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## Abstract

The implicit vertical diffusion (IVD) convective adjustment scheme in common use in ocean general circulation models (OGCMs) could have large residual static gravitational instability at each time step. An iterative and explicit scheme is devised, based on similar physical considerations as the ones for the IVD scheme. It guarantees a complete removal of static instability in a vertical water column and is more efficient than the IVD scheme in overall spinup of the model.

The two convective schemes are compared in an ocean model that is in a state of interdecadal limit cycles. While the model solution with either of these two schemes is characterized by interdecadal oscillations, the variability is different in each scheme. The primary oscillation has a period of about 11 years, but the basin mean kinetic energy shows large differences. The 11-year cycle is modulated by a 33-year oscillation with the IVD scheme, while it is modulated by a 22-year cycle with the complete scheme. The amplitude of the variation of kinetic energy with the IVD scheme is also about twice as large as that with a complete adjustment scheme. It is therefore suggested that complete and incomplete convective schemes can lead to different model variability when convective changes in temperature and salinity have large variations over a short period of time.

## Abstract

The implicit vertical diffusion (IVD) convective adjustment scheme in common use in ocean general circulation models (OGCMs) could have large residual static gravitational instability at each time step. An iterative and explicit scheme is devised, based on similar physical considerations as the ones for the IVD scheme. It guarantees a complete removal of static instability in a vertical water column and is more efficient than the IVD scheme in overall spinup of the model.

The two convective schemes are compared in an ocean model that is in a state of interdecadal limit cycles. While the model solution with either of these two schemes is characterized by interdecadal oscillations, the variability is different in each scheme. The primary oscillation has a period of about 11 years, but the basin mean kinetic energy shows large differences. The 11-year cycle is modulated by a 33-year oscillation with the IVD scheme, while it is modulated by a 22-year cycle with the complete scheme. The amplitude of the variation of kinetic energy with the IVD scheme is also about twice as large as that with a complete adjustment scheme. It is therefore suggested that complete and incomplete convective schemes can lead to different model variability when convective changes in temperature and salinity have large variations over a short period of time.

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## Abstract

Oceanic interdecadal thermohaline oscillations are investigated with a coarse-resolution version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. The geometry of the model is a box with a depth of 5000 m and a longitudinal width of 60°, spanning latitudes from 14.5° to 66.5°N. The model ocean is forced by a zonal wind stress, a heat flux parameterized by restoring the surface temperature toward a reference value, and a specified surface freshwater flux. Zonal wind stress, reference temperature, and freshwater flux are all longitudinally uniform, time-independent, and vary meridionally.

It is shown that the ocean model can be in a state of interdecadal oscillations, and a physical mechanism is explained. For these oscillatory solutions, both surface mean heat flux and basin mean kinetic energy vary with interdecadal periods. Temperature and salinity budget analyses reveal that these oscillations depend primarily on advective and convective processes. Horizontal advective heat transports from the subtropical region warm the subsurface water in the subpolar region, destablize the water column, and thereby enhance convection. Convection, in turn, induces surface cyclonic and equatorward flows, which, together with horizontal diffusion and surface freshwater input, transport subpolar fresh water into convecting regions, subsequently weakening or suppressing convection. During an oscillation, convection vertically homogenizes the water column, increases the surface salinity, creates a larger meridional gradient of surface salinity, and increases the efficiency of surface advective freshening in the convective region. The periodic strengthening and weakening of convection caused by subsurface advective warming and surface freshening in the subpolar region results in model interdecadal oscillations.

These advective and convective interdecadal oscillations are not sensitive to either the detailed distribution of subpolar freshwater flux or the horizontal diffusivity. They are mainly a result of halocline and inverted thermocline structure in the subpolar region, maintained by horizontal advective subsurface heating and surface freshening processes.

## Abstract

Oceanic interdecadal thermohaline oscillations are investigated with a coarse-resolution version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. The geometry of the model is a box with a depth of 5000 m and a longitudinal width of 60°, spanning latitudes from 14.5° to 66.5°N. The model ocean is forced by a zonal wind stress, a heat flux parameterized by restoring the surface temperature toward a reference value, and a specified surface freshwater flux. Zonal wind stress, reference temperature, and freshwater flux are all longitudinally uniform, time-independent, and vary meridionally.

