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## Abstract

The axial Ω and relative angular momenta, *M*
_{Ω} and *M*
_{
r
}, depend on the meridional mass distribution and relative zonal velocity, respectively. According to the conventional formulation, the time rate of change of *M*
_{Ω} is determined by the Coriolis conversion induced by meridional velocity, *M*
_{
r
} is accelerated by

This note decomposes _{
a
}. The decomposition identifies _{
a
} as the only forcing of *M*
_{
r
}. The resulting budgets suggest that the torques change the angular momentum of a rotating fluid with the aid of mass transports, rather than by directly accelerating the rotation speed, as in the case of a rigid body.

## Abstract

The axial Ω and relative angular momenta, *M*
_{Ω} and *M*
_{
r
}, depend on the meridional mass distribution and relative zonal velocity, respectively. According to the conventional formulation, the time rate of change of *M*
_{Ω} is determined by the Coriolis conversion induced by meridional velocity, *M*
_{
r
} is accelerated by

This note decomposes _{
a
}. The decomposition identifies _{
a
} as the only forcing of *M*
_{
r
}. The resulting budgets suggest that the torques change the angular momentum of a rotating fluid with the aid of mass transports, rather than by directly accelerating the rotation speed, as in the case of a rigid body.

## Abstract

The reddest atmospheric modes are studied using a 500-yr integration performed with the coupled ECHAM1/LSG general circulation model. By fitting a first-order autoregressive process to the considered time series, a simple measure of the spectral shape is obtained that allows an objective intercomparison of the spectra and the time series. Two modes, the tropical and the Southern Hemisphere modes, are identified as the reddest modes of the model atmosphere. Both are strongly anisotropic. The Southern Hemisphere mode, characterized by a dipole of zonal wind anomalies at Southern Hemispheric mid- and high latitudes, is related to a mass redistribution and a well-defined meridional circulation, whereas no significant anomalies of surface pressure and meridional velocity are found for the tropical mode, which is characterized by a maximum of zonal wind anomalies in the upper tropical troposphere. On timescales longer than a month, the two modes make, relative to other motions, the largest contributions to the global axial relative and Ω angular momenta *M*
_{
r
} and *M*
_{Ω} (i.e., the portions of the angular momentum that are related to the relative motions and the distributions of mass, respectively) and control the variations of *M*
_{
r
} and *M*
_{Ω}. Based on these relationships, the separated budgets of *M*
_{
r
} and *M*
_{Ω} are used to study the forcings of the spectra of the modes. The results suggest that the forcings of the low-frequency parts of the spectra are extremely feeble, whereas the forcings of the high-frequency parts of the spectra can be easily captured. For the Southern Hemisphere mode, the forcings of the high-frequency variations involve processes that are related to large meridional velocity near the surface.

## Abstract

The reddest atmospheric modes are studied using a 500-yr integration performed with the coupled ECHAM1/LSG general circulation model. By fitting a first-order autoregressive process to the considered time series, a simple measure of the spectral shape is obtained that allows an objective intercomparison of the spectra and the time series. Two modes, the tropical and the Southern Hemisphere modes, are identified as the reddest modes of the model atmosphere. Both are strongly anisotropic. The Southern Hemisphere mode, characterized by a dipole of zonal wind anomalies at Southern Hemispheric mid- and high latitudes, is related to a mass redistribution and a well-defined meridional circulation, whereas no significant anomalies of surface pressure and meridional velocity are found for the tropical mode, which is characterized by a maximum of zonal wind anomalies in the upper tropical troposphere. On timescales longer than a month, the two modes make, relative to other motions, the largest contributions to the global axial relative and Ω angular momenta *M*
_{
r
} and *M*
_{Ω} (i.e., the portions of the angular momentum that are related to the relative motions and the distributions of mass, respectively) and control the variations of *M*
_{
r
} and *M*
_{Ω}. Based on these relationships, the separated budgets of *M*
_{
r
} and *M*
_{Ω} are used to study the forcings of the spectra of the modes. The results suggest that the forcings of the low-frequency parts of the spectra are extremely feeble, whereas the forcings of the high-frequency parts of the spectra can be easily captured. For the Southern Hemisphere mode, the forcings of the high-frequency variations involve processes that are related to large meridional velocity near the surface.

