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- Author or Editor: William W. Hsieh x
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Abstract
Recent advances in neural network modeling have led to the nonlinear generalization of classical multivariate analysis techniques such as principal component analysis and canonical correlation analysis (CCA). The nonlinear canonical correlation analysis (NLCCA) method is used to study the relationship between the tropical Pacific sea level pressure (SLP) and sea surface temperature (SST) fields. The first mode extracted is a nonlinear El Niño–Southern Oscillation (ENSO) mode, showing the asymmetry between the warm El Niño states and the cool La Niña states. The nonlinearity of the first NLCCA mode is found to increase gradually with time. During 1950–75, the SLP showed no nonlinearity, while the SST revealed weak nonlinearity. During 1976–99, the SLP displayed weak nonlinearity, while the weak nonlinearity in the SST was further enhanced. The second NLCCA mode displays longer timescale fluctuations, again with weak, but noticeable, nonlinearity in the SST but not in the SLP.
Abstract
Recent advances in neural network modeling have led to the nonlinear generalization of classical multivariate analysis techniques such as principal component analysis and canonical correlation analysis (CCA). The nonlinear canonical correlation analysis (NLCCA) method is used to study the relationship between the tropical Pacific sea level pressure (SLP) and sea surface temperature (SST) fields. The first mode extracted is a nonlinear El Niño–Southern Oscillation (ENSO) mode, showing the asymmetry between the warm El Niño states and the cool La Niña states. The nonlinearity of the first NLCCA mode is found to increase gradually with time. During 1950–75, the SLP showed no nonlinearity, while the SST revealed weak nonlinearity. During 1976–99, the SLP displayed weak nonlinearity, while the weak nonlinearity in the SST was further enhanced. The second NLCCA mode displays longer timescale fluctuations, again with weak, but noticeable, nonlinearity in the SST but not in the SLP.
Abstract
With data from 12 coupled models in the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), climate under year 2000 greenhouse gas (GHG) + aerosol forcing was compared with climate under preindustrial conditions. In the tropical Pacific, the warming in the mean sea surface temperatures (SST) was found to have an El Niño–like pattern, while both the equatorial zonal overturning circulation and the meridional overturning circulation weakened under increased GHG forcing.
For the El Niño–Southern Oscillation (ENSO), the asymmetry in the SST anomalies between El Niño and La Niña was found to be enhanced under increased GHG, for both the ensemble model data and the observed data (1900–99). Enhanced asymmetry between El Niño and La Niña was also manifested in the anomalies of the zonal wind stress, the equatorial undercurrent, and the meridional overturning circulation in the increased GHG simulations. The enhanced asymmetry in the model SST anomalies was mainly caused by the greatly intensified vertical nonlinear dynamic heating (NDH) anomaly (i.e., product of the vertical velocity anomaly and the negative vertical temperature gradient anomaly) during El Niño (but not during La Niña). Under increased GHG, the enhanced positive NDH anomalies during El Niño, when time averaged over the whole record, would change the SST mean state by an El Niño–like pattern.
Abstract
With data from 12 coupled models in the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change (IPCC), climate under year 2000 greenhouse gas (GHG) + aerosol forcing was compared with climate under preindustrial conditions. In the tropical Pacific, the warming in the mean sea surface temperatures (SST) was found to have an El Niño–like pattern, while both the equatorial zonal overturning circulation and the meridional overturning circulation weakened under increased GHG forcing.
For the El Niño–Southern Oscillation (ENSO), the asymmetry in the SST anomalies between El Niño and La Niña was found to be enhanced under increased GHG, for both the ensemble model data and the observed data (1900–99). Enhanced asymmetry between El Niño and La Niña was also manifested in the anomalies of the zonal wind stress, the equatorial undercurrent, and the meridional overturning circulation in the increased GHG simulations. The enhanced asymmetry in the model SST anomalies was mainly caused by the greatly intensified vertical nonlinear dynamic heating (NDH) anomaly (i.e., product of the vertical velocity anomaly and the negative vertical temperature gradient anomaly) during El Niño (but not during La Niña). Under increased GHG, the enhanced positive NDH anomalies during El Niño, when time averaged over the whole record, would change the SST mean state by an El Niño–like pattern.
