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- Author or Editor: Hirofumi Tomita x
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Abstract
In large-eddy simulations (LES), it is crucial to ensure that discretization errors do not contaminate the subgrid effect of the turbulence model in a wavelength range larger than the effective resolution. Recently, we showed that a seventh- or eighth-order accuracy is required for advection terms in planetary boundary layer simulations when using conventional gridpoint methods. However, a significant amount of communication between parallel computers is necessary to achieve high-order accuracy in gridpoint methods, and this can degrade computational efficiency. The discontinuous Galerkin method (DGM) is a promising approach for overcoming these limitations. Therefore, this study focuses on the numerical criteria of the DGM at LES from the viewpoint of numerical diffusion and dispersion. We extend our earlier study to the DGM framework and clarify the necessary order of the polynomial (p). We find that p = 4 is required based on the numerical criteria at the grid spacing of O(10) m with sufficiently scale-selective modal filters. The examination of temporal accuracy suggests that the fourth-order is sufficient when a fully explicit temporal scheme is used. In addition, we investigate the effect of hyperupwinding that is usually met when the Rusanov flux is employed in the low Mach number flows. It suggests that the choice of numerical flux has little effect on simulation results when the high-order DGM is used. Furthermore, we perform a series of LES in the planetary boundary layer and confirm that the indication obtained from the criteria holds for an actual LES.
Abstract
In large-eddy simulations (LES), it is crucial to ensure that discretization errors do not contaminate the subgrid effect of the turbulence model in a wavelength range larger than the effective resolution. Recently, we showed that a seventh- or eighth-order accuracy is required for advection terms in planetary boundary layer simulations when using conventional gridpoint methods. However, a significant amount of communication between parallel computers is necessary to achieve high-order accuracy in gridpoint methods, and this can degrade computational efficiency. The discontinuous Galerkin method (DGM) is a promising approach for overcoming these limitations. Therefore, this study focuses on the numerical criteria of the DGM at LES from the viewpoint of numerical diffusion and dispersion. We extend our earlier study to the DGM framework and clarify the necessary order of the polynomial (p). We find that p = 4 is required based on the numerical criteria at the grid spacing of O(10) m with sufficiently scale-selective modal filters. The examination of temporal accuracy suggests that the fourth-order is sufficient when a fully explicit temporal scheme is used. In addition, we investigate the effect of hyperupwinding that is usually met when the Rusanov flux is employed in the low Mach number flows. It suggests that the choice of numerical flux has little effect on simulation results when the high-order DGM is used. Furthermore, we perform a series of LES in the planetary boundary layer and confirm that the indication obtained from the criteria holds for an actual LES.
Abstract
Recently, large-eddy simulation (LES) has been increasingly employed in meteorological simulations because it is a promising method for turbulent parameterization. However, it is still difficult to affirm that the numerical accuracy required for a dynamical core is fully understood. In this study, we derived two theoretical criteria for the order of accuracy of the advection term in a typical situation of the atmospheric boundary layer, and demonstrate their validity by numerical experiments. In the targeted grid-spacing of O(10) m, we determined the required order of accuracy as follows: Based on the criterion of the numerical diffusion error, the upwind scheme must have at least seventh-order accuracy. The fourth-order central scheme is barely acceptable with fourth-order explicit diffusion, provided that its coefficient is one or two orders of magnitude smaller than the implicit diffusion coefficient of the third-order upwind scheme. Based on the criterion of numerical dispersion error, at minimum, the seventh or eighth order is required. The dispersion error was indirect for the energy spectra, although we expect it may affect the local turbulence mechanism. We also investigated the effects of temporal discretization for compressible models, and found that relatively lower-order time schemes are available up to the O(10) m grid spacing if the time step is sufficiently small due to sound wave limitations. The importance of the derived criteria is that the required order of accuracy increases as the grid spacing decreases. This suggests that considerable care should be taken regarding the numerical error problem for future high-resolution LES.
