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Charles Knight is completing a detailed survey of all the complete radar cases of early echo development in the small, warm cumuli observed during the Small Cumulus Microphysics Study (SCMS) in Florida during 1995. The results show extreme variability in the development of the first precipitation echo in terms of any of the simple correlates, such as cloud top height or rise rate. Probably much of the variability stems from dynamics variables, such as the strength and duration of the boundary-layer convergence forcing the cloud, but there are enough poorly-observed but probably important factors, such as this, that the main conclusion is that there is not enough information to explain the variability. It is interesting, however, that clouds capped with inversions seem to have the most persistent updrafts and to show the fastest early echo growth.

L. Jay Miller and Knight continued their study of cloud-scale processes leading to droplet coalescence in small, warm cumulus clouds. They used measurements from the CP2 dual-wavelength (10- and 3-cm) radar system and aircraft operating in Florida during the SCMS in 1995 to identify adiabatic and mixed regions in these clouds. The observed values of S- and X-band reflectivities were partitioned into their separate Bragg (scattering from spatial variations in refractive index at scales near one-half the radar wavelength) and Rayleigh (scattering from small, water drops) components for comparison with reflectivities derived from aircraft FSSP-100 cloud droplet size distributions. Typically, in the early stages of cloud development, strong S-band mantle echo indicative of mixing between cloud and environment surrounded the X-band, near-adiabatic core (see figure). This interpretation of the radar measurements is consistent with the Gaussian-like shape of horizontal profiles of vertical motions and cloud droplet concentrations observed by aircraft penetrating near mid-cloud levels. Reflectivity factors computed from the FSSP measurements were within 3 dB of the radar-deduced Rayleigh signal in the cloud core. However, on the cloud flanks the dominance of Bragg scattering at both wavelengths precluded radar detection of the very small values of -20 to -40 dBZ from the FSSP.

The vertical extent of adiabatic and mixed regions was determined by comparing the radar-deduced Rayleigh reflectivities with adiabatic values calculated from aircraft-measured cloud base conditions (see figure). A vertical profile of adiabatic cloud liquid water content was converted to reflectivity by noting that the observed size distributions were narrow enough that any drop-size dependence could be eliminated and that the number concentration at all levels was determined only by the number of droplets activated just above cloud base. Adiabatic cores were apparent only in the lower parts of the clouds and within the echo cores, and this only in the very earliest 5-10 minutes of cloud life times. Once the echo cores reached about 2 km, radar-observed reflectivities typically exceeded adiabatic values. These larger-than-adiabatic values were likely caused by coalescence into larger droplets, which the radar would be most sensitive to.

Sonia Lasher-Trapp (visitor, University of Oklahoma) is finishing a model study examining the possible role of ultra-giant nuclei in initiating precipitation in a small cumulus cloud in SCMS, in collaboration with Knight. She and others are also working on the SCMS aircraft data, with the purpose of checking some of the most important instrument results and applying the data to the problem of the cloud inhomogeneity and to the broadening of the droplet spectrum. The SCMS radar did not provide good multiparameter data, which has a lot of potential for revealing when the first raindrops develop, through their cross-polarization echoes.

Knight obtained a number of complete early-echo cases with the S-pol radar in Florida during PRECIP-98 in August. Several cases expect to provide detailed and sensitive ZDR and LDR measurements at S-band that were not available in SCMS. The data will be analyzed to reveal the time and location of detection of the larger water-drop sizes in the early echo history of the clouds to better understand precipitation development in warm clouds.

Under funding provided by the ONR, Richard Rotunno, Joseph Klemp, and William Skamarock continued their studies of the dynamics of spring and summer season coastally trapped disturbances (CTDs) observed along the U.S. west coast. Development of the theory and conceptual models for the most common CTD events was completed. The theory highlights the critical role earth's rotation plays in allowing the large-scale offshore flow to push out the marine layer and climatological northerly coastal jet, in producing onshore flow south of the localized lee through, and in trapping the northward propagating disturbance that is generated as a result of the onshore flow being blocked by the coastal mountains.

Both observations and the numerical simulations mentioned above indicate a higher-order vertical structure to the CTD that is not accounted for in a single-layer shallow water model. Rajul Pandya (ASP) and Rotunno investigated the disturbances that occur in a two-layer shallow water model, which supports modes with more realistic vertical structure than the single-layer system. Preliminary investigations showed that the two-layer model can support a mode that appears to be a Rossby-Kelvin hybrid; the upper-layer flow resembles a topographic Rossby Wave and the lower-layer flow resembles a Kelvin wave. They continued to examine a range of environmental conditions to investigate the sensitivity of this vertical structure to environmental conditions, and the possible impact of nonlinearity by running parallel simulations with a numerical two-layer shallow water model.

