Laser ranging error budget for the TOPEX/POSEIDON satellite.
A laser ranging error budget is detailed, and a specific error budget is derived for the TOPEX/POSEIDON satellite. A ranging uncertainty of 0.76 cm is predicted for TOPEX/POSEIDON at 20 degrees elevation using the presently designed laser retroreflector array and only modest improvements in present system operations. Atmospheric refraction and satellite attitude effects cause the predicted range error to vary with satellite elevation angle from 0.71 cm at zenith to 0.76 cm at 20 degrees elevation. This a priori error budget compares well with the ~1.2-cm rms a posteriori polynomial orbital fit using existing data taken for an extant satellite of similar size and orbit.
Correction of laser range tracking data for atmospheric refraction at elevations above 10 degrees
A formula for correcting laser measurements of satellite range for the effect of atmospheric refraction is given. The corrections apply above 10 deg elevation to satellites whose heights exceed 70 km. The meteorological measurements required are the temperature, pressure, and relative humidity of the air at the laser site at the time of satellite pass. The accuracy of the formula was tested by comparison with corrections obtained by ray-tracing radiosonde profiles. The standard deviation of the difference between the refractive retardation given by the formula and that calculated by ray-tracing was less than about 0.04% of the retardation or about 0.5 cm at 10 deg elevation, decreasing to 0.04 cm near zenith.
Pyrite multiple-sulfur isotope evidence for rapid expansion and contraction of the early Paleoproterozoic seawater sulfate reservoir
Abstract Earthʼs oxygenation is often described in terms of two unidirectional steps at the beginning and end of the Proterozoic Eon, separated by a long-lived intermediate redox state. Recent work defines a more complicated path to oxygenation, exemplified by an apparent drop in oxidation state following the early Paleoproterozoic Lomagundi carbon isotope excursion. The timing of this proposed drop in oxidation state is not well constrained, and it is not clear how it relates to redox conditions during the remainder of the Proterozoic. Here we present a study of pyrite multiple-sulfur isotopes, supported by Fe speciation and organic carbon isotopes, from early Paleoproterozoic black shales. We find evidence for the rapid expansion of the seawater sulfate reservoir during the Great Oxidation Event at ca. 2.3 Ga followed by a subsequent contraction in the size of the seawater sulfate reservoir at ca. 2.05 Ga. This scenario is consistent with the emerging view of a rise and fall in surface oxidation state during the early Paleoproterozoic. Comparison of our new data to other records of the seawater sulfate reservoir suggests that the elevated sulfate concentrations that characterize the early Paleoproterozoic did not return until the late Neoproterozoic.