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Ronald Gelaro

Abstract

Global-scale interactions between the tropics and extratropics are investigated using a version of tile U.S. Navy's global operational numerical weather prediction model. The primary goals of this study are 1) to demonstrate the importance of atmospheric teleconnections for medium-range numerical weather prediction and 2) to analyze the evolution and dynamic structure of the response in a sophisticated numerical forecast model. The model normal modes are used as the principal diagnostic tool for analyzing the response to sea surface temperature anomalies in the tropical Pacific. By monitoring the energy growth in the dominant horizontal and vertical modes and comparing these with conventional difference-field diagnostics, it is shown that the character of the long-term response is well established within one to two weeks after the heating anomaly is introduced. The growth rates and structures of these modes provide insights into the dynamic processes that control the model response. In the tropics, enhanced convection is clearly the dominant forcing mechanism for these modes. In the extratropics, a more complicated picture arises in which both meridionally propagating energy and in situ instabilities in the ambient flow appear to be important mechanisms for producing the observed wave patterns. The results clearly demonstrate that tropical forcing can have a significant global impact on time scales relevant to medium-range numerical weather prediction.

In Part II of this study, the normal-mode diagnostic approach is extended by developing a technique for partitioning the modes according to their latitudinal variances in order to examine the tropical and extratropical responses in further detail. It is shown that the modes are a powerful and flexible tool for diagnosing the behavior of a complicated model.

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Ronald Gelaro

Abstract

A unique analysis is applied to the normal modes of the U.S. Navy's global operational numerical weather prediction model to investigate time-varying responses in the tropics and extratropics to tropical Pacific sea surface temperature anomalies. With this new analysis, the modes are partitioned according to their latitudinal variances. This allows the response energy to be separated into tropical and extratropical contributions. The partitioned responses are derived by grouping those modes whose fractional variance within a prescribed latitudinal band δμ exceeds some threshold value β. Since the parameters δμ and β may be chosen arbitrarily, this technique greatly increases the flexibility of the normal-mode diagnostic approach.

The partitioned responses reveal distinct differences between the evolution and vertical scales of the dominant modes in the tropics and extratropics. In the tropics, the structure is dominated by the external mode and a medium-depth internal mode. The internal mode is determined by the profile of the large-scale divergence and subsequent rotational wind (Walker circulation) response driven by enhanced convection. In the extratropics, the dominant structure is equivalent barotropic. The external rotational modes grow rapidly within the extratropics in a manner that suggests that meridional propagation alone does not fully explain the growth of the extratropical response.

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Ronald Gelaro and Ronald M. Errico

Abstract

The temporal behavior of the zonal wavenumber 0 Hadley modes in the U.S. Navy's operational numerical weather prediction model is investigated. Time series of individual gravitational normal modes are examined in forecasts using different initialization strategies to determine the existence and nature of any nonlinear balance and the impact of initial conditions. A form of diabatic initialization based on a least-squares fit to the modes' trajectories in the forecast model is developed. A straightforward interpretation of the results, particularly how they relate to the principles of nonlinear normal-mode initialization, is afforded via a simple prognostic equation for a single gravitational mode. A limited number of behavior types is observed, which varies depending on the temporal and meridional scales of the modes. Only the largest-scale zonally symmetric modes show any evidence of diabatic balance and may thus be suitable candidates for diabatic initialization. Convective heating is the primary stationary forcing for these modes. Most medium-scale modes, whose natural periods may be close to the diurnal period, behave in a forced, wavelike manner due, apparently, to near-resonant diurnal forcing. Those modes with the smallest temporal and meridional scales exhibit both balanced and forced behavior. The dominant forcing for these modes appears to be adiabatic.

