Elsevier

Applied Ocean Research

Volume 30, Issue 2, April 2008, Pages 120-129
Applied Ocean Research

Inverse modeling to derive wind parameters from wave measurements

https://doi.org/10.1016/j.apor.2008.08.002Get rights and content

Abstract

The problem of deriving wind parameters from measured waves is discussed in this paper. Such a need reportedly arises in the field when the wind sensor attached to a wave rider buoy at high elevation from the sea level gets disconnected during rough weather, or otherwise needs repairs. This task is viewed as an inverse modeling approach as against the direct and common one of evaluating the wind-wave relationship. Two purely nonlinear approaches of soft computing, namely genetic programming (GP) and artificial neural network (ANN) have been used. The study is oriented towards measurements made at five different offshore locations in the Arabian Sea and around the western Indian coastline. It is found that although the results of both soft approaches rival each other, GP has a tendency to produce more accurate results than the adopted ANN. It was also noticed that the equation-based GP model could be equally useful as the one based on computer programs, and hence for the sake of simplicity in implementation, the former can be adopted. In case the entire wave rider buoy does not function for some period, a common regional GP model prescribed in this work can still produce the desired wind parameters with the help of wave observations available from anywhere in the region. A graphical user interface is developed that puts the derived models to their actual use in the field.

Introduction

A large amount of ocean data is routinely collected with the help of floating wave rider buoys. Such wave buoys are fitted with both wave and wind sensors. Sometimes during rough weather, the wind anemometer usually located at the height of 3 m above mean sea level (MSL) gets disconnected, and the wind data collection stops, but the floating wave sensor continues to work. This problem has been experienced vividly by India’s National Institute of Ocean Technology which had deployed a large number of data collection buoys around the country’s coastline. The information of short interval wind speed and direction in a continuous and uninterrupted manner and also in a real time mode is needed for a variety of operation related work in the ocean, such as planning for coastal aircraft movements, recreational works, installation and construction activities, and also for output power prediction in case of wind turbines. Further, collection of historical wind data facilitates analysis and design of structures at a given location. In such cases it becomes necessary to carry out an inverse modeling to retrieve wind speed and direction from the measured wave height and period. It is therefore desirable to prescribe a method to derive the wind speed, along with its direction from the measured values of significant wave heights and periods. This work could be seen as inverse modeling, since it needs to be handled in an opposite manner to normal wind-wave modeling. Currently, there are no known methods to do so. This study therefore addresses this issue. Considering the complexity and non-linearity of the wind-wave relationship it was decided to tackle this problem through two soft computing tools that are purely non-linear in nature, namely, genetic programming (GP) and artificial neural networks (ANN).

The attempts to derive wind speed using soft computing are limited. Oztopal [17], and Mehmet et al. [15] employed an artificial neural network (ANN) to carry out regional wind speed estimations at certain locations in Turkey, based on observations at nearby locations. These studies involved speed estimation only. Attempts to derive the direction of wind using ANN are sparse, a few noticeable among them are, Thiria et al. [18], who applied the ANN approach to obtain wind direction using simulated data as well as a spatial input context, Cornford et al. [3], who used ANN based techniques to estimate wind vectors form scatterometer data. Studies dealing wind speed and direction evaluation based on GP have however not been reported so far.

Applications of GP in civil engineering related to water flow started around 5 years ago. The tool of GP has been used for a variety of purposes, like pattern recognition, classification and regression. Unlike the other soft computing tool of ANN, the GP applications are restricted to relatively fewer areas in hydraulics and water resources, e.g., [4], [22], [16]. Some of these authors have presented a comparison with other models. Drecourt [4] reported that GP handles peak flow better, while ANN takes care of the noise efficiently. Muttil and Liong [16] found the performance of GP marginally better than ANN. The applications of GP in ocean engineering are very sparse, and these include evaluation of ocean component concentration from sunlight reflectance or luminance values ([5]), coastal current prediction [2] and in-filling of missing wave data [20], [8].

Some of the studies in recent past had worked out wave parameters and sea levels in an inverse manner, by establishing spatial correlations (unlike the present causal relationship) in between similar variables and based on ANN. These include Makarynskyy [12], who obtained wave conditions at a given location, based on the same at a distant site; Makasrynskyy et al. [14] who retrieved and predicted hourly tidal levels at one station given their values at another one, and Makasynskyy and Makarynska [13] who did a similar work in case of wave parameters. The use of fuzzy systems and adaptive neuro-fuzzy inference system (ANFIS) in addition to ANN was recently made by Mahjoobi et al. [11] to hindcast waves from wind through causal mapping.

