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Multiscale Convective Cloud Systems and Waves

The systemic properties of moist convection are fundamental to weather and climate and, in particular, to the Earth’s water and energy cycles. Multiscale numerical simulation and mathematical models provide a pathway to improved parameterization. Figure 56 shows the cross-disciplinary approach adopted in the multiscale investigations reported in this section, which range from observed systems in need of explanation, numerical simulation, super-parameterization and mathematical reductionism, to improved parameterization. History shows that the latter is resistent to solution and thus a major challenge.

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Figure 56.
Approach uses in studies of multiscale cloud systems and waves

The research themes reported below center on atmospheric convection, its interaction with the boundary layer and ocean/land interfaces, and wave dynamics. Since no geophysical model can simulate convection from first principles (cloud-microphysics and radiative transfer must be parameterized), improved parameterization of microphysics is needed. Because the multiscale cloud-system models (grid interval ~1 km) resolve mesoscale circulations, the large-scale role of organized convection with its strong dynamical effects, is high on the research agenda.

The multipurpose numerical model framework known as EULAG developed by Piotr Smolarkiewicz and collaborators is the mainstay of the multiscale simulation approach. When a data-assimilating model is required (i.e., real-world case studies), MM5 is used.

EULAG development

EULAG is a numerical code for simulating geophysical flows on all scales – a facility for numerical experimentation in a virtual laboratory with time-dependent adaptive meshes and complex, even time-dependent, computational domains. The underlying anelastic equations are solved in either a EULerian (flux form) or a LAGrangian (advective form) framework. EULAGs generality derives from a unique model design that combines the nonoscillatory forward-in-time (NFT) numerical algorithms (based on the MPDATA family of transport schemes) and a robust elliptic solver in generalized coordinates. The numerical code contains options for controlling numerical accuracy and allows a wide range of numerical sensitivity tests. The model equations are formulated with various options. For example, in addition to simulation of the Earth’s atmosphere, options are available for stellar atmospheres, ocean dynamics, sand-dune propagation and biomechanical flows. The EULAG code is fully parallelized and easily portable between computer platforms. Previous model development and details of the numerical algorithms are published in peer-reviewed papers by P. Smolarkiewicz and colleagues. Developments of EULAG during FY2004 are now summarized.

Dynamic Grid Deformation

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Figure 57. Moist stratified rotating flow past a winding valley, with inclusion of boundary layer diabatic effects. Vertical velocity (left upper panel) and cloud water mixing ratio (right upper panel) in the yz cross section at x = 120 km and cloud-water mixing ratio at bottom surface of teh model (bottom panel).

Joseph Prusa (Iowa State University) and P. Smolarkiewicz continued the development of a deformable-coordinate option designed using synergetic interaction between rules of continuous mapping and the strengths of the NFT methods. Previously, they demonstrated that effective multi-scale adaptive numerical models for high Reynolds number geophysical flows can dispense with rigorous evaluation of more cumbersome vector differential operators, such as the curl of the velocity and the strain rate. Nevertheless, these operators are important for budget analyses of the model results, estimating physical uncertainties, driving the mesh adaptivity, and extending applicability beyond standard meteorological situations. Recently they documented extensions of the generic explicitly inviscid approach for curvilinear representation of the vorticity, Fickian diffusion, strain, and stress as well as tensor identities complement the entire development. The benefits of their approach are substantial. The narrower and more complex the geometry of the problem, the more prohibitive the cost of standard simulations on rectangular domains. For example, for a valley flow in the following figure, the gain is about a factor of two.

Spectral Preconditioners

Thomas et al. (MWR, 2003) reported advantages of elementary constant-coefficient spectral preconditioners for elliptic problems in atmospheric flows, in the context of the Canadian MC2 model (a semi-Lagrangian, semi-implicit, elastic, nonhydrostatic, multiscale research/weather-prediction model). A follow-up study by P. Smolarkiewicz, Steven Thomas (SCD), Clive Temperton (ECMWF), and Andrzej Wyszogrodzki (LANL) incorporated spectral preconditioners in EULAG. They tested performance of spectral preconditioners in extreme settings covering a broad range of scales and physical applications: from canonical decaying turbulence in a triply periodic box, through homogeneous flows past large-amplitude undulating boundaries, mesoscale flows past long winding valleys, to idealized climate. Their results do not corroborate the universal superiority of spectral preconditioners (over simple line-relaxation schemes) found in MC2. While elementary spectral preconditioners offer substantial advantages in many applications; in general, their performance is unsatisfactory when significant horizontal inhomogeneity occurs.

