Abstract

A method is presented in which the adjoint of a four-dimensional variational data assimilation system (4D-Var) was used to compute the expected analysis and forecast error variances of linear functions of the ocean state vector. The power and utility of the approach are demonstrated using the Regional Ocean Modeling System configured for the California Current system. Linear functions of the ocean state vector were considered in the form of indices that characterize various aspects of the coastal upwelling circulation. It was found that for configurations of 4D-Var typically used in ocean models, reliable estimates of the expected analysis error variances can be obtained both for variables that are observed and unobserved. In addition, the contribution of uncertainties in the model control variables to the forecast error variance was also quantified. One particularly powerful and illuminating aspect of the adjoint 4D-Var approach to the forecast problem is that the contribution of individual observations to the predictability of the circulation can be readily computed. An important finding of the work presented here is that despite the plethora of available satellite observations, the relatively modest fraction of in situ subsurface observations sometimes exerts a significant influence on the predictability of the coastal ocean. Independent checks of the analysis and forecast error variances are also presented, which provide a direct test of the hypotheses that underpin the prior error and observation error estimates used during 4D-Var.

Abstract

Adjoint sensitivity analysis is used to study the New York Bight circulation for three idealized situations: an unforced buoyant river plume, and upwelling and downwelling wind forcing. A derivation of adjoint sensitivity is presented that clarifies how the method simultaneously addresses initial, boundary, and forcing sensitivities. Considerations of interpretation and appropriate definitions of sensitivity scalar indices are discussed. The adjoint method identifies the oceanic conditions and forcing that are “dynamically upstream” to a region or feature of interest, as well as the relative roles of the prior ocean state, forcing, and dynamical influences. To illustrate the method, which is quite general, the authors consider coastal sea surface temperature (SST) variability and define the adjoint scalar index as the temporal–spatial mean squared SST anomaly on a segment of the New Jersey coast at the conclusion of a 3-day period. In the absence of wind, surface temperature advection dominates the SST anomaly with two sources of surface water identified. Downwelling winds amplify upstream advective influence. Sensitivity to temperature is separated into direct advection and the dynamic effect on density stratification and mixing. For upwelling conditions, this decomposition shows that coastal SST is controlled by both advection from the south and subsurface, but above the 5-m depth, and temperature-related density stratification between 5 and 15 m to 10 km offshore. By identifying the timing and location of ocean conditions crucial to subsequent prediction of specific circulation features, the adjoint sensitivity method has application to quantitative evaluation of observational sampling strategies.

Abstract

Adjoint methods of sensitivity analysis were applied to the California Current using the Regional Ocean Modeling Systems (ROMS) with medium resolution, aimed at diagnosing the circulation sensitivity to variations in surface forcing. The sensitivities of coastal variations in SST, eddy kinetic energy, and baroclinic instability of complex time-evolving flows were quantified. Each aspect of the circulation exhibits significant interannual and seasonal variations in sensitivity controlled by mesoscale circulation features. Central California SST is equally sensitive to wind stress and surface heat flux, but less so to wind stress curl, displaying the greatest sensitivity when upwelling-favorable winds are relaxing and the least sensitivity during the peak of upwelling. SST sensitivity is typically 2–4 times larger during summer than during spring, although larger variations occur during some years.

The sensitivity of central coast eddy kinetic energy to surface forcing is constant on average throughout the year. Perturbations in the wind that align with mesoscale eddies to enhance the strength of the circulation by local Ekman pumping yield the greatest sensitivities.

The sensitivity of the potential for baroclinic instability is greatest when nearshore horizontal temperature gradients are largest, and it is associated with variations in wind stress concentrated along the core of the California Current. The sensitivity varies by a factor of ∼1.5 throughout the year. A new and important aspect of this work is identification of the complex flow dependence and seasonal dependence of the sensitivity of the ROMS California Current System (CCS) circulation to variations in surface forcing that was hitherto not previously appreciated.

Abstract

Using a hydrocast survey of the Iceland-Faroe Front (IFF) from October 1992, quasigeostrophic forecasts are studied to validate their efficacy and to diagnose the physical processes involved in the rapid growth of a cold tongue intrusion. Explorations of 1) the choice of initial objective analysis parameters, 2) the depth of the unknown level of no motion, 3) the effects of surrounding mesoscale activity, 4) variations in the boundary conditions, and 5) simple assimilation of newly acquired data into the forecasts are carried out.

Using a feature validation technique, which incorporates a 1) validating hydrocast survey, 2) satellite SST images, and 3) surface drifter observations, most of the forecasts are found to perform well in capturing the key events of the validation strategy, particularly the development of the cold tongue intrusion (though it tends to develop somewhat more weakly and slightly farther downstream than observed). Sharp resolution of frontal structure (to capture seed anomalies in the IFF, which later can grow to large amplitude) and smooth representation of far-field boundary conditions (to eliminate spurious persistent inflow/outflow at the boundaries, which can corrupt developing interior flows) are found to be crucial in generating good forecasts.

An analysis of the potential and kinetic energy equations in the region of the developing cold tongue intrusion reveals a clear signature of baroclinic instability. Topography has little influence on this particular instability event because it tends to be surface intensified and occurs rapidly over a timescale of 3–5 days.