On the parameterization of precipitation in warm clouds

The Sundqvist parameterization for warm rain production by autoconversion processes as the function of cloud liquid water mixing ratio m is tested by defining a realistic ‘driving’ profile m(z) for a maritime low, warm stratocumulus cloud, and comparing with various recent observations. The results show that the parameterization is acceptable, especially after tuning its rain collection constant C₁. It is somewhat sensitive to the vertical resolution of the host model, though. Extending the calculations by considering typical cloud and raindrop size spectra, extra variables such as drizzle amounts and droplet effective radii (forced by the bulk Sundqvist rain rates) could be estimated by numerical integration. Also, these seem to agree fairly well with the available observations.     

On convective entrainment in a mass flux cumulus parameterization

Summary A new entrainment/detrainment formulation in the Tiedtke’s mass flux cumulus parameterization is discussed here. Apart from validating it with observations both in one and three dimensional cases, it is also evaluated in the light of the results from the original Tiedtke scheme and another mass flux scheme due to Emanuel. The proposed analytical profiles of entrainment and detrainment, easier to implement in any mass flux scheme, give reasonable results in GCM experiments.     

On the sensitivity of mesoscale models to surface-layer parameterization constants

The Colorado State University standard mesoscale model is used to evaluate the sensitivity of one-dimensional (1D) and two-dimensional (2D) fields to differences in surface-layer parameterization constants. Such differences reflect the range in the published values of the von Karman constant, Monin-Obukhov stability functions and the temperature roughness length at the surface. The sensitivity of 1D boundary-layer structure, and 2D sea-breeze intensity, is generally less than that found in published comparisons related to turbulence closure schemes generally.     

On the influence of frictional parameterization in wind-driven ocean circulation models

In a series of numerical experiments the wind-driven ocean circulation is studied in an idealized, rectangular model ocean, which is forced by steady zonal winds and damped by lateral and/or bottom friction. The problem as described by the barotropic vorticity equation is characterized by a Rossby number (R) and horizontal and/or vertical Ekman numbers (E_L, E_B) only.With free-slip conditions at the boundaries steady solutions for all chosen values of R are obtained, provided the diffusivity is sufficiently large. For both the forms of frictional parameterization a northern boundary current emerges with an eastward penetration scale depending on R. The recirculation pattern in the oceanically relevant ‘intermediate’ range of R is strongly affected by the type of friction. If lateral diffusion dominates bottom friction, a strong recirculating sub-gyre emerges in the northwestern corner of the basin. Its shape resembles the vertically integrated transport fields in recent eddy resolving model (EGCM) studies. The maximum transport is increased to values several times larger than the Sverdrup transport. The increase in transport is coupled with a development of closed contours of potential vorticity, enabling a nearly free inertial flow.This behaviour provides a sharp contrast to the bottom friction case (Veronis) where inertial recirculation only takes place with values of R so large that the eastward jet reaches the eastern boundary. It is shown that the linear friction law puts a strong constraint on the flow by preventing an intense recirculation in a small part of the basin.A reduction of the diffusivity (E_L) in the lateral friction case leads to quasi-steady solutions. The interaction with eddies becomes an integral part of the time mean energetics but does not influence the recirculation character of the flow.The main conclusion of the study is that the horizontal structure of the EGCM-transport fields can be explained in terms of a steady barotropic model where lateral friction represents the dominant dissipation mechanism.     

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.     

On the bulk parameterization of surface fluxes for various conditions and parameter ranges

A comparison between various parameterizations for the bulk transfercoefficient for heat and momentum is carried out for a wide range ofatmospheric stability and values of the roughness lengths for momentum and heat,z_0m and z_0h respectively.It is confirmed that the parameterization of Launiainen compares wellto a numerical iterative solution for the Obukhov length L as function of the gradients of wind speed and temperatureover a limited range of z_0m/z_0h and stability conditions.For _0m/z_0h > 500, an alternativeinterpolation formulation of Holtslag and Ek,in combination with the formulation of Launiainen, provides a better approximation.     

