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## Abstract

A series of studies are performed to examine the response of the tropical atmosphere to a prescribed steady, large-scale, elevated heat source (i.e., a region of persistent precipitation). Special emphasis is placed on the surface wind response in two idealized cases in which dissipation is achieved exclusively by Rayleigh friction or by Newtonian cooling. Starting from the linearized equations on an equatorial beta plane, theoretical arguments are presented that suggest there are qualitative differences in the solutions of these two models. A dry spectral primitive equation model of the atmosphere is employed and confirms the results obtained from the analytical studies.

The results from both the analytical study and the numerical simulations are consistent in showing that Rayleigh friction and Newtonian cooling play totally different roles in the tropical atmosphere. Newtonian cooling homogenizes the atmospheric motion in the vertical direction, and a strong, vertically uniform wind is found below the base of the heat source. When Rayleigh friction dominates, the circulation driven by the heat source is confined to the layer where the heat source is located. It is also shown that a strong Hadley circulation is associated with reasonable strong Rayleigh friction, but not with Newtonian cooling alone.

Finally, the numerical solution is found for the case where Newtonian cooling acts uniformly in the vertical *and* Rayleigh friction is included in the lower atmosphere to mimic crudely the dissipation of momentum in the boundary layer. The introduction of the simple boundary layer dramatically reduces the surface circulation that was supported in the Newtonian cooling alone case. Together these results suggest a significant surface circulation is unlikely to be driven by an elevated heat source if it resides above the top of the boundary layer.

## Abstract

A series of studies are performed to examine the response of the tropical atmosphere to a prescribed steady, large-scale, elevated heat source (i.e., a region of persistent precipitation). Special emphasis is placed on the surface wind response in two idealized cases in which dissipation is achieved exclusively by Rayleigh friction or by Newtonian cooling. Starting from the linearized equations on an equatorial beta plane, theoretical arguments are presented that suggest there are qualitative differences in the solutions of these two models. A dry spectral primitive equation model of the atmosphere is employed and confirms the results obtained from the analytical studies.

The results from both the analytical study and the numerical simulations are consistent in showing that Rayleigh friction and Newtonian cooling play totally different roles in the tropical atmosphere. Newtonian cooling homogenizes the atmospheric motion in the vertical direction, and a strong, vertically uniform wind is found below the base of the heat source. When Rayleigh friction dominates, the circulation driven by the heat source is confined to the layer where the heat source is located. It is also shown that a strong Hadley circulation is associated with reasonable strong Rayleigh friction, but not with Newtonian cooling alone.

Finally, the numerical solution is found for the case where Newtonian cooling acts uniformly in the vertical *and* Rayleigh friction is included in the lower atmosphere to mimic crudely the dissipation of momentum in the boundary layer. The introduction of the simple boundary layer dramatically reduces the surface circulation that was supported in the Newtonian cooling alone case. Together these results suggest a significant surface circulation is unlikely to be driven by an elevated heat source if it resides above the top of the boundary layer.

## Abstract

An empirically derived linear dynamical model is constructed using the Comprehensive Oceanâ€“Atmosphere Data Set enhanced sea surface temperature data in the tropical Pacific during the period 1956â€“95. Annual variation in the Markov model is sought using various tests. A comparison of NiÃ±o-3.4 forecast skill using a seasonally varying Markov model to forecast skill in which the seasonal transition matrices are applied during opposite times of the year from which they were derived is made. As a result, it is determined that the seasonal transition matrices are probably not interchangeable, indicating that the Markov model is not annually constant. Stochastic forcing, which has been hypothesized to exhibit seasonality, is therefore not the sole source of the annual variation of El NiÃ±oâ€“Southern Oscillation (ENSO) dynamics and the phase locking of ENSO events to peak during November.

## Abstract

An empirically derived linear dynamical model is constructed using the Comprehensive Oceanâ€“Atmosphere Data Set enhanced sea surface temperature data in the tropical Pacific during the period 1956â€“95. Annual variation in the Markov model is sought using various tests. A comparison of NiÃ±o-3.4 forecast skill using a seasonally varying Markov model to forecast skill in which the seasonal transition matrices are applied during opposite times of the year from which they were derived is made. As a result, it is determined that the seasonal transition matrices are probably not interchangeable, indicating that the Markov model is not annually constant. Stochastic forcing, which has been hypothesized to exhibit seasonality, is therefore not the sole source of the annual variation of El NiÃ±oâ€“Southern Oscillation (ENSO) dynamics and the phase locking of ENSO events to peak during November.

