Abstract

In this work the performance of ensembles generated by commonly used methods in a nonlinear system with multiple attractors is examined. The model used here is a spectral truncation of a barotropic quasigeostrophic channel model. The system studied here has 44 state variables, great enough to exhibit the problems associated with high state dimension, but small enough so that experiments with very large ensembles are practical, and relevant probability density functions (PDFs) can be evaluated explicitly. The attracting sets include two stable limit cycles.

To begin, the basins of attraction of two known stable limit cycles are characterized. Large ensembles are then used to calculate the evolution of initially Gaussian PDFs with a range of initial covariances. If the initial covariances are small, the PDF remains essentially unimodal, and the probability that a point drawn from the initial PDF lies in a different basin of attraction from the mean of that PDF is small. If the initial covariances are so large that there is significant probability that a given point in the initial ensemble does not lie in the same basin of attraction as the mean, the initial Gaussian PDF will evolve into a bimodal PDF. In this case, graphical representation of the PDF appears to split into two distinct regions of relatively high probability.

The ability of smaller ensembles drawn from spaces spanned by singular vectors and by bred vectors to capture this splitting behavior is then investigated, with the objective here being to see how well they capture multimodality in a highly nonlinear system. The performance of similarly small random ensembles drawn without dynamical constraints is also evaluated.

In this application, small ensembles chosen from subspaces of singular vectors performed well, their weakest performance being for an ensemble with relatively large initial variance for which the Gaussian character of the initial PDF remained intact. This was the best case for the bred vectors because of their tendency to align tangent to the attractor, but the bred vectors were at a disadvantage in detection of the tendency of an initially Gaussian PDF to evolve into a bimodal one, as were the unconstrained ensembles.

Abstract

Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength.

It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, we note that the region of instability (i.e., critical Ri) is increased, the extent of which is greater for longer wavelength. For Prandtl number = 1, permitting the angle to be nonsymmetric demonstrates the existence of two maxima in growth rate at opposite angles of orientation and with very different energetics. For Prandtl number far enough from one and for large enough dissipation, only one of these two modes has positive growth rates. Growing oscillatory modes were found for some cases.

Abstract

A theoretical model for the removal of aerosol particles by falling columnar ice crystals which incorporates gravitational, inertial, thermophoreic, diffusiophoretic, and electrostatic mechanisms has been formulated. The results of this trajectory model, combined with earlier resuslts, determine the collection efficiency for submicron particles as a flux onto a collector surface for any geometry and due to Brownian diffusion, thermo- and diffusio-phoresis as well as electrostatic forcing. The combination of these two models provides scavenging efficiencies for aerosol particles of radii 0.001 ≤ r ≤ 10.0μm by columnar ice crystals with associated Reynolds numbers ranging from 0.5 to 20.0. This quantiative study indicates the effect of particle size, charge, and atmospheric conditions.

Abstract

Formulas suitable for calculating the electrostatic, temperature, and vapor density fields surrounding stationary columnar ice crystals are derived. Columnar ice crystals are approximated as circular cylinders of finite lengths. In this way the effects of sharp edges are taken into account. Results of electrostatic fields for some columnar ice crystals are shown. The potential distribution of a prolate spheroid is also determined and compared to that of a circular cylinder. The results show that the approximation of a columnar crystal by a prolate spheroid is inadequate. Formulas are also given to convert the electric fields into temperature and vapor density fields.

Abstract

Spatial correlations based on monthly rainfall totals from northwest Georgia for the period 1949–77 are studied. This work, a part of the Meteorological Effects of Thermal Energy Releases (METER) Program, determines natural variability rainfall trends and assists the field studies of potential precipitation effects of the Bowen Electric Generating Plant near Cartersville, Georgia. The spatial correlations, based on the overall record as well as the stratified data in terms of “wet” and “dry” seasons, are investigated with regard to distance between stations, wind direction and topography. The results indicate a strong dependence of the spatial correlation patterns on the prevailing storm tracks in the area.

A method is developed using the spatial correlation as an indicator of effects in weather modification experiments. This method is based on the generation of empirical distribution functions by randomization for various sample sizes. The application of this technique to the Plant Bowen study in a control-target statistical design reveals preliminary positive evidence of rainfall modification in the target area.

Abstract

Land surface heterogeneity and its effects on surface processes have been a concern to hydrologists and climate scientists for the past several decades. The contrast between the fine spatial scales at which heterogeneity is significant (1 km and finer) and the coarser scales at which most climate simulations with land surface models are generated (hundreds of kilometers) remains a challenge, especially when incorporating land surface and subsurface lateral fluxes of mass. In this study, long-term observational land surface forcings and derived solar radiation were used to force high-resolution land surface model simulations over the Arkansas–Red River basin in the Southern Great Plains region of the United States. The most unique aspect of these simulations is the fine space (1 km²) and time (hourly) resolutions within the model relative to the total simulation period (51 yr) and domain size (575 000 km²). Runoff simulations were validated at the subbasin scale (600–10 000 km²) and were found to be in good agreement with observed discharge from several unregulated subbasins within the system. A hydroclimatological approach was used to assess simulated annual evapotranspiration for all subbasins. Simulated evapotranspiration values at the subbasin scale agree well with predictions from a simple one-parameter empirical model developed in this study according to Budyko’s concept of “geographical zonality.” The empirical model was further extended to predict runoff and evapotranspiration sensitivity to precipitation variability, and good agreement with computed statistics was also found. Both the empirical model and simulation results demonstrate that precipitation variability was amplified in the simulated runoff. The finescale at which the study is performed allows analysis of various aspects of the hydrologic cycle in the system including general trends in precipitation, runoff, and evapotranspiration, their spatial distribution, and the relationship between precipitation anomalies and runoff and soil water storage anomalies at the subbasin scale.

