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The utility of a Kalman filter (KF) for initialization of an intermediate nonlinear coupled model for El Nino-Southern Oscillation prediction is studied via an approximation of the nonlinear coupled model by a system of seasonally dependent linear models. The low-dimensional nature of such an approximation allows one to determine a sequence of “perfect” initial states that start a trajectory segment best fitting the observed data. Defining these perfect initial conditions as “true” states of the model, we compute a priori parameters of the KF and test its ability to produce an estimate of the “truth” superior to the less theoretically sound estimates. We find that in this application such a KF does not produce an estimate outperforming a pure observational projection as an initial condition for the coupled model forecast. The violation of standard KF assumptions on temporal whiteness of observational errors and system noise is identified as the reason for this failure.

Decadal variability in upper ocean temperature in the Pacific is studied by using observations and results from model experiments. Especially propagation of upper ocean thermal anomalies from the midlatitudes to the tropics is studied as a possible source for decadal equatorial thermocline variability. In the observations, propagation along the subtropical gyre of the North Pacific is clear. However, no propagation into the equatorial region is found. Model experiments with an ocean model forced with observed monthly wind and wind stress anomalies are performed to study the apparent propagation. Distinct propagation of thermal anomalies in the subtropics is found in the model, although the amplitude of the anomalies is small. The anomalies clearly propagate into the tropics, but they do not reach the equatorial region. The small response at the equator to extratropical variability consists of a change in the mean depth of the thermocline. It appears that most variability in the subtropics and tropics is generated by local wind stress anomalies. The results are discussed by using results from a linear shallow water model in which similar features are found.

A modeling study of the bomb 14C transient is presented for the Pacific Ocean. A primitive equation ocean circulation model has been configured for a high-resolution domain that accounts for the Indonesian Throughflow (ITF). Four separate runs were performed: (1) seasonal forcing with 20 Sv of ITF transport, (2) seasonal forcing with 10 Sv of ITF transport, (3) seasonal forcing with no ITF transport, and (4) interannual forcing with 15 Sv of ITF transport. This study has two main objectives. First, it is intended to describe the time evolution of the bomb 14C transient. This serves as a tool with which one can identify the physical processes controlling the evolving bomb 14C distribution in the Pacific thermocline and thus provides an interpretive framework for the database of Δ14C measurements in the Pacific. Second, transient tracers are applied to the physical oceanographic problem of intergyre exchange. This is of importance in furthering our understanding of the potential role of the upper Pacific Ocean in climate variability. We use bomb 14C as a dye tracer of intergyre exchange between the subtropical gyres and the equatorial upwelling regions of the equatorial Pacific. Observations show that while the atmospheric Δ14C signal peaked in the early to mid-1960s, the Δ14C levels in the surface water waters of the subtropical gyres peaked near 1970, and the Δ14C of surface waters in the equatorial Pacific continued to rise through the 1980s. It is shown that the model exhibits skill in representing the large-scale observed features observed for the bomb 14C transient in the Pacific Ocean. The model successfully captures the basin-scale inventories of bomb 14C in the tropics as well as in the extratropics of the North Pacific. For the equatorial Pacific this is attributed to the model's high meridional resolution. The discrepancies in the three-dimensional distribution of bomb 14C between the model and data are discussed within the context of the dynamical controls on the Δ14C distribution of bomb 14C in the Pacific.

The role of the Indonesian Throughflow (ITF) in the thermocline circulation of the low-latitude Pacific Ocean is explored using a high-resolution primitive equation ocean circulation model. Seasonally forced runs for a domain with an open Indonesian passage are compared with seasonally forced runs for a closed Pacific domain. Three cases are considered: one with no throughflow, one with 10 Sv of imposed ITF transport, and one with 20 Sv of ITF transport. Two idealized tracers, one that tags northern component subtropical water and another that tags southern component subtropical water, are used to diagnose the mixing ratio of northern and southern component waters in the equatorial thermocline. It is found that the mixing ratio of north/south component waters in the equatorial thermocline is highly sensitive to whether the model accounts for an ITF. Without an ITF, the source of equatorial undercurrent water is primarily of North Pacific origin, with the ratio of northern to southern component water being approximately 2.75 to 1. The ratio of northern to southern component water in the Equatorial Undercurrent with 10 Sv of ITF is approximately 1.4 to 1, and the ratio with 20 Sv of imposed ITF is 1 to 1.25. Estimates from data suggest a mean mixing ratio of northern to southern component water of less than 1 to 1. Assuming that the mixing ratio changes approximately linearly as the ITF transport varies between 10 and 20 Sv, an approximate balance between northern and southern component water is reached when the ITF transport is approximately 16 Sv. It is also shown that for the isopycnal surfaces within the core of the equatorial undercurrent, a 2°C temperature front exists across the equator in the western equatorial Pacific, beneath the warm pool. The implications of the model results and the temperature data for the heat budget of the equatorial Pacific are considered.

