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Regularly spaced low walls and rectangular lattices on a hard ground have been investigated as a means for reducing noise levels from surface transport. Predictions of the insertion loss of such surfaces has involved the use of computationally intensive numerical methods such as the Boundary Element Method (BEM) or Finite difference techniques (FDTD and PSTD). By considering point-to-point propagation above regularly spaced acoustically hard grooves with rectangular cross sections, a modal model used hitherto to predict electromagnetic and ultrasonic surface waves is adapted to derive an effective impedance for such a grooved surface. When this effective impedance is used in the classical theory for propagation from a point source above an impedance plane, the modal model enables predictions of excess attenuation spectra that compare closely with those obtained by numerical methods but take a fraction of the time. Also the modal method is extended to predict excess attenuation spectra above phase gradient metasurfaces with porous material in each constituent groove. [ABSTRACT FROM AUTHOR]