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- Author or Editor: Andreas Bott x
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Abstract
A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes.
Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion and simultaneously requires only small computational effort. For Corant numbers with absolute values not exceeding one, the scheme preserves numerical stability except in strong deformational flow fields where slight instabilities may occur.
Abstract
A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes.
Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion and simultaneously requires only small computational effort. For Corant numbers with absolute values not exceeding one, the scheme preserves numerical stability except in strong deformational flow fields where slight instabilities may occur.
Abstract
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Abstract
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Abstract
The area-preserving flux-form advection algorithm is extended to monotonicity. For this, the nonlinear positive-definite flux limitation of the original approach is replaced by new monotone flux limiters. The monotone fluxes are derived for one-dimensional constant transport velocities. The deformation occurring in divergent flow is accounted for by adding to the monotone advection fluxes a correction term, which has been derived from the deformation of the upstream method. The final algorithm is applicable to arbitrary multidimensional transport problems. However, due to the use of the time-splitting method, it is strictly monotone only in uniform flow fields.
Results of different one- and two-dimensional advection experiments are presented, demonstrating that the monotone flux limitation is an attractive alternative to the positive-definite algorithm. Amplitude and phase speed errors are somewhat larger in the monotone advection scheme. The computational effort of the new version is not much larger than that of the positive definite scheme. Thus, it is concluded that for many applications of atmospheric modeling, the monotone area-preserving flux-form advection algorithm is an accurate and numerically efficient method for the solution of the transport equation.
Abstract
The area-preserving flux-form advection algorithm is extended to monotonicity. For this, the nonlinear positive-definite flux limitation of the original approach is replaced by new monotone flux limiters. The monotone fluxes are derived for one-dimensional constant transport velocities. The deformation occurring in divergent flow is accounted for by adding to the monotone advection fluxes a correction term, which has been derived from the deformation of the upstream method. The final algorithm is applicable to arbitrary multidimensional transport problems. However, due to the use of the time-splitting method, it is strictly monotone only in uniform flow fields.
Results of different one- and two-dimensional advection experiments are presented, demonstrating that the monotone flux limitation is an attractive alternative to the positive-definite algorithm. Amplitude and phase speed errors are somewhat larger in the monotone advection scheme. The computational effort of the new version is not much larger than that of the positive definite scheme. Thus, it is concluded that for many applications of atmospheric modeling, the monotone area-preserving flux-form advection algorithm is an accurate and numerically efficient method for the solution of the transport equation.
Abstract
A new mass conservative flux method is presented for the numerical solution of the stochastic collection equation. The method consists of a two-step procedure. In the first step the mass distribution of drops with mass x′ that have been newly formed in a collision process is entirely added to grid box k of the numerical grid mesh with x k ⩽ x′ ⩽ x k+1. In the second step a certain fraction of the water mass in grid box k is transported to k + 1. This transport is done by means of an advection procedure.
Different numerical test runs are presented in which the proposed method is compared with the Berry–Reinhardt scheme. These tests show a very good agreement between the two approaches. In various sensitivity studies it is demonstrated that the flux method remains numerically stable for different choices of the grid mesh and the integration time step. Since a time step of 10 s may be used without significant loss of accuracy, the flux method is numerically very efficient in comparison to the Berry–Reinhardt scheme.
Abstract
A new mass conservative flux method is presented for the numerical solution of the stochastic collection equation. The method consists of a two-step procedure. In the first step the mass distribution of drops with mass x′ that have been newly formed in a collision process is entirely added to grid box k of the numerical grid mesh with x k ⩽ x′ ⩽ x k+1. In the second step a certain fraction of the water mass in grid box k is transported to k + 1. This transport is done by means of an advection procedure.
Different numerical test runs are presented in which the proposed method is compared with the Berry–Reinhardt scheme. These tests show a very good agreement between the two approaches. In various sensitivity studies it is demonstrated that the flux method remains numerically stable for different choices of the grid mesh and the integration time step. Since a time step of 10 s may be used without significant loss of accuracy, the flux method is numerically very efficient in comparison to the Berry–Reinhardt scheme.