It is shown that the ocean model can be in a state of interdecadal oscillations, and a physical mechanism is explained. For these oscillatory solutions, both surface mean heat flux and basin mean kinetic energy vary with interdecadal periods. Temperature and salinity budget analyses reveal that these oscillations depend primarily on advective and convective processes. Horizontal advective heat transports from the subtropical region warm the subsurface water in the subpolar region, destablize the water column, and thereby enhance convection. Convection, in turn, induces surface cyclonic and equatorward flows, which, together with horizontal diffusion and surface freshwater input, transport subpolar fresh water into convecting regions, subsequently weakening or suppressing convection. During an oscillation, convection vertically homogenizes the water column, increases the surface salinity, creates a larger meridional gradient of surface salinity, and increases the efficiency of surface advective freshening in the convective region. The periodic strengthening and weakening of convection caused by subsurface advective warming and surface freshening in the subpolar region results in model interdecadal oscillations.

These advective and convective interdecadal oscillations are not sensitive to either the detailed distribution of subpolar freshwater flux or the horizontal diffusivity. They are mainly a result of halocline and inverted thermocline structure in the subpolar region, maintained by horizontal advective subsurface heating and surface freshening processes.

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## Abstract

Seasonal heat transport is examined in a simple, linear shallow-water model on the equatorial beta plane. It is found in this model that meridional transport by the seasonally varying western boundary current is of the same magnitude but opposite phase to the seasonally varying interior transport and therefore tends to cancel.

## Abstract

Seasonal heat transport is examined in a simple, linear shallow-water model on the equatorial beta plane. It is found in this model that meridional transport by the seasonally varying western boundary current is of the same magnitude but opposite phase to the seasonally varying interior transport and therefore tends to cancel.

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## Abstract

Restoring boundary conditions, wherein the temperature and salinity are restored to surface target fields of temperature and salinity, are traditionally used for studies of the ocean circulation in ocean general circulation models. The canonical problem with these boundary conditions is that, when the target fields are chosen as the observed fields, accurate simulation of the surface fields of temperature and salinity would imply that the surface fluxes and therefore the ocean heat transports approach zero, a clearly unrealistic situation. It is clear that the target fields cannot be chosen as the observed fields. A simple but effective method of modifying conventional restoring boundary conditions is introduced, designed to keep the calculated values of surface temperature and salinity as close to observations as possible. The technique involves calculating the optimal target fields in the restoring boundary conditions by an iterative procedure. The method accounts for oceanic processes, such as advection and eddy mixing in the derivation of the new boundary conditions. A reduced version of this method is introduced that produces comparable results but offers greater simplicity in implementation. The simplicity of the method is particularly attractive in idealized studies, which often employ restoring surface boundary conditions. The success of the new method is, however, limited by several factors that cannot be easily compensated by the adjustment of the target profiles. These factors include inaccurate model dynamics, errors in the observations, and the too-simplified form of restoring surface boundary conditions themselves. The application of the method in this study with a coarse-resolution model leads to considerable improvements of the simulation of sea surface temperature (SST) and sea surface salinity (SSS). Both amplitude and phase of the annual cycle in SST greatly improve. The resulting magnitudes of surface heat and freshwater fluxes increase on average, and the meridional heat transport gets stronger. However, the fluxes in some regions remain unrealistic, notably the too-strong freshwater forcing of the western boundary currents in the Northern Hemisphere. Southern Ocean cooling and freshening are also likely to be too strong. The subsurface values of temperature improve greatly, proving that a large part of errors in the subsurface temperature distribution in our model can be corrected by reducing errors at the surface. In contrast, the reduction of errors in surface salinity fails to improve uniformly the simulated subsurface salinity values.