## Abstract

The angular momentum anomalies associated with the Antarctic and Arctic Oscillations are examined in a coupled general circulation model. The size of the global-mean anomaly of the Ω angular momentum is unexpectedly larger than that of the relative angular momentum. The result is a simple consequence of mass conservation. Since the mass anomaly at high latitudes is equal and opposite to that at low latitudes, and since the high-latitude mass anomaly is relatively close to the rotation axis, the global-mean Ω angular momentum is significantly nonzero. Analysis of the meridional mass transport indicates that the Antarctic and Arctic Oscillations are persistent but damped modes.

## Abstract

The angular momentum anomalies associated with the Antarctic and Arctic Oscillations are examined in a coupled general circulation model. The size of the global-mean anomaly of the Ω angular momentum is unexpectedly larger than that of the relative angular momentum. The result is a simple consequence of mass conservation. Since the mass anomaly at high latitudes is equal and opposite to that at low latitudes, and since the high-latitude mass anomaly is relatively close to the rotation axis, the global-mean Ω angular momentum is significantly nonzero. Analysis of the meridional mass transport indicates that the Antarctic and Arctic Oscillations are persistent but damped modes.

## Abstract

In order to understand the spectrum Γ_{
x
}(*ω*) of a climate variable *x*
_{
t
}, the relation between Γ_{
x
}(*ω*) and its forcing has to be considered. If the evolution of *x*
_{
t
} over (discretized) time is determined by *f*
_{
t
}, that is, Δ*x*/Δ*t* ≡ (*x*
_{
t
} − *x*
_{
t−1})/Δ*t* = *f*
_{
t
}, the only existing relation is the one between Γ_{
x
}(*ω*) and the spectrum Γ_{
f
}(*ω*) of *f*
_{
t
}. The gain function *G*(*ω*) of the difference operator Δ/Δ*t,* which acts as a high-pass filter, controls the relation between Γ_{
x
}(*ω*) and Γ_{
f
}(*ω*). For Γ_{
x
}(*ω*), which is bounded at zero frequency, *G*(*ω*) completely suppresses the variations of *f*
_{
t
} at zero frequency, so that Γ_{
x
}(0) cannot be related to Γ_{
f
}(0). In practice, the efficiency of the difference operator as a high-pass filter can make the detection of the low-frequency spectral relation between *x*
_{
t
} and *f*
_{
t
} difficult.

## Abstract

In order to understand the spectrum Γ_{
x
}(*ω*) of a climate variable *x*
_{
t
}, the relation between Γ_{
x
}(*ω*) and its forcing has to be considered. If the evolution of *x*
_{
t
} over (discretized) time is determined by *f*
_{
t
}, that is, Δ*x*/Δ*t* ≡ (*x*
_{
t
} − *x*
_{
t−1})/Δ*t* = *f*
_{
t
}, the only existing relation is the one between Γ_{
x
}(*ω*) and the spectrum Γ_{
f
}(*ω*) of *f*
_{
t
}. The gain function *G*(*ω*) of the difference operator Δ/Δ*t,* which acts as a high-pass filter, controls the relation between Γ_{
x
}(*ω*) and Γ_{
f
}(*ω*). For Γ_{
x
}(*ω*), which is bounded at zero frequency, *G*(*ω*) completely suppresses the variations of *f*
_{
t
} at zero frequency, so that Γ_{
x
}(0) cannot be related to Γ_{
f
}(0). In practice, the efficiency of the difference operator as a high-pass filter can make the detection of the low-frequency spectral relation between *x*
_{
t
} and *f*
_{
t
} difficult.

## Abstract

Various types of air–sea interactions are studied based on the general properties of cross-covariance function and the well-defined shapes of these functions obtained from conceptual models.

The analysis is applied to sea surface temperature and surface fluxes obtained from a long integration with the coupled ECHAM3/LSG model. The results suggest that the atmosphere plays a dominant role in generating the coupled variability. Covariances between SST and wind stress in the extratropics are close to zero when SST leads, suggesting that SST anomalies, once being generated, do not feed back to the atmosphere. The interactions between SST and tropical wind stress involve various types of feedbacks. For heat flux, the antisymmetric shape of cross-covariance functions indicates that heat flux anomalies generate SST variations and the interaction tends to reverse the sign of the earlier SST anomalies. The atmosphere plays also an important role in generating coupled variations of SST and evaporation, and of SST and extratropical precipitation. The most dominant role of the ocean is found in the Tropics.

