Observation-Based Physics for the Third Generation Wave Models Alexander Babanin, Ian Young, Erick Rogers and Stefan Zieger Centre for Ocean Engineering, Science and Technology Swinburne University, Melbourne Australian National University, Canberra Naval Research Laboratory, MS, USA Hobart, Australia May, 2014

Radiative Transfer Equation is used in spectral models for wave forecast Describes temporal and spatial evolution of the wave energy spectrum E(k,f,q,t,x) Stot – all physical processes which affect the energy transfer Sin – energy input from the wind Sds – dissipation due to wave breaking Snl – nonlinear interaction between spectral components Sbf – dissipation due to interaction with the bottom To predict waves in these demanding situations requires resort to a model, which represents the physical processes, which occur in nature (as best we understand them). With the advent of science and technology, like in other fields, there has also been considerable development in this field. There are still many aspects of wind waves, which are not fully understood. The most significant source of error, in deep-water wave models, is the driving wind. Another notable example is - breaking of waves.   A comprehensive model, which incorporates our full understanding of wind wave physics and is applicable in all situations, would be prohibitively expensive. Instead a variety of models have been proposed for applications in specific situations.

Motivation physics (parameterisations of the source terms) was cursory had not been updated for some 20 years was not based on observations bulk calibration Requirements for the modern-day models: more accurate forecast/hindcast being used in the whole range of conditions, from swell to hurricanes coupling with weather, ocean circulation and climate models

Lake George experiment sponsored by ONR 20 km x 10km uniform finite water depth (0.3m - 2.2m) steep waves fp > 0.3 Hz strongly forced waves 1 < U/cp < 8 source functions measured

following the waves

The full flow separation

The parameterisation, growth rate γ

Flow separation due to breaking (f) = 0(f)(1+bT)

Wind Input – Sin Donelan, Babanin, Young and Banner (Part I, JTEC, 2005; Part II, JPO, 2006, Part III, JPO, 2007) the parameterisation includes very strongly forced and steep wave conditions, the wind input for which has never before been directly measured in field conditions new physical features of air-sea exchange have been found: - full separation of the air flow at strong wind over steep waves - the exchange mechanism is non-linear and depends on the wave steepness - enhancement of the input over breaking waves γ=γ0(1+bT) - pressure-height decay is very rapid for strong winds – young seas combination

Breaking Dissipation Sds As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function. two passive acoustic methods to study spectral dissipation segmenting a record into breaking and non-breaking segments using acoustic signatures of individual bubble-formation events Babanin et al., 2001, 2007, 2010, Babanin & Young (2005), Manasseh et al. (2006), Young and Babanin (2006), Babanin (2011)

White Cap Dissipation Sds 1) Spectrogram method Frequency distribution of dissipation due to dominant breaking. - Cumulative effect As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function. Young and Babanin, 2006, JPO

White Cap Dissipation Sds 1) Segmenting the record Directional dissipation fp As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function. 2fp fp

Sds Bubble-detection method Manasseh et al., 2006, JTEC Cumulative effect Dependence on the wind As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function. two-phase behaviour of spectral dissipation: linear dependence of Sds on the spectrum at the peak cumulative effect at smaller scales bT depends on the wind for U10 > 14 m/s

White Cap Dissipation Sds Spectrogram method Threshold behaviour of the dissipation Babanin and Young, WAVES-2005 Babanin & van der Weshuysen, JPO, 2008 Babanin et al., 2001, JGR threshold behaviour is also predicted by the modulational instability

White Cap Dissipation Sds Babanin, APS, 2009 spectral dissipation was approached by two independent means based on passive acoustic methods threshold: if the wave energy dissipation at each frequency were due to whitecapping only, it should be a function of the excess of the spectral density above a dimensionless threshold spectral level, below which no breaking occurs at this frequency. This was found to be the case around the wave spectral peak: dominant breaking dissipation at a particular frequency above the peak demonstrates a cumulative effect, depending on the rates of spectral dissipation at lower frequencies As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function. dimensionless saturation threshold value of should be used to obtain the dimensional spectral threshold Fthr(f) at each frequency f dissipation depends on the wind for U10 > 14 m/s

