiative cooling rate except for a layer above 7 km where it is more significantly impacted by the uniform hydrometeor assumption. The radiative cooling above upper-tropospheric anvils and the warming below these clouds are overestimated by about 0.5 K day−1 using the domain-averaged outputs. These results are used to further quantify intermodel differences in radiative properties due to different treatments of cloud microphysics among 10 CRMs. The magnitudes of the intermodel differences, as measured by the deviations from the consensus of 10 CRMs, are found to be smaller than those due to the cloud overlap assumption and comparable to those due to the uniform hydrometeor assumption for most shortwave radiative fluxes and the net radiative fluxes at the top of the atmosphere (TOA) and at the surface. For all longwave radiative fluxes, they are smaller than those due to cloud overlap and uniform hydrometeor assumptions. The consensus of all diagnosed radiative fluxes except for the surface downward shortwave flux agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements.
Abstract
This study examines the sensitivity of diagnosed radiative fluxes and heating rates to different treatments of cloud microphysics among cloud-resolving models (CRMs). The domain-averaged CRM outputs are used in this calculation. The impacts of the cloud overlap and uniform hydrometeor assumptions are examined using outputs having spatially varying cloud fields from a single CRM. It is found that the cloud overlap assumption impacts the diagnosis more significantly than the uniform hydrometeor assumption for all radiative fluxes. This is also the case for the longwave radiative cooling rate except for a layer above 7 km where it is more significantly impacted by the uniform hydrometeor assumption. The radiative cooling above upper-tropospheric anvils and the warming below these clouds are overestimated by about 0.5 K day−1 using the domain-averaged outputs. These results are used to further quantify intermodel differences in radiative properties due to different treatments of cloud microphysics among 10 CRMs. The magnitudes of the intermodel differences, as measured by the deviations from the consensus of 10 CRMs, are found to be smaller than those due to the cloud overlap assumption and comparable to those due to the uniform hydrometeor assumption for most shortwave radiative fluxes and the net radiative fluxes at the top of the atmosphere (TOA) and at the surface. For all longwave radiative fluxes, they are smaller than those due to cloud overlap and uniform hydrometeor assumptions. The consensus of all diagnosed radiative fluxes except for the surface downward shortwave flux agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements.
Abstract
Implementation of a broadband radiation parameterization in the UCLA cumulus ensemble model (CEM) is discussed in this study, with emphasis on the specific problems associated with adequate calculation of radiative transfer processes in the CEM. The radiation parameterization is based on the Harshvardhan et al. broadband radiative transfer model with cloud optical properties as formulated by Stephens et al. The lowest CEM layer is divided into a thick layer and a very thin layer near the surface for the longwave radiation calculation. Diagnostic tests have been performed to compare the accuracy of this parameterization with results from a more complicated radiative transfer model.
Simulations with fully interactive radiation are performed to compare two methods for invoking the radiation module. The time interval for calling the radiation module has to be very small for the conventional method, which keeps the radiative heating rate constant until the radiation module is called again. It can be larger for the “accumulated” method, which accumulates and averages cloud microphysical properties within the time interval and applies the amount of radiative heating over the time interval at the time when the radiation module is called. Additional sensitivity tests are also performed to justify the omission of the radiative effects of rapidly falling precipitating particles.
Other sensitivity tests are related to the adequacy of the domain size and horizontal resolution for studying the cloud-radiation interaction problems discussed in Part II.
Abstract
Implementation of a broadband radiation parameterization in the UCLA cumulus ensemble model (CEM) is discussed in this study, with emphasis on the specific problems associated with adequate calculation of radiative transfer processes in the CEM. The radiation parameterization is based on the Harshvardhan et al. broadband radiative transfer model with cloud optical properties as formulated by Stephens et al. The lowest CEM layer is divided into a thick layer and a very thin layer near the surface for the longwave radiation calculation. Diagnostic tests have been performed to compare the accuracy of this parameterization with results from a more complicated radiative transfer model.
Simulations with fully interactive radiation are performed to compare two methods for invoking the radiation module. The time interval for calling the radiation module has to be very small for the conventional method, which keeps the radiative heating rate constant until the radiation module is called again. It can be larger for the “accumulated” method, which accumulates and averages cloud microphysical properties within the time interval and applies the amount of radiative heating over the time interval at the time when the radiation module is called. Additional sensitivity tests are also performed to justify the omission of the radiative effects of rapidly falling precipitating particles.
