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- Author or Editor: J. D. Opsteegh x
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Abstract
A nonmodal approach based on the potential vorticity (PV) perspective is used to compute the singular vector (SV) that optimizes the growth of kinetic energy at the surface for the β-plane Eady model without an upper rigid lid. The basic-state buoyancy frequency and zonal wind profile are chosen such that the basic-state PV gradient is zero.
If the f-plane approximation is made, the SV growth at the surface is dominated by resonance, resulting from the advection of basic-state potential temperature (PT) by the interior PV anomalies. This resonance generates a PT anomaly at the surface. The PV unshielding and PV–PT unshielding contribute less to the final kinetic energy at the surface.
The general conclusion of the present paper is that surface cyclogenesis (of the 48-h SV) is stronger if β is included. Three cases have been considered. In the first case, the vertical shear of the basic state is modified in order to retain the zero basic-state PV gradient. The increased shear enhances SV growth significantly first because of a lowering of the resonant level (enhanced resonance), and second because of a more rapid PV unshielding process. Resonance is the most important contribution at optimization time. In the second case, the buoyancy frequency of the basic state is modified. The surface cyclogenesis is stronger than in the absence of β but less strong than if the shear is modified. It is shown that the effect of the modified buoyancy frequency profile is that PV unshielding occurs more efficiently. The contribution from resonance to the SV growth remains almost the same. Finally, the SV is calculated for a more realistic buoyancy frequency profile based on observations. In this experiment the increased value of the surface buoyancy frequency reduces the SV growth significantly as compared to the case in which the surface buoyancy frequency takes a standard value. All growth mechanisms are affected by this change in the surface buoyancy frequency.
Abstract
A nonmodal approach based on the potential vorticity (PV) perspective is used to compute the singular vector (SV) that optimizes the growth of kinetic energy at the surface for the β-plane Eady model without an upper rigid lid. The basic-state buoyancy frequency and zonal wind profile are chosen such that the basic-state PV gradient is zero.
If the f-plane approximation is made, the SV growth at the surface is dominated by resonance, resulting from the advection of basic-state potential temperature (PT) by the interior PV anomalies. This resonance generates a PT anomaly at the surface. The PV unshielding and PV–PT unshielding contribute less to the final kinetic energy at the surface.
The general conclusion of the present paper is that surface cyclogenesis (of the 48-h SV) is stronger if β is included. Three cases have been considered. In the first case, the vertical shear of the basic state is modified in order to retain the zero basic-state PV gradient. The increased shear enhances SV growth significantly first because of a lowering of the resonant level (enhanced resonance), and second because of a more rapid PV unshielding process. Resonance is the most important contribution at optimization time. In the second case, the buoyancy frequency of the basic state is modified. The surface cyclogenesis is stronger than in the absence of β but less strong than if the shear is modified. It is shown that the effect of the modified buoyancy frequency profile is that PV unshielding occurs more efficiently. The contribution from resonance to the SV growth remains almost the same. Finally, the SV is calculated for a more realistic buoyancy frequency profile based on observations. In this experiment the increased value of the surface buoyancy frequency reduces the SV growth significantly as compared to the case in which the surface buoyancy frequency takes a standard value. All growth mechanisms are affected by this change in the surface buoyancy frequency.
Abstract
Adopting the viewpoint that atmospheric flow regimes can be associated with steady states, this work investigates the hypothesis that regime transitions in deterministic atmosphere models are related to the existence of heteroclinic connections between these steady states. A low-order barotropic model with topography is studied, in which topographic and barotropic instabilities are the mechanisms dominating the dynamics. By parameter tuning, the Hopf bifurcation corresponding to barotropic instability can be made to coincide with one of the saddle-node bifurcations that are due to the topography in the model. This coincidence is called a fold-Hopf bifurcation. Among the dynamical structures related to such a bifurcation are heteroclinic connections and homoclinic orbits, connected to the equilibria. A heteroclinic cycle back and forth between the equilibria, existing in the truncated normal form of the fold-Hopf bifuraction, will be perturbed in the full model, leaving orbits homoclinic to one of the equilibria. The impact of these mathematical structures explains several characteristics of regime behavior known from previous model studies.
