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- Author or Editor: Ping Chang x
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Abstract
The role of dynamic ocean-atmosphere interactions on the evolution of the tropical seasonal cycle is explored using a simple coupled model. It is shown that the seasonal cycle in the coupled system can be divided into two parts-a forced part that is a direct response to seasonal changes in the solar radiation and a coupled part that involves dynamic feedbacks between the oceans and atmosphere. The latter part contributes significantly to the pronounced annual cycle in the eastern equatorial Pacific, but is less influential in the western Pacific, owing to the different climate mean conditions. The study further suggests that the ocean-atmosphere interactions in the meridional and zonal direction play different roles in the evolution of the tropical annual cycle. The former is crucial to the development of the strong annual cycle in the near-coastal zone of the eastern Pacific (eastward of 100°W), whereas the latter is instrumental in the westward expansion of the annual cycle along the equator. The results of this study suggest that many important features of the tropical seasonal cycle can be modeled with a relatively simple coupled model, provided that the climate mean conditions are correctly established.
Abstract
The role of dynamic ocean-atmosphere interactions on the evolution of the tropical seasonal cycle is explored using a simple coupled model. It is shown that the seasonal cycle in the coupled system can be divided into two parts-a forced part that is a direct response to seasonal changes in the solar radiation and a coupled part that involves dynamic feedbacks between the oceans and atmosphere. The latter part contributes significantly to the pronounced annual cycle in the eastern equatorial Pacific, but is less influential in the western Pacific, owing to the different climate mean conditions. The study further suggests that the ocean-atmosphere interactions in the meridional and zonal direction play different roles in the evolution of the tropical annual cycle. The former is crucial to the development of the strong annual cycle in the near-coastal zone of the eastern Pacific (eastward of 100°W), whereas the latter is instrumental in the westward expansion of the annual cycle along the equator. The results of this study suggest that many important features of the tropical seasonal cycle can be modeled with a relatively simple coupled model, provided that the climate mean conditions are correctly established.
Abstract
We look at the effect of a slow zonal variation in thermocline depth on the propagation of a finite-amplitude Kelvin wave pulse in a single layer model. Dispersive effects are included by also allowing a weak meridional variation in background state.
Analytical results are obtained using the method of multiple scales—in essence a WKB approximation. The evolution of wave amplitude riding with the Kelvin wave is found to be governed by a KdV equation with variable coefficients. As expected from energy conservation, the amplitude must increase as the thermocline depth decreases; however, the power appearing in the analog of “Green's Law” is different than that found for shallow water waves impinging on a beach. This modified “Green's Law” is verified using a numerical model.
The most interesting conclusion, which is also checked numerically, is that a significant portion of the mass flux carried by a Kelvin wave pulse propagating eastward into a shoaling thermocline (the oceanographically relevant solution) is reflected by westward-propagating Rossby and gravity modes. This is not true of the energy flux, and we explain this seeming paradox using scaling arguments.
Abstract
We look at the effect of a slow zonal variation in thermocline depth on the propagation of a finite-amplitude Kelvin wave pulse in a single layer model. Dispersive effects are included by also allowing a weak meridional variation in background state.
Analytical results are obtained using the method of multiple scales—in essence a WKB approximation. The evolution of wave amplitude riding with the Kelvin wave is found to be governed by a KdV equation with variable coefficients. As expected from energy conservation, the amplitude must increase as the thermocline depth decreases; however, the power appearing in the analog of “Green's Law” is different than that found for shallow water waves impinging on a beach. This modified “Green's Law” is verified using a numerical model.
The most interesting conclusion, which is also checked numerically, is that a significant portion of the mass flux carried by a Kelvin wave pulse propagating eastward into a shoaling thermocline (the oceanographically relevant solution) is reflected by westward-propagating Rossby and gravity modes. This is not true of the energy flux, and we explain this seeming paradox using scaling arguments.
