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Abstract
It is noted that the results of recent experiments on the enhancement of turbulent kinetic energy (TKE) dissipation below surface waves can be stated as follows. TKE dissipation is enhanced by a factor 15H
ws
/z at depths 0.5H
ws
< z < 20H
ws
with respect to the wall-layer result ϵ =
Abstract
It is noted that the results of recent experiments on the enhancement of turbulent kinetic energy (TKE) dissipation below surface waves can be stated as follows. TKE dissipation is enhanced by a factor 15H
ws
/z at depths 0.5H
ws
< z < 20H
ws
with respect to the wall-layer result ϵ =
Abstract
A numerical model of the boundary layer of the atmosphere above a gravity surface wave is reviewed. The model results are used to obtain an expression for the wind input, the wave growth due to the wind. This is done for wave components that propagate at an arbitrary angle to the wind. Like other purely theoretical expressions for the wind input, the wind input from the boundary-layer model is much smaller than the wind input inferred from field experiments.
To study the growth of wind sea, the wind input of the third-generation wave model WAM is replaced by the wind input from the boundary-layer model. The original WAM used a wind input that was inferred from field experiments. For the wave-wave interactions the discrete-interaction approximation is used, while the dissipation is tuned to get an appropriate saturation sea state.
The balance between wind input, dissipation, and wave-wave interactions in the energy-containing range of the wave spectrum in this version of the WAM is very different from the balance between these terms in the original version of the WAM. Nevertheless, in both versions of the WAM the development of the wave spectrum of growing wind sea is in agreement with experimental data.
It is concluded that a wave model based on the wave boundary-layer wind-input term is quite capable of reproducing the observed growth of wind sea.
Abstract
A numerical model of the boundary layer of the atmosphere above a gravity surface wave is reviewed. The model results are used to obtain an expression for the wind input, the wave growth due to the wind. This is done for wave components that propagate at an arbitrary angle to the wind. Like other purely theoretical expressions for the wind input, the wind input from the boundary-layer model is much smaller than the wind input inferred from field experiments.
To study the growth of wind sea, the wind input of the third-generation wave model WAM is replaced by the wind input from the boundary-layer model. The original WAM used a wind input that was inferred from field experiments. For the wave-wave interactions the discrete-interaction approximation is used, while the dissipation is tuned to get an appropriate saturation sea state.
The balance between wind input, dissipation, and wave-wave interactions in the energy-containing range of the wave spectrum in this version of the WAM is very different from the balance between these terms in the original version of the WAM. Nevertheless, in both versions of the WAM the development of the wave spectrum of growing wind sea is in agreement with experimental data.
It is concluded that a wave model based on the wave boundary-layer wind-input term is quite capable of reproducing the observed growth of wind sea.
Abstract
The use of ocean wave data in new data assimilation techniques prompted the development of a real-time quality control system for wave height and wave period observations. Over the North Sea, a relatively large number of wave observations, as well as a reliable wave model, are available. Therefore, a variety of tests can be made, allowing for a quite sophisticated wave-data quality control system.
The system uses some of the ideas of Gandin's comprehensive quality control. In particular, an ensemble of single-variate tests is used instead of one large multivariate test, and data are not rejected and thrown away in successive tests but can be rehabilitated until the very end.
Three months of data have been used to test the system. The decisions of the system are found to agree with manual analyses. The statistical properties of the accepted and rejected data are checked. After quality control, the residuals of the quality control tests have almost Gaussian distributions.
Abstract
The use of ocean wave data in new data assimilation techniques prompted the development of a real-time quality control system for wave height and wave period observations. Over the North Sea, a relatively large number of wave observations, as well as a reliable wave model, are available. Therefore, a variety of tests can be made, allowing for a quite sophisticated wave-data quality control system.
The system uses some of the ideas of Gandin's comprehensive quality control. In particular, an ensemble of single-variate tests is used instead of one large multivariate test, and data are not rejected and thrown away in successive tests but can be rehabilitated until the very end.
Three months of data have been used to test the system. The decisions of the system are found to agree with manual analyses. The statistical properties of the accepted and rejected data are checked. After quality control, the residuals of the quality control tests have almost Gaussian distributions.
Abstract
While sea surface temperature (SST) anomalies in the eastern equatorial Pacific are dominated by the thermocline feedback, in the central equatorial Pacific local wind effects, such as zonal advection, are important as well. El Niño–Southern Oscillation (ENSO) simulations with a linear model improve markedly if these effects are included as a local wind stress feedback on SST. An atmosphere model that reacts both to eastern and central Pacific SST anomalies is needed for producing a realistic ENSO cycle.
