Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37A degrees 27.6' N, 122A degrees 15.1' E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (nu=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.

On SAR wind speed ambiguities and related geophysical model functions

Recent investigations show that normalized radar cross sections for C-band microwave sensors decrease under high wind conditions with certain incident angles instead of increase, as is the case for low to moderate wind speeds. This creates the problem of ambiguities in high wind speed retrievals from synthetic aperture radar (SAR). In the present work, four geophysical model functions (GMFs) are studied, namely the high wind C-band model 4 (CMOD4HW), C-band model 5 (CMOD5), the high wind vertical polarized GMF (HWGMF_VV), and the high wind horizontal polarized GMF (HWGMF_HH). Our focus is on model behaviours relative to wind speed ambiguities. We show that, except for CMOD4HW, the other GMFs exhibit the wind speed ambiguity problem. To consider this problem in high wind speed retrievals from SAR, we focus on hurricanes and propose a method to remove the speed ambiguity using the dominant hurricane wind structure.

Modeling vertical heat transport in the wave affected surface layer of the ocean

In considering the vertical heat transport problems in the upper ocean, the flat upper boundary approximation for the free surface and the horizontal homogenous hypothesis are usually applied. However, due to the existence of the wave motion, the application of this approximation may result in some errors to the solar irradiation since it decays quickly in respect to the actual thickness of the water layer below the surface; on the other hand, due to the fluctuation of the water layer depth, it is improper to neglect the effects of the horizontal advection and turbulent diffusion since they also contribute to the vertical heat transport. A new model is constructed in this study to reflect these effects. The corresponding numerical simulations show that the wave motion may remarkably accelerate the vertical heat transferring process and the variation of the temperature in the wave affected layer appears in an oscillating manner.

Interannual horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean: assimilation versus TAO analysis

The interannual anomalies of horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean in an assimilation experiment are studied and compared with existing observational analyses. The assimilation builds upon a hindcast study that has produced a good simulation of the observed equatorial currents and optimizes the simulation of the Reynolds sea surface temperature (SST) data. The comparison suggests that the assimilation has improved the simulation of the interannual horizontal heat advection of the surface mixed layer significantly. During periods of interrupted current measurements, the assimilation is shown to produce more meaningful anomalies of the heat advection than the interpolation of the observational data does. The assimilation also shows that the eddy heat flux due to the correlation between high-frequency current and SST variations, which is largely overlooked by the existing observational analyses, is important for the interannual SST balance over the equatorial Pacific. The interannual horizontal heat advection anomalies are found to be sensitive to SST errors where oceanic currents are strong, which is a challenge for ENSO prediction. The study further suggests that the observational analyses of the tropical SST balance based on the TAO and the Reynolds SST data contain significant errors due to the large gradient errors in the Reynolds SST data, which are amplified into the advection anomalies by the large equatorial currents.

Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society

El Nino phenomenon in simple ocean data assimilation data

To study how the air and sea interact with each other during El Nino/La Nina onsets, extended associate pattern analysis (EAPA) is adopted with the simple ocean data assimilation (SODA) data. The results show that as El Nino/La Nina's parents their behaviors are quite different, there does not exist a relatively independent tropical atmosphere but does exist a relatively independent tropical Pacific Ocean because the air is heated from the bottom surface instead of the top surface and of much stronger baroclinic instability than the sea and has a very large inter-tropical convergence zone covering the most tropical Pacific Ocean. The idea that it is the wester burst and wind convergence, coming from middle latitudes directly that produce the seawater eastward movement and meridional convergence in the upper levels and result in the typical El Nino sea surface temperature warm signal is confirmed again.

Physical mechanism and numerical simulations of surface layer temperature inversion in tropical ocean

The one-dimensional Kraus-Turner mixed layer model improved by Liu is developed to consider the effect of salinity and the equations of temperature and salinity under the mixed layer. On this basis, the processes of growth and death of surface layer temperature inversion is numerically simulated under different environmental parameters. At the same time, the physical mechanism is preliminarily discussed combining the observations at the station of TOGA-COARE 0 degrees N, 156 degrees E. The results indicate that temperature inversion sensitively depends on the mixed layer depth, sea surface wind speed and solar shortwave radiation, etc., and appropriately meteorological and hydrological conditions often lead to the similarly periodical occurrence of this inversion phenomenon.

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.

A microwave emissivity model of sea surface under wave breaking

With the effective medium approximation theory of composites, a remedial model is proposed for estimating the microwave emissivity of sea surface under wave breaking driven by strong wind on the basis of an empirical model given by Pandey and Kakar. In our model, the effects of the shapes of seawater droplets and the thickness of whitecap layer (i.e. a composite layer of air and sea water droplets) over the sea surface on the microwave emissivity are investigated by calculating the effective dielectric constant of whitecaps layer. The wind speed is included in our model, and the responses of water droplets shapes, such as sphere and ellipsoid, to the emissivity are also discussed at different microwave frequencies. The model is in good agreement with the experimental data of microwave emissivity of sea surface at microwave frequencies of 6.6, 10.7 and 37GHz.

