Estimation of Uncertainty of Wind Energy Predictions

With Application to Weather Routing and Wind Power Generation

by David Zastrau (Author)
©2017 Thesis XVI, 123 Pages


Currently, a new generation of fuel-efficient ships, which use wind force in addition to conventional propulsion technology, is being developed. This study describes a mathematical method for a probabilistic estimate of the wind propulsion force on a ship route. The method is based on quantile regression, which makes it suitable for various ship routes with variable weather conditions. Furthermore, the author takes different macro weather situations into account for the calculation of the statistical distributions. He validates the results for a multi-purpose carrier, a ship route in the North Atlantic Ocean and archived weather forecasts. It showed that the wind force can be estimated more accurately if the macro weather situation is taken into account properly.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author(s)/editor(s)
  • About the book
  • This eBook can be cited
  • Contents
  • Glossary
  • Acronyms
  • Acknowledgements
  • 1. Introduction
  • 1.1. Uncertainty in wind energy predictions
  • 1.2. Approaches from the literature
  • 2. Uncertainty in Wind Power Generation and Weather Routing
  • 2.1. Weather prediction uncertainty in wind power generation (WPG)
  • 2.1.1. Offshore wind power logistics
  • 2.2. Prediction uncertainty in weather routing
  • 2.2.1. Wind propulsion systems (WPS)
  • 2.2.2. Speed power curve
  • 2.2.3. Wind resistance
  • 2.2.4. Wave resistance
  • 2.2.5. Ship propulsion energy
  • 2.2.6. Prediction uncertainty with WPS
  • 2.3. Wind power generation versus weather routing
  • 2.4. Weather forecasting
  • 2.4.1. Numerical weather analyses and predictions
  • 2.4.2. Limitations and trends in weather forecasting
  • 3. Statistical Patterns of Uncertainty in Weather Predictions
  • 3.1. Prediction error metrics
  • 3.2. Predictions for the North Atlantic Ocean
  • 3.2.1. DWD wind and wave predictions
  • 3.2.2. Regional and seasonal prediction uncertainty
  • 3.3. Predictions for the North and Baltic Seas
  • 3.3.1. FINO measurements
  • 3.3.2. Prediction uncertainty
  • 3.3.3. Wave prediction uncertainty
  • 3.3.4. Wind prediction uncertainty
  • 3.3.5. Conclusions
  • 4. Estimation of Prediction Uncertainty
  • 4.1. Theoretical and empirical models
  • 4.2. Ensemble prediction systems
  • 4.2.1. Multi-model and multi-analyses ensembles
  • 4.2.2. Super ensembles
  • 4.3. Statistical methods
  • 4.3.1. Probability density estimation methods
  • 4.3.2. Clustering
  • 4.3.3. Prediction intervals
  • 4.3.4. Quantile regression
  • 5. The Quantile Regression Model
  • 5.1. Linear quantile regression (QR)
  • 5.2. Regressors for the QR model
  • 5.2.1. Principal component analysis
  • 5.2.2. North Atlantic Oscillation Index (NAOI)
  • 5.2.3. Other climatological indices
  • 5.2.4. Statistical moments
  • 5.2.5. Local Energy Distribution Moments (LEDM)
  • 5.2.6. Relation between LEDM and NAOI
  • 6. Implementation
  • 6.1. Database with historical weather predictions
  • 6.2. A* route optimization
  • 6.3. Route optimization with uncertainty
  • 6.4. Quantile regression
  • 7. Evaluation and Results
  • 7.1. Evaluation of prediction intervals
  • 7.2. Application to wind-assisted sailing propulsion
  • 7.3. Prediction intervals for ship propulsion energy
  • 7.4. Prediction intervals for travel time
  • 7.5. Uncertainty in weather routing with WaSP
  • 7.6. Prediction interval benchmarks
  • 7.7. Runtime discussion
  • 7.8. Annual cost savings for a multi-purpose carrier
  • 8. Conclusions and Outlook
  • 8.1. New approach and scientific contribution
  • 8.2. Outlook
  • 8.2.1. Prediction uncertainty of wind turbine power output
  • 8.2.2. Uncertainty in weather routing
  • 8.2.3. Further applications
  • Bibliography
  • List of Figures
  • List of Tables
  • A. Parameters of Wind Propulsion Systems
  • B. Parameters of the wind and wave resistance models
  • C. UML diagrams of the Java implementation
  • D. The Global Sea Model (GSM)

| ix →


EA actual energy (calculated with weather analyses)

EP predicted energy (calculated with weather prediction)

ET estimated propulsion energy in A* for the complete route

EP,Err prediction error for EA

FN normalized force of WPS

FWPS force of WPS

Iα prediction interval

IαR reliability of prediction intervals (coverage)

IαS skill score of prediction intervals (uncertainty & coverage)

IαU sharpness of prediction intervals (uncertainty)

IαErr error of prediction intervals

PWPS power of WPS

PWa power of waves

PWi power of wind

Pcw propulsion power of the ship in calm water

Q quantile

QRLEDM quantile regression model with LEDM regressors

T draft of ship

Vs speed of ship

α significance coefficient of prediction intervals

β weight vector for quantile regression model

ηT efficiency of transformation from motor power to propulsion power

ρα check function

k size of roi

roi region of interest (a vector with coordinates)

x vector with regressors for the quantile regression model ← ix | x →

dynamic programming mathematical technique to solve optimization problems by constructing a solution from multiple partial solutions

ensemble prediction set of numerical weather predictions (NWP) calculated with slightly different initial model conditions

genetic algorithm search heuristic which imitates processes from natural selection to find the solution to a problem

great circle circle on the earth sphere with maximum perimeter

jack-up vessel ship which has been designed for the footing and construction of offshore wind power plants

lagged ensemble consists of multiple succeeding weather forecasts which predict the same future state of weather


XVI, 123
ISBN (Hardcover)
Publication date
2017 (February)
Prediction Intervals Quantile Regression Numerical Weather Predictions Offshore Logistics Wind Drives Heuristical Planning
Frankfurt am Main, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2017. XVI, 123 pp., 38 b/w ill., 15 coloured ill., 17 b/w tables

Biographical notes

David Zastrau (Author)

David Zastrau studied Computer Science at the University of Bremen where he received his PhD. He researches artificial intelligence, maritime logistics, as well as weather and wave forecast accuracy.


Title: Estimation of Uncertainty of Wind Energy Predictions
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142 pages