## Sampling for Climate Accuracy

Sampling the diurnal cycle differs for Sun-synchronous orbits (≈ 99° inclination), polar orbits, and low-inclination, precessing orbits. A polar-orbiting satellite remains in a fixed orbital plane, sampling at two times of day, 12 hours apart. Both local times cycle through 24 hours in the course of a year as the plane of the satellite orbit rotates with respect to the Earth-Sun line. A Sun-synchronous satellite orbits in a plane that corresponds to the Earth-Sun line, and samples two, fixed, discrete, local times only. A low-latitude orbiter can sample the diurnal cycle many times in a year (six times for an inclination of 33° and an altitude of 662 km), at the expense of limited coverage of the surface.

It is not practical to have all climate satellites in the
same Sun-synchronous orbits with the same equator crossing times, *nor would
this be desirable*, because the diurnal variation is not simple and varies
over the globe. The only way to ensure benchmark quality is to adopt an
observing strategy that leads to accurate climate means. This gives rise to
another problem, namely aliasing the diurnal signal into the climate mean
because of the periodicity of satellite measurements.

A theoretical study of aliasing errors for constellations of
satellites in Sun-synchronous orbits has been made by Leroy (2001) for the case
of large-amplitude diurnal variability in surface temperature. The following
discussion is based on a numerical study of different orbits using the Salby
Global Cloud Imagery data set (GCI, Salby and Callaghan, 1997). The GCI Data
are regridded 11 *μ*m radiances on a 612 × 512 grid of regions that cover 0.35° of latitude and 0.7° of longitude. The
variance of 11 *μ*m radiation is close to the maximum
in the thermal spectrum, so that calculations using GCI
data constitute a worst-case yield an upper limit to radiance
temperature retrieval errors.

11*μ*m brightness temperature is a measure of cloud-top
temperature, or surface temperature if the skies are clear. As shown in Figure 5 brightness temperature is a minimum over Antarctica, a local minimum at the
equator where deep convection is strongest, and a maximum over the subtropical
deserts (Figure 5a). Variability (Figure 5b) is strongest in the equatorial belt, where
brightness temperature varies between 190 K and 302 K, but weakest over the
great stratocumulus fields of the subtropical oceans. There are secondary
maxima in the mid-latitude storm tracks.

Figure 5c shows the diurnal variation of the brightness temperature. It dominates the total variance for clear skies in desert locations. In other regions, variations in cloud fraction dominate. Here we are concerned with the systematic errors caused by aliasing.

Figure 6: Retrieval errors for 11*μ* brightness temperature for single satellites, averaged for 1992. The grid boxes are 22.5° square. A sampling error less than 0.1 K is distinguished with an asterisk (*). Histograms of sampling errors are shown on the right. a. A single polar orbiter (inclination: 90°, altitude: 833 km). b. A single sun-synchronous orbiter (inclination: 98.765°, altitude: 833km). c. A single tropical orbiter (inclination: 33° altitude: 662km).

Figure 7. As for Figure 6 but for constellations of orbiters, equally spaced in longitude. a. Two polar orbiters. b. Three polar orbiters. c. Three sun-synchronous orbiters.