Abstract
Adopting the viewpoint that atmospheric flow regimes can be associated with steady states, this work investigates the hypothesis that regime transitions in deterministic atmosphere models are related to the existence of heteroclinic connections between these steady states. A low-order barotropic model with topography is studied, in which topographic and barotropic instabilities are the mechanisms dominating the dynamics. By parameter tuning, the Hopf bifurcation corresponding to barotropic instability can be made to coincide with one of the saddle-node bifurcations that are due to the topography in the model. This coincidence is called a fold-Hopf bifurcation. Among the dynamical structures related to such a bifurcation are heteroclinic connections and homoclinic orbits, connected to the equilibria. A heteroclinic cycle back and forth between the equilibria, existing in the truncated normal form of the fold-Hopf bifuraction, will be perturbed in the full model, leaving orbits homoclinic to one of the equilibria. The impact of these mathematical structures explains several characteristics of regime behavior known from previous model studies.
Abstract
The variability in the subpolar Southern Hemisphere is studied with a coupled atmosphere–ocean–sea-ice model (the ECBilt). After having reached an approximate statistical equilibrium in coupled mode without flux corrections, a subsequent 1000-yr integration is performed and analyzed. A singular value decomposition of austral winter SST anomalies and 800-hPa geopotential height in the Antarctic Circumpolar Current region reveals a mode of covariability that resembles the observed Antarctic circumpolar wave. Subsequent analysis of this mode shows that it is basically an oscillation in the subsurface of the ocean. Additional experiments suggest that it is generated by the advective resonance mechanism: the oscillation is excited by the dominant modes of variability in the atmosphere, whereas the timescale is set by the ratio of the horizontal scale of these atmospheric modes and the advection velocity of the mean oceanic currents. The atmospheric response mainly consists of a local temperature adjustment to the SST anomaly, which reduces the damping of the SST anomalies. Salinity, wind stress, and sea-ice anomalies do modify the structure and intensity of the mode without playing an essential role.
Abstract
The variability in the subpolar Southern Hemisphere is studied with a coupled atmosphere–ocean–sea-ice model (the ECBilt). After having reached an approximate statistical equilibrium in coupled mode without flux corrections, a subsequent 1000-yr integration is performed and analyzed. A singular value decomposition of austral winter SST anomalies and 800-hPa geopotential height in the Antarctic Circumpolar Current region reveals a mode of covariability that resembles the observed Antarctic circumpolar wave. Subsequent analysis of this mode shows that it is basically an oscillation in the subsurface of the ocean. Additional experiments suggest that it is generated by the advective resonance mechanism: the oscillation is excited by the dominant modes of variability in the atmosphere, whereas the timescale is set by the ratio of the horizontal scale of these atmospheric modes and the advection velocity of the mean oceanic currents. The atmospheric response mainly consists of a local temperature adjustment to the SST anomaly, which reduces the damping of the SST anomalies. Salinity, wind stress, and sea-ice anomalies do modify the structure and intensity of the mode without playing an essential role.
Abstract
An ensemble prediction system, especially designed for the short to early-medium range for the European domain, is presented. The initial perturbations of each ensemble are based on singular vectors that maximize the 3-day total energy error growth above the European area and the northern Atlantic. In total, a set of 51 ensembles, each consisting of 51 members, has been integrated, comprising 28 winter cases in 1996 and 1997, 2 spring, and 21 autumn cases in 1997. The impact on performance, relative to the operational ensemble prediction system at ECMWF, appears to be modest for the winter set. However, for the combined spring and autumn set, the impact is significantly positive, especially for rare (extreme) events of large-scale precipitation, 2-m temperature, 10-m wind speed, and the pressure at mean sea level. For the targeted ensembles, the situation that a complete ensemble misses an extreme event occurs much less than for the operational ensemble system. As a result, the range of cost–loss ratios for which a user has benefit is larger. The benefit of the targeted ensembles is maximal between days 2 and 3. For this range in spring–autumn, an ensemble system consisting of a subset of 21 targeted members performs comparable to the 51-member operational ensemble prediction system (EPS), when evaluated for the same area of interest. The spread within a targeted ensemble prediction system (TEPS) is somewhat larger than within the EPS ensembles. However, both systems appear to be underdispersive for large-scale precipitation, 2-m temperature, and 10-m wind speed. Only for mean sea level pressure is the spread of the TEPS ensemble, on average, comparable to the magnitude of the forecast error of the ensemble mean between days 2 and 3.5.