## Abstract

In this paper, the three-dimensional structure of the thermally forced atmosphere on an equatorial *Î²* plane is investigated. Special emphasis is placed on the relations between the vertical structure of heating and the horizontal structure of the forced response.

By solving the vertical eigenvalueâ€“eigenfunction problem in a vertically semi-infinite domain, the authors obtain a complete set of vertical eigenfunctions that includes a single barotropic (external) mode and a continuous spectrum of baroclinic (internal) modes. These eigenfunctions are used to decompose vertical heating profiles for two types of tropical heating: 1) deep heating representing the convective plume (CP) heating and 2) shallow heating representing mature cloud (MC) cluster heating. By examining the spectral energy density of the heating profile, the contributions of each vertical mode (spectral interval) to the overall structure are explored for each case, and the difference between the responses to these two profiles of heating is discussed. A dry spectral primitive equation model of the atmosphere is employed to verify the analytical results.

The results from both the analytical approach and the numerical simulations are consistent in showing that the vertical structure of the heating is fundamental to the structure of the forced response. The CP is deep relative to the MC. Thus, the CP projects onto the vertical eigenfunctions of relatively larger equivalent depth more so than does the MC. As a result, the CP-forced signals propagate away from the heat source much faster than those forced by the MC. Hence, when the atmosphere is subjected to the same linear dampings (Rayleigh friction and Newtonain cooling), the spatial (mainly in the horizontal) decay rate of the CP-forced signals is significantly smaller than that of the MC-forced signals, and the CP-forced signals extend farther.

To what extent a shallow-water system of a specified vertical mode (e.g., the Gill model) can approximate the three-dimensional response is also examined. Results show that the effective gravity wave speed of the multimode system varies greatly with location. Hence, it is extremely difficult to select a globally suitable equivalent depth so that a one-mode shallow-water system can approximate the spatially three-dimensional structure of the response to a given heating.

## Abstract

In this paper, the three-dimensional structure of the thermally forced atmosphere on an equatorial *Î²* plane is investigated. Special emphasis is placed on the relations between the vertical structure of heating and the horizontal structure of the forced response.

By solving the vertical eigenvalueâ€“eigenfunction problem in a vertically semi-infinite domain, the authors obtain a complete set of vertical eigenfunctions that includes a single barotropic (external) mode and a continuous spectrum of baroclinic (internal) modes. These eigenfunctions are used to decompose vertical heating profiles for two types of tropical heating: 1) deep heating representing the convective plume (CP) heating and 2) shallow heating representing mature cloud (MC) cluster heating. By examining the spectral energy density of the heating profile, the contributions of each vertical mode (spectral interval) to the overall structure are explored for each case, and the difference between the responses to these two profiles of heating is discussed. A dry spectral primitive equation model of the atmosphere is employed to verify the analytical results.

The results from both the analytical approach and the numerical simulations are consistent in showing that the vertical structure of the heating is fundamental to the structure of the forced response. The CP is deep relative to the MC. Thus, the CP projects onto the vertical eigenfunctions of relatively larger equivalent depth more so than does the MC. As a result, the CP-forced signals propagate away from the heat source much faster than those forced by the MC. Hence, when the atmosphere is subjected to the same linear dampings (Rayleigh friction and Newtonain cooling), the spatial (mainly in the horizontal) decay rate of the CP-forced signals is significantly smaller than that of the MC-forced signals, and the CP-forced signals extend farther.

To what extent a shallow-water system of a specified vertical mode (e.g., the Gill model) can approximate the three-dimensional response is also examined. Results show that the effective gravity wave speed of the multimode system varies greatly with location. Hence, it is extremely difficult to select a globally suitable equivalent depth so that a one-mode shallow-water system can approximate the spatially three-dimensional structure of the response to a given heating.

