A statistical comparison of amps 10 km and 3 3 km domains
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A STATISTICAL COMPARISON OF AMPS 10-KM AND 3.3-KM DOMAINS. Michael G. Duda, Kevin W. Manning, and Jordan G. Powers Mesoscale and Microscale Meteorology Division, NCAR AMPS Users’ Workshop 2004 June 8-10, 2004. Introduction. Purpose:

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A STATISTICAL COMPARISON OF AMPS 10-KM AND 3.3-KM DOMAINS

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A STATISTICAL COMPARISON OF AMPS 10-KM AND 3.3-KM DOMAINS

Michael G. Duda, Kevin W. Manning,

and Jordan G. Powers

Mesoscale and Microscale Meteorology Division, NCAR

AMPS Users’ Workshop 2004

June 8-10, 2004


Introduction

  • Purpose:

    • Demonstrate the usefulness of statistical significance testing in comparing biases of two domains

    • Determine where biases at McMurdo Station are significantly different in the 3.3-km and 10-km AMPS domains

    • Examine a 7 day period beginning 12Z Nov. 27, 2003 when McMurdo Station was affected by a snowstorm

  • Methodology:

    • Use hypothesis testing to identify statistically significant differences in mean bias

    • Consider only differences that are statistically significant


Domain Configuration

Compaq OSF/AlphaLinux/Xeon

(SPAWAR machine)


Forecast Analysis Times


Why Consider Statistical Significance?

  • Mean bias curves do not indicate the variance in the biases

  • Some differences between curves are not as relevant


Hypothesis Testing

  • Consider biases to be from a hypothetical population (assumed to be normally distributed)

  • Let d = x3.3 – x10

    • x3.3 and x10 are biases in 3.3-km and 10-km domains at a given time

  • Perform one-sample Student’s t test

  • H0: d=0

  • Reject H0 with 95% confidence if t t

  • Test statistic:


Hypothesis Testing Example

Circled pressure levels will be examined in the next two slides


Example: 150 hPa Temperature

  • For this data we can reject the null hypothesis at the 5 percent level

  • This means we reject the hypothesis that the means of the 3.3-km and 10-km bias populations are the same

differences between curves


Example: 850 hPa Temperature

  • For this data we cannot reject the null hypothesis at the 5 percent level

  • This means we cannot reject the hypothesis that the 3.3-km and 10-km bias populations have the same mean

differences between curves


Comparison Results: Temperature

  • Statistically significant differences

    • Surface: 3.3-km grid has warm bias while 10-km grid has a cool bias at hours 24, 36

    • 925 hPa: 3.3-km grid has warm bias while 10-km grid has a cool bias at hours 24, 36

    • 300 hPa: 3.3-km grid has larger warm bias than 10-km grid

  • No statistically significant differences

    • At hours 24 and 36, no significant differences in MAE at any level


24hr Temperature (Mean Bias)


36hr Temperature (Mean Bias)


24hr Temperature (MAE)


Comparison Results: Wind U-Component

  • Statistically significant differences

    • Surface: 3.3-km grid has lower positive bias than 10-km grid at forecast hours 12, 24, 36

    • 850 hPa: 3.3-km grid has larger negative bias at forecast hours 12, 24, 36

    • 500 hPa: 3.3-km grid has smaller bias, but MAEs of both grids are similarly large

  • Differences at other levels are not statistically significant


24hr Wind U-Component (Mean Bias)


36hr Wind U-Component (Mean Bias)


24hr Wind U-Component (MAE)


Example: Surface Temperature

35 hr forecast valid 23Z Dec 01, 2003

10-km domain 3.3-km domain


Summary

  • Use a Student’s t test (at 5 percent level) to perform statistical significance testing on difference between 3.3-km and 10-km biases

  • Identify statistically significant differences on model bias v. pressure plots for McMurdo

  • Consider only statistically significant differences between mean biases to improve objectivity

    • Apparently large differences in mean bias may be statistically insignificant and misleading


Questions?


Hypothesis Testing Example

* Biases at these pressure levels will be examined in the following slides

*

*


Example: 400 hPa Wind V-Component

For this data we do not reject the null hypothesis at the 95 percent level

differences between curves


Example: 925 hPa Wind V-Component

For this data we do reject the null hypothesis at the 95 percent level

differences between curves


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