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- Author or Editor: Li Xu x
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Abstract
The method of statistical analysis of wind innovation (observation minus forecast) vectors is refined upon the work of Hollingsworth and Lönnberg (HL). The new refinements include (i) improved spectral representations of wind forecast error covariance functions, and (ii) simplified and yet more rigorously constrained formulations for multilevel analysis. The method is applied to wind innovation data over North America from the Navy Operational Global Atmospheric Prediction System (NOGAPS). The major products of the analysis include (i) wind observation error variance and vertical correlation, (ii) wind forecast error covariances as functions of height and horizontal distance, (iii) their spectra as functions of height and horizontal wavenumber, and (iv) partitioned vector wind error variances and correlation structures for the large-scale and synoptic-scale components and for the rotational and divergent components of synoptic scale. The results are compared with HL, showing a 20% overall reduction in wind forecast errors and a slight reduction in wind observation errors for the NOGAPS data in comparison with the European Centre for Medium-Range Weather Forecasts (ECMWF) global model data 16 years ago. The spatial structures of the estimated observation and forecast error correlation functions are found to be roughly comparable to those in HL.
Abstract
The method of statistical analysis of wind innovation (observation minus forecast) vectors is refined upon the work of Hollingsworth and Lönnberg (HL). The new refinements include (i) improved spectral representations of wind forecast error covariance functions, and (ii) simplified and yet more rigorously constrained formulations for multilevel analysis. The method is applied to wind innovation data over North America from the Navy Operational Global Atmospheric Prediction System (NOGAPS). The major products of the analysis include (i) wind observation error variance and vertical correlation, (ii) wind forecast error covariances as functions of height and horizontal distance, (iii) their spectra as functions of height and horizontal wavenumber, and (iv) partitioned vector wind error variances and correlation structures for the large-scale and synoptic-scale components and for the rotational and divergent components of synoptic scale. The results are compared with HL, showing a 20% overall reduction in wind forecast errors and a slight reduction in wind observation errors for the NOGAPS data in comparison with the European Centre for Medium-Range Weather Forecasts (ECMWF) global model data 16 years ago. The spatial structures of the estimated observation and forecast error correlation functions are found to be roughly comparable to those in HL.
Abstract
The method of statistical analysis of wind innovation (observation minus forecast) vectors is extended and applied to the innovation data collected over North America for a 3-month period from the Navy Operational Global Atmospheric Prediction System to estimate the height–wind forecast error correlation and to evaluate the related geostrophy. Both single-level and multilevel analyses are performed. The single-level analysis shows that the geostrophy is well satisfied in the middle troposphere but is not well satisfied in the boundary layer and around the tropopause. The multilevel analysis indicates that the cross correlation between height and tangential wind forecast errors at different vertical levels is not small and thus should not be neglected.
Abstract
The method of statistical analysis of wind innovation (observation minus forecast) vectors is extended and applied to the innovation data collected over North America for a 3-month period from the Navy Operational Global Atmospheric Prediction System to estimate the height–wind forecast error correlation and to evaluate the related geostrophy. Both single-level and multilevel analyses are performed. The single-level analysis shows that the geostrophy is well satisfied in the middle troposphere but is not well satisfied in the boundary layer and around the tropopause. The multilevel analysis indicates that the cross correlation between height and tangential wind forecast errors at different vertical levels is not small and thus should not be neglected.
Abstract
The prognostic equation for the radial velocity field observed with a Doppler radar is derived to include the effects of atmospheric refraction and earth curvature on radar-beam height and slope angle. The derived equation, called the radial velocity equation, contains a high-order small term that can be truncated. The truncated radial velocity equation is shown to be much more accurate than its counterpart radial velocity equation derived without considering the effects of atmospheric refraction and earth curvature. The truncated equation has the same concise form as its counterpart radial velocity equation but remains to be sufficiently accurate as a useful dynamic constraint for radar wind analysis and assimilation (in normal situations) even up to the farthest 300-km radial range of operational Weather Surveillance Radar-1988 Doppler (WSR-88D) scans where its counterpart radial velocity equation becomes erroneous.
Abstract
The prognostic equation for the radial velocity field observed with a Doppler radar is derived to include the effects of atmospheric refraction and earth curvature on radar-beam height and slope angle. The derived equation, called the radial velocity equation, contains a high-order small term that can be truncated. The truncated radial velocity equation is shown to be much more accurate than its counterpart radial velocity equation derived without considering the effects of atmospheric refraction and earth curvature. The truncated equation has the same concise form as its counterpart radial velocity equation but remains to be sufficiently accurate as a useful dynamic constraint for radar wind analysis and assimilation (in normal situations) even up to the farthest 300-km radial range of operational Weather Surveillance Radar-1988 Doppler (WSR-88D) scans where its counterpart radial velocity equation becomes erroneous.