On drag coefficient parameterization with post processed direct fluxes measurements over the ocean

This study presents an evaluation of the atmospheric factors influencing the post-processing for fast-response data of horizontal momentum, vertical wind component, temperature, and water vapor to measure turbulent fluxes. They are observed at the Ieodo ocean research station over the Yellow Sea during the period of October 2004 to February 2008. The post process methods employed here are composed of quality control and tilt correction for turbulent flux measurement. The present result of quality control on the fast-response data shows that total removal ratio of the data generally depends on the factors such as a wind speed, relative humidity, significant wave height, visibility, and stability parameter (z/L). Especially, the removal ratio of water vapor data is significantly increased on light wind and strong stability conditions. The results show that the total removal ratio of water vapor data increases when wind speed is less than 3 m s^?1 and wave height is less than 1 m. The total removal ratio of water vapor data also increases with the value of the stability parameter. Three different algorithms of tilt correction methods (double rotation, triple rotation, and planar fit) are applied to correct the tilt of the sonic anemometer used in the observation. Friction velocities in near neutral state are greater than friction velocity in other states. Drag coefficients are categorized in terms of stabilities and seasons.     

On the sensitivity of the continuous accretion rate equation used in bulk-water parameterization schemes

The analytical solutions of the continuous accretion rate equation are compared regarding two different size distributions for cloud and rain water, two hail terminal velocities for different turbulent regimes and two solution types. The Khrgian-Mazin and Marshall-Palmer size distributions are assumed for rain water fraction, while the Khrgian-Mazin and monodisperse ones are applied to cloud water. In all cases the exponential-type size distribution for hail is used. In the calculation procedure for hail terminal velocity we take into consideration that the drag coefficient may be fixed or dependent on Reynolds number. Both approximate and exact solutions of the accretion rate under the same other conditions are also compared.Results show that the Khrgian-Mazin size distribution makes the approximate accretion rate between hail and rain considerably higher compared to its former parameterization for both hail terminal velocity assumptions. On the other side, the new treatment of hail terminal velocity with a variable drag coefficient produces lower accretion rates compared to the fixed drag coefficient case for all size distributions used. The approximate solution of the accretion rate equation is mainly lower than the exact one. Only in the case of raindrops-cloud droplets interaction it is much higher than the exact one with the Khrgian-Mazin size distribution used.     

On the parameterization of the vertical velocity at the top of planetary boundary layer

In this paper, an equation of the vertical velocity at the top of PBL is derived by use of a PBL model which is based on an analytic and actual form of K. Results show that the vertical velocity is a function of geostrophic vorticity, geostrophic wind speed, Coriolis parameter and the roughness of the ground, thus improving Charney-Eliassen’s formula. The order of magnitude of the vertical velocity computed from our equation is in agreement with that from the latter, but more factors affecting the vertical velocity are included.     

A subgrid parameterization of orographic precipitation

Summary Estimates of the impact of global climate change on land surface hydrology require climate information on spatial scales far smaller than those explicitly resolved by global climate models of today and the foreseeable future. To bridge the gap between what is required and what is resolved, we propose a subgrid-scale parameterization of the influence of topography on clouds, precipitation, and land surface hydrology. The parameterization represents subgrid variations in surface elevation in terms of probability distributions of discrete elevation classes. Separate cloud, radiative, and surface processes are calculated for each elevation class. Rainshadow effects are not treated by the parameterization; they have to be explicitly resolved by the host model. The simulated surface temperature, precipitation, and snow cover for each elevation class are distributed to different geographical locations according to the spatial distribution of surface elevation within each grid cell.The subgrid parameterization has been implemented in the Pacific Northwest Laboratory's climate version of the Penn State/NCAR Mesoscale Model. The scheme is evaluated by driving the regional climate model with observed lateral boundary conditions for the Pacific Northwest and comparing simulated fields with surface observations. The method yields more realistic spatial distributions of precipitation and snow cover in mountainous areas and is considerably more computationally efficient than achieving high resolution by the use of nesting in the regional climate model.With 17 Figures     

Supercell simulations with simple ice parameterization

Summary A three-dimensional cloud model derived from the Klemp-Wilhelmson model has been used to perform simulations of a right-moving supercell with the purpose of testing the effects of terminal velocity of precipitation on the storm dynamics. The model has no ice variables and computes a fall velocity for condensed water. We simulate one of the effects of ice presence, without including phase transition, by reducing the fall velocity of the precipitation in the coldest cloud layers. The reduction of precipitation terminal velocity is shown to have a strong influence on supercell dynamics and to be responsible for nearly all the improvements in the simulation of supercells that are obtained with full ice microphysics. This includes the transition to tornadic phase, which is sharper than in the case of a pure rain supercell. The vertical component of vorticity is seen to increase at all levels, as observed in real storms, instead of just at the surface as is common in simulations with no ice phase.Our results indicate the primary importance of terminal fall speed among the effects due to the presence of ice.With 13 Figures     

Gravel parameterization scheme and verification using BCC_CSM

Theoretical and Applied Climatology - The soil in China contains an abundance of gravels, but it is poorly described in land surface models. To solve this problem, the Beijing Climate Center...     