## Abstract

Restoring boundary conditions, wherein the temperature and salinity are restored to surface target fields of temperature and salinity, are traditionally used for studies of the ocean circulation in ocean general circulation models. The canonical problem with these boundary conditions is that, when the target fields are chosen as the observed fields, accurate simulation of the surface fields of temperature and salinity would imply that the surface fluxes and therefore the ocean heat transports approach zero, a clearly unrealistic situation. It is clear that the target fields cannot be chosen as the observed fields. A simple but effective method of modifying conventional restoring boundary conditions is introduced, designed to keep the calculated values of surface temperature and salinity as close to observations as possible. The technique involves calculating the optimal target fields in the restoring boundary conditions by an iterative procedure. The method accounts for oceanic processes, such as advection and eddy mixing in the derivation of the new boundary conditions. A reduced version of this method is introduced that produces comparable results but offers greater simplicity in implementation. The simplicity of the method is particularly attractive in idealized studies, which often employ restoring surface boundary conditions. The success of the new method is, however, limited by several factors that cannot be easily compensated by the adjustment of the target profiles. These factors include inaccurate model dynamics, errors in the observations, and the too-simplified form of restoring surface boundary conditions themselves. The application of the method in this study with a coarse-resolution model leads to considerable improvements of the simulation of sea surface temperature (SST) and sea surface salinity (SSS). Both amplitude and phase of the annual cycle in SST greatly improve. The resulting magnitudes of surface heat and freshwater fluxes increase on average, and the meridional heat transport gets stronger. However, the fluxes in some regions remain unrealistic, notably the too-strong freshwater forcing of the western boundary currents in the Northern Hemisphere. Southern Ocean cooling and freshening are also likely to be too strong. The subsurface values of temperature improve greatly, proving that a large part of errors in the subsurface temperature distribution in our model can be corrected by reducing errors at the surface. In contrast, the reduction of errors in surface salinity fails to improve uniformly the simulated subsurface salinity values.

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## Abstract

The authors identify and describe the important dynamical mechanisms that explain the significant sensitivity of the Atlantic thermohaline circulation to the parameterization of heat and salt transports by mesoscale eddies in numerical models. In particular, the effects of the Gent–McWilliams (GM) scheme, which has a strong flattening effect on isopycnals, and a simple horizontal diffusion scheme are considered and compared. Two control runs, one with each scheme, exhibit very different circulations and density structures. To analyze the dynamical reasons for the differences between the control runs, a number of numerical experiments with regionally varying diffusion coefficients are carried out, emphasizing the effects of different schemes in key regions. The main effect of eddies in the Southern Ocean in nature is to shoal the subsurface isopycnal surfaces, thus increasing the density of the northward inflow of relatively dense intermediate waters into the Atlantic—as will be seen, this is more effectively done by the GM parameterization of the eddies. The resulting increase in the subsurface density at low latitudes decreases the meridional density contrast with the high latitudes of the North Atlantic, shoals the pycnocline, and consequently weakens the meridional overturning. By contrast, the effect of the eddy transports in the western boundary current in the Northern Hemisphere on the strength of the North Atlantic Deep Water (NADW) formation is shown to be smaller. The Northern Hemisphere upwelling and horizontal flow structure is strongly affected by local eddy transports, and the outflow of the NADW is very sensitive to the Northern Hemisphere eddy transports as a result. The original scaling of Gnanadesikan is modified to include the effects of horizontal mixing in low latitudes. The results confirm the leading role of the Southern Ocean eddies in affecting the strength of NADW formation, while the Northern Hemisphere horizontal mixing mostly affects local upwelling. The eddy transports in the Southern Ocean also affect the properties of Antarctic Bottom Water, which influences the vertical penetration of the NADW overturning cell as well as the density of the deep ocean.

## Abstract

The authors identify and describe the important dynamical mechanisms that explain the significant sensitivity of the Atlantic thermohaline circulation to the parameterization of heat and salt transports by mesoscale eddies in numerical models. In particular, the effects of the Gent–McWilliams (GM) scheme, which has a strong flattening effect on isopycnals, and a simple horizontal diffusion scheme are considered and compared. Two control runs, one with each scheme, exhibit very different circulations and density structures. To analyze the dynamical reasons for the differences between the control runs, a number of numerical experiments with regionally varying diffusion coefficients are carried out, emphasizing the effects of different schemes in key regions. The main effect of eddies in the Southern Ocean in nature is to shoal the subsurface isopycnal surfaces, thus increasing the density of the northward inflow of relatively dense intermediate waters into the Atlantic—as will be seen, this is more effectively done by the GM parameterization of the eddies. The resulting increase in the subsurface density at low latitudes decreases the meridional density contrast with the high latitudes of the North Atlantic, shoals the pycnocline, and consequently weakens the meridional overturning. By contrast, the effect of the eddy transports in the western boundary current in the Northern Hemisphere on the strength of the North Atlantic Deep Water (NADW) formation is shown to be smaller. The Northern Hemisphere upwelling and horizontal flow structure is strongly affected by local eddy transports, and the outflow of the NADW is very sensitive to the Northern Hemisphere eddy transports as a result. The original scaling of Gnanadesikan is modified to include the effects of horizontal mixing in low latitudes. The results confirm the leading role of the Southern Ocean eddies in affecting the strength of NADW formation, while the Northern Hemisphere horizontal mixing mostly affects local upwelling. The eddy transports in the Southern Ocean also affect the properties of Antarctic Bottom Water, which influences the vertical penetration of the NADW overturning cell as well as the density of the deep ocean.

