Graduate Thesis Or Dissertation

Parameter estimation in a stochastic model of ocean currents

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  • In 1962 a large amount of data was collected in an effort to establish the existence of subsurface ocean currents off the coast of Oregon. The presence of several phenomena, including tides and measurement errors not directly associated with the hypothetical currents, complicates the interpretation of the data and the estimation of current velocities. This thesis advances a stochastic model to represent the sources of the data, and discusses alternative procedures for the estimation of parameters in the model. The local motion of a small volume of water is, in the first approximation, assumed a sum of a linear drift current plus a periodic tidal current. The motion of any given particle of water is then a sum of the above mentioned currents plus a random motion due to the characteristic turbulence of the ocean's waters. This random motion is shown similar to Brownian motion or more specifically the motion of the Wiener process. From the properties of the Wiener process the joint probability distribution of the observed displacements of the parachute drogue is found to be Normal with a given variance-covariance structure. By suitable linear transformation of the observed displacements, a new set of independent random variables may be obtained, where the variances due to random motion and measurement inaccuracies are combined in a known manner to form variances of the new set. A Maximum Likelihood procedure for estimating the mean velocity of the currents is proposed, and shown to coincide with the methods of Least Squares in certain special cases.
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