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J. L. Lee and G. L. Browning

Abstract

The vorticity method is applied to determine horizontal divergence using the dynamical balance of terms in the vorticity equation. The viability of the method is analyzed in terms of dynamical approximations, sensitivity to observation and truncation errors, and numerical experiments. This analysis is also applied to the kinematic method, which calculates the horizontal divergence by adding together the, appropriate finite-difference approximations of its individual terms. The analysis of errors in the vorticity and kinematic methods is based on the accuracy of the data. It is proven analytically that errors in the divergence derived from the vorticity method are smaller than those of the kinematic method by a factor equal to the Rossby number, even though the former method involves higher-order derivatives. When a 10% random error is included, the error of the large-scale divergence in the kinematic method exceeds 100%, whereas the error derived by the vorticity method is less than 30% and is comparable to the error in the horizontal wind as expected from the error analysis. An essential result is that the temporal variation of the vorticity is not adequately resolved by the 12-h rawinsonde observing systems and must instead be derived from high temporal resolution wind data such as those measured by the Wind Profiler Demonstration Network. Due to the unavailability of the profiler data in the planetary boundary layer, the vorticity method is primarily applicable to the free atmosphere.

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J. T. Lee and Clarence L. David

This paper is a description of the Tornado Research Airplane Project during 1958 and 1959. The instrumentation of the aircraft, as well as the organization of the project, is described. A section on instrument calibration and a description of data reduction and processing are included. The results of a radiosonde comparison test made in 1959 are given, and these results are compared with the results of radiosonde comparison tests made during 1958. A sample of the graphical presentation that is available for each of the flights is shown. For the information of anyone interested in these data, a listing of all operational flights for both 1958 and 1959 is given.

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J. L. Lee and A. E. MacDonald

Abstract

Mesoscale bounded derivative initialization (BDI) is utilized to derive dynamical constraints, from which elliptic equations are formulated to derive smooth initial fields over complex terrain for mesoscale models. The initialization is implemented specifically for the quasi-nonhydrostatic (QNH) model. This study presents the first real data application of the mesoscale BDI and the QNH model to simulate a mesoscale storm that produced heavy precipitation along the Colorado Front Range. In this study, the focus is on (i) smooth numerical solution over complex terrain, (ii) baroclinic instability associated with condensational heating and high mountains, and (iii) the simulation of orographic precipitation. Numerical results show that initial fields derived from BDI were smooth and evolved smoothly in the QNH model for 48 h. It is noteworthy that the smooth solution existed up to the lateral boundaries. During the 48-h simulation, the midtropospheric storm moved freely in and out of the limited-area domain as if there were no lateral boundaries. The mesoscale storm for northeast Colorado was initiated by the persistent upslope easterlies and strong upward motions that triggered heavy precipitation. The simulated precipitation amounts and pattern were in good agreement with those observed. In general, both the large-scale dynamic system and the mesoscale precipitation event evolved smoothly and accurately, which indicates the value of BDI and QNH for mesoscale weather prediction.

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W. J. Emery, W. G. Lee, and L. Magaard

Abstract

Long-term mean temperature and salinity profiles, computed from an edited set of historical hydrographic data, have been used to calculate mean profiles of density and Brunt–Väisäl&auml frequency by 5° squares for the North Atlantic and the North Pacific. With these stratification profiles the internal Rossby deformation radii are computed and displayed in map form alone, with the external Rossby radii. Seasonal variations are examined in a limited number of 5° squares selected to have an equal number of hydrographic observations for each of the four seasons. In most Brunt–Väisäl&auml frequency profiles significant seasonal variations are limited to the upper 250 m; seasonal variations in internal Rossby radii are everywhere surprisingly small.

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Conrad L. Ziegler, Tsengdar J. Lee, and Roger A. Pielke Sr.

Abstract

A nonhydrostatic, three-dimensional version of the Colorado State University Regional Atmospheric Modeling System (CSU-RAMS) is used to deduce the processes responsible for the formation of drylines and the subsequent initiation of deep, moist dryline convection. A range of cumuliform cloud types are explicitly simulated along drylines on 15, 16, and 26 May 1991 in accordance with observations.

