Directional Spectra of Surface Waves from Spatial Arrays: Positional Uncertainty

Abstract: Measuring directional properties of waves at the sea surface is important for myriad of coastal and deep water applications. The theory and practice of measuring directional wave spectra with coherent spatial arrays is well established for arrays with fixed elements (Young 1994). In this contribution, we are curious about the practical limitations of measuring accurate directional spectra when there is error in the position of an element within the array. To explore this question, we developed a system for testing hypothetical measurements systems based on sampling a simulated sea surface. With this system, we show that for spectra measured by pentagonal spatial array, directional spectra are robust to small offsets in position. However, as the offset increases to 0.3% of the peak wavelength, the error in directional spread at the spectral peak increases exponentially. This result should give confidence, as nearshore instruments can be placed with centimeter precision (and instruments on platforms with even greater precision) and peak ocean waves are typically 10s to 100s of meters long. Keywords: Surface Wave, Ocean Wave, Wave Observation, Directional Wave Spectra, Array Processing