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Uncertainty in marine weather routing

Thomas Dickson, Helen Farr, David Sear, James Blake

TL;DR

The study addresses how to quantify the significance of numerical error and performance-model uncertainty in marine weather routing. It uses a dynamic-programming based shortest-path method on discretized environmental grids and perturbs the performance model linearly to assess impact, with Grid Convergence Index used to quantify numerical error. Applied to ethnographic Polynesian voyaging canoes, the results show numerical error is small on average ($0.396\%$ or about $1.05$ h for $V_t≈266.40$ h), while performance-uncertainty has a much larger effect on voyage time, producing standard-deviation increases of $0.8-3.08\%$ depending on perturbation magnitude. The findings underscore the need to quantify and reduce performance-model uncertainty to improve the credibility of routing predictions, and demonstrate a general methodology that can be applied to other long-course marine routing problems with irregular weather data cadences.

Abstract

Weather routing methods are essential for planning routes for commercial shipping and recreational craft. This paper provides a methodology for quantifying the significance of numerical error and performance model uncertainty on the predictions returned from a weather routing algorithm. The numerical error of the routing algorithm is estimated by solving the optimum path over different discretizations of the environment. The uncertainty associated with the performance model is linearly varied in order to quantify its significance. The methodology is applied to a sailing craft routing problem: the prediction of the voyaging time for an ethnographic voyaging canoe across long distance voyages in Polynesia. We find that the average numerical error is $0.396\%$, corresponding to $1.05$ hours for an average voyage length of $266.40$ hours. An uncertainty level of $2.5 \%$ in the performance model is seen to correspond to a standard deviation of $\pm 2.41-3.08\%$ of the voyaging time. These results illustrate the significance of considering the influence of numerical error and performance uncertainty when performing a weather routing study.

Uncertainty in marine weather routing

TL;DR

The study addresses how to quantify the significance of numerical error and performance-model uncertainty in marine weather routing. It uses a dynamic-programming based shortest-path method on discretized environmental grids and perturbs the performance model linearly to assess impact, with Grid Convergence Index used to quantify numerical error. Applied to ethnographic Polynesian voyaging canoes, the results show numerical error is small on average ( or about h for h), while performance-uncertainty has a much larger effect on voyage time, producing standard-deviation increases of depending on perturbation magnitude. The findings underscore the need to quantify and reduce performance-model uncertainty to improve the credibility of routing predictions, and demonstrate a general methodology that can be applied to other long-course marine routing problems with irregular weather data cadences.

Abstract

Weather routing methods are essential for planning routes for commercial shipping and recreational craft. This paper provides a methodology for quantifying the significance of numerical error and performance model uncertainty on the predictions returned from a weather routing algorithm. The numerical error of the routing algorithm is estimated by solving the optimum path over different discretizations of the environment. The uncertainty associated with the performance model is linearly varied in order to quantify its significance. The methodology is applied to a sailing craft routing problem: the prediction of the voyaging time for an ethnographic voyaging canoe across long distance voyages in Polynesia. We find that the average numerical error is , corresponding to hours for an average voyage length of hours. An uncertainty level of in the performance model is seen to correspond to a standard deviation of of the voyaging time. These results illustrate the significance of considering the influence of numerical error and performance uncertainty when performing a weather routing study.

Paper Structure

This paper contains 12 sections, 2 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Uncertainty analysis
  4. Method
  5. Routing model
  6. Uncertainty simulation
  7. Application
  8. Numerical uncertainty
  9. Illustration of simulation convergence
  10. Numerical error of voyaging simulations
  11. Performance uncertainty
  12. Summary and conclusions

Figures (9)

  • Figure 1: Method used to quantify uncertainty in marine weather routing.
  • Figure 2: Discretized domain along great circle line between voyage start and finish.
  • Figure 3: Performance of marine vessel used in study.
  • Figure 4: Routes between Upolu and Moorea starting at 00:00 GMT on the 1st January 1985 solved over several different grid widths.
  • Figure 5: Voyaging time, $V_t$, as a function of grid width for voyages between Upolu and Moorea starting at 00:00 GMT on the 1st January 1985.
  • ...and 4 more figures