Wave Modeling and Applications

Wave Modeling and Applications Hellenic Naval Academy Section of Mathematics Joint work with - Hellenic Navy Hydrographic Service - Atmospheric Modeling Group, Department of Physics, University of Athens, Greece - Oceanography Center, University of Cyprus - Naval Ocean Analysis and Prediction Laboratory, Naval Postgraduate School, USA

A new framework for environmental sciences Over the last two decades a new competitive framework has been set for the research and technological community working on environmental issues as a result of the concerns for the global warming, the questions on the climate change and the strict environmental policies regarding the production of greenhouses gases. Within this framework the validity of high quality environmental, and in particular, sea state information is constantly increasing in accordance with the significant number of applications that are affected: Supporting navy activities Transportation optimal ship routing Ship safety Early warning systems for extreme sea state condition Marine pollution, runoff, oil spill Tourist activities (local forecast) Wave energy production Wave climate or microclimate change

Modeling the sea waves What kind of waves can be simulated by the wave models today? Wind-generated waves and swells Tsunamis Tides

Modeling the sea waves We are working on Wind-generated waves and swells Tsunamis Tides Based on mathematical and physical models

Modeling the sea waves: procedures that are simulated by the wave models Refraction When waves enter shallow water and start to shoal, they slow down. If the crest of the shoaling wave is not parallel to the bathymetric contours, the wave refracts and becomes oriented more parallel to the contours.

Modeling the sea waves: procedures that are simulated by the wave models Refraction against wharves, breakwaters or other obstacles. Depending on the nature of the obstacle the reflected waves can range from very coherent to quite scattered.

Modeling the sea waves: procedures that are simulated by the wave models Diffraction Wave diffraction occurs when wave crests bend around barriers. Wave energy can be diffracted into the shadow of an object Waves will diffract on the lee side of small islands and breakwaters.

Modeling the sea waves: procedures that are simulated by the wave models Wave current interaction Currents play a significant role in shaping nearshore waves. Wave-current interactions near shore, can lead to strong refraction effects shown in this satellite image. When waves and currents run in opposing directions, both wave speed and wavelength decrease, while wave height increases. This results in steeper, more dangerous, waves. Conversely, when waves and currents have the same direction both wave speed and wavelength increase, while wave height decreases

The Wave Model WAM WAM is a 3 rd generation 2D spectral wave model WAM model describes the evolution of a two-dimensional ocean wave spectrum. In contrast to first and second generation models, the third generation model WAM introduces no ad hoc assumptions on the spectral shape. It computes the 2-d wave variance spectrum through integration of the transport equation F represents the spectral density with respect to (f,θ,φ,λ) f denotes frequencies, θ directions, φ latitudes, λ longitudes The source function S is represented as a superposition of the wind input Sin, white capping dissipation Sdis, and nonlinear transfer Snl

The Wave Model WAM WAM is a 3 rd generation 2D spectral wave model This classification was made according to the method used by the model in order to describe the non-linear source term S nl 1 st generation models do not calculate the S nl term overestimation of wind role 2 nd generation models handle S nl term by parametric methods the initial description of the spectrum shape was necessary, because of limitations on the parameterization with linear transportation Problems with complex sea waves from fast varying winds 3 rd generation models calculate the non-linear energy transfers explicitly, although it is necessary to assume both analytic and numerical approximations to expedite the calculations.

The Wave Model WAM What does WAM simulate? The model describes the wave field by simulating how wave energy is distributed: Over wavelength Over direction at each grid point of the model s domain. Wave Spectrum

The Wave Model WAM What does WAM simulate? Waves at any given moment are the combination of local wind waves and Long distance travelled swell resulting in different wave fields. Each wave field travels at its own direction, frequency and energy level. WAM model tracks the energy as waves grow, dissipate or propagate across the model domain by means of wave energy spectrum at every grid point in the model domain.

