An Inverse Model for Near-Surface Velocity from Infrared Images

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Abstract
An inverse model to infer the near-surface velocity from the heat equation was applied to a series of six infrared satellite images from northern California. The inversion used a two-dimensional nondiffusive heat equation with a simple representation of surface heat fluxes and vertical entrainment. The along-isotherm component of the velocity was in the null space of this problem. An overdetermined problem was defined by adding weighted constraints on the energy, divergence and curl of the velocity and representative solutions were chosen from the family of solutions corresponding to a designated misfit level for the heat equation. A series of solutions with an average energy of 250 km2 d−2 and a divergence of 0.36 d−1 compared well with simultaneous Doppler acoustic log (DAL) measurements in regions with strong temperature gradients. The decorrelation time for the solutions was about one day. Horizontal advection accounted for about 40% of the variance of the temporal temperature derivative. There was little statistical skill in predicting temperature changes with the velocity fields inferred from previous images because of the short decorrelation time; however the average solutions provided a qualitative picture of movement of features seen in the series of images. The strongest region of divergence, the leading edge of a cold eddy near the coast, was consistent with average divergence calculations from DAL surveys for the same region. The velocity solutions from these inversions supported the theory that the apparent cold filaments in the images were actually meanders of the California Current.

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