1 Analyzing Statistical Models of Hourly Precipitation Events Jennifer Esker Oklahoma Weather Center Research Experience for Undergraduates NOAA/National Severe Storms Laboratory, Norman, Oklahoma Southern Illinois University Edwardsville, Edwardsville, Illinois Mentors Harold Brooks NOAA/National Severe Storms Laboratory, Norman, Oklahoma Michael Baldwin Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma and NOAA/National Severe Storms Laboratory, Norman, Oklahoma 1 August 2003 Corresponding author address: 711 E. Broadway, Steeleville, IL 62288 Email: [email protected]
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Analyzing Statistical Models of Hourly Precipitation Events
Jennifer Esker
Oklahoma Weather Center Research Experience for Undergraduates NOAA/National Severe Storms Laboratory, Norman, Oklahoma Southern Illinois University Edwardsville, Edwardsville, Illinois
Mentors
Harold Brooks NOAA/National Severe Storms Laboratory, Norman, Oklahoma
Michael Baldwin Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma and
NOAA/National Severe Storms Laboratory, Norman, Oklahoma
1 August 2003
Corresponding author address: 711 E. Broadway, Steeleville, IL 62288 Email: [email protected]
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Abstract
Understanding the national precipitation distribution can be useful in many fields
of study, but finding those patterns is not easy. Overwhelming amounts of data create
roadblocks for detailed analysis, but constructing statistical models can reduce the mount
of data needed. This study applied gamma distributions to a year’s worth of processed
hourly precipitation data to examine the national precipitation. The set represents all
precipitation events of the contiguous United States as elliptical objects and produced a
precipitation regime classification based on the gamma parameters assigned to the
precipitation within the object. Starting with a general model of the national precipitation
the analysis continues to categorize the data by location, season and precipitation regime
to produce detailed relationships. Examining plots of the gamma parameters also
provides insights into the variability of these categories and additionally confirms that
these models present an accurate representation of annual precipitation.
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I. Introduction
Understanding annual precipitation distributions is useful for all types of fields—
forecasting, public planning, farmers, flood areas, etc.—but doing this proposes many
difficult problems. The amount of data for every hourly precipitation event is
overwhelming, so it is necessary to develop methods of describing the data and still
producing useful information. This study presents the results of a gamma distribution
model. Using a processed set of the National Center for Environmental Prediction Stage
IV data, patterns are identified and analyzed in different regions of the nation during
different times of the year, with different precipitation regimes and then employ other
plots to further describe the variability of these trends.
II. Data
The data set comprises the hourly precipitation from 2002 from the 48 contiguous
states in the form of precipitation “objects” from the NCEP Stage IV data processed by
Baldwin (2003), hereafter B03. The Stage IV data, a combination of radar images and
rain gauge measurements, is separated into objects of rain and for each object B03
interprets the implied precipitation into two parameters, α and β, creates a regime
classification, and simplifies all other information into a small set of parameters (Baldwin
2003).
To construct this set, B03 modeled each Stage IV precipitation object as an
ellipse. The amount of rain at points within each object is patterned with a gamma
Table 1. A tally of the specific number of objects and points analyzed along with the area for each region.
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Fig. 2. The regional divisions of the data. 1—West (W); 2—West Central (WC); 3—Plains (P); 4—North Central (NC); 5—Midwest; 6—Southeast (SE); 7—Northeast.
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1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+000.01 0.1 1 10 100 1000
Precipitation Threshold (mm)
Prob
abili
ty
Fig. 3 The national hourly precipitation displayed as a function of a threshold of rain verses the probability that a point in an object has over that threshold. Each triangle on the curve represents an analyzed threshold amount. The vertical lines provide specific examples of the information given by the curve. The darker line displays 17.8% of the points have more than 1mm of precipitation, while the lighter line expresses that 1 in every 5 million points have at least 100 mm of precipitation.
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0.000000001
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
NationalSENCCPWC
Fig. 4. The same as Figure 3, but shown with regional plots. The heavy line with triangles still represents the national precipitation, the line with circles represents the West (W), the line with squares represents the North Central (NC), the line with diamonds represents the Southeast and the smaller line with triangles represents the Plains (P).
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10001001010.10.011
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
Winter
10001001010.10.011
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
Spring
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Summer
10.01 0.1 1 10 100 1000
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
Fall
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Fig. 5. Seasonal depictions of the region curves in Figure 4 without the national curve. The curve descriptions remain the same.
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West
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
North Central
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
20
Plains
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
Southeast
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
Fig. 6. Gamma parameters for regional plots of summer and winter in the Figure 5. The summer objects are the lighter squares plotted behind dark diamond winter points. α is plotted on the x axis and β is potted on the y axis. The guide lines are set at specific means. The dark line is set at .1 and the light line is set at 1.
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Winter
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Spring
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
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Summer
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Fall
10.01 0.1 1 10 100 1000
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0.00000001
Fig. 7. The same plot as Figure 5 for only the convective objects of each region. The curves still represent the same regions.
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Winter
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Spring
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
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Summer
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Fall
0.00000001
0.0000001
0.000001
0.00001
0.0001
0.001
0.01
0.1
10.01 0.1 1 10 100 1000
Fig. 8. The same as Figure 5 for only the stratiform objects. The curves still represent the same regions.
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0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
Fig. 9. NC gamma parameters for the summer and winter plots in Figure 8. Same plot type as Figure 6.
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0.01
0.1
1
10
100
0.01 0.1 1 10 100
Alpha
Bet
a
Fig. 10. P gamma parameters for the summer and winter plots in Figure 7. Same plot type as Figure 6.