Monthly Mean Significant Wave Research Articles

A novel hybrid model based on grey wolf optimizer and group method of data handling for the prediction of monthly mean significant wave heights

Significant wave height prediction is challenging owing to the nonlinear and nonsmooth attributes of wave heights. This study presents a hybrid model coupling group method of data handling (GMDH) with grey wolf optimizer (GWO) for the prediction of significant wave heights. The datasets were assembled from three different observations, Stations 41001, 41002 and 44004 in the Atlantic; the datasets of Stations 41001 and 41002 were used for training, and those of Station 44004 were used for testing. The performance of the GWO-GMDH model was compared with four artificial intelligence models, the GMDH, gene expression programming (GEP), adaptive neuro-fuzzy inference system (ANFIS) and back propagation (BP) neural network models, and one empirical equation derived by Buckingham π-theorem. Both regression plots and statistical indices (e.g., correlation coefficient (R), root mean squared error (RMSE), mean squared error (MSE) and mean absolute percentage error (MAPE)) were adopted to evaluate the performance of the hybrid GWO-GMDH model. The MSE, RMSE, MAPE and R values were 0.041, 0.202, 7.353% and 0.953, respectively, for the training datasets and 0.031, 0.175, 7.598% and 0.941, respectively, for the testing datasets. Compared with the single GMDH model, the statistical indices of the training datasets of the hybrid GWO-GMDH model were almost the same; however, the MSE, RMSE and MAE values decreased by 24.39%, 13.37% and 7.95%, respectively, and the R value increased by 2.28% in the testing datasets. Compared with the GEP, BP, and ANFIS models and empirical equation models, the GWO-GMDH model also shows high accuracy and robustness, especially compared with empirical formulations. In addition, a graphical user interface (GUI) was developed to facilitate the application of practical engineering use.

Wind-wave hindcast in the Yellow Sea and the Bohai Sea from the year 1988 to 2002

We performed long-term wind-wave hindcast in the Yellow Sea and the Bohai Sea from the year 1988 to 2002, and then analyzed the regional wave climate. Comparisons between model results and satellite data are generally consistent on monthly mean significant wave height. Then we discuss the temporal and spatial characteristics of the climatological monthly mean significant wave heights and mean wave periods. The climatologically spatial patterns are observed as increasing from northwest to southeast and from offshore to deep-water area for both significant wave height and mean wave period, and the patterns are highly related to the wind forcing and local topography. Seasonal variations of wave parameters are also significant. Furthermore, we compute the extreme values of wind and significant wave height using statistical methods. Results reveal the spatial patterns of N-year return significant wave height in the Yellow Sea and the Bohai Sea, and we discuss the relationship between extreme values of significant wave height and wind forcing.

Global dynamical projections of surface ocean wave climate for a future high greenhouse gas emission scenario

A global 1° implementation of the spectral wave model, WaveWatch III, was forced with surface winds from two atmosphere–ocean general circulation models (AOGCMs: ECHAM5 and CSIRO Mk3.5), dynamically downscaled to 60km using the Cubic Conformal Atmospheric Model. Two 30-yr time slices were simulated: 1979–2009 representing current climate, and 2070–2099 representing a future climate scenario under a high greenhouse gas emission scenario (SRES A2). A further wave model simulation with forcing from the NCEP Climate Forecast System Reanalysis for 1979–2009, using the same model settings as the climate model forced runs, serves as a benchmark hindcast to assess skill of climate-model-derived wave fields. Climate model forced wave simulations for the 1979–2009 time-slice display biases relative to the benchmark wave climate – notably an overestimation of wave generation in the Southern Ocean, which influences broad regions of the Pacific which receive these waves as swell. Wave model runs were repeated following bias-adjustment of the climate model forcing winds with the aim to reduce biases, but model skill to simulate the monthly 99th percentile of significant wave heights deteriorates severely.Projected future changes in wave climate (between 1979–2009 and 2070–2099) under the SRES A2 greenhouse gas emission scenario are relatively insensitive to whether bias-adjustment of winds has been applied. Two robust features of projected change are observed from the two climate model sets which are qualitatively consistent with previous studies: a projected increase of Southern Ocean wave generation leading to approximately 10% increase in Southern Ocean mean significant wave heights (HSm), and a projected decrease in wave generation in the North Atlantic, with changes in HSm of similar magnitude.Interannual anomalies of monthly mean significant wave height, HSm, were regressed against climate indices (Southern Oscillation Index – SOI; North Atlantic Oscillation – NAO and the Southern Annular Mode – SAM) over each time-slice. Significant differences in the relationships between wave height variability and these climate indices between current and projected climates are observed. For example, a significant shift from negative to positive correlation between the NAO and HSm anomalies along the western European and north-west African coasts in the projected future climate is noted. The potential future changes in wind-wave characteristics, and the changing relationships between interannual variability of wave climate with identified climate indices, as a response to projected future climate scenarios have broad implications for a range of processes and activities in the coastal, near-and-off-shore environments.

