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Abstract
A novel neural network (NN)–based scheme performs nonlinear model output statistics (MOS) for generating precipitation forecasts from numerical weather prediction (NWP) model output. Data records from the past few weeks are sufficient for establishing an initial MOS connection, which then adapts itself to the ongoing changes and modifications in the NWP model. The technical feasibility of the algorithm is demonstrated in three numerical experiments using the NCEP reanalysis data in the Alaskan panhandle and the coastal region of British Columbia. Its performance is compared with that of a conventional NN-based nonadaptive scheme. When the new adaptive method is employed, the degradation in the precipitation forecast skills due to changes in the NWP model is small and is much less than the degradation in the performance of the conventional nonadaptive scheme.
Abstract
A novel neural network (NN)–based scheme performs nonlinear model output statistics (MOS) for generating precipitation forecasts from numerical weather prediction (NWP) model output. Data records from the past few weeks are sufficient for establishing an initial MOS connection, which then adapts itself to the ongoing changes and modifications in the NWP model. The technical feasibility of the algorithm is demonstrated in three numerical experiments using the NCEP reanalysis data in the Alaskan panhandle and the coastal region of British Columbia. Its performance is compared with that of a conventional NN-based nonadaptive scheme. When the new adaptive method is employed, the degradation in the precipitation forecast skills due to changes in the NWP model is small and is much less than the degradation in the performance of the conventional nonadaptive scheme.
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
Given equal amounts of kinetic energy near the coast, different shelf wave modes (at the same frequency) have different magnitudes of sea-level oscillations—the magnitudes decrease with increasing mode number. Hence, an intrinsic bias for the lowest mode is present when using sea-level data for shelf wave detection.
Shelf waves have many modal-dependent structures in their cross-shelf dimension, which can be used to accurately identify the excited modes in the current fluctuations. In addition to rotary spectral analysis, a new technique that involves fitting (at a particular frequency of interest) the theoretical current ellipses of various barotropic shelf wave modes to the observed current ellipses at stations spread across the continental shelf, is introduced. This technique shows how the current energy is distributed among the modes.
These techniques are illustrated using Oregon shelf data from the summer of 1973. The cross-shelf fitting shows that at frequencies below 0.45 cycles day−1, the current fluctuations on the Oregon shelf were completely dominated by the second mode. Furthermore, the observed alongshore phase speed also agreed very closely with the theoretical value for the second mode shelf wave. This is the clearest shelf wave identification achieved to date.
Abstract
Given equal amounts of kinetic energy near the coast, different shelf wave modes (at the same frequency) have different magnitudes of sea-level oscillations—the magnitudes decrease with increasing mode number. Hence, an intrinsic bias for the lowest mode is present when using sea-level data for shelf wave detection.
Shelf waves have many modal-dependent structures in their cross-shelf dimension, which can be used to accurately identify the excited modes in the current fluctuations. In addition to rotary spectral analysis, a new technique that involves fitting (at a particular frequency of interest) the theoretical current ellipses of various barotropic shelf wave modes to the observed current ellipses at stations spread across the continental shelf, is introduced. This technique shows how the current energy is distributed among the modes.
These techniques are illustrated using Oregon shelf data from the summer of 1973. The cross-shelf fitting shows that at frequencies below 0.45 cycles day−1, the current fluctuations on the Oregon shelf were completely dominated by the second mode. Furthermore, the observed alongshore phase speed also agreed very closely with the theoretical value for the second mode shelf wave. This is the clearest shelf wave identification achieved to date.
Abstract
The low-frequency current fluctuations on the Oregon shelf changed dramatically from winter to spring, 1975. A much faster offshore energy decay occurred simultaneously with a sharp decrease in the alongshore propagation speed. Cross-shelf analysis in a frequency band around 0.16 cpd showed the emergence of the third-mode shelf wave, in spring from the predominantly first-mode motion in winter. At frequencies <0.1 cpd, the current fluctuations propagated southward in winter, opposite to the direction of shelf waves.
On the Oregon and Washington shelves during summer (and early fall) 1972, the location of moorings on irregular topography rendered data interpretation difficult. Nevertheless, the general cross-shelf and alongshore properties of the current fluctuations were consistent with the first-mode shelf wave, in contrast to the situation during summer 1973 when the second mode was excited.
The excitation of relatively high modes and the generally sharp concentration of energy in one particular mode are surprising and difficult to explain with the present shelf-wave generation theories. Nonlinear resonance between wind and current is proposed as a possible explanation.
Abstract
The low-frequency current fluctuations on the Oregon shelf changed dramatically from winter to spring, 1975. A much faster offshore energy decay occurred simultaneously with a sharp decrease in the alongshore propagation speed. Cross-shelf analysis in a frequency band around 0.16 cpd showed the emergence of the third-mode shelf wave, in spring from the predominantly first-mode motion in winter. At frequencies <0.1 cpd, the current fluctuations propagated southward in winter, opposite to the direction of shelf waves.