Abstract
When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an important issue concerning the sensitivities of analyzed vortex flow (VF) fields by the VF-Var (formulated in Part I of this paper series and tested in Part II) to vortex center location errors, denoted by Δx c . Numerical experiments are performed to address this issue with the following findings: The increase of |Δx c | from zero to a half of vortex core radius causes large analysis error increases in the vortex core but the increased analysis errors decrease rapidly away from the vortex core especially for dual-Doppler analyses. The increased horizontal-velocity errors in the vortex core are mainly in the Δx c -normal component, because this component varies much more rapidly than the other component along the Δx c direction in the vortex core. The vertical variations of Δx c distort the vertical correlation structure of Δx c -dislocated VF-dependent background error covariance, which can increase the analysis errors in the vortex core. The dual-Doppler analyses have adequate accuracies outside the vortex core even when |Δx c | increases to a half of vortex core radius, while single-Doppler analyses can also have adequate accuracies outside the vortex core mainly for the single-Doppler-observed velocity component. The sensitivities to Δx c are largely unaffected by the vortex slanting. The above findings are important and useful for assessing the accuracies of analyzed VFs for real radar-observed tornadic mesocyclones.
Significance Statement
When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an issue concerning the sensitivity of analyzed vortex flow (VF) by the VF-Var (formulated in Part I of this paper series and tested with simulated radar observations in Part II) to vortex center location error. This issue and its required investigations are very important for the VF-Var to be applied to real radar-observed tornadic mesocyclones, especially in an operational setting with the WSR-88Ds. Numerical experiments are performed to address this issue. The findings from these experiments are important and useful for assessing the accuracies of VF-Var analyzed VF fields for real radar-observed tornadic mesocyclones.
Abstract
When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an important issue concerning the sensitivities of analyzed vortex flow (VF) fields by the VF-Var (formulated in Part I of this paper series and tested in Part II) to vortex center location errors, denoted by Δx c . Numerical experiments are performed to address this issue with the following findings: The increase of |Δx c | from zero to a half of vortex core radius causes large analysis error increases in the vortex core but the increased analysis errors decrease rapidly away from the vortex core especially for dual-Doppler analyses. The increased horizontal-velocity errors in the vortex core are mainly in the Δx c -normal component, because this component varies much more rapidly than the other component along the Δx c direction in the vortex core. The vertical variations of Δx c distort the vertical correlation structure of Δx c -dislocated VF-dependent background error covariance, which can increase the analysis errors in the vortex core. The dual-Doppler analyses have adequate accuracies outside the vortex core even when |Δx c | increases to a half of vortex core radius, while single-Doppler analyses can also have adequate accuracies outside the vortex core mainly for the single-Doppler-observed velocity component. The sensitivities to Δx c are largely unaffected by the vortex slanting. The above findings are important and useful for assessing the accuracies of analyzed VFs for real radar-observed tornadic mesocyclones.
Significance Statement
When the vortex center location is estimated from a radar-scanned tornadic mesocyclone, the estimated location is not error-free. This raises an issue concerning the sensitivity of analyzed vortex flow (VF) by the VF-Var (formulated in Part I of this paper series and tested with simulated radar observations in Part II) to vortex center location error. This issue and its required investigations are very important for the VF-Var to be applied to real radar-observed tornadic mesocyclones, especially in an operational setting with the WSR-88Ds. Numerical experiments are performed to address this issue. The findings from these experiments are important and useful for assessing the accuracies of VF-Var analyzed VF fields for real radar-observed tornadic mesocyclones.
Abstract
The variational method formulated in Part I for analyzing vortex flow (VF), called VF-Var, is tested with simulated radar radial-velocity observations from idealized and pseudo-operational Doppler scans of analytically formulated benchmark vortices with spiral-band structures to resemble VFs in observed tornadic mesocyclones. The idealized Doppler scans are unidirectional in parallel along horizontal grid lines of a coarse-resolution grid, so they measure only the horizontal components of three-dimensional velocities in the analysis domain. The pseudo-operational Doppler scans mimic a scan mode used by operational WSR-88Ds for severe storms. Paired numerical experiments are designed and performed to test the two-step analysis versus single-step analysis formulated in VF-Var. Both analyses perform very well with dual-Doppler scans and reasonably well with single-Doppler scans. Errors in the analyzed velocities from single-Doppler scans are mainly in the unobserved velocity components and only in fractions of the benchmark velocities. When the vortex is upright or slanted in the direction perpendicular to idealized single-Doppler scans, the two-step analysis slightly outperforms the single-step analysis for idealized Doppler scans and pseudo-operational dual-Doppler scans. When the vortex becomes slanted in the direction largely along or against Doppler scans, both analyses become less (more) accurate in analyzing the horizontal (slantwise vertical) velocity, and the single-step analysis outperforms the two-step analysis especially for single-Doppler scans. By considering the projections of analyzed velocity on radar beams in the original Cartesian coordinates, useful insights are gained for understanding why and how the analysis accuracies are affected by vortex slanting.