Abstract
An ensemble prediction system, especially designed for the short to early-medium range for the European domain, is presented. The initial perturbations of each ensemble are based on singular vectors that maximize the 3-day total energy error growth above the European area and the northern Atlantic. In total, a set of 51 ensembles, each consisting of 51 members, has been integrated, comprising 28 winter cases in 1996 and 1997, 2 spring, and 21 autumn cases in 1997. The impact on performance, relative to the operational ensemble prediction system at ECMWF, appears to be modest for the winter set. However, for the combined spring and autumn set, the impact is significantly positive, especially for rare (extreme) events of large-scale precipitation, 2-m temperature, 10-m wind speed, and the pressure at mean sea level. For the targeted ensembles, the situation that a complete ensemble misses an extreme event occurs much less than for the operational ensemble system. As a result, the range of cost–loss ratios for which a user has benefit is larger. The benefit of the targeted ensembles is maximal between days 2 and 3. For this range in spring–autumn, an ensemble system consisting of a subset of 21 targeted members performs comparable to the 51-member operational ensemble prediction system (EPS), when evaluated for the same area of interest. The spread within a targeted ensemble prediction system (TEPS) is somewhat larger than within the EPS ensembles. However, both systems appear to be underdispersive for large-scale precipitation, 2-m temperature, and 10-m wind speed. Only for mean sea level pressure is the spread of the TEPS ensemble, on average, comparable to the magnitude of the forecast error of the ensemble mean between days 2 and 3.5.
Abstract
For 35 seasons in the years 1974–84, the importance of seasonal anomalies in tropical diabatic heating was investigated for the circulation in the tropics and in the extratropics. The heating was estimated from anomalies in outgoing longwave radiation as measured by satellite and was prescribed as a forcing in a linear study state model. With this model a small part of the observed spatial variance in the streamfunction anomalies in the tropics and lower midlatitudes in the northern hemispheric winter and autumn (5–10%) could be explained. In the tropics, in particular in the central Pacific at 700 mb, the explained variance was largest (10–25%). When the beating was exceptionally large, as during El Niño 1982–83, the similarity between observed and simulated streamfunction anomalies was much better than average not only directly over the major heat sources in the tropics but also in midlatitudes. In spite of the simplicity of the model and the neglect of the other forcing terms, the explained variance was between 25 and 60% in these regions.
Abstract
For 35 seasons in the years 1974–84, the importance of seasonal anomalies in tropical diabatic heating was investigated for the circulation in the tropics and in the extratropics. The heating was estimated from anomalies in outgoing longwave radiation as measured by satellite and was prescribed as a forcing in a linear study state model. With this model a small part of the observed spatial variance in the streamfunction anomalies in the tropics and lower midlatitudes in the northern hemispheric winter and autumn (5–10%) could be explained. In the tropics, in particular in the central Pacific at 700 mb, the explained variance was largest (10–25%). When the beating was exceptionally large, as during El Niño 1982–83, the similarity between observed and simulated streamfunction anomalies was much better than average not only directly over the major heat sources in the tropics but also in midlatitudes. In spite of the simplicity of the model and the neglect of the other forcing terms, the explained variance was between 25 and 60% in these regions.
Abstract
North Atlantic decadal climate variability is studied with a coupled atmosphere–ocean–sea ice model (ECBILT). After having reached an approximate statistical equilibrium in coupled mode without applying flux corrections, a subsequent 1000-yr integration is performed and analyzed. Compared to the current climate, the surface temperatures are 2°C warmer in the Tropics to almost 8°C warmer in the polar regions.
The covariability between the atmosphere and ocean is explored by performing a singular value decomposition (SVD) of boreal winter SST anomalies and 800-hPa geopotential height anomalies. The first SVD pair shows a red variance spectrum in SST and a white spectrum in 800-hPa height. The second mode shows a peak in both spectra at a timescale of about 16–18 yr. The geopotential height pattern is the model’s equivalent of the North Atlantic oscillation (NAO) pattern; the SST anomaly pattern is a north–south oriented dipole.