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## Abstract

Four different datasets of monthly mean new-equatorial Pacific sea surface temperature for 1982–83 are compared, and the space-time regions for which there was consensus that cooling or warming took place, are determined. There was consensus that warming took place east of the date line, averaged over the period July-December 1982, and that the warming progressed eastward from the central Pacific. There was also consensus that weak cooling took place in April 1983, and that substantial cooling occurred in June-July 1983, generally over the central and eastern Pacific. However, the analyses tend to agree on the sign of SST change only in periods of cooling or warming in excess of 1°C/month; quantitative agreement at the level of 0.5°C/month or better is almost never found.

SST changes in five ocean-circulation model hindcasts of the 1982–83 period (differing only in that each used a different analyzed monthly mean surface wind stress field to drive the ocean), are compared with the observations and with each other. There is agreement that net warming occurred in the July-December 1982 period and cooling in mid-1983. The heat budgets of these experiments indicate that the major model central Pacific warmings occurred primarily from anomalous eastward surface advection of warm water. Further, east zonal advection remains significant but a diminished cooling tendency from meridional advection can also be important; different hindcasts differ on the relative importance of these terms. Surface heat flux changes do not contribute to the warmings. The reduced cooling tendency from meridional advection is consistent with diminished surface Ekman divergence, suggesting that southward transport of warm north equatorial counter current water was not a major factor in the model warmings. The hindcasts do not agree on the relative importance of local or remote forcing of the eastward surface currents; while there is clear evidence of remote forcing in some hindcasts in particular regions, local forcing is also often significant. The main 1983 midocean cooling began because of increased vertical advection of cool water; but once cooling began horizontal advection often contributed. Further east, where the easterlies generally return later than they do in midocean, upwelling and horizontal advection all can be important. Again no model consensus exists concerning the details of SST evolution.

Because the observations do not agree on the sign of SST change during much of the 1982–83 period, improved SST data is needed in order to document the behavior of the ocean through future ENSO periods. Better forcing data will be needed to carry out improved ocean-model validation studies, and to explore the mechanisms likely responsible for SST change through entire ENSO cycles.

## Abstract

Four different datasets of monthly mean new-equatorial Pacific sea surface temperature for 1982–83 are compared, and the space-time regions for which there was consensus that cooling or warming took place, are determined. There was consensus that warming took place east of the date line, averaged over the period July-December 1982, and that the warming progressed eastward from the central Pacific. There was also consensus that weak cooling took place in April 1983, and that substantial cooling occurred in June-July 1983, generally over the central and eastern Pacific. However, the analyses tend to agree on the sign of SST change only in periods of cooling or warming in excess of 1°C/month; quantitative agreement at the level of 0.5°C/month or better is almost never found.

SST changes in five ocean-circulation model hindcasts of the 1982–83 period (differing only in that each used a different analyzed monthly mean surface wind stress field to drive the ocean), are compared with the observations and with each other. There is agreement that net warming occurred in the July-December 1982 period and cooling in mid-1983. The heat budgets of these experiments indicate that the major model central Pacific warmings occurred primarily from anomalous eastward surface advection of warm water. Further, east zonal advection remains significant but a diminished cooling tendency from meridional advection can also be important; different hindcasts differ on the relative importance of these terms. Surface heat flux changes do not contribute to the warmings. The reduced cooling tendency from meridional advection is consistent with diminished surface Ekman divergence, suggesting that southward transport of warm north equatorial counter current water was not a major factor in the model warmings. The hindcasts do not agree on the relative importance of local or remote forcing of the eastward surface currents; while there is clear evidence of remote forcing in some hindcasts in particular regions, local forcing is also often significant. The main 1983 midocean cooling began because of increased vertical advection of cool water; but once cooling began horizontal advection often contributed. Further east, where the easterlies generally return later than they do in midocean, upwelling and horizontal advection all can be important. Again no model consensus exists concerning the details of SST evolution.

