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- Author or Editor: Hirofumi Tomita x
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Abstract
Solving the surface energy balance equation is the most important task when combining an atmospheric model and a land surface model. However, while the surface energy balance equation determines the interface temperature between the models, this temperature is often oscillatory and without physical significance. This paper discusses the spurious mode of surface temperature. The energy balance equation is solved by the linearization around the surface temperature in most models. When this conventional scheme is used, oscillation of surface temperature occurs, caused by the exclusion or poor consideration of the surface temperature dependence of the turbulent transfer coefficient at the surface. By more strictly solving the surface energy balance equation, no spurious mode appears. However, it is often difficult to obtain such a solution because the equation is highly nonlinear. Indeed, the Newton–Raphson method at times cannot find the convergence solution. To overcome this difficulty, a new method based on a modified Newton–Raphson method is proposed to solve the surface energy balance equation. As confirmed by conducting a long-term climate simulation, the new method can robustly obtain the true solution with reasonable computational efficiency.
Abstract
Solving the surface energy balance equation is the most important task when combining an atmospheric model and a land surface model. However, while the surface energy balance equation determines the interface temperature between the models, this temperature is often oscillatory and without physical significance. This paper discusses the spurious mode of surface temperature. The energy balance equation is solved by the linearization around the surface temperature in most models. When this conventional scheme is used, oscillation of surface temperature occurs, caused by the exclusion or poor consideration of the surface temperature dependence of the turbulent transfer coefficient at the surface. By more strictly solving the surface energy balance equation, no spurious mode appears. However, it is often difficult to obtain such a solution because the equation is highly nonlinear. Indeed, the Newton–Raphson method at times cannot find the convergence solution. To overcome this difficulty, a new method based on a modified Newton–Raphson method is proposed to solve the surface energy balance equation. As confirmed by conducting a long-term climate simulation, the new method can robustly obtain the true solution with reasonable computational efficiency.
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
This study investigated the multiscale organization of tropical convection on an aquaplanet in a model experiment with a horizontal mesh size of 3.5 km (for a 10-day simulation) and 7 km (for a 40-day simulation). The numerical experiment used the nonhydrostatic icosahedral atmospheric model (NICAM) with explicit cloud physics.
The simulation realistically reproduced multiscale cloud systems: eastward-propagating super cloud clusters (SCCs) contained westward-propagating cloud clusters (CCs). SCCs (CCs) had zonal sizes of several thousand (hundred) kilometers; typical propagation speed was 17 (10) m s−1. Smaller convective structures such as mesoscale cloud systems (MCs) of O(10 km) and cloud-scale elements (<10 km) were reproduced. A squall-type cluster with high cloud top (z > 16 km) of O(100 km) area was also reproduced.
Planetary-scale equatorial waves (with wavelengths of 10 000 and 40 000 km) had a major influence on the eastward propagation of the simulated SCC; destabilization east of the SCC facilitated generation of new CCs at the eastern end of the SCC. Large-scale divergence fields associated with the waves enhanced the growth of deep clouds in the CCs. A case study of a typical SCC showed that the primary mechanism forcing westward propagation varies with the life stages of the CCs or with vertical profiles of zonal wind. Cold pools and synoptic-scale waves both affected CC organization. Cloud-scale elements systematically formed along the edges of cold pools to sustain simulated MCs. The location, movement, and duration of the MCs varied with the large-scale conditions.
Abstract
This study investigated the multiscale organization of tropical convection on an aquaplanet in a model experiment with a horizontal mesh size of 3.5 km (for a 10-day simulation) and 7 km (for a 40-day simulation). The numerical experiment used the nonhydrostatic icosahedral atmospheric model (NICAM) with explicit cloud physics.
The simulation realistically reproduced multiscale cloud systems: eastward-propagating super cloud clusters (SCCs) contained westward-propagating cloud clusters (CCs). SCCs (CCs) had zonal sizes of several thousand (hundred) kilometers; typical propagation speed was 17 (10) m s−1. Smaller convective structures such as mesoscale cloud systems (MCs) of O(10 km) and cloud-scale elements (<10 km) were reproduced. A squall-type cluster with high cloud top (z > 16 km) of O(100 km) area was also reproduced.
