Production Of Potential Energy Research Articles

Modelling wind speed with a univariate probability distribution depending on two baseline functions

Characterizing the wind speed distribution properly is essential for the satisfactory production of potential energy in wind farms, being the mixture models usually employed in the description of such data. However, some mixture models commonly have the undesirable property of non-identifiability. In this work, we present an alternative distribution which is able to fit the wind speed data decently. The new model, called Normal-Weibull-Weibull, is identifiable and its cumulative distribution function is written as a composition of two baseline functions. We discuss structural properties of the class that generates the proposed model, such as the linear representation of the probability density function, moments and moment generating function. We perform a Monte Carlo simulation study to investigate the behavior of the maximum likelihood estimates of the parameters. Finally, we present applications of the new distribution for modelling wind speed data measured in five different cities of the Northeastern Region of Brazil.

Turbulent Convection Insights from Small-Scale Thermal Forcing with Zero Net Heat Flux at a Horizontal Boundary.

A large-scale circulation, a turbulent boundary layer, and a turbulent plume are noted features of convection at large Rayleigh numbers under differential heating on a single horizontal boundary. These might be attributed to the forcing, which in all studies has been limited to a unidirectional gradient over the domain scale. We instead apply forcing on a length scale smaller than the domain, and with variation in both horizontal directions. Direct numerical simulations show turbulence throughout the domain, a regime transition to a dominant domain-scale circulation, and a region of logarithmic velocity in the boundary layer, despite zero net heat flux. The results show significant similarities to Rayleigh-Bénard convection, demonstrate the significance of plume merging, support the hypothesis that the key driver of convection is the production of available potential energy without necessarily supplying total potential energy, and imply that contributions to domain-scale circulation in the oceans need not be solely from the large-scale gradients of forcing.

Distinctive Roles of Air–Sea Coupling on Different MJO Events: A New Perspective Revealed from the DYNAMO/CINDY Field Campaign*

Abstract Previous observational analysis and modeling studies indicate that air–sea coupling plays an essential role in improving MJO simulations and extending MJO forecasting skills. However, whether the SST feedback plays an indispensable role for the existence of the MJO remains controversial, and the precise physical processes through which the SST feedback may lead to better MJO simulations and forecasts remain elusive. The DYNAMO/Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY) field campaign recently completed over the Indian Ocean reveals a new perspective and provides better data to improve understanding of the MJO. It is found that among the five MJO events that occurred during the DYNAMO/CINDY field campaign, only two MJO events (the November and March ones) have robust SST anomalies associated with them. For the other three MJO events (the October, December, and January ones), no coherent SST anomalies are observed. This observational scenario suggests that the roles of air–sea coupling on the MJO vary greatly from event to event. To elucidate the varying roles of air–sea coupling on different MJO events, a suite of hindcast experiments was conducted with a particular focus on the October and November MJO events. The numerical results confirm that the October MJO is largely controlled by atmospheric internal dynamics, while the November MJO is strongly coupled with underlying ocean. For the November MJO event, the positive SST anomalies significantly improve MJO forecasting by enhancing the response of a Kelvin–Rossby wave couplet, which prolongs the feedback between convection and large-scale circulations, and thus favors the development of stratiform rainfall, in turn, facilitating the production of eddy available potential energy and significantly amplifying the intensity of the model November MJO.

Large‐scale character of an atmosphere in rotating radiative‐convective equilibrium

AbstractA rotating radiative‐convective equilibrium on a sphere is reached using a global atmospheric model with prescribed globally uniform sea surface temperature and no insolation. In such an equilibrium state, multiple tropical cyclone‐like vortices coexist in the extratropics, moving slowly poleward and westward. Many vortices have a lifetime longer than 2 months and travel from the tropics to the polar regions. The typical spacing of simulated tropical cyclone‐like vortices is comparable to the deformation radius, while the production of available potential energy is at a scale slightly smaller than those vortices. It is hypothesized that the growth of tropical cyclone‐like vortices is driven by the self‐aggregation of convection, while baroclinic instability destabilizes any vortices that grow significantly larger than the deformation radius. A weak Hadley circulation dominates in the deep tropics, and an eastward propagating wave number 1 Kelvin‐like mode having a period of 30–40 days develops at the equator. The weak Hadley circulation is found to emerge from an initially quiescent atmosphere due to poleward momentum transport by the vortices.