## Abstract

An atmospheric GCM coupled to a slab ocean model is used to investigate how temperature and precipitation over South America and Africa affect the annual cycle of the Atlantic ITCZ. The main conclusion of this study is that variations in precipitation and temperature forced by the annual cycle of insolation over the continents are as important as variations in insolation over the ocean and in ocean heat transport convergence in forcing the annual march of the Atlantic ITCZ observed in the control simulation. The processes involved are as follows.

The intensity of precipitation over land affects the stability of the atmosphere over the tropical Atlantic Ocean, and thus modulates the intensity of deep convection and convergence in the ITCZ. Both the imposed changes in land precipitation and the subsequent changes in the strength of the ITCZ drive surface wind anomalies, thereby changing the meridional gradient of SST in proximity of the basic-state ITCZ. Finally, atmosphereâ€“ocean feedbacks cause the ITCZ to be displaced meridionally.

Seasonal changes in surface temperature in the Sahara also have a strong influence on the position of the Atlantic ITCZ. Cold wintertime temperatures produce high surface pressure anomalies over Africa and into the tropical North Atlantic and drive stronger trade winds, which cool the North Atlantic by evaporation. The coupled interactions between the SST, the wind, and the ITCZ intensify the anomalies in the equatorial region, causing the southward displacement of the ITCZ in boreal spring.

## Abstract

An atmospheric GCM coupled to a slab ocean model is used to investigate how temperature and precipitation over South America and Africa affect the annual cycle of the Atlantic ITCZ. The main conclusion of this study is that variations in precipitation and temperature forced by the annual cycle of insolation over the continents are as important as variations in insolation over the ocean and in ocean heat transport convergence in forcing the annual march of the Atlantic ITCZ observed in the control simulation. The processes involved are as follows.

The intensity of precipitation over land affects the stability of the atmosphere over the tropical Atlantic Ocean, and thus modulates the intensity of deep convection and convergence in the ITCZ. Both the imposed changes in land precipitation and the subsequent changes in the strength of the ITCZ drive surface wind anomalies, thereby changing the meridional gradient of SST in proximity of the basic-state ITCZ. Finally, atmosphereâ€“ocean feedbacks cause the ITCZ to be displaced meridionally.

Seasonal changes in surface temperature in the Sahara also have a strong influence on the position of the Atlantic ITCZ. Cold wintertime temperatures produce high surface pressure anomalies over Africa and into the tropical North Atlantic and drive stronger trade winds, which cool the North Atlantic by evaporation. The coupled interactions between the SST, the wind, and the ITCZ intensify the anomalies in the equatorial region, causing the southward displacement of the ITCZ in boreal spring.

## Abstract

The authors present a new model of the tropical surface circulation, forced by changes in sensible heat and evaporative flux anomalies that are associated with prescribed sea surface temperature anomalies. The model is similar to the Lindzen and Nigam (LN) boundary layer model, also driven by the above flux anomalies; but here, since the boundary layer is assumed well mixed and capped by an inversion, the model reduces to a two-layer, reduced-gravity system. Furthermore, the rate of exchange of mass across the boundary layerâ€“free atmosphere interface is dependent on the moisture budget in the boundary layer. When moist convection is diagnosed to occur, detrainment operates on the timescale associated with the life cycle of deep convection, approximately eight hours. Otherwise, the detrainment is assumed to be associated with the mixing out of the stable tropical boundary layer, which has a timescale of about one day. The model provides a diagnostic estimate of the anomalies in precipitation. However, it is assumed that the latent heat is released above the boundary layer, and it drives a circulation that does not impact the boundary layer.

The authors discuss the derivations of the Gillâ€“Zebiak (GZ) and Lindzenâ€“Nigam models and highlight some apparent inconsistencies between their derivation and the values of several of the parameters that are required for these models to achieve realistic solutions for the circulations. Then, the new reduced-gravity boundary model equations are rewritten in the form of the GZ and LN models. Using realistic values for the parameters in the new model geometry, it is shown that the constants combine in the rewritten equations to produce the physically doubtful constants in the GZ and LN models, hence, the reason for the apparent success of these models.