Planetary-scale equatorial waves (with wavelengths of 10 000 and 40 000 km) had a major influence on the eastward propagation of the simulated SCC; destabilization east of the SCC facilitated generation of new CCs at the eastern end of the SCC. Large-scale divergence fields associated with the waves enhanced the growth of deep clouds in the CCs. A case study of a typical SCC showed that the primary mechanism forcing westward propagation varies with the life stages of the CCs or with vertical profiles of zonal wind. Cold pools and synoptic-scale waves both affected CC organization. Cloud-scale elements systematically formed along the edges of cold pools to sustain simulated MCs. The location, movement, and duration of the MCs varied with the large-scale conditions.
Abstract
Large-scale tropical convective disturbances simulated in a 7-km-mesh aquaplanet experiment are investigated. A 40-day simulation was executed using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). Two scales of eastward-propagating disturbances were analyzed. One was tightly coupled to a convective system resembling super–cloud clusters (SCCs) with a zonal scale of several thousand kilometers (SCC mode), whereas the other was characterized by a planetary-scale dynamical structure (40 000-km mode). The typical phase velocity was 17 (23) m s−1 for the SCC (40 000 km) mode. The SCC mode resembled convectively coupled Kelvin waves in the real atmosphere around the equator, but was accompanied by a pair of off-equatorial gyres. The 40 000-km mode maintained a Kelvin wave–like zonal structure, even poleward of the equatorial Rossby deformation radius. The equatorial structures in both modes matched neutral eastward-propagating gravity waves in the lower troposphere and unstable (growing) waves in the upper troposphere. In both modes, the meridional mass divergence exceeded the zonal component, not only in the boundary layer, but also in the free atmosphere. The forcing terms indicated that the meridional flow was primarily driven by convection via deformation in pressure fields and vertical circulations. Moisture convergence was one order of magnitude greater than the moisture flux from the sea surface. In the boundary layer, frictional convergence in the (anomalous) low-level easterly phase accounted for the buildup of low-level moisture leading to the active convective phase. The moisture distribution in the free atmosphere suggested that the moisture–convection feedback operated efficiently, especially in the SCC mode.
Abstract
Large-scale tropical convective disturbances simulated in a 7-km-mesh aquaplanet experiment are investigated. A 40-day simulation was executed using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM). Two scales of eastward-propagating disturbances were analyzed. One was tightly coupled to a convective system resembling super–cloud clusters (SCCs) with a zonal scale of several thousand kilometers (SCC mode), whereas the other was characterized by a planetary-scale dynamical structure (40 000-km mode). The typical phase velocity was 17 (23) m s−1 for the SCC (40 000 km) mode. The SCC mode resembled convectively coupled Kelvin waves in the real atmosphere around the equator, but was accompanied by a pair of off-equatorial gyres. The 40 000-km mode maintained a Kelvin wave–like zonal structure, even poleward of the equatorial Rossby deformation radius. The equatorial structures in both modes matched neutral eastward-propagating gravity waves in the lower troposphere and unstable (growing) waves in the upper troposphere. In both modes, the meridional mass divergence exceeded the zonal component, not only in the boundary layer, but also in the free atmosphere. The forcing terms indicated that the meridional flow was primarily driven by convection via deformation in pressure fields and vertical circulations. Moisture convergence was one order of magnitude greater than the moisture flux from the sea surface. In the boundary layer, frictional convergence in the (anomalous) low-level easterly phase accounted for the buildup of low-level moisture leading to the active convective phase. The moisture distribution in the free atmosphere suggested that the moisture–convection feedback operated efficiently, especially in the SCC mode.