First, simulations are studied of a linear 1.5-layer reduced-gravity ocean model and a linear SST anomaly equation, forced by observed monthly wind stress. If only the thermocline feedback is present in the SST equation, SST can be simulated well in the eastern Pacific, but, contrary to observations, central Pacific SST is out of phase with the eastern Pacific. If a wind stress feedback is added in the SST equation, as a term proportional to the zonal wind stress, correlations between observed and simulated SST are above 0.8 in both the central and eastern Pacific, and the correlation between the Niño-3 (5°S–5°N, 90°–150°W) and Niño-4 (5°S–5°N, 150°W–160°E) indexes is close to the observed value of 0.75.
Next, a statistical atmosphere is added to the ocean module that is based on a regression of observed wind stress to the observed Niño-3 and Niño-4 indexes. The coupled system is driven by noise that is inferred from the residues of the fit and has a red component. The observed Niño-3–Niño-4 index correlation can be reproduced only with a wind stress feedback in the central Pacific. Also, the level of SST variability rises and the ENSO period increases to more realistic values.
The interplay between the local wind stress and the thermocline feedbacks, therefore, is an important factor in the structure of ENSO in the coupled linear model. In the eastern Pacific, the thermocline feedback dominates SST anomalies; in the central Pacific, the local wind stress feedback. Due to the local wind stress feedback, the ENSO wind stress response excites SST anomalies in the central Pacific, extending the ENSO SST anomaly pattern well into the central Pacific. In turn, these central Pacific SST anomalies give rise to wind stress anomalies that are situated more westward than the response to eastern Pacific SST anomalies. As a result, the ENSO amplitude is enhanced and the ENSO period increased. Also, central Pacific SST anomalies are not completely determined by eastern Pacific SST anomalies and they persist longer.
Abstract
While sea surface temperature (SST) anomalies in the eastern equatorial Pacific are dominated by the thermocline feedback, in the central equatorial Pacific local wind effects, such as zonal advection, are important as well. El Niño–Southern Oscillation (ENSO) simulations with a linear model improve markedly if these effects are included as a local wind stress feedback on SST. An atmosphere model that reacts both to eastern and central Pacific SST anomalies is needed for producing a realistic ENSO cycle.
First, simulations are studied of a linear 1.5-layer reduced-gravity ocean model and a linear SST anomaly equation, forced by observed monthly wind stress. If only the thermocline feedback is present in the SST equation, SST can be simulated well in the eastern Pacific, but, contrary to observations, central Pacific SST is out of phase with the eastern Pacific. If a wind stress feedback is added in the SST equation, as a term proportional to the zonal wind stress, correlations between observed and simulated SST are above 0.8 in both the central and eastern Pacific, and the correlation between the Niño-3 (5°S–5°N, 90°–150°W) and Niño-4 (5°S–5°N, 150°W–160°E) indexes is close to the observed value of 0.75.
Next, a statistical atmosphere is added to the ocean module that is based on a regression of observed wind stress to the observed Niño-3 and Niño-4 indexes. The coupled system is driven by noise that is inferred from the residues of the fit and has a red component. The observed Niño-3–Niño-4 index correlation can be reproduced only with a wind stress feedback in the central Pacific. Also, the level of SST variability rises and the ENSO period increases to more realistic values.
The interplay between the local wind stress and the thermocline feedbacks, therefore, is an important factor in the structure of ENSO in the coupled linear model. In the eastern Pacific, the thermocline feedback dominates SST anomalies; in the central Pacific, the local wind stress feedback. Due to the local wind stress feedback, the ENSO wind stress response excites SST anomalies in the central Pacific, extending the ENSO SST anomaly pattern well into the central Pacific. In turn, these central Pacific SST anomalies give rise to wind stress anomalies that are situated more westward than the response to eastern Pacific SST anomalies. As a result, the ENSO amplitude is enhanced and the ENSO period increased. Also, central Pacific SST anomalies are not completely determined by eastern Pacific SST anomalies and they persist longer.
