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Xiaoqing Wu and Mitchell W. Moncrieff

Abstract

Most atmospheric general circulation models (GCMs) and coupled atmosphere–ocean GCMs are unable to get the tropical energy budgets at the top of the atmosphere and the surface to simultaneously agree with observations. This aspect is investigated using a cloud-resolving model (CRM) that treats cloud-scale dynamics explicitly, a single-column model (SCM) of the National Center for Atmospheric Research (NCAR) Community Climate Model that parameterizes convection and clouds, and observations made during Tropical Oceans and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE). The same large-scale forcing and radiation parameterizations were used in both modeling approaches. We showed that the time-averaged top-of-atmosphere and surface energy budgets agree simultaneously with observations in a 30-day (5 December 1992–3 January 1993) cloud-resolving simulation of tropical cloud systems. The 30-day time-averaged energy budgets obtained from the CRM are within the observational accuracy of 10 W m−2, while the corresponding quantities derived from the SCM have large biases. The physical explanation for this difference is that the CRM realization explicitly represents cumulus convection, including its mesoscale organization, and produces vertical and horizontal distributions of cloud condensate (ice and liquid water) that interact much more realistically with radiation than do parameterized clouds in the SCM.

The accuracy of the CRM-derived surface fluxes is also tested by using the fluxes to force a one-dimensional (1D) ocean model. The 1D model, together with the surface forcing from the CRM and the prescribed advection of temperature and salinity, simulates the long-term evolution and diurnal variation of the sea surface temperature. This suggests that the atmosphere–ocean coupling requires accurate representation of cloud-scale and mesoscale processes.

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Xiaoqing Wu and Mitchell W. Moncrieff

Abstract

The collective effects of organized convection the environment were estimated using a two-dimensional, two-way nested cloud-resolving numerical model with a large outer domain (4500 km). As initial conditions, the authors used an idealized environment of the onset stage of the December 1992 westerly wind burst that occurred during the Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment.

Two key aspects relating to convective parameterization were examined. First, the transports, sources, and sinks of heat, moisture, and momentum were derived using the model-produced dataset. In particular, the total momentum flux compares well with Moncrieff's dynamical theory. Second, the bulk energetics of the cloud system were examined using the model-produced dataset. The authors found that the shear generation of kinetic energy is comparable to the buoyancy generation and dominates the sum of the buoyancy and water-loading generation. This means that, in addition to the thermodynamic generation of kinetic energy, shear generation should be included in the closure condition for the parameterization of organized convection in large-scale models.

A simple mass-flux-based parameterization scheme is outlined for organized convection that consistently treats dynamical and thermodynamical fluxes.

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Xiaoqing Wu and Mitchell W. Moncrieff

Abstract

Two sets of single-column model (SCM) simulations are performed to determine whether the SCM solutions are more sensitive to model parameterization schemes than to initial perturbations in temperature and moisture profiles. The first set of simulations (S3) used the Zhang and McFarlane scheme for the deep convection and the Hack scheme for the shallow convection, while the second set (S2) used the Hack scheme for all types of convection. The same random perturbation used by Hack and Pedretti is applied in S2 and S3. The observed total (horizontal and vertical) advections of temperature and moisture during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are used to force all simulations. A major difference in temperature and moisture biases occurs between the ensemble means of the two sets of simulations, and is much larger than the standard deviation of each set. Differences are also evident in cloud and radiative properties. This demonstrates that SCM solutions can be more sensitive to the model physics than to the initial perturbations. In other words, the deterministic aspects of SCM solutions dominate the nondeterministic aspects, which is important for their continued use in developing parameterization schemes of convection and clouds in large-scale models. This point is also supported by the SCM simulations using several available longer observational datasets over different regions.

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Zhaohua Wu and Dennis W. Moore

Abstract

The approximate tidal theory on an equatorial beta plane has been widely applied to tropical atmospheric dynamics. There are many successful examples of such applications. However, the mathematical and physical origin of the recently discovered continuous spectrum associated with meridional eigenfunctions of negative equivalent depth is yet to be given, and the completeness of the meridional eigenfunctions in the approximate tidal theory remains to be proved.

In this note, a proof of the completeness of the meridional eigenfunction is presented. The differential equation is first transformed into an equivalent integral equation that relates the solution of the differential equation to the corresponding Green's function. It is then shown that the Green's function corresponding to the meridional eigenvalue–eigenfunction problem is linear, self-adjoint, completely continuous, and square integrable over the meridional infinite domain under the principle of analytic continuation. Therefore, the eigenfunctions form a complete Hilbert space. All the eigenvalues and eigenfunctions are then identified using the method of spectral representation of a second-order differential operator. Related physical properties of the eigenfunctions are also discussed.

