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E. Kirkwood and J. Derome


Some consequences of applying the boundary condition dp/dt=0 at p=0 in a linearized middle-latitude β-plane model of forced stationary planetary waves are investigated. The perturbations, which are assumed to be quasi-geostrophic and subject to Newtonian cooling, are superimposed on an isothermal basic state having a realistic vertical profile of the mean zonal wind. Computations of the wave structures are made using finite differences in the vertical with various resolutions. They are compared with those obtained in a model which uses a radiation condition at its upper boundary. The influence of the mean zonal wind distribution is investigated by using vertical profiles which are representative of winter, spring and fall.

In general, the results show that insufficient resolution in the stratosphere can lead to a spurious energy reflection at the upper boundary and to a wave structure which is completely in error.

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Nicholas M. J. Hall and Jacques Derome


A dry primitive equation model is used to investigate the remote response to a fixed tropical heat source. The basic forcing for the model takes the form of time-independent terms added to the prognostic equations in two configurations. One produces a perturbation model, in which anomalies grow on a fixed basic state. The other gives a simple GCM, which can be integrated for a long time and delivers a realistic climate simulation with realistic storm tracks. A series of experiments is performed, including 15-day perturbation runs, ensemble experiments, and long equilibrium runs, to isolate different dynamical influences on the fully developed Pacific–North American (PNA) type response to an equatorial heating anomaly centered on the date line.

The direct linear response is found to be very sensitive to changes in the basic state of the same order as the atmosphere’s natural variability, and to the natural progression of the basic state over the time period required to set up the response. However, interactions with synoptic-scale noise in the ambient flow are found to have very little systematic effect on the linear response. Nonlinear interactions with a fixed basic state lead to changes in the position, but not the amplitude, of the response. Feedback with finite-amplitude transient eddies leads to downstream amplification of the PNA pattern, both within the setup time for the response and in a fully adjusted equilibrium situation.

Nonlinearity of the midlatitude dynamics gives rise to considerable asymmetry between the response to tropical heating and the response to an equal and opposite cooling.

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Nicholas M. J. Hall, Hai Lin, and Jacques Derome


A simple GCM based on a primitive equation model with empirically derived time-independent forcing is used to make forecasts in the extended to seasonal range. The results are analyzed in terms of the response to a midlatitude Pacific sea surface temperature anomaly (SSTA), represented here by a heating perturbation. A set of 90-day, 30-member ensemble forecasts is made with 54 widely differing initial conditions, both with and without the SSTA. The development of the response, defined as the difference between ensemble means, is split into three 30-day averages: month 1, month 2, and month 3.

During month 1, ensemble members separate, and the local response and remote teleconnections are established. The local response is not very sensitive to the initial condition.

In month 2, the extended range, the responses are relatively strong and vary greatly from one initial condition to another. However, a linear analysis reveals that large variations in the response do not correlate strongly with large variations in the initial condition. The initial perturbations required to generate the observed variations in the response are relatively small, and may be difficult to isolate in a real forecasting situation.

In month 3, the seasonal range, variations between responses are much smaller. The initial condition loses its influence and the responses all start to resemble the equilibrium response discussed in Part I.

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Nicholas M. J. Hall, Jacques Derome, and Hai Lin


A simple GCM (SGCM) is constructed by adding empirically derived time-independent forcing terms to a dry primitive equation model. This yields a model with realistic time-mean jets and storm tracks. The SGCM is then used to study the equilibrium response to an imposed heating anomaly in the midlatitude Pacific, meant to represent an anomaly in the sea surface temperature. Using the SGCM’s own climatology as a basic state, the same model is then used to find the time-independent linear response to the same heating anomaly. The difference between the two responses is clearly attributed to the forcing due to anomalous transient eddies.

The sensitivity of the response to the strength and vertical profile of the heating, and to the presence of the wind speed in the surface flux parameterization, is explored. It is found that for a reasonable range of heating amplitude the transient eddy forcing is proportional to the heating and the responses to heating and cooling are almost antisymmetric. The antisymmetry breaks down at large amplitude. The vertical profile of heating has a small but systematic effect on the response: deeper heating leads to stronger equivalent barotropic features. The inclusion of wind speed in the surface flux parameterization alters the response mainly by virtue of altering the basic model climatology, rather than by any local effect on the heating.

The position of the heating anomaly is varied in both latitude and longitude to gain insight into the possible effects of systematic errors in GCMs. The time-independent linear response tends to move with the heating, but the eddy-driven nonlinear part remains relatively fixed and varies only in amplitude. The heating perturbation slightly modifies the first empirical orthogonal function of the model’s internal low frequency variability. The response projects strongly onto this pattern and the probability distribution function of the projection is significantly skewed.

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Shiling Peng, L. A. Mysak, J. Derome, H. Ritchie, and B. Dugas


Using an atmospheric global spectral model, it is shown that the winter atmosphere in the midlatitudes is capable of reacting to prescribed sea surface temperature (SST) anomalies in the northwest Atlantic with two very different responses. The nature of the response is determined by the climatological conditions of the winter regime. Experiments are performed using either the perpetual November or January conditions with or without the prescribed SST anomalies.

Warm SST anomalies in November result in a highly significant anomalous ridge downstream over the Atlantic with a nearly equivalent barotropic structure; in January, the response is a statistically less significant trough. The presence of the SST anomalies also causes a northward (southward) shift of the Atlantic storm track in the November (January) cases. A diagnostic analysis of the anomalous heat advection in the simulations reveals that in the January cases, the surface heating is offset primarily by the strong horizontal cold advection in the lower troposphere. In the November cases, there is a vitally important vertical heat advection through which a potential positive ocean-atmosphere feedback was found. The positive air temperature anomalies exhibit a deep vertical penetration in the November cases but not in the January cases.

The simulated atmospheric responses to the warm SST anomalies in the November and January cases are found to be in qualitative agreement with the observational results using 50-yr ( 1930-1979) records. The atmospheric responses to the cold SST anomalies in the simulations are found to be insignificant.

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