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Yanqiu Zhu and Ronald Gelaro

Abstract

The adjoint of a data assimilation system provides an efficient way of estimating sensitivities of analysis or forecast measures with respect to observations. The NASA Global Modeling and Assimilation Office (GMAO) has developed an exact adjoint of the Gridpoint Statistical Interpolation (GSI) analysis scheme developed at the National Centers for Environmental Prediction (NCEP). The development approach is unique in that the adjoint is derived from a line-by-line tangent linear version of the GSI. Availability of the tangent linear scheme provides an explicit means of assessing not only the fidelity of the adjoint, but also the effects of nonlinear processes in the GSI itself. In this paper, the development of the tangent linear and adjoint versions of the GSI are discussed and observation sensitivity results for a near-operational version of the system are shown. Results indicate that the GSI adjoint provides accurate assessments of the sensitivities with respect to observations of wind, temperature, satellite radiances, and, to a lesser extent, moisture. Sensitivities with respect to ozone observations are quite linear for the ozone fields themselves, but highly nonlinear for other variables. The sensitivity information provided by the adjoint is used to estimate the contribution, or impact, of various observing systems on locally defined response functions based on the analyzed increments of temperature and zonal wind. It is shown, for example, that satellite radiances have the largest impact of all observing systems on the temperature increments over the eastern North Pacific, while conventional observations from rawinsondes and aircraft dominate the impact on the zonal wind increments over the continental United States. The observation impact calculations also provide an additional means of validating the observation sensitivities produced by the GSI adjoint.

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Carolyn Reynolds and Ronald Gelaro

Abstract

The effect of model bias on the equatorward propagation of extratropical waves in a GCM simulation is assessed within the context of simple wave-guiding principles. The modes representing these waves are identified through the use of empirical orthogonal function analysis performed on the 200-mb zonal wind filtered to retain variations between 6 and 30 days. The temporal evolution and vertical structure of these modes are examined through the use of time-lagged composite analysis. The differences between observed and simulated wave propagation is examined in relationship to the theoretical wave-guiding properties associated with the observed and simulated time-mean flow. The utility of simple wave-guiding theory for describing the observed and modeled wave propagation is assessed.

The model bias in the time-mean flow is closely associated with the differences in the propagation of the transient waves. The excessively strong wave-guiding properties associated with the simulated Pacific jet appear to inhibit the proper meridional propagation of wave energy into the tropical central and eastern Pacific. In the simulation, waves that do propagate into the tropical Pacific either dissipate or are reflected near the equator, while in the observations, wave energy propagates into the Southern Hemisphere. On the other hand, the wave guiding by the subtropical and midlatitude jets over the Atlantic is weaker in the simulation than in the observations. In this region, wave energy propagates primarily into the Tropics in the simulation, while some of the observed wave energy is reflected toward the east and northeast over the Atlantic and northern Africa. The locations of the theoretical critical lines and wave guides of the time-mean flow, although based on many simplifying assumptions, are remarkably consistent with the propagation characteristics of these waves.

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Ronald Gelaro and Hampton N. Shirer

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The feasibility of developing an objective parameterization technique is examined for general nonlinear hydrodynamical systems. The typical structure of these hydrodynamical systems, regardless of their complexity, is one in which the rates of change of the dependent variables depend on homogeneous quadratic and linear forms, as well as on inhomogeneous forcing terms. As a prototype of the generic problem containing this typical structure, we apply the parameterization technique to various three-component subsets of a five-component nonlinear spectral model of forced, dissipative quasi-geostrophic flow in a channel. The results obtained here lead to specification of the necessary data coverage requirements for applying the technique in general.

The emphasis of this work is on preserving some behavior of the steady states by incorporating in the parameterized models information concerning the topological structure of the original solutions. By formulating the parameterization in terms of the steady states, we intend primarily to illustrate the general technique, but not to suggest that the preservation of temporal behavior can be achieved by addressing the steady solutions alone. The parameterized spectral components are expressed as power series involving the retained components, and it is found that the optimum parameterization is obtained when these series are terminated at quadratic terms. The values of the coefficients in these series are determined from the moments of the original set of spectral components over some range of forcing.

For testing convenience, the moments are computed using the steady solutions to the original five-component model as data. This is accomplished by assuming that the values of the zonal forcing rate obey some standard statistical distributions. In regions of phase space in which multiple steady solutions occur, the likelihood of the occurrence of any one solution may be weighted according to its stability. Thus, the datasets can be viewed as simulating either idealized data, in which both stable and unstable solutions are permitted, or observational data, in which only stable solutions are permitted. Special attention is paid to the sensitivity of the parameterization to data coverage requirements, and to the relation of these requirements to the general structure of the solution surfaces. Significantly, it is shown that with sufficient data coverage, a successful parameterization may be obtained even in the more restrictive case when only stable (observable) solutions are used as data.

