Search Results
You are looking at 11 - 20 of 24 items for
- Author or Editor: William W. Hsieh x
- Refine by Access: All Content x
Abstract
The scattering of an incident shelf wave by a long thin offshore barrier located parallel to the coast is solved for a general monotonically increasing depth profile, using the unforced, inviscid barotropic shallow water equations under rigid lid and alongshore geostrophy approximation. In particular, simple analytic formulas for the scattering coefficients are derived for the exponential shelf profile. In the channel between the barrier and the coast, much of the incident shelf wave energy is transferred to the zero (or Kelvin) mode. Seaward of the barrier, substantial energy transfer from an incident second-mode shelf wave to the first mode is possible. Downstream from the barrier, the incident mode may vanish, leaving a different mode to dominate.
Abstract
The scattering of an incident shelf wave by a long thin offshore barrier located parallel to the coast is solved for a general monotonically increasing depth profile, using the unforced, inviscid barotropic shallow water equations under rigid lid and alongshore geostrophy approximation. In particular, simple analytic formulas for the scattering coefficients are derived for the exponential shelf profile. In the channel between the barrier and the coast, much of the incident shelf wave energy is transferred to the zero (or Kelvin) mode. Seaward of the barrier, substantial energy transfer from an incident second-mode shelf wave to the first mode is possible. Downstream from the barrier, the incident mode may vanish, leaving a different mode to dominate.
Abstract
Some numerical experiments On geostrophic adjustment in a gratified channel were carried out, partly to test the use of an ocean general circulation model (GCM), and partly to elucidate the dynamical effects of sloping bottom topography on the adjustment at different latitudes. Interesting dynamical effects include the release of potential energy through shelf waves, the nonlinear generation of barotropic flow by a baroclinic Kelvin wave and the nonlinear generation of shelf waves with approximately half the inertial frequency by internal Poincaré waves of near-inertial frequency. Problems that inevitably occur in the use of GCMs were also highlighted.
Abstract
Some numerical experiments On geostrophic adjustment in a gratified channel were carried out, partly to test the use of an ocean general circulation model (GCM), and partly to elucidate the dynamical effects of sloping bottom topography on the adjustment at different latitudes. Interesting dynamical effects include the release of potential energy through shelf waves, the nonlinear generation of barotropic flow by a baroclinic Kelvin wave and the nonlinear generation of shelf waves with approximately half the inertial frequency by internal Poincaré waves of near-inertial frequency. Problems that inevitably occur in the use of GCMs were also highlighted.
Abstract
From the inviscid, unforced, barotropic long-wave equations for a rotating system, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. While the shelf waves typically have periods of several days, the energy transfer has a time scale of order 12 days. Observational evidence of resonant shelf wave interactions on the Oregon shelf is found in the spectral analyses of Cutchin and Smith (1973) and Huyer et al. (1975), where their observed signals agree well with the resonant frequencies deduced from the theory. The good agreement between theory and observation suggests that nonlinear energy transfer may play a much more significant role in shelf wave dynamics than was previously realized.
Abstract
From the inviscid, unforced, barotropic long-wave equations for a rotating system, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. While the shelf waves typically have periods of several days, the energy transfer has a time scale of order 12 days. Observational evidence of resonant shelf wave interactions on the Oregon shelf is found in the spectral analyses of Cutchin and Smith (1973) and Huyer et al. (1975), where their observed signals agree well with the resonant frequencies deduced from the theory. The good agreement between theory and observation suggests that nonlinear energy transfer may play a much more significant role in shelf wave dynamics than was previously realized.
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
A novel methodology is presented for the identification of the mean cycle of the Madden–Julian oscillation (MJO) along the equator. The methodology is based on a nonlinear principal component (NLPC) computed with a neural network model. The bandpass-filtered input data encompass 30 yr with zonal winds at 850 and 200 hPa plus outgoing longwave radiation (OLR). The NLPC is conditioned on a sufficiently strong MJO activity and is computed both for the pooled dataset and for the dataset stratified into seasons. The NLPC for all data depicts a circular mode formed by the first two linear principal components (LPCs) with marginal contributions by the higher-order LPCs. Hence, the mean MJO cycle throughout the year is effectively captured by the amplitude of the leading two LPCs varying in quadrature. The NLPC for individual seasons shows additional variability, which mainly arises from a subordinate oscillation of the second pair of LPCs superimposed on the annual MJO signal. In reference to the all-year solution, the difference in resolved variability approximately accounts for 9% in solstitial seasons and 3% in equinoctial seasons. The phasing of the third LPC is such that convective activity oscillations over the Maritime Continent as well as wind oscillations over the Indian Ocean appear enhanced (suppressed) during boreal winter (summer). Also, convective activity oscillations appear more pronounced at the date line during both winter and summer. The phasing of the fourth LPC is such that upper-level westerlies over the Atlantic region are more persistent during boreal spring than during other seasons.