Catalina eddies, a cyclonic circulation in the southern California bight region that appears occasionally from late spring to early fall, can sometimes be a prelude to a CTD that propagates far to the north of the bight, but most times does not lead to a CTD event. The climatology of the Catalina eddy events is similar to that for a CTD, except that for CTD events the synoptic scale offshore flow is more easterly, whereas in Catalina eddy events the flow is northerly onto the bight. Three-dimensional model simulations conducted by Skamarock, Rotunno, and Klemp, using an idealized coastal topography that includes the bight and the climatological northerly marine-layer jet, showed that Catalina eddies are generated when forced with an imposed northerly offshore flow in the bight region, and a easterly offshore flow. For the imposed northerly offshore flow, a CTD-like disturbance was produced, but does not propagate around the northern point of the bight because it is blocked by the strong northerly marine-layer jet; the jet is not displaced by the imposed offshore flow. In the case of easterly offshore flow, the CTD propagates around the bend far to the north of the bight because the imposed flow displaces the marine-layer jet. Thus, the dynamics producing CTDs and Catalina eddies are essentially the same, with the strength, direction, and location of the offshore flow relative to the bight determining whether or not a long-lived CTD is produced from the evolving Catalina eddy circulation.

Davis, in collaboration with Simon Low-Nam and Clifford Mass (University of Washington) continued to examine the dynamics of the Catalina Eddy in a case study of an event on 26-30 June 1988. Their numerical simulations revealed two time scales governing eddy formation, that of the synoptic-scale flow and the diurnal cycle. Enhanced synoptic-scale, northerly flow traversed the high mountains north of the bight and strongly depressed the marine layer over the bight, resulting in a warm-core vortex. A decrease in the synoptic-scale northerlies, resulting from the movement of the anticyclone to the northeast of the region, reduced the mean advecting velocity and allowed vorticity, once formed, to remain nearly in the bight. The diurnal cycle caused a regime transition from blocked flow (morning) to flow over the mountains (evening). The latter resulted in a pronounced depression of the marine layer in the lee and in an eddy forming preferentially at night; the former produced a wake during the daytime with numerous elongated filaments of vorticity, but no coherent eddy.

Kevin Manning continued studying the simulation of coastal fog with the MM5 model. The Gayno-Seaman planetary boundary layer (PBL) parameterization scheme was further tested in the framework of MM5 and several cases were simulated. Horizontal grid spacing in the nested-grid simulations was as small as 6 km, in order to begin to resolve interactions of fog coastal features. Shallow model layers were used near the surface in order to better resolve the boundary layer and surface processes. Comparison to satellite and surface observations is underway, and indicates that the model may have some skill in simulating the onset and evolution of coastal fog events. A comparison among several simulations, each using a different PBL scheme (Blackadar, Burk-Thompson, MRF, and Gayno-Seaman parameterizations), is also being conducted, and these simulations show considerable scatter among the different schemes with respect to almost all aspects of the fog (i.e., depth, water content, and location).

Christopher Davis (joint appointment with RAP) and Mark Stoelinga (visitor, Univerisity of Washington) concluded their examination of quasigeostrophic linear and nonlinear simulations of idealized baroclinic waves interacting with topography. They developed a perturbation expansion, with the small parameter being proportional to topographic slope, to isolate fundamentally different topographic effects, and showed how these effects enter systematically at each order. First and second order corrections appeared to capture the essence of the topographic effect for all cases considered, even for values of the "small" parameter as large as 0.5, and were qualitatively useful for a parameter value of unity.

Results indicated the importance of surface Rossby wave dynamics at first order near the mountain and downshear from the mountain a distance inversely proportional to the growth rate of the most unstable mode of the system. The second order correction projected strongly onto the initial baroclinic wave. Being primarily out of phase with the initial wave, it contributed systematically to weakening the initial disturbance. This behavior changed notably for meridionally localized topography offset from the symmetry axis of the initial zonally invariant jet flow. The first order correction strongly affected the translational speed of the initial wave, and, downshear from the mountain, grew as an unstable mode projecting strongly onto the scale of the initial wave. For a mountain to the south of the jet, the incident baroclinic wave was accelerated; for a mountain to the north, it was slowed. The dominant effect at second order was still a weakening of the initial wave.