## Abstract

The authors present a new model of the tropical surface circulation, forced by changes in sensible heat and evaporative flux anomalies that are associated with prescribed sea surface temperature anomalies. The model is similar to the Lindzen and Nigam (LN) boundary layer model, also driven by the above flux anomalies; but here, since the boundary layer is assumed well mixed and capped by an inversion, the model reduces to a two-layer, reduced-gravity system. Furthermore, the rate of exchange of mass across the boundary layerâ€“free atmosphere interface is dependent on the moisture budget in the boundary layer. When moist convection is diagnosed to occur, detrainment operates on the timescale associated with the life cycle of deep convection, approximately eight hours. Otherwise, the detrainment is assumed to be associated with the mixing out of the stable tropical boundary layer, which has a timescale of about one day. The model provides a diagnostic estimate of the anomalies in precipitation. However, it is assumed that the latent heat is released above the boundary layer, and it drives a circulation that does not impact the boundary layer.

The authors discuss the derivations of the Gillâ€“Zebiak (GZ) and Lindzenâ€“Nigam models and highlight some apparent inconsistencies between their derivation and the values of several of the parameters that are required for these models to achieve realistic solutions for the circulations. Then, the new reduced-gravity boundary model equations are rewritten in the form of the GZ and LN models. Using realistic values for the parameters in the new model geometry, it is shown that the constants combine in the rewritten equations to produce the physically doubtful constants in the GZ and LN models, hence, the reason for the apparent success of these models.

## Abstract

Empirical dynamical modeling (EDM) is employed to determine if ENSO forecasting skill using monthly mean SST data can be enhanced by including subsurface temperature anomaly data. The NiÃ±o 3.4 index is forecast first using an EDM constructed from the principal component time series corresponding to EOFs of SST anomaly maps of the central and eastern tropical Pacific (32Â°Nâ€“32Â°S, 120Â°Eâ€“70Â°W) for the period 1965â€“93. Cross validation is applied to minimize the artificial skill of the forecasts, which are made over the same 29-yr period. The forecasting is then repeated with the inclusion of principal components of heat content of the upper 300 m over the northern tropical Pacific (30Â°Nâ€“0Â°, 120Â°Eâ€“72Â°W).

The forecast skill using SST alone and SST plus subsurface temperature is compared for lead times ranging between 3 and 12 months. The EDM, which includes the subsurface information, forecasts with greater skill at all lead times; particularly important is the second principal component of the heat content, which appears to contribute information on the transition phase between warm and cold ENSO events. The apparent improvement by including subsurface information, although robust, does not appear to be statistically significant. However, the temporal and spatial coverage of the subsurface data is limited, so this study probably underestimates the usefulness of including subsurface temperature data in efforts to predict ENSO. Finally, cross-validated forecasts using a Markov model that includes an annual cycle are shown to be less skillful than forecasts using a seasonally invariant Markov model. The reason for this appears to be that dividing the data yields an insufficient database to derive an accurate Markov model.

## Abstract

Empirical dynamical modeling (EDM) is employed to determine if ENSO forecasting skill using monthly mean SST data can be enhanced by including subsurface temperature anomaly data. The NiÃ±o 3.4 index is forecast first using an EDM constructed from the principal component time series corresponding to EOFs of SST anomaly maps of the central and eastern tropical Pacific (32Â°Nâ€“32Â°S, 120Â°Eâ€“70Â°W) for the period 1965â€“93. Cross validation is applied to minimize the artificial skill of the forecasts, which are made over the same 29-yr period. The forecasting is then repeated with the inclusion of principal components of heat content of the upper 300 m over the northern tropical Pacific (30Â°Nâ€“0Â°, 120Â°Eâ€“72Â°W).

The forecast skill using SST alone and SST plus subsurface temperature is compared for lead times ranging between 3 and 12 months. The EDM, which includes the subsurface information, forecasts with greater skill at all lead times; particularly important is the second principal component of the heat content, which appears to contribute information on the transition phase between warm and cold ENSO events. The apparent improvement by including subsurface information, although robust, does not appear to be statistically significant. However, the temporal and spatial coverage of the subsurface data is limited, so this study probably underestimates the usefulness of including subsurface temperature data in efforts to predict ENSO. Finally, cross-validated forecasts using a Markov model that includes an annual cycle are shown to be less skillful than forecasts using a seasonally invariant Markov model. The reason for this appears to be that dividing the data yields an insufficient database to derive an accurate Markov model.

