Prediction Uncertainties in MeasureCorrelatePredict Analyses

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Prediction Uncertainties in MeasureCorrelatePredict Analyses

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Title: Prediction Uncertainties in MeasureCorrelatePredict Analyses

1
Prediction Uncertainties in Measure-Correlate-Pred
ict Analyses

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

2
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

3
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
4
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

5
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

6
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
7
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

8
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

9
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

10
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

11
Jackknife Results Mean Wind Speed

Inland Offshore
Blue measured, Red Estimated

12
Jackknife Results Mean Wind Speed

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

13
Jackknife Results Weibull Shape Factor

Inland Offshore
Blue measured, Red Estimated

14
Jackknife Results Weibull Shape Factor

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

15
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
16
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?

17
Alternative Approaches

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

18
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