Abstract
Recently, large-eddy simulation (LES) has been increasingly employed in meteorological simulations because it is a promising method for turbulent parameterization. However, it is still difficult to affirm that the numerical accuracy required for a dynamical core is fully understood. In this study, we derived two theoretical criteria for the order of accuracy of the advection term in a typical situation of the atmospheric boundary layer, and demonstrate their validity by numerical experiments. In the targeted grid-spacing of O(10) m, we determined the required order of accuracy as follows: Based on the criterion of the numerical diffusion error, the upwind scheme must have at least seventh-order accuracy. The fourth-order central scheme is barely acceptable with fourth-order explicit diffusion, provided that its coefficient is one or two orders of magnitude smaller than the implicit diffusion coefficient of the third-order upwind scheme. Based on the criterion of numerical dispersion error, at minimum, the seventh or eighth order is required. The dispersion error was indirect for the energy spectra, although we expect it may affect the local turbulence mechanism. We also investigated the effects of temporal discretization for compressible models, and found that relatively lower-order time schemes are available up to the O(10) m grid spacing if the time step is sufficiently small due to sound wave limitations. The importance of the derived criteria is that the required order of accuracy increases as the grid spacing decreases. This suggests that considerable care should be taken regarding the numerical error problem for future high-resolution LES.
Abstract
The dependence of lightning frequency on the life cycle of an idealized tropical cyclone (TC) was investigated using a three-dimensional meteorological model coupled with an explicit lightning model. To investigate this dependence, an idealized numerical simulation covering the initial state to the steady state (SS) of an idealized TC was conducted. The simulation was consistent with the temporal evolution of lightning frequency reported by previous observational studies. Our analyses showed that the dependence originates from changes in the types of convective cloud with lightning over the life cycle of the TC. Before rapid intensification (RI) and in the early stage of RI, convective cloud cells that form under high-convective available potential energy (CAPE) conditions are the main contributors to lightning. As the TC reaches the late stage of RI and approaches SS, the secondary circulation becomes prominent and convective clouds in the eyewall region alongside the secondary circulation gradually become the main contributors to the lightning. In the convective cloud cells formed under high-CAPE conditions, upward velocity is strong and large charge density is provided through noninductive charge separation induced by graupel collisions. This large charge density frequently induces lightning in the clouds. On the other hand, the vertical velocity in the eyewall is weak, and it tends to contribute to lightning only when the TC reaches the mature stage. Our analyses imply that the maximum lightning frequency that occurs before the maximum intensity of a TC corresponds to the stage of a TC’s life cycle in which convective cloud cells are generated most frequently and moisten the upper troposphere.
Abstract
The dependence of lightning frequency on the life cycle of an idealized tropical cyclone (TC) was investigated using a three-dimensional meteorological model coupled with an explicit lightning model. To investigate this dependence, an idealized numerical simulation covering the initial state to the steady state (SS) of an idealized TC was conducted. The simulation was consistent with the temporal evolution of lightning frequency reported by previous observational studies. Our analyses showed that the dependence originates from changes in the types of convective cloud with lightning over the life cycle of the TC. Before rapid intensification (RI) and in the early stage of RI, convective cloud cells that form under high-convective available potential energy (CAPE) conditions are the main contributors to lightning. As the TC reaches the late stage of RI and approaches SS, the secondary circulation becomes prominent and convective clouds in the eyewall region alongside the secondary circulation gradually become the main contributors to the lightning. In the convective cloud cells formed under high-CAPE conditions, upward velocity is strong and large charge density is provided through noninductive charge separation induced by graupel collisions. This large charge density frequently induces lightning in the clouds. On the other hand, the vertical velocity in the eyewall is weak, and it tends to contribute to lightning only when the TC reaches the mature stage. Our analyses imply that the maximum lightning frequency that occurs before the maximum intensity of a TC corresponds to the stage of a TC’s life cycle in which convective cloud cells are generated most frequently and moisten the upper troposphere.