Unstructured-Grids

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Figure 58. Computational mesh for the NACA0012 test cases, and a comparison of the results using MPDATA and the reference AGARD results.

Testing a numerical approach in a parameter space distinct from its normal application is enlightening. Joanna Szmelter (Cranfield University, UK) and Piotr Smolarkiewicz (MMM) continued development of MPDATA in an arbitrary finite-volume framework with a fully unstructured polyhedral hybrid mesh. They advanced the stability theory, included the monotonicity enhancement and generalized the approach to a fully compressible flow solver. The new framework is well suited to adapting the Cartesian mesh experience with MPDATA in an unstructured grid environment. Their results reported for the transonic flow around airfoils are promising from the perspective that the method is substantially less diffusive than contemporary computations normally used in aeronautical design. Their studies of flow past 2D airfoils are the first documented application of an MPDATA-based flow solver in multi-connected domains. The ease of modeling multi-connected domains using unstructured meshes opens new avenues for MPDATA for atmospheric/oceanic flows, for which the scheme was developed originally.

Dynamical analogues

The objective here is to reduce complex multiscale dynamical systems to simple forms, which is a necessary step toward the understanding that can help parameterization of the systemic effects, especially dynamically based aspects such as momentum transport. Progress toward achieving this objective is summarized below.

Quasi-Biennial Oscillation (QBO)

The QBO represents the dominant variability in the equatorial lower stratosphere, yet complete understanding has remained elusive despite numerous studies. Nils Wedi (ECMWF) and P. Smolarkiewicz continued their basic research of the QBO. Using EULAG, they conducted a direct numerical simulation of the celebrated laboratory experiment of Plumb and McEwan (1978) and its Kyoto-University counterpart---often employed to demonstrate basic properties of the QBO--- reproducing the laboratory results. A series of 2D and 3D numerical simulations exhibits a number of internal gravity wave processes: wave reflection, wave-wave-mean flow interaction, critical-layer formation and subsequent wave breaking. All have atmospheric counterparts. A comprehensive analysis led to the conclusion that spatial background flow perturbations due to internal wave-wave interactions and subsequent momentum flux changes enhanced by wave breaking, grow locally to critical magnitude and merge to form a downward propagating mean shear layer. Furthermore, in contrast to the original explanation the next phase of the laboratory oscillation is a result of the reversed background wind forcing acting against the oscillating membrane.

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Figure 59.
Time-height cross-section of the zonal-mean zonal flow velocity component at mid-channel in the 3D numerical simulation of the Plumb and McEwan experiment. The numerical setup is as repeated by the Kyoto university, where the oscillating membrane has been placed at the top of the annulus.

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Figure 60. The animation in time shows the corresponding x-z cross section of the zonal velocity component at mid-channel in the 3D numerical simulation of the Kyoto laboratory setup for the QBO analogue.

Madden-Julian Oscillation (MJO)

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Figure 61.

Mitch Moncrieff completed a study of nonlinear MJO dynamics. By formulating a dynamical model he showed the pivotal role of the mesoscale organization of convection on the large-scale coherence of tropical convection. The general model formulation consists of two interlocked systems: a mesoscale parameterization of organized convection and a two-layer model of large-scale equatorial dynamics. The lower-layer dynamics is Rossby gyre–like, whereas outflow from organized convection maintains the upper-layer circulation. The transports of zonal momentum in the vertical and meridional directions are key processes. An archetype of the general model (Figure 61), in spite of being brutally simplified, represents the convective organization, momentum transport, and equatorial super-rotation realized by the cloud resolving convection parameterization (CRCP) approach developed by Wojciech Grabowski. The mesoscale parameterization is an analytic equivalent of the cloud-system-resolving models used in the CRCP approach. Finally, issues in the parameterization of convective organization were quantified.

Diurnal cycle of convection and effects of orography

The relationship among organized convection, orography (local and remote effects), large-scale flow and the diurnal cycle is inadequately represented in large-scale models that apply convective parameterization. For this reason, simulations that resolve convection, or at least its mesoscale organization, are compared to simulations that apply convective parameterization.

Organized Traveling Precipitation over the U.S. Continent

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Figure 62. Caption. Traveling precipitation over the continental U.S. a) sequences of precipitation from Carbone et al (2002); b) numerically simulated precipitation; c) structure of airflow in the vertical pane; and d) idealized dynamical model and travel speed formula.