In the simulations, narrow convergence bands along the dryline provide the lift to initiate deep moist convection. The thermally direct secondary convective boundary layer (CBL) circulations along the dryline are frontogenetic and solenoidally forced. Maximum updrafts reach 5 m s−1 and the bands are 3–9 km wide and 10–100 km or more in length. The updrafts penetrate and are decelerated by the overlying stable air above the CBL, reaching depths of about 2000 m in the cases studied. Moisture convergence along the mesoscale updraft bands destabilizes the local sounding to deep convection, while simultaneously decreasing the CIN to zero where storms subsequently develop. The lapse rates of vapor mixing ratio and potential temperature in the mesoscale updrafts are rather small, indicating that increases of the lifted condensation level (LCL) and level of free convection (LFC) due to mixing following the parcel motion are also small. Simulated convective clouds of all modes, including shallow forced cumulus and storms, develop in regions where the CIN ranges from zero up to the order of the peak kinetic energy of the boundary layer updraft and moisture is sufficiently deep to permit water saturation to develop in the boundary layer.

The findings suggest that classic cloud models may not adequately simulate the early development of dryline storms due to their use of thermal bubbles to initiate convection and their assumption of a horizontally homogeneous environment. In contrast, cautious optimism may be warranted in regard to operational numerical prediction of drylines and the threat of attendant deep convection with mesoscale models.

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Sang-Ki Lee, J. L. Pelegrí, and John Kroll

Abstract

An analytic solution is presented for the steady-state depth-averaged western boundary current flowing over the continental slope by combining three highly idealized models: the Stommel model, the Munk model, and the arrested topographic wave model. The main vorticity balance over the slope is between planetary vorticity advection and the slope-induced bottom stress torque, which is proportional to r υ(h −1)x where r is the Rayleigh friction coefficient, h is the water depth, and υ is the meridional velocity. This slope-induced torque provides the necessary source of vorticity for poleward flow over the slope, its simple interpretation being that vorticity is produced because the bottom stress has to act over the seaward-deepening water column. The character of the solution depends on the slope α as well as on the assumed bottom drag coefficient, and the length scale of the boundary current is ∼2r/(βα). It is further shown that, if the depth-averaged velocity flows along isobaths, then the stretching of water columns associated with cross-isobath geostrophic flow, which compensates bottom Ekman transport, is identical to the slope-induced torque by the geostrophic velocities.

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A. E. MacDonald, J. L. Lee, and Y. Xie

Abstract

In recent years, there has been extensive study of the mathematical basis of weather prediction leading to a new system of continuous equations that are well posed, and a set of conditions that make discrete atmospheric and other models stable and potentially more accurate. In particular, the theory deals with initial boundary value problems that admit multiple timescales. Using this theory, a quasi-nonhydrostatic model called QNH was developed at NOAA’s Forecast Systems Laboratory. The model is fully compressible and explicit in the vertical as well as the horizontal direction. It is characterized by a parameter, “α” (typically the square of the vertical to horizontal aspect ratio), which multiplies the hydrostatic terms in the vertical equation of motion. In this paper, the authors describe the theoretical basis for the use of these models in mesoscale weather prediction. It is shown that for the mesoscale, the parameter has the effect of decreasing both the frequency and amplitude of the gravity wave perturbation response to small-scale impulses in forcing and to unbalanced initial conditions. This allows a modeler to choose a length scale below which gravity wave generation is suppressed. A weakness of the approach is that the hydrostatic adjustment process is slowed down. The analysis indicates that the parameter does not have an effect on the Rossby waves, the larger horizontal-scale gravity waves, nor on forced solutions such as those created by heating. The bounded derivative initialization is discussed. Since the speeds of the vertical acoustic waves are decreased, quasi-nonhydrostatic models can calculate the vertical equations explicitly and still meet the Courant–Friedrichs–Levy criteria. It is concluded that the unique characteristics of quasi-nonhydrostatic models may make them valuable in mesoscale weather prediction, particularly of clouds and precipitation.