The results can be used to verify simple atmospheric models that are used in ocean-only modeling studies. Cross-covariance functions found in such simple coupled models should be similar to those found in a fully coupled atmosphere–ocean GCM, if the simple models produce the same interactions found in fully coupled GCMs.

## Abstract

Various types of air–sea interactions are studied based on the general properties of cross-covariance function and the well-defined shapes of these functions obtained from conceptual models.

The analysis is applied to sea surface temperature and surface fluxes obtained from a long integration with the coupled ECHAM3/LSG model. The results suggest that the atmosphere plays a dominant role in generating the coupled variability. Covariances between SST and wind stress in the extratropics are close to zero when SST leads, suggesting that SST anomalies, once being generated, do not feed back to the atmosphere. The interactions between SST and tropical wind stress involve various types of feedbacks. For heat flux, the antisymmetric shape of cross-covariance functions indicates that heat flux anomalies generate SST variations and the interaction tends to reverse the sign of the earlier SST anomalies. The atmosphere plays also an important role in generating coupled variations of SST and evaporation, and of SST and extratropical precipitation. The most dominant role of the ocean is found in the Tropics.

The results can be used to verify simple atmospheric models that are used in ocean-only modeling studies. Cross-covariance functions found in such simple coupled models should be similar to those found in a fully coupled atmosphere–ocean GCM, if the simple models produce the same interactions found in fully coupled GCMs.

## Abstract

Predictability studies of the second kind are often carried out to address the potential in predicting atmospheric variables based on knowledge of changes in sea surface temperature (SST). Here a predictability study of the second kind is performed for the coupled atmosphere–ocean system based on knowledge of changes in CO_{2} concentration. The focus is on potential predictabilities obtained after imposing a CO_{2} forcing over a short time period (i.e., a few years), which are less sensitive to the exact future time evolution of the CO_{2} forcing. Potential predictability is measured by the ensemble mean difference resulting from the CO_{2} forcing relative to the ensemble spread subjected to the same forcing. The measure is calculated from a 50-member prediction ensemble obtained from an atmosphere–ocean GCM forced by a 3% increase in CO_{2} concentration per year and a reference ensemble obtained under a constant CO_{2} concentration.

The largest potential predictabilities are found in and over the Southern Ocean. The origin of these predictabilities is a positive feedback involving interactions between the atmosphere and the upper ocean. An increase in the meridional gradient of SST resulting from a large SST increase in the southern subtropics leads to a strengthening of atmospheric circulation, and from that increases in surface zonal wind stress result. The latter enhances the northward Ekman transport over the southern high latitudes, which transports polar water equatorward, whereby maintaining the meridional temperature gradient. Potential predictability is also found in the deep ocean, characterized by the downward propagation of the surface warming within a few years through two “corridors,” located at 40°S and 40°N and extending from the near surface to about 3000–3500 m. The warming in the atmosphere and the upper ocean is reduced by half because of this downward heat propagation.

## Abstract

Predictability studies of the second kind are often carried out to address the potential in predicting atmospheric variables based on knowledge of changes in sea surface temperature (SST). Here a predictability study of the second kind is performed for the coupled atmosphere–ocean system based on knowledge of changes in CO_{2} concentration. The focus is on potential predictabilities obtained after imposing a CO_{2} forcing over a short time period (i.e., a few years), which are less sensitive to the exact future time evolution of the CO_{2} forcing. Potential predictability is measured by the ensemble mean difference resulting from the CO_{2} forcing relative to the ensemble spread subjected to the same forcing. The measure is calculated from a 50-member prediction ensemble obtained from an atmosphere–ocean GCM forced by a 3% increase in CO_{2} concentration per year and a reference ensemble obtained under a constant CO_{2} concentration.