## Abstract

The annual cycle over land can be thought of as being forced locally by the direct action of the sun and remotely by circulations forced by regions of persistent precipitation organized primarily by SST and, secondarily, by land. This study separates these two sources of annual variability in order to indicate where and when the remote effects are important.

Two main sets of AGCM experiments were performed: one with fixed SST boundary conditions and seasonally varying insolation, another with fixed insolation and seasonally varying SST. For each experiment, the evolution of the annual cycle is presented as the differences from the reference month of March. The comparison of other months to March in the fixed-SST runs separates out the direct response of the landâ€“atmosphere system to the annual insolation changes overhead. Similarly, the same comparison in the annual cycle of the fixed-insolation runs reveals the response of the landâ€“atmosphere system to changes in SST.

Over most of the domain, insolation is the dominant forcing on land temperature during June and December, but SST dominates during September. Insolation determines the northâ€“south displacement of continental convection at the solstices and greatly modulates the intensity of precipitation over the tropical Atlantic Ocean.

The SST determines the location of the ITCZ over the oceans and influences continental precipitation in coastal regions and in the Sahel/Sudan region. In September, when SST deviations from the March reference values are largest, the SST influence on both precipitation and surface air temperature extends to most of the tropical land. SST is an important forcing for the surface air temperature in the Guinea highlands and northeast Brazil throughout the year.

## Abstract

The annual cycle over land can be thought of as being forced locally by the direct action of the sun and remotely by circulations forced by regions of persistent precipitation organized primarily by SST and, secondarily, by land. This study separates these two sources of annual variability in order to indicate where and when the remote effects are important.

Two main sets of AGCM experiments were performed: one with fixed SST boundary conditions and seasonally varying insolation, another with fixed insolation and seasonally varying SST. For each experiment, the evolution of the annual cycle is presented as the differences from the reference month of March. The comparison of other months to March in the fixed-SST runs separates out the direct response of the landâ€“atmosphere system to the annual insolation changes overhead. Similarly, the same comparison in the annual cycle of the fixed-insolation runs reveals the response of the landâ€“atmosphere system to changes in SST.

Over most of the domain, insolation is the dominant forcing on land temperature during June and December, but SST dominates during September. Insolation determines the northâ€“south displacement of continental convection at the solstices and greatly modulates the intensity of precipitation over the tropical Atlantic Ocean.

The SST determines the location of the ITCZ over the oceans and influences continental precipitation in coastal regions and in the Sahel/Sudan region. In September, when SST deviations from the March reference values are largest, the SST influence on both precipitation and surface air temperature extends to most of the tropical land. SST is an important forcing for the surface air temperature in the Guinea highlands and northeast Brazil throughout the year.

## Abstract

In this paper, the atmospheric circulations on an equatorial beta plane in response to steady tropical heating are investigated by analytically solving a set of linear equations. Special emphasis is placed on the horizontal structure of forced response under the different combinations of momentum damping and thermal damping, as well as the effect of the zonal domain on the forced responses. Two zonal domains are considered: a zonally cyclic domain and a zonally unbounded domain.

The linear model is decomposed in terms of the vertical eigenfunctions in a vertically semi-infinite domain. A new feature of the solution is the existence of a continuous spectrum corresponding to energy propagation out the top of the troposphere. The resulting shallow-water equations are then solved using a method similar to that of Gill.

Since the zonal decay scale is proportional to the inverse of the square root of the product of the Rayleigh friction rate and the Newtonian cooling rate, the solutions in a zonally unbounded domain can be good approximations for the solutions in a zonally cyclic domain only when both Rayleigh friction and Newtonian cooling are large enough. When either Rayleigh friction or Newtonian cooling is very weak, the solutions are essentially zonally uniform regardless of the longitudinal location of the heat source in a zonally cyclic domain except in a very narrow zone along the equator.

