In the preceding discussion of the satellite range measurement, it was mentioned that an estimate of the index of refraction along the path of the radar pulse is required. Two atmospheric effects that determine the actual speed of the radar pulse need to be considered in order for us to convert the time delay into an accurate range measurement. The two dominant effects are the ionosphere and troposphere shown schematically in Fig. 6.1. Those familiar with the structure of the atmosphere will note immediately that this drawing is not to scale, but is rather intended to indicate the importance of these portions of the atmosphere in the determination of the index of refraction. The ionosphere retards the pulse due to electromagnetic interactions with free electrons. In the troposphere we separate the effect into two parts, the dry correction that measures the dry-air mass the pulse must traverse, and the wet correction that takes into account the additional retardation due to water vapor in the troposphere.
Discussing the effect of the free electrons in the ionosphere first, we start by noting that the amount of retardation, converted to a change in the range measurement, is up to about 100 mm, with a typical value being of order 30 mm. This value, however, changes significantly with several variables. First, the free electrons are primarily due to the interaction of the solar wind with the upper atmosphere. Therefore there is a large difference between the day and night sides of the earth and thus over a single satellite orbit. Also, there is a significant change seasonally as the solar flux on a unit area changes. That is, there are fewer free electrons at higher latitudes than at low latitudes where the sun is more directly overhead. Finally, the electron content, and thus the correction to the range measurement, varies with the solar wind changes during the solar sunspot cycle—an effect that is well known to amateur radio operators.
Correcting for the time delay associated with the ionosphere requires knowledge of the total electron content in the path connecting the satellite to the sea surface. For so-called single frequency altimeters these estimates are provided by models of the ionosphere. We will not discuss these models, however, since the T/P mission, which carries a dual-frequency altimeter, adopts a different approach (Imel, 1994). With a dual-frequency altimeter, the radar observations of the time delay are done at two different frequencies. The reason for this is that the difference between these two measurements enables determining the ionospheric correction without an external model because the interaction with the free electrons has a known dependence on the frequency of the electromagnetic wave.
As the radar pulse leaves the ionosphere and traverses the troposphere we need to consider the wet and dry corrections to the range that were mentioned above. The dry correction is simply proportional to the total mass in the satellite to sea surface path and typically gives rather large range correction of order 2.3 m. The correction itself is computed from the surface atmospheric pressure taken from a numerical weather prediction model; this is appropriate since the surface atmospheric pressure at any point is very nearly a measure of the total mass over that point on the sea surface. Although the dry correction is rather large, its variation in time or space is typically less than 20-30 mm, because of the relatively small range over which the surface atmospheric pressure changes.
The wet tropospheric correction is quite different. This correction is due to the retarding effect of water vapor in the atmosphere, which is highly variable in space and time. There is more water vapor at low latitudes where the water is warmer; the range correction there is of order 300 to 400 mm. A more typical global value is 100 to 150 mm, since at mid-to-high latitudes the range correction is much smaller. But in both cases the day-to-day and season-to-season changes are comparable to these typical values and can therefore introduce significant errors if not properly accounted for. Unlike the dry correction case, numerical weather models are not adequate for doing this correction because the water vapor is both more variable than the surface pressure and less accurately computed by the models. To correct the range it is necessary to obtain independent measurements of the integrated water vapor. This is accomplished by flying a microwave radiometer along with the altimeter, as is done for T/P (Ruf et al., 1994), ERS 1 and 2, and Seasat.
As before, we want to consider the types of errors that might be expected from these atmospheric corrections. In particular we ask whether low-frequency drift is likely. To our knowledge there is no evidence that the ionospheric correction from the dual-frequency altimeter on T/P is subject to low-frequency drift, although we cannot absolutely rule out the possibility. For the dry tropospheric correction, low-frequency drift could arise if the surface pressure fields from the numerical weather models used were drifting with time. This is not as likely as it might seem, however, since the weather models are constantly assimilating actual weather observations, including a great deal of in situ pressure data. This assimilation should keep the atmospheric pressure field in the model from drifting significantly. Also, since the variability associated with the dry correction is rather small, a drift should be relatively easy to detect.
The wet correction, depending as it does on another complex observational system, requires more careful scrutiny. In fact, a drift in the radiometer observations, and thus in the wet range correction, has already been detected and corrected during the course of the T/P mission. The possibility of such a drift was suggested by an analysis of the drift of the T/P height measurements relative to tide gauge measurements (Mitchum, 1998), and subsequently identified by Keihm et al. (1998). This will be discussed again in the next section of this chapter; for now we only note that the wet correction is a likely place to look for possible drifts in the overall T/P system.
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