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## Abstract

A method to incorporate synoptic eddies into the diagnosis of circulation regimes using cluster analysis is illustrated using boreal winter reanalyses of the National Centers of Environmental Prediction (hereafter observations) over the Pacific–North American region. The motivation is to include the configuration of the high-frequency (periods less than 10 days) transients as well as the low-frequency (periods greater than 10 days) flow explicitly into the definition of the regimes.

Principle component analysis is applied to the low-frequency 200-hPa height field, and also to the low-frequency “envelope” modulations of the rms of high-frequency meridional velocity at 200 hPa. A maximum covariance analysis of the height and envelope fields, carried out using the appropriate principal components, defines three modes as explaining most of the covariance. This defines the minimum dimensionality of the space in which to apply *k*-means cluster analysis to the covariance coefficients. Clusters found using this method agree with results of the previous work.

Significance is assessed by comparing cluster analyses with results from synthetic datasets that have the same spectral amplitudes (but random phases) of seasonal means and, separately, intraseasonal fluctuations as do the original observed time series. This procedure ensures that the synthetic series have similar autocovariance structures to the observations. Building on earlier work, the clusters obtained are newly tested to be highly significant without the need for quasi-stationary prefiltering.

## Abstract

A method to incorporate synoptic eddies into the diagnosis of circulation regimes using cluster analysis is illustrated using boreal winter reanalyses of the National Centers of Environmental Prediction (hereafter observations) over the Pacific–North American region. The motivation is to include the configuration of the high-frequency (periods less than 10 days) transients as well as the low-frequency (periods greater than 10 days) flow explicitly into the definition of the regimes.

Principle component analysis is applied to the low-frequency 200-hPa height field, and also to the low-frequency “envelope” modulations of the rms of high-frequency meridional velocity at 200 hPa. A maximum covariance analysis of the height and envelope fields, carried out using the appropriate principal components, defines three modes as explaining most of the covariance. This defines the minimum dimensionality of the space in which to apply *k*-means cluster analysis to the covariance coefficients. Clusters found using this method agree with results of the previous work.

Significance is assessed by comparing cluster analyses with results from synthetic datasets that have the same spectral amplitudes (but random phases) of seasonal means and, separately, intraseasonal fluctuations as do the original observed time series. This procedure ensures that the synthetic series have similar autocovariance structures to the observations. Building on earlier work, the clusters obtained are newly tested to be highly significant without the need for quasi-stationary prefiltering.

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## Abstract

A two-level quasi-geostrophic beta-plane channel model with a smooth lower surface is used to study the dynamics of the growth of errors, with particular attention paid to the roles of wave-wave interactions via-a-vis those of baroclinic instability. The model has 16 zonal wavenumbers and 6 meridional modes on a midlatitude channel of width 5000 km and length 28 306 km. For a cross-channel “radiative equilibrium” temperature drop of 61°K and a radiative time constant of 20 days, the model produces a zonally averaged temperature drop of 30°K. The energy spectrum shows a peak at zonal wavenumber 4 to 5 due to baroclinic instability, and a planetary wave peak due solely to nonlinear interactions which extract energy from the unstable scales.

Three predictability experiments were performed, involving sample sizes of 110 to 220 forecasts of length 30 days. With the initial error in the smallest scales (with 1% of climatological variance), the error spectrum develops a peak in the unstable scales (zonal wavenumbers 4 to 6) within the first few days. This peak is the result of the interactions of stable waves, and is not due directly to baroclinic instability. By day 15 in the forecast, baroclinic instability becomes the dominant mechanism for error energy creation in the unstable scales, but the stable wave-wave interactions do not approach their equilibrium configuration as an energy sink for the unstable waves until after day 20. A distinct planetary wave peak in the error spectrum doe not appear until day 25. Nonlinear interactions involving one stable and one unstable wave are an important source of planetary wave error energy for most of the forecast.