Section snippets

The database used

In this study, the time series measurements of various ocean parameters made at different locations, namely: DS1, SW2, SW3, OB3 and DS7 (Fig. 1), in the Arabian Sea were considered. The observations were made under the national data buoy program of National Institute of Ocean Technology (NIOT) at Chennai, India. The parameters were the significant wave height, Hs, average zero cross wave period, Tz, average wave period, Tm, wind speed, Ws and wind direction, θ. The time interval of sampling was

Artificial neural network

An ANN consists of an interconnection of computational elements or neurons (Fig. 2), each of which combines the input, determines its strength by comparing the combination with a bias or alternatively passing it through a non-linear transfer function, and fires out the result in proportion to such strength. Mathematically, O=1[1+eS] where, S=(x1w1+x2w2+x3w3+)+θ in which, O = output from a neuron; x1,x2, = input values; w1,w2, = weights along the linkages connecting two neurons and they

Station DS1

Station DS1 is in deep water, and it is located far away from the shoreline. The period of data collection varied from 09-04-2004 to 26-07-2005 and from 01-05-2006 to 30-09-2006; out of which observations for the first 12 months were used for training and those for the remaining 4 months (in the first set) were used for testing the network. Data for the year 2006 were additionally used to carry out the testing. The type of network used was feed forward. (Fig. 2). This was trained using a

Prediction of direction in addition to speed

The earlier section dealt with prediction of the magnitude of wind. Knowledge of the wind speed obtained in this way can be utilized for work such as derivation of statistical distributions, and estimation of design wind speed parameters. However, there are many applications where information of both speed and direction is required, such as drawing wind rose diagrams and deriving wave height and period values.

As reported in the preceding section, the GP technique was found to be very

Development of common regional GP model

The earlier sections dealt with the prediction of wind speed and its direction, based on the measured parameters of Hs, Tz and Tm. The ANN and GP models were built at locations DS1, SW2, SW3, OB3 and DS7 individually and thereafter two separate models of GP were also developed in order to determine the wind speed and its direction. Calibrated GP models in the form of equations were specified at each of the sites as in Section 5.

An attempt was thereafter made to see if a common regional GP model

A regional GP model based on combined data

After noticing good performance through a common GP model, as in the previous section, attempts were made to develop another equation trained on the entire dataset collected at all the five locations. Similar input–output schemes and methodology (used in the case of individual database) were adopted for development of such a common regional equation. The dataset used in training this model also included the cyclonic period at location DS1 and SW2. The development of such a model trained on

A regional GP model based on the entire data and the resolved components

In another alternative for combined–speed and direction–two GP models were calibrated separately based on the uv components of the speed. The evolved equations for uv components are respectively as follows: Ws(u)=(Tmexp(Hs)Tz)(Hslogexp(logTm)).Ws(v)=expHs(Hs+logTm)log(TmHs)/log((Hs+expTz)+Tm).

The evolved equations were further tested at each location. A similar pattern of results as in the previous sections was obtained. It was accordingly noted that the model performance with the uv

Putting the developed model into practice

The studies described so far for the prediction of wind speed and direction, based on an inverse cause-effect modeling can be put into practice through an integrating platform of the graphical user interface (GUI). It was seen that although results produced by both ANN and GP were close to each other, the GP outcome was marginally, but consistently better, than that of the ANN. Hence the present GUI was developed on the basis of the GP models. The 3-hourly measurements of wind speed and

Conclusions

The preceding sections described how the unobserved values of wind speed and direction at a wave buoy location can be calculated from the observed wave parameters through an inverse modeling exercise, based on genetic programming and artificial neural networks.

The GP models were able to learn the underlying complex inversed relationship well. Although the results of both soft approaches rivaled each other, the GP showed a tendency to produce more accurate values than the ANN adopted.

It was also

Acknowledgements

Authors thank Dr. K. Premkumar, Director, NDBP and Dr. G. Latha, Scientist (F) of NIOT, Chennai, India for sparing data used in this project and also for useful technical input.

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