Abstract
In the present paper a new method is introduced for the numerical solution of the stochastic collection equation in cloud models dealing with two-dimensional cloud microphysics. The method is based on the assumption that the probability for the collision of two cloud drops only depends on the water mass of each and not on the mass of the aerosol nuclei. With this assumption it is possible to reduce the two-dimensional solution of the stochastic collection equation to a one-dimensional approach. First, the two-dimensional particle spectrum is integrated over the aerosol mass yielding a one-dimensional drop spectrum in the water mass grid. For this intermediate drop distribution the stochastic collection equation is solved. The resulting new drop spectrum is redistributed into the two-dimensional aerosol–water grid. Numerical sensitivity studies are presented demonstrating that the flux method yields very good results. In the two-dimensional aerosol–water grid the drop distributions move from initially small aerosol and water masses toward larger values whereby the drops remain more or less concentrated along a straight line. In several calculations the numerical diffusivity of the method is investigated. The corresponding results show that in these investigations the artificial broadening of the drop distribution remains tolerably low.
Abstract
In the present paper a new method is introduced for the numerical solution of the stochastic collection equation in cloud models dealing with two-dimensional cloud microphysics. The method is based on the assumption that the probability for the collision of two cloud drops only depends on the water mass of each and not on the mass of the aerosol nuclei. With this assumption it is possible to reduce the two-dimensional solution of the stochastic collection equation to a one-dimensional approach. First, the two-dimensional particle spectrum is integrated over the aerosol mass yielding a one-dimensional drop spectrum in the water mass grid. For this intermediate drop distribution the stochastic collection equation is solved. The resulting new drop spectrum is redistributed into the two-dimensional aerosol–water grid. Numerical sensitivity studies are presented demonstrating that the flux method yields very good results. In the two-dimensional aerosol–water grid the drop distributions move from initially small aerosol and water masses toward larger values whereby the drops remain more or less concentrated along a straight line. In several calculations the numerical diffusivity of the method is investigated. The corresponding results show that in these investigations the artificial broadening of the drop distribution remains tolerably low.
Abstract
An intensive observation period was conducted in September 2017 in the central Namib, Namibia, as part of the project Namib Fog Life Cycle Analysis (NaFoLiCA). The purpose of the field campaign was to investigate the spatial and temporal patterns of the coastal fog that occurs regularly during nighttime and morning hours. The fog is often linked to advection of a marine stratus that intercepts with the terrain up to 100 km inland. Meteorological data, including cloud base height, fog deposition, liquid water path, and vertical profiles of wind speed/direction and temperature, were measured continuously during the campaign. Additionally, profiles of temperature and relative humidity were sampled during five selected nights with stratus/fog at both coastal and inland sites using tethered balloon soundings, drone profiling, and radiosondes. This paper presents an overview of the scientific goals of the field campaign; describes the experimental setup, the measurements carried out, and the meteorological conditions during the intensive observation period; and presents first results with a focus on a single fog event.
Abstract
An intensive observation period was conducted in September 2017 in the central Namib, Namibia, as part of the project Namib Fog Life Cycle Analysis (NaFoLiCA). The purpose of the field campaign was to investigate the spatial and temporal patterns of the coastal fog that occurs regularly during nighttime and morning hours. The fog is often linked to advection of a marine stratus that intercepts with the terrain up to 100 km inland. Meteorological data, including cloud base height, fog deposition, liquid water path, and vertical profiles of wind speed/direction and temperature, were measured continuously during the campaign. Additionally, profiles of temperature and relative humidity were sampled during five selected nights with stratus/fog at both coastal and inland sites using tethered balloon soundings, drone profiling, and radiosondes. This paper presents an overview of the scientific goals of the field campaign; describes the experimental setup, the measurements carried out, and the meteorological conditions during the intensive observation period; and presents first results with a focus on a single fog event.