The largest potential predictabilities are found in and over the Southern Ocean. The origin of these predictabilities is a positive feedback involving interactions between the atmosphere and the upper ocean. An increase in the meridional gradient of SST resulting from a large SST increase in the southern subtropics leads to a strengthening of atmospheric circulation, and from that increases in surface zonal wind stress result. The latter enhances the northward Ekman transport over the southern high latitudes, which transports polar water equatorward, whereby maintaining the meridional temperature gradient. Potential predictability is also found in the deep ocean, characterized by the downward propagation of the surface warming within a few years through two “corridors,” located at 40°S and 40°N and extending from the near surface to about 3000–3500 m. The warming in the atmosphere and the upper ocean is reduced by half because of this downward heat propagation.

## Abstract

Subgrid-scale fluctuations with zero means have generally been neglected in ocean modeling, despite their potential role in affecting the oceanic state following Hasselmann's seminal paper on stochastic climate models and series of studies conducted thereafter. When representing effects of these fluctuations in a stochastic parameterization, knowledge of basic properties of these fluctuations is essential. Here, the authors quantify these properties using hourly output of a simulation performed with a global

## Abstract

Subgrid-scale fluctuations with zero means have generally been neglected in ocean modeling, despite their potential role in affecting the oceanic state following Hasselmann's seminal paper on stochastic climate models and series of studies conducted thereafter. When representing effects of these fluctuations in a stochastic parameterization, knowledge of basic properties of these fluctuations is essential. Here, the authors quantify these properties using hourly output of a simulation performed with a global

## Abstract

Decadal climate prediction is a challenging aspect of climate research. It has been and will be tackled by various modeling groups. This study proposes a simple empirical forecasting system for the near-surface temperature that can be used as a benchmark for climate predictions obtained from atmosphere–ocean GCMs (AOGCMs). It is assumed that the temperature time series can be decomposed into components related to external forcing and internal variability. The considered external forcing consists of the atmospheric CO_{2} concentration. Separation of the two components is achieved by using the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4) twentieth-century integrations. Temperature anomalies due to changing external forcing are described by a linear regression onto the forcing. The future evolution of the external forcing that is needed for predictions is approximated by a linear extrapolation of the forcing prior to the initial time. Temperature anomalies owing to the internal variability are described by an autoregressive model. An evaluation of hindcast experiments shows that the empirical model has a cross-validated correlation skill of 0.84 and a cross-validated rms error of 0.12 K in hindcasting global-mean temperature anomalies 10 years ahead.

## Abstract

Decadal climate prediction is a challenging aspect of climate research. It has been and will be tackled by various modeling groups. This study proposes a simple empirical forecasting system for the near-surface temperature that can be used as a benchmark for climate predictions obtained from atmosphere–ocean GCMs (AOGCMs). It is assumed that the temperature time series can be decomposed into components related to external forcing and internal variability. The considered external forcing consists of the atmospheric CO_{2} concentration. Separation of the two components is achieved by using the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4) twentieth-century integrations. Temperature anomalies due to changing external forcing are described by a linear regression onto the forcing. The future evolution of the external forcing that is needed for predictions is approximated by a linear extrapolation of the forcing prior to the initial time. Temperature anomalies owing to the internal variability are described by an autoregressive model. An evaluation of hindcast experiments shows that the empirical model has a cross-validated correlation skill of 0.84 and a cross-validated rms error of 0.12 K in hindcasting global-mean temperature anomalies 10 years ahead.

## Abstract

The climate response to increased CO_{2} concentration is generally studied using climate models that have finite spatial and temporal resolutions. Different parameterizations of the effect of unresolved processes can result in different representations of small-scale fluctuations in the climate model. The representation of small-scale fluctuations can, on the other hand, affect the modeled climate response. In this study the mechanisms by which enhanced small-scale fluctuations alter the climate response to CO_{2} doubling are investigated. Climate experiments with preindustrial and doubled CO_{2} concentrations obtained from a comprehensive climate model [ECHAM5/Max Planck Institute Ocean Model (MPI-OM)] are analyzed both with and without enhanced small-scale fluctuations. By applying a stochastic model to the experimental results, two different mechanisms are found. First, the small-scale fluctuations can change the statistical behavior of the global mean temperature as measured by its statistical damping. The statistical damping acts as a restoring force that determines, according to the fluctuation–dissipation theory, the amplitude of the climate response to a change in external forcing (here, CO_{2} doubling). Second, the small-scale fluctuations can affect processes that occur only in response to the CO_{2} increase, thereby altering the change of the effective forcing on the global mean temperature.