Other sensitivity tests are related to the adequacy of the domain size and horizontal resolution for studying the cloud-radiation interaction problems discussed in Part II.
Abstract
The two-dimensional UCLA cumulus ensemble model is used to examine the impact of cloud-radiation interactions on the macroscopic behavior of cumulus ensembles. Two sets of simulations are performed with noninteractive (NI) and fully interactive (FI) radiative transfer, and with prescribed large-scale advective effects. The time-varying horizontally averaged radiative heating rates QR from the FI simulators are used to prescribe the time-varying, horizontally homogeneous QR in the NI simulations. The effects of both longwave radiation and diurnally varying solar radiation are examined from these two sets of simulations.
The diurnally varying solar radiation can drive a diurnal cycle of deep convection over the tropical oceans by stabbing the large-scale environment during the daytime relative to the nighttime. The results presented in this study confirm the dominant role of the direct radiation-convection interaction mechanism for the diurnal cycle of oceanic precipitation. Comparison of the results of the FI and NI simulations suggests that the horizontal differential heating mechanism of Gray and Jacobson plays a secondary role in the diurnal cycle of precipitation. The presence of interactive radiation in the FI simulation, however, postpones the maxima and minima of convective activity due to the greater persistence of upper-tropospheric clouds. These clouds can survive against the solar absorption effects during the daytime.
The impact of longwave-cloud interactions on the macroscopic behavior of cumulus ensembles is a slightly stronger modulation of cumulus activity by large-scale processes. Upper-tropospheric clouds are somewhat more active and last longer in the presence of interactive radiation. The longwave-cloud interactions are achieved by the so called continuously destabilizing mechanism, which has its greatest effects on thin cloud layers.
Abstract
The two-dimensional UCLA cumulus ensemble model is used to examine the impact of cloud-radiation interactions on the macroscopic behavior of cumulus ensembles. Two sets of simulations are performed with noninteractive (NI) and fully interactive (FI) radiative transfer, and with prescribed large-scale advective effects. The time-varying horizontally averaged radiative heating rates QR from the FI simulators are used to prescribe the time-varying, horizontally homogeneous QR in the NI simulations. The effects of both longwave radiation and diurnally varying solar radiation are examined from these two sets of simulations.
The diurnally varying solar radiation can drive a diurnal cycle of deep convection over the tropical oceans by stabbing the large-scale environment during the daytime relative to the nighttime. The results presented in this study confirm the dominant role of the direct radiation-convection interaction mechanism for the diurnal cycle of oceanic precipitation. Comparison of the results of the FI and NI simulations suggests that the horizontal differential heating mechanism of Gray and Jacobson plays a secondary role in the diurnal cycle of precipitation. The presence of interactive radiation in the FI simulation, however, postpones the maxima and minima of convective activity due to the greater persistence of upper-tropospheric clouds. These clouds can survive against the solar absorption effects during the daytime.
The impact of longwave-cloud interactions on the macroscopic behavior of cumulus ensembles is a slightly stronger modulation of cumulus activity by large-scale processes. Upper-tropospheric clouds are somewhat more active and last longer in the presence of interactive radiation. The longwave-cloud interactions are achieved by the so called continuously destabilizing mechanism, which has its greatest effects on thin cloud layers.
Abstract
The influence of large-scale advective cooling and/or moistening on the quasi-equilibrium behavior of simulated, tropical oceanic cumulus ensembles is examined in this study. Two sensitivity simulations are performed by imposing time varying/invariant large-scale advective cooling effects and time invariant/varying large-scale advective moistening effects. The results are compared with a control simulation performed with both large-scale advective cooling and moistening effects that are time varying.
It is found that the generalized convective available potential energy (GCAPE) tendency is almost one order of magnitude smaller than the GCAPE production in all simulations. This indicates that the quasi-equilibrium assumption of Arakawa and Schubert is well justified. The higher-order behavior of quasi-equilibrium cumulus ensemble is then examined. It is found that the GCAPE variations are nearly equally contributed by temperature and water vapor variations in the control simulation. In the sensitivity simulations, they are mainly contributed by the temperature (water vapor) variations even though the imposed large-scale advective cooling (moistening) is time invariant. A significant finding of this study is that there is a negative lag correlation between GCAPE and the intensity of cumulus convection. The lag corresponding to the largest negative correlation ranges from 1 to 5 h in various simulations. The existence of a negative correlation and the maximum lag of a few hours is independent of the character and period of the imposed large-scale advective forcing. The maximum lag can be interpreted as the adjustment timescale from disequilibrium to quasi-equilibrium states in the presence of time-varying large-scale forcing.