Abstract
Reducing the computational cost of weather and climate simulations would lower electric energy consumption. From the standpoint of reducing costs, the use of reduced precision arithmetic has become an active area of research. Here the impact of using single-precision arithmetic on simulation accuracy is examined by conducting Jablonowski and Williamson’s baroclinic wave tests using the dynamical core of a global fully compressible nonhydrostatic model. The model employs a finite-volume method discretized on an icosahedral grid system and its mesh size is set to 220, 56, 14, and 3.5 km. When double-precision arithmetic is fully replaced by single-precision arithmetic, a spurious wavenumber-5 structure becomes dominant in both hemispheres, rather than the expected baroclinic wave growth only in the Northern Hemisphere. It was found that this spurious wave growth comes from errors in the calculation of gridcell geometrics. Therefore, an additional simulation was conducted using double precision for calculations that only need to be performed for model setup, including calculation of gridcell geometrics, and single precision everywhere else, meaning that all calculations performed each time step used single precision. In this case, the model successfully simulated the growth of the baroclinic wave with only small errors and a 46% reduction in runtime. These results suggest that the use of single-precision arithmetic will allow significant reduction of computational costs in next-generation weather and climate simulations using a fully compressible nonhydrostatic global model with the finite-volume method.
Abstract
Reducing the computational cost of weather and climate simulations would lower electric energy consumption. From the standpoint of reducing costs, the use of reduced precision arithmetic has become an active area of research. Here the impact of using single-precision arithmetic on simulation accuracy is examined by conducting Jablonowski and Williamson’s baroclinic wave tests using the dynamical core of a global fully compressible nonhydrostatic model. The model employs a finite-volume method discretized on an icosahedral grid system and its mesh size is set to 220, 56, 14, and 3.5 km. When double-precision arithmetic is fully replaced by single-precision arithmetic, a spurious wavenumber-5 structure becomes dominant in both hemispheres, rather than the expected baroclinic wave growth only in the Northern Hemisphere. It was found that this spurious wave growth comes from errors in the calculation of gridcell geometrics. Therefore, an additional simulation was conducted using double precision for calculations that only need to be performed for model setup, including calculation of gridcell geometrics, and single precision everywhere else, meaning that all calculations performed each time step used single precision. In this case, the model successfully simulated the growth of the baroclinic wave with only small errors and a 46% reduction in runtime. These results suggest that the use of single-precision arithmetic will allow significant reduction of computational costs in next-generation weather and climate simulations using a fully compressible nonhydrostatic global model with the finite-volume method.
Abstract
A newly developed global nonhydrostatic model is used for life cycle experiments (LCEs) of baroclinic waves, and the resolution dependency of frontal structures is examined. LCEs are integrated for 12 days with horizontal grid intervals ranging from 223 to 3.5 km in a global domain. In general, fronts become sharper and corresponding vertical flow strengthens as horizontal resolution increases. However, if the ratio of vertical and horizontal grid intervals is sufficiently small compared to the frontal slope s, the overall frontal structure remains unchanged. In contrast, when the ratio of horizontal and vertical grid intervals exceeds 2s − 4s, spurious gravity waves are generated at the cold front. A linear model for mountain waves quantitatively explains the mechanism of the spurious waves. The distribution of the basic wind is the major factor that determines wave amplitude and propagation. The spurious waves propagate up to a critical level at which the basic wind speed normal to the front is equal to the propagation speed of the front. Results from the linear model suggest that an effective way to eliminate spurious waves is to choose a stretched grid with a smaller vertical grid interval in lower layers where strong horizontal winds exist.
Abstract
A newly developed global nonhydrostatic model is used for life cycle experiments (LCEs) of baroclinic waves, and the resolution dependency of frontal structures is examined. LCEs are integrated for 12 days with horizontal grid intervals ranging from 223 to 3.5 km in a global domain. In general, fronts become sharper and corresponding vertical flow strengthens as horizontal resolution increases. However, if the ratio of vertical and horizontal grid intervals is sufficiently small compared to the frontal slope s, the overall frontal structure remains unchanged. In contrast, when the ratio of horizontal and vertical grid intervals exceeds 2s − 4s, spurious gravity waves are generated at the cold front. A linear model for mountain waves quantitatively explains the mechanism of the spurious waves. The distribution of the basic wind is the major factor that determines wave amplitude and propagation. The spurious waves propagate up to a critical level at which the basic wind speed normal to the front is equal to the propagation speed of the front. Results from the linear model suggest that an effective way to eliminate spurious waves is to choose a stretched grid with a smaller vertical grid interval in lower layers where strong horizontal winds exist.