Using the NASA scatterometer (NSCAT) winds for initialization has greatly improved the Lamont-Doherty Earth Observatory model forecasts of the 1997/1998 E1 Nifio. The improvement is mostly attributed to the better resolved wind field in the southeast tropical Pacific. Because of the simplicity of the model and the short record of the NSCAT data, our model results should be taken as indicative rather than conclusive. Nevertheless, it is crucial to assimilate accurate information into the initial model state to predict the development of E1 Nifio. Satellite-derived wind products certainly have the potential to provide such information for real-time forecasting.

The effects of temporal and spatial smoothing of wind forcing were evaluated in a model simulation of the tropical Pacific Ocean variability during the onset phase of the 1997/1998 El Nino. A total of 16 experiments were performed using the NASA scatterometer wind data smoothed at time intervals from 1 to 30 days and on spatial scales from 1° to 10°. A major effect of the temporal smoothing of winds is to warm sea surface temperature (SST) by reducing the energy input for vertical turbulent mixing. When the daily wind forcing was replaced by the monthly average, the mean SST increased by 0.5° to 1° over most of the tropical Pacific. The spatial smoothing of winds is not as effective as the temporal smoothing in causing SST warming, but it has a more severe influence on dynamical ocean response for smoothing scales above 5°. The onset of the 1997/1998 El Nino can be successfully simulated using the wind forcing averaged to monthly intervals and 2° squares. For climate models the spatial smoothing of wind forcing on scales larger than the width of the equatorial waveguide is a more serious limitation than the temporal smoothing on scales up to 1 month.

Global analyses of monthly sea surface temperature (SST) anomalies from 1856 to 1991 are produced using three statistically based methods: optimal smoothing (OS), the Kalrnan filter (KF) and optimal interpolation (OI). Each of these is accompanied by estimates of the error covariance of the analyzed fields. The spatial covariance function these methods require is estimated from the available data; the time-marching model is a first-order autoregressive model again estimated from data. The data input for the analyses are monthly anomalies from the United Kingdom Meteorological Office historical sea surface temperature data set (MOHSST5) (Parker et al., 1994) of the Global Ocean Surface Temperature Atlas (COSTA) (Bottoraley et al., 1990). These analyses are compared with each other, with COSTA, and with an analy- sis generated by projection (P) onto a set of empirical orthogonal functions (as in Smith et al. (1996)). In theory, the quality of the analyses should rank in the order OS, KF, OI, P, and COSTA. It is found that the first four give comparable results in the data-rich periods (1951-1991), but at times when data is sparse the first three differ significantly from P and COSTA. At these times the latter two often have extreme and fluctuating values, prima facie evidence of error. The statistical schemes are also verified against data not used in any of the analyses (proxy records derived from corals and air temperature records from coastal and island stations). We also present evidence that the analysis error estimates are indeed indicative of the quality of the products. At most times the OS and KF products are close to the OI product, but at times of especially poor coverage their use of information from other times is advantageous. The methods appear to reconstruct the major features of the global SST field from very sparse data. Comparison with other indications of the E1 Nifio - Southern Oscillation cycle show that the analyses provide usable information on interannual variability as far back as the 1860s.

A hierarchy of El Niño-Southern Oscillation (ENSO) prediction schemes has been developed during the Tropical Ocean-Global Atmosphere (TOGA) program which includes statistical schemes and physical models. The statistical models are, in general, based on linear statistical techniques and can be classified into models which use atmospheric (sea level pressure or surface wind) or oceanic (sea surface temperature or a measure of upper ocean heat content) quantities or a combination of oceanic and atmospheric quantities as predictors. The physical models consist of coupled ocean-atmosphere models of varying degrees of complexity, ranging from simplified coupled models of the “shallow water” type to coupled general circulation models. All models, statistical and physical, perform considerably better than the persistence forecast in predicting typical indices of ENSO on lead times of 6 to 12 months. The TOGA program can be regarded as a success from this perspective. However, despite the demonstrated predictability, little is known about ENSO predictability limits and the predictability of phenomena outside the tropical Pacific. Furthermore, the predictability of anomalous features known to be associated with ENSO (e.g., Indian monsoon and Sahel rainfall, southern African drought, and off-equatorial sea surface temperature) needs to be addressed in more detail. As well, the relative importance of different physical mechanisms (in the ocean or atmosphere) has yet to be established. A seasonal dependence in predictability is seen in many models, but the processes responsible for it are not fully understood, and its meaning is still a matter of scientific discussion. Likewise, a marked decadal variation in skill is observed, and the reasons for this are still under investigation. Finally, the different prediction models yield similar skills, although they are initialized quite differently. The reasons for these differences are also unclear.