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A. E. MacDonald, J. L. Lee, and S. Sun

Abstract

A new mesoscale weather prediction model, called QNH, is described. It is characterized by a parameter that multiplies the hydrostatic terms in the vertical equation of motion. Models of this type are referred to generically as “quasi-nonhydrostatic.” The quasi-nonhydrostatic parameter gives the model a character that is essentially nonhydrostatic, but with properties that are theoretically thought to result in smoother, more accurate, and stable predictions. The model is unique in a number of other aspects, such as its treatment of lateral boundary conditions, the use of explicit calculation in the vertical direction, and the use of the bounded derivative theory for initialization. This paper reports on the design and test of the QNH model, which represents the first time the applicability of this type of model has been demonstrated for full-physics, mesoscale weather prediction. The dynamic formulation, discretization, numerical formulation, and physics packages of the model are described. The results of a comprehensive validation of the model are presented. The validation includes barotropic, baroclinic (Eady wave), mountain wave, tropical storm, and sea breeze tests. A simulation of a winter storm (with updated lateral boundary conditions) is presented, which shows that the model has significant skill in forecasting terrain-forced heavy precipitation. It is concluded that the QNH model may be valuable for mesoscale weather prediction.

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J. L. Schols, J. A. Weinman, G. D. Alexander, R. E. Stewart, L. J. Angus, and A. C. L. Lee

Abstract

Microwave brightness temperatures emanating from a North Atlantic cyclone were measured by the Special Sensor Microwave/Imager (SSM/I) on the Defense Meteorological Satellite Program satellite. As other investigators have found before, low 85.5-GHz brightness temperatures (215 ± 20 K) were observed from cumulonimbus clouds along the squall line; however, 85.5-GHz microwave brightness temperatures observed from the nimbostratus clouds north of the low center were significantly higher (255 ± 20 K). In situ measurements from aircraft during the Canadian Atlantic Storm Program II showed that heavy snowfall consisting of large tenuous aggregates existed in the nimbostratus clouds at the time of the SSM/I overpass.

Distributions of snow, rain, liquid cloud water, and cloud ice mass were computed from a modified version of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model. That model employed a mixed-phase ice microphysics (MPIM) scheme that only considered one type of frozen hydrometeor. The frozen hydrometeor size distributions, density, and mass flux were modified to match the in situ observations where they were available and to account for the SSM/I observations using radiative transfer theory. Those revised hydrometeor representations were constrained to preserve the vertical hydrometeor mass flux distributions obtained from the MPIM scheme throughout the analysis.

Frozen dense accreted particles were required near the squall line to account for the microwave scattering effect. Snow aggregates, with density that decreased with increasing size, were needed to reproduce the high brightness temperatures observed from the nimbostratus clouds.

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M. D. Humphrey, J. D. Istok, J. Y. Lee, J. A. Hevesi, and A. L. Flint

Abstract

Existing methods for dynamic calibration of tipping-bucket rain gauges (TBRs) can be time consuming and labor intensive. A new automated dynamic calibration system has been developed to calibrate TBRs with minimal effort. The system consists of a programmable pump, datalogger, digital balance, and computer. Calibration is performed in two steps: 1) pump calibration and 2) rain gauge calibration. Pump calibration ensures precise control of water flow rates delivered to the rain gauge funnel; rain gauge calibration ensures precise conversion of bucket tip times to actual rainfall rates. Calibration of the pump and one rain gauge for 10 selected pump rates typically requires about 8 h. Data files generated during rain gauge calibration are used to compute rainfall intensities and amounts from a record of bucket tip times collected in the field.

The system was tested using 5 types of commercial TBRs (15.2-, 20.3-, and 30.5-cm diameters; 0.1-, 0.2-, and 1.0-mm resolutions) and using 14 TBRs of a single type (20.3-cm diameter; 0.1-mm resolution). Ten pump rates ranging from 3 to 154 mL min−1 were used to calibrate the TBRs and represented rainfall rates between 6 and 254 mm h−1 depending on the rain gauge diameter. All pump calibration results were very linear with R 2 values greater than 0.99. All rain gauges exhibited large nonlinear underestimation errors (between 5% and 29%) that decreased with increasing rain gauge resolution and increased with increasing rainfall rate, especially for rates greater than 50 mm h−1. Calibration curves of bucket tip time against the reciprocal of the true pump rate for all rain gauges also were linear with R 2 values of 0.99. Calibration data for the 14 rain gauges of the same type were very similar, as indicated by slope values that were within 14% of each other and ranged from about 367 to 417 s mm h−1. The developed system can calibrate TBRs efficiently, accurately, and virtually unattended and could be modified for use with other rain gauge designs. The system is now in routine use to calibrate TBRs in a large rainfall collection network at Yucca Mountain, Nevada.

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