Because the observations do not agree on the sign of SST change during much of the 1982–83 period, improved SST data is needed in order to document the behavior of the ocean through future ENSO periods. Better forcing data will be needed to carry out improved ocean-model validation studies, and to explore the mechanisms likely responsible for SST change through entire ENSO cycles.

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## Abstract

The vertical structure of the low-level atmospheric response to an elevated large-scale, low-frequency heat source in the Tropics is explored using linear tidal theory on an equatorial beta plane. Through the calculation of the projection of a large-scale, low-frequency thermal source onto the meridional eigenfunctions, the contributions from a set of discrete meridional eigenfunctions with positive equivalent depths, and a continuous spectrum of meridional eigenfunctions with negative equivalent depth, are examined. The positive equivalent depth eigenfunctions have been discussed in some literature while the continuous spectrum of the negative equivalent depth eigenfunctions is new. The authors find that, at lower frequencies, the forced response is mainly supported by those continuous modes for which the absolute values of the negative equivalent depths are neither very small nor very large.

The implications of these results for thermally driven surface winds are discussed and summarized by and . In the inviscid case, since the solution associated with the continuous modes with negative equivalent depth is vertically evanescent, it is expected that the vertical energy transfer from the elevated thermal source to the surface is limited. However, in the presence of Newtonian cooling, the continuous modes that contribute significantly to accounting for the large-scale heat source are those modes with moderate values of negative equivalent depth as frequencies goes to zero so that the forced horizontal winds become vertically uniform below the heating. Hence, surface winds can be driven by the elevated heat source in the presence of only linear thermal damping.

## Abstract

The vertical structure of the low-level atmospheric response to an elevated large-scale, low-frequency heat source in the Tropics is explored using linear tidal theory on an equatorial beta plane. Through the calculation of the projection of a large-scale, low-frequency thermal source onto the meridional eigenfunctions, the contributions from a set of discrete meridional eigenfunctions with positive equivalent depths, and a continuous spectrum of meridional eigenfunctions with negative equivalent depth, are examined. The positive equivalent depth eigenfunctions have been discussed in some literature while the continuous spectrum of the negative equivalent depth eigenfunctions is new. The authors find that, at lower frequencies, the forced response is mainly supported by those continuous modes for which the absolute values of the negative equivalent depths are neither very small nor very large.

The implications of these results for thermally driven surface winds are discussed and summarized by and . In the inviscid case, since the solution associated with the continuous modes with negative equivalent depth is vertically evanescent, it is expected that the vertical energy transfer from the elevated thermal source to the surface is limited. However, in the presence of Newtonian cooling, the continuous modes that contribute significantly to accounting for the large-scale heat source are those modes with moderate values of negative equivalent depth as frequencies goes to zero so that the forced horizontal winds become vertically uniform below the heating. Hence, surface winds can be driven by the elevated heat source in the presence of only linear thermal damping.

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## 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 friction–dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian cooling–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 friction–dominant case, and the forced response can extend far outside the heating latitude. In contrast, in the Newtonian cooling–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.

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## 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 Niño 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 (32°N–32°S, 120°E–70°W) for the period 1965–93. 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 (30°N–0°, 120°E–72°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 Niño 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 (32°N–32°S, 120°E–70°W) for the period 1965–93. 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 (30°N–0°, 120°E–72°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.

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## Abstract

An empirically derived linear dynamical model is constructed using the Comprehensive Ocean–Atmosphere Data Set enhanced sea surface temperature data in the tropical Pacific during the period 1956–95. Annual variation in the Markov model is sought using various tests. A comparison of Niño-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 Niño–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 Ocean–Atmosphere Data Set enhanced sea surface temperature data in the tropical Pacific during the period 1956–95. Annual variation in the Markov model is sought using various tests. A comparison of Niño-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 Niño–Southern Oscillation (ENSO) dynamics and the phase locking of ENSO events to peak during November.