Global Ocean Surface Wave Simulation Using a Coupled Atmosphere–Wave Model

Abstract This study describes a 29-yr (1981–2009) global ocean surface gravity wave simulation generated by a coupled atmosphere–wave model using NOAA/GFDL’s High-Resolution Atmosphere Model (HiRAM) and the WAVEWATCH III surface wave model developed and used operationally at NOAA/NCEP. Extensive evaluation of monthly mean significant wave height (SWH) against in situ buoys, satellite altimeter measurements, and the 40-yr ECMWF Re-Analysis (ERA-40) show very good agreements in terms of magnitude, spatial distribution, and scatter. The comparisons with satellite altimeter measurements indicate that the SWH low bias in ERA-40 reanalysis has been improved in these model simulations. The model fields show a strong response to the North Atlantic Oscillation (NAO) in the North Atlantic and the Southern Oscillation index (SOI) in the Pacific Ocean that are well connected with the atmospheric responses. For the NAO in winter, the strongest subpolar wave responses are found near the northern Europe coast and the coast of Labrador rather than in the central-northern Atlantic where the wind response is strongest. Similarly, for the SOI in the Pacific Ocean, the wave responses are strongest in the northern Bering Sea and the Antarctic coast.

Evidence for Changes to the Northeast Pacific Wave Climate

SEYMOUR, R.J., 2011. Evidence for changes to the northeast Pacific wave climate. Journal of Coastal Research, 27(1), 194–201. West Palm Beach (Florida), ISSN 0749-0208. A large database of deep water wave buoy measurements over a 24-year period is created for four regions comprising the West Coast of the United States. The regional monthly mean significant wave height (MMSWH) is selected as the defining wave climate parameter and averaging multiple data sources within a region is found to significantly reduce data gaps. Two 12-year periods are compared, showing significant temporal variability but high correlation between regions, allowing the further collapse of the data to a northern and a southern region. Correlations between MMSWH records with three global-scale climate indices are investigated and only the North Pacific Index (NPI), a measure of atmospheric pressure in the Gulf of Alaska, shows strong correlation. The Multivariate ENSO Index (MEI) is less correlated and the Pacific Decadal Index (PDO), which is a measure of ocean surface temperature, provides no significant correlation. A method for displaying multiple correlations is developed that shows the mean of all MMSWH records that occur at unique temporal combinations of two climate indices. The graphics depicting the mean wave height as a function of NPI and MEI for the two 12-year periods are shown to be very instructive in establishing why the two periods are so different. On the contrary, the same procedure with PDO substituted for MEI produces uniform distributions with little interpretive value. Century-scale variation in the climate indices is investigated, and significant linear trends are found for NPI and MEI, both consistent with causing increases in mean wave energy in these regions. Causal relationships for the observed correlations are discussed, and conclusions are reached indicating that global warming is a likely contributor to observed increases in wave intensity in the North Pacific.

Influence of the NAO on the northwestern Mediterranean wave climate

This study examines teleconnections between the North Atlantic Oscillation (NAO) and the wave climate of the northwestern Mediterranean Sea (NWM), defined by the monthly mean significant wave height (SWH) and the 95th percentile significant wave height (95th percentile SWH), in the period ranging from 1958 to 2001. The data analyzed comes from the multidecadal hindcast over Europe carried out during the HIPOCAS project. In order to avoid fictitious cross-correlations, data were prewhitened by fitting a p-order autoregressive model. To split the temporal and spatial variability, an EOF encoding technique was applied to residuals before searching for teleconnections. We found the northwestern Mediterranean wave climate to be influenced by the North Atlantic Oscillation (NAO) with an instantaneous response. When the NAO is in its positive phase, positive anomalies in the SWH and the 95th percentile SWH appear in the area between the Balearic Islands, the Gulf of Lions and the Catalonian coast.