Additional experiments have revealed that the decadal oscillation in ECBILT is basically an oscillation in the subsurface of the ocean. The oscillation is excited by anomalies in the atmospheric NAO pattern, both through anomalous surface heat fluxes and anomalous Ekman transports. The atmospheric response to the SST anomaly enhances the oscillation and slightly modifies it, but is not essential. The atmospheric response consists primarily of a local surface air temperature adjustment to the SST anomaly. An important element in the physical mechanism of the oscillation is the geostrophic response of the ocean circulation to the forced temperature anomalies creating surface salinity anomalies through anomalous horizontal advection. These salinity anomalies influence the convective activity in the area of the temperature anomaly such as to break down the subsurface temperature anomaly. Both temperature and salinity anomalies slowly propagate eastward at a rate consistent with the mean current.
Abstract
North Atlantic decadal climate variability is studied with a coupled atmosphere–ocean–sea ice model (ECBILT). After having reached an approximate statistical equilibrium in coupled mode without applying flux corrections, a subsequent 1000-yr integration is performed and analyzed. Compared to the current climate, the surface temperatures are 2°C warmer in the Tropics to almost 8°C warmer in the polar regions.
The covariability between the atmosphere and ocean is explored by performing a singular value decomposition (SVD) of boreal winter SST anomalies and 800-hPa geopotential height anomalies. The first SVD pair shows a red variance spectrum in SST and a white spectrum in 800-hPa height. The second mode shows a peak in both spectra at a timescale of about 16–18 yr. The geopotential height pattern is the model’s equivalent of the North Atlantic oscillation (NAO) pattern; the SST anomaly pattern is a north–south oriented dipole.
Additional experiments have revealed that the decadal oscillation in ECBILT is basically an oscillation in the subsurface of the ocean. The oscillation is excited by anomalies in the atmospheric NAO pattern, both through anomalous surface heat fluxes and anomalous Ekman transports. The atmospheric response to the SST anomaly enhances the oscillation and slightly modifies it, but is not essential. The atmospheric response consists primarily of a local surface air temperature adjustment to the SST anomaly. An important element in the physical mechanism of the oscillation is the geostrophic response of the ocean circulation to the forced temperature anomalies creating surface salinity anomalies through anomalous horizontal advection. These salinity anomalies influence the convective activity in the area of the temperature anomaly such as to break down the subsurface temperature anomaly. Both temperature and salinity anomalies slowly propagate eastward at a rate consistent with the mean current.
Abstract
The mean state and variability of deep convection in the ocean influence the North Atlantic climate. Using an ensemble experiment with a coupled atmosphere–ocean–sea ice model, it is shown that cooling and subdued warming areas can occur over the North Atlantic Ocean and adjacent landmasses under global warming. Different “present-day” convection patterns in the Greenland–Iceland–Norway (GIN) Sea result in different future surface-air temperature changes. At higher latitudes, the more effective positive sea ice feedback increases the likelihood of changes in convection causing a regional cooling that is larger than the warming brought about by the enhanced greenhouse effect. The modeled freshening of deep ocean layers in the North Atlantic in a time period preceding a reorganization of GIN Sea convection is consistent with recent observations. Low-frequency internal variability in the ocean model has relatively little impact on the response patterns.
Abstract
The mean state and variability of deep convection in the ocean influence the North Atlantic climate. Using an ensemble experiment with a coupled atmosphere–ocean–sea ice model, it is shown that cooling and subdued warming areas can occur over the North Atlantic Ocean and adjacent landmasses under global warming. Different “present-day” convection patterns in the Greenland–Iceland–Norway (GIN) Sea result in different future surface-air temperature changes. At higher latitudes, the more effective positive sea ice feedback increases the likelihood of changes in convection causing a regional cooling that is larger than the warming brought about by the enhanced greenhouse effect. The modeled freshening of deep ocean layers in the North Atlantic in a time period preceding a reorganization of GIN Sea convection is consistent with recent observations. Low-frequency internal variability in the ocean model has relatively little impact on the response patterns.
Abstract
A linear steady-state primitive equation model has been developed for the computation of stationary atmospheric waves that are forced by anomalies in surface conditions. The model has two levels in the vertical. In the zonal direction the variables are represented by Fourier series, while in the meridional direction a grid-point representation is used. The equations governing atmospheric motion are linearized around a zonally symmetric state which depends on latitude and height according to Oort (1980).
