• Arkell, R., , and Hudlow M. , 1977: GATE International Meteorological Radar Atlas. NOAA, Washington, DC, 222 pp.

  • Bell, T. L., , Abdullah A. , , Martin R. L. , , and North G. R. , 1990: Sampling error for satellite-derived tropical rainfall: Monte Carlo study using a space–time stochastic model. J. Geophys. Res, 95 , 21952205.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chiu, L. S., , North G. R. , , Short D. A. , , and McConnell A. , 1990: Rain estimation from satellites: Effect of finite field of view. J. Geophys. Res, 95 , 21772185.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ha, E., , and North G. R. , 1994: Use of multiple gauges and microwave attenuation of precipitation for satellite verification. J. Atmos. Oceanic Technol, 11 , 629636.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ha, E., , and North G. R. , 1995: Model studies of the beam-filling errors for rain-rate retrieval with microwave radiometers. J. Atmos. Oceanic Technol, 12 , 268281.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ha, E., , and North G. R. , 1999: Error analysis for some ground validation designs for satellite observations of precipitation. J. Atmos. Oceanic Technol, 16 , 19491957.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kedem, B., , Chiu L. S. , , and North G. R. , 1990: Estimation of mean rain rate: Application to the satellite observations. J. Geophys. Res, 95 , 19651972.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McConnell, A., , and North G. R. , 1987: Sampling errors in satellite estimates of tropical rain. J. Geophys. Res, 92 , (D8),. 95679570.

  • North, G. R., , and Nakamoto S. , 1989: Formalism for comparing rain estimation designs. J. Atmos. Oceanic Technol, 6 , 985992.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • North, G. R., , Shen S. S. P. , , and Upson R. B. , 1991: Combining rain gages with satellite measurements for optimal estimates of area-time averaged rain rate. Water Resour. Res, 27 , 27852790.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • North, G. R., , Valdes J. B. , , Ha E. , , and Shen S. P. , 1994: The ground-truth problem for satellite estimates of rain rate. J. Atmos. Oceanic Technol, 11 , 10351041.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parzen, E., 1962: Stochastic Processes. Holden-Day, 324 pp.

  • Patterson, V. L., , Hudlow M. D. , , Pytlowany P. J. , , Richards F. P. , , and Hoff J. D. , 1979: GATE radar rainfall processing system. NOAA Tech. Memo. EDIS 26, Washington DC, 158 pp.

    • Search Google Scholar
    • Export Citation
  • Shin, K. S., , and North G. R. , 1988: Sampling error study for rainfall estimates by satellite using a stochastic model. J. Appl. Meteor, 27 , 12181231.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J., , Adler R. F. , , and North G. R. , 1988: A proposed Tropical Rainfall Measuring Mission (TRMM) satellite. Bull. Amer. Meteor. Soc, 69 , 278295.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Theon, J. S., , Matsuno T. , , Sakata T. , , and Fugono N. , 1992: The Global Role of Tropical Rainfall. A. Deepak, 280 pp.

  • Thiele, O. W., 1992: Ground truth for rain measurement from space. The Global Role of Tropical Rainfall, J. S. Theon et al., Eds., A. Deepak, 245–260.

    • Search Google Scholar
    • Export Citation
  • Wilheit, T. T., , Cheng A. T. C. , , and Chiu L. S. , 1991: Retrieval of monthly rainfall indices from microwave radiometric measurements using probability distribution functions. J. Atmos. Oceanic Technol, 8 , 118136.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 130 130 0
PDF Downloads 3 3 0

Evaluation of Some Ground Truth Designs for Satellite Estimates of Rain Rate

View More View Less
  • 1 Department of Statistics, Yonsei University, Wonju, Korea
  • | 2 Department of Atmospheric Sciences, Texas A&M University, College Station, Texas
  • | 3 Department of Environmental Engineering, Korea University, Seochang, Korea
  • | 4 Department of Atmospheric Sciences, Pusan National University, Pusan, Korea
© Get Permissions
Restricted access

Abstract

In this paper point gauge measurements are analyzed as part of a ground truth design to validate satellite retrieval algorithms at the field-of-view spatial level (typically about 20 km). Even in the ideal case the ground and satellite measurements are fundamentally different, since the gauge can sample continuously in time but at a discrete point, while a satellite samples an area average but a snapshot in time. The design consists of comparing a sequence of pairs of measurements taken from the ground and from space. Since real rain is patchy, that is, its probability distribution has large nonzero contributions at zero rain rate, the following ground truth designs are proposed. Design 1 uses all pairs. Design 2 uses the pairs only when the field-of-view satellite average has rain. Design 3 uses the pairs only when the gauge has rain. For the nonwhite noise random field having a mixed distribution, the authors evaluate each design theoretically by deriving the ensemble mean and the mean-square error of differences between the two systems. It is found that design 3 has serious disadvantage as a ground truth design due to its large design bias. It is also shown that there is a relationship between the mean-square error of design 1 and design 2. These results generalize those presented recently by Ha and North for the Bernoulli white noise random field. The strategy developed in this study is applied to a real rain rate field. For the Global Atmospheric Program (GARP) Atlantic Tropical Experiment (GATE) data, it is found that by combining 50 data pairs (containing rain) of the satellite to the ground site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the system alone. For the less realistic case of a white noise random field, the number of data pairs is about 100. Hence, the use of more realistic fields means that only about half as many pairs are needed to detect a 10% bias.

Corresponding author address: Dr. Gerald R. North, Department of Atmospheric Science, Texas A&M University, MS 3150, College Station, TX 77843-3150. Email: northead@ariel.tamu.edu

Abstract

In this paper point gauge measurements are analyzed as part of a ground truth design to validate satellite retrieval algorithms at the field-of-view spatial level (typically about 20 km). Even in the ideal case the ground and satellite measurements are fundamentally different, since the gauge can sample continuously in time but at a discrete point, while a satellite samples an area average but a snapshot in time. The design consists of comparing a sequence of pairs of measurements taken from the ground and from space. Since real rain is patchy, that is, its probability distribution has large nonzero contributions at zero rain rate, the following ground truth designs are proposed. Design 1 uses all pairs. Design 2 uses the pairs only when the field-of-view satellite average has rain. Design 3 uses the pairs only when the gauge has rain. For the nonwhite noise random field having a mixed distribution, the authors evaluate each design theoretically by deriving the ensemble mean and the mean-square error of differences between the two systems. It is found that design 3 has serious disadvantage as a ground truth design due to its large design bias. It is also shown that there is a relationship between the mean-square error of design 1 and design 2. These results generalize those presented recently by Ha and North for the Bernoulli white noise random field. The strategy developed in this study is applied to a real rain rate field. For the Global Atmospheric Program (GARP) Atlantic Tropical Experiment (GATE) data, it is found that by combining 50 data pairs (containing rain) of the satellite to the ground site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the system alone. For the less realistic case of a white noise random field, the number of data pairs is about 100. Hence, the use of more realistic fields means that only about half as many pairs are needed to detect a 10% bias.

Corresponding author address: Dr. Gerald R. North, Department of Atmospheric Science, Texas A&M University, MS 3150, College Station, TX 77843-3150. Email: northead@ariel.tamu.edu

Save