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J. R. Bates

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J. R. Bates

Abstract

The CISK theory is generalized by incorporating an explicit solution of the time-dependent boundary layer equations for the case of exponential growth and allowing the interior flow to be unbalanced. Two separate modes of solution are found, which are termed CISK of Types A and B.

CISK of Type A, a generalization of the well-known CISK solution, has the following characteristics: the instability is essentially dependent on rotation, friction, and the latent energy of moisture converged at levels below cloud base; the low-level convergence is comprised of frictional and allobaric components which act in the same direction, their relative magnitudes depending on the ratio of the growth rate to the Coriolis parameter; and the growth rate increases with latitude and is bounded above by f/3.

CISK of Type B, a new solution, has the following characteristics: the instability depends on friction but can exist without rotation; the energy is derived from moisture converged at levels above cloud base; the low-level convergence is opposed by friction and exists through the predominance of the allobaric effect; and the growth rate is bounded below by 1.8f and attains its maximum value on the equator.

The mean thermodynamic parameters of the tropical atmosphere favor Type A CISK. However, the range of parameters required for the existence of Type B CISK would seem to be attainable. This may help to explain why the ITCZ cloud bands, though normally found away from the equator, are sometimes, observed on the equator.

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J. R. Bates

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A grid-point method for integrating the shallow water equations based on a split semi-Lagrangian treatment of advection and an Eulerian alternating direction implicit treatment of the adjustment terms is presented. The scheme is simpler than the semi-implicit scheme, involving only the solution of linear tridiagonal systems of equations rather than a Helmholz equation. The theoretical properties of the scheme are examined for the E-grid. It is unconditionally stable for advection and for simple Rossby waves and has a very lenient stability criterion for gravity-inertia waves. Though two-level in time, it is shown to give second-order accuracy for both types of wave solution. No splitting errors occur in either case.

The scheme is used to carry out 24-hour integrations of a limited area barotropic model with real initial data. It is shown to be more efficient than a previous semi-Lagrangian scheme presented by Bates and McDonald.

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Minghang Chen and J. Ray Bates

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A series of 10-day forecast experiments has been carried out to investigate the sensitivity of a global semi-Lagrangian model to the value of the uncentering parameter ε, the magnitude of the time step for the dynamics, and the numerical treatment of the physical parameterizations (semi-Lagrangian versus Eulerian). The model has been run at a resolution of 2° latitude by 2.5° longitude with 20 vertical levels. Results from the experiments with values of ε ranging from 0 to 0.4 show that ε = 0.2 gives the best overall forecasts. The experiments with the time step for the dynamics varying from 15 to 60 min indicate that the forecasts are sensitive to the time step for the dynamics, even when the time steps for the physical parameterizations are held constant. The forecasts with the 60-min time step for the dynamics show the best overall objective skill scores. The two versions of the semi-Lagrangian model, one with Eulerian physics and the other with semi-Lagrangian physics, give similar forecast skill scores.

The semi-Lagrangian model is also compared with a corresponding Eulerian model. It is found that the forecasts from the two models have similar quality, even though the time step for the dynamics in the semi-Lagrangian model is 16 times as long as that in the Eulerian model and the physical parameterizations have been developed and tuned for the Eulerian model.

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A. McDonald and J. R. Bates

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A method for improving the estimate of the departure point position in a two-time level semi-Lagrangian integration scheme is introduced. It involves “centering in space and time” to arrive at the best value of the advecting velocity. A set of 60 multilevel model forecasts were run to demonstrate the efficacy of the method. These showed that, with a spatial resolution of 1.4° × 1.4° in a C-grid, a 90-min time step gave forecasts as accurate as did a 10-min time step.

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Minghang Chen and J. Ray Bates

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Two parallel 5-year climate simulations have been carried out to assess the effect of changing from an Eulerian to a semi-Lagrangian formulation of a general circulation model's dynamical core with the physical parameterizations unchanged. It has been found that the change in formulation leads to significant differences in the simulated climates, both for fields determined mainly by the dynamics, such as sea level pressure, and for those determined mainly by the physics, such as precipitation. The differences result both directly from the changes in the dynamics and indirectly from the interactions of the dynamics with the physics. Compared to the simulation with the Eulerian model, the principal improvement with the semi-Lagrangian model is a significant reduction in, or even elimination of, the cold bias in the polar upper troposphere and lower stratosphere in both hemispheres. This improvement is evident in both the winter and summer seasons. It results from the more efficient poleward heat transport in the semi-Lagrangian model. The effect on other simulated fields can give results either closer to or farther from the corresponding analyses and observations.

The physical parameterizations used in the semi-Lagrangian model have been developed and tuned for the Eulerian model. To optimize the performance of the semi-Lagrangian model, it will be necessary to tune the physical parameterizations explicitly for this model.

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A. McDonald and J. R. Bates

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A stable, semi-Lagrangian, semi-implicit, two-time-level, gridpoint integration scheme for the shallow water equations on the sphere is presented. A rotated spherical coordinate system is used to integrate the equations of motion at each gridpoint poleward of a certain latitude, thus overcoming problems associated with the polar singularity. The results of medium term integrations of large scale test patterns using a long time step are presented.

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J. R. Bates and A. McDonald

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The stability properties of some simple semi-Lagrangian advective schemes, based on a multiply-upstream interpolation, are examined. In these schemes, the interpolation points are chosen to surround the departure points of the fluid particles at the beginning of a time step. It is shown that the schemes, though explicit, are unconditionally stable for a constant wind field.

Application of the schemes to a multi-level split explicit model shows that they enable full advantage to be taken of the splitting method by allowing a long time step for advection. It is shown that they can thus lead to a considerable saving of computer time compared to Eulerian schemes, while giving comparable accuracy.

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Lei Shi, Ge Peng, and John J. Bates

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High-latitude ocean surface air temperature and humidity derived from intersatellite-calibrated High-Resolution Infrared Radiation Sounder (HIRS) measurements are examined. A neural network approach is used to develop retrieval algorithms. HIRS simultaneous nadir overpass observations from high latitudes are used to intercalibrate observations from different satellites. Investigation shows that if HIRS observations were not intercalibrated, then it could lead to intersatellite biases of 1°C in the air temperature and 1–2 g kg−1 in the specific humidity for high-latitude ocean surface retrievals. Using a full year of measurements from a high-latitude moored buoy site as ground truth, the instantaneous (matched within a half-hour) root-mean-square (RMS) errors of HIRS retrievals are 1.50°C for air temperature and 0.86 g kg−1 for specific humidity. Compared to a large set of operational moored and drifting buoys in both northern and southern oceans greater than 50° latitude, the retrieval instantaneous RMS errors are within 2.6°C for air temperature and 1.4 g kg−1 for specific humidity. Compared to 5 yr of International Maritime Meteorological Archive in situ data, the HIRS specific humidity retrievals show less than 0.5 g kg−1 of differences over the majority of northern high-latitude open oceans.

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CARLOS G. BATES and ALFRED J. HENRY

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