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At low grazing angles (LGA), sophisticated electromagnetic scattering of sea surfaces may give rise to complicated surface-current distribution. Therefore, for the multilevel fast multipole algorithm (MLFMA) with the Rao-Wilton-Glisson basis function, the sea scatterer must be meshed fine enough to ensure the precision of the scattering at LGA, which brings huge computational costs. The higher order hierarchical Legendre vector basis functions can bring a great reduction of the unknowns and sparsification of the impedance matrix. The MLFMA with higher order hierarchical Legendre basis functions is applied in the electromagnetic-scattering approach of 3-D breaking water wave crests at LGA for the first time. In addition, an adaptive-order technique is also introduced for the first time in describing the currents which can achieve accurate results and maximally reduce the computational costs from some case analysis. It has been investigated in analyzing the vertically (VV) and horizontally (HH) polarized scattering of profiles of the LONGTANK breaking waves. "Sea-spike" phenomenon has been demonstrated at LGA.