Abstract
A linear stability analysis of an intermediate coupled ocean–atmosphere model reveals that the tropical Atlantic has two types of coupled modes: a meridional mode at the decadal time scale and a zonal mode at the interannual time scale. The meridional mode, which manifests itself as an interhemispheric SST fluctuation, is controlled by the thermodynamical feedback between winds, latent heat flux, and SST, further modified by ocean heat transport. The zonal mode, which manifests itself as an SST fluctuation in the eastern equatorial basin, is dominated by the dynamical feedback between winds, thermocline, upwelling, and SST. The relative strength of thermodynamical versus dynamical feedback determines the behavior of the coupled system. When the thermodynamical feedback dominates, the meridional mode is the leading coupled mode; when the dynamical feedback dominates, the zonal mode leads all other coupled modes. Interestingly, a nonoscillatory regime exists for the leading mode when both feedbacks are comparable in strength, suggesting a destructive interference between the meridional and zonal modes.
Abstract
A linear stability analysis of an intermediate coupled ocean–atmosphere model reveals that the tropical Atlantic has two types of coupled modes: a meridional mode at the decadal time scale and a zonal mode at the interannual time scale. The meridional mode, which manifests itself as an interhemispheric SST fluctuation, is controlled by the thermodynamical feedback between winds, latent heat flux, and SST, further modified by ocean heat transport. The zonal mode, which manifests itself as an SST fluctuation in the eastern equatorial basin, is dominated by the dynamical feedback between winds, thermocline, upwelling, and SST. The relative strength of thermodynamical versus dynamical feedback determines the behavior of the coupled system. When the thermodynamical feedback dominates, the meridional mode is the leading coupled mode; when the dynamical feedback dominates, the zonal mode leads all other coupled modes. Interestingly, a nonoscillatory regime exists for the leading mode when both feedbacks are comparable in strength, suggesting a destructive interference between the meridional and zonal modes.
Abstract
The coupled variability and predictability of the tropical Atlantic ocean–atmosphere system were analyzed within the framework of a linear stochastic climate model. Despite the existence of a meridional dipole as the leading mode, tropical Atlantic variability (TAV) is dominated by equatorial features and the subtropical variability is largely uncorrelated between the northern and southern Atlantic. This suggests that atmospheric stochastic forcing plays a dominant role in defining the spatial patterns of TAV, whereas the active air–sea feedbacks mainly enhance variability at interannual and decadal time scales, causing the spectra distinctive from the red spectrum. Under the stochastic forcing, the useful predictive skill for sea surface temperature measured by normalized error variance is limited to 2 months on average, which is 1 month longer than the predictive skill of damped persistence, indicating that the contribution of ocean dynamics and air–sea feedbacks is moderate in the tropical Atlantic. To achieve maximum predictability, processes such as ocean dynamics, thermodynamical and dynamical air–sea feedbacks, and the delicate mode–mode interactions should be correctly resolved in the coupled models. Therefore, predicting TAV poses more challenge than predicting El Niño in the tropical Pacific.
Abstract
The coupled variability and predictability of the tropical Atlantic ocean–atmosphere system were analyzed within the framework of a linear stochastic climate model. Despite the existence of a meridional dipole as the leading mode, tropical Atlantic variability (TAV) is dominated by equatorial features and the subtropical variability is largely uncorrelated between the northern and southern Atlantic. This suggests that atmospheric stochastic forcing plays a dominant role in defining the spatial patterns of TAV, whereas the active air–sea feedbacks mainly enhance variability at interannual and decadal time scales, causing the spectra distinctive from the red spectrum. Under the stochastic forcing, the useful predictive skill for sea surface temperature measured by normalized error variance is limited to 2 months on average, which is 1 month longer than the predictive skill of damped persistence, indicating that the contribution of ocean dynamics and air–sea feedbacks is moderate in the tropical Atlantic. To achieve maximum predictability, processes such as ocean dynamics, thermodynamical and dynamical air–sea feedbacks, and the delicate mode–mode interactions should be correctly resolved in the coupled models. Therefore, predicting TAV poses more challenge than predicting El Niño in the tropical Pacific.