With the initial errors in the most unstable scales (Experiment 2), the model exhibits more vigorous baroclinic instability. This leads to instability overtaking nonlinearity as the principal source of time-integrated total (wave) error energy four days earlier than in the previous experiment Paradoxically the planetary wave peak (due solely to wave-wave interactions) appears earlier than in the first experiment. This is due to enhanced forcing of the planetary wave by interactions of the large initial error in the unstable waves with stable waves, and to reduced forcing of the unstable waves by wave-wave interactions early in the forecast.

Interactions of the unstable waves with initial errors in the planetary wave lead to the appearance of an error energy peak in intermediate scales in a third experiment. These latter waves dominate the time-integrated error spectrum until instability catches up (at day 10) and produces large errors in the unstable scales.

## Abstract

A two-level quasi-geostrophic beta-plane channel model with a smooth lower surface is used to study the dynamics of the growth of errors, with particular attention paid to the roles of wave-wave interactions via-a-vis those of baroclinic instability. The model has 16 zonal wavenumbers and 6 meridional modes on a midlatitude channel of width 5000 km and length 28 306 km. For a cross-channel “radiative equilibrium” temperature drop of 61°K and a radiative time constant of 20 days, the model produces a zonally averaged temperature drop of 30°K. The energy spectrum shows a peak at zonal wavenumber 4 to 5 due to baroclinic instability, and a planetary wave peak due solely to nonlinear interactions which extract energy from the unstable scales.

Three predictability experiments were performed, involving sample sizes of 110 to 220 forecasts of length 30 days. With the initial error in the smallest scales (with 1% of climatological variance), the error spectrum develops a peak in the unstable scales (zonal wavenumbers 4 to 6) within the first few days. This peak is the result of the interactions of stable waves, and is not due directly to baroclinic instability. By day 15 in the forecast, baroclinic instability becomes the dominant mechanism for error energy creation in the unstable scales, but the stable wave-wave interactions do not approach their equilibrium configuration as an energy sink for the unstable waves until after day 20. A distinct planetary wave peak in the error spectrum doe not appear until day 25. Nonlinear interactions involving one stable and one unstable wave are an important source of planetary wave error energy for most of the forecast.

With the initial errors in the most unstable scales (Experiment 2), the model exhibits more vigorous baroclinic instability. This leads to instability overtaking nonlinearity as the principal source of time-integrated total (wave) error energy four days earlier than in the previous experiment Paradoxically the planetary wave peak (due solely to wave-wave interactions) appears earlier than in the first experiment. This is due to enhanced forcing of the planetary wave by interactions of the large initial error in the unstable waves with stable waves, and to reduced forcing of the unstable waves by wave-wave interactions early in the forecast.

Interactions of the unstable waves with initial errors in the planetary wave lead to the appearance of an error energy peak in intermediate scales in a third experiment. These latter waves dominate the time-integrated error spectrum until instability catches up (at day 10) and produces large errors in the unstable scales.

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## Abstract

The seasonal cycle is defined as the projection of an atmospheric time series onto a suitably defined subset of orthogonal basis functions, the choice of which depends on the length of the series involved. This procedure guarantees that any atmospheric covariance can be expressed as the sum of a seasonal cycle part and a transient part, where transient refers to departures from the seasonal cycle, not the lime mean.

Results for the seasonal cycle contribution to the zonally averaged fluxes of momentum (200 mb) and heat (850 mb) and for the zonally averaged height variance (500 mb) in NMC data are given for 1) the winter season (seasonal cycle defined in terms of a few Legendre functions), 2) 7-year mean (seasonal cycle defined as annual and semiannual Fourier harmonies), and 3) the winter season, but utilizing the Fourier basis act appropriate for the 7-year time series. The latter calculation indicates that the interannual variability of the momentum flux is dominated by the interactions between the seasonal cycle and the meteorologically low-frequency flow. Possible applications to other problems are discussed.

## Abstract

The seasonal cycle is defined as the projection of an atmospheric time series onto a suitably defined subset of orthogonal basis functions, the choice of which depends on the length of the series involved. This procedure guarantees that any atmospheric covariance can be expressed as the sum of a seasonal cycle part and a transient part, where transient refers to departures from the seasonal cycle, not the lime mean.