Abstract
This study investigated the resolution dependence of diurnal variation in tropical convective systems represented by a global nonhydrostatic model without cumulus parameterization. This paper describes the detailed characteristics of diurnal variation in surface precipitation based on three-dimensional data, with the aim of explicitly clarifying the mechanism that underlies the variation. The study particularly focused on the evolution in the size of the precipitation area for deep convective systems with an analysis of the vertical structure of thermodynamic fields. This analysis compares the results of simulations with horizontal grid sizes of 14 and 7 km (R14 and R7, respectively). Over land, the phase delay of diurnal variations in R7 is about 3 h less than that in R14. R7 produces a pronounced diurnal variation in the size distributions of precipitating area(s), especially for areas with a radius of 0–100 km; this characteristic is not found for R14. Such areas actively evolve between noon and evening, leading to the smooth development of larger-scale precipitating areas having a radius of 100–150 km. The maximum surface precipitation in R7 over land occurs at around 2000 local time throughout the tropics, approximately 2 h prior to the development of nighttime deep convection. Deep convective regimes are important as agents of vertical heat transport in the tropics. The present results suggest that precipitating areas with a radius <100 km make a strong contribution to the total amount of precipitation and to mass transport.
Abstract
This study investigated the resolution dependence of diurnal variation in tropical convective systems represented by a global nonhydrostatic model without cumulus parameterization. This paper describes the detailed characteristics of diurnal variation in surface precipitation based on three-dimensional data, with the aim of explicitly clarifying the mechanism that underlies the variation. The study particularly focused on the evolution in the size of the precipitation area for deep convective systems with an analysis of the vertical structure of thermodynamic fields. This analysis compares the results of simulations with horizontal grid sizes of 14 and 7 km (R14 and R7, respectively). Over land, the phase delay of diurnal variations in R7 is about 3 h less than that in R14. R7 produces a pronounced diurnal variation in the size distributions of precipitating area(s), especially for areas with a radius of 0–100 km; this characteristic is not found for R14. Such areas actively evolve between noon and evening, leading to the smooth development of larger-scale precipitating areas having a radius of 100–150 km. The maximum surface precipitation in R7 over land occurs at around 2000 local time throughout the tropics, approximately 2 h prior to the development of nighttime deep convection. Deep convective regimes are important as agents of vertical heat transport in the tropics. The present results suggest that precipitating areas with a radius <100 km make a strong contribution to the total amount of precipitation and to mass transport.
Abstract
The relationship between upper-tropospheric ice cloud properties and the Hadley circulation intensity is examined through parameter sensitivity studies of global cloud-system-resolving simulations with explicit cloud convection. Experiments under a perpetual July condition were performed by changing parameters in the boundary layer and cloud microphysics schemes, with a mesh size of approximately 14 km. One additional experiment with a mesh size of approximately 7 km was also conducted. These experiments produced a variety of upper-cloud coverage and outgoing longwave radiation (OLR) distributions. The authors found that, as the upper-cloud coverage increased, the total precipitation decreased and the intensity of the Hadley circulation weakened because of energy balance constraints that radiative cooling are balanced by adiabatic warming. Interestingly, the ice water path was not correlated with the upper ice-loud coverage or OLR, indicating that the spatial coverage of upper ice clouds, rather than the ice water content, was the key factor in the radiation budget.
Abstract
The relationship between upper-tropospheric ice cloud properties and the Hadley circulation intensity is examined through parameter sensitivity studies of global cloud-system-resolving simulations with explicit cloud convection. Experiments under a perpetual July condition were performed by changing parameters in the boundary layer and cloud microphysics schemes, with a mesh size of approximately 14 km. One additional experiment with a mesh size of approximately 7 km was also conducted. These experiments produced a variety of upper-cloud coverage and outgoing longwave radiation (OLR) distributions. The authors found that, as the upper-cloud coverage increased, the total precipitation decreased and the intensity of the Hadley circulation weakened because of energy balance constraints that radiative cooling are balanced by adiabatic warming. Interestingly, the ice water path was not correlated with the upper ice-loud coverage or OLR, indicating that the spatial coverage of upper ice clouds, rather than the ice water content, was the key factor in the radiation budget.