Abstract
The interaction between tropical Atlantic variability and El Niño–Southern Oscillation (ENSO) is investigated using three ensembles of atmospheric general circulation model integrations. The integrations are forced by specifying observed sea surface temperature (SST) variability over a forcing domain. The forcing domain is the global ocean for the first ensemble, limited to the tropical ocean for the second ensemble, and further limited to the tropical Atlantic region for the third ensemble. The ensemble integrations show that extratropical SST anomalies have little impact on tropical variability, but the effect of ENSO is pervasive in the Tropics. Consistent with previous studies, the most significant influence of ENSO is found during the boreal spring season and is associated with an anomalous Walker circulation. Two important aspects of ENSO’s influence on tropical Atlantic variability are noted. First, the ENSO signal contributes significantly to the “dipole” correlation structure between tropical Atlantic SST and rainfall in the Nordeste Brazil region. In the absence of the ENSO signal, the correlations are dominated by SST variability in the southern tropical Atlantic, resulting in less of a dipole structure. Second, the remote influence of ENSO also contributes to positive correlations between SST anomalies and downward surface heat flux in the tropical Atlantic during the boreal spring season. However, even when ENSO forcing is absent, the model integrations provide evidence for a positive surface heat flux feedback in the deep Tropics, which is analyzed in a companion study by Chang et al. The analysis of model simulations shows that interannual atmospheric variability in the tropical Pacific–Atlantic system is dominated by the interaction between two distinct sources of tropical heating: (i) an equatorial heat source in the eastern Pacific associated with ENSO and (ii) an off-equatorial heat source associated with SST anomalies near the Caribbean. Modeling this Caribbean heat source accurately could be very important for seasonal forecasting in the Central American–Caribbean region.
Abstract
The interaction between tropical Atlantic variability and El Niño–Southern Oscillation (ENSO) is investigated using three ensembles of atmospheric general circulation model integrations. The integrations are forced by specifying observed sea surface temperature (SST) variability over a forcing domain. The forcing domain is the global ocean for the first ensemble, limited to the tropical ocean for the second ensemble, and further limited to the tropical Atlantic region for the third ensemble. The ensemble integrations show that extratropical SST anomalies have little impact on tropical variability, but the effect of ENSO is pervasive in the Tropics. Consistent with previous studies, the most significant influence of ENSO is found during the boreal spring season and is associated with an anomalous Walker circulation. Two important aspects of ENSO’s influence on tropical Atlantic variability are noted. First, the ENSO signal contributes significantly to the “dipole” correlation structure between tropical Atlantic SST and rainfall in the Nordeste Brazil region. In the absence of the ENSO signal, the correlations are dominated by SST variability in the southern tropical Atlantic, resulting in less of a dipole structure. Second, the remote influence of ENSO also contributes to positive correlations between SST anomalies and downward surface heat flux in the tropical Atlantic during the boreal spring season. However, even when ENSO forcing is absent, the model integrations provide evidence for a positive surface heat flux feedback in the deep Tropics, which is analyzed in a companion study by Chang et al. The analysis of model simulations shows that interannual atmospheric variability in the tropical Pacific–Atlantic system is dominated by the interaction between two distinct sources of tropical heating: (i) an equatorial heat source in the eastern Pacific associated with ENSO and (ii) an off-equatorial heat source associated with SST anomalies near the Caribbean. Modeling this Caribbean heat source accurately could be very important for seasonal forecasting in the Central American–Caribbean region.
Abstract
The purpose of this paper is to clarify the relation between canonical correlation analysis, autoregressive models (also called linear inverse models), and a relatively new statistical technique known as predictable component analysis. Predictable component analysis is a procedure for decomposing forecast error into a complete set of uncorrelated patterns that optimize the normalized error variance. As such, the procedure determines the components of a forecast, out of all possible components, that are predicted the best and worst on average, in a normalized error variance sense. This procedure has been suggested previously in the context of information theory and of maximizing the variance of prewhitened forecast errors. It is shown that the most predictable components of a linear, first-order, autoregressive model are identical to the canonical patterns that optimize the temporal correlation between the original and time-lagged time series. Also, canonical patterns define a transformation that diagonalizes the propagator of the autoregressive model. Finally, the singular vectors of an autoregressive propagator have a one-to-one correspondence to the canonical patterns, provided that the singular vectors are computed with respect to a norm related to a prewhitening transformation. Forecasts based on canonical correlation analysis are shown to be identical to forecasts based on autoregressive models when all canonical patterns are superposed. The advantage of canonical correlation analysis is that it allows one to filter out the “unpredictable components” of autoregressive models, defined as components in the forecast with skill below some statistical threshold of significance. Predictable component analysis allows a generalization of this filtering procedure to any forecast model.