Results for the seasonal cycle contribution to the zonally averaged fluxes of momentum (200 mb) and heat (850 mb) and for the zonally averaged height variance (500 mb) in NMC data are given for 1) the winter season (seasonal cycle defined in terms of a few Legendre functions), 2) 7-year mean (seasonal cycle defined as annual and semiannual Fourier harmonies), and 3) the winter season, but utilizing the Fourier basis act appropriate for the 7-year time series. The latter calculation indicates that the interannual variability of the momentum flux is dominated by the interactions between the seasonal cycle and the meteorologically low-frequency flow. Possible applications to other problems are discussed.

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## Abstract

The most unstable normal modes have been obtained for a global model of the atmosphere which extends from the ground to 70 km. The model is quasi-geostrophic and in spectral form, including wavenumbers 1–6. Two sets of calculations were performed. In the first set, the basic state is representative of Northern Hemisphere winter solstice conditions. The long waves growing on this basic state are deep modes which have maximum kinetic energy in the stratosphere, and clearly are analogous to the stratosphere modes found for one-dimensional wind profiles by Geisler and Garcia. In the present calculations these internal modes exist even in the presence of a stratospheric wind minimum—but they propagate vertically into the stratosphere only to the north of this minimum, at the latitudes of the polar jet. The shorter wave normal modes are confined to the troposphere, and more closely resemble external (Charney) modes. The energy for all the modes ultimately derives from the available potential energy of the basic state in the lower troposphere, but local energy conversion in the stratosphere can play a role in supporting the deep, long waves.

The basic state for the second set of calculations was the axisymmetric solution corresponding to radiative equilibrium. The vertical wind shear in this state is very large, and all the modes are basically external, tropospheric Charney modes. In this case the large shear of the mean state causes the boundary between tropospheric (external) and stratospheric (internal) modes to fall to wavenumbers less than 1. Hence the latter cannot exist on the sphere.

## Abstract

The most unstable normal modes have been obtained for a global model of the atmosphere which extends from the ground to 70 km. The model is quasi-geostrophic and in spectral form, including wavenumbers 1–6. Two sets of calculations were performed. In the first set, the basic state is representative of Northern Hemisphere winter solstice conditions. The long waves growing on this basic state are deep modes which have maximum kinetic energy in the stratosphere, and clearly are analogous to the stratosphere modes found for one-dimensional wind profiles by Geisler and Garcia. In the present calculations these internal modes exist even in the presence of a stratospheric wind minimum—but they propagate vertically into the stratosphere only to the north of this minimum, at the latitudes of the polar jet. The shorter wave normal modes are confined to the troposphere, and more closely resemble external (Charney) modes. The energy for all the modes ultimately derives from the available potential energy of the basic state in the lower troposphere, but local energy conversion in the stratosphere can play a role in supporting the deep, long waves.

The basic state for the second set of calculations was the axisymmetric solution corresponding to radiative equilibrium. The vertical wind shear in this state is very large, and all the modes are basically external, tropospheric Charney modes. In this case the large shear of the mean state causes the boundary between tropospheric (external) and stratospheric (internal) modes to fall to wavenumbers less than 1. Hence the latter cannot exist on the sphere.

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## Abstract

The growth of geographically confined errors is studied in six experiments with a five-level global spectral (rhomboidal 30) general circulation model. Each experiment consists of 36 identical twin integrations with the initial errors localized in the same region. The centers of the regions are 180°, 120°W, 60°W, 0°, 60°E, and 120°E; all at 45°N. The perturbations are derived from differences in model states taken from a long integration. They reflect the natural distribution of variance in the model atmosphere, and are representative of realistic analysis errors.

By day 10 the errors have propagated (predominantly eastward) until they have reached either of the oceanic baroclinic waveguides and have amplified dramatically there. Errors originating in the central Pacific or western North America amplify over the Atlantic. Errors from the European, central Asian, and East Asian regions grow most strongly over the Pacific. Errors originating over the Atlantic show a mixed behavior. The rates of propagation involved are consistent with the downstream development of baroclinic instability. The behavior of the errors normalized by the climatological variance is similar. The cause of preferential error growth in the oceanic waveguides is the markedly baroclinic structure of the errors in these regions.