We have studied the amplitude and phase relations of the model response as a function of latitude for a very simple beating, which is sinusoidal in the zonal direction, with zonal wavenumber m (m=1, 10) and constant in the meridional direction, using February mean conditions.
The response of the model indicates that a heating in the tropics can have a substantial influence on the middle and high latitudes, provided that part of the heating is in the westerlies. We have compared the model response for such a heating with the results of similar experiments with GCM and a linear barotropic model and also with mean anomaly patterns at middle and high latitudes derived from observations for Northern Hemispheric winters with a warm equatorial Pacific. In all cases we find strong similarities of hemispheric wave patterns.
We plan to test the model for the prediction of that part of the anomalies in the monthly or seasonal mean circulation that comes from persistent abnormal surface conditions In order to predict more than a persistent atmospheric response, such an anomaly in the surface conditions must have different effects in different months or seasons. We have tested the hypothesis that due to a changing zonally symmetric state, the response to a prescribed beating will be different in the four seasons. This effect is computed for a heating in the tropics and in the middle latitudes. Both in amplitude and phase the response to exactly the same heating can change significantly from one season to the next.
Abstract
A linear steady-state primitive equation model has been developed for the computation of stationary atmospheric waves that are forced by anomalies in surface conditions. The model has two levels in the vertical. In the zonal direction the variables are represented by Fourier series, while in the meridional direction a grid-point representation is used. The equations governing atmospheric motion are linearized around a zonally symmetric state which depends on latitude and height according to Oort (1980).
We have studied the amplitude and phase relations of the model response as a function of latitude for a very simple beating, which is sinusoidal in the zonal direction, with zonal wavenumber m (m=1, 10) and constant in the meridional direction, using February mean conditions.
The response of the model indicates that a heating in the tropics can have a substantial influence on the middle and high latitudes, provided that part of the heating is in the westerlies. We have compared the model response for such a heating with the results of similar experiments with GCM and a linear barotropic model and also with mean anomaly patterns at middle and high latitudes derived from observations for Northern Hemispheric winters with a warm equatorial Pacific. In all cases we find strong similarities of hemispheric wave patterns.
We plan to test the model for the prediction of that part of the anomalies in the monthly or seasonal mean circulation that comes from persistent abnormal surface conditions In order to predict more than a persistent atmospheric response, such an anomaly in the surface conditions must have different effects in different months or seasons. We have tested the hypothesis that due to a changing zonally symmetric state, the response to a prescribed beating will be different in the four seasons. This effect is computed for a heating in the tropics and in the middle latitudes. Both in amplitude and phase the response to exactly the same heating can change significantly from one season to the next.
Abstract
A diagnostic study has been performed to investigate the prospects for developing a time-averaged statistical-dynamical model for making long-range weather forecasts. Estimates are made of nearly all terms in the equations describing the evolution of the time-mean quantities (ū, v̄, T̄, ω¯) and the horizontal second-order eddy statistics (u′2¯, v′2¯, u′v′¯, u′T′¯) and v′T′¯. These calculations were performed over northwestern Europe, using radiosonde observations of wind, temperature and height for the winter of 1976/11977. Geostrophic winds were estimated from objective analyses, while vertical velocities were determined with a quasi-geostrophic baroclinic model. For each equation, approximate balances are presented on the basis of these estimates.
In the equations for the mean quantities the time derivatives are more than one order of magnitude smaller than the unknown second-order eddy statistics. The same holds for the time derivatives of second-order eddy statistics compared with the unknown third-order and ageostrophic terms in the equations for these eddy fluxes. We therefore conclude that the system of time-averaged equations has no capability of describing the evolution of the atmosphere from one specific mean state to another mean state in the future–since for this purpose a closure of the system or a parameterization of second- order or third-order terms has to be extremely accurate. Even in the case in which only the stationary waves of the mean flow are treated, a higher order closure scheme does not seem to be feasible, for third-order terms and ageostrophic second-order terms are probably large and very difficult to parameterize. This implies that a preferable approach is to explore in greater depth the possibility of parameterizing the second-order statistics directly.