Abstract
A novel methodology is presented for the identification of the mean cycle of the Madden–Julian oscillation (MJO) along the equator. The methodology is based on a nonlinear principal component (NLPC) computed with a neural network model. The bandpass-filtered input data encompass 30 yr with zonal winds at 850 and 200 hPa plus outgoing longwave radiation (OLR). The NLPC is conditioned on a sufficiently strong MJO activity and is computed both for the pooled dataset and for the dataset stratified into seasons. The NLPC for all data depicts a circular mode formed by the first two linear principal components (LPCs) with marginal contributions by the higher-order LPCs. Hence, the mean MJO cycle throughout the year is effectively captured by the amplitude of the leading two LPCs varying in quadrature. The NLPC for individual seasons shows additional variability, which mainly arises from a subordinate oscillation of the second pair of LPCs superimposed on the annual MJO signal. In reference to the all-year solution, the difference in resolved variability approximately accounts for 9% in solstitial seasons and 3% in equinoctial seasons. The phasing of the third LPC is such that convective activity oscillations over the Maritime Continent as well as wind oscillations over the Indian Ocean appear enhanced (suppressed) during boreal winter (summer). Also, convective activity oscillations appear more pronounced at the date line during both winter and summer. The phasing of the fourth LPC is such that upper-level westerlies over the Atlantic region are more persistent during boreal spring than during other seasons.
Abstract
The feasibility of sequential open-boundary control by data assimilation in a regional ocean model has been investigated using a barotropic wind-driven ocean circulation model. A simple open-boundary scheme has been constructed based on the idea of optimal boundary control of a diagnostic equation and illustrated with the problem of modeling the subpolar gyre subject to an open southern boundary. The results show that use of such a scheme in conjunction with traditional radiation boundary conditions allows for a longer model integration that would otherwise be unstable when only the radiation boundary conditions are imposed due to presence of dispersive waves.
Abstract
The feasibility of sequential open-boundary control by data assimilation in a regional ocean model has been investigated using a barotropic wind-driven ocean circulation model. A simple open-boundary scheme has been constructed based on the idea of optimal boundary control of a diagnostic equation and illustrated with the problem of modeling the subpolar gyre subject to an open southern boundary. The results show that use of such a scheme in conjunction with traditional radiation boundary conditions allows for a longer model integration that would otherwise be unstable when only the radiation boundary conditions are imposed due to presence of dispersive waves.
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 effects of viscosity and finite- differencing on free Kelvin waves in numerical models (which employ the Arakawa B- or C-grid difference schemes) are investigated using the f-plane shallow-water equations with offshore finite-difference grids, (assuming alongshore geostrophy). Three nondimensional parameters arise: Δ [=(offshore grid spacing)/(Rossby radius)], ε characterizes the offshore lateral viscous effect and α the combined vertical and alongshore viscous effect. This study is more relevant to baroclinic Kelvin waves which tend to suffer poor offshore resolution because of their small Rossby radii.
For inviscid models (ε = α = 0), as Δ increases (resolution worsens), the alongshore speed increases dramatically in the B-grid, but stays constant at the gravity wave speed in the C-grid. Models with damping only (α > 0, ε = 0) behave similarly. With lateral viscosity (ε > 0, α > 0), increasing ε decreases the speed in both the B- and C-grids—the drop in speed being less severe when the free-slip boundary condition is imposed instead of the no-slip one. As Δ increases, the speed declines in the B-grid, but in the C-grid, worsening resolution cancels the viscous slow-down, with speed rising to that when ε = 0.
Our theory predicts the alongshore phase speed, the temporal decay rate and the offshore structure for B- and C-grid models of given viscosity and grid-spacing and of given boundary conditions (e.g., no-slip or free-slip). The predictions are checked against observations from two- and three-dimensional model—including the Bryan-Cox model—with good agreement.
Abstract
The effects of viscosity and finite- differencing on free Kelvin waves in numerical models (which employ the Arakawa B- or C-grid difference schemes) are investigated using the f-plane shallow-water equations with offshore finite-difference grids, (assuming alongshore geostrophy). Three nondimensional parameters arise: Δ [=(offshore grid spacing)/(Rossby radius)], ε characterizes the offshore lateral viscous effect and α the combined vertical and alongshore viscous effect. This study is more relevant to baroclinic Kelvin waves which tend to suffer poor offshore resolution because of their small Rossby radii.
For inviscid models (ε = α = 0), as Δ increases (resolution worsens), the alongshore speed increases dramatically in the B-grid, but stays constant at the gravity wave speed in the C-grid. Models with damping only (α > 0, ε = 0) behave similarly. With lateral viscosity (ε > 0, α > 0), increasing ε decreases the speed in both the B- and C-grids—the drop in speed being less severe when the free-slip boundary condition is imposed instead of the no-slip one. As Δ increases, the speed declines in the B-grid, but in the C-grid, worsening resolution cancels the viscous slow-down, with speed rising to that when ε = 0.
Our theory predicts the alongshore phase speed, the temporal decay rate and the offshore structure for B- and C-grid models of given viscosity and grid-spacing and of given boundary conditions (e.g., no-slip or free-slip). The predictions are checked against observations from two- and three-dimensional model—including the Bryan-Cox model—with good agreement.
