Vertical Grid Spacing Research Articles

Effect of Acceleration on Bottom Shear Stress in Tidal Estuaries

A formulation specifying the bottom shear stress boundary condition for an unsteady, tidal flow model is derived through theoretical analysis. The unsteady boundary layer equation is solved for the velocity distribution adjacent to the boundary using a regular perturbation expansion. When applied to the bottom layer of the computation grid of a numerical model, the solution relates the bottom shear stress to the velocity and acceleration computed in that layer. Numerical experiments with a hypothetical homogeneous estuary indicate that the error in calculated bottom stress increases with vertical grid spacing if the logarithmic profile is used to relate bottom stress to velocity. The use of the formulation including the correction terms can significantly reduce this error and adequately specify the boundary condition in a numerical model of estuarine flow with a practical range of vertical grid spacing. The numerical experiments also show that, if the roughness height and bottom stress are estimated by fitting a logarithmic profile to the velocity distribution, they may be off by more than 100%.

Deep-Water Renewal in the Upper Basin of Loch Sunart, a Scottish Fjord

Recording current meters were deployed near the surface and bottom in the upper basin of Loch Sunart during the summers of 1987, 1989, and 1990. The measurements revealed frequent, though irregular, deep-water renewal events when the basin water was replaced by density driven intrusions. The data suggested that these events were induced by wind-enhanced estuarine circulation during periods of low fresh water runoff. A semi-implicit, laterally integrated estuarine model was modified to allow variable vertical grid spacing and to permit the sea surface to move vertically through the grid, both modifications being necessary in order to apply the model to the sea loch environment. A turbulence closure scheme was also incorporated. The model can simulate the evolution of the salinity field over periods of several weeks and was used to examine the mechanisms that induce deep-water renewal. Model results suggested that very weak stratification in the basin is required for renewal to occur and indicated that recirculation of brackish surface water, caused by the very shallow sill, may increase the regularity of renewal by accelerating the rate of density reduction of the bottom water.

A three‐dimensional general circulation model with coupled chemistry for the middle atmosphere

We document a new middle atmosphere general circulation model that includes ozone photochemistry. The dynamical model component is based on the NCAR middle atmosphere version of the Community Climate Model. The chemistry model component simulates the evolution of 24 chemically reactive gases. The horizontal resolution is approximately 3° in latitude and 6° in longitude. It includes 44 levels, with a maximum vertical grid spacing of about 2.5 km and a top level at around 75 km. The chemical model distinguishes between species where we judge transport to be critical and those for which it may be neglected. Nine longer‐lived species (N2O, CH4, H2O, HNO3, N2O5, CO, ClONO2, HCl, and HOCl) and four chemical families (NOy, NOx, Ox and Clx) are advected. Concentrations of 15 species which are typically shorter‐lived or are members of the chemical families are diagnosed using quasi‐equilibrium assumptions ( O(1D), OH, Cl, O(3P), O3, HO2, NO2, ClO, NO, HNO4, NO3, N, OClO, Cl2O2, H2O2). Distributions for a number of other species are prescribed. Results are presented from a 2‐year simulation, which include only gas phase photochemical reactions and in which the ozone distribution forecast from the chemistry module does not affect the radiative forcing of the dynamical fields. The calculated distributions of trace species and their seasonal evolution are often quite realistic, particularly in the northern hemisphere extratropics. Distributions of long‐lived species such as N2O and CH4 correspond well to satellite observations. Some features, such as the double peak structure occurring during equinoxes, are not reproduced. The latitudinal variation and seasonal evolution of the ozone column abundance is quite realistic. The calculated vertical distribution of the ozone mixing ratio exhibits significant differences from measured values. The model underestimates significantly the ozone in the upper stratosphere (40 km) and in the extratropics, where the maximum values occur at too low an altitude. The model reproduces the key features expected in the distribution of fast reacting nitrogen and chlorine compounds. Problems in the southern polar simulation (which we attribute to the lack of a comprehensive parameterization of gravity waves) are discussed. The model currently parameterizes only stationary gravity waves generated by flow over orography. Other sources of gravity waves may be required to improve the model simulation.

