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We present mathematical methods for the interpretation of high frequency radar sea‐echo measured by narrow‐beam and CODAR systems. (CODAR is a small transportable radar with a scanning broad beam). These methods are based Barrick's equations for the ocean radar cross section in terms of the directional ocean waveheight spectrum and surface current, using a dimensionless mathematical formulation. In this paper, we describe the simulation of narrow‐ and broad‐beam radar sea‐echo from both deep and shallow water, discussing the effect of ocean surface currents, including vertical and horizontal current shear. This paper provides the mathematical tools for the modeling of common experimental situations in HF radar oceanography; such models are used in subsequent papers that describe the extraction of sea‐state information from HF radar sea‐echo data.

This paper describes methods used for the derivation of wave information from SeaSonde data, and gives examples of their application to measured data. The SeaSonde is a compact high-frequency (HF) radar system operated from the coast or offshore platform to produce current velocity maps and local estimates of the directional wave spectrum. Two methods are described to obtain wave information from the second-order radar spectrum: integral inversion and fitting with a model of the ocean wave spectrum. We describe results from both standardand long-range systems and include comparisons with simultaneous measurements from an S4 current meter. Due to general properties of the radar spectrum common to all HF radar systems, existing interpretation methods fail when the waveheight exceeds a limiting value defined by the radar frequency. As a result, standard-and long-range SeaSondes provide wave information for different wave height conditions because of their differing radar frequencies. Standard-range SeaSondes are useful for low and moderate waveheights, whereas long-range systems with lower transmit frequencies provide information when the waves are high. We propose a low-cost low-power system, to be used exclusively for local wave measurements, which would be capable of switching transmit frequency when the waveheight exceeds the critical limit, thereby allowing observation of waves throughout the waveheight range.

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