Circulation in the western tropical Pacific Ocean and its seasonal variation

An assimilation data set based on the GFDL MOM3 model and the NODC XBT data set is used to examine the circulation in the western tropical Pacific and its seasonal variations. The assimilated and observed velocities and transports of the mean circulation agree well. Transports of the North Equatorial Current (NEC), Mindanao Current (MC), North Equatorial Countercurrent (NECC) west of 140degreesE and Kuroshio origin estimated with the assimilation data display the seasonal cycles, roughly strong in boreal spring and weak in autumn, with a little phase difference. The NECC transport also has a semi-annual fluctuation resulting from the phase lag between seasonal cycles of two tropical gyres' recirculations. Strong in summer during the southeast monsoon period, the seasonal cycle of the Indonesian throughflow (ITF) is somewhat different from those of its upstreams, the MC and New Guinea Coastal Current (NGCC), implying the monsoon's impact on it.

Ocean wave imaging mechanism by imaging radar

Analytical representations of the high frequency spectra of ocean wave and its variation due to the variation of ocean surface current are derived from the wave-number spectrum balance equation. The ocean surface imaging formulation of real aperture radar (RAR) is given using electromagnetic wave backscattering theory of ocean surface and the modulations of ocean surface winds, currents and their variations to RAR are described. A general representation of the phase modulation induced by the ocean surface motion is derived according to standard synthetic aperture radar (SAR) imaging theory. The detectability of ocean current and sea bottom topography by imaging radar is discussed. The results constitute the theoretical basis for detecting ocean wave fields, ocean surface winds, ocean surface current fields, sea bottom topography, internal wave and so on.

Intraseasonal variability of Indian Ocean sea surface temperature during boreal winter: Madden-Julian Oscillation versus submonthly forcing and processes

[ 1] Intraseasonal variability of Indian Ocean sea surface temperature (SST) during boreal winter is investigated by analyzing available data and a suite of solutions to an ocean general circulation model for 1998 - 2004. This period covers the QuikSCAT and Tropical Rainfall Measuring Mission (TRMM) observations. Impacts of the 30 - 90 day and 10 - 30 day atmospheric intraseasonal oscillations (ISOs) are examined separately, with the former dominated by the Madden-Julian Oscillation (MJO) and the latter dominated by convectively coupled Rossby and Kelvin waves. The maximum variation of intraseasonal SST occurs at 10 degrees S - 2 degrees S in the wintertime Intertropical Convergence Zone (ITCZ), where the mixed layer is thin and intraseasonal wind speed reaches its maximum. The observed maximum warming ( cooling) averaged over ( 60 degrees E - 85 degrees E, 10 degrees S - 3 degrees S) is 1.13 degrees C ( - 0.97 degrees C) for the period of interest, with a standard deviation of 0.39 degrees C in winter. This SST change is forced predominantly by the MJO. While the MJO causes a basin-wide cooling ( warming) in the ITCZ region, submonthly ISOs cause a more complex SST structure that propagates southwestward in the western-central basin and southeastward in the eastern ocean. On both the MJO and submonthly timescales, winds are the deterministic factor for the SST variability. Short-wave radiation generally plays a secondary role, and effects of precipitation are negligible. The dominant role of winds results roughly equally from wind speed and stress forcing. Wind speed affects SST by altering turbulent heat fluxes and entrainment cooling. Wind stress affects SST via several local and remote oceanic processes.

Effect of Stokes drift on upper ocean mixing

Stokes drift is the main source of vertical vorticity in the ocean mixed layer. In the ways of Coriolis - Stokes forcing and Langmuir circulations, Stokes drift can substantially affect the whole mixed layer. A modified Mellor-Yamada 2.5 level turbulence closure model is used to parameterize its effect on upper ocean mixing conventionally. Results show that comparing surface heating with wave breaking, Stokes drift plays the most important role in the entire ocean mixed layer, especially in the subsurface layer. As expected, Stokes drift elevates both the dissipation rate and the turbulence energy in the upper ocean mixing. Also, influence of the surface heating, wave breaking and wind speed on Stokes drift is investigated respectively. Research shows that it is significant and important to assessing the Stokes drift into ocean mixed layer studying. The laboratory observations are supporting numerical experiments quantitatively.

Application of effective medium approximation theory to ocean remote sensing under wave breaking

Based on the effective medium approximation theory of composites, the empirical model proposed by Pandey and Kakar is remedied to investigate the microwave emissivity of sea surface under wave breaking driven by strong wind. In the improved model, the effects of seawater bubbles, droplets and difference in temperature of air and sea interface (DTAS) on the emissivity of sea surface covered by whitecaps are discussed. The model results indicate that the effective emissivity of sea surface increases with DTAS increasing, and the impacts of bubble structures and thickness of whitecaps layer on the emissivity are included in the model by introducing the effective dielectric constant of whitecaps layer. Moreover, a good agreement is obtained by comparing the model results with the Rose's experimental data.

Effects of winds, tides and storm surges on ocean surface waves in the Sea of Japan

Ocean surface waves are strongly forced by high wind conditions associated with winter storms in the Sea of Japan. They are also modulated by tides and storm surges. The effects of the variability in surface wind forcing, tides and storm surges on the waves are investigated using a wave model, a high-resolution atmospheric mesoscale model and a hydrodynamic ocean circulation model. Five month-long wave model simulations are inducted to examine the sensitivity of ocean waves to various wind forcing fields, tides and storm surges during January 1997. Compared with observed mean wave parameters, results indicate that the high frequency variability in the surface wind filed has very great effect on wave simulation. Tides and storm surges have a significant impact on the waves in nearshores of the Tsushima-kaihyo, but not for other regions in the Sea of Japan. High spatial and temporal resolution and good quality surface wind products will be crucial for the prediction of surface waves in the JES and other marginal seas, especially near the coastal regions.