ボックスラグランジアン雨滴落下スキーム

A new rain-drop scheme named box-Lagrangian rain-drop scheme is developed. In the Eulerian rain-drop scheme, since the change of the mixing ratio of rainwater q during unit time is calculated from ∂q/∂t=V∂q/∂z, the time step interval Δt is restricted by the Courant-Friedrichs-Lewy (CFL) condition for rain falling: V Δt/Δz<1, where V is the terminal velocity of rain falling, Δz the vertical grid spacing. In the box-Lagrangian rain-drop scheme, the above numerical constraint can be relaxed by the following method. The bulk of rainwater in a vertical grid box is dropped while keeping V constant during a time step interval, and it is partitioned into grid boxes existing in the space where it is dropped. When Δt is less than the critical value, Δz c , which is calculated from the CFL condition (i.e., Δt c =Δz/V), the box-Lagrangian scheme coincides with the Eulerian scheme. Furthermore, even when Δt is several times larger than Δt c , the box-Lagrangian scheme drops rainwater stably with sufficient accuracy. The box-Lagrangian scheme is effective especially when many vertical layers are employed in the lower part of the model domain to express the atmospheric boundary layer in detail

Sensitivity of PBL model predictions to model design and uncertainties in environmental inputs

A simple time-dependent one-dimensional model of the planetary boundary layer (PBL) is described and used to examine the degree to which model design decisions affect model output variables. The model's sensitivity to changes in the environmental conditions is also explored. Averages of the surface fluxes, near-ground wind speeds and other PBL properties from 48 h simulations are compared to control runs. The model-calculated surface fluxes are most sensitive, in decreasing order of importance, to the vertical grid spacing, the form of closure between the surface temperature and the atmosphere, the use of vertical diffusivity smoothing, the choice of maximum time step and choice of turbulence closure scheme. These fluxes are relatively insensitive to mixing-length scaling or choice of implicit time step weighting factor. Sensitivity to changes in soil type exceeds any of the design criteria tested. The modeled fluxes are moderately sensitive to small variations in the horizontal pressure gradient, to unsteadiness in the geostrophic wind and to variations in surface roughness. They are relatively insensitive to uncertainties in local vertical velocities and small (25%) variations applied separately to soil thermal diffusivity or heat capacity. The sensitivity of the average PBL depth (Zi) to model and environmental changes are similar to those of surface fluxes except thatZi is more sensitive to changes in mixing length, albedo and imposed vertical velocity then are the surface fluxes.

Nonlinear Hydrostatic Conditional Symmetric Instability: Implications for Numerical Weather Prediction

A simplified two-dimensional version of the Pennsylvania State University-NCAR Mm scale Model (MM4) was used to investigate the nonlinear evolution of unforced conditional symmetric instability (CSI). Sensitivity tests examines the effects of the model resolution, the magnitudes and formulation of the vertical and horizontal diffusion, and the Prandtl number on various aspects of the CSI circulations. Aspects of the circulations that are considered include the transverse velocity, the growth rate, and the updraft slope, as well as the existence of a CSI circulation. With the fairly unstable initial conditions used in these tests, unstable CSI modes are explicitly resolved with horizontal grid spacing of at most 30 km, using a fairly weak horizontal diffusion. The vertical grid spacing needs to be no greater than 340 m to be consistent with the horizontal grid spacing and the sloping thermal structures. To resolve the most unstable nonlinear CSI modes, horizontal resolutions of no more than 15 km and vertical resolutions less than 170 m are necessary. The magnitude of the horizontal diffusion, the magnitude and the formulation of the vertical diffusion, and the Prandtl number all affect the simulated CSI circulations. Comparisons to linear theory allow the generalization of the results. These generalizations suggest that the combined effects of model resolution, model diffusion, scale height of the instability, and environmental conditions (e.g., N2) determine whether CSI will be explicitly released in a numerical model, and also whether the resolved unstable modes include the desirable most unstable mode. Unstable CSI modes that do not correspond to the most unstable mode can be explicitly resolved with a grid spacing that is coarser than that necessary for the most unstable mode. If the resolved modes do not include the most unstable mode, the evolution of the CSI circulations will be substantially slower and the amplitudes reduced from what should be expected in the real atmosphere in which the most unstable mode should be present.

Adaptation of a matrix parameterization of the middle atmospheric radiative cooling for an arbitrary vertical coordinate grid

One of the major drawbacks of recently proposed matrix parameterizations of the middle atmospheric radiative cooling is their rigidly fixed vertical coordinate grid. A straightforward matrix transformation method is described to adjust the parameterization matrix to an arbitrary vertical grid. Applied to the 15 μm CO 2 band parameterization proposed by Akmaev and Shved]^[(1982) J. atmos. terr. Phys. 44, 993] for local thermodynamic equilibrium (LTE) region of the middle atmosphere, the method is shown to introduce cooling rate errors not exceeding 0.11 K day −1 for a vertical grid spacing of up to 5 km.

