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An Operational Search and Rescue Model for the Norwegian Sea and the North Sea
Øyvind Breivik, Arthur A Allen
TL;DR
Maritime search and rescue needs rapid search-area forecasts despite uncertain object motion and environmental forcing. The paper develops an operational Monte Carlo trajectory model using empirical leeway components and operational wind and current fields. The ensemble produces evolving search-area probabilities, while higher-order stochastic dispersion is found unlikely to materially improve expansion rates.
Problem
Search-area estimation is complicated by uncertain drifting-object motion, environmental-field errors, and uncertainty in the object's last known position.
Method
LEEWAY uses Monte Carlo ensembles that perturb leeway properties, wind and current forcing, and initial position to estimate object-location probability densities.
Results
The model's search-area expansion is not significantly affected by higher-order stochastic trajectory models because leeway-property uncertainty dominates wind- and current-induced dispersion.
Takeaways & Limitations
Operational search planning can use evolving probability-based search areas derived from high-resolution forcing fields and empirically decomposed leeway coefficients.
Takeaways & Limitations
Higher-order random-flight formulations require geographically and seasonally varying integral-time-scale estimates that can be difficult to obtain operationally.
Abstract
from arXiv · showhide
A new operational, ensemble-based search and rescue model for the Norwegian Sea and the North Sea is presented. The stochastic trajectory model computes the net motion of a range of search and rescue objects. A new, robust formulation for the relation between the wind and the motion of the drifting object (termed the leeway of the object) is employed. Empirically derived coefficients for 63 categories of search objects compiled by the US Coast Guard are ingested to estimate the leeway of the drifting objects. A Monte Carlo technique is employed to generate an ensemble that accounts for the uncertainties in forcing fields (wind and current), leeway drift properties, and the initial position of the search object. The ensemble yields an estimate of the time-evolving probability density function of the location of the search object, and its envelope defines the search area. Forcing fields from the operational oceanic and atmospheric forecast system of The Norwegian Meteorological Institute are used as input to the trajectory model. This allows for the first time high-resolution wind and current fields to be used to forecast search areas up to 60 hours into the future. A limited set of field exercises show good agreement between model trajectories, search areas, and observed trajectories for liferafts and other search objects. Comparison with older methods shows that search areas expand much more slowly using the new ensemble method with high resolution forcing fields and the new leeway formulation. It is found that going to higher-order stochastic trajectory models will not significantly improve the forecast skill and the rate of expansion of search areas.
Regional terms
The paper concerns the North Atlantic, Norwegian Sea, and North Sea.
- The study region includes the North Atlantic.
- The study region includes the Norwegian Sea.
- The study region includes the North Sea.
1 Introduction
Maritime search and rescue requires rapidly estimating evolving search areas despite uncertain object motion, environmental forcing, and last-known position. The paper introduces the operational LEEWAY model and distinguishes it from earlier Monte Carlo approaches through improved forcing fields and leeway formulation.
- Maritime search and rescue estimates an evolving search area from uncertain position, object type, wind, sea state, and currents.
- Drifting-object motion is difficult to compute because real-world geometries require simplifying assumptions that introduce errors.
- Environmental fields contain model, observation, sub-grid-scale, and representativeness errors that affect estimated object motion.
- Monte Carlo perturbations estimate a time-evolving spatial probability density rather than an exact trajectory.
- LEEWAY computes net motion from wind and surface current and was developed as an operational search model.
- Compared with earlier Monte Carlo SAR models, the approach uses real-time currents and downwind/crosswind leeway components instead of a leeway divergence angle.
2 The forces on a drifting object
The model represents drifting-object motion through wind-related leeway, surface currents, and wave effects, using empirical leeway coefficients and operational environmental fields. Wave effects are omitted under stated assumptions, while Stokes-drift interaction remains a limitation.
- Small SAR objects are assumed to reach terminal velocity rapidly, supporting instantaneous adjustment and constant velocity during each model timestep.Life rafts reach terminal velocity in approximately 20s under 20m/s winds.
- Leeway is measured relative to the 10 m, 10-minute averaged wind and represents wind force on an object's overwater structure.
- Empirical data for 63 search-object categories are converted into downwind and crosswind leeway components for operational use.
- The downwind leeway component is approximately linear with 10 m wind speed, while left- and right-drifting observations are modeled with a 50/50 distribution.
- Operational winds come from HIRLAM forecasts extending to +60 hours, while currents are supplied by a 4 km ocean model and interpolated to 0.5 m depth.
- Stokes drift is excluded because it is difficult to separate from empirical wind effects and is assumed to be included in the leeway coefficients.
- Wave effects are ignored for objects shorter than 30 m, although wave-current interactions may become important in high seas and strongly sheared currents.
3 The operational ensemble trajectory model
The operational ensemble trajectory model estimates evolving search areas by repeatedly perturbing uncertain drift properties, forcing fields, and initial conditions. It retains a simple stochastic formulation because leeway-property uncertainty dominates dispersion for typical SAR objects, while higher-order wind and current perturbations add little to search-area expansion.
- 3 The operational ensemble trajectory model: The model estimates probability of containment by rerunning trajectories with perturbed leeway coefficients, forcing fields, and initial position.The ensemble represents uncertainty in the last known position, object properties, wind, and currents.
- 3 The operational ensemble trajectory model: The trajectory is treated as a first-order Markov process, so the future state depends on the current state rather than the path taken to reach it.The state comprises the drifting object's location and whether it is drifting or stranded.
- 3 The operational ensemble trajectory model: Leeway perturbations remain fixed for each ensemble member to represent object-specific drift properties throughout the simulation.Examples include variations in loading or sagging among life rafts.
