Improvement of wave height forecast in deep and intermediate waters with the use of stochastic methods Zoe Theocharis, Constantine Memos, Demetris Koutsoyiannis National Technical University of Athens School of Civil Engineering WISE 2006, Venice
Presentation Structure. Introduction 2. Methodology 3. Applications 4. Conclusions WISE 2006, Venice 2
Introduction WISE 2006, Venice 3
Introduction OBJECTIVE: : Improvement of the forecast power of numerical wave models using real time measurements Improvement of wave predictions can be achieved by three different approaches: Data assimilation techniques (require re-run run and space coverage) Stochastic tools Neural networks techniques WISE 2006, Venice 4
Only a few stochastic applications concerning real time improvement of the wave forecast Caires & Sterl,, 2004: non parametric correction of ERA-40 reanalysis data, using a learning dataset In this work a stochastic technique is applied to measured data of wave height for improving forecasts of the wave model WISE 2006, Venice 5
Methodology WISE 2006, Venice 6
Bivariate Linear Regression models Yˆ t + k t = ak X t + k t + t β ky + γ κ Ŷ : Y : Χ : Wave height estimate Wave height measurement Wave height model forecast k=0,,2 < model 0,,2 > Trivariate linear model < model 3> WISE 2006, Venice 7
Bivariate Non-Linear Regression models Y λ t+ t = α Χ λ t+ t + β Y λ t + γ, if Y t c, Y λ t+ t = α Χ λ t+ t + β 2 Yλ t + γ 2, if Y t c γ 2 = γ + (β - β 2 ) c λ (continuity c) <model 4> WISE 2006, Venice 8
Applications WISE 2006, Venice 9
First Application: The Aegean Sea The Stations Used WISE 2006, Venice 0
very irregular coastline complicated bottom topography presence of a large number of islands scattered over the area abrupt changes in magnitude and direction of the wind field WISE 2006, Venice
WAM Underestimation Mean Wave Height Measurement-WAM Forecast ΜΕΣΟΙ ΟΡΟΙ ΥΨΟΥΣ ΚΥΜΑΤΟΣ (m).6.4.2 0.8 0.6 0.4 0.2 0 Measurements through POSEIDON System ΜΕΣΟΙ ΟΡΟΙ ΜΕΤΡΗΣΕΙΣ Measurement ΜΕΣΟΙ ΟΡΟΙ WAM WAM 2 3 4 5 6 7 8 9 0 2 ΜΗΝΕΣ months 3-hour time step Measur WAM WISE 2006, Venice ATHOS STATION 2
WAM Underestimation Measurements through POSEIDON System 7 6 5 4 3 2 0 ΜΕΤΡΗΣΗ Measur ΠΡΟΒΛΕΨΗ WAM WAM Measurement WAM 203 405 607 809 0 23 45 67 89 202 2223 2425 2627 2829 303 3233 3435 3637 3839 404 4243 4445 4647 4849 505 5253 5455 5657 5859 606 6263 6465 6667 6869 707 7273 Wave ΥΨΟΣ Height ΚΥΜΑΤΟΣ Measurement-WAM ΜΕΤΡΗΣΕΙΣ-WAM (m) forecast 3-hour months time step ΧΡΟΝΙΚΑ ΒΗΜΑΤΑ 3 ΩΡΩΝ WISE 2006, Venice ATHOS STATION 3
Μodel 3.5 3 --Measurement ΜΕΤΡΗΣΗ --WAM Forecast ΜΟΝΤΕΛΟ 6. ΜΟΝΤΕΛΟ WAM --Model 2.5 2.5 0.5 0 4 7 0 3 6 9 22 25 28 3 34 37 40 43 46 49 52 55 58 6 64 67 70 73 76 79 82 85 88 9 94 97 00 Wave Height (m) ΥΨΟΣ ΚΥΜΑΤΟΣ (m) 3-hour time step ΧΡΟΝΙΚΑ ΒΗΜΑΤΑ 3 ΩΡΩΝ WISE 2006, Venice ATHOS STATION 4
7 6 5 4 3 Approximation of the measured average wave height Significant decrease of the standard deviation --Measurement ΜΕΤΡΗΣΗ --WAM Forecast ΜΟΝΤΕΛΟ 6. --Model 2 0 77 53 229 305 38 457 533 609 685 76 837 93 989 065 4 27 293 369 445 52 597 673 749 825 90 977 2053 229 2205 228 2357 2433 Wave ΥΨΟΣ Height ΚΥΜΑΤΟΣ (m) (m) WISE 2006, Venice 5
4.5 4 ΥΨΟΣ ΚΥΜΑΤΟΣ-WAM 3.5 3 2.5 2.5 y = 0.6804x + 0.0999 R 2 = 0.728 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ Wave 6.4.Α (m) Height Forecast (m) 0.5 0 0 2 3 4 5 6 5 4.5 4 3.5 3 2.5 2.5 0.5 y = 0.994x + 0.067 R 2 = 0.9079 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ Wave Height Measurement (m) 0 0 2 3 4 5 6 39.6 N 39.4 N 39.2 N 39 N 38.8 N ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m) Wave Height Measurement (m) 25.5 E 26 E 26.5 E WISE 2006, Venice 6 Dardan Ocean Data View 00m 250m 500m 000m 2000m