The Wave Model WAM What does WAM simulate? The spectrum is divided in bins (degrees of freedom) Frequency range df Direction equally divided dθ Total Bins (degrees of freedom) = df dθ The model for each timestep at each grid point and every bin estimates the wave energy in order to use it for the simulation of the wave generation and the swell propagation. THIS IS TOO MUCH INFORMATION TO WORK WITH

The Wave Model WAM WAM calculates the statistical properties of the wave field directly from the wave spectrum. Significant Wave Height (H m0 ) The average of the largest one-third of wave heights. It is estimated based on the zero spectral moment of the wave spectrum: H m0 = 4 m 0 = 4 S f df 0 Swell Height The average of the largest one-third of long-wavelength, and therefore longperiod, surface wave heights. This type of waves is far more stable in their direction and frequency than normal wind waves, having often travelled long distances since their formation. Individual waves H max Hs=H 1/3

The Wave Model WAM WAM simulates the statistical properties of the wave field directly from the wave spectrum. Mean Wave Period (T m02 ) The mean time interval between the passage of two successive crests from a fixed point in an irregular sea state. It is calculated as the fraction of the zero and the second spectral moments: T m02 = m 0 m 2 = 0 0 S f df f 2 S f df It is the inverse of mean frequency: T m02 = Peak Wave Period (T p ) A measure of the time between the most energetic waves (those producing the most energy) obtained from the energy spectrum. It is the inverse of peak 1 f m02 frequency: T p = 1 f p

The Wave Model WAM Spectral Polar plots What kind of information we can derive? Wind waves Higher frequencies-lower period Wind wave energy is distributed in a wide range of frequencies and directions. Swells Lower Frequency (near to the polar center) Swell energy is distributed in a narrow range of frequencies and directions Longer periods: toward center Shorter period: toward outer circle Wave direction: waves move toward the center of the polar plot.

The Wave Model WAM Bathymetry Coastline 10m Winds, SST, Currents Wave propagation Dispersion Refraction Diffraction Shoaling WAM Generation/Dissipation Wave generation Whitecapping Wave breaking Bottom friction Wave-wave interactions Wave/current interaction Full spectral outputs. Integrated parameters Hs & direction Tmean, & Tpeak Swell height & direction Wind Sea height & direction Maximum expected wave height

Wave modeling and applications The wave model WAM at the Hellenic Naval Academy Very high spatial (5 km) and temporal (1 h) resolution Assimilation of observations from buoys and satellites Statistical optimization and local adaptation processes (Κalman & Kolmogorov-Zurbenko filters)

Wave modeling and applications The wave model WAM at the Hellenic Naval Academy Main model outputs Wave height and direction Mean and peak wave period Maximum expected wave height Swell height and direction Wind-Wave height and direction The full spectra of wave energy at selected grid points

Wave modeling applications Supporting Navy operations Wave energy estimation and production Marine pollution, runoff, oil spill Transportation optimal ship routing Ship safety Early warning system for extreme sea state condition Tourist activities (local forecast) Wave climate or microclimate change

Supporting Hellenic Navy operations Every day forecast of wind speed, 6 1 wave height and direction for supporting fleet operations though the Hellenic Navy Hydrographic Service 5 4 2 7 3

"Α" 37.0-38.0 / 23.5-24.5 "Β" 37.4-38.4 / 24.5-25.5 "Γ" 37.7-38.7 / 25.5-26.5 "Γ" 37.0-38.0 / 26.5-27.5 "Δ" 36.0-37.0 / 25.5-26.5 "ΣΤ" 36.0-37.0 / 26.5-27.5 "Ε" 36.0-37.0 / 27.5-28.5 Supporting Hellenic Navy operations

Renewable Energy Resources - Wave Energy Over the last years, the use of renewable resources for energy production is receiving increased attention as a result of the threat posed by climate change and the strict environmental policies regarding the production of greenhouses gases. Within this framework, wave energy (the energy that can be captured by sea waves) is a promising alternative energy resource with critical advantages: Low variability (easier integration to the general grid) High predictability Good seasonal load for the most energetic seas (NW Europe) It can be produced even in the absence of local winds by exploiting the swell component of waves Ocean energy technologies produce no emissions of harmful pollutants or greenhouse gasses

What kind of information we need? Wave Energy is dependent on the joint distribution of Significant Wave Height (H s ) and Wave Energy Period (T e ) 2 2 1 g 2 Pw g f E( f, ) dfd [ / ] 0 0 ste W m 64 Different types of WECs are suitable to different combinations of wave height and period. Detailed high resolution atlases for the wave climate of the area of interest are critical for wave energy exploitation and engineering design.