This work is collaborative with the Water Cycle Across Scales initiative, which is now part of The Institute for Multidisciplinary Earth Studies (TIMES). Changhai Liu and M. Moncrieff continued their multiscale simulation of warm-season convection over the U.S. continent using explicit and parameterized approaches -- a set of 7-day simulations (from 3 to 10 July 2003) using MM5 with 3-km, 10-km, and 30-km grid resolution and model domain 2400km x 1800km. MM5 is initialized with the 3-hourly 40-km ETA model analysis. This period is characterized by moderate synoptic forcing, in contrast to relatively benign large-scale conditions in the 10-day period (20 to 30 July 1998) reported in FY2003. Remarkably, both the explicit and parameterized simulations reproduce the observed daily convective regeneration over the Rockies and subsequent eastward propagation (Figure 62a). Diagnostic analyses show that cold-pool dynamics and interaction between latent heating and the ambient flow are responsible for the simulated coherent precipitation. The propagation speed is explained by a nonlinear theoretical-dynamical model of convection in shear. Figure 62b compares Budget analysis indicate that the coarse-grid simulations underestimate the lower-tropospheric cooling and upper-tropospheric warming and overestimate the convective drying at most levels.

Temporal Variability of Precipitation over the U.S. Continent

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Figure 63.

Hsiao-ming Hsu (RAP), Wen-wen Tung (ASP), C. Liu and M. Moncrieff analyzed directionally averaged time series of rain rates derived from NEXRAD measurements over the continental U. S. by Carbone et al (2002). Using spectral decomposition methods they found distinct classes of temporal variability. Latitudinally-averaged time series indicated a remarkable self-similarity for the frequency band higher than semi-diurnal, quantified by a power-law scaling with an exponent of -4/3 (Figure 63). For the longitudinally -averaged series, the scaling exponent for the frequency band higher than semi-diurnal changes from -4/3 to -5/3. The difference between the latitudinal and longitudinal spectra is interpreted as a consequence of the anisotropy of the patterns of high-frequency precipitation. The scale-invariance is useful for evaluating the statistics of precipitation in fine-scale prediction models and cloud-resolving models. Composites of the higher-frequency bands display eastward propagation of the re-constructed convective patterns, whereas the low-frequency patterns propagate westward. There is a marked inter-annual variability in the dominant periods and the propagation speeds.

Diurnal Variability over the Bay of Bengal

Satellite observations by Yang and Slingo, (2001) show that propagating deep convection over the Bay of Bengal during the summer monsoon originates over the mountainous region of eastern India, in broad agreement with observations over the Bay obtained during the JASMINE Pilot Study (Webster et al. 2002). C. Liu, M. Moncrieff and John Tuttle have started an observational analysis of organized convection and diurnal variability over the Bay of Bengal. TRMM rainfall data, zonally averaged from 82.5E to 92.5E for three warm seasons (May-September 2002, 2003 and 2004), show frequent propagating convection during active phases of the monsoon. Convection initiates over the Eastern Ghats in the afternoon or evening and subsequently travels hundreds of kilometers towards the equator. Documentation of the statistical properties of propagation speed, longitudinal scale, and morphology of the rainfall streaks is underway. This is intended to be a basis for idealized numerical simulation and theoretical-dynamical modeling of diurnal variability and convective organization.

Diurnal Variability over the Tibetan Plateau

Xiaodong Liu (Institute of Earth Environment, Chinese Academy of Sciences, China) and C. Liu have started investigations of the warm-season diurnal variations of convective activities over the Tibetan Plateau and adjacent regions. This research is intended to document the mean diurnal variabilities of rainfall, radiative fluxes, and clouds and to quantify the performance of modern mesoscale numerical models in capturing the observed diurnal variations. In the observational analysis, the TRMM rainfall data, the Japanese GMS IR data, and the ERBE data are used to examine the diurnal variations of precipitation, cloudiness, and outgoing long-wave radiation, respectively. In the numerical modeling, a regional climate model is employed to conduct a set of three-year simulations.

Resolved Orographic Forcing in a Global Model

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Figure 64. Instantaneous vorticity at the Earth’s surface. The upper panel shows the field resulting from the global simulation with idealized Andes topography; the lower panel shows the corresponding result without topography. Both results are based upon horizontal grid with (12 8zonal x 64 meridional) nodes. Grid stretching in the upper panel results in 3x higher horizontal resolution near the topography (depicted by elongated vertical ellipse) compared to lower panel.