Abstract
The purpose of this paper is to clarify the relation between canonical correlation analysis, autoregressive models (also called linear inverse models), and a relatively new statistical technique known as predictable component analysis. Predictable component analysis is a procedure for decomposing forecast error into a complete set of uncorrelated patterns that optimize the normalized error variance. As such, the procedure determines the components of a forecast, out of all possible components, that are predicted the best and worst on average, in a normalized error variance sense. This procedure has been suggested previously in the context of information theory and of maximizing the variance of prewhitened forecast errors. It is shown that the most predictable components of a linear, first-order, autoregressive model are identical to the canonical patterns that optimize the temporal correlation between the original and time-lagged time series. Also, canonical patterns define a transformation that diagonalizes the propagator of the autoregressive model. Finally, the singular vectors of an autoregressive propagator have a one-to-one correspondence to the canonical patterns, provided that the singular vectors are computed with respect to a norm related to a prewhitening transformation. Forecasts based on canonical correlation analysis are shown to be identical to forecasts based on autoregressive models when all canonical patterns are superposed. The advantage of canonical correlation analysis is that it allows one to filter out the “unpredictable components” of autoregressive models, defined as components in the forecast with skill below some statistical threshold of significance. Predictable component analysis allows a generalization of this filtering procedure to any forecast model.
Abstract
Dynamics of small-scale (<10 km) superinertial internal waves (SSIWs) of intense vertical motion are investigated theoretically and numerically. It is shown that near-inertial internal waves (NIWs) have a pronounced influence on modulation of SSIW strength. In convergence zones of NIWs, energy flux of SSIWs converge and energy is transferred from NIWs to SSIWs, leading to rapid growth of SSIWs. The opposite occurs when SSIWs enter divergence zones of NIWs. The underlying dynamics can be understood in terms of wave action conservation of SSIWs in the presence of background NIWs. The validity of the theoretical finding is verified using realistic high-resolution numerical simulations in the Gulf of Mexico. The results reveal significantly stronger small-scale superinertial vertical motions in convergence zones of NIWs than in divergence zones. By removing near-inertial wind forcing, model simulations with identical resolution show a substantial decrease in the small-scale superinertial vertical motions associated with the suppression of NIWs. Therefore, these numerical simulations support the theoretical finding of SSIW–NIW interaction.
Abstract
Dynamics of small-scale (<10 km) superinertial internal waves (SSIWs) of intense vertical motion are investigated theoretically and numerically. It is shown that near-inertial internal waves (NIWs) have a pronounced influence on modulation of SSIW strength. In convergence zones of NIWs, energy flux of SSIWs converge and energy is transferred from NIWs to SSIWs, leading to rapid growth of SSIWs. The opposite occurs when SSIWs enter divergence zones of NIWs. The underlying dynamics can be understood in terms of wave action conservation of SSIWs in the presence of background NIWs. The validity of the theoretical finding is verified using realistic high-resolution numerical simulations in the Gulf of Mexico. The results reveal significantly stronger small-scale superinertial vertical motions in convergence zones of NIWs than in divergence zones. By removing near-inertial wind forcing, model simulations with identical resolution show a substantial decrease in the small-scale superinertial vertical motions associated with the suppression of NIWs. Therefore, these numerical simulations support the theoretical finding of SSIW–NIW interaction.
