1. Renewable Energy Research Laboratory University of Massachusetts Prediction Uncertainties in Measure- Correlate-Predict Analyses Anthony L. Rogers, Ph.D. March 1, 2006

2. Renewable Energy Research Laboratory University of Massachusetts 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. Renewable Energy Research Laboratory University of Massachusetts Measure-Correlate-Predict (MCP) Apply relationship between concurrent target and reference site data to long-term reference site data. Mean of X = 6.5X = Y = Y = aX+bPredicted Mean of Y = 5.2

4. Renewable Energy Research Laboratory University of Massachusetts Measure-Correlate-Predict (MCP) Relationship may be a function of wind speed, direction, time, temperature, … (Speed T, Dir T )=f(Speed R, Dir R, Time, Temp R ) “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. Renewable Energy Research Laboratory University of Massachusetts Determining Prediction Uncertainties Assemble multiple pairs of long-term concurrent data sets –e.g. US176-US127 97,357 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. Renewable Energy Research Laboratory University of Massachusetts Data Sets Used for Analysis Six inland pairs –Oregon, Iowa, Indiana Six offshore pairs –N. Atlantic, Hawaii 4 to 16 years of data SiteLocation Distance km Years of good data Inland 1Kennewick - Goodnoe*Oregon11211.52 2Red Oak/Cedar*Iowa2194.53 3Estherville/Forest City*Iowa1004.23 4Inwood/Sibley*Iowa664.33 5Radcliffe/Sutherland*Iowa1863.15 6US176x1 /US127x07*Indiana910.00 Offshore 744005/44007*New England8710.23 8Buoy 44013/44008*New England23113.49 9Buoy BUZM3/IOSN3*New England17814.33 10Buoy MDRM1/MISM1*New England6216.71 11Buoy 51001/51003*Hawaii49713.49 12Buoy 51002/51004*Hawaii56613.75 * Reference site

7. Renewable Energy Research Laboratory University of Massachusetts Measured Mean Wind Speed Uncertainties 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. Renewable Energy Research Laboratory University of Massachusetts 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. Renewable Energy Research Laboratory University of Massachusetts 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. Renewable Energy Research Laboratory University of Massachusetts Jackknife Estimate of Variance Applicable to any MCP algorithm Typically works when other methods not available 1)Find long-term predicted value,, using all of concurrent data 2)Find n long term predicted values,, using concurrent data sets that each have a different 1/nth of the data file missing 3)Number of subsets, n, fixed at value that minimizes RMS error over all data sets 4)The estimated uncertainty is: Jackknife subsets need to be independent

11. Renewable Energy Research Laboratory University of Massachusetts Jackknife Results – Mean Wind Speed InlandOffshore Blue = measured, Red = Estimated

12. Renewable Energy Research Laboratory University of Massachusetts Jackknife Results – Mean Wind Speed Ratio of measured to estimated standard deviation Jackknife estimate of uncertainty of mean typically somewhat underestimates correct value

13. Renewable Energy Research Laboratory University of Massachusetts Jackknife Results – Weibull Shape Factor InlandOffshore Blue = measured, Red = Estimated

14. Renewable Energy Research Laboratory University of Massachusetts Jackknife Results – Weibull Shape Factor Ratio of measured to estimated standard deviation: Jackknife estimate of uncertainty of Weibull shape factor provides reasonable estimates

15. Renewable Energy Research Laboratory University of Massachusetts Limitations of Estimating Uncertainty from Short Data Sets Uncertainty within concurrent data set may not be same as uncertainty at longer time intervals Uncertainty within 1000 pt segments << variability of 1000 pt MCP predictions Uncertainty within 9000 pt segments ~ variability of 9000 pt MCP predictions Better estimates at one year

16. Renewable Energy Research Laboratory University of Massachusetts 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 deviation of mean wind speed by 1.6 –Ratios show great improvement –Does empirical factor apply to all sites?

17. Renewable Energy Research Laboratory University of Massachusetts Alternative Approaches Correlation coefficients –Uncertainty weakly correlated with correlation coefficients –No improvement over jackknife at these sites

18. Renewable Energy Research Laboratory University of Massachusetts 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