Abstract
The changes in model ENSO behavior due to an increase in greenhouse gases, according to the Intergovernmental Panel on Climate Change (IPCC) Business-As-Usual scenario, are investigated using a 62-member ensemble 140-yr simulation (1940–2080) with the National Center for Atmospheric Research Community Climate System Model (CCSM; version 1.4). Although the global mean surface temperature increases by about 1.2 K over the period 2000–80, there are no significant changes in the ENSO period, amplitude, and spatial patterns. To explain this behavior, an analysis of the simulation results is combined with results from intermediate complexity coupled ocean–atmosphere models. It is shown that this version of the CCSM is incapable of simulating a correct meridional extension of the equatorial wind stress response to equatorial SST anomalies. The wind response pattern is too narrow and its strength is insensitive to background SST. This leads to a more stable Pacific climate system, a shorter ENSO period, and a reduced sensitivity of ENSO to global warming.
Abstract
The changes in model ENSO behavior due to an increase in greenhouse gases, according to the Intergovernmental Panel on Climate Change (IPCC) Business-As-Usual scenario, are investigated using a 62-member ensemble 140-yr simulation (1940–2080) with the National Center for Atmospheric Research Community Climate System Model (CCSM; version 1.4). Although the global mean surface temperature increases by about 1.2 K over the period 2000–80, there are no significant changes in the ENSO period, amplitude, and spatial patterns. To explain this behavior, an analysis of the simulation results is combined with results from intermediate complexity coupled ocean–atmosphere models. It is shown that this version of the CCSM is incapable of simulating a correct meridional extension of the equatorial wind stress response to equatorial SST anomalies. The wind response pattern is too narrow and its strength is insensitive to background SST. This leads to a more stable Pacific climate system, a shorter ENSO period, and a reduced sensitivity of ENSO to global warming.
Abstract
The time dependence of the local relation between sea surface temperature (SST) and thermocline depth in the central and eastern equatorial Pacific Ocean is analyzed for the period 1990–99, using subsurface temperature measurements from the Tropical Atmosphere–Ocean Array/Triangle Trans-Ocean Buoy Network (TAO/TRITON) buoy array. Thermocline depth anomalies lead SST anomalies in time, with a longitude-dependent delay ranging from 2 weeks in the eastern Pacific to 1 year in the central Pacific. The lagged correlation between thermocline depth and SST is strong, ranging from r > 0.9 in the east to r ≈ 0.6 at 170°W. Time-lagged correlations between thermocline depth and subsurface temperature anomalies indicate vertical advection of temperature anomalies from the thermocline to the surface in the eastern Pacific. The measurements are compared with the results of forced OGCM and linear model experiments. Using model results, it is shown that the delay between thermocline depth and SST is caused mainly by upwelling and mixing between 140° and 90°W. Between 170°E and 140°W the delay has a different explanation: thermocline depth anomalies travel to the eastern Pacific, where upwelling creates SST anomalies that in turn cause anomalous wind in the central Pacific. SST is then influenced by these wind anomalies.
Abstract
The time dependence of the local relation between sea surface temperature (SST) and thermocline depth in the central and eastern equatorial Pacific Ocean is analyzed for the period 1990–99, using subsurface temperature measurements from the Tropical Atmosphere–Ocean Array/Triangle Trans-Ocean Buoy Network (TAO/TRITON) buoy array. Thermocline depth anomalies lead SST anomalies in time, with a longitude-dependent delay ranging from 2 weeks in the eastern Pacific to 1 year in the central Pacific. The lagged correlation between thermocline depth and SST is strong, ranging from r > 0.9 in the east to r ≈ 0.6 at 170°W. Time-lagged correlations between thermocline depth and subsurface temperature anomalies indicate vertical advection of temperature anomalies from the thermocline to the surface in the eastern Pacific. The measurements are compared with the results of forced OGCM and linear model experiments. Using model results, it is shown that the delay between thermocline depth and SST is caused mainly by upwelling and mixing between 140° and 90°W. Between 170°E and 140°W the delay has a different explanation: thermocline depth anomalies travel to the eastern Pacific, where upwelling creates SST anomalies that in turn cause anomalous wind in the central Pacific. SST is then influenced by these wind anomalies.
Abstract
This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low.
This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
Abstract
This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low.
This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
Abstract
According to the delayed-oscillator picture of ENSO, a positive SST anomaly in the eastern tropical Pacific will cause westerly wind anomalies closer to the date line to first give a positive feedback, and later, via planetary wave reflection at the western boundary, a negative feedback. The aim of this study is to follow a chain of sensitivities that lead to a delayed-oscillator mechanism in a general circulation model. To this end, the adjoint of such an ocean model is used for studying sensitivities of ENSO indices.
