Time-lagged Ensemble Model Verification for Short-term Prediction of Drifter Trajectories

Predicting trajectories of objects at the ocean’s surface, such as oil slicks or their utilization in search-and-rescue operations, relies heavily on underlying geophysical models. Uncertainties are inevitably present in the modeled ocean and atmospheric fields, and are inherited by the Lagrangian models, thus limiting drift forecasts up to a few days. Estimating and subsequently addressing the uncertainty of the background hydrodynamic model is critical for short-window response and preparedness. Uncertainty estimation in drift modeling has traditionally been performed by varying the magnitude of the so-called wind drift factor. Such an approach results essentially in a greater diffusion of the cloud of virtual particles as the geophysical dynamic system is fundamentally the same. This can be overcome by perturbing by hydrodynamic ensemble generation through e.g. initial condition and surface forcing perturbations.

To derive estimates of the uncertainties, we evaluate short-term (1-5 days) trajectory forecasts forced by the Barents-2.5 km operational ensemble prediction system (EPS) against observed trajectories of undrogued drifters deployed in Fram Strait and Barents Sea. Seventeen low-cost devices (OpenMetBuoy) were deployed in sea ice free conditions during two field campaigns in April and August 2022, respectively, with life spans varying between 10 days and 10 months. Using 48 time-lagged ensemble members, the uncertainty in drift predictions is quantified via error/spread ratio, two-dimensional (2D) rank histograms and reliability diagrams. The ability of the EPS to capture physical processes is verified through rotary auto- and cross-spectral analysis on 5-day segments.

Our results show that the EPS manages to capture the main rotary spectral features well, but it underestimates with up to two orders of magnitude the spectral energy density towards the higher frequencies (> 0.08 cycles per hour) for both regions. High coherence (> 0.7) between observed and modeled drifter velocities, obtained through rotary cross-spectral, was found for the Barents Sea region, decreasing to less than 0.4 for the simulations performed in the Fram Strait. Additionally, we did not find indications that the observed and modeled drifter velocities are coherent to each other relative to the wind forcing in the latter area. 

The error/spread and 2D rank histograms revealed that Barents-2.5 is underdispersive, with the Fram Strait simulations presenting higher deviation from the ideal uniform distribution and higher error/spread (2.5-5) in comparison to the Barents Sea case (1-2). Despite its lack of dispersion, the EPS is nonetheless reliable in the Barents Sea for cumulative traveled distances up to approximately 1 inertial cycle. In Fram Strait, the model over- (under-) estimates trajectory displacements for super- (sub-) inertial frequencies.

Three key outcomes are highlighted in this work: (1) Forcing simulations with wind observations marginally improves the energy spectral density, indicating that modeling improvements should focus on the ocean model; (2) Adding further ensemble members through time-lagging does not necessarily improve ensemble dispersion; (3) Ensemble underdispersion does not imply lack of reliability if the main driving forces (e.g. wind and tides) are well resolved by the model.