Genesis Criteria for Diabatic Rossby Vortices: A Model Study

Abstract A suite of idealized mesoscale model simulations are conducted to examine the dynamic pathway to the genesis of short-scale, moist baroclinic disturbances. It is shown that in an initially subsaturated environment, two distinct stages of development are necessary before a preexisting surface-concentrated, warm-core vortex can begin to amplify. The first stage, termed environmental preconditioning, involves the moistening of the lower atmosphere via the transport of relatively high equivalent potential temperature air into the immediate environment of the translating vortex. The second stage results from continuous cloud diabatic processes and it involves the emergence of a low-level positive potential vorticity (PV) anomaly with some evidence of a further, more diffuse, negative PV anomaly at higher elevations. The PV structure is characteristic of a diabatic Rossby vortex (DRV). The disturbance does not begin to amplify until the magnitude and coherence of the low-level PV structure allows for the sufficient production of eddy available potential energy through diabatic processes to overcome frictional dissipation, and this necessitates forced convection for a finite period of time. A comparison of the simulated disturbance structure with observed DRVs lends credence to the idealized model results. Furthermore, the simulations facilitate the identification of an amplitude threshold for DRV genesis that is defined as a function of both environmental parameters (baroclinicity and moisture content) and the strength of an initial disturbance. In particular, if, given a background environment, the amplitude of an initial disturbance is not sufficiently large, frictional processes will inhibit the genesis of a growing disturbance within a realistic time frame.

Moist versus Dry Baroclinic Instability in a Simplified Two-Layer Atmospheric Model with Condensation and Latent Heat Release

AbstractThe authors undertake a detailed analysis of the influence of water vapor condensation and latent heat release upon the evolution of the baroclinic instability. The framework consists in a two-layer rotating shallow-water model with moisture coupled to dynamics through mass exchange between the layers due to condensation/precipitation. The model gives all known in literature models of this kind as specific limits. It is fully nonlinear and ageostrophic. The reference state is a baroclinic Bickley jet. The authors first study its “dry” linear instability and then use the most unstable mode to initialize high-resolution numerical simulations of the life cycle of the instability in nonprecipitating (moisture being a passive tracer) and precipitating cases. A new-generation well-balanced finite-volume scheme is used in these simulations.The evolution in the nonprecipitating case follows the standard cyclonic wave-breaking life cycle of the baroclinic instability, which is reproduced with a high fidelity. In the precipitating case, the onset of condensation significantly increases the growth rate of the baroclinic instability at the initial stages due to production of available potential energy by the latent heat release. Condensation occurs in frontal regions and wraps up around the cyclone, which is consistent with the moist cyclogenesis theory and observations. Condensation induces a clear-cut cyclone–anticyclone asymmetry. The authors explain the underlying mechanism and show how it modifies the equilibration of the flow at the late stages of the saturation of the instability. In spite of significant differences in the evolution, only weak differences in various norms of the perturbations remain between precipitating and nonprecipitating cases at the end of the saturation process.

Mesoscale Convective Vortices in Multiscale, Idealized Simulations: Dependence on Background State, Interdependency with Moist Baroclinic Cyclones, and Comparison with BAMEX Observations

Abstract A set of multiscale, nested, idealized numerical simulations of mesoscale convective systems (MCSs) and mesoscale convective vortices (MCVs) was conducted. The purpose of these simulations was to investigate the dependence of MCV development and evolution on background conditions and to explore the relationship between MCVs and larger, moist baroclinic cyclones. In all experiments, no mesoscale convective system (MCS) developed until a larger-scale, moist baroclinic system with surface pressure amplitude of at least 2 hPa was present. The convective system then enhanced the development of the moist baroclinic system by its diabatic production of eddy available potential energy (APE), which led to the enhanced baroclinic conversion of basic-state APE to eddy APE. The most rapid potential vorticity (PV) development occurred in and just behind the leading convective line. The entire system grew upscale with time as the newly created PV rotated cyclonically around a common center as the leading convective line continued to expand outward. Ten hours after the initiation of deep moist convection, the simulated MCV radii, heights of maximum winds, tangential velocity, and shear corresponded reasonably well to their counterparts in BAMEX. The increasing strength of the simulated MCVs with respect to larger values of background CAPE and shear supports the hypothesis that as long as convection is present, CAPE and shear both add to the strength of the MCV.