- 3 The operational ensemble trajectory model: The leeway ensemble accounts for heteroscedastic experimental variance by perturbing both regression slope and offset with a common normally distributed term.At lower wind speeds the offset contributes most of the perturbation, whereas at higher speeds the slope contributes most.
- Ignoring higher-order dispersion: Leeway-property uncertainty contributes two orders of magnitude more dispersion than time-varying wind and current perturbations for SAR objects with appreciable windage.With wind standard deviation 2.6m/s and current standard deviation 0.25m/s, turning off wind and current perturbations changed ensemble spread by less than 2% after O(250) timesteps.
- Ignoring higher-order dispersion: Because wind- and current-induced dispersion is generally secondary, a random flight model is not expected to discernibly change search-area expansion, although strong shear or sharp fronts can accelerate divergence.Reliable turbulent time-scale estimates are difficult across geographic areas and seasons, supporting retention of the simpler operational model.
- 3.4 Object taxonomy: Life rafts and sailboats produce different evolving search areas because their leeway divergence and experimental variance differ.A sailboat can generate disjoint left- and right-of-wind areas, while a life raft's faster, less divergent drift produces more overlap and a smaller overall area.
4.1 Drift exercises
The limited drift exercises generally showed good agreement between modeled and observed trajectories, while one comparison found substantially slower search-area expansion than older methods. These cases illustrate model behavior rather than constituting controlled evaluation.
- Controlled experiments were lacking, so the reported cases illustrate forecast ability rather than provide a formal model evaluation.
- The benthic lander’s ensemble-mean trajectory corresponded quite well with observed intermediate positions.The lander was tracked irregularly by ARGOS until pickup.
- The liferaft in the 2003 exercise was picked up near the search-area center, and its ensemble-mean trajectory agreed well with intermediate positions.
- 25-50%: the LEEWAY search area expanded at this fraction of the rate produced by older methods in the 2004 exercise.The raft was picked up near the center of the LEEWAY search area, but no intermediate positions were available.
4.2 Possible model extensions and improvements
The model’s extensions target operational realism by improving object-specific drift information, representing additional object behaviors, and increasing forcing-field resolution. Important limitations remain because data are incomplete, uncertain, or unavailable for several effects and object classes.
- The model is intended to remain fast, easy to operate, and conservative about search-area expansion while improving precision.
- Leeway data: Existing leeway categories have variable quality, and high experimental variance can substantially inflate search areas.Reducing leeway-coefficient variance directly reduces the rate of search-area inflation.
- Leeway data: Several region-specific SAR object classes are missing, while categories such as life rafts require further refinement.
- Object behavior: The model omits jibing, swamping, and capsizing because experimental data are scarce, although dedicated experiments could quantify their probabilities.
- Object behavior: Including jibes could make the search area more continuous by filling the gap between left- and right-drifting ensemble distributions.
- Forcing resolution: Higher resolution is motivated by resolving eddies more realistically and representing near-shore currents where most rescue operations occur.The discussion identifies 1-2 km resolution as a path toward a more realistic current spectrum and notes that most operations occur within 40 km of shore.
4.3 Conclusion
The paper presents an operational ensemble model for evolving SAR search areas, combining object-specific leeway modeling with stochastic trajectories. It forecasts up to 60 hours ahead, shows promising but limited field-trial agreement, and identifies leeway uncertainty as the dominant source of spread.
- The paper presents an operational search-area model and a taxonomy of common SAR objects based on available field experiments.
- 25-50%: the new leeway decomposition makes search areas inflate at approximately this rate relative to older methods.The downwind and crosswind formulation is designed to improve low-wind robustness and ensemble perturbations.
- 60 hours: the operational ensemble model can forecast search areas this far ahead, while a seven-day archive supports retrospective starts.Retrospective initialization matters because incidents may not be reported immediately.
- Leeway-property perturbations disperse particles primarily, whereas wind- and current-field random walks contribute negligibly by comparison.Higher-order stochastic particle models make very little difference to search-area expansion.
- Further horizontal-resolution increases are argued to support searches nearer shore and in bays and fjords while representing eddy-driven spread more realistically.
- Further field work is required because some SAR objects are inadequately modeled and older leeway categories have high experimental error.
- The limited field-trial set captured features of several drifting-object trajectories, but definite conclusions about forecast skill require further studies.The reported results are described as promising rather than conclusive.
Figures
The figures define the leeway components, ensemble initialization, operational forcing domain, and search-area construction. They also illustrate object-dependent search-area divergence and trajectory agreement with observations.
- Leeway components: Leeway is decomposed into downwind and crosswind components, with the latter determining divergence from the downwind direction.The figures identify the leeway divergence angle as the angle between downwind and the object's drift direction.
- Operational forcing: The operational ocean model resolves currents at 4 km, uses 20 km 10 m winds, and produces daily forecasts to +60 h within its grid.The setup includes major tidal constituents on the boundary and retains a seven-day archive for delayed trajectory calculations.
- Ensemble initialization: Ensemble members are seeded randomly between two uncertain positions and times, allowing moving-vessel accidents or simpler point-release scenarios.The initial spatial distribution uses circles with radii r0 and r1, while continuous release spans t0 to t1.
- Object-dependent search areas: At t = +32 hours, the sailboat has a significantly larger, split search area than the contiguous liferaft area because its leeway divergence is higher.The liferaft's smaller crosswind component produces approximately 50% overlap between the two ensemble halves.
- Observed trajectories: A benthic lander trajectory was followed for more than four days, and the ensemble mean captured its general observed trajectory features.For the liferaft exercise, the ensemble mean agreed reasonably with intermediate GPS positions and the search area reached approximately 90 nm2 after 24 hours.