Abstract
The variational method formulated in Part I for analyzing vortex flow (VF), called VF-Var, is tested with simulated radar radial-velocity observations from idealized and pseudo-operational Doppler scans of analytically formulated benchmark vortices with spiral-band structures to resemble VFs in observed tornadic mesocyclones. The idealized Doppler scans are unidirectional in parallel along horizontal grid lines of a coarse-resolution grid, so they measure only the horizontal components of three-dimensional velocities in the analysis domain. The pseudo-operational Doppler scans mimic a scan mode used by operational WSR-88Ds for severe storms. Paired numerical experiments are designed and performed to test the two-step analysis versus single-step analysis formulated in VF-Var. Both analyses perform very well with dual-Doppler scans and reasonably well with single-Doppler scans. Errors in the analyzed velocities from single-Doppler scans are mainly in the unobserved velocity components and only in fractions of the benchmark velocities. When the vortex is upright or slanted in the direction perpendicular to idealized single-Doppler scans, the two-step analysis slightly outperforms the single-step analysis for idealized Doppler scans and pseudo-operational dual-Doppler scans. When the vortex becomes slanted in the direction largely along or against Doppler scans, both analyses become less (more) accurate in analyzing the horizontal (slantwise vertical) velocity, and the single-step analysis outperforms the two-step analysis especially for single-Doppler scans. By considering the projections of analyzed velocity on radar beams in the original Cartesian coordinates, useful insights are gained for understanding why and how the analysis accuracies are affected by vortex slanting.
Abstract
Snow–atmosphere coupling strength, the degree to which the atmosphere (temperature and precipitation) responds to underlying snow anomalies, is investigated using the Community Climate System Model (CCSM) with realistic snow information obtained from satellite and data assimilation. The coupling strength is quantified using seasonal simulations initialized in late boreal winter with realistic initial snow states or forced with realistic large-scale snow anomalies, including both snow cover fraction observed by remote sensing and snow water equivalent from land data assimilation. Errors due to deficiencies in the land model snow scheme and precipitation biases in the atmospheric model are mitigated by prescribing realistic snow states. The spatial and temporal distributions of strong snow–atmosphere coupling in this model are revealed to track the continental snow cover edge poleward during the ablation period in spring, with secondary maxima after snowmelt. Compared with prescribed “perfect” snow simulations, the free-running CCSM captures major regions of strong snow–atmosphere coupling strength, with only minor departures in magnitude, but showing uneven biases over the Northern Hemisphere. Signals of strong coupling to air temperature are found to propagate vertically into the troposphere, at least up to 500 hPa over the coupling “cold spots.” The main mechanism for this vertical propagation is found to be longwave radiation and condensation heating.
Abstract
Snow–atmosphere coupling strength, the degree to which the atmosphere (temperature and precipitation) responds to underlying snow anomalies, is investigated using the Community Climate System Model (CCSM) with realistic snow information obtained from satellite and data assimilation. The coupling strength is quantified using seasonal simulations initialized in late boreal winter with realistic initial snow states or forced with realistic large-scale snow anomalies, including both snow cover fraction observed by remote sensing and snow water equivalent from land data assimilation. Errors due to deficiencies in the land model snow scheme and precipitation biases in the atmospheric model are mitigated by prescribing realistic snow states. The spatial and temporal distributions of strong snow–atmosphere coupling in this model are revealed to track the continental snow cover edge poleward during the ablation period in spring, with secondary maxima after snowmelt. Compared with prescribed “perfect” snow simulations, the free-running CCSM captures major regions of strong snow–atmosphere coupling strength, with only minor departures in magnitude, but showing uneven biases over the Northern Hemisphere. Signals of strong coupling to air temperature are found to propagate vertically into the troposphere, at least up to 500 hPa over the coupling “cold spots.” The main mechanism for this vertical propagation is found to be longwave radiation and condensation heating.