J. Prusa and P. Smolarkiewicz examined the effects of grid refinement in the vicinity of the Andes Mountains, in the context of Held-Suarez climate simulations. The complex geometry and narrow east-west extent of the Andes is a challenge for numerical models. To address this problem, the adaptive grid-refinement approach in EULAG was utilized in global simulations to locally enhance resolution in the vicinity of an idealized topography. Their results show that insufficient local resolution strongly impacts global behavior. The conditions under which regional errors produce significant global errors depend on the terrain elevation and local climate. At mid-southern latitudes, their model gives reasonable global climate statistics even with resolution so coarse that the mountains are approximated (longitudinally) by a Delta function. However, for the weaker zonal flow in the equatorial region, insufficient resolution spuriously generates a westerly jet near the equatorial tropopause, making it necessary to fully resolve significant orography. About an order of magnitude gain is achieved by the adaptive grid compared to a uniform high-resolution grid. Figure 64 shows the global effect of orography.

Multiscale convective organization in the Tropics

Understanding the multiscale behavior of convection over the tropical oceans is largely a problem in convective-radiative-dynamical quasi-equilibrium, which is addressed by multiscale numerical models in large domains, global models operating super-parameterization and regional prediction models.

Large-Scale Organization in the Indian Summer Monsoon Region

Wen-wen Tung (ASP), M. Moncrieff and Hsiao-ming Hsu (RAP) have started a regional modeling study of the meso- to large-scale convective organization in the Indian summer monsoon region. They are running MM5 with three interactively nested domains. ECMWF TOGA analysis provides large-scale background and lateral boundary conditions. The simulation in the largest domain is nudged toward the analysis using the FDDA technique. The subsequent domains with finer resolution are judiciously placed to further resolve the convective events in the Bay of Bengal. Their objective is to understand the multiscale organization of convection and its predictability in the Bay, with the emphasis on the physical processes controlling diurnal to several-day convective variability. The results are compared against TRMM satellite-observed rainfall during Auguest 2003. Numerous tests are being done on the effectiveness of cumulus parameterization and microphysical schemes. Preliminary results suggest that, under the current FDDA and nesting framework, the combination of the Betts-Miller cumulus parameterization and the GSFC microphysical schemes produces convective organizations with realistic phase and orientation over the Bay.

Vertical Evolution of Convection

Tetsuya Takemi (Osaka University, Japan) and C. Liu completed investigations of the relationship between the vertical development of tropical cumulus convection and the vertical profiles of environmental temperature and moisture. The analyses of observational data obtained in the tropical western Pacific region reveal a strong correlation between the development of shallow and middle-topped cumulus clouds and the existence of dry layers in the middle to upper troposphere. In contrast, the difference in static stability profiles is insignificant among cloud regimes. The observed importance of the tropospheric moisture in modulating cumulus modes is supported by cloud-resolving numerical simulations, which show a strong sensitivity of cumulus heights to the mid- to upper-level relative humidity, while the mid-level stable layer has less impact.

Variability over the Tropical Pacific

Wen-wen Tung (ASP), M. Moncrieff and Jian-Bos Gao (University of Florida) completed a study of multiscale convective variability over the Pacific Ocean using a high-resolution index (ITBB) derived from satellite imagery. They found that convective activity with lifetimes ranging from about 1 h to 21 days have a cross-scale interdependence described by power laws. The ITBB displays long-range dependency, meaning that intense convection tends to be followed by another intense event, and vice versa for weakened events or droughts. This tendency is stronger with larger- domain averaging due to larger-scale variability such as superclusters associated with the MJO. The evolution of cloud clusters within an MJO event showed that convective activity along the front, center, and rear parts of the event continuously intensify approaching the date line and indicate multifractal features in the range of 1 h to about 5–10 days. Convective activity along the front and rear edges of the MJO event are more intermittent than in the center. The multifractal features of the ITBB time series were approximated by a random multiplicative cascade process, suggesting multiscale behavior and sobering for the predictability of observed phenomena.

NCAR-NCMRWF Collaborative Research

NCAR and the National Centre for Medium Range Weather Forecasting (NCMRWF), New Delhi, India have a memorandum of understanding addressing three objectives:

  1. Mesoscale data assimilation and convection studies in the Indian monsoon region;
  2. simulation of tropical weather systems observed in tropical field campaigns, and
  3. the genesis of MJOs in the eastern Indian Ocean. The first objective is being met by incorporating the MM5-3DVAR data assimilation system into the NCMRWF operational weather prediction model. Dale Barker and M. Moncrieff helped two visitors from the NCMRWF (Munmun Das and John George) address the first objective. Because the background fields are provided by a short-term NWP forecast, the background model error has to be computed for a strongly convective environment. Preliminary tests were performed at NCAR, and the data assimilation system is now being tested in an operational environment at the NCMRWF. Besides being important for improved operational prediction in the Indian locale, this progress will enable the second and third research objectives associated with the Indian summer monsoon, and the MJO in particular, to be addressed with increased fidelity.