The largest 10-day errors originate in the Pacific and grow and propagate into the Atlantic, while the smallest ten-day forecast errors arise from initial errors over Europe. The largest 10-day *relative error* (error divided by its initial value) arise from errors originally confined to East Asia and Asia, which develop over the Pacific.

The experiments with perturbations centered at 60°E, 120°E, and 180° were repeated using initial errors that were identical in structure and magnitude but were zonally translated. At day 10 the errors that originate over the East Asian coast and developed in the mid-Pacific were the largest. The relative error in these modified experiments behaved very much like that in the original experiments.

After the initial period of growth, a stagnation of the errors is seen in the primary of the two oceanic areas, accompanied by error growth in the other (secondary) oceanic region. For certain experiments (those with initial errors in the Pacific, Asia, and East Asia) the latter development can be quite rapid.

There is a substantial variation in the growth rates from case to case, with the rms of the most rapidly growing perturbation as large as three times that of the average. The identity of the pair of states leading to the largest error depends on the forecast time.

## Abstract

The growth of geographically confined errors is studied in six experiments with a five-level global spectral (rhomboidal 30) general circulation model. Each experiment consists of 36 identical twin integrations with the initial errors localized in the same region. The centers of the regions are 180°, 120°W, 60°W, 0°, 60°E, and 120°E; all at 45°N. The perturbations are derived from differences in model states taken from a long integration. They reflect the natural distribution of variance in the model atmosphere, and are representative of realistic analysis errors.

By day 10 the errors have propagated (predominantly eastward) until they have reached either of the oceanic baroclinic waveguides and have amplified dramatically there. Errors originating in the central Pacific or western North America amplify over the Atlantic. Errors from the European, central Asian, and East Asian regions grow most strongly over the Pacific. Errors originating over the Atlantic show a mixed behavior. The rates of propagation involved are consistent with the downstream development of baroclinic instability. The behavior of the errors normalized by the climatological variance is similar. The cause of preferential error growth in the oceanic waveguides is the markedly baroclinic structure of the errors in these regions.

The largest 10-day errors originate in the Pacific and grow and propagate into the Atlantic, while the smallest ten-day forecast errors arise from initial errors over Europe. The largest 10-day *relative error* (error divided by its initial value) arise from errors originally confined to East Asia and Asia, which develop over the Pacific.

The experiments with perturbations centered at 60°E, 120°E, and 180° were repeated using initial errors that were identical in structure and magnitude but were zonally translated. At day 10 the errors that originate over the East Asian coast and developed in the mid-Pacific were the largest. The relative error in these modified experiments behaved very much like that in the original experiments.

After the initial period of growth, a stagnation of the errors is seen in the primary of the two oceanic areas, accompanied by error growth in the other (secondary) oceanic region. For certain experiments (those with initial errors in the Pacific, Asia, and East Asia) the latter development can be quite rapid.

There is a substantial variation in the growth rates from case to case, with the rms of the most rapidly growing perturbation as large as three times that of the average. The identity of the pair of states leading to the largest error depends on the forecast time.

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## Abstract

The relationship between Pacific blocking and large-scale circulation regimes is investigated. The large-scale circulation regimes are obtained by cluster analysis using the *k*-means method and tested against significance and reproducibility. Pacific blocking is described using two different methods. In a direct approach, blocking is described by a recently developed blocking index, which is defined in terms of potential temperature anomaly on a surface of constant potential vorticity. In an indirect approach, the occurrence of extreme events is used as a proxy for blockings. Between the two methods there is a causal relationship; the direct one is an indication of the occurrence of the blocking, while the indirect one is a measure of some of the effects caused by the blocking. The results indicate that large-scale circulation regimes are related to but not necessarily tightly coupled to blocking and weather extremes in the Pacific–North America region.