Equatorial Waves in a Stratospheric GCM: Effects of Vertical Resolution

It is noted that equatorially trapped wave modes, e.g., Kelvin and Rossby-gravity waves, are thought to play a critical role in forcing the quasi-biennial oscillation of the lower tropical stratosphere. The ability of a GCM to simulate these waves is examined and the changes in the wave properties as a function of the vertical resolution of the model are investigated. The dependence of the equatorial wave simulation of vertical resolution is examined utilizing three experiments with vertical grid spacings of about 2.8, 1.4, and 0.7 km. At high vertical resolution, the simulated waves are shown to agree with the available observations.

Removal model suitable for air pollutants emitted from an elevated source

A time-dependent removal model for air pollutants from an elevated source is presented. The model considers the first-order (delayed) removal. The deposition of pollutants is accounted for by applying the absorptive boundary on the ground surface. The transport equation representing instantaneous and delayed removal is solved numerically by the fractional step method. A Lagrangian (moving cell) frame is used to solve the advection step, while a Eulerian (multibox) frame is applied to the diffusion and removal processes. Variable wind velocity and coefficient of diffusivity are considered. Velocity profile is approximated by a step function, which provides compatibility with the Eulerian grid spacing. Variable vertical grid spacing is considered to get good resolution concentration profile near the source.

Sensitivity of Simulated Climate to Model Resolution

Dynamical measures of the climate (e.g., winds, eddy fluxes) simulated by a general circulation model are compared at different horizontal and vertical resolutions for the December, January, and February period. The simulations of the troposphere are found to improve significantly as the horizontal resolution increases in the range of spectral truncations from T21 to T63. Little sensitivity is found to changes in vertical resolution between about 2.8 km and 0.7 km vertical grid spacing. The improvements in the Southern Hemisphere troposphere are greater than in the Northern Hemisphere as the horizontal resolution increases. The eddy momentum fluxes and kinetic energies in both hemispheres increase monotonically with horizontal resolution. At T63, the Southern Hemisphere winds, eddy fluxes, and eddy kinetic energies agree favorably with observations, while serious discrepancies are present at lower resolutions. In the Northern Hemisphere, the eddy momentum flux at T63 is slightly larger than observed, while the transient eddy kinetic energy is still barely half of the observed. The gravity wave drag parameterization plays a significant role in the simulations at all resolutions. Eddy momentum fluxes increase when gravity wave drag is removed with a corresponding increase in low-level winds and surface stress.

Observational Study of a Multiple Microburst-Producing Storm Part I: Kinematic, Dynamic and Thermodynamic Structures

Some kinematic, dynamic, and thermodynamic structures of a multiple microburst-producing storm, which occurred on 5 August 1982 in Colorado, were studied for three analysis times at 1845, 1847, and 1850 MDT. Dual Doppler data collected during the project of Joint Airport Weather Studies (JAWS) at Denver's Stapleton International Airport were objectively analyzed to produce a three- dimensional wind field. The domain of interest had a horizontal dimension of 15 km by 15 km covering three microbursts. There were five analysis levels in the vertical ranging from 0.25 to 1.25 km AOL. The horizontal and vertical grid spacings were 0.5 and 0.25 km, respectively. Vertical velocities were computed by integrating the anelastic continuity equation upward from the surface. Subsequently, fields of deviation perturbation pressure and temperature were recovered from a detailed wind field using the three momentum equations. These fields were then subjected to internal consistency checks to determine the level of confidence before interpretation. Results show that the microbursts being investigated are embedded within the high-reflectivity cores with heavy precipitation. A wet microburst is accompanied by the misocyclone at levels above 0.75 km in the downdraft. It has the slowly descending downfiow forming a cold core at the lowest levels due to the evaporation of raindrops. Near the gust front (GF), a mesocyclone-like circulation develops in the area where the warm, dry environmental air interacts with the negatively buoyant microburst outflow. High pressure forms inside the microburst core with low pressure in the strong wind regions. Pronounced horizontal pressure gradients occur from the microburst center outward to balance the strong diverging outflow that region. The retrieved pressure and temperature fields agree well with the storm's kinematic structure. The combined effects of misocyclone circulations, perturbation pressure gradients, buoyancy and precipitation loading are responsible for maintaining the microburst downdrafts in the atmospheric boundary layer (ABL).