Discussion on ‘‘the estimation of monthly mean significant wave heights by using artificial neural network and regression methods” by Kemal Günaydın [Ocean Engineering 35 (2008) 1406–1415

Discussion on ‘‘the estimation of monthly mean significant wave heights by using artificial neural network and regression methods” by Kemal Günaydın [Ocean Engineering 35 (2008) 1406–1415

Author response to “Discussion on ‘The estimation of monthly mean significant wave heights by using artificial neural network and regression methods’” by Tarkan Erdik

Author response to “Discussion on ‘The estimation of monthly mean significant wave heights by using artificial neural network and regression methods’” by Tarkan Erdik

The estimation of monthly mean significant wave heights by using artificial neural network and regression methods

This paper focuses on the prediction of monthly mean significant wave heights from meteorological data by using both artificial neural network (ANN) and regression methods. Waves and meteorological data used in the study were collected by three different buoys located offshore in the Atlantic. Seven different ANN models comprising of various input combinations of monthly mean wind speeds, sea level pressures and air temperature ratios based on hourly observations were performed to evaluate wave height prediction performance of each meteorological parameter for each buoy. The results indicated that the ANN model, having all parameters in the input layer, gave the best prediction performance. In order to obtain wave heights, some empirical formulas were also suggested through the regression analysis in which wave and meteorological parameters were expressed as two dimensionless groups by using π theorem. The results of these suggested formulas were compared with those of the ANN models. From these comparisons, good performances of proposed formulas were verified by the ANN model results under waves and meteorological conditions of the studied buoys.

Wave height variations in the North Sea and on the Norwegian Continental Shelf, 1881–1999

Analyses of overlapping Norwegian Meteorological Institute (DNMI) hindcast squared monthly mean wind speeds and monthly mean significant wave heights show a linear relation. Based on available time series of wind speed, computed from sea level pressure (SLP), this enables us to establish long and consistent time series of monthly mean significant wave heights. Data sets of monthly mean 10 m wind speeds from nine locations in the North Sea and on the Norwegian Continental Shelf have been investigated. The data sets include World Meteorological Organization (WMO) data, 1881–1982, DNMI hindcast data, 1955–1999, and National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) data, 1948–1999. From these time series it is evident that mean wave heights are subject to significant variations within a variety of time scales. There is a positive trend starting in the 1960s, mainly in northern parts of the North Sea, with significant regional variation. The increase is, however, not more dramatic than the decrease which occurred from 1881 and towards the beginning of the 20th century. Analyses of annual maximum significant wave heights based on 6 h values of DNMI data, 1955–1999, strongly indicate increasing wave heights and rougher wave climate at the stations off the coast of mid-Norway. At the other stations the trends are only weakly positive or not apparent at all.

Statistical analysis and intercomparison of WAM model data with global ERS‐1 SAR wave mode spectral retrievals over 3 years

Ocean wave spectra were retrieved from a set of ERS‐I synthetic aperture radar (SAR) wave mode (SWM) spectra between January 1993 and December 1995. An assessment is given of the SWM data quality and the retrieval performance as well as the operational feasibility of the retrieval algorithm. Sensitivity studies are performed to demonstrate the weak residual dependence of the retrieval on the first‐guess input spectrum. The mean spectral parameters of the SWM retrievals are compared with spectral parameters from collocated wave model (WAM) spectra. The time series of SWM‐retrieved and WAM‐derived monthly mean significant wave heights Hs in various ocean basins show good overall agreement but with a small systematic underestimation of Hs by the WAM. A decomposition of the wave spectra into wind sea and swell reveals an average 10% overprediction of the wind sea by the WAM while swell is underpredicted by 20–30%. The positive wind‐sea bias exhibits no clear wave height dependence, while the negative swell bias decreases with swell wave height. This could be due to a too strong damping in the WAM at low frequencies. Detailed regional investigations point to the existence of smaller‐scale phenomena, which may not be adequately reproduced by the WAM at the present resolution of the wind forcing. Finally, an intercomparison is made of the observed and modeled azimuthal cutoff length scales, and global distributions are investigated. Ratios of the observed azimuthal cutoff wavenumber to the mean azimuthal wavenumber component indicate that about 75% of the swell can be directly resolved by the SAR, while about 70% of the wind sea lies at least partially beyond the cutoff.

Neural Networks for Wave Height Interpolation

Information on the heights of ocean waves at a site can be collected by a variety of instruments—each involving different methods of data retrieval and synthesis. Typically, sensing of wave heights by satellite requires the wave information to be presented in the form of values that are averaged over space and time intervals. In order to use such data for operational applications, it then becomes necessary to derive the wave heights over shorter intervals from their values available over long durations. This paper attempts to do this by employing the technique of neural networks. A simple three–layered feedforward network trained with the supervised backpropagation technique was used. The values of monthly mean significant wave heights available at different grid locations around the Indian coastline were given as input to obtain the output of weekly mean wave heights at the same locations. Analysis of the results indicated usefulness of the neural network technique in wave height interpolation problems.