## Abstract

The relationship between Pacific blocking and large-scale circulation regimes is investigated. The large-scale circulation regimes are obtained by cluster analysis using the *k*-means method and tested against significance and reproducibility. Pacific blocking is described using two different methods. In a direct approach, blocking is described by a recently developed blocking index, which is defined in terms of potential temperature anomaly on a surface of constant potential vorticity. In an indirect approach, the occurrence of extreme events is used as a proxy for blockings. Between the two methods there is a causal relationship; the direct one is an indication of the occurrence of the blocking, while the indirect one is a measure of some of the effects caused by the blocking. The results indicate that large-scale circulation regimes are related to but not necessarily tightly coupled to blocking and weather extremes in the Pacific–North America region.

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## Abstract

The reanalyses of the Data Assimilation Office (DAO) of the National Aeronautics and Space Administration (NASA) are compared to those of the National Centers for Environmental Prediction (NCEP) with regard to the vertical structure and important horizontal scales of the baroclinic transients. Attention is focused on the eight Northern Hemisphere winters of 1985/86–1992/93 and on (bandpass) transients of timescales 2–8 days.

The local seasonal mean vertical shear (normalized by the square root of the static stability) is very similar between the two sets of analyses. The upper-level vorticity gradient (dominated by the meridional derivative) also shows little sensitivity to which reanalysis is used. The condition for barotropic instability (change of sign of total vorticity gradient) is satisfied.

The vertical structure of bandpass kinetic energy, meridional sensible heat flux, and variance of temperature gradient all show consistent differences between the NCEP and NASA reanalyses, with the NCEP signal significantly stronger at upper levels. The difference is modest for the kinetic energy (∼10%) and is much stronger for the heat flux (∼100%) and the variance of temperature gradient (∼70%). The NCEP reanalyses also have a stronger midlevel temperature gradient variance by about 20%. The differences in this quantity reflect the treatment of the National Environmental Satellite, Data, and Information Service (NESDIS) operational retrievals used by both reanalyses, and these satellite data affect the NASA reanalyses more strongly.

There are significant differences in the synoptic waves. The positive difference between the 300-hPa bandpass kinetic energy (NCEP minus NASA) as a function of the global wave number used to truncate the fields reaches nearly half (two-thirds) its total value by wavenumber 15 in the eastern Pacific (Atlantic). For the 200-hPa sensible heat flux the difference is a maximum at wavenumber 10 over the whole midlatitude belt.

Differences in midlevel temperature gradient variance between the first three winters (using NESDIS statistical retrievals) and the last five winters (using NESDIS physically based retrievals) include (i) NASA deficit compared to NCEP is slightly greater in the latter period and (ii) NASA variance is nearly 20% less in the latter period over the Pacific.

## Abstract

The reanalyses of the Data Assimilation Office (DAO) of the National Aeronautics and Space Administration (NASA) are compared to those of the National Centers for Environmental Prediction (NCEP) with regard to the vertical structure and important horizontal scales of the baroclinic transients. Attention is focused on the eight Northern Hemisphere winters of 1985/86–1992/93 and on (bandpass) transients of timescales 2–8 days.

The local seasonal mean vertical shear (normalized by the square root of the static stability) is very similar between the two sets of analyses. The upper-level vorticity gradient (dominated by the meridional derivative) also shows little sensitivity to which reanalysis is used. The condition for barotropic instability (change of sign of total vorticity gradient) is satisfied.

The vertical structure of bandpass kinetic energy, meridional sensible heat flux, and variance of temperature gradient all show consistent differences between the NCEP and NASA reanalyses, with the NCEP signal significantly stronger at upper levels. The difference is modest for the kinetic energy (∼10%) and is much stronger for the heat flux (∼100%) and the variance of temperature gradient (∼70%). The NCEP reanalyses also have a stronger midlevel temperature gradient variance by about 20%. The differences in this quantity reflect the treatment of the National Environmental Satellite, Data, and Information Service (NESDIS) operational retrievals used by both reanalyses, and these satellite data affect the NASA reanalyses more strongly.

There are significant differences in the synoptic waves. The positive difference between the 300-hPa bandpass kinetic energy (NCEP minus NASA) as a function of the global wave number used to truncate the fields reaches nearly half (two-thirds) its total value by wavenumber 15 in the eastern Pacific (Atlantic). For the 200-hPa sensible heat flux the difference is a maximum at wavenumber 10 over the whole midlatitude belt.