Abstract
The degree of gradient wind balance was investigated in a number of tropical cyclones (TCs) simulated under realistic environments. The results of global-scale numerical simulations without cumulus parameterization were used, with a horizontal mesh size of 7 km. On average, azimuthally averaged maximum tangential velocities at 850 (925) hPa in the simulated TCs were 0.72% (1.95%) faster than gradient wind–balanced tangential velocity (GWV) during quasi-steady periods. Of the simulated TCs, 75% satisfied the gradient wind balance at the radius of maximum wind speed (RMW) at 850 and at 925 hPa to within about 4.0%. These results were qualitatively similar to those obtained during the intensification phase. In contrast, averages of the maximum and minimum deviations from the GWV, in all the azimuths at the RMW, achieved up to 40% of the maximum tangential velocity. Azimuthally averaged tangential velocities exceeded the GWV (i.e., supergradient) inside the RMW in the lower troposphere, whereas the velocities were close to or slightly slower than GWV (i.e., subgradient) in the other regions. The tangential velocities at 925 hPa were faster (slower) in the right-hand (left hand) side of the TC motion. When the tangential velocities at the RMW were supergradient, the primary circulation tended to decay rapidly in the vertical direction and slowly in the radial direction, and the eyewall updraft and the RMW were at larger radii. Statistical analyses revealed that the TC with supergradient wind at the RMW at 850 hPa was characterized by stronger intensity, larger RMW, more axisymmetric structure, and an intensity stronger than potential intensity.
Abstract
The degree of gradient wind balance was investigated in a number of tropical cyclones (TCs) simulated under realistic environments. The results of global-scale numerical simulations without cumulus parameterization were used, with a horizontal mesh size of 7 km. On average, azimuthally averaged maximum tangential velocities at 850 (925) hPa in the simulated TCs were 0.72% (1.95%) faster than gradient wind–balanced tangential velocity (GWV) during quasi-steady periods. Of the simulated TCs, 75% satisfied the gradient wind balance at the radius of maximum wind speed (RMW) at 850 and at 925 hPa to within about 4.0%. These results were qualitatively similar to those obtained during the intensification phase. In contrast, averages of the maximum and minimum deviations from the GWV, in all the azimuths at the RMW, achieved up to 40% of the maximum tangential velocity. Azimuthally averaged tangential velocities exceeded the GWV (i.e., supergradient) inside the RMW in the lower troposphere, whereas the velocities were close to or slightly slower than GWV (i.e., subgradient) in the other regions. The tangential velocities at 925 hPa were faster (slower) in the right-hand (left hand) side of the TC motion. When the tangential velocities at the RMW were supergradient, the primary circulation tended to decay rapidly in the vertical direction and slowly in the radial direction, and the eyewall updraft and the RMW were at larger radii. Statistical analyses revealed that the TC with supergradient wind at the RMW at 850 hPa was characterized by stronger intensity, larger RMW, more axisymmetric structure, and an intensity stronger than potential intensity.
Abstract
Japan’s new geostationary satellite Himawari-8, the first of a series of the third-generation geostationary meteorological satellites including GOES-16, has been operational since July 2015. Himawari-8 produces high-resolution observations with 16 frequency bands every 10 min for full disk, and every 2.5 min for local regions. This study aims to assimilate all-sky every-10-min infrared (IR) radiances from Himawari-8 with a regional numerical weather prediction model and to investigate its impact on real-world tropical cyclone (TC) analyses and forecasts for the first time. The results show that the assimilation of Himawari-8 IR radiances improves the analyzed TC structure in both inner-core and outer-rainband regions. The TC intensity forecasts are also improved due to Himawari-8 data because of the improved TC structure analysis.
Abstract
Japan’s new geostationary satellite Himawari-8, the first of a series of the third-generation geostationary meteorological satellites including GOES-16, has been operational since July 2015. Himawari-8 produces high-resolution observations with 16 frequency bands every 10 min for full disk, and every 2.5 min for local regions. This study aims to assimilate all-sky every-10-min infrared (IR) radiances from Himawari-8 with a regional numerical weather prediction model and to investigate its impact on real-world tropical cyclone (TC) analyses and forecasts for the first time. The results show that the assimilation of Himawari-8 IR radiances improves the analyzed TC structure in both inner-core and outer-rainband regions. The TC intensity forecasts are also improved due to Himawari-8 data because of the improved TC structure analysis.