Integrated High Resolution System for Monitoring and Quantifying the Wave Energy Potential in the EEZ of Cyprus Zodiatis G., Galanis G., Hayes D., Nikolaides A., Georgiou G., Stylianou S., Kallos G., Michaelides S., Chu P.C., Charalampous A., Karaolia A., Kyriakou O., Savvidou K.

Main Objectives The development of an integrated, high resolution system for monitoring the wave power potential at the Exclusive Economical Zone (EEZ) of Cyprus and of the Levantine basin, coupled with the Cyprus Coastal Ocean Forecasting System CYCOFOS The project results include: A high resolution digital atlas containing detailed maps for the EEZ of Cyprus with all the relevant sea wave characteristics, as well the distribution of the wave energy potential. Novel models for the prediction and quantification of wave energy for operational forecasts, a tool of significant value for grid designers and regulators.

The numerical models used: The new parallel version of the wave model WAM The OC-UCY in cooperation with the UOA/AM&WFG has adopted the latest version of the new WAM model from the ECMWF (parallel version). A new advection scheme (Corner Transport Upstream) has been adopted providing a more uniform propagation in all directions For the E-wave project the wave model s domain cover the whole east Med region in order to capture all the swell information that could reach the study area (Levantine Basin) Wave model WAM ECMWF CY33R1 Characteristics Model s domain East Mediterranean (30N 41N, 15E 37E) Study area Levantine Horizontal Resolution 1/60 x 1/60 degrees (0.01667 km approximately) Frequencies Directions Timestep 25 (range 0.0417-0.54764Hz logarithmically spaced) 24 (equally spaced) 45 sec The wave model s domain

west and south offshore Cyprus EEZ Project results The results of the E-Wave project indicate higher values for the two sea state parameters (Hs and Te) that mainly affect the wave energy estimation, in the

Project results Non trivial deviations are also recorded

Project results The impact of extreme/non-frequent values of the sea state is limited, as revealed by the low kurtosis (4 th statistical moment) values

Project MOSEP Support of postdoctoral researchers, funded by: General Secretariat of Research and Technology, in the framework of ESPA 2007-2013 action Title: Development and application of new mathematical and physical models for MOnitoring the wind and Sea wave Energy Potential Hosted by Hellenic Naval Academy, Scientific coordinator: George Galanis Postdoctoral researcher: George Emmanouil Cooperation with: CYPRUS OCEANOGRAPHY CENTER

Short description: Main target: The development of an integrated, high resolution system for quantifying and monitoring the energy potential from wind and sea waves in the region of Eastern Mediterranean Sea with special emphasis to the Greek sea area. In particular: New-advanced models for the estimation of the energy potential from wind and waves over sea areas will be developed. Atmospheric and sea wave numerical models for monitoring the wind and wave conditions that are necessary for estimating the corresponding energy potential, will be used.

Atmospheric Model setup (WRF-ARW) Horizontal Resolution 0.1 0.05 degrees 35 vertical levels 4 soil levels 60 hours forecasting (up to 120h) GFS atmospheric input (GRIB2 format) 00UTC start time (may change to 12UTC) Nested domains: tested Model output: Netcdf files Post process tools: NCL

PREMARPOL Prevention and Combating of Marine Pollution in Ports and Marinas

Project goals Monitoring of pollution resources Categorize characterize the problem based on biochemical characteristics Monitoring and mapping of the local wave environment Risk analysis Forecasting and different case studies

Examples of application areas Zygi

The MEDSLIK model in Limassol port for oil spill monitoring/forecasting Application#3: after escape Application#1: if no action of the small portion of the was taken to combat the oil oil spill through the port spill, simulations from entrance, 06:00h on 8 May to 11:00h on simulations 11 May 2004 from 08:00h on 10 May to 11:00h on 11 May 2004 Application#2: after deployment of booms at the port entrance, simulations from 06:00h on 8 May to 11:00h on 11 May 2004

Limitations of numerical wave models Numerical wave (and atmospheric) models have been proved successful for the simulation of the general sea state conditions on global or intermediate scale. When focusing on local characteristics systematic errors may appear due to: the strong dependence of wave models on the corresponding wind input the inability to capture sub-scale phenomena the parametrization of certain wave procedures the lack of a dense observation network which could help on the systematic correction of initial conditions.