The characteristic meridional scale of the shallow-water system is the equatorial radius of deformation of the shallow-water system multiplied by the fourth root of the ratio between the Rayleigh friction rate and the Newtonian cooling rate. Therefore, the characteristic meridional scale is very large for the Rayleigh frictionâ€“dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian coolingâ€“dominant case the characteristic meridional scale is very small and the forced response is confined to the heating latitudes.

The implications of these solutions for both the thermally driven surface winds and the zonally uniform low-frequency variation in pressure and temperature in the upper half of the tropical troposphere are also discussed.

## Abstract

In this paper, the atmospheric circulations on an equatorial beta plane in response to steady tropical heating are investigated by analytically solving a set of linear equations. Special emphasis is placed on the horizontal structure of forced response under the different combinations of momentum damping and thermal damping, as well as the effect of the zonal domain on the forced responses. Two zonal domains are considered: a zonally cyclic domain and a zonally unbounded domain.

The linear model is decomposed in terms of the vertical eigenfunctions in a vertically semi-infinite domain. A new feature of the solution is the existence of a continuous spectrum corresponding to energy propagation out the top of the troposphere. The resulting shallow-water equations are then solved using a method similar to that of Gill.

Since the zonal decay scale is proportional to the inverse of the square root of the product of the Rayleigh friction rate and the Newtonian cooling rate, the solutions in a zonally unbounded domain can be good approximations for the solutions in a zonally cyclic domain only when both Rayleigh friction and Newtonian cooling are large enough. When either Rayleigh friction or Newtonian cooling is very weak, the solutions are essentially zonally uniform regardless of the longitudinal location of the heat source in a zonally cyclic domain except in a very narrow zone along the equator.

The characteristic meridional scale of the shallow-water system is the equatorial radius of deformation of the shallow-water system multiplied by the fourth root of the ratio between the Rayleigh friction rate and the Newtonian cooling rate. Therefore, the characteristic meridional scale is very large for the Rayleigh frictionâ€“dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian coolingâ€“dominant case the characteristic meridional scale is very small and the forced response is confined to the heating latitudes.

The implications of these solutions for both the thermally driven surface winds and the zonally uniform low-frequency variation in pressure and temperature in the upper half of the tropical troposphere are also discussed.

## Abstract

The authors examine the sensitivity of the Battisti coupled atmosphereâ€“ocean modelâ€”considered as a forecast model for the El NiÃ±oâ€“Southern Oscillation (ENSO)â€”to perturbations in the sea surface temperature (SST) field applied at the beginning of a model integration. The spatial structures of the fastest growing SST perturbations are determined by singular vector analysis of an approximation to the propagator for the linearized system. Perturbation growth about the following four reference trajectories is considered: (i) the annual cycle, (ii) a freely evolving model ENSO cycle with an annual cycle in the basic state, (iii) the annual mean basic state, and (iv) a freely evolving model ENSO cycle with an annual mean basic state. Singular vectors with optimal growth over periods of 3, 6, and 9 months are computed.

The magnitude of maximum perturbation growth is highly dependent on both the phase of the seasonal cycle and the phase of the ENSO cycle at which the perturbation is applied and on the duration over which perturbations are allowed to evolve. However, the spatial structure of the optimal perturbation is remarkably insensitive to these factors. The structure of the optimal perturbation consists of an eastâ€“west dipole spanning the entire tropical Pacific basin superimposed on a northâ€“south dipole in the eastern tropical Pacific. A simple physical interpretation for the optimal pattern is provided. In most cases investigated, there is only one structure that exhibits growth.

Maximum perturbation growth takes place for integrations that include the period Juneâ€“August, and the minimum growth for integrations that include the period Januaryâ€“April. Maxima in potential growth also occur for forecasts of ENSO onset and decay, while minima occur for forecasts initialized during the beginning of a warm event, after the transition from a warm to a cold event, and continuing through the cold event. The physical processes responsible for the large variation in the amplitude of the optimal perturbation growth are identified. The implications of these results for the predictability of short-term climate in the tropical Pacific are discussed.