On the Oregon and Washington shelves during summer (and early fall) 1972, the location of moorings on irregular topography rendered data interpretation difficult. Nevertheless, the general cross-shelf and alongshore properties of the current fluctuations were consistent with the first-mode shelf wave, in contrast to the situation during summer 1973 when the second mode was excited.
The excitation of relatively high modes and the generally sharp concentration of energy in one particular mode are surprising and difficult to explain with the present shelf-wave generation theories. Nonlinear resonance between wind and current is proposed as a possible explanation.
Abstract
The advent of the feed-forward neural network (
Two cases of the Lorenz model—(i) the weakly nonlinear case of quasiperiodic oscillations, and (ii) the highly nonlinear, chaotic case—were chosen to test the forecast skills of the hybrid model. Numerical experiments showed that for the weakly nonlinear case, the hybrid model can be very successful, with forecast skills similar to the original Lorenz model. For the highly nonlinear case, the hybrid model could produce reasonable predictions for at least one cycle of oscillation for most experiments, although poor results were obtained for some experiments. In these failed experiments, the data used for assimilation were often located on one wing of the Lorenz butterfly-shaped attractor, while the system moved to the second wing during the forecast period. The forecasts failed as the model had never been trained with data from the second wing.
Abstract
The advent of the feed-forward neural network (
Two cases of the Lorenz model—(i) the weakly nonlinear case of quasiperiodic oscillations, and (ii) the highly nonlinear, chaotic case—were chosen to test the forecast skills of the hybrid model. Numerical experiments showed that for the weakly nonlinear case, the hybrid model can be very successful, with forecast skills similar to the original Lorenz model. For the highly nonlinear case, the hybrid model could produce reasonable predictions for at least one cycle of oscillation for most experiments, although poor results were obtained for some experiments. In these failed experiments, the data used for assimilation were often located on one wing of the Lorenz butterfly-shaped attractor, while the system moved to the second wing during the forecast period. The forecasts failed as the model had never been trained with data from the second wing.
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
The release of freshwater from a midlatitude estuary to the continental shelf is modeled numerically as a Rossby adjustment problem using a primitive equation model. As the initial salinity front is relaxed, a first baroclinic-mode Kelvin wave propagates into the estuary, while along the continental shelf, the disturbance travels in the direction of coastally trapped waves but with a relatively slow propagation speed.
When a submarine canyon extends offshore from the estuary, the joint effect of baroclinicity and bottom relief provides forcing for barotropic flow. The disturbance now propagates along the shelf at the first coastally trapped wave-mode phase speed, and the shelf circulation is significantly more energetic and barotropic than in the case without the canyon.
For both the experiments with and without a canyon an anticyclonic circulation, generated by the surface outflow and deeper inflow over changing bottom topography, is formed off the mouth of the estuary. As the deeper inflow encounters shallower depth, the column of fluid is vertically compressed, thereby spinning up anticyclonically due to the conservation of potential vorticity. This feature is in qualitative agreement with the Tully eddy observed off Juan de Fuca Strait.
A study of the reverse estuary (where the estuarine water is denser than the oceanic water) shows that this configuration has more potential energy available for conversion to kinetic energy than the normal estuary. Brass Strait may be considered as a possible reverse estuary for generating coastally trapped waves.
The effects of a wider shelf and a wider estuary are examined by two more experiments. For the wider shelf, the resulting baroclinic flow is similar to that of the other runs, although the barotropic flow is weaker. The wide estuary model proves to be the most dynamic of all, with the intensified anticyclonic circulation now extending well into the estuary.
Abstract
The release of freshwater from a midlatitude estuary to the continental shelf is modeled numerically as a Rossby adjustment problem using a primitive equation model. As the initial salinity front is relaxed, a first baroclinic-mode Kelvin wave propagates into the estuary, while along the continental shelf, the disturbance travels in the direction of coastally trapped waves but with a relatively slow propagation speed.
When a submarine canyon extends offshore from the estuary, the joint effect of baroclinicity and bottom relief provides forcing for barotropic flow. The disturbance now propagates along the shelf at the first coastally trapped wave-mode phase speed, and the shelf circulation is significantly more energetic and barotropic than in the case without the canyon.
For both the experiments with and without a canyon an anticyclonic circulation, generated by the surface outflow and deeper inflow over changing bottom topography, is formed off the mouth of the estuary. As the deeper inflow encounters shallower depth, the column of fluid is vertically compressed, thereby spinning up anticyclonically due to the conservation of potential vorticity. This feature is in qualitative agreement with the Tully eddy observed off Juan de Fuca Strait.
A study of the reverse estuary (where the estuarine water is denser than the oceanic water) shows that this configuration has more potential energy available for conversion to kinetic energy than the normal estuary. Brass Strait may be considered as a possible reverse estuary for generating coastally trapped waves.
The effects of a wider shelf and a wider estuary are examined by two more experiments. For the wider shelf, the resulting baroclinic flow is similar to that of the other runs, although the barotropic flow is weaker. The wide estuary model proves to be the most dynamic of all, with the intensified anticyclonic circulation now extending well into the estuary.
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.
