Prediction Uncertainties in MeasureCorrelatePredict Analyses

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Prediction Uncertainties in Measure-Correlate-Pred
ict Analyses

• Anthony L. Rogers, Ph.D.
• March 1, 2006

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Measure-Correlate-Predict (MCP)

• Provides estimate of mean wind speed and wind
  speed and direction distributions
• Uses a short-term data set and a long-term
  reference site data set
• How can we estimate prediction uncertainties?
• Review of measured uncertainties
• Evaluation of jackknife estimate of variance
• Discussion of issues

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Measure-Correlate-Predict (MCP)

• Apply relationship between concurrent target and
  reference site data to long-term reference site
  data.

Mean of X 6.5
X
Y aXb
Predicted Mean of Y 5.2
Y
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Measure-Correlate-Predict (MCP)

• Relationship may be a function of wind speed,
  direction, time, temperature,
• (SpeedT, DirT)f(SpeedR, DirR , Time, TempR)
• Variance Method used here
• Slope ratio of standard deviations of x and y
  data
• Line goes through the mean of x and y
• Provides unbiased estimates
• Correlations done in 8 direction sectors

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Determining Prediction Uncertainties

• Assemble multiple pairs of long-term concurrent
  data sets
• e.g. US176-US12797,357 hourly averages
• Determine MCP estimates for multiple independent
  concurrent subsets
• e.g. 21 MCP estimates for 4000 hr segments
• Estimate long-term mean, Weibull parameters
• Evaluate how estimates vary

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Data Sets Used for Analysis

• Six inland pairs
• Oregon, Iowa, Indiana
• Six offshore pairs
• N. Atlantic, Hawaii
• 4 to 16 years of data

Reference site
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Measured Mean Wind SpeedUncertainties

• Normalized standard deviation of mean
• Uncertainty decreases as concurrent data length
  increases
• Beyond 8000 hrs little improvement
• Value depends on site
• Normalized standard deviation of Weibull shape
  factor
• Value very site dependant

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Estimating Uncertainty

• In practice
• Only one set of concurrent data
• Characteristics of concurrent data may not
  represent long-term behavior
• Confidence interval may not fall out of the
  analysis
• Are there methods to determine the confidence one
  can have in the MCP results?
• Linear regression statistics
• Jackknife estimate of variance
• Estimates from correlation coefficients

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Estimating Uncertainty from Linear Regression

• Linear regression estimate ? measured!
• Linear regression assumes data are not serially
  correlated
• But wind data ARE serially correlated
• Linear regression estimate measured value when
  data are randomly jumbled, removing serial
  correlation

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Jackknife Estimate of Variance

• Applicable to any MCP algorithm
• Typically works when other methods not available
• Find long-term predicted value, , using all of
  concurrent data
• Find n long term predicted values, , using
  concurrent data sets that each have a different
  1/nth of the data file missing
• Number of subsets, n, fixed at value that
  minimizes RMS error over all data sets
• The estimated uncertainty is
• Jackknife subsets need to be independent

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Jackknife Results Mean Wind Speed

• Inland Offshore
• Blue measured, Red Estimated

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Jackknife Results Mean Wind Speed

• Ratio of measured to estimated standard deviation
• Jackknife estimate of uncertainty of mean
  typically somewhat underestimates correct value

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Jackknife Results Weibull Shape Factor

• Inland Offshore
• Blue measured, Red Estimated

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Jackknife Results Weibull Shape Factor

• Ratio of measured to estimated standard
  deviation
• Jackknife estimate of uncertainty of Weibull
  shape factor provides reasonable estimates

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Limitations of EstimatingUncertainty from Short
Data Sets

• Uncertainty within concurrent data set may not be
  same as uncertainty at longer time intervals

Uncertainty within 1000 pt segments ltlt
variability of 1000 pt MCP predictions Uncertaint
y within 9000 pt segments variability of
9000 pt MCP predictions Better estimates at one
year
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Possible Jackknife Modifications

• Inclusion of seasonal model
• e.g Monthly correlations
• If no correlation for month,use overall
  correlation
• Little improvement in ratios
• Empirical correction factors
• e.g Scale estimate of standard deviationof mean
  wind speed by 1.6
• Ratios show great improvement
• Does empirical factor apply to all sites?

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Alternative Approaches

• Correlation coefficients
• Uncertainty weakly correlated with correlation
  coefficients
• No improvement over jackknife at these sites

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Conclusions

• Jackknife should correctly estimate uncertainty
  based on concurrent data
• Much better than using linear regression results
• Better than using fit to correlation coefficients
• Empirical correction may be used to account for
  variability at time scales greater than
  concurrent data length
• Variability at time scales greater than
  concurrent data length still a problem
• Jackknife estimate can be used with any MCP
  algorithm