Available Potential Energy and Irreversible Mixing in the Meridional Overturning Circulation

Abstract The overturning circulation of the global oceans is examined from an energetics viewpoint. A general framework for stratified turbulence is used for this purpose; first, it highlights the importance of available potential energy in facilitating the transfer of kinetic energy to the background potential energy (defined as the adiabatically rearranged state with no motion). Next, it is shown that it is the rate of transfer between different energy reservoirs that is important for the maintenance of the ocean overturning, rather than the total amount of potential or kinetic energy. A series of numerical experiments is used to assess which energy transfers are significant in the overturning circulation. In the steady state, the rate of irreversible diapycnal mixing is necessarily balanced by the production of available potential energy sourced from surface buoyancy fluxes. Thus, the external inputs of available potential energy from surface buoyancy forcing and of kinetic energy from other sources (such as surface winds and tides, and leading to turbulent mixing) are both necessary to maintain the overturning circulation.

Modeling mesoscale eddies

Mesoscale eddies are not resolved in coarse resolution ocean models and must be modeled. They affect both mean momentum and scalars. At present, no generally accepted model exists for the former; in the latter case, mesoscales are modeled with a bolus velocity u ∗ to represent a sink of mean potential energy. However, comparison of u ∗ (model) vs. u ∗ (eddy resolving code, [J. Phys. Ocean. 29 (1999) 2442]) has shown that u ∗ (model) is incomplete and that additional terms, “unrelated to thickness source or sinks”, are required. Thus far, no form of the additional terms has been suggested. To describe mesoscale eddies, we employ the Navier–Stokes and scalar equations and a turbulence model to treat the non-linear interactions. We then show that the problem reduces to an eigenvalue problem for the mesoscale Bernoulli potential. The solution, which we derive in analytic form, is used to construct the momentum and thickness fluxes. In the latter case, the bolus velocity u ∗ is found to contain two types of terms: the first type entails the gradient of the mean potential vorticity and represents a positive contribution to the production of mesoscale potential energy; the second type of terms, which is new, entails the velocity of the mean flow and represents a negative contribution to the production of mesoscale potential energy, or equivalently, a backscatter process whereby a fraction of the mesoscale potential energy is returned to the original reservoir of mean potential energy. This type of terms satisfies the physical description of the additional terms given by [J. Phys. Ocean. 29 (1999) 2442]. The mesoscale flux that enters the momentum equations is also contributed by two types of terms of the same physical nature as those entering the thickness flux. The potential vorticity flux is also shown to contain two types of terms: the first is of the gradient-type while the other terms entail the velocity of the mean flow. An expression is derived for the mesoscale diffusivity κ M and for the mesoscale kinetic energy K in terms of the large-scale fields. The predicted κ M( z) agrees with that of heuristic models. The complete mesoscale model in isopycnal coordinates is presented in Appendix D and can be used in coarse resolution ocean global circulation models.

Scale Interactions Involved in the Initiation, Structure, and Evolution of the 15 December 1992 MCS Observed during TOGA COARE. Part I: Synoptic-Scale Processes

This paper, the first of a series, examines the synoptic-scale mechanisms involved in the initiation, structure, and evolution of a mesoscale convective system observed during TOGA COARE. This study relies upon the use of the Japanese Geosynchronous Meteorological Satellite-4 imagery and ECMWF model outputs, from which diagnostic parameters are derived and interpreted. This mesoscale convective system consists initially of two groups of convective entities that progressively move toward each other and merge. It is shown that the synoptic-scale flow creates a favorable environment for the formation of this large convective system through the production of convective available potential energy (CAPE) by horizontal advection and the enhancement of low-level convergence in the region where the convective system formed. Moreover, the general evolution of the system is found to be governed by the synoptic-scale circulation and, more precisely, by the temporal evolution of CAPE and low-level convergence. The mechanisms leading to the initiation and general evolution of the system are examined. The easterly equatorial jet at 500 hPa triggered positive potential vorticity areas that propagated westward and generated an anticyclonic circulation. This anticyclonic circulation was enhanced during the development phase of the convective system through vortex stretching and tilting, which accelerated the low-level westerlies (corresponding to the southern branch of this circulation) and enhanced the low-level convergence associated with the studied convective system. In a companion paper, the mesoscale and convective-scale processes involved in the internal organization of this mesoscale convective system are examined using the airborne Doppler radar dataset collected within the system from 1700 to 2100 UTC. The downscale interactions (i.e., from synoptic scale to mesoscale and convective scale) are scrutinized using both the synoptic-scale context described in this paper and the mesoscale and convective-scale characteristics derived from the airborne radar observations.