Differences in midlevel temperature gradient variance between the first three winters (using NESDIS statistical retrievals) and the last five winters (using NESDIS physically based retrievals) include (i) NASA deficit compared to NCEP is slightly greater in the latter period and (ii) NASA variance is nearly 20% less in the latter period over the Pacific.

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## Abstract

In order to better understand planetary wave–synoptic wave interactions in the atmosphere, and to develop a tool for further studies, the authors have applied a wavenumber-dependent external forcing to a general circulation model (GCM). The forcing constrains various length scales of the GCM to be close to those in the evolving analyses of the European Centre for Medium-Range Weather Forecasts and the National Centers for Environmental Prediction. The forcing acts either on the planetary waves (PW, defined as zonal wavenumbers 0–5), the synoptic waves (SW, defined as zonal wavenumbers 6–20), the synoptic waves plus the zonal mean (SW0), or the synoptic waves plus the zonal mean and wavenumber 1 (SW01). The form of the forcing is a linear relaxation to the (evolving) analyses with a time constant of 8 h. This forcing is applied only to the temperature and vorticity equations of the GCM, which has a spectral truncation of T42.

Control integrations of length 30 days have been run starting on 15 December, 1 January, and 15 January for each of the 12 winters in the period 1982/83–1993/94. This set of 36 integrations was repeated for PW forcing, SW forcing, SW0 forcing, and SW01 forcing.

The effectiveness of the SW forcing is measured by the mean zonal error variance of each wavenumber, normalized by the zonal variance in the analyses. This ratio is generally less than 0.2 when the analysis variance is large.

The systematic error of the pentad-mean 500-hPa height is very small in the PW-forced experiments compared to the control. The error reduction is very modest in the SW-forced experiments, and the zonal mean bias is *increased* compared to the control. Implications regarding errors in the GCM formulation of the planetary wave system are discussed. Dramatic reduction in the systematic error occurs only for the SW01 experiment, indicating the importance of wavenumber 1 errors in the GCM. The very modest reduction of the random pentad mean height error in the SW forced experiments compared to the control reflects the instrinsically chaotic nature of the PWs.

The 5-day mean streamfunction tendency due to bandpass transient SW–SW interactions in the control experiment tends to extend the Pacific jet too far east, and the Atlantic jet too far equatorward. The SW forcing reduces the systematic error in this transient–mean flow interaction, but systematic errors remain in the Atlantic, where the mean flow is in error. The PW-forced experiments show very low systematic error in this interaction, indicating 1) the strong steering effect of the PWs on the SWs, and 2) the ability of the GCM to simulate SWs realistically. The random error of the SW–SW transient–mean flow interaction emphasizes the intrinsic lack of predictability of the SWs.

The 5-day mean streamfunction tendency due to bandpass transient PW–SW interactions in the control experiment tends to support excessive meridional flow in the eastern Pacific, and to force the Atlantic jet too far equatorward. The reduction of the systematic error of this interaction from its value in the control experiment is marginal in the SW, SW0, and SW01 experiments, but is much greater for the PW-forced experiment, emphasizing the steering of the SWs by the mean PWs. The reduction in the random error of the PW–SW tendency from its control value is also significant for the PW-forced experiments at high latitudes.

## Abstract

In order to better understand planetary wave–synoptic wave interactions in the atmosphere, and to develop a tool for further studies, the authors have applied a wavenumber-dependent external forcing to a general circulation model (GCM). The forcing constrains various length scales of the GCM to be close to those in the evolving analyses of the European Centre for Medium-Range Weather Forecasts and the National Centers for Environmental Prediction. The forcing acts either on the planetary waves (PW, defined as zonal wavenumbers 0–5), the synoptic waves (SW, defined as zonal wavenumbers 6–20), the synoptic waves plus the zonal mean (SW0), or the synoptic waves plus the zonal mean and wavenumber 1 (SW01). The form of the forcing is a linear relaxation to the (evolving) analyses with a time constant of 8 h. This forcing is applied only to the temperature and vorticity equations of the GCM, which has a spectral truncation of T42.

