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- Author or Editor: Shian-Jiann Lin x
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Abstract
A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split-explicit, with large time steps for scalar transport, and small fractional steps for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for remapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with “physical parameterizations” and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave-growth tests and long-term integrations using the Held–Suarez forcing are presented. Impact of the monotonicity constraint is discussed.
Abstract
A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split-explicit, with large time steps for scalar transport, and small fractional steps for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for remapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with “physical parameterizations” and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave-growth tests and long-term integrations using the Held–Suarez forcing are presented. Impact of the monotonicity constraint is discussed.
Abstract
Contour dynamics (CD) is applied to study the mechanism responsible for the breakup of an isolated tornado-like vortex into multiple vortices, the nonlinear interaction between a tornado and its parent storm, and the impact of tornadoes, which are subgrid features in any existing prediction model, on the more resolvable storm-scale motion.The genesis of the multiple vortex via the linear and eventually nonlinear barotropic/inertial instability of an observed tornado's mean tangential wind profile is studied in unprecedented detail using a high-resolution CD model. The most unstable eigenmodes obtained from the linear stability analyses were used as the initial perturbations to initialize the CD model. Despite that multiple vortices at the fully nonlinear stage bear little resemblance to the linear eigenmode structure, it is found that normal-mode barotropic/inertial instability can, indeed, trigger the formation of these vortices. In addition, the number of the secondary vortices identified in the fully nonlinear phase is found to be equal to the most unstable azimuthal wavenumber.The interaction between a tornado and its environment (the parent storm) is studied using highly idealized initial conditions. The formation of the hook-echo-like flow pattern by the outside air spiraling in is revealed in the high-resolution CD simulations. It is found that the rotation of the parent storm may be strongly influenced by the feedback from the tornado.
Abstract
Contour dynamics (CD) is applied to study the mechanism responsible for the breakup of an isolated tornado-like vortex into multiple vortices, the nonlinear interaction between a tornado and its parent storm, and the impact of tornadoes, which are subgrid features in any existing prediction model, on the more resolvable storm-scale motion.The genesis of the multiple vortex via the linear and eventually nonlinear barotropic/inertial instability of an observed tornado's mean tangential wind profile is studied in unprecedented detail using a high-resolution CD model. The most unstable eigenmodes obtained from the linear stability analyses were used as the initial perturbations to initialize the CD model. Despite that multiple vortices at the fully nonlinear stage bear little resemblance to the linear eigenmode structure, it is found that normal-mode barotropic/inertial instability can, indeed, trigger the formation of these vortices. In addition, the number of the secondary vortices identified in the fully nonlinear phase is found to be equal to the most unstable azimuthal wavenumber.The interaction between a tornado and its environment (the parent storm) is studied using highly idealized initial conditions. The formation of the hook-echo-like flow pattern by the outside air spiraling in is revealed in the high-resolution CD simulations. It is found that the rotation of the parent storm may be strongly influenced by the feedback from the tornado.
Abstract
A nested-grid model is constructed using the Geophysical Fluid Dynamics Laboratory finite-volume dynamical core on the cubed sphere. The use of a global grid avoids the need for externally imposed lateral boundary conditions, and the use of the same governing equations and discretization on the global and regional domains prevents inconsistencies that may arise when these differ between grids. A simple interpolated nested-grid boundary condition is used, and two-way updates use a finite-volume averaging method. Mass conservation is achieved in two-way nesting by simply not updating the mass field.
Despite the simplicity of the nesting methodology, the distortion of the large-scale flow by the nested grid is such that the increase in global error norms is a factor of 2 or less in shallow-water test cases. The effect of a nested grid in the tropics on the zonal means and eddy statistics of an idealized Held–Suarez climate integration is minor, and artifacts due to the nested grid are comparable to those at the edges of the cubed-sphere grid and decrease with increasing resolution. The baroclinic wave train in a Jablonowski–Williamson test case was preserved in a nested-grid simulation while finescale features were represented with greater detail in the nested-grid region. The authors also found that lee vortices could propagate out of the nested region and onto a coarse grid, which by itself could not produce vortices. Finally, the authors discuss how concurrent integration of the nested and coarse grids can be significantly more efficient than when integrating the two grids sequentially.