Davis and Stoelinga also offered a new explanation of topographic normal modes that grow in a zonal flow with a zonally symmetric mountain. The issue of practical importance was whether the maximum surface amplitude occurred poleward or equatorward of a mountain localized in the cross-stream direction. The occurrence of maximum amplitude to the south of the mountain occurs only for longer waves. For a given wave of medium scale, the amplitude is also more likely to maximize to the south of the mountain for steeper slopes.

Quasi-geostrophic theory represents a leading-order theory in the sense that it is derivable from the full primitive equations in the asymptotic limit of zero Rossby number. Building upon quasi-geostrophic theory, David Muraki (Courant Institute, New York University), Chris Snyder and Rotunno developed a systematic asymptotic framework from which balanced, next-order corrections in Rossby number are obtained. This past year Rotunno, Muraki, and Snyder completed numerical solutions of the extended equation set (dubbed "QG+1") for the case of growing baroclinic waves. Of particular interest is that QG+1 captures the important and pervasive cyclone/anticyclone asymmetry noted over the years in simulations using primitive-equation models. Research is in progress toward the development of a physical theory.

Muraki, Rotunno, and Snyder also investigated the effects of rotation on flow over topography using the same framework. Preliminary results suggest that lee vortices are characteristic of the steady balanced flow over topography at finite but small Rossby and Froude numbers, even in the absence of dissipation. In related research, Muraki and Gregory Hakim (ASP) developed analytic solutions for finite-amplitude waves on the tropopause.

Donald Lenschow, in collaboration with Steven Siems (Monash University, Australia) and Paul Krummel (CSIRO, Australia), carried out an analysis of measurement accuracy requirements for obtaining entrainment, divergence, and vorticity from an aircraft. The entrainment rate at the top of the PBL is an important variable for understanding PBL evolution, but is difficult to measure. To address this issue, Lenschow and collaborators devised three independent techniques to measure entrainment using a single aircraft flight pattern: (1) measuring the terms in the budget of a scalar and solving for the entrainment term; (2) estimating the entrainment velocity as the negative of the ratio of a scalar flux at the top of the PBL to the jump in its mean value across the top; and (3) measuring the divergence within closed (circular) flight paths, integrating with height to obtain the mean vertical motion at the PBL top, and estimating the time rate-of-change of the PBL top to solve for the entrainment velocity. The first two techniques were previously used with some success, but the divergence technique, as far as the researchers know, has not been used for entrainment measurements. The closed flight track can also be used to measure vorticity, with somewhat greater accuracy than for divergence, since the vorticity is typically several times larger than the divergence. These techniques were implemented using the NCAR C-130 in the Aerosol Characterization Experiment (ACE-1). They conclude that measuring divergence and vorticity with an aircraft is feasible, but is at the edge of currently used air motion sensing technology.

Margaret LeMone began to use several techniques to estimate divergence from ground-based measurements. In the first, she used profiler data and compared the divergence with those derived from aircraft tracks between the profilers at different levels. Although the comparisons were encouraging, the divergences seemed about an order of magnitude too large. However, they compared well with those found by Richard Coulter (Argonne National Laboratory), using sodars at the same locations. Aircraft and profiler data will be combined to eliminate the need to assume linear variation between the profilers. The heat and moisture budget above the boundary layer will be used to estimate divergence.

Lenschow, in collaboration with Volker Wulfmeyer and Christoph Senff (CIRES), developed a technique for removing random uncorrelated noise from measurements of third- and fourth-order moments of atmospheric variables. The technique was demonstrated by applying it to lidar measurements of water vapor (differential absorption lidar) and vertical velocity (Doppler lidar). In both cases, the lidar was located on the ground and pointed up, and thus used to obtain vertical profiles of PBL statistics.

Peter Sullivan, Chin-Hoh Moeng, Lenschow, Stephen Cohn (ATD), and Andreas Muschinski (CIRES and NOAA) explored the feasibility of using four-dimensional (x,y,z,t) data from large eddy simulations (LES) to aid in calibration and interpretation of atmospheric radar data. Their premise is that a realistic simulation of clear-air Doppler-radar returns has to include the spatial and temporal distribution of the three-dimensional wind and refractivity field within the radar's resolution volume. LES can simulate time-space distributions of wind, temperature, and specific humidity down to length scales that are small compared to the size of the radar's resolution volume but large compared to the radar wavelength. Muschinski used a recently generated large LES database (more than 50 gigabytes) to systematically investigate the characteristics of biases and sampling errors in atmospheric variables retrieved from clear-air Doppler radar signals.

