Fits and Forecasts of eddies in the Iceland-Faroe Front

Ocean mesoscale eddy forecasting is typically limited by a number of factors, including inadequate initialization information, unknown boundary conditions, inaccurate model physics, and atmospheric forcing functions that must also be predicted. Moreover, establishing skill levels in mesoscale forecasting is also limited by inadequate validation data and the ambiguity of defining skill. It is of interest to explore the consequences of these issues to aid the development of mesoscale ocean forecasting techniques such as have been developed by the Harvard Ocean Modeling Group.
The region around the Iceland-Faroe Front (IFF) is vigorously unstable with rapidly evolving small-scale eddies and frontal meanders that have time scales as short as 2 days and length scales as small 10 km. A unique dataset for mesoscale forecasting experiments was collected in the IFF during August 1993. The data contains a relatively finely resolved initial hydrographic survey, an updating survey, and a final verification survey (Fig. 1). This data was used to make real-time forecasts at sea and the results have been evaluated quantitatively for forecast skill (pattern correlation and rms error) for both a primitive equation model (Robinson et al., 1996, BAMS, 243-259) and a quasigeostrophic model (Miller et al., 1995, JGR, 10,833-10,849).
Although the skill scores for those sets of forecasts were encouraging, there are many issues that can be explored with a dataset designed specifically for forecasting and validation. For example, the Initialization Survey was collected over a 3-day time interval which poses a problem with choosing synoptic initial conditions. Robinson et al. (1996) used a feature model strategy combined with optimal interpolation to launch forecasts from the end of the 3-day survey. Can a more objective initialization strategy that allows for this non-synopticity improve the skill of forecasts of independent data?
In this project, we examine the issues of initialization and verification of IFF ocean forecasts by applying an inverse method for initialization in two sets of experiments. The inverse method is similar to Bennett's (1992, Cambridge University Press, 346 pp.) representer method and Wunsch's (1996, Cambridge University Press, 442 pp.) Green's function approach, and enforces the dynamics as a strong constraint. We adjust only the most energetic scales of the model initial conditions to minimize the model-data misfit variance in the fitting time interval. This trucation is related to the ensemble Kalman filter discussed by van Leeuwen and Evensen (1996, MWR, 2898-2913) and by Lermusiaux (1997, dissertation, Harvard University, 402 pp.) for the same Harvard primitive equation model used here. We first test the inverse method by generating synthetic data, sampled in the same way the observations were collected, in `identical twin' predictability experiments. We then test our techniques on the observations to determine if the fits are successful and if forecast skill is enhanced over the results of Robinson et al. (1996).

RESULTS

A fitting procedure was tested and applied with the Harvard primitive equation model to non-synoptic hydrographic surveys of unstable current meandering of the Iceland-Faeroe Front. The initial conditions (including the fields outside the data domain) were adjusted with eddy-scale basis functions to optimize the model fit to the observations, with no additional forcing or adjustment of boundary conditions during the model runs.
The technique was first tested with an `identical twin' predictability experiment. This showed the inverse technique can successfully fit the non-synoptic Initialization Survey data, correct a large fraction of the initial condition error, and allow the model to move closer to the true evolution. However, although additional iterations of the fitting procedure could improve the fit to the Initialization Survey, the model could not be adjusted closer to the true initial state because of the limited initialization data. Moreover, the limited verification data was inadequate to show unambiguous forecast skill even for short 2-day forecasts which were known to have skill in the identical twin framework.
The PE model was then fit to the observed hydrographic data from August 1993 in several scenarios. With only a few iterations, temperature and salinity model-data misfit variance was reduced 70-80% relative to initializing the model from a time-independent objective analysis. The success of the fit was supported by qualitative realism of the frontal variability as described previously (Miller et al., 1995; Robinson et al., 1996).
The model run from the optimized initialization constitutes a possible dynamically consistent scenario explaining some of the variability seen in the IFF observations as a meandering of the front. To the extent that the model is accurate, the observations have been reconstructed into a four-dimensional picture of the flow field in the area. The results here set the stage for diagnostic analyses of the frontal baroclinic instabilities.
Although hindcast skill increased, quantitative forecast skill (measured by error variance) was not always increased relative to the time-independent OA initialization. Qualitative skill assessment proved necessary to distinguish the integrity of the hindcasts and forecasts, especially the occurrence of a hammerhead baroclinic instability of the IFF. Since the model was able to be successfully fit to the hammerhead instability, the incorrect forecasts of the hammerhead from the Zig-Zag Survey fits are most likely a consequence of inadequate initialization data. The highly nonlinear IFF variability leads to major differences in the evolution of flow from slightly different initial states (Figure 10). This suggests that finely resolved and nearly synoptic hydrography is necessary in the IFF to constrain the initialization. The successful hindcasts argue against inadequate model physics or incomplete basis functions as being the major factors limiting forecast skill. The quantitative forecast skill shown by Robinson et al. (1996), who used an optimal interpolation technique in real time, is comparable to what was obtained here for the hammerhead when the model was initialized from or fit to the antecedent (Zig-Zag) survey.
The main difference between this method and the representer method of Bennett (1992) is our use of the truncated set of basis functions. An adjoint model can give the grid point structure of the data sensitivity in the forward problem, but using smoothing assumptions (i.e. a covariance matrix) similar to those used here should lead to similar solutions. Due to non-linearity, the small-scale structure of the sensitivity is often less reliable than the large-scale structure. This is a justification for only fitting the larger scale structures.
An ocean model is a valuable tool for the interpolation and interpretation of data, as well as practical prediction problems, but it is dependent on obtaining adequate data for judging model quality. The techniques tested here could easily accommodate other data types, but the best type of data for constraining the model initializations and for testing forecasts skill would appear to be finely resolved synoptic hydrographic surveys as could be obtained from aerial XBT surveys. For this particular IFF dataset there are also drifter observations, current meter observations, and a satellite SST image which can be used in future applications of this technique to improve the fits and forecasts. Higher vertical resolution in the model is of greatest priority in improving the details of the model fit, especially the baroclinic structure of the hammerhead instability.

PUBLICATIONS

Miller, Arthur J., Bruce D. Cornuelle, 1999: Forecasts from fits of frontal fluctuations ,
Dynamics of Atmospheres and Oceans, 29, 305-333.

TEAM MEMBERS

Dr. Arthur J. Miller (CRD/SIO)

Dr. Bruce D. Cornuelle (PORD-CRD/SIO)