Momentum and eddy kinetic energy transports by a multiple microburst‐producing storm

A comprehensive study of the structure and internal dynamics was made for a multiple microburst‐producing storm for August 5, 1982, in Colorado during the Joint Airport Weather Studies (JAWS) Project at Denver's Stapleton International Airport. The analysis levels were contained between 0.25 and 2 km. The horizontal and vertical grid spacings were 0.5 and 0.25 km, respectively. These fields were subjected to internal consistency checks to determine the level of confidence before interpretation. Results show that the combined effects of misocyclone circulations, perturbation‐pressure gradients, melting, buoyancy, and precipitation loading contribute to the maintenance of the microburst downdrafts in the atmospheric boundary layer (ABL). At low levels where the microbursts dominate, the presence of microburst gust fronts and diverging outflow enhances the vertical transport of horizontal momentum and eddy kinetic energy. The misocyclones located above the microbursts largely determine the transport of horizontal momentum and eddy kinetic energy there. In the microburst subdomain, a net transport of horizontal momentum and eddy kinetic energy is downward from the misocyclone to the surface. Its magnitude is directly proportional to the strength of a microburst at low levels and the misocyclone aloft. Budget studies of horizontal momentum flux and eddy kinetic energy within the storm domain and the microburst subdomain have added to a further understanding of the storm's structure and internal dynamics. The pressure and buoyancy effects are two main contributors to the generation/decay of horizontal momentum fluxes and eddy kinetic energy at the microburst levels.

Application of a sigma coordinate sea model to the calculation of wind-induced currents

A three-dimensional numerical sea model is formulated in terms of sigma coordinates in the vertical. The vertical grid spacing in the model is arbitrary and can be refined to give enhanced resolution in high shear regions (e.g., close to the sea surface in wind-driven flows, and/or across the thermocline in stratified flows). A method of accurately determining surface currents and indicating how fine a grid is required in the surface layer is described. The problem of determining a suitable formulation of vertical eddy viscosity to use in a model of wind-induced flow in a tidal sea is considered in detail. A formulation in which surface eddy viscosity depends upon the roughness of the sea surface and the transfer of momentum to depth by surface waves appears reasonable. Below the surface layer turbulence is related to the current at depth. Idealized calculations are performed to demonstrate the accuracy and stability of the sigma coordinate model. Results of these calculations indicate that the formulation of eddy viscosity developed in this paper can explain the high surface shears reported in lake measurements of wind-induced surface currents, and the lack of shear under strong wind conditions in the open sea ( GORDON, 1982, Journal of Geophysical Research, 87, 1939–1951 ). Surface current to surface wind ratio are also computed.

Comparison of the Nimbus-4 BUV ozone data with the Ames two-dimensional model

A comparison is made of the first two years of Nimbus-4 backscattered ultraviolet (BUV) ozone measurements with the predictions of the Ames two-dimensional model. The ozone observations used in this study consist of the mixing ratio on the 1-, 2-, 5-, and 10-mb pressure surfaces. These data are zone and time averaged to obtain seasonal means for 1970 and 1971 and are found to show strong and repeatable meridional and seasonal dependencies. The model used for comparison with the observations extends from 80°N to 80°S latitude and from altitudes of 0 to 60 km with 5° horizontal grid spacing and 2.5-km vertical grid spacing. The chemical reaction and photolysis rate constants used in the model are those recommended in the report of the NASA Panel for Data Evaluation (1979) Chemical reaction and photolysis rates are diurnally averaged, and the photodissociation rates are corrected for the effects of scattering.

An Objective Analysis Technique for Constructing Three-Dimensional Urban-Scale Wind Fields

An objective analysis procedure for generating mass-consistent, urban-scale three-dimensional wind fields is presented together with a comparison against existing techniques. The algorithm employs terrain following coordinates and variable vertical grid spacing. Initial estimates of the velocity field are developed by interpolating surface and upper level wind measurements. A local terrain adjustment technique, involving solution of the Poisson equation, is used to establish the horizontal components of the surface field. Vertical velocities are developed from successive solutions of the continuity equation followed by an iterative procedure which reduces anomalous divergence in the complete field. Major advantages of the procedure are that it is computationally efficient and allows boundary values to adjust in response to changes in the interior flow. The method has been successfully tested using field measurements and problems with known analytic solutions.

An Examination of Frontal Structure in a Fine–Primitive Equation Model for Numerical Weather Prediction

Abstract The structure of upper level and surface frontal zones associated with a cyclone developing over the central United States on 21–22 February 1971, as predicted by a limited-area, moist, primitive equation model with horizontal and vertical grid spacing on the order of 100 and 1.5 km, respectively, Is qualitatively examined and discussed. A comparison of crow-section analyses of the frontal zones, constructed from rawinsondo observations and from model output data, reveals that the horizontal and vertical scales of the observed fronts are ∼100 and ∼1 km, while those for the model-predicted fronts are ∼200–400 and ∼1–2 km. The discrepancy in scale can be explained by the coarse model resolution, which essentially renders be frontal zones subgrid-scale phenomena. Despite the model's lack of fidelity in reproduce the observed details in frontal structure, point calculations with Miller' equation appear reasonable in view of those results obtained in previous synoptic investigations. Vertical tilting ...