Convective parameterization

From the start of numerical weather prediction over half a century ago and the start of modern climate modeling in the early 1990’s, the parameterization of convection and the radiative properties of convectively generated clouds has been the root of major uncertainty. Reducing uncertainty is a problem having many facets. Our approach is to use cloud-system-resolving models, evaluation of single-column models, with focus on the diurnal cycle and organization of deep convection. Much effort has been put into improving convective parameterization using fine-scale models, and is now a world-wide effort involving international programs.

Daytime Convective Development over Land

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Figure 65.

The GEWEX (Global Energy and Water Cycle Experiment) Cloud System Study (GCSS), which is an international coordinating body consisting of five working groups, has existed since the early 1990s. For two years, ending January 2004, the working group on Precipitating Convective Cloud Systems was chaired by W. Grabowski. He fostered collaborative work on daytime convective development over land in single-column models (SCMs) and cloud-resolving models (CRMs). The scientists involved are Peter Bechtold (ECMWF), Anning Cheng and Kuan-Man Xu (both NASA-Langley), Richard Forbes, Carol Halliwell, Jon Petch, and Ricky Wong (all from UK Met Office), Marat Khairoutdinov (Colorado State University), Steve Lang and Wei-Kuo Tao (NASA Goddard), Tomoe Nasuno (Japan Agency for Marine-Earth Science and Technology), and Xiaoqing Wu (Iowa State University). They developed an idealized model intercomparison based on observations of the diurnal cycle during the rainy season in Amazonia. The focus was a 6-hr period between sunrise and early afternoon, previously identified as being critical for the diurnal cycle over summertime continents. This period is characterized by the formation and growth of a well-mixed convective boundary layer, proceeding to shallow convective clouds as the convective boundary layer deepens,and subsequent transition to precipitating convection around local noon. A benchmark custom-designed set of simulations was devised. The SCMs reproduced previously-identified problems with premature development of deep convection, less than two hours after sunrise. CRMs with ~1 km horizontal grid-resolution capture the benchmark simulations qualitatively, but with significant differences among the models. Two-dimensional CRMs tend to simulate too rapid a transition from shallow to deep convection and too-high a cloud cover.

Cloud-Resolving Convection Parameterization in the CAM

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Figure 66.

Michal Ziemianski (visiting post-doctoral fellow from the Institute of Meteorology and Water Management, Poland), in collaboration with W. Grabowski, M. Moncrieff, and William Collins (CGD) completed an investigation of convective organization over the tropical western Pacific warm pool using the cloud-resolving convection parameterization (CRCP, or super-parameterization) and the Community Atmospheric Model (CAM) of the Community Climate System Model (CCSM). The CRCP simulations show significant improvements of the warm pool climate. The cloud condensate distribution is much improved as well as the bias of the tropopause height. More realistic structure of the inter-tropical convergence zone (ITCZ) during the boreal winter and better representation of the variability of convection are evident. In particular, the diurnal cycle of precipitation has phase and amplitude in good agreement with observations. Also improved is the large-scale organization of the tropical convection involving superclusters associated with Madden-Julian Oscillation (MJO)-like systems. Location and propagation characteristics, as well as lower tropospheric cyclonic and upper-tropospheric anticyclonic gyres are more realistic than in the standard CAM. The simulations support an analytic theory of dynamical coupling between organized convection and equatorial beta-plane dynamics.

Evaluation of Cumulus Parameterization

James Hack, Julie Caron (both CGD), C. Liu, and M. Moncrieff have started the evaluation of the convective parameterization scheme in CCSM through cloud-resolving and single-column model (SCM) modeling. They are particularly interested in the capability of the cumulus parameterization in reproducing the observed phase of the diurnal cycle of US middle-summer convection. In their three-step approach, multi-day cloud-resolving simulations are conducted with a mesoscale model. Then, the advective tendencies for temperature and moisture averaged over a selective area are derived and are used to drive an SCM as "large-scale" forcing. Finally, the performance of the convective parameterization is evaluated through comparing the SCM results against cloud-resolving model results and observations. They are currently focusing on two 300km x 300km regions, which are characteristic of afternoon-evening maximum convection over the Continental Divide and nocturnal maximum rainfall over the Great Plains, respectively. The cloud-resolving simulations have been completed, and the SCM simulations are still under way.

 

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National Center for Atmospheric Research University Corporation for Atmospheric Research National Science Foundation Annual Scientific Report - Home Atmospheric Chemistry Division Advanced Studies Program Atmospheric Chemistry Division Climate and Global Dynamics Division Environmental and Societal Impacts Group High Altitude Observatory Mesoscale & Microscale Meteorological Division Research Applications Program National Center for Atmospheric Research Scientific Computing Division