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# A STATISTICAL COMPARISON OF AMPS 10-KM AND 3.3-KM DOMAINS PowerPoint PPT Presentation

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:

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)

### 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

### 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

### 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