Abstract
A nested-grid model is constructed using the Geophysical Fluid Dynamics Laboratory finite-volume dynamical core on the cubed sphere. The use of a global grid avoids the need for externally imposed lateral boundary conditions, and the use of the same governing equations and discretization on the global and regional domains prevents inconsistencies that may arise when these differ between grids. A simple interpolated nested-grid boundary condition is used, and two-way updates use a finite-volume averaging method. Mass conservation is achieved in two-way nesting by simply not updating the mass field.
Despite the simplicity of the nesting methodology, the distortion of the large-scale flow by the nested grid is such that the increase in global error norms is a factor of 2 or less in shallow-water test cases. The effect of a nested grid in the tropics on the zonal means and eddy statistics of an idealized Held–Suarez climate integration is minor, and artifacts due to the nested grid are comparable to those at the edges of the cubed-sphere grid and decrease with increasing resolution. The baroclinic wave train in a Jablonowski–Williamson test case was preserved in a nested-grid simulation while finescale features were represented with greater detail in the nested-grid region. The authors also found that lee vortices could propagate out of the nested region and onto a coarse grid, which by itself could not produce vortices. Finally, the authors discuss how concurrent integration of the nested and coarse grids can be significantly more efficient than when integrating the two grids sequentially.
Abstract
In finite-difference representations of the conservation equations, the flux form of the advection terms is often preferred to the advective form because of the immediate conservation of advected quantity. The scheme can be designed to further conserve higher-order moments, for example, the kinetic energy, which is important to the suppression of nonlinear instability. It is pointed out here that in most cases an advective form that is numerically equivalent to the flux form can be found, for schemes based on centered difference. This is also true for higher-order schemes and is not restricted to a particular grid type. An advection scheme that is fourth-order accurate in space for uniform advective flows is proposed that conserves both first and second moments of the advected variable in a nonhydrostatic framework. The role of the elastic correction term in addition to the pure flux term in compressible nonhydrostatic models is also discussed.
Abstract
In finite-difference representations of the conservation equations, the flux form of the advection terms is often preferred to the advective form because of the immediate conservation of advected quantity. The scheme can be designed to further conserve higher-order moments, for example, the kinetic energy, which is important to the suppression of nonlinear instability. It is pointed out here that in most cases an advective form that is numerically equivalent to the flux form can be found, for schemes based on centered difference. This is also true for higher-order schemes and is not restricted to a particular grid type. An advection scheme that is fourth-order accurate in space for uniform advective flows is proposed that conserves both first and second moments of the advected variable in a nonhydrostatic framework. The role of the elastic correction term in addition to the pure flux term in compressible nonhydrostatic models is also discussed.
Abstract
An algorithm for extending one-dimensional, forward-in-time, upstream-biased, flux-form transport schemes (e.g., the van Leer scheme and the piecewise parabolic method) to multidimensions is proposed. A method is also proposed to extend the resulting Eulerian multidimensional flux-form scheme to arbitrarily long time steps. Because of similarities to the semi-Lagrangian approach of extending time steps, the scheme is called flux-form semi-Lagrangian (FFSL). The FFSL scheme can be easily and efficiently implemented on the sphere. Idealized tests as well as realistic three-dimensional global transport simulations using winds from data assimilation systems are demonstrated. Stability is analyzed with a von Neuman approach as well as empirically on the 2D Cartesian plane. The resulting algorithm is conservative and upstream biased. In addition, it contains monotonicity constraints and conserves tracer correlations, therefore representing the physical characteristics of constituent transport.
Abstract
An algorithm for extending one-dimensional, forward-in-time, upstream-biased, flux-form transport schemes (e.g., the van Leer scheme and the piecewise parabolic method) to multidimensions is proposed. A method is also proposed to extend the resulting Eulerian multidimensional flux-form scheme to arbitrarily long time steps. Because of similarities to the semi-Lagrangian approach of extending time steps, the scheme is called flux-form semi-Lagrangian (FFSL). The FFSL scheme can be easily and efficiently implemented on the sphere. Idealized tests as well as realistic three-dimensional global transport simulations using winds from data assimilation systems are demonstrated. Stability is analyzed with a von Neuman approach as well as empirically on the 2D Cartesian plane. The resulting algorithm is conservative and upstream biased. In addition, it contains monotonicity constraints and conserves tracer correlations, therefore representing the physical characteristics of constituent transport.