Abstract

The performance of data assimilation methods in an idealized three-dimensional time-dependent coastal baroclinic model is assessed by computing ensemble error statistics. The analytical representer solution allows for computation of posterior error statistics for the variational generalized inverse method (GIM) as well as sequential methods such as the Kalman filter (KF) and optimal interpolation (OI). Computations can be made in a straightforward way, given the statistics of errors in the model equations and data. The GIM yields solutions with significantly smaller variance than that given by KF or OI if the data contain valuable information about the past flow. This is the case, for instance, when a large fraction of the model error is due to uncertainty in the wind stress. In the scope of the model presented here, the plausibility of simplifications made in a practical OI scheme is analyzed. The unified study of the GIM, KF, and OI allows for the demonstratation of how the forecast error covariance used in a practical OI sequential scheme may be optimized with the use of lagged covariances for the model solution. The effect of the misspecified input error statistics on the solution quality is also assessed. In some practically relevant cases the use of future data by the GIM, in contrast to KF and OI, compensates for incorrectly specified input error covariances.

Abstract

The initiation of deep convection through forcing along boundary layer convergence lines is examined using observations from the Convection and Precipitation/Electrification Experiment conducted in east-central Florida during the summer of 1991. The study is concerned with the evolution and interaction of two converging air masses that were initially separated by an intervening boundary layer characterized by neutral stability and horizontal convective rolls. As anticipated, major thunderstorm erupt when the east coast breeze eventually collides with thunderstorm outflows from the west, but unexpected convection takes place prior to their merger along a well-defined confluence zone associated with a persistent quasi-stationary roll vortex signature. Analyses using wavelet transforms confirm that linear boundary layer reflectivity features are strongly correlated with radial convergence associated with roll vortices. In this study, complementary interactions between roll vortex convergence lines and the sea-breeze front are not sufficient to trigger deep convection. However, organized convergence along the eastward-spreading thunderstorm outflows did interact periodically with roll vortex convergence maxima to initiate a series of new storms.

Results from two-dimensional numerical model simulations replicate many of the observed boundary layer features. Surface heating produces circulations similar to sea-breeze frontal zones that appear near the coastlines and progress steadily toward each other as the interior boundary layer deepens. Vertical velocity maxima develop over the associated convergence zones, but weaker periodic maxima also occur within the interior air mass at intervals similar to the spacing of observed horizontal roll vortices. As the boundary layer deepens, a layer immediately above it cools, confirming organized large-scale ascent within the interior air mass. When surface heating is removed, circulation associated with this large-scale ascent collapses to a near-steady state where the width of the remaining prominent updraft is similar to its depth. This results from a balance between momentum advected by large-scale circulations and excess pressure developed at low levels near the center of the interior domain.

Abstract

Results from a model of wind-driven circulation are analyzed to study spatial and temporal variability in the bottom mixed layer (BML) on the mid-Oregon shelf in summer 2001. The model assimilates acoustic Doppler profiler velocities from two cross-shore lines of moorings 90 km apart to provide improved accuracy of near-bottom velocities and turbulence variables in the area between the mooring lines. Model results suggest that the response of the BML thickness to upwelling- and downwelling-favorable winds differs qualitatively between an area of “simple” bathymetric slope at 45°N and a wider shelf area east of Stonewall Bank (44.5°N). At 45°N, the BML grows in response to downwelling-favorable conditions, in agreement with known theories. East of Stonewall Bank, the BML thickness is increased following upwelling events. In this area, the southward upwelling jet detaches from the coast and flows over a wider part of the Oregon shelf, creating conditions for Ekman pumping near the bottom. Based on computations of bottom stress curl, the vertical pumping velocity in this area may reach 15 m day⁻¹ following periods of intensified upwelling-favorable winds. A column of denser, near-bottom water upwelled over the Ekman flow convergence area is tilted as a result of vertical shear in horizontal velocities, causing unstable stratification and convective overturning. As a result of this process, BML thickness values east of Stonewall Bank can be in excess of 20 m following upwelling, comparable to maximum values at 45°N following downwelling.

Abstract

Cumulus formation and convection initiation are examined near a cold front–dryline “triple point” intersection on 24 May 2002 during the International H₂O Project (IHOP). A new Lagrangian objective analysis technique assimilates in situ measurements using time-dependent Doppler-derived 3D wind fields, providing output 3D fields of water vapor mixing ratio, virtual potential temperature, and lifted condensation level (LCL) and water-saturated (i.e., cloud) volumes on a subdomain of the radar analysis grid. The radar and Lagrangian analyses reveal the presence of along-wind (i.e., longitudinal) and cross-wind (i.e., transverse) roll circulations in the boundary layer (BL). A remarkable finding of the evolving radar analyses is the apparent persistence of both transverse rolls and individual updraft, vertical vorticity, and reflectivity cores for periods of up to 30 min or more while moving approximately with the local BL wind. Satellite cloud images and single-camera ground photogrammetry imply that clouds tend to develop either over or on the downwind edge of BL updrafts, with a tendency for clouds to elongate and dissipate in the downwind direction relative to cloud layer winds due to weakening updrafts and mixing with drier overlying air. The Lagrangian and radar wind analyses support a parcel continuity principle for cumulus formation, which requires that rising moist air parcels achieve their LCL before moving laterally out of the updraft. Cumuli form within penetrative updrafts in the elevated residual layer (ERL) overlying the moist BL east of the triple point, but remain capped by a convection inhibition (CIN)-bearing layer above the ERL. Dropsonde data suggest the existence of a convergence line about 80 km east of the triple point where deep lifting of BL moisture and locally reduced CIN together support convection initiation.