Abstract
In this study of snow–atmosphere coupling strength, the previous snow–atmosphere coupled modeling experiment is extended to investigate the separate impacts on the atmosphere of the radiatively driven snow albedo effect and the snow hydrological effect that operates through soil moisture, evapotranspiration, and precipitation feedbacks. The albedo effect is governed by snow cover fraction, while the hydrological effect is controlled by anomalies in snow water equivalent. Realistic snow cover from satellite estimates is prescribed and compared with model-generated values to isolate the snow albedo effect. Similarly, imparting realistic snow water equivalent from the Global Land Data Assimilation System in the model allows for estimation of the snow hydrological effect. The snow albedo effect is found to be active before, and especially during, the snowmelt period, and regions of strong albedo-driven coupling move northward during spring, with the retreating edge of the snowpack in the Northern Hemisphere. The snow hydrological effect appears first during snowmelt and can persist for months afterward. The contributing factors to the snow albedo effect are analyzed in a theoretical framework.
Abstract
In this study of snow–atmosphere coupling strength, the previous snow–atmosphere coupled modeling experiment is extended to investigate the separate impacts on the atmosphere of the radiatively driven snow albedo effect and the snow hydrological effect that operates through soil moisture, evapotranspiration, and precipitation feedbacks. The albedo effect is governed by snow cover fraction, while the hydrological effect is controlled by anomalies in snow water equivalent. Realistic snow cover from satellite estimates is prescribed and compared with model-generated values to isolate the snow albedo effect. Similarly, imparting realistic snow water equivalent from the Global Land Data Assimilation System in the model allows for estimation of the snow hydrological effect. The snow albedo effect is found to be active before, and especially during, the snowmelt period, and regions of strong albedo-driven coupling move northward during spring, with the retreating edge of the snowpack in the Northern Hemisphere. The snow hydrological effect appears first during snowmelt and can persist for months afterward. The contributing factors to the snow albedo effect are analyzed in a theoretical framework.
Abstract
In this study, the 2D and 3D cloud-resolving model simulations of the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX) are compared to study the impact of dimensionality on barotropic processes during tropical convective development. Barotropic conversion of perturbation kinetic energy is associated with vertical transport of horizontal momentum under vertical shear of background horizontal winds. The similarities in both 2D and 3D model simulations show that 1) vertical wind shear is a necessary condition for barotropic conversion, but it does not control the barotropic conversion; 2) the evolution of barotropic conversion is related to that of the vertical transport of horizontal momentum; and 3) the tendency of vertical transport of horizontal momentum is mainly determined by the covariance between horizontal wind and the cloud hydrometeor component of buoyancy. The differences between the 2D and 3D model simulations reveal that 1) the barotropic conversion has shorter time scales and a larger contribution in the 2D model simulation than in the 3D model simulation and 2) kinetic energy is generally converted from the mean circulations to perturbation circulations in the 3D model simulation. In contrast, more kinetic energy is transferred from perturbation circulations to the mean circulations in the 2D model simulation. The same large-scale vertical velocity may account for the similarities, whereas the inclusion of meridional winds in the 3D model simulation may be responsible for the differences in barotropic conversion between the 2D and 3D model simulations.
Abstract
In this study, the 2D and 3D cloud-resolving model simulations of the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX) are compared to study the impact of dimensionality on barotropic processes during tropical convective development. Barotropic conversion of perturbation kinetic energy is associated with vertical transport of horizontal momentum under vertical shear of background horizontal winds. The similarities in both 2D and 3D model simulations show that 1) vertical wind shear is a necessary condition for barotropic conversion, but it does not control the barotropic conversion; 2) the evolution of barotropic conversion is related to that of the vertical transport of horizontal momentum; and 3) the tendency of vertical transport of horizontal momentum is mainly determined by the covariance between horizontal wind and the cloud hydrometeor component of buoyancy. The differences between the 2D and 3D model simulations reveal that 1) the barotropic conversion has shorter time scales and a larger contribution in the 2D model simulation than in the 3D model simulation and 2) kinetic energy is generally converted from the mean circulations to perturbation circulations in the 3D model simulation. In contrast, more kinetic energy is transferred from perturbation circulations to the mean circulations in the 2D model simulation. The same large-scale vertical velocity may account for the similarities, whereas the inclusion of meridional winds in the 3D model simulation may be responsible for the differences in barotropic conversion between the 2D and 3D model simulations.