Methodology Important! observe known physical constrains Tsagareli et al, 2010, JPO Babanin et al., 2010, JPO Important! observe known physical constrains calibrate the source functions, if necessary, separately As waves grow under the influence of wind, they tend to break with the increasing steepness, and dissipate energy through various mechanisms. The appearance of 'white caps' is one of the indications of this dissipative process. It is generally believed that white capping is the dominant dissipative mechanism in a wave field at moderate and higher wind speeds - simply because other dissipative processes such as molecular viscosity and turbulence appear to be inadequate to remove the energy which is known to be imparted to the waves by the wind [Hasselmann (1974)]. This process of gravitational breaking is transient and initiated when wave becomes unstable. A number of attempts have been made to describe this highly nonlinear process of wave breaking - these include both experimental [Banner, Babanin and Young, (2000)] and theoretical studies [Banner and Young, (1994)]. Such studies generally consider it as an isolated phenomenon related to individual waves. In numerical modeling of waves, however, it must be formulated as a source term applicable to the wave spectrum. A number of approaches have been applied to model wave dissipation by breaking. Two of these approaches, the pressure pulse model [Hasselmann (1974)] and the quasi-saturated model [Phillips (1985), Donelan and Pierson (1987)] treat dissipation as a quasi-linear function of the wave spectrum, whereas the probability model [Longuet-Higgins (1969), Yuan et al. (1986)] considers it to be exponentially dependent on the wave spectrum. The pressure pulse or quasi-saturated models are deterministic. Observations of wave, however, indicate that white-capping is highly variable. There can be two waves, which for all practical purposes appear identical with same height, period and steepness. One will break and the other will not. Thus it may be appropriate to represent white-capping as a stochastic process where each wave is assigned a probability of white-capping, which proposed in probability model. The discussion above shows that whitecap dissipation is a process, which is poorly understood. No rigorous theory exists for either the onset of white-capping or the resulting energy loss, neither does an experimentally measured spectral dissipation function.

Swell attenuation b1=0.002 Dissipation volumetric per unit of surface Babanin, CUP, 2011 Swell attenuation b1=0.002 Dissipation volumetric per unit of surface per unit of propagation distance

Young, Babanin, Zieger, JPO, 2013 Swell attenuation

TESTING, CALIBRATION, VALIDATIONS

Charles James, PIRSA-SARDI (UA), Spencer Gulf SWAN model, default and new physics (Rogers et al., 2012)

Cyclone Yasi Deep water track, winds (top), waves (bottom) waves next to Townsville (ADCP) and Cape Cleveland (buoy)

validations/updates TEST451 if based on physics, incremental improvements of the model are possible changing a source term does not require re-turning the other source terms integrals of the sources can be used as fluxes for coupling with GCMs BYDRZ Hindcast 2006 Spatial bias in mean wave height TEST451 with BETAmax=1.33 BYDRZ swell parameter b1=0.25E-3

observation-based source terms Implemented in WAVEWATCH-III and SWAN Wind input (Donelan et al. 2006, Babanin et al, 2010) weakly nonlinear in terms of spectrum slows down at strong winds (drag saturation) constraint on the total input in terms of wind stress Breaking dissipation (Babanin & Young 2005, Rogers et al. 2012) threshold in terms of spectral density cumulative effect away from the spectral peak strongly nonlinear in terms of spectrum Non-breaking (swell) dissipation (Babanin 2011, Young et al. 2013) interaction of waves with water turbulence Negative input (adverse or oblique winds, Donelan 1999, unpublished Lake George observations) of principal significance for modelling waves in tropical cyclones Physical constraints (Babanin et al. 2010, Tsagareli et al. 2010)

Where to go?

work in progress Wave-bottom interactions (completed) Boundary layer model instead of wind input parameterisation New term for non-linear interactions (non-homogeneous, quasi-resonant, Stokes corrections, wave breaking) Wave-current interactions Wave-ice interactions

Model Based on Full Physics Can be used for prediction of adverse events (dangerous seas, freak waves, swells, breaking, steepness, PDF tail) outputting the fluxes coupling with extreme weather (hurricane) models coupling with atmospheric and oceanic modules of GCMs, atmospheric boundary layer, ocean circulation, climate

Input and total stress f-4 to f-5 JONSWAP DHH

Whitecapping dissipation now, coefficients a and b need to be found Young and Babanin a = 0.0069 (only one record analysed) coeff. a and b based on the input/dissipation ratio Donelan (1998) showing the fraction of momentum (dashed line) and of energy (plain line) retained by the waves