The Life Cycle of the Madden–Julian Oscillation

A composite life cycle of the Madden-Julian oscillation (MJO) is constructed from the cross covariance between outgoing longwave radiation (OLR), wind, and temperature. To focus on the role of convection, the composite is based on episodes when a discrete signal in OLR is present. The composite convective anomaly possesses a predominantly zonal wavenumber 2 structure that is confined to the eastern hemisphere. There, it propagates eastward at about 5 m/s and evolves through a systematic cycle of amplification and decay. Unlike the convective anomaly, the circulation anomaly is not confined to the eastern hemisphere. The circulation anomaly displays characteristics of both a forced response, coupled to the convective anomaly as it propagates across the eastern hemisphere, and a radiating response, which propagates away from the convective anomaly into the western hemisphere at about 10 m/s. The forced response appears as a coupled Rossby-Kelvin wave while the radiating response displays predominantly Kelvin wave features. When it is amplifying, the convective anomaly is positively correlated to the temperature perturbation, which implies production of eddy available potential energy (EAPE). A similar correlation between upper-tropospheric divergence and temperature implies conversion of EAPE to eddy kinetic energy during this time. When it is decaying, temperature has shifted nearly into quadrature with convection, so their correlation and production of EAPE are then small. The same correspondence to the amplification and decay of the disturbance is mirrored in the phase relationship between surface convergence and anomalous convection. The correspondence of surface convergence to the amplification and decay of the convective anomaly suggests that frictional wave- Conditional Instability of the Second Kind (CISK) plays a key role in generating the MJO.

The energetics of the plastic deformation of pack ice by ridging

A large-scale area of pack ice contains ice of various thicknesses from zero to many meters. As the area deforms, thin ice is ridged into thicker ice, in a way that depends on the strain rate and the instantaneous thickness distribution. By equating the plastic work to the production of gravitational potential energy and the frictional dissipation in this ridging process we relate the yield curve for plastic deformation of the ice pack to the way ice thicknesses are redistributed by ridging.

Further studies of the properties of cellular convection in a conditionally unstable atmosphere

The problem of convection in an atmosphere which is stable for dry adiabatic descending motion but unstable for saturated ascending motion is analyzed, with a view to the determinations of the preferred areas of the ascending and descending regions and the distributions of the convection currents. Two somewhat different approaches have been formulated, one is based on an integral relation obtained from the governing linearized differential equation while the other is based on the energy integral. It is found that the area of the ascending region tends to decrease while that of the descending region tends to increase with increasing static stability for unsaturated motion, but both of them are finite under all realistic conditions. On the other hand, when the mean lapse-rate is far above the moist-adiabatic lapse-rate, the consideration of the maximum efficiency in the production of available potential energy gives a much larger preferred area ratio, which tends to approach a constant value for every given static stability factor in the descending region. The theory predicts that for large stability factor R ′ 2 (> 100) in the descending region the area ratio A a / A d increases linearly with the ratio R 1 / R ′ 2 of the stability factors whereas for smaller R ′ 2 (< 100) A a / A d increases more slowly. The predicted area ratio of the ascending and descending regions may vary from 1/2 to 1/30 from nearly neutral to normal conditions in the atmosphere, which agree quite closely with that obtained from satellite observations when reasonable values of eddy viscosity and eddy conductivity are assumed. Alternatively, we may also make use of this theory and the observed area ratio to determine the appropriate eddy viscosity coefficient, if the static stability factor in either the ascending or the descending region is known. The nonlinear heat transfer has also been analyzed. DOI: 10.1111/j.2153-3490.1965.tb00204.x

TROPOSPHERIC HEAT SOURCES AND SINKS AT WASHINGTON, D.C., SUMMER 1961, RELATED TO THE PHYSICAL FEATURES AND ENERGY BUDGET OF THE CIRCULATION

Estimates of atmospheric heating in the troposphere at Washington, D.C., for each successive 12 hr. during June and July 1961, were used to study the relation between local heating and the large-scale features of the circulation, to determine the local production of available potential energy, and to assist in interpreting cloud and radiation data from meteorological satellites. Some interesting inter-connections are found between heating and the circulation: e.g., it is shown that there is a very critical phase relation between heating and the temperature field which is important in determining the generation or destruction of the atmosphere's potential energy. This suggests that special care is needed in designing numerical computations of diabatic heating. A major effort should be directed to interpreting satellite data in terms of the atmospheric heat budget, because such global estimates may be useful (using a procedure suggested in this paper) in determining the world-wide distribution of regions of maintenance or destruction of potential energy.