5 4.5 ΥΨΟΣ ΚΥΜΑΤΟΣ-WAM (m) ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ 6.4.Α Wave (m) Height Forecast (m) 3.5 2.5.5 0.5 6 5 4 3 2 4 3 2 0 y = 0.52x + 0.936 R 2 = 0.729 0 2 3 4 5 37.7 N 6 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m) y = 0.929x + 0.33 R 2 = 0.9357 37.6 N 37.5 N 37.4 N 37.3 N 37.2 N 25 E 25.2 E 25.4 E 25.6 E Ocean Data View 0 25 50 0 0 WISE 2006, Venice 7 0 2 3 4 5 6 ΥΨΟΣ ΚΥΜΑΤΟΣ ΜΕΤΡΗΣΗ (m) Wave Height Measurement (m)
4 ΥΨΟΣ ΚΥΜΑΤΟΣ-WAM (m) ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ (6.) Wave (m) Height Forecast (m) 3.5 3 2.5 2.5 0.5 y = 0.5564x + 0.808 R 2 = 0.6772 0 0 0.5.5 2 2.5 3 3.5 4 4.5 4.5 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m) 4 3.5 3 2.5 2.5 0.5 y = 0.9075x + 0.0884 R 2 = 0.9075 36.6 N 36.5 N 36.4 N 36.3 N 00m 250m 500m 000m 0 0 0.5.5 2 2.5 3 3.5 4 4.5 36.2 N WISE 2006, Venice ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΕΙΣ (m) 25. E 25.2 E 25.3 E 25.4 E 25.5 E 25.6 E8 Wave Height Measurement (m) Ocean Data View
Summary Table R 2 Athos R 2 Lesvos R 2 Mykonos R 2 Santorini WAM MODEL 0.78 0.73 0.722 0.676 MODEL 0.920 0.892 0.927 0.906 MODEL 2 0.865 0.83 0.860 0.820 MODEL 3 0.924 0.895 0.93 0.9 MODEL 4a 0.929 0.897 0.936 0.909 MODEL 4b 0.929 0.898 0.935 0.908 WISE 2006, Venice 9
Total improvement οbtained: For all four stations For all four models tested For all periods of implementation For high and low values of the wave height No outliers Increase of the forecast time step decreases the predictive accuracy of our technique Our technique s s R^2 equals WAM s for forecasts horizon more than 3 days WISE 2006, Venice 20
2 nd application: Indian Ocean Two stations: one in deep waters (station ) One in intermediate waters (station 2) Distance: 900Km WAM cycle4 WISE 2006, Venice 2
WAVE ΥΨΟΣ ΚΥΜΑΤΟΣ. HEIGHT ΜΕΤΡΗΣΕΙΣ ΚΑΙ measurement-wam ΜΟΝΤΕΛΟ WAM, ANOIXTA ΙΝ ΙΚΗΣ ΧΕΡΣΟΝΗΣΟΥ (station ) 4,5 4 WAVE HEIGHT ΥΨΟΣ ΚΥΜΑΤΟΣ 3,5 3 2,5 2,5 WAM overestimation 0,5 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 3 32 33 34 WAM No Assim Buoy Active Swell Subroutine WAVE HEIGHT ΥΨΟΣ ΚΥΜΑΤΟΣ 2,00,80,60,40,20,00 0,80 0,60 ΥΨΟΣ ΚΥΜΑΤΟΣ. ΜΕΤΡΗΣΕΙΣ ΚΑΙ ΜΟΝΤΕΛΟ WAM, ΠΑΡΑΚΤΙΑ ΙΝ ΙΚΗΣ ΧΕΡΣΟΝΗΣΟΥ WAVE HEIGHT measurement-wam (station 2) Outliers for two days both in deep and intermediate waters 0,40 0,20 0,00 2 23 34 45 56 67 78 89 00 22 33 44 55 66 77 88 99 20 22 232 243 254 265 276 287 298 309 320 33 WISE 2006, Venice 22 WAM No Assim Buoy
ΕΦ ΑΡΜΟΓΗ Non linear ΣΤΟΧΑΣΤΙΚΟΥ stochastic model ΜΟΝΤΕΛΟΥ to improve ΑΠΟ station ΒΑΘΕΙΑ 2 ΣΕ ΡΗΧΑ ΝΕΡΑ. ΙΝ ΙΚΟΣ ΩΚΕΑΝΟΣ. ΠΡΟΓΝΩΣΗ ΣΤΟ +9 wave height forecast using station data ΥΨΟΣ Wave ΚΥΜΑΤΟΣ height 4,5 4 3,5 3 2,5 2,5 0,5 0 ΜΕΤΡΗΣΗ MEASUREMENT WAM NON LINEAR REGRESSION 20 39 58 77 96 5 34 53 72 9 20 229 248 267 286 Remarkable improvement Coefficient of determination (R^2=0.9) Approximation of the measured average wave height Absorbing the outliers K time step selection WISE 2006, Venice 23
Conclusions WISE 2006, Venice 24
All models improve significantly the forecast in applications tested The parameters (weights) in all models indicate the same performance in all stations and in all periods of implementation The relation between measurements and predictions seems to be the same (error source, systematic error) If we have/measure the wave height for a small period of 3-43 months irrespectively of the season, we can:. Estimate the variable weights and then 2. Significantly improve in real time the forecast of the wave model without re-running running it and within an area of considerable extent containing the point of measurement Stochastic models are a useful tool for wave forecast. Future research is needed WISE 2006, Venice 25