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Statistical Considerations for ABFM Radar Parameters

This document presents an overview of statistical considerations for the ABFM radar parameters discussed in the 2nd ABFM/LAP Joint Workshop on May 16, 2003. We focus on core issues such as peak vs. average values, the impact of various averaging methods, and the importance of truncation in data analysis. Key recommendations include using averages of dBZ for better consistency and ensuring that the analysis box size is significantly larger than radar beam uncertainties. Planned future efforts aim to enhance spectral analysis, correlation studies, and data processing methodologies.

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Statistical Considerations for ABFM Radar Parameters

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  1. Statistical Considerations for ABFM Radar Parameters Francis J. Merceret 2d ABFM/LAP Joint Workshop 16 May 2003

  2. Overview • Core Issues • Relevant Results to Date • Things Planned for Near Term

  3. Core Issues • Peak or average? • What kind of average? • dBZ, Z, or Z-derived LWC? • Truncated (where)? • How big a box?

  4. Peak or Average? • Peak values are extremely sensitive to statistical sampling fluctuation. • See Reflectivity Averaging: A Monte Carlo Study under the reports link at ABFM Home Page for details • Use of average is strongly recommended.

  5. What Kind of Average? - 1 • Averages of Z are extremely sensitive to peaks and share disadvantages of peak values. • Averages of Zn such as LWC (n ~ 0.5) behave much like averages of Z • Averages of dBZ seem more consistent and repeatable as shown in Monte Carlo report.

  6. What Kind of Average? - 2 • Averages of data truncated at a lower bound are biased upward. Bias is severe if actual mean is within one std. dev. of boundary • Without truncation, how handle • Clear air (dBZ <<< 0) ? • Radar noise floor (range dependent) ? • Recommendation: Truncate at highest noise floor in the range of interest but no higher than two standard deviations below LLCC trigger threshold • See Monte Carlo report for quantitative analysis

  7. How Big a Box? • Box should be much bigger than radar beam position uncertainties. These are of order 1 Km. See Radar Beam Geometry Effects for ABFM under report link for details. • Box should be of same order as correlation length of phenomena being averaged. This is of order 10 – 20 Km. See Autocorrelation Presentation under report link for details.

  8. Things Planned for Near Term • Spectral analysis to determine scales of features most contributing to variance and covariance of radar and electric fields • Improved correlation analysis to determine degree of independence of the data • Correct QC error in preliminary work • Process entire data set • Include new averaged variables

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