Control integrations of length 30 days have been run starting on 15 December, 1 January, and 15 January for each of the 12 winters in the period 1982/83–1993/94. This set of 36 integrations was repeated for PW forcing, SW forcing, SW0 forcing, and SW01 forcing.

The effectiveness of the SW forcing is measured by the mean zonal error variance of each wavenumber, normalized by the zonal variance in the analyses. This ratio is generally less than 0.2 when the analysis variance is large.

The systematic error of the pentad-mean 500-hPa height is very small in the PW-forced experiments compared to the control. The error reduction is very modest in the SW-forced experiments, and the zonal mean bias is *increased* compared to the control. Implications regarding errors in the GCM formulation of the planetary wave system are discussed. Dramatic reduction in the systematic error occurs only for the SW01 experiment, indicating the importance of wavenumber 1 errors in the GCM. The very modest reduction of the random pentad mean height error in the SW forced experiments compared to the control reflects the instrinsically chaotic nature of the PWs.

The 5-day mean streamfunction tendency due to bandpass transient SW–SW interactions in the control experiment tends to extend the Pacific jet too far east, and the Atlantic jet too far equatorward. The SW forcing reduces the systematic error in this transient–mean flow interaction, but systematic errors remain in the Atlantic, where the mean flow is in error. The PW-forced experiments show very low systematic error in this interaction, indicating 1) the strong steering effect of the PWs on the SWs, and 2) the ability of the GCM to simulate SWs realistically. The random error of the SW–SW transient–mean flow interaction emphasizes the intrinsic lack of predictability of the SWs.

The 5-day mean streamfunction tendency due to bandpass transient PW–SW interactions in the control experiment tends to support excessive meridional flow in the eastern Pacific, and to force the Atlantic jet too far equatorward. The reduction of the systematic error of this interaction from its value in the control experiment is marginal in the SW, SW0, and SW01 experiments, but is much greater for the PW-forced experiment, emphasizing the steering of the SWs by the mean PWs. The reduction in the random error of the PW–SW tendency from its control value is also significant for the PW-forced experiments at high latitudes.

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## Abstract

A statistical approach to correct a dynamical ensemble forecast of future seasonal means based on the past performance of a general circulation model (GCM) is formulated. The approach combines principal component (PC) analysis with the regression technique to remove the systematic structural (distortion) error from the GCM ensemble. The performance of this statistical–dynamical method is assessed by comparing its cross-validated skill with the explicit skill achieved in the raw GCM ensembles.

When the PC regression technique is applied to seasonal means from an ensemble of the Center for Ocean–Land–Atmosphere Studies (COLA) GCM, it not only recovers most of the explicit skill in the original ensemble mean, but also acts to correct significant errors in the ensemble. It is shown that some ensemble errors are due to noise that can be easily removed by applying a simple regression scheme. A novel aspect of the PC regression technique, however, is that it goes beyond the simple filtering of noise and is able to correct systematic errors in the structure of predicted fields. Thus, it has the ability to diagnose and make use of implicit skill. In the authors' application, this skill appears in the extratropical western Pacific and in east Asia, and leads to significant improvement of seasonal forecast skill.

To make the PC regression scheme operationally useful, the authors develop a screening procedure for selecting skillful PCs as predictors for the regression equation. The predictors are chosen by the screening procedure based on their cross-validated performance within the training data over the whole domain or over a specified regional domain. When the procedure is applied to the COLA ensemble over the whole domain of the Northern Hemisphere, it achieves significant skill that is close to its upper bound achievable only through a postprocessing procedure. The authors also present a regional down-scaling exercise focused over eastern Canada and the northeast United States. This exercise reveals some nonlinear, asymmetric atmospheric responses to the ENSO forcing. Applications of the PC regression scheme to ensembles generated by other GCMs are also discussed. It is clear that when the SST-forced signal in the GCM is either very weak or not easily separated from noise, the regression scheme proposed will not be very successful.