Abstract
A diagnostic study has been performed to investigate the prospects for developing a time-averaged statistical-dynamical model for making long-range weather forecasts. Estimates are made of nearly all terms in the equations describing the evolution of the time-mean quantities (ū, v̄, T̄, ω¯) and the horizontal second-order eddy statistics (u′2¯, v′2¯, u′v′¯, u′T′¯) and v′T′¯. These calculations were performed over northwestern Europe, using radiosonde observations of wind, temperature and height for the winter of 1976/11977. Geostrophic winds were estimated from objective analyses, while vertical velocities were determined with a quasi-geostrophic baroclinic model. For each equation, approximate balances are presented on the basis of these estimates.
In the equations for the mean quantities the time derivatives are more than one order of magnitude smaller than the unknown second-order eddy statistics. The same holds for the time derivatives of second-order eddy statistics compared with the unknown third-order and ageostrophic terms in the equations for these eddy fluxes. We therefore conclude that the system of time-averaged equations has no capability of describing the evolution of the atmosphere from one specific mean state to another mean state in the future–since for this purpose a closure of the system or a parameterization of second- order or third-order terms has to be extremely accurate. Even in the case in which only the stationary waves of the mean flow are treated, a higher order closure scheme does not seem to be feasible, for third-order terms and ageostrophic second-order terms are probably large and very difficult to parameterize. This implies that a preferable approach is to explore in greater depth the possibility of parameterizing the second-order statistics directly.
Abstract
Using a two-level linear, steady state model, we diagnose the 40-day mean response of a GCM to a tropical sea surface temperature (SST) anomaly. The time-mean anomalies produced by the GCM are simulated as linear response to the anomalous hemispheric distributions of latent heating, sensible heating and transient eddy forcing. Also, the anomalous effect of mountains, caused by anomalies in the zonal mean surface wind is taken into account. All anomalies are defined as the difference between perturbation and control runs. For our analysis, we have taken the tropical Atlantic SST anomaly experiment performed by Rowntree.
We have compared the linear model's response in temperature at 600 mb and winds at 400 mb with the same anomalous quantities produced by the GCM. The similarity between the time-mean anomalies of the GCM experiment and the linear model's response is very high. The pattern correlation coefficients are between 0.6 and 0.7 in the region between 30°N and 60°N. The response to each of the anomalous forcings separately is positively correlated with the GCM anomaly pattern. The amplitude of the response to anomalous forcing by transient eddies is a factor of two or three larger than the effects of anomalous sensible and latent heating. The anomalous effect of the orography is negligible.
Although intended to be a tropical SST anomaly GCM experiment, the difference between control and perturbation runs does not seem to be directly related to tropical heating near the SST anomaly. Instead, most of the forcing of anomalies in the midlatitudes took place in the midlatitudes itself and, in particular, the remote effects of forcing by tropical latent heat sources were minor.
Abstract
Using a two-level linear, steady state model, we diagnose the 40-day mean response of a GCM to a tropical sea surface temperature (SST) anomaly. The time-mean anomalies produced by the GCM are simulated as linear response to the anomalous hemispheric distributions of latent heating, sensible heating and transient eddy forcing. Also, the anomalous effect of mountains, caused by anomalies in the zonal mean surface wind is taken into account. All anomalies are defined as the difference between perturbation and control runs. For our analysis, we have taken the tropical Atlantic SST anomaly experiment performed by Rowntree.
We have compared the linear model's response in temperature at 600 mb and winds at 400 mb with the same anomalous quantities produced by the GCM. The similarity between the time-mean anomalies of the GCM experiment and the linear model's response is very high. The pattern correlation coefficients are between 0.6 and 0.7 in the region between 30°N and 60°N. The response to each of the anomalous forcings separately is positively correlated with the GCM anomaly pattern. The amplitude of the response to anomalous forcing by transient eddies is a factor of two or three larger than the effects of anomalous sensible and latent heating. The anomalous effect of the orography is negligible.
Although intended to be a tropical SST anomaly GCM experiment, the difference between control and perturbation runs does not seem to be directly related to tropical heating near the SST anomaly. Instead, most of the forcing of anomalies in the midlatitudes took place in the midlatitudes itself and, in particular, the remote effects of forcing by tropical latent heat sources were minor.