Abstract
Nonlinear projections of the tropical Pacific sea surface temperature anomalies (SSTAs) onto North American winter (November–March) surface air temperature (SAT) and precipitation anomalies have been performed using neural networks. During El Niño, the linear SAT response has positive anomalies centered over Alaska and western Canada opposing weaker negative anomalies centered over the southeastern United States. In contrast, the nonlinear SAT response, which is excited during both strong El Niño and strong La Niña, has negative anomalies centered over Alaska and northwestern Canada and positive anomalies over much of the United States and southern Canada.
For precipitation, the linear response during El Niño has a positive anomaly area stretching from the east coast to the southwest coast of the United States and another positive area in northern Canada, in opposition to the negative anomaly area over much of southern Canada and northern United States, and another negative area over Alaska. In contrast, the nonlinear precipitation response, which is excited during both strong El Niño and strong La Niña, displays positive anomalies over much of the United States and southern Canada, with the main center on the west coast at around 45°N and a weak center along the southeast coast, and negative anomalies over northwestern Canada and Alaska.
The nonlinear response accounts for about one-fourth and one-third as much variance as the linear response of the SAT and precipitation, respectively. A polynomial fit further verifies the nonlinear response of both the SAT and precipitation to be mainly a quadratic response to ENSO. Both the linear and nonlinear response patterns of the SAT and precipitation are basically consistent with the circulation anomalies (the 500-mb geopotential height anomalies), detected separately by nonlinear projection. A cross-validation test shows that including the nonlinear (quadratic) response can potentially contribute to additional forecast skill over North America.
Abstract
Nonlinear projections of the tropical Pacific sea surface temperature anomalies (SSTAs) onto North American winter (November–March) surface air temperature (SAT) and precipitation anomalies have been performed using neural networks. During El Niño, the linear SAT response has positive anomalies centered over Alaska and western Canada opposing weaker negative anomalies centered over the southeastern United States. In contrast, the nonlinear SAT response, which is excited during both strong El Niño and strong La Niña, has negative anomalies centered over Alaska and northwestern Canada and positive anomalies over much of the United States and southern Canada.
For precipitation, the linear response during El Niño has a positive anomaly area stretching from the east coast to the southwest coast of the United States and another positive area in northern Canada, in opposition to the negative anomaly area over much of southern Canada and northern United States, and another negative area over Alaska. In contrast, the nonlinear precipitation response, which is excited during both strong El Niño and strong La Niña, displays positive anomalies over much of the United States and southern Canada, with the main center on the west coast at around 45°N and a weak center along the southeast coast, and negative anomalies over northwestern Canada and Alaska.
The nonlinear response accounts for about one-fourth and one-third as much variance as the linear response of the SAT and precipitation, respectively. A polynomial fit further verifies the nonlinear response of both the SAT and precipitation to be mainly a quadratic response to ENSO. Both the linear and nonlinear response patterns of the SAT and precipitation are basically consistent with the circulation anomalies (the 500-mb geopotential height anomalies), detected separately by nonlinear projection. A cross-validation test shows that including the nonlinear (quadratic) response can potentially contribute to additional forecast skill over North America.
Abstract
Nonlinear principal component analysis (NLPCA), via a neural network (NN) approach, was applied to an ensemble of six 47-yr simulations conducted by the Canadian Centre for Climate Modelling and Analysis (CCCma) second-generation atmospheric general circulation model (AGCM2). Each simulation was forced with the observed sea surface temperature [from the Global Sea Ice and Sea Surface Temperature dataset (GISST)] from January 1948 to November 1994. The NLPCA modes reveal nonlinear structures in both the winter 500-mb geopotential height (Z500) anomalies and surface air temperature (SAT) anomalies over North America, with asymmetric spatial anomaly patterns during the opposite phases of an NLPCA mode. Only during its negative phase is the first NLPCA mode related to the El Niño–Southern Oscillation (ENSO); the positive phase is related to a weakened jet stream. Spatial patterns of the NLPCA mode for the Z500 anomalies generally agree with those for the SAT anomalies.
