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James J. Hack

Abstract

The implied meridional ocean energy transport diagnosed from uncoupled integrations of two atmospheric general circulation models—the National Center for Atmospheric Research Community Climate Model versions 2 and 3 (CCM2 and CCM3)—shows radically different transport characteristics throughout much of the Southern Hemisphere. The CCM2 simulation requires an equatorward transport of energy by the oceans, and the CCM3 exhibits a poleward energy transport requirement, very similar to what is derived from observational analyses. Previous studies have suggested that errors in the implied ocean energy transport are largely attributable to errors in the simulated cloud radiative forcing. The results of this analysis show that although the proper simulation of the radiative effects of clouds is likely to be a necessary condition for realistic meridional ocean energy transport, it is not sufficient. Important changes in the CCM3 equatorial surface latent heat fluxes, associated with a deep formulation for parameterized moist convection, are primarily responsible for the improved ocean energy transport, where this change in the surface energy budget is much more weakly reflected in top-of-atmosphere differences in cloud radiative forcing.

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James J. Hack

Abstract

The accurate treatment of clouds and their radiative properties is widely regarded to be among the most important problems facing global climate modeling. A number of the more serious systematic simulation biases in the NCAR Community Climate Model (CCM2) appear to be related to deficiencies in the treatment of cloud optical properties. In this paper, a simple diagnostic parameterization for cloud liquid water is presented. The sensitivity of the simulated climate to this alternative formulation, both in terms of mean climate metrics and measures of the climate system response, is illustrated. Resulting simulations show significant reductions in CCM2 systematic biases, particularly with respect to surface temperature, precipitation, and extratropical geopotential height-field anomalies. Many aspects of the simulated response to ENSO forcing are also substantially improved.

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J. T. Kiehl
,
J. J. Hack
, and
J. W. Hurrell

Abstract

The energy budget of the latest version of the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM3) is described. The energy budget at the top of the atmosphere and at the earth’s surface is compared to observational estimates. The annual mean, seasonal mean, and seasonal cycle of the energy budget are evaluated in comparison with earth radiation budget data at the top of the atmosphere and with the NCAR Ocean Model (NCOM) forcing data at the ocean’s surface. Individual terms in the energy budget are discussed. The transient response of the top-of-atmosphere radiative budget to anomalies in tropical sea surface temperature is also presented. In general, the CCM3 is in excellent agreement with ERBE data in terms of annual and seasonal means. The seasonal cycle of the top-of-atmosphere radiation budget is also in good (<10 W m−2) agreement with ERBE data. At the surface, the model shortwave flux over the oceans is too large compared to data obtained by W. G. Large and colleagues (∼20–30 W m−2). It is argued that this bias is related to a model underestimate of shortwave cloud absorption. The major biases in the model are related to the position of deep convection in the tropical Pacific, summertime convective activity over land regions, and the model’s inability to realistically represent marine stratus and stratocumulus clouds. Despite these deficiencies, the model’s implied ocean heat transport is in very good agreement with the explicit ocean heat transport of the NCOM uncoupled simulations. This result is a major reason for the success of the NCAR Climate System Model.

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James J. Hack
and
Wayne H. Schubert

Abstract

Under certain circumstances a large fraction of the energy generated by the release of latent heat in a tropical cyclone cab be partitioned to gravity-inertia wave motion rather than to balanced flow. In this way most of the generated energy is radiated away to the far field. If a primitive equation tropical cyclone model is to successfully simulate this process, its lateral boundary condition must be able to transmit the gravity-inertia wave energy generated in the interior of the model. Most present models seem deficient in this regard. As an improvement we explore the possibility of using a cylindrical, pure gravity wave radiation condition. Since there is a wide range of gravity wave phase velocities in a stratified atmosphere, it is necessary to apply the radiation condition vertical mode by vertical mode rather than level by level. The usefulness of this radiation condition and several other conditions in present use is tested both by a reflectivity analysis and by simple numerical time integrations.

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Wayne H. Schubert
and
James J. Hack

Abstract

We consider the frictionless, axisymmetric, balanced flow occurring in a thermally forced vortex on an f-plane. Following Eliassen (1952) we derive the diagnostic equation for the forced secondary circulation. This equation contains the spatially varying coefficients A (static stability), B (baroclinity), C (inertial stability), and the thermal forcing Q. Assuming that A is a constant, B = 0, and that C and Q are piecewise constant functions of radius, we obtain analytical solutions for the forced secondary circulation. The solutions illustrate the following points. 1) For a given Q an increase in inertial stability leads to a decrease in the forced secondary circulation and a change in the radial distribution of local temperature change, with enhanced ∂θ/∂t; in the region of high inertial stability. 2) Lower tropospheric tangential wind accelerations are larger inside the radius of maximum wind, which leads to a collapse of the radius of maximum wind. 3) The fraction of Q which ends up as ∂θ/∂t; increases during the tropical cyclone development, particularly if the horizontal extent of Q is small and close to the region of high inertial stability. 4) One can regard the formation of an eye as a process which tends to stabilize the vortex since it removes Q from the protected, highly stable inner region.