The ocean model used in this study is the Hamburg Ocean Primitive Equation (HOPE) ocean general circulation model. Its adjoint has been constructed using the Adjoint Model Compiler. Applied to a scalar function computed with a forward model run, an adjoint run goes back in time and calculates sensitivities as the derivatives of this function to forcing fields or ocean state variables at earlier times.
Results from six adjoint runs are reported, tracing the sensitivities of the NINO3 and NINO3.4 indices in October 1987, December 1987, and December 1988, as simulated by a Pacfic-only version of HOPE forced by ECHAM-3 fluxes.
The sensitivities to sea level can be followed back in time for more than a year. They are nonlocal: patterns propagate back in time that are identified as adjoint Kelvin and n = 1, 2, and 3 Rossby waves, with speeds compatible with those obtained from model density profiles. Both the first and the second baroclinic modes seem to play a role. In contrast, the model sensitivities to heat flux, zonal surface currents, and SST are local and decay in about a month.
The sensitivities to the wind stress agree with the wave interpretation of the sea-level sensitivities, but only the n = 1 Rossby wave is visible. Going back in time, the sensitivity to westerly anomalies along the equator changes sign, in agreement with the delayed-oscillator picture.
Finally, a statistical atmosphere model is used to convert sensitivities to wind stress at a given time to sensitivities to SST through the atmosphere at that time. Focusing on the sensitivities to the ENSO index region itself at an earlier time then closes the circle. These sensitivities have a natural interpretation as delayed-oscillator coefficients and show the expected behavior of a positive sensitivity in the recent past changing to a negative sensitivity at longer lags. However, the strength of these feedbacks, and hence the relevance of this mechanism in ENSO simulated in HOPE, cannot be determined accurately.
Abstract
According to the delayed-oscillator picture of ENSO, a positive SST anomaly in the eastern tropical Pacific will cause westerly wind anomalies closer to the date line to first give a positive feedback, and later, via planetary wave reflection at the western boundary, a negative feedback. The aim of this study is to follow a chain of sensitivities that lead to a delayed-oscillator mechanism in a general circulation model. To this end, the adjoint of such an ocean model is used for studying sensitivities of ENSO indices.
The ocean model used in this study is the Hamburg Ocean Primitive Equation (HOPE) ocean general circulation model. Its adjoint has been constructed using the Adjoint Model Compiler. Applied to a scalar function computed with a forward model run, an adjoint run goes back in time and calculates sensitivities as the derivatives of this function to forcing fields or ocean state variables at earlier times.
Results from six adjoint runs are reported, tracing the sensitivities of the NINO3 and NINO3.4 indices in October 1987, December 1987, and December 1988, as simulated by a Pacfic-only version of HOPE forced by ECHAM-3 fluxes.
The sensitivities to sea level can be followed back in time for more than a year. They are nonlocal: patterns propagate back in time that are identified as adjoint Kelvin and n = 1, 2, and 3 Rossby waves, with speeds compatible with those obtained from model density profiles. Both the first and the second baroclinic modes seem to play a role. In contrast, the model sensitivities to heat flux, zonal surface currents, and SST are local and decay in about a month.
The sensitivities to the wind stress agree with the wave interpretation of the sea-level sensitivities, but only the n = 1 Rossby wave is visible. Going back in time, the sensitivity to westerly anomalies along the equator changes sign, in agreement with the delayed-oscillator picture.
Finally, a statistical atmosphere model is used to convert sensitivities to wind stress at a given time to sensitivities to SST through the atmosphere at that time. Focusing on the sensitivities to the ENSO index region itself at an earlier time then closes the circle. These sensitivities have a natural interpretation as delayed-oscillator coefficients and show the expected behavior of a positive sensitivity in the recent past changing to a negative sensitivity at longer lags. However, the strength of these feedbacks, and hence the relevance of this mechanism in ENSO simulated in HOPE, cannot be determined accurately.
Abstract
The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.
Abstract
The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.
Abstract
The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensional wave spectra fields, respecting the wave model dynamics. To investigate the relation merits of the two methods, a number of realistic assimilation experiments have been performed showing the potential of the adjoint technique for wave data assimilation.
Abstract
The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensional wave spectra fields, respecting the wave model dynamics. To investigate the relation merits of the two methods, a number of realistic assimilation experiments have been performed showing the potential of the adjoint technique for wave data assimilation.