## Abstract

The climate response to increased CO_{2} concentration is generally studied using climate models that have finite spatial and temporal resolutions. Different parameterizations of the effect of unresolved processes can result in different representations of small-scale fluctuations in the climate model. The representation of small-scale fluctuations can, on the other hand, affect the modeled climate response. In this study the mechanisms by which enhanced small-scale fluctuations alter the climate response to CO_{2} doubling are investigated. Climate experiments with preindustrial and doubled CO_{2} concentrations obtained from a comprehensive climate model [ECHAM5/Max Planck Institute Ocean Model (MPI-OM)] are analyzed both with and without enhanced small-scale fluctuations. By applying a stochastic model to the experimental results, two different mechanisms are found. First, the small-scale fluctuations can change the statistical behavior of the global mean temperature as measured by its statistical damping. The statistical damping acts as a restoring force that determines, according to the fluctuation–dissipation theory, the amplitude of the climate response to a change in external forcing (here, CO_{2} doubling). Second, the small-scale fluctuations can affect processes that occur only in response to the CO_{2} increase, thereby altering the change of the effective forcing on the global mean temperature.

## Abstract

Principal oscillation pattern (POP) analysis is a diagnostic technique for deriving the space-time characteristics of a dataset objectively. A multiyear dataset of monthly mean sea level pressure (SLP) in the area 15°S to 40°S is examined with the POP technique. In the low-frequency band one physically significant pair of patterns is identified, which is clearly associated with the Southern Oscillation (SO).

According to the POP analysis, the 50 may be described as a damped oscillatory sequence of patterns …→**P**
^{1}→**P**
^{2}→**-P**
^{1}→**-P**
^{2}→**P**
^{1}… having a time scale of two to three years. The first pattern, **P ^{1}
**, representative of the “peak” phase of ENSO, exhibits a dipole with anomalies of opposite sign over the central and eastern Pacific and over the Indian Ocean/Australian sector. The second,

**P**, pattern is dominated by an anomaly in the SPCZ region and describes an intermediate, or “onset” phase.

^{2}The time coefficients of the two patterns, **P _{1}
** and

**P**, may be interpreted as a bivariate index of the SO. Generalizing the original diagnostic concept, the POP framework is used to predict this index and the traditional univariate SO index.

_{2}The POP prediction scheme is tested in a series of hindcast experiments. The scheme turns out to be skillful for a lead time of two to three seasons. In terms of a correlation skill score, the POP model is better than persistence and a conventional ARMA model in hindcasting the traditional SO index.

## Abstract

Principal oscillation pattern (POP) analysis is a diagnostic technique for deriving the space-time characteristics of a dataset objectively. A multiyear dataset of monthly mean sea level pressure (SLP) in the area 15°S to 40°S is examined with the POP technique. In the low-frequency band one physically significant pair of patterns is identified, which is clearly associated with the Southern Oscillation (SO).

According to the POP analysis, the 50 may be described as a damped oscillatory sequence of patterns …→**P**
^{1}→**P**
^{2}→**-P**
^{1}→**-P**
^{2}→**P**
^{1}… having a time scale of two to three years. The first pattern, **P ^{1}
**, representative of the “peak” phase of ENSO, exhibits a dipole with anomalies of opposite sign over the central and eastern Pacific and over the Indian Ocean/Australian sector. The second,

**P**, pattern is dominated by an anomaly in the SPCZ region and describes an intermediate, or “onset” phase.

^{2}The time coefficients of the two patterns, **P _{1}
** and

**P**, may be interpreted as a bivariate index of the SO. Generalizing the original diagnostic concept, the POP framework is used to predict this index and the traditional univariate SO index.

_{2}The POP prediction scheme is tested in a series of hindcast experiments. The scheme turns out to be skillful for a lead time of two to three seasons. In terms of a correlation skill score, the POP model is better than persistence and a conventional ARMA model in hindcasting the traditional SO index.