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# 106handout3 [Compatibility Mode] - (Chapter3 1)Introduction...

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Statistical Consideration (Chapter 3) 1) Introduction Statistic method can not provide definite answer, but helps in establishing relationship (through correlation, regression, and other analysis) and quantifying uncertainties within climatic data. Because the climate system is complex, many are not well known, statistical methods are important in providing meaningful and useful simplification of system variability.
2) Some basic statistical methods (1) The mean Time ( ‾‾‾‾‾ ) t , space ( ‾‾‾‾‾ ) s , and ensemble ( ‾‾‾‾‾ ) e averages are three ways to define a mean. The time average applies at one specific point in space and consists of a sum or integral over time period.

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Example, We use anemometers to measure the U wind component. We record the instantaneous wind speeds, resulting the following 10 wind observations:
(2) Variance and standard deviation One statistical measure of the dispersion of data about the mean is the variance, σ 2 , defined by:

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Example, We use anemometers to measure the U wind component. We record the instantaneous wind speeds, resulting the following 10 wind observations:

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(3) Correlation Correlation (r AB ) represents the relationship between two variables ( 100% to 100%). r AB: Linear Correlation coefficient. r AB 2 represents the percent of the variability in A(or B) can be attributed to variability in B (or A).

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(3) Correlation Correlation (r AB ) represents the relationship between two variables ( 100% to 100%). r AB: Linear Correlation coefficient. r AB 2 represents the percent of the variability in A(or B) can be attributed to variability in B (or A). B A AB r B) COVAR(A,
0 1 2 3 4 5 6 7 8 9 U W

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3) Time series analysis Nearly all climatological data can be ordered as a time series.

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Climatological processes operate over a wide range of timescale (diurnal, annual, interannual, decadal, . ...). Diurnal Cycle Annual Cycle

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A traditional time series plot provides a quick look for temporal patterns in data including trend, cycle, discontinuities. Duration: (1)N: number of values. (2) t: time interval. Time series analysis : detecting, describing, and modeling climate variability and impacts.
Care must be taken when you work on a time series data.

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106handout3 [Compatibility Mode] - (Chapter3 1)Introduction...

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