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James J. Hack
and
Wayne H. Schubert

Abstract

Using an axisymmetric primitive tropical cyclone model, we first illustrate the way in which nonlinear processes contribute to the development of an atmospheric vortex. These numerical experiment show that nonlinearities allow a given diabatic beat source to induce larger tangential wind (and kinetic energy) changes as the vortex develops and the inertial stability becomes large. In an attempt to gain a deeper theoretical understanding of this process, we consider the energy cycle in the balanced vortex equations of Eliassen. The temporal behavior of the total potential energy P is governed by dP/dt=HC where H is the rate of generation of total potential energy by diabatic heating, and C is the rate of conversion to kinetic energy. We define a time-dependent system efficiency parameter as η¯(t)=C/H. Then, using the dynamical simplifications of balanced vortex theory, we express η¯(t) as a weighted average of a dynamic efficiency factor η(r, z, t). The dynamic efficiency factor is a measure of the efficacy of diabatic heating at any point in generating kinetic energy and can be determined by solving a second-order partial differential equation whose coefficients and right-hand side depend only on the instantaneous vortex structure. The diagnostic quantities η¯(t) and η(r, z, t) are utilized in the analysis of several balanced numerical experiments with different vertical and radial distributions of a diabatic heat source.

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James J. Hack
and
John A. Pedretti

Abstract

Single-column models (SCMs) have been extensively promoted in recent years as an effective means to develop and test physical parameterizations targeted for more complex three-dimensional climate models. Although there are some clear advantages associated with single-column modeling, there are also some significant disadvantages, including the absence of large-scale feedbacks. Basic limitations of an SCM framework can make it difficult to interpret solutions, and at times contribute to rather striking failures to identify even first-order sensitivities as they would be observed in a global climate simulation. This manuscript will focus on one of the basic experimental approaches currently exploited by the single-column modeling community, with an emphasis on establishing the inherent uncertainties in the numerical solutions. The analysis will employ the standard physics package from the NCAR CCM3 and will illustrate the nature of solution uncertainties that arise from nonlinearities in parameterized physics. The results of this study suggest the need to make use of an ensemble methodology when conducting single-column modeling investigations.

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J. P. Hacker
and
W. M. Angevine

Abstract

Experiments with the single-column implementation of the Weather Research and Forecasting Model provide a basis for deducing land–atmosphere coupling errors in the model. Coupling occurs both through heat and moisture fluxes through the land–atmosphere interface and roughness sublayer, and turbulent heat, moisture, and momentum fluxes through the atmospheric surface layer. This work primarily addresses the turbulent fluxes, which are parameterized following the Monin–Obukhov similarity theory applied to the atmospheric surface layer. By combining ensemble data assimilation and parameter estimation, the model error can be characterized. Ensemble data assimilation of 2-m temperature and water vapor mixing ratio, and 10-m wind components, forces the model to follow observations during a month-long simulation for a column over the well-instrumented Atmospheric Radiation Measurement (ARM) Central Facility near Lamont, Oklahoma. One-hour errors in predicted observations are systematically small but nonzero, and the systematic errors measure bias as a function of local time of day. Analysis increments for state elements nearby (15 m AGL) can be too small or have the wrong sign, indicating systematically biased covariances and model error. Experiments using the ensemble filter to objectively estimate a parameter controlling the thermal land–atmosphere coupling show that the parameter adapts to offset the model errors, but that the errors cannot be eliminated. Results suggest either structural errors or further parametric errors that may be difficult to estimate. Experiments omitting atypical observations such as soil and flux measurements lead to qualitatively similar deductions, showing the potential for assimilating common in situ observations as an inexpensive framework for deducing and isolating model errors.

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Wayne H. Schubert
and
James J. Hack

Abstract

We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½fR 2=rvfr 2 is conserved. We refer to R as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component v to zero. Using R as one of the dependent variables we review the equations of the Eliassen balanced vortex model.

We next reverse the roles of the actual radius r and the potential radius R, i.e., we treat R as an independent variable and r as a dependent variable. Introducing transformed components (u *, w *) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is R which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component w *, the coefficient of which is the potential vorticity q; 3) the equation for r contains only the transverse circulation component u *; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity q and the inertial stability s, where pq=(ζ/f)(g0)(∂θ/∂Z) and ρs=f 2 R 4/r 4.

The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (q/s)½. A typical distribution Of (q/s)½ is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (q/s)½ is then illustrated with a simple analytical example.

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G. L. Browning
,
J. J. Hack
, and
P. N. Swarztrauber

Abstract

We compare three numerical methods for solving vector differential equations on a sphere. A composite mesh finite-difference method using overlapping stereographic coordinate systems is compared to transform methods based on scalar and vector spherical harmonics. The methods are compared in terms of total computer time, memory requirements, and execution rates for relative accuracy requirements of two and four digits in a five-day forecast. The computational requirements of the three methods were well within an order of magnitude of one another. In most of the cases that are examined, the time step was limited by accuracy rather than stability. This problem can be overcome by the use of a higher order time integration scheme, but at the expense of an increase in the memory requirements.

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