Piotr Smolarkiewicz, Vanda Grubišic (ASP), Len Margolin (Los Alamos National Laboratory), and Andrzej Wyszogrodzki (visitor, University of Warsaw, Poland) continued advancement of the nonhydrostatic global model based on nonoscillatory forward-in-time (NFT) numerical methods (a long-term project funded by the DOE CHAMMP program). The development of the semi-implicit variant of the model (reported last year) turned out to be an important step in the progress of the project. During the past year, they incorporated an Eulerian (conservative) option of the fluid algorithm into the new model, included a subgridscale turbulence parameterization, and developed a massively parallel message-passing variant of the model. With these developments, their NFT global model is quickly becoming a viable and flexible research tool. They performed numerous numerical experiments (in the context of idealized global orographic flows and climates) assessing relative sensitivity of the model solutions to numerical algorithms and various formulations of the governing equations.

Margolin, Mikhail Shashkov (Los Alamos National Laboratory), and Smolarkiewicz adapted a new idea from the Lagrangian simulation of high-speed flows to Eulerian simulations of atmospheric flows. This idea, termed compatible differencing, allows one to preserve selected properties of the analytic equations by enforcing particular relationships between the discrete spatial operators’ divergence, gradient and curl. For example, by choosing the discrete gradient to be adjoint to discrete divergence, one can ensure the conservation of total energy even when a total energy equation is not used. They extended this idea to derive relations between the advective fluxes of mass and momentum that are required in Eulerian simulations of two-dimensional shallow water. The new schemes have both physical and numerical advantages. Physically the new schemes conserve total energy, which is important in global simulations over climate time scales; numerically, the new schemes reduce the necessary applications of (expensive) advection routines and so reduce the total computational expense.

Smolarkiewicz continued his collaborative effort on high performance computing strategies for atmospheric models. In order to accommodate a rapidly evolving computing environment, the message-passing version of his small-to-mesoscale model (reported in previous years) has been designed such as to enable its execution on different massively-parallel architectures as well as on single-processor vector Crays and workstations. The basic issues of parallelization (scaleability, message passing versus data parallel implementation, relative performance of various numerical options, etc.) have been already reported in the literature. This past year, Smolarkiewicz and Wyszogrodzki emphasized the relative model performance across several machines (Crays T3E and T3D, Hewlett-Packard Exemplar SPP2000 and Crays PVP systems) using both MPI and Shmem communication software (where applicable). The semi-Lagrangian results obtained for the physical scenario of gravity-wave-induced turbulence were corroborated with a series of experiments for Eulerian LES study of convective planetary boundary layer. The gravity-wave computations which exceed technical capabilities of standard vector supercomputers, were performed on the 512-processor Cray T3E machine at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California.

Smolarkiewicz designed a vorticity budget analysis customized for nonoscillatory forward-in-time (NFT) fluid models based on multidimensional positive definite advection transport algorithm (MPDATA) methods. Although MPDATA schemes for momentum transport do not exactly preserve vorticity as so-called mimetic methods do, Smolarkiewicz found that the resulting errors in the vorticity fields in complex flows past irregular lower boundary are acceptably small. This is an important finding that appears essential for substantiating the theoretical bases on vorticity and potential vorticity generation in mountain wakes. This development forms the basis for other budget analyses, and is important as it counters the mimetic methods pursued aggressively in the literature.

In an independent effort, Smolarkiewicz in collaboration with Margolin and Zbigniew Sorbjan (Marquette University) explored the feasibility of using MPDATA's viscous properties as a subgrid-scale model in turbulent flows. In LES PBL studies with explicit subgrid-scale (SGS) models based on either a Smagorinsky or turbulent-kinetic-energy closure model, they found MPDATA reproduced the standard results reported in the literature. This documented that in the presence of an explicit SGS model, MPDATA's implicit viscosity is negligible compared to that explicit in the SGS model. Curiously, in the absence of an explicit SGS model, MPDATA still reproduced the standard results surprisingly close. Together, this suggests that MPDATA's self-adaptive viscosity can be exploited to design effective SGS models for problems where standard schemes do not apply (e.g., strongly stratified turbulence, and planetary flows).

Table of Contents	Director's Message
Significant Accomplishments	FY 98 Publications
Community and Educational Activities	Staff, Vistors & Collaborators