Nonlinear canonical correlation analysis (NLCCA), also via an NN approach, was then applied to the midlatitude winter GCM data and the observed SST of the tropical Pacific. Nonlinearity was detected in both the forcing field (SST) and the response field (Z500 or SAT) at zero time lag. The leading NLCCA mode for the SST anomalies is a nonlinear ENSO mode, with a 30°–40° eastward shift of the positive SST anomalies during El Niño relative to the negative SST anomalies during La Niña. The leading NLCCA mode for the Z500 anomaly field is a nonlinear Pacific–North American (PNA) teleconnection pattern. The ray path of the Rossby waves induced during El Niño is 10°–15° east of that induced during La Niña. The nonlinear atmospheric response to ENSO is also found in the leading NLCCA mode for the SAT anomalies.
Abstract
Nonlinear principal component analysis (NLPCA), via a neural network (NN) approach, was applied to an ensemble of six 47-yr simulations conducted by the Canadian Centre for Climate Modelling and Analysis (CCCma) second-generation atmospheric general circulation model (AGCM2). Each simulation was forced with the observed sea surface temperature [from the Global Sea Ice and Sea Surface Temperature dataset (GISST)] from January 1948 to November 1994. The NLPCA modes reveal nonlinear structures in both the winter 500-mb geopotential height (Z500) anomalies and surface air temperature (SAT) anomalies over North America, with asymmetric spatial anomaly patterns during the opposite phases of an NLPCA mode. Only during its negative phase is the first NLPCA mode related to the El Niño–Southern Oscillation (ENSO); the positive phase is related to a weakened jet stream. Spatial patterns of the NLPCA mode for the Z500 anomalies generally agree with those for the SAT anomalies.
Nonlinear canonical correlation analysis (NLCCA), also via an NN approach, was then applied to the midlatitude winter GCM data and the observed SST of the tropical Pacific. Nonlinearity was detected in both the forcing field (SST) and the response field (Z500 or SAT) at zero time lag. The leading NLCCA mode for the SST anomalies is a nonlinear ENSO mode, with a 30°–40° eastward shift of the positive SST anomalies during El Niño relative to the negative SST anomalies during La Niña. The leading NLCCA mode for the Z500 anomaly field is a nonlinear Pacific–North American (PNA) teleconnection pattern. The ray path of the Rossby waves induced during El Niño is 10°–15° east of that induced during La Niña. The nonlinear atmospheric response to ENSO is also found in the leading NLCCA mode for the SAT anomalies.
Abstract
The output from a coupled general circulation model (CGCM) is used to develop evidence showing that the tropical Pacific decadal oscillation can be driven by an interaction between the El Niño–Southern Oscillation (ENSO) and the slowly varying mean background climate state. The analysis verifies that the decadal changes in the mean states are attributed largely to decadal changes in ENSO statistics through nonlinear rectification. This is seen because the time evolutions of the first principal component analysis (PCA) mode of the decadal-varying tropical Pacific SST and the thermocline depth anomalies are significantly correlated to the decadal variations of the ENSO amplitude (also skewness). Its spatial pattern resembles the residuals of the SST and thermocline depth anomalies after there is uneven compensation from El Niño and La Niña events. In addition, the stability analysis of a linearized intermediate ocean–atmosphere coupled system, for which the background mean states are specified, provides qualitatively consistent results compared to the CGCM in terms of the relationship between changes in the background mean states and the characteristics of ENSO. It is also shown from the stability analysis as well as the time integration of a nonlinear version of the intermediate coupled model that the mean SST for the high-variability ENSO decades acts to intensify the ENSO variability, while the mean thermocline depth for the same decades acts to suppress the ENSO activity. Thus, there may be an interactive feedback consisting of a positive feedback between the ENSO activity and the mean state of the SST and a negative feedback between the ENSO activity and the mean state of the thermocline depth. This feedback may lead to the tropical decadal oscillation, without the need to invoke any external mechanisms.