新冠肺炎流行病学模型的最优参数化

现如今,新冠肺炎(COVID-19)严重威胁着世界各国人民的生命健康.许多流行病学模型已经被用于为政策制定者和世界卫生组织提供决策参考.为了更加深刻的理解疫情趋势的变化特征,许多参数优化算法被用于反演模型参数.本文提议使用结合了高斯-牛顿法和梯度下降法的Levenberg-Marquardt(LMA)算法来优化模型参数...     

A synoptic parameterization of the drag coefficient

Abstract

The problem areas affecting the evaluation of hail suppression experiments are reviewed. These include the hail sensors and networks, trop damage data, statistical analysis, the hail‐suppression hypothesis, and the technology of cloud seeding. General directions of needed research are proposed.     

On the radiative properties of ice clouds: Light scattering,remote sensing,and radiation parameterization

Presented is a review of the radiative properties of ice clouds from three perspectives: light scattering simulations, remote sensing applications, and broadband radiation parameterizations appropriate for numerical models. On the subject of light scattering simulations, several classical computational approaches are reviewed, including the conventional geometric-optics method and its improved forms, the finite-difference time domain technique, the pseudo-spectral time domain technique, the discrete dipole approximation method, and the T-matrix method, with specific applications to the computation of the singlescattering properties of individual ice crystals. The strengths and weaknesses associated with each approach are discussed.With reference to remote sensing, operational retrieval algorithms are reviewed for retrieving cloud optical depth and effective particle size based on solar or thermal infrared(IR) bands. To illustrate the performance of the current solar- and IR-based retrievals, two case studies are presented based on spaceborne observations. The need for a more realistic ice cloud optical model to obtain spectrally consistent retrievals is demonstrated. Furthermore, to complement ice cloud property studies based on passive radiometric measurements, the advantage of incorporating lidar and/or polarimetric measurements is discussed.The performance of ice cloud models based on the use of different ice habits to represent ice particles is illustrated by comparing model results with satellite observations. A summary is provided of a number of parameterization schemes for ice cloud radiative properties that were developed for application to broadband radiative transfer submodels within general circulation models(GCMs). The availability of the single-scattering properties of complex ice habits has led to more accurate radiation parameterizations. In conclusion, the importance of using nonspherical ice particle models in GCM simulations for climate studies is proven.     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Climate model sensitivity to sea ice albedo parameterization

Summary Three one-year experimental simulations with the National Center for Atmospheric Research Community Climate Model (NCAR CCM) were performed with three sea ice albedo parameterizations and compared with control run results to examine their impact on polar surface temperature, planetary albedo and clouds. The first integration utilized sea ice albedos of the Arctic Basin for the spring and summer of 1977 derived from defence Meteorological Satellite Imagery (DMSP). The second simulation employed prescribed lead and melt pond fractions and an albedo weighting scheme. The third simulation involved the coupling of an interactive sea ice/snow albedo parameterization made a function of surface state.Results show that prescribed, and assumed true satellite sea ice albedos produced higher planetary albedos than those calculated with the standard CCM sea ice albedo scheme in the control run. As a result, lower temperatures (up to 0.5 K) and increased cloudiness are generated for the Arctic region. The standard CCM sea ice albedo scheme is used as an adjustment to maintain normal temperatures for the polar oceans. The radiative impact of leads and melt ponds warmed sea ice regions only for short time periods. The third scheme generated markedly lower planetary albedos (reductions of 0.07 to 0.17) and higher surface temperatures (up to 2.0 K) than control values.The CCM simulates a gradual decrease in spring and summer Arctic cloud cover whereas observations show a sharp spring increase. Examination of the CCM code, particularly the cloud parameterization, is required to address this problem.With 12 Figures     

Development of a new sea ice growth and lead parameterization

A thermodynamic sea ice model that has been numerically structured to take time steps on the order of a week has been shown to be sensitive to time step size. This sensitivity was caused by the extrapolation of initial ice growth rates over the long time step. A new parameterization of new sea ice growth on open ocean and in leads that can be used over a large range of time step sizes (at least from 0.3 to 12 days) is described here. In this parameterization new sea ice growth is computed as a power law function of the initial energy deficit in the ocean. This power law takes into account the rapid reduction of the ice growth rate as the sea ice gets thicker, and therefore reduces sensitivity to time step size. Tests of this parameterization show that this method does a good job of simulating the rate of new ice growth when compared to data from Mawson, Antarctica, and is relatively insensitive to the length of the time step.