CE 397 Statistics in Water Resources, Lecture 2, 2009
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Transcript of CE 397 Statistics in Water Resources, Lecture 2, 2009
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CE 397 Statistics in Water Resources, Lecture 2, 2009
David R. MaidmentDept of Civil Engineering
University of Texas at Austin
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Key Themes
• Statistics– Parametric and non-parametric approach
• Data Visualization• Distribution of data and the distribution of statistics
of those data• Reading: Helsel and Hirsch p. 17-51 (Sections 2.1 to
2.3• Slides from Helsel and Hirsch (2002) “Techniques of
water resources investigations of the USGS, Book 4, Chapter A3.
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Characteristics of Water Resources Data
• Lower bound of zero• Presence of “outliers”• Positive skewness• Non-normal distribution
of data• Data measured with
thresholds (e.g. detection limits)
• Seasonal and diurnal patterns
• Autocorrelation – consecutive measurements are not independent
• Dependence on other uncontrolled variables e.g. chemical concentration is related to discharge
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Normal Distribution
From Helsel and Hirsch (2002)
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Lognormal Distribution
From Helsel and Hirsch (2002)
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Method of Moments
From Helsel and Hirsch (2002)
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Statistical measures
• Location (Central Tendency)– Mean– Median– Geometric mean
• Spread (Dispersion)– Variance– Standard deviation– Interquartile range
• Skewness (Symmetry)– Coefficient of skewness
• Kurtosis (Flatness)– Coefficient of kurtosis
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8From Helsel and Hirsch (2002)
y = xθ
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Histogram
From Helsel and Hirsch (2002)
Annual Streamflow for the Licking River at Catawba, Kentucky 03253500
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Histogram revised
From Helsel and Hirsch (2002)
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Quantile Plot
From Helsel and Hirsch (2002)
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Plotting positions
i = rank of the data with i = 1 is the lowestn = number of datap = cumulative probability or “quantile” of the data value (its percentile value)
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Box and Whisker Plot(Tukey (1977) “Exploratory data analysis”)
Step = 1.5 * IQR
IQR = 75th % – 25th %
Box
Whisker
From Helsel and Hirsch (2002)
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Variants on the Box Plot
Largest value
Largest value within“one step”
90th %
From Helsel and Hirsch (2002)
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Normal Distribution Quantile Plot
From Helsel and Hirsch (2002)
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Probability Plot with Normal Quantiles (Z values)
qzsqq
q
z
q
From Helsel and Hirsch (2002)
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Probabilty Plot on Probability Paper
From Helsel and Hirsch (2002)
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Time Series Analyst for Licking Riverhttp://tsa.usu.edu/nwisanalyst/
00060 = Daily streamflow
SiteID
Time Series Plot
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Probability Plot
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Histogram
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Box and Whisker Plot
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GetSiteInfo in HydroExcelhttp://river.sdsc.edu/wateroneflow/NWIS/DailyValues.asmx?WSDL
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Daily Flows in HydroExcel
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“Dimensions” of Time in HydroExcel
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Annual Flows From HydroExcel
Annual Flows produced using Pivot Tables in Excel
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0 10 20 30 40 50 60 70 80 900
1000
2000
3000
4000
5000
6000
Estimating the mean annual discharge
MeanMean +SeMean - Se
Number of years of Data
Mea
n Di
scha
rge
(cfs
)
Licking River at Catawba, Kentucky, 1934-2008 (75 years of data)