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Ziv Sirkes
and
Eli Tziperman

Abstract

Adjoint models are used for atmospheric and oceanic sensitivity studies in order to efficiently evaluate the sensitivity of a cost function (e.g., the temperature or pressure at some target time t f , averaged over some region of interest) with respect to the three-dimensional model initial conditions. The time-dependent sensitivity, that is the sensitivity to initial conditions as function of the initial time t i , may be obtained directly and most efficiently from the adjoint model solution. There are two approaches to formulating an adjoint of a given model. In the first (“finite difference of adjoint”), one derives the continuous adjoint equations from the linearized continuous forward model equations and then formulates the finite-difference implementation of the continuous adjoint equations. In the second (“adjoint of finite difference”), one derives the finite-difference adjoint equations directly from the finite difference of the forward model. It is shown here that the time-dependent sensitivity obtained by using the second approach may result in a very strong nonphysical behavior such as a large-amplitude two-time-step leapfrog computational mode, which may prevent the solution from being used for time-dependent sensitivity studies. This is an especially relevant problem now, as this second approach is the one used by automatic adjoint compilers that are becoming widely used. The two approaches are analyzed in detail using both a simple model and the adjoint of a primitive equations ocean general circulation model. It is emphasized that both approaches are valid as long as they are used for obtaining the gradient or sensitivity at a single time, as needed in data assimilation, for example. Criteria are presented for the choice of the appropriate adjoint formulation for a given problem.

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Ziv Sirkes
and
Eli Tziperman

Abstract

A damped oscillatory mode of the thermohaline circulation (THC), which may play a role in interdecadal climate variability, is identified in a global primitive equation model. This analysis is done under mixed boundary conditions using an adjoint of the primitive equation model.

The linearized versus nonlinear stability behavior of the model is studied by comparing the adjoint analysis to runs of the fully nonlinear model. It is shown that a steady-state solution obtained under larger amplitude freshwater surface forcing (and hence with a weaker North Atlantic overturning) is unstable, while a steady-state solution with stronger THC is stable. In a certain intermediate parameter regime it is found that the full nonlinear model state may be unstable, while the linearized analysis indicates that the model state is stable. It is proposed that this may be because either the instability mechanism at this intermediate regime is nonlinear or, while the model is linearly stable at this regime, it allows for temporary growth of small perturbations due to the non-normal nature of the problem.

A clear signal of variations is not found in the amplitude of the horizontal gyre circulation, possibly indicating that the gyre effect that was found in THC oscillations in some previous studies may not be essential for the existence of the THC oscillation. The long timescale of the oscillation in the present model also seems to indicate that the gyre effect may not be a main active participant in the thermohaline oscillation mechanism.

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Eli Galanti
,
Eli Tziperman
,
Matthew Harrison
,
Anthony Rosati
, and
Ziv Sirkes

Abstract

An experimental ENSO prediction system is presented, based on an ocean general circulation model (GCM) coupled to a statistical atmosphere and the adjoint method of 4D variational data assimilation. The adjoint method is used to initialize the coupled model, and predictions are performed for the period 1980–99. The coupled model is also initialized using two simpler assimilation techniques: forcing the ocean model with observed sea surface temperature and surface fluxes, and a 3D variational data assimilation (3DVAR) method, similar to that used by the National Centers for Environmental Prediction (NCEP) for operational ENSO prediction. The prediction skill of the coupled model initialized by the three assimilation methods is then analyzed and compared. The effect of the assimilation period used in the adjoint method is studied by using 3-, 6-, and 9-month assimilation periods. Finally, the possibility of assimilating only the anomalies with respect to observed climatology in order to circumvent systematic model biases is examined.

It is found that the adjoint method does seem to have the potential for improving over simpler assimilation schemes. The improved skill is mainly at prediction intervals of more than 6 months, where the coupled model dynamics start to influence the model solution. At shorter prediction time intervals, the initialization using the forced ocean model or the 3DVAR may result in a better prediction skill. The assimilation of anomalies did not have a substantial effect on the prediction skill of the coupled model. This seems to indicate that in this model the climatology bias, which is compensated for by the anomaly assimilation, is less significant for the predictive skill than the bias in the model variability, which cannot be eliminated using the anomaly assimilation. Changing the optimization period from 6 to 3 to 9 months showed that the period of 6 months seems to be a near-optimal choice for this model.

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Tal Ezer
,
George L. Mellor
,
Dong-Shan Ko
, and
Ziv Sirkes

Abstract

Two types of satellite data, Geosat altimeter data and sea surface temperature data (SST), are compared and evaluated for their usefulness in assimilation into a numerical model of the Gulf Stream region. Synoptic sea surface height (SSH) fields are derived from the SST data in the following way: first three-dimensional temperature and salinity analysis fields are obtained through the Optimum Thermal Interpolation System (OTIS), and then SSH fields are calculated using a primitive equation, free-surface, numerical model running in a diagnostic mode. The aforementioned SSH fields are compared with SSH fields obtained from the Geosat altimeter data. Use of Geosat data requires an estimate of the cream SSH field relative to the earth geoid. Three different methods to obtain the mean SSH field are demonstrated. The first method uses altimetry and SST data, the second uses a diagnostic calculation with climatological data; and the third uses prognostic numerical calculations. The three estimates compared favorably with each other and with estimates obtained elsewhere.

The comparison of the synoptic SSH fields derived from both data types reveals similarity in the Gulf Stream meanders and some mesoscale features, but shows differences in strength of eddies and in variability far from the Gulf Stream. Due to the smoothed nature of the OTIS analysis fields, the SSH derived from altimetry data has larger variability amplitudes compared to that derived from SST data.

The statistical interpolation method, which is used to interpolate altimetry data from satellite tracks onto the model grid, is also evaluated for its filtering effect and its sensitivity to different parameters. The SSH variability of the Gulf Stream was calculated from two years of the exact repeat mission of the Geosat satellite, where altimeter data were interpolated daily onto the model grid. It is suggested here that some of the underestimation of mesoscale variations by statistical interpolation methods, as indicated by previous studies, may be explained by the filtering effect of the scheme.

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Eli Galanti
,
Eli Tziperman
,
Matthew Harrison
,
Antony Rosati
,
Ralf Giering
, and
Ziv Sirkes

Abstract

One of the major factors determining the strength and extent of ENSO events is the instability state of the equatorial Pacific coupled ocean–atmosphere system and its seasonal variations. This study analyzes the coupled instability in a hybrid coupled model of the Indo–Pacific region, using the adjoint method for sensitivity studies.

It is found that the seasonal changes in the ocean–atmosphere instability strength in the model used here are related to the outcropping of the thermocline in the east equatorial Pacific. From July to December, when the thermocline outcrops over a wide area in the east Pacific, there is a strong surface–thermocline connection and anomalies that arrive as Kelvin waves from the west along the thermocline can reach the surface and affect the SST and thus the coupled system. Conversely, from February to June, when the thermocline outcropping is minimal, the surface decouples from the thermocline and temperature anomalies in the thermocline depth range do not affect the surface and dissipate within the thermocline. The role of vertical mixing rather than upwelling in linking vertical thermocline movements to SST changes is emphasized.

It is therefore suggested that the seasonal ocean–atmosphere instability strength in the equatorial Pacific is strongly influenced by the thermocline outcropping and its seasonal modulation, a physical mechanism that is often neglected in intermediate coupled models and that can be represented properly only in models that employ the full dynamics of the mixed layer.

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