Abstract
A two-way nested grid version of the Geophysical Fluid Dynamics Laboratory High Resolution Atmosphere Model (HiRAM) has been developed that uses simple methods for providing nested grid boundary conditions and mass-conserving nested-to-global communication. Nested grid simulations over the Maritime Continent and over North America were performed, each at two different resolutions: a 110-km mean grid cell width refined by a factor of 3, and a 50-km mean grid cell width refined by a factor of 2. Nested grid simulations were compared against uniform-resolution simulations, and against reanalyses, to determine the effect of grid nesting on both the modeled global climate and the simulation of small-scale features.
Orographically forced precipitation was robustly found to be simulated with more detail and greater realism in a nested grid simulation compared with when only the coarse grids were simulated alone. Tropical precipitation biases were reduced in the Maritime Continent region when a nested grid was introduced. Both results were robust to changes in the nested grid parameterization tunings. In North America, cold-season orographic precipitation was improved by nesting, but precipitation biases in the central and eastern United States were little changed. Improving the resolution through nesting also allowed for more intense rainfall events, greater Kelvin wave activity, and stronger tropical cyclones. Nested grid boundary artifacts were more pronounced when a one-way, noninteractive nested grid was used.
Abstract
A two-way nested grid version of the Geophysical Fluid Dynamics Laboratory High Resolution Atmosphere Model (HiRAM) has been developed that uses simple methods for providing nested grid boundary conditions and mass-conserving nested-to-global communication. Nested grid simulations over the Maritime Continent and over North America were performed, each at two different resolutions: a 110-km mean grid cell width refined by a factor of 3, and a 50-km mean grid cell width refined by a factor of 2. Nested grid simulations were compared against uniform-resolution simulations, and against reanalyses, to determine the effect of grid nesting on both the modeled global climate and the simulation of small-scale features.
Orographically forced precipitation was robustly found to be simulated with more detail and greater realism in a nested grid simulation compared with when only the coarse grids were simulated alone. Tropical precipitation biases were reduced in the Maritime Continent region when a nested grid was introduced. Both results were robust to changes in the nested grid parameterization tunings. In North America, cold-season orographic precipitation was improved by nesting, but precipitation biases in the central and eastern United States were little changed. Improving the resolution through nesting also allowed for more intense rainfall events, greater Kelvin wave activity, and stronger tropical cyclones. Nested grid boundary artifacts were more pronounced when a one-way, noninteractive nested grid was used.
Abstract
Retrospective seasonal predictions of tropical cyclones (TCs) in the three major ocean basins of the Northern Hemisphere are performed from 1990 to 2010 using the Geophysical Fluid Dynamics Laboratory High-Resolution Atmospheric Model (HiRAM) at 25-km resolution. Atmospheric states are initialized for each forecast, with the sea surface temperature anomaly (SSTA) “persisted” from that at the starting time during the 5-month forecast period (July–November). Using a five-member ensemble, it is shown that the storm counts of both tropical storm (TS) and hurricane categories are highly predictable in the North Atlantic basin during the 21-yr period. The correlations between the 21-yr observed and model predicted storm counts are 0.88 and 0.89 for hurricanes and TSs, respectively. The prediction in the eastern North Pacific is skillful, but it is not as outstanding as that in the North Atlantic. The persistent SSTA assumption appears to be less robust for the western North Pacific, contributing to less skillful predictions in that region. The relative skill in the prediction of storm counts is shown to be consistent with the quality of the predicted large-scale environment in the three major basins. It is shown that intensity distribution of TCs can be captured well by the model if the central sea level pressure is used as the threshold variable instead of the commonly used 10-m wind speed. This demonstrates the feasibility of using the 25-km-resolution HiRAM, a general circulation model designed initially for long-term climate simulations, to study the impacts of climate change on the intensity distribution of TCs.