## Abstract

The authors examine the sensitivity of the Battisti coupled atmosphereâ€“ocean modelâ€”considered as a forecast model for the El NiÃ±oâ€“Southern Oscillation (ENSO)â€”to perturbations in the sea surface temperature (SST) field applied at the beginning of a model integration. The spatial structures of the fastest growing SST perturbations are determined by singular vector analysis of an approximation to the propagator for the linearized system. Perturbation growth about the following four reference trajectories is considered: (i) the annual cycle, (ii) a freely evolving model ENSO cycle with an annual cycle in the basic state, (iii) the annual mean basic state, and (iv) a freely evolving model ENSO cycle with an annual mean basic state. Singular vectors with optimal growth over periods of 3, 6, and 9 months are computed.

The magnitude of maximum perturbation growth is highly dependent on both the phase of the seasonal cycle and the phase of the ENSO cycle at which the perturbation is applied and on the duration over which perturbations are allowed to evolve. However, the spatial structure of the optimal perturbation is remarkably insensitive to these factors. The structure of the optimal perturbation consists of an eastâ€“west dipole spanning the entire tropical Pacific basin superimposed on a northâ€“south dipole in the eastern tropical Pacific. A simple physical interpretation for the optimal pattern is provided. In most cases investigated, there is only one structure that exhibits growth.

Maximum perturbation growth takes place for integrations that include the period Juneâ€“August, and the minimum growth for integrations that include the period Januaryâ€“April. Maxima in potential growth also occur for forecasts of ENSO onset and decay, while minima occur for forecasts initialized during the beginning of a warm event, after the transition from a warm to a cold event, and continuing through the cold event. The physical processes responsible for the large variation in the amplitude of the optimal perturbation growth are identified. The implications of these results for the predictability of short-term climate in the tropical Pacific are discussed.

## Abstract

The stability and internal variability of the ocean's thermohaline circulation is investigated using a coarse-resolution general circulation model of an idealized ocean basin, in one hemisphere. The model circulation is driven, in addition to wind forcing, by restoring the surface temperature to prescribed values, and by specifying freshwater fluxes in the surface salinity budget (mixed boundary conditions). All forcing functions are constant in time.

The surface freshwater forcing is the dominant factor in determining the model's stability and internal variability. Increasing the relative importance of freshwater flux versus thermal forcing, in turn, one stable steady state of the model, two stable ones, one stable, and one unstable equilibrium, or no stable steady states at all are found. If the freshwater forcing is sufficiently strong, self-sustained oscillations exist in the deep-water formation rate, which last thousands of years. One type of oscillation occurs on the time scale of decades and is associated with the advection of high-latitude salinity anomalies. The other type has a diffusive time scale of centuries or longer and marks periods of complete absence of deep-water formation followed by violent overturning events (flushes).

When a stochastic component is added to the steady freshwater flux forcing, internal decadal variability persists if the background steady freshwater flux is sufficiently strong. Periodic flushes also exist under stochastic forcing; with increasing magnitude of the stochastic term the frequency of the flush events increases while their intensity decreases.

## Abstract

The stability and internal variability of the ocean's thermohaline circulation is investigated using a coarse-resolution general circulation model of an idealized ocean basin, in one hemisphere. The model circulation is driven, in addition to wind forcing, by restoring the surface temperature to prescribed values, and by specifying freshwater fluxes in the surface salinity budget (mixed boundary conditions). All forcing functions are constant in time.

The surface freshwater forcing is the dominant factor in determining the model's stability and internal variability. Increasing the relative importance of freshwater flux versus thermal forcing, in turn, one stable steady state of the model, two stable ones, one stable, and one unstable equilibrium, or no stable steady states at all are found. If the freshwater forcing is sufficiently strong, self-sustained oscillations exist in the deep-water formation rate, which last thousands of years. One type of oscillation occurs on the time scale of decades and is associated with the advection of high-latitude salinity anomalies. The other type has a diffusive time scale of centuries or longer and marks periods of complete absence of deep-water formation followed by violent overturning events (flushes).

When a stochastic component is added to the steady freshwater flux forcing, internal decadal variability persists if the background steady freshwater flux is sufficiently strong. Periodic flushes also exist under stochastic forcing; with increasing magnitude of the stochastic term the frequency of the flush events increases while their intensity decreases.