Abstract
The effect of oceanic advection on the predictability of sea surface temperature (SST) is investigated in the framework of a linear stochastic model. An analytical solution of a one-dimensional model shows that even though advection can give rise to a pair of low-frequency normal modes, no enhancement in the predictability is found in terms of domain-averaged error variance. However, a predictable component analysis shows that advection can play a role in redistributing the predictable variance. When forced with a spatially coherent stochastic forcing, advection enables certain regions to be more predictable than others. This analytical result is further examined in a more realistic two-dimensional North Atlantic model with observed mean currents. It is shown that the predictability of SST averaged over the whole North Atlantic basin is determined by the thermal damping time scale (∼3 months), not the advective time scale (∼6 years). However, the most predictable pattern reveals that the predictable variance along the west boundary is substantially enhanced by the strong currents, and the potential predictability limit in this region is on the order of 5 months.
Abstract
The effect of oceanic advection on the predictability of sea surface temperature (SST) is investigated in the framework of a linear stochastic model. An analytical solution of a one-dimensional model shows that even though advection can give rise to a pair of low-frequency normal modes, no enhancement in the predictability is found in terms of domain-averaged error variance. However, a predictable component analysis shows that advection can play a role in redistributing the predictable variance. When forced with a spatially coherent stochastic forcing, advection enables certain regions to be more predictable than others. This analytical result is further examined in a more realistic two-dimensional North Atlantic model with observed mean currents. It is shown that the predictability of SST averaged over the whole North Atlantic basin is determined by the thermal damping time scale (∼3 months), not the advective time scale (∼6 years). However, the most predictable pattern reveals that the predictable variance along the west boundary is substantially enhanced by the strong currents, and the potential predictability limit in this region is on the order of 5 months.
Abstract
An intermediate coupled ocean–atmosphere model that permits dynamical interactions between the seasonal cycle and interannual oscillations is used to conduct large ensembles of ENSO prediction experiments. By varying seasonal backgrounds, the impact of the annual cycle on the model’s forecast skills is explored. The results show that the sensitivity of the skills to changes in the seasonal cycle is weak, although correlation skills drop and rms errors increase systematically by a small amount as the amplitude of the seasonal cycle is enhanced. This suggests that the nature of the model’s prediction skills is largely determined by the seasonal information hidden in the initial conditions and the actual varying seasonal background is of secondary importance.
As in other anomaly coupled models, the spring predictability barrier is a predominant feature of this model’s prediction skills. This seasonal dependence of the forecast skills exhibits a decadal modulation with strong barriers in the 1960s and 1970s and weak ones in the 1950s and 1980s. The best skills of the model occur in the 1950s and 1980s and the worst in the 1970s. The decadal modulation of the skills is more likely to come from decadal shifts in the mean state of the tropical Pacific than from nonlinear interactions between the seasonal cycle and interannual oscillations.
Abstract
An intermediate coupled ocean–atmosphere model that permits dynamical interactions between the seasonal cycle and interannual oscillations is used to conduct large ensembles of ENSO prediction experiments. By varying seasonal backgrounds, the impact of the annual cycle on the model’s forecast skills is explored. The results show that the sensitivity of the skills to changes in the seasonal cycle is weak, although correlation skills drop and rms errors increase systematically by a small amount as the amplitude of the seasonal cycle is enhanced. This suggests that the nature of the model’s prediction skills is largely determined by the seasonal information hidden in the initial conditions and the actual varying seasonal background is of secondary importance.
As in other anomaly coupled models, the spring predictability barrier is a predominant feature of this model’s prediction skills. This seasonal dependence of the forecast skills exhibits a decadal modulation with strong barriers in the 1960s and 1970s and weak ones in the 1950s and 1980s. The best skills of the model occur in the 1950s and 1980s and the worst in the 1970s. The decadal modulation of the skills is more likely to come from decadal shifts in the mean state of the tropical Pacific than from nonlinear interactions between the seasonal cycle and interannual oscillations.
Abstract
A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I of this two-part paper. The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board the Upper Atmosphere Research Satellite are described in this paper.
A robust χ 2 criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only 3 days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. Further, it was found that the model error due to numerical discretization, as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, an analysis of the variance and correlation dynamics was conducted to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.
Abstract
A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I of this two-part paper. The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board the Upper Atmosphere Research Satellite are described in this paper.
A robust χ 2 criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only 3 days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. Further, it was found that the model error due to numerical discretization, as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, an analysis of the variance and correlation dynamics was conducted to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.
