Sampling Errors in Rainfall Estimates by Multiple Satellites

Gerald R. North Climate System Research Program, College of Geosciences, Texas A&M University, College Station, Texas

Search for other papers by Gerald R. North in
Current site
Google Scholar
PubMed
Close
,
Samuel S. P. Shen Mathematics Department, University of Alberta, Edmonton, Canada

Search for other papers by Samuel S. P. Shen in
Current site
Google Scholar
PubMed
Close
, and
Robert Upson Climate System Research Program, College of Geosciences, Texas A&M University, College Station, Texas

Search for other papers by Robert Upson in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

This paper examines the sampling characteristics of combining data collected by several low-orbiting satellites attempting to estimate the space–time average of rain rates. The several satellites can have different orbital and swath-width parameters. The satellite overpasses are allowed to make partial coverage snapshots of the grid box with each overpass. Such partial visits are considered in an approximate way, letting each intersection area fraction of the grid box by a particular satellite swath be a random variable with mean and variance parameters computed from exact orbit calculations. The derivation procedure is based upon the spectral minimum mean-square error formalism introduced by North and Nakamoto. By using a simple parametric form for the space–time spectral density, simple formulas are derived for a large number of examples, including the combination of the Tropical Rainfall Measuring Mission with an operational sun-synchronous orbiter. The approximations and results are discussed and directions for future research are summarized.

Abstract

This paper examines the sampling characteristics of combining data collected by several low-orbiting satellites attempting to estimate the space–time average of rain rates. The several satellites can have different orbital and swath-width parameters. The satellite overpasses are allowed to make partial coverage snapshots of the grid box with each overpass. Such partial visits are considered in an approximate way, letting each intersection area fraction of the grid box by a particular satellite swath be a random variable with mean and variance parameters computed from exact orbit calculations. The derivation procedure is based upon the spectral minimum mean-square error formalism introduced by North and Nakamoto. By using a simple parametric form for the space–time spectral density, simple formulas are derived for a large number of examples, including the combination of the Tropical Rainfall Measuring Mission with an operational sun-synchronous orbiter. The approximations and results are discussed and directions for future research are summarized.

Save