Abstract
Retrospective seasonal predictions of tropical cyclones (TCs) in the three major ocean basins of the Northern Hemisphere are performed from 1990 to 2010 using the Geophysical Fluid Dynamics Laboratory High-Resolution Atmospheric Model (HiRAM) at 25-km resolution. Atmospheric states are initialized for each forecast, with the sea surface temperature anomaly (SSTA) “persisted” from that at the starting time during the 5-month forecast period (July–November). Using a five-member ensemble, it is shown that the storm counts of both tropical storm (TS) and hurricane categories are highly predictable in the North Atlantic basin during the 21-yr period. The correlations between the 21-yr observed and model predicted storm counts are 0.88 and 0.89 for hurricanes and TSs, respectively. The prediction in the eastern North Pacific is skillful, but it is not as outstanding as that in the North Atlantic. The persistent SSTA assumption appears to be less robust for the western North Pacific, contributing to less skillful predictions in that region. The relative skill in the prediction of storm counts is shown to be consistent with the quality of the predicted large-scale environment in the three major basins. It is shown that intensity distribution of TCs can be captured well by the model if the central sea level pressure is used as the threshold variable instead of the commonly used 10-m wind speed. This demonstrates the feasibility of using the 25-km-resolution HiRAM, a general circulation model designed initially for long-term climate simulations, to study the impacts of climate change on the intensity distribution of TCs.
Abstract
The effect of Ekman friction on baroclinic instability is reexamined in order to address questions raised by Farrell concerning the existence of normal mode instability in the atmosphere. As the degree of meridional confinement is central to the result, a linearized two-dimensional (latitude-height) quasi-geostrophic model is used to obviate the arbitrariness inherent in choosing a channel width in one-dimensional (vertical shear only) models. The two-dimensional eigenvalue problem was solved by pseudospectral method using rational Chebyshev expansions in both vertical and meridional directions. It is concluded that the instability can be eliminated only by the combination of strong Ekman friction with weak large-scale wind shear. Estimates of Ekman friction based on a realistic boundary-layer model indicate that such conditions can prevail over land when the boundary layer is neutrally stratified. For values of Ekman friction appropriate to the open ocean, friction can reduce the growth rate of the most unstable mode by at most a factor of two but cannot eliminate the instability.
By reducing the growth rate and shifting the most unstable mode to lower zonal wavenumbers, viscous effects make the heat and momentum fluxes of the most unstable mode deeper and less meridionally confined than in the inviscid case. Nevertheless, linear theory still underestimates the penetration depth of the momentum fluxes, as compared to observations and nonlinear numerical models.
Abstract
The effect of Ekman friction on baroclinic instability is reexamined in order to address questions raised by Farrell concerning the existence of normal mode instability in the atmosphere. As the degree of meridional confinement is central to the result, a linearized two-dimensional (latitude-height) quasi-geostrophic model is used to obviate the arbitrariness inherent in choosing a channel width in one-dimensional (vertical shear only) models. The two-dimensional eigenvalue problem was solved by pseudospectral method using rational Chebyshev expansions in both vertical and meridional directions. It is concluded that the instability can be eliminated only by the combination of strong Ekman friction with weak large-scale wind shear. Estimates of Ekman friction based on a realistic boundary-layer model indicate that such conditions can prevail over land when the boundary layer is neutrally stratified. For values of Ekman friction appropriate to the open ocean, friction can reduce the growth rate of the most unstable mode by at most a factor of two but cannot eliminate the instability.
By reducing the growth rate and shifting the most unstable mode to lower zonal wavenumbers, viscous effects make the heat and momentum fluxes of the most unstable mode deeper and less meridionally confined than in the inviscid case. Nevertheless, linear theory still underestimates the penetration depth of the momentum fluxes, as compared to observations and nonlinear numerical models.
Abstract
A new framework for interpreting the origin of the tropical intraseasonal oscillation (TISO), which avoids the speed and scale selection problems in the previous theories, is proposed in this study. In this interpretation TISO is viewed as an oscillation driven by an eastward moving convective region. This convective region consists of one or more super cloud clusters originating in the Indian Ocean and terminating in mid-Pacific, and is then followed by another convective region arising in the Indian Ocean in a period of 40–50 days. Additionally, a formal analogy is pointed out between super cloud clusters and the middle-latitude baroclinic wave packets.