Abstract
The output from a coupled general circulation model (CGCM) is used to develop evidence showing that the tropical Pacific decadal oscillation can be driven by an interaction between the El Niño–Southern Oscillation (ENSO) and the slowly varying mean background climate state. The analysis verifies that the decadal changes in the mean states are attributed largely to decadal changes in ENSO statistics through nonlinear rectification. This is seen because the time evolutions of the first principal component analysis (PCA) mode of the decadal-varying tropical Pacific SST and the thermocline depth anomalies are significantly correlated to the decadal variations of the ENSO amplitude (also skewness). Its spatial pattern resembles the residuals of the SST and thermocline depth anomalies after there is uneven compensation from El Niño and La Niña events. In addition, the stability analysis of a linearized intermediate ocean–atmosphere coupled system, for which the background mean states are specified, provides qualitatively consistent results compared to the CGCM in terms of the relationship between changes in the background mean states and the characteristics of ENSO. It is also shown from the stability analysis as well as the time integration of a nonlinear version of the intermediate coupled model that the mean SST for the high-variability ENSO decades acts to intensify the ENSO variability, while the mean thermocline depth for the same decades acts to suppress the ENSO activity. Thus, there may be an interactive feedback consisting of a positive feedback between the ENSO activity and the mean state of the SST and a negative feedback between the ENSO activity and the mean state of the thermocline depth. This feedback may lead to the tropical decadal oscillation, without the need to invoke any external mechanisms.
Abstract
The nonlinear principal component analysis (NLPCA), via a neural network approach, was applied to thermocline anomalies in the tropical Pacific. While the tropical sea surface temperature (SST) anomalies had been nonlinearly mapped by the NLPCA mode 1 onto an open curve in the data space, the thermocline anomalies were mapped to a closed curve, suggesting that ENSO is a cyclic phenomenon. The NLPCA mode 1 of the thermocline anomalies reveals the nonlinear evolution of the ENSO cycle with much asymmetry for the different phases: The weak heat accumulation in the whole equatorial Pacific is followed by the strong El Niño, and the subsequent strong drain of equatorial heat content toward the off-equatorial region precedes a weak La Niña. This asymmetric ENSO evolution implies that the nonlinear instability enhances the growth of El Niño, but dwarfs the growth of La Niña. The nonlinear ENSO cycle was found to have changed since the late 1970s. For the pre-1980s the ENSO cycle associated with the thermocline is less asymmetrical than that during the post-1980s, indicating that the nonlinearity of the ENSO cycle has become stronger since the late 1970s.
Abstract
The nonlinear principal component analysis (NLPCA), via a neural network approach, was applied to thermocline anomalies in the tropical Pacific. While the tropical sea surface temperature (SST) anomalies had been nonlinearly mapped by the NLPCA mode 1 onto an open curve in the data space, the thermocline anomalies were mapped to a closed curve, suggesting that ENSO is a cyclic phenomenon. The NLPCA mode 1 of the thermocline anomalies reveals the nonlinear evolution of the ENSO cycle with much asymmetry for the different phases: The weak heat accumulation in the whole equatorial Pacific is followed by the strong El Niño, and the subsequent strong drain of equatorial heat content toward the off-equatorial region precedes a weak La Niña. This asymmetric ENSO evolution implies that the nonlinear instability enhances the growth of El Niño, but dwarfs the growth of La Niña. The nonlinear ENSO cycle was found to have changed since the late 1970s. For the pre-1980s the ENSO cycle associated with the thermocline is less asymmetrical than that during the post-1980s, indicating that the nonlinearity of the ENSO cycle has become stronger since the late 1970s.