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Will McCarty, Ronald M. Errico, and Ronald Gelaro

Abstract

A successful observing system simulation experiment (OSSE) is fundamentally dependent on the simulation of the global observing system used in the experiment. In many applications, a free-running numerical model simulation, called a nature run, is used as the meteorological truth from which the observations are simulated. To accurately and realistically simulate observations from any nature run, the simulated observations must contain realistic cloud effects representative of the meteorological regimes being sampled. This study provides a validation of the clouds in the Joint OSSE nature run generated at ECMWF. Presented is the methodology used to validate the nature run cloud fraction fields with seasonally aggregated combined CloudSat/Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) cloud geometric profile retrievals and the Wisconsin High Resolution Infrared Radiation Sounder (HIRS) cloud climatology. The results show that the Joint OSSE nature run has a correct vertical distribution of clouds but lacks globally in cloud amount compared to the validation data. The differences between the nature run and validation datasets shown in this study should be considered and accounted for in the generation of the global observing system for use in full OSSE studies.

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Carolyn Reynolds, Ronald Gelaro, and Tom Murphree

Abstract

The ability of an atmospheric general circulation model to simulate the observed primary modes of intraseasonal variability in the Northern Hemisphere upper-tropospheric winds during boreal winter is examined. The model used is the Navy Operational Global Atmospheric Prediction System. The authors examine differences between the observed and modeled modes of variability in the context of various model deficiencies, where the observed modes are derived from the European Centre for Medium-Range Weather Forecasts analyses. Rotated empirical orthogonal function analysis is used to determine the primary modes of variability in the Pacific and Atlantic regions. EOFs are computed for both the zonal and meridional wind components. Time-lagged composite analysis is used to examine the temporal evolution of these modes, as well as their relationship to tropical convection. Wave activity flux vectors are used to examine further the characteristics of these intraseasonal modes and their relationship to tropical and extratropical forcing.

It is found that the model simulates the extratropically forced modes well but simulates modes associated with tropical heating poorly. The poor tropical simulation is due primarily to the model's poor representation of the Madden–Julian oscillation (MJO). The model's inability to produce the MJO-related modes is reflected in the model upper-tropospheric wind field variability being too weak in the tropical and subtropical Indian and Pacific Ocean regions. Model biases in the simulated time-mean winds may also account for differences between the observed and modeled modes of variability.

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Ronald Gelaro, Thomas Rosmond, and Roger Daley

Abstract

Singular vectors of the navy's global forecast model are calculated using an initial norm consistent with an estimate of analysis error variance provided by the Naval Research Laboratory's (NRL) Atmospheric Variational Data Assimilation System (NAVDAS). The variance estimate is based on a decomposition of the block diagonal preconditioner for the conjugate-gradient descent algorithm used in NAVDAS. Because the inverse square root of the operator that defines the variance norm is readily computed, the leading singular vectors are obtained using a standard Lanczos algorithm, as with diagonal norms such as total energy.

The resulting singular vectors are consistent with the expected distribution of analysis errors. Compared with singular vectors based on a total energy norm, the variance singular vectors at initial time have less amplitude over well-observed areas, as well as greater amplitude in the middle and upper troposphere. The variance singular vectors are in some ways similar to the full covariance (Hessian) singular vectors developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). However, unlike the Hessian singular vectors, the variance singular vectors exhibit only minor difference in structure and growth rate compared with total energy singular vectors. This is because the variance singular vectors exclude covariance information used in NAVDAS that significantly penalizes smaller scales.

The 20 leading analysis error variance singular vectors explain approximately the same fraction of forecast error variance as the total energy singular vectors in a linear context, but less in a nonlinear context. Deficiencies in the current experimental configuration are among the reasons suspected for this. Implications for targeted observing are also examined. The results show that the variance norm can have a significant impact on determining the locations for supplemental observations.

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Daniel Holdaway, Ronald Errico, Ronald Gelaro, and Jong G. Kim

Abstract

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa–Schubert (RAS) convection scheme has been developed and tested in NASA’s Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

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