This study includes a simulation of TISO in a 2D model to support our interpretation. Experiments were conducted with four different convection schemes. The authors advocate that the successful simulation of TISO depends on the successful simulation of super cloud clusters, which in turn depends on the successful simulation of the life cycle of cloud clusters, which further in turn depends on the choice of cumulus convection scheme. What makes a cumulus convection scheme successful in simulating TISO is discussed.
Abstract
A new framework for interpreting the origin of the tropical intraseasonal oscillation (TISO), which avoids the speed and scale selection problems in the previous theories, is proposed in this study. In this interpretation TISO is viewed as an oscillation driven by an eastward moving convective region. This convective region consists of one or more super cloud clusters originating in the Indian Ocean and terminating in mid-Pacific, and is then followed by another convective region arising in the Indian Ocean in a period of 40–50 days. Additionally, a formal analogy is pointed out between super cloud clusters and the middle-latitude baroclinic wave packets.
This study includes a simulation of TISO in a 2D model to support our interpretation. Experiments were conducted with four different convection schemes. The authors advocate that the successful simulation of TISO depends on the successful simulation of super cloud clusters, which in turn depends on the successful simulation of the life cycle of cloud clusters, which further in turn depends on the choice of cumulus convection scheme. What makes a cumulus convection scheme successful in simulating TISO is discussed.
Abstract
A nested version of the cubed-sphere finite-volume dynamical core (FV3) with GFS physics (fvGFS) is capable of tropical cyclone (TC) prediction across multiple space and time scales, from subseasonal prediction to high-resolution structure and intensity forecasting. Here, a version of fvGFS with 2-km resolution covering most of the North Atlantic is evaluated for its ability to simulate TC track, intensity, and finescale structure. TC structure is evaluated through a comparison of forecasts with three-dimensional Doppler radar from P-3 flights by NOAA’s Hurricane Research Division (HRD), and the structural metrics evaluated include the 2-km radius of maximum wind (RMW), slope of the RMW, depth of the TC vortex, and horizontal vortex decay rate. Seven TCs from the 2010–16 seasons are evaluated, including 10 separate model runs and 38 individual flights. The model had some success in producing rapid intensification (RI) forecasts for Earl, Edouard, and Matthew. The fvGFS model successfully predicts RMWs in the 25–50-km range but tends to have a small bias at very large radii and a large bias at very small radii. The wind peak also tends to be somewhat too sharp, and the vortex depth occasionally has a high bias, especially for storms that are observed to be shallow. Composite radial wind shows that the boundary layer tends to be too deep, although the outflow structure aloft is relatively consistent with observations. These results highlight the utility of the structural evaluation of TC forecasts and also show the promise of fvGFS for forecasting TCs.
Abstract
A nested version of the cubed-sphere finite-volume dynamical core (FV3) with GFS physics (fvGFS) is capable of tropical cyclone (TC) prediction across multiple space and time scales, from subseasonal prediction to high-resolution structure and intensity forecasting. Here, a version of fvGFS with 2-km resolution covering most of the North Atlantic is evaluated for its ability to simulate TC track, intensity, and finescale structure. TC structure is evaluated through a comparison of forecasts with three-dimensional Doppler radar from P-3 flights by NOAA’s Hurricane Research Division (HRD), and the structural metrics evaluated include the 2-km radius of maximum wind (RMW), slope of the RMW, depth of the TC vortex, and horizontal vortex decay rate. Seven TCs from the 2010–16 seasons are evaluated, including 10 separate model runs and 38 individual flights. The model had some success in producing rapid intensification (RI) forecasts for Earl, Edouard, and Matthew. The fvGFS model successfully predicts RMWs in the 25–50-km range but tends to have a small bias at very large radii and a large bias at very small radii. The wind peak also tends to be somewhat too sharp, and the vortex depth occasionally has a high bias, especially for storms that are observed to be shallow. Composite radial wind shows that the boundary layer tends to be too deep, although the outflow structure aloft is relatively consistent with observations. These results highlight the utility of the structural evaluation of TC forecasts and also show the promise of fvGFS for forecasting TCs.