A computationally efficient method for analyzing meteorological and oceanographic historical data sets has been developed. The method combines data reduction and least squares optimal estimation. The data reduction involves computing empirical orthogonal functions (EOFs) of the data based on their recent, high-quality portion and using a leading EOF subset as a basis for the analyzed solution and for fitting a first-order linear model of time transitions. We then formulate optimal estimation problems in terms of the EOF projection of the analyzed field to obtain reduced space analogues of the optimal smoother, the Kalman filter, and optimal interpolation techniques. All reduced space algorithms are far cheaper computationally than their full grid prototypes, while their solutions are not necessarily inferior since the sparsity and error in available data often make estimation of small-scale features meaningless. Where covariance patterns can be estimated from the available data, the analysis methods fill gaps, correct sampling errors, and produce spatially and temporally coherent analyzed data sets. As with classical least squares estimation, the reduced space versions also provide theoretical error estimates for analyzed values. The methods are demonstrated on Atlantic monthly sea surface temperature (SST) anomalies for 1856–1991 from the United Kingdom Meteorological Office historical sea surface temperature data set (version MOHSST5). Choice of a reduced space dimension of 30 is shown to be adequate. The analyses are tested by withholding a significant part of the data and prove to be robust and in agreement with their own error estimates; they are also consistent with a partially independent optimal interpolation (OI) analysis by Reynolds and Smith [1994] produced in the National Centers for Environmental Prediction (NCEP)(known as the NCEP OI analysis). A simple statistical model is used to depict the month-to-month SST evolution in the optimal smoother algorithm. Results are somewhat superior to both the Kalman filter, which relies less on the model, and the optimal interpolation, which does not use it at all. The method generalizes a few recent works on using a reduced space for data set analyses. Difficulties of methods which simply fit EOF patterns to observed data are pointed out, and the more complete analysis procedures developed here are suggested as a remedy.

The object of this modeling study is to identify the physical mechanisms responsible for seasonal variability in sea surface Δ14C for the equatorial Pacific Ocean. Analyses of Δ14C in corals from Guam, Galapagos, Fanning, and Canton reveal seasonal variability between 30 and 50 per mil during the 1970s and early 1980s. Given that this variability occurs on seasonal timescales, whereas air-sea isotopic equilibration occurs on a timescale of 5 to 10 years, the variability must be due to seasonal variability in the physical circulation of the ocean. We use the primitive equation ocean circulation model of Gent and Cane [1989], along with the hybrid mixed layer model of Chen et al. [1994a], to study the dynamical mechanisms responsible. Upwelling in the eastern equatorial Pacific brings up Δ14C-depleted waters, and air-sea exchange creates high Δ14C in the western equatorial Pacific, establishing horizontal gradients in sea surface Δ14C. Seasonally varying lateral advection, acting on these gradients, is the dominant mechanism for Δ14C variability in the equatorial Pacific. In addition to the runs which were forced with seasonally varying winds, a run which used interannual winds between 1971 and 1985 was performed. The substantial interannual Δ14C variability present in this run is associated with advective anomalies in the equatorial waveguide.

The well-known fact that tropical sea level can be usefully simulated by linear wind driven models recommends it as a realistic test problem for data assimilation schemes. Here we report on an assimilation of monthly data for the period 1975-1992 from 34 tropical Pacific tide gauges into such a model using a Kalman filter. We present an approach to the Kalman filter that uses a reduced state space representation for the required error covariance matrices. This reduction makes the calculation highly feasible. We argue that a more complete representation will be of no value in typical oceanographic practice, that in principle it is unlikely to be helpful, and that it may even be harmful if the data coverage is sparse, the usual case in oceanography. This is in part a consequence of ignorance of the correct error statistics for the data and model, but only in part. The reduced state space is obtained from a truncated set of multivariate empirical orthogonal functions (EOFs) derived from a long model run without assimilation. The reduced state space filter is compared with a full grid point Kalman filter using the same dynamical model for the period 1979-1985, assimilating eight tide gauge stations and using an additional seven for verification (Miller et al., 1995). Results are not inferior to the full grid point filter, even when the reduced filter retains only nine EOFs. Five sets of reduced space filter assimilations are run with all tide gauge data for the period 1975-1992. In each set a different number of EOFs is retained: 5, 9, 17, 32, and 93, accounting for 60, 70, 80, 90, and 99% of the model variance, respectively. Each set consists of 34 runs, in each of which one station is withheld for verification. Comparing each set to the nonassimilation run, the average rms error at the withheld stations decreases by more than 1 cm. The improvement is generally larger for the stations at lowest latitudes. Increasing the number of EOFs increases agreement with data at locations where data are assimilated; the added structures allow better fits locally. In contrast, results at withheld stations are almost insensitive to the number of EOFs retained. We also compare the Kalman filter theoretical error estimates with the actual errors of the assimilations. Features agree on average, but not in detail, a reminder of the fact that the quality of theoretical estimates is limited by the quality of error models they assume. We briefly discuss the implications of our work for future studies, including the application of the method to full ocean general circulation models and coupled models.