Conditional Predictability in Assimilation: Ocean Frontogenesis Filaments

Ocean submesoscale frontogenesis features that are not directly dynamically observed are predictable conditioned on accurate placement of the observable ocean mesoscale field. Numerical experiments demonstrate that ocean frontogenesis filaments, of scales 10 to 20 km across and hundreds of km long, produce shallowing mixed layers in areas of ocean mesoscale activity, as diagnosed by the omega or vector that is the total derivative of the horizontal buoyancy gradient. Prediction of these filament features does not fall clearly into the two broad classes of environmental prediction: deterministic and non-deterministic. For the ocean, deterministic processes traditionally include processes such as tides, and these have benefited greatly from satellite observations of sea level. Nondeterministic mesoscale eddies in the ocean have reached the level of operational prediction with the regular delivery of altimeter sea surface height products. The new frontier for ocean prediction is the submesoscale, and this presents a challenge from the perspective of numerical representation, observation and assimilation capabilities. Submesoscale frontogenesis occurs in ocean areas in which the buoyancy field is under high strain, and these areas are typically associated with the edges of mesoscale eddies where buoyancy gradients and velocities are large. Submesoscale physics occur predominantly within the mixed layer due to ageostrophic motions forced by potential energy from horizontal density gradients that sharpen in the strained fronts of the mesoscale field. The spatial scales are small (order 10 km). Dynamical pressure gradients are likewise small, and thus the signal in sea surface height observed by satellite is below the noise level. Given the typical along ground track spacing of 6.5km and cross track distance of 300km, the filaments are not resolved by the satellite sea surface height, and since the frontogenesis effects are within the surface mixed layer they do not have large volume expansion impact on the observed values. Therefore, assimilation of satellite altimeter data does not directly affect the submesoscale frontogenesis predictability. However, prediction of submesoscale may still be achieved, and this is demonstrated through a series of Observation System Experiments (OSEs).

Predictability of frontogenesis filaments in the ocean is possible if the mesoscale field is accurately predicted because the filaments are deterministically connected to the mesoscale field velocity and buoyancy gradients. The ocean mesoscale field is non-deterministic, and satellite sea surface height and surface temperature observations are used to constrain error growth in cycling assimilation systems through assimilation. Through the OSE experiments, it is demonstrated that with no altimeter data, there is no skill in predicting either steric height or mixed layer depth spatial structure at scales of the mesoscale field or time scales less than 60 days. The experiments demonstrate that mesoscale representation accuracy increases as data streams are incrementally added. The time period from June 1994 through December 1995 is used with all permutations of 4 available satellite altimeter data streams assimilated into a 3km resolution ocean model covering the western Pacific Ocean. This area contains strong western boundary current, mesoscale and surface layer processes. The assimilation experiments are each run over the 1.5 year time period with a daily assimilation cycle. All experiments are forced with the same surface atmospheric stress, temperature and humidity, and all experiments start from the same initial condition except for the nature run that starts from an initial condition that is offset by 1 year. This allows nondeterministic features not constrained by the observations to deviate substantially between each experiment and the nature run. The comparison of the nature run that assimilates all data with the OSE experiment assimilating all data provides an estimate of the error floor that can be achieved with 4 satellite data streams. Additional experiments also include using only in situ and satellite sea surface temperature observations. Even with in situ and satellite SST observations, at scales of the ocean mesoscale, there is no skill in predicting mixed layer depth. Spatial correlation of mixed layer depth structure increases from a time-averaged value 0.21 with no altimeter observations to about 0.67 with one altimeter data source to 0.89 as all 4 altimeter data streams are added. The conclusion is that accurate prediction of the mesoscale field due to the assimilation of satellite data is leading to reconstruction of the small scale frontogenesis filaments and the subsequent impact on mixed layer. Thus, the submesoscale frontogenesis filaments are deterministically predictable conditioned on accurate prediction of the mesoscale.