Abstract
A computationally efficient method is developed to analyze the vortex wind fields of radar-observed mesocyclones. The method has the following features. (i) The analysis is performed in a nested domain over the mesocyclone area on a selected tilt of radar low-elevation scan. (ii) The background error correlation function is formulated with a desired vortex-flow dependence in the cylindrical coordinates cocentered with the mesocyclone. (iii) The square root of the background error covariance matrix is derived analytically to precondition the cost function and thus enhance the computational efficiency. Using this method, the vortex wind analysis can be performed efficiently either in a stand-alone fashion or as an additional step of targeted finescale analysis in the existing radar wind analysis system developed for nowcast applications. The effectiveness and performance of the method are demonstrated by examples of analyzed wind fields for the tornadic mesocyclones observed by operational Doppler radars in Oklahoma on 24 May 2011 and 20 May 2013.
Abstract
A computationally efficient method is developed to analyze the vortex wind fields of radar-observed mesocyclones. The method has the following features. (i) The analysis is performed in a nested domain over the mesocyclone area on a selected tilt of radar low-elevation scan. (ii) The background error correlation function is formulated with a desired vortex-flow dependence in the cylindrical coordinates cocentered with the mesocyclone. (iii) The square root of the background error covariance matrix is derived analytically to precondition the cost function and thus enhance the computational efficiency. Using this method, the vortex wind analysis can be performed efficiently either in a stand-alone fashion or as an additional step of targeted finescale analysis in the existing radar wind analysis system developed for nowcast applications. The effectiveness and performance of the method are demonstrated by examples of analyzed wind fields for the tornadic mesocyclones observed by operational Doppler radars in Oklahoma on 24 May 2011 and 20 May 2013.
Abstract
The vertical wind shear over the tropical Atlantic Ocean and its relationship with ENSO are analyzed in the superparameterized Community Climate System Model, version 4 (SP-CCSM4) and in the conventional CCSM4. The climatology of vertical wind shear over the tropical Atlantic and the ENSO–shear relationship are well simulated in the control runs of SP-CCSM4 and CCSM4. However, because of different representations of cloud processes, in a warmer climate such as the representative concentration pathway 8.5 (RCP8.5) scenario, SP-CCSM4 projects increased mean westerlies at 200 hPa during July through October (JASO), whereas CCSM4 projects decreased mean westerlies at 200 hPa over the equatorial Atlantic. The different changes in the upper-level wind further contribute to different projection of JASO mean vertical wind shear over the equatorial Atlantic. In the RCP8.5 scenario, when excluding the linear trend, projection of the ENSO–shear relationships by SP-CCSM4 retains similar features as in the observed current climate, whereas the ENSO–shear relationship projected by CCSM4 indicates an increase in the vertical wind shear dominating the tropical Atlantic during El Niño events. The difference in projection of ENSO–shear relationship is, to a certain extent, related to the different response of the tropical Atlantic SST to ENSO. Analysis of the climate change projection of Walker circulation, cloud cover, and convective activity illustrates that superparameterization simulates a stronger suppression of African convection than the conventional parameterization of moist processes. The weak convective activity diminishes the divergent wind associated with the vertical motion, which contributes to increased westerlies projected in SP-CCSM4.
Abstract
The vertical wind shear over the tropical Atlantic Ocean and its relationship with ENSO are analyzed in the superparameterized Community Climate System Model, version 4 (SP-CCSM4) and in the conventional CCSM4. The climatology of vertical wind shear over the tropical Atlantic and the ENSO–shear relationship are well simulated in the control runs of SP-CCSM4 and CCSM4. However, because of different representations of cloud processes, in a warmer climate such as the representative concentration pathway 8.5 (RCP8.5) scenario, SP-CCSM4 projects increased mean westerlies at 200 hPa during July through October (JASO), whereas CCSM4 projects decreased mean westerlies at 200 hPa over the equatorial Atlantic. The different changes in the upper-level wind further contribute to different projection of JASO mean vertical wind shear over the equatorial Atlantic. In the RCP8.5 scenario, when excluding the linear trend, projection of the ENSO–shear relationships by SP-CCSM4 retains similar features as in the observed current climate, whereas the ENSO–shear relationship projected by CCSM4 indicates an increase in the vertical wind shear dominating the tropical Atlantic during El Niño events. The difference in projection of ENSO–shear relationship is, to a certain extent, related to the different response of the tropical Atlantic SST to ENSO. Analysis of the climate change projection of Walker circulation, cloud cover, and convective activity illustrates that superparameterization simulates a stronger suppression of African convection than the conventional parameterization of moist processes. The weak convective activity diminishes the divergent wind associated with the vertical motion, which contributes to increased westerlies projected in SP-CCSM4.