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Longtao Wu and Grant W. Petty

Abstract

Four spiraliform polar lows, two over the Sea of Japan and two over the Nordic Seas, were simulated with the Weather Research and Forecasting (WRF) model. Five mixed-phase bulk microphysics schemes (BMS) provided with WRF were run respectively in order to compare their performance in polar low simulations. The observed cloud-top temperatures (CTTs) were compared with the model simulations. Precipitation rates estimated by the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) and gauge-calibrated surface radar precipitation estimates around Japan were also used for validation. Although definitive validation is not possible with the available data, results from the WRF Single-Moment 6-class (WSM6) scheme appear to reproduce the cloud and precipitation processes most realistically. The model produced precipitation intensities comparable to validation products over the Sea of Japan. However, in the Nordic Seas cases, all five schemes produced significantly more precipitation than the AMSR-E estimates even though the latter estimates are known to average slightly high in the same region when validated against monthly totals measured at Jan Mayen Island (Norway).

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Xingren Wu, Ian Simmonds, and W. F. Budd

Abstract

A dynamic-thermodynamic sea ice model is developed and coupled with the Melbourne University general circulation model to simulate the seasonal cycle of the Antarctic sea ice distribution. The model is efficient, rapid to compute, and useful for a range of climate studies. The thermodynamic part of the sea ice model is similar to that developed by Parkinson and Washington, the dynamics contain a simplified ice rheology that resists compression. The thermodynamics is based on energy conservation at the top surface of the ice/snow, the ice/water interface, and the open water area to determine the ice formation, accretion, and ablation. A lead parameterization is introduced with an effective partitioning scheme for freezing between and under the ice floes. The dynamic calculation determines the motion of ice, which is forced with the atmospheric wind, taking account of ice resistance and rafting. The simulated sea ice distribution compares reasonably well with observations. The seasonal cycle of ice extent is well simulated in phase as well as in magnitude. Simulated sea ice thickness and concentration are also in good agreement with observations over most regions and serve to indicate the importance of advection and ocean drift in the determination of the sea ice distribution.

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Aiming Wu, William W. Hsieh, and Amir Shabbar

Abstract

Nonlinear projections of the tropical Pacific sea surface temperature anomalies (SSTAs) onto North American winter (November–March) surface air temperature (SAT) and precipitation anomalies have been performed using neural networks. During El Niño, the linear SAT response has positive anomalies centered over Alaska and western Canada opposing weaker negative anomalies centered over the southeastern United States. In contrast, the nonlinear SAT response, which is excited during both strong El Niño and strong La Niña, has negative anomalies centered over Alaska and northwestern Canada and positive anomalies over much of the United States and southern Canada.

For precipitation, the linear response during El Niño has a positive anomaly area stretching from the east coast to the southwest coast of the United States and another positive area in northern Canada, in opposition to the negative anomaly area over much of southern Canada and northern United States, and another negative area over Alaska. In contrast, the nonlinear precipitation response, which is excited during both strong El Niño and strong La Niña, displays positive anomalies over much of the United States and southern Canada, with the main center on the west coast at around 45°N and a weak center along the southeast coast, and negative anomalies over northwestern Canada and Alaska.

The nonlinear response accounts for about one-fourth and one-third as much variance as the linear response of the SAT and precipitation, respectively. A polynomial fit further verifies the nonlinear response of both the SAT and precipitation to be mainly a quadratic response to ENSO. Both the linear and nonlinear response patterns of the SAT and precipitation are basically consistent with the circulation anomalies (the 500-mb geopotential height anomalies), detected separately by nonlinear projection. A cross-validation test shows that including the nonlinear (quadratic) response can potentially contribute to additional forecast skill over North America.

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Wojciech W. Grabowski, Xiaoqing Wu, and Mitchell W. Moncrieff

Abstract

A formal framework is established for the way in which cloud-resolving numerical models are used to investigate the role of precipitating cloud systems in climate and weather forecasting models. Emphasis is on models with periodic lateral boundary conditions that eliminate unrealistic numerically generated circulations caused by open boundary conditions in long-term simulations. Defined in this formalism is the concept of large-scale forcing and the cloud-environment interactions that are consistent with the periodic boundary conditions.