## Abstract

A statistical approach to correct a dynamical ensemble forecast of future seasonal means based on the past performance of a general circulation model (GCM) is formulated. The approach combines principal component (PC) analysis with the regression technique to remove the systematic structural (distortion) error from the GCM ensemble. The performance of this statistical–dynamical method is assessed by comparing its cross-validated skill with the explicit skill achieved in the raw GCM ensembles.

When the PC regression technique is applied to seasonal means from an ensemble of the Center for Ocean–Land–Atmosphere Studies (COLA) GCM, it not only recovers most of the explicit skill in the original ensemble mean, but also acts to correct significant errors in the ensemble. It is shown that some ensemble errors are due to noise that can be easily removed by applying a simple regression scheme. A novel aspect of the PC regression technique, however, is that it goes beyond the simple filtering of noise and is able to correct systematic errors in the structure of predicted fields. Thus, it has the ability to diagnose and make use of implicit skill. In the authors' application, this skill appears in the extratropical western Pacific and in east Asia, and leads to significant improvement of seasonal forecast skill.

To make the PC regression scheme operationally useful, the authors develop a screening procedure for selecting skillful PCs as predictors for the regression equation. The predictors are chosen by the screening procedure based on their cross-validated performance within the training data over the whole domain or over a specified regional domain. When the procedure is applied to the COLA ensemble over the whole domain of the Northern Hemisphere, it achieves significant skill that is close to its upper bound achievable only through a postprocessing procedure. The authors also present a regional down-scaling exercise focused over eastern Canada and the northeast United States. This exercise reveals some nonlinear, asymmetric atmospheric responses to the ENSO forcing. Applications of the PC regression scheme to ensembles generated by other GCMs are also discussed. It is clear that when the SST-forced signal in the GCM is either very weak or not easily separated from noise, the regression scheme proposed will not be very successful.

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## Abstract

The atmospheric response to boreal summer tropical diabatic heating is studied in the atmospheric model component of the Community Atmosphere Model [CAM, version 3 (CAM3)] of the National Center for Atmospheric Research. An idealized heating function (with broad vertical but localized horizontal structure) is *added* to CAM3 near the equator; the circulation response is studied as a function of the sign of the heating and its longitude (Indian Ocean to eastern Pacific Ocean). The atmospheric circulation forced by the added heating interacts with all the physical and dynamical processes in CAM3; the total heating is the sum of the added heating and that produced by CAM3. In experiments using climatological sea surface temperature, added cooling (heating) over the Maritime Continent induces asymmetric anticyclonic (cyclonic) circulation extending toward India, opposing (reinforcing) the climatological monsoon flow and weakening (strengthening) the Indian monsoon. The anchoring of the anticyclonic (cyclonic) circulation over India as the added cooling (heating) is moved eastward over warm SST regions is greatly reduced when a slab ocean model is used. A negative (positive) air–sea feedback over the Indian Ocean is identified when heating (cooling) is added in the Indonesian region. Experiments in which the total heating is similar to estimates of the observed heating for the summer of 1987 are examined.

## Abstract

The atmospheric response to boreal summer tropical diabatic heating is studied in the atmospheric model component of the Community Atmosphere Model [CAM, version 3 (CAM3)] of the National Center for Atmospheric Research. An idealized heating function (with broad vertical but localized horizontal structure) is *added* to CAM3 near the equator; the circulation response is studied as a function of the sign of the heating and its longitude (Indian Ocean to eastern Pacific Ocean). The atmospheric circulation forced by the added heating interacts with all the physical and dynamical processes in CAM3; the total heating is the sum of the added heating and that produced by CAM3. In experiments using climatological sea surface temperature, added cooling (heating) over the Maritime Continent induces asymmetric anticyclonic (cyclonic) circulation extending toward India, opposing (reinforcing) the climatological monsoon flow and weakening (strengthening) the Indian monsoon. The anchoring of the anticyclonic (cyclonic) circulation over India as the added cooling (heating) is moved eastward over warm SST regions is greatly reduced when a slab ocean model is used. A negative (positive) air–sea feedback over the Indian Ocean is identified when heating (cooling) is added in the Indonesian region. Experiments in which the total heating is similar to estimates of the observed heating for the summer of 1987 are examined.