Abstract
The authors constructed neural network models to forecast the sea surface temperature anomalies (SSTA) for three regions: Niño 4, Niño 3.5, and Niño 3, representing the western-central, the central, and the eastern-central parts of the equatorial Pacific Ocean, respectively. The inputs were the extended empirical orthogonal functions (EEOF) of the sea level pressure (SLP) field that covered the tropical Indian and Pacific Oceans and evolved for a duration of 1 yr. The EEOFs greatly reduced the size of the neural networks from those of the authors’ earlier papers using EOFs. The Niño 4 region appeared to be the best forecasted region, with useful skills up to a year lead time for the 1982–93 forecast period. By network pruning analysis and spectral analysis, four important inputs were identified: modes 1, 2, and 6 of the SLP EEOFs and the SSTA persistence. Mode 1 characterized the low-frequency oscillation (LFO, with 4–5-yr period), and was seen as the typical ENSO signal, while mode 2, with a period of 2–5 yr, characterized the quasi-biennial oscillation (QBO) plus the LFO. Mode 6 was dominated by decadal and interdecadal variations. Thus, forecasting ENSO required information from the QBO, and the decadal–interdecadal oscillations. The nonlinearity of the networks tended to increase with lead time and to become stronger for the eastern regions of the equatorial Pacific Ocean.
Abstract
The authors constructed neural network models to forecast the sea surface temperature anomalies (SSTA) for three regions: Niño 4, Niño 3.5, and Niño 3, representing the western-central, the central, and the eastern-central parts of the equatorial Pacific Ocean, respectively. The inputs were the extended empirical orthogonal functions (EEOF) of the sea level pressure (SLP) field that covered the tropical Indian and Pacific Oceans and evolved for a duration of 1 yr. The EEOFs greatly reduced the size of the neural networks from those of the authors’ earlier papers using EOFs. The Niño 4 region appeared to be the best forecasted region, with useful skills up to a year lead time for the 1982–93 forecast period. By network pruning analysis and spectral analysis, four important inputs were identified: modes 1, 2, and 6 of the SLP EEOFs and the SSTA persistence. Mode 1 characterized the low-frequency oscillation (LFO, with 4–5-yr period), and was seen as the typical ENSO signal, while mode 2, with a period of 2–5 yr, characterized the quasi-biennial oscillation (QBO) plus the LFO. Mode 6 was dominated by decadal and interdecadal variations. Thus, forecasting ENSO required information from the QBO, and the decadal–interdecadal oscillations. The nonlinearity of the networks tended to increase with lead time and to become stronger for the eastern regions of the equatorial Pacific Ocean.
Abstract
Among the statistical methods used for seasonal climate prediction, canonical correlation analysis (CCA), a more sophisticated version of the linear regression (LR) method, is well established. Recently, neural networks (NN) have been applied to seasonal climate prediction. Unlike CCA and LR, NN is a nonlinear method, which leads to the question whether the nonlinearity of NN brings any extra prediction skill.
In this study, an objective comparison between the three methods (CCA, LR, and NN) in predicting the equatorial Pacific sea surface temperatures (in regions Niño1+2, Niño3, Niño3.4, and Niño4) was made. The skill of NN was found to be comparable to that of LR and CCA. A cross-validated t test showed that the difference between NN and LR and the difference between NN and CCA were not significant at the 5% level. The lack of significant skill difference between the nonlinear NN method and the linear methods suggests that at the seasonal timescale the equatorial Pacific dynamics is basically linear.
Abstract
Among the statistical methods used for seasonal climate prediction, canonical correlation analysis (CCA), a more sophisticated version of the linear regression (LR) method, is well established. Recently, neural networks (NN) have been applied to seasonal climate prediction. Unlike CCA and LR, NN is a nonlinear method, which leads to the question whether the nonlinearity of NN brings any extra prediction skill.
In this study, an objective comparison between the three methods (CCA, LR, and NN) in predicting the equatorial Pacific sea surface temperatures (in regions Niño1+2, Niño3, Niño3.4, and Niño4) was made. The skill of NN was found to be comparable to that of LR and CCA. A cross-validated t test showed that the difference between NN and LR and the difference between NN and CCA were not significant at the 5% level. The lack of significant skill difference between the nonlinear NN method and the linear methods suggests that at the seasonal timescale the equatorial Pacific dynamics is basically linear.
