Estimate of wind stressed sea level excitation of the Earth's annual wobble

Abstract

Summary. This article estimates the contribution to the Earth's annual wobble caused by the wind stressed non-isostatic sea level variations in the oceans. Since there is a lack of data on these sea level changes, an analytic approach is taken. An ocean basin is assumed to be bounded by two meridians of longitude and two parallels of latitude, and is symmetric about the equator. A simple zonal wind stress profile based on observed data represents the seasonal changes in each hemisphere with a simple annual cosine variation. The one layer barotropic ocean has a frictionally controlled boundary layer giving rise to a western boundary current. From the equations of motion a stream function and vorticity equation are developed. The ocean is assumed to be always in adjustment to the wind stress forcing so that the steady state solution yields the velocity and height fields. Model parameters are adjusted so that these sea level changes correspond to estimates of nonisostatic sea level changes. The expression for the annual height field changes caused by the wind stress forcing is substituted into the equations governing the wobble excitation. From the resulting expression it is seen that for an ocean basin and wind regime symmetric about the equator, the contributions to the excitation of wobble from the northern and southern oceans add, while the contributions to the length of day cancel. The pole of excitation for the resultant of all oceans moves along an ellipse of eccentricity unity (line segment), aligned nearly along the Greenwich meridian, with semi-major axes of 19 cm, and is farthest from the pole of reference along 11° E longitude in mid-February. This indicates that the major contribution to the sea level excitation comes from the set up in the western Pacific. The positive annual frequency vector is calculated to be (1.2–0.8i)×10−8 rad. Comparisons with the results of Wilson & Haubrich (1976a) show that this wind stressed sea level excitation of wobble is of the phase and probable magnitude to significantly reduce the discrepancy between the astronomically observed excitation and the calculated geophysical excitations due to air mass redistribution, continental water storage and mountain torque.