Ways of optimizing the final forecasting products Increase the model resolution It remains an open question if this leads to a considerable improvement of the forecast skill. Even if this is true, it also results to increased computational cost. Assimilation systems. Used for correcting the initial conditions based on available observations In WAM corrected analysis fields are provided by the assimilation method developed by Breivik and Reistad, 1994, at the Norwegian Meteorological Institute: Bratseth analysis scheme converging to the classical Statistical Interpolation by setting a proper choice of parameters for the analysis weights Problems: Limited available/quality controlled observations over oceans Limited spatial and temporal impact

Ways of optimizing the final forecasting products Use of post-processing methods based on statistics MOS methods emerge discrepancies in short time local weather changes or updates of the model. Neural networks: Do not take into consideration the involved forcing. Kalman filters: Remove successfully possible systematic prediction errors.

The Kalman Filter The statistically optimal sequential estimation procedure for dynamic systems. Observations are recursively combined with recent forecasts with weights that minimize the corresponding biases Main advantages: Easy adaptation to any alteration of the observation or forecast type Only short series of background information are needed The filter developed: The bias y t is estimated as a function of the forecasting model direct output System and Observation equations :

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 239 246 253 260 267 274 281 288 295 Overestimation in significant wave height simulations (Monterey Bay, California, USA in cooperation with the Naval Ocean Analysis and Prediction Lab, NPS) 5 4,5 4 3,5 3 2,5 2 obs mod 1,5 1 0,5 0 Some statistics (June August 2009) : Model Bias -0.86 RMSE 0.93 Normalized Bias 0.56

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106 113 120 127 134 141 148 155 162 169 176 183 190 197 204 211 218 225 232 239 246 253 260 267 274 281 288 295 Bias correction by mean of Kalman filters (Monterey Bay, California, USA) 5 4,5 4 3,5 3 2,5 2 obs mod Kalman 1,5 1 0,5 0 Some statistics (June August 2009) : Model Model + Kalman Bias -0.86-0.01 RMSE 0.93 0.58 Normalized Bias 0.56 0.18

Kalman combined with assimilation SWH Analysis Forecasting Period Available Observations and WAM forecasts are used by the filter to produce a new improved forecast This is assimilated during the forecasting period improving significantly the assimilation impact in time and space

f(x) f(x) Distribution fitting (Extreme conditions case) Satellites WAM Probability Density Function Probability Density Function 0.18 0.16 0.14 0.12 0.1 0.08 Weibull distribution shape parameter 4.4 scale 5.8 0.2 0.18 0.16 0.14 0.12 0.1 0.08 Weibull distribution shape parameter 3.4 scale 7.0 0.06 0.06 0.04 0.04 0.02 0.02 0 1.6 2.4 3.2 4 x 4.8 5.6 6.4 7.2 0 1 2 3 4 5 x 6 7 8 9 10 Histogram Weibull Histogram Weibull For both systems, SWH does not follow the classical Rayleigh distribution (Weibull with scale parameter 2) that is usually the case for non extreme conditions

Bias Treatment and Correction In both assimilation and post process bias correction methods, the algorithms are based on the minimization of a cost function. Recent advances in Statistics and Differential Geometry (Information Geometry) suggests that the results of the distribution fitting should be taken into account for the minimization of the error function. The family of two parameter Weibull distributions form a statistical 2-dimensional manifold with Fisher information matrix This matrix defines the inner product, and therefore the geometrical framework, in which the Weibull manifolds are categorized. This distance should be minimized instead of using least square methods (classical Euclidean Geometry).

Monthly wave height values from satellite records (left) and WAM simulations (right) as elements of the Weibull distributions statistical manifold

Thank you for your attention Suggestions - Comments: ggalanis@mg.uoa.gr