Two-dimensional numerical simulations of the evolution of cloud systems during 1–7 September 1974 in Phase III of the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) are conducted. Based on the above formalism, a simple technique is used to force an anelastic cloud-resolving model with evolving large-scale horizontal wind field and large-scale forcing for the temperature and moisture obtained from the GATE data. The 7-day period selected is characterized by transitions of the cloud systems through several regimes, in response to evolving large-scale forcing and vertical wind shear as an easterly wave passes over the region. The observed nonsquall cloud clusters, squall lines (squall clusters), and scattered convection are all simulated. Model-produced budgets of heat and moisture compare well with GATE observations. It is argued that differences between simulations and observations (most apparent in the relative humidity) result from the treatment of condensed water. In particular, the lack of observed fields to prescribe forcing for the upper-tropospheric ice, together with the periodic lateral boundary conditions, results in a middle and upper troposphere that is too moist by 10%–20%.

A key conclusion is that tropical convection, forced in a simple way by large-scale analysis, is sorted into specific regimes as a result of dynamic control by the wind shear. The quantification of this large-scale control is fundamental to the concept of convective parameterization. Furthermore, the cloud-resolving model results by design satisfy the large-scale budgets and, therefore, can be applied directly to the strategic problem of convective parameterization in weather forecasting and climate models.

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Aiming Wu, William W. Hsieh, and Francis W. Zwiers

Abstract

Nonlinear principal component analysis (NLPCA), via a neural network (NN) approach, was applied to an ensemble of six 47-yr simulations conducted by the Canadian Centre for Climate Modelling and Analysis (CCCma) second-generation atmospheric general circulation model (AGCM2). Each simulation was forced with the observed sea surface temperature [from the Global Sea Ice and Sea Surface Temperature dataset (GISST)] from January 1948 to November 1994. The NLPCA modes reveal nonlinear structures in both the winter 500-mb geopotential height (Z500) anomalies and surface air temperature (SAT) anomalies over North America, with asymmetric spatial anomaly patterns during the opposite phases of an NLPCA mode. Only during its negative phase is the first NLPCA mode related to the El Niño–Southern Oscillation (ENSO); the positive phase is related to a weakened jet stream. Spatial patterns of the NLPCA mode for the Z500 anomalies generally agree with those for the SAT anomalies.

Nonlinear canonical correlation analysis (NLCCA), also via an NN approach, was then applied to the midlatitude winter GCM data and the observed SST of the tropical Pacific. Nonlinearity was detected in both the forcing field (SST) and the response field (Z500 or SAT) at zero time lag. The leading NLCCA mode for the SST anomalies is a nonlinear ENSO mode, with a 30°–40° eastward shift of the positive SST anomalies during El Niño relative to the negative SST anomalies during La Niña. The leading NLCCA mode for the Z500 anomaly field is a nonlinear Pacific–North American (PNA) teleconnection pattern. The ray path of the Rossby waves induced during El Niño is 10°–15° east of that induced during La Niña. The nonlinear atmospheric response to ENSO is also found in the leading NLCCA mode for the SAT anomalies.

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Wojciech W. Grabowski, Xiaoqing Wu, and Mitchell W. Moncrieff

Abstract

Large-scale conditions during the 7-day period of Phase III of the Global Atmospheric Research Program Atlantic Tropical Experiment are used to study effects of cloud microphysics on the convecting tropical atmosphere. Two-dimensional numerical experiments evaluate the effects of extreme changes to the cloud microphysics in the cloud resolving model. The main conclusions are the following. (a) Extreme changes in cloud microphysics affect the temperature and moisture profiles in a way that approximately retains relative humidity profiles in all experiments. (b) With prescribed radiative tendencies, effects of cloud microphysics on surface processes are paramount. Extreme changes in warm rain microphysics indirectly affect the temperature and moisture profiles by modifying surface sensible and latent heat fluxes. For instance, smaller raindrops, and to a lesser degree slower conversion of cloud water into rain, result in enhanced updraft and downdraft cloud mass fluxes, a colder and drier boundary layer, larger surface fluxes, a warmer and more humid free atmosphere, and a lower convective available potential energy. c) With fully interactive radiation, the above picture is modified mostly through the effect of cloud microphysics on the upper-tropospheric anvil clouds. Higher condensate mixing ratios inside anvil clouds consisting of small ice particles and greater upper-tropospheric cloud cover due to longer residence time of these particles result in the less negative temperature tendency in the upper troposphere. This change in the radiative flux divergence extends the modifications in the free-tropospheric temperature profiles associated with small cloud and precipitation particles into the upper troposphere. Changes in warm rain processes (e.g., in the rate of conversion of cloud water into rain) have some effect on the lower-tropospheric radiative flux divergence as well. d) Particle sizes applied in the radiation transfer model exaggerate this effect because smaller effective sizes of cloud and precipitation particles lead to less negative radiative tendencies, which, in turn, affect the temperature and moisture profiles.

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