Abstract
The influence of large-scale advective cooling and/or moistening on the quasi-equilibrium behavior of simulated, tropical oceanic cumulus ensembles is examined in this study. Two sensitivity simulations are performed by imposing time varying/invariant large-scale advective cooling effects and time invariant/varying large-scale advective moistening effects. The results are compared with a control simulation performed with both large-scale advective cooling and moistening effects that are time varying.
It is found that the generalized convective available potential energy (GCAPE) tendency is almost one order of magnitude smaller than the GCAPE production in all simulations. This indicates that the quasi-equilibrium assumption of Arakawa and Schubert is well justified. The higher-order behavior of quasi-equilibrium cumulus ensemble is then examined. It is found that the GCAPE variations are nearly equally contributed by temperature and water vapor variations in the control simulation. In the sensitivity simulations, they are mainly contributed by the temperature (water vapor) variations even though the imposed large-scale advective cooling (moistening) is time invariant. A significant finding of this study is that there is a negative lag correlation between GCAPE and the intensity of cumulus convection. The lag corresponding to the largest negative correlation ranges from 1 to 5 h in various simulations. The existence of a negative correlation and the maximum lag of a few hours is independent of the character and period of the imposed large-scale advective forcing. The maximum lag can be interpreted as the adjustment timescale from disequilibrium to quasi-equilibrium states in the presence of time-varying large-scale forcing.
Abstract
This study describes some results from several simulations of cumulus ensembles at the Southern Great Plains site of the Atmospheric Radiation Measurement (ARM) program during the July 1995 Intensive Observation Period (IOP). A 2D cloud ensemble model (CEM) is used to simulate the macroscopic properties of midlatitude cumulus ensembles. The observed large-scale, horizontal advective tendencies and large-scale vertical velocity or the total advective tendencies are used to drive the CEM, in addition to nudging of the simulated, domain-averaged horizontal wind components toward the observed winds.
A detailed comparison with available observations and tropical convection is made in this study. In general, the CEM-simulated results agree reasonably well with the available observations from the July 1995 IOP. The differences between simulations and observations are, however, much larger than those obtained in tropical cases, especially those based on the Global Atmospheric Research Program Atlantic Tropical Experiment Phase III data. Significant differences exist between the statistical properties of tropical and midlatitude cumulus convection, especially in the vertical structures of the cumulus mass fluxes, apparent heat source (Q 1), and apparent moisture sink (Q 2). The strong variations of the subcloud-layer thermodynamic structure and the surface fluxes in midlatitude continents have large impacts on the heat and moisture budgets. The radiative budgets and satellite-observed cloud amounts are also compared with observations. Although the agreements are reasonably good, some deficiencies of the simulations and inadequate accuracy of large-scale advective tendencies can be clearly seen from the comparisons. Sensitivity tests are performed to address these issues.
Abstract
This study describes some results from several simulations of cumulus ensembles at the Southern Great Plains site of the Atmospheric Radiation Measurement (ARM) program during the July 1995 Intensive Observation Period (IOP). A 2D cloud ensemble model (CEM) is used to simulate the macroscopic properties of midlatitude cumulus ensembles. The observed large-scale, horizontal advective tendencies and large-scale vertical velocity or the total advective tendencies are used to drive the CEM, in addition to nudging of the simulated, domain-averaged horizontal wind components toward the observed winds.
A detailed comparison with available observations and tropical convection is made in this study. In general, the CEM-simulated results agree reasonably well with the available observations from the July 1995 IOP. The differences between simulations and observations are, however, much larger than those obtained in tropical cases, especially those based on the Global Atmospheric Research Program Atlantic Tropical Experiment Phase III data. Significant differences exist between the statistical properties of tropical and midlatitude cumulus convection, especially in the vertical structures of the cumulus mass fluxes, apparent heat source (Q 1), and apparent moisture sink (Q 2). The strong variations of the subcloud-layer thermodynamic structure and the surface fluxes in midlatitude continents have large impacts on the heat and moisture budgets. The radiative budgets and satellite-observed cloud amounts are also compared with observations. Although the agreements are reasonably good, some deficiencies of the simulations and inadequate accuracy of large-scale advective tendencies can be clearly seen from the comparisons. Sensitivity tests are performed to address these issues.
