Matrix-analog measure-cerrelatepredict

Matrix-analog measure-cerrelatepredict approach ICEM 2015 22-26 June 2015, Boulder David Hanslian Institute of Atmospheric Physics AS CR

"Measure-correlate-predict" (MCP) = methods to estimate long-term wind conditions from short-term (target) series using correlated long-term (reference) series Targets of MCP average wind speed => basic information wind speed distribution => enables energy calculation wind rose => wake effects, model inputs individual values => replacement of missing records, prediction tasks Critical issues - correlation between reference and target data - length of concurrent (training) period - homogeneity of reference data - simulation of wind distribution and wind rose - complex methods + little reference data => overfitting (overtraining)

1) simple methods of ratios MCP methods 2) methods based on relationship between wind speeds (regression, quantile mapping, wind speed bins,...) - linear regression most common (+ model of residuals if wind speed distribution is desired) - influence of wind direction => separation of data into wind direction bins 3) "matrix methods" - data are separated into "matrix" of bins - wide range of methods is labeled as matrix, but they are often prinicipially different each other (speed direction, target reference etc.) 4) artificial neural networks - advanced, complex, computionally demanding 5) other methods (less frequented) Most published methods do not perform wind rose simulation. Comprehensive review: Carta, J. A., Velázquez, S., & Cabrera, P. (2013). A review of measure-correlate-predict (MCP) methods used to estimate long-term wind characteristics at a target site. Renewable and Sustainable Energy Reviews, 27, 362 400.

Matrix-analog approach = general approach, which enables to simulate complete wind climatology 1) Define bins (by reference series) basic bins merged bins Schema of used algorithm of definition of bins rows = wind speed bins columns = wind direction bins Refers to the reference series = basic bins are merged by any algorithm, so that resulting bins contain enough data from the training period 2) Find the analog: Each time record of long-term period is assigned to a time record of training period, corresponding to the same bin. 3) Calculate wind speed and wind direction of the long-term time record 4) Correct the result to remove eventual statistical distortions. Each of these steps can be modified / optimized. Time series is a result.

Calculation methods Method 1 Application of wind speed ratios and wind direction differences on refernce data. period training target series ref. target Method 2 Direct use of the wind data of target series. Based on joint probabilistic approach. period training target series ref. target Application of "analog" principle preserves the wind speed vs. wind direction relationship => both methods simulate both wind speed distribution and wind rose.

Comparison of MCP methods/data Used data and procedure - 12 Czech manned weather stations (measurement height 10 m) reference, target - reanalyses NCEP/NCAR, ERA Interim and MERRA (different height/pressure levels, geostrophic/model wind) only reference - period 2005-2008 (only 4 years used to reduce homogeneity issues) - 12 months of training period (continual 3-month blocks of data, seasonally stratified), remaining data used for verification - fixed set of 50 resampled runs Tested metrics average wind speed, average power density wind speed distribution (Kolmogorov-Smirnov integral) wind rose (differences of frequencies, Kolmogorov-Smirnov integral) individual values

Example of simulated data

Example of simulated data comparison with real values

Example of wind rose simulation

method DD Comparison: methods average wind speed power density speed distribution wind rose freq. KSI individual values Method of ratios 1 4.19% 31.6% 13.54% 57.4% Method of ratios 12 4.03% 26.1% 10.88% 53.8% Method of ratios 36 4.08% 25.8% 10.65% 53.8% Linear regression 1 3.68% 42.7% 22.94% 53.8% Linear regression 12 3.33% 34.6% 18.32% 49.9% Linear regression 36 3.28% 32.9% 17.45% 49.9% Variance ratio 1 4.74% 12.3% 4.80% 60.4% Variance ratio 12 4.47% 12.0% 4.02% 56.8% Variance ratio 36 4.60% 14.2% 4.04% 57.1% Method 1 1 3.58% 9.8% 3.24% 35.4% 13.66 74.8% Method 1 12 3.36% 8.8% 2.91% 15.6% 4.33 69.0% Method 1 36 3.32% 9.1% 2.91% 10.8% 4.06 68.5% Method 2 1 3.58% 9.9% 3.27% 14.7% 7.40 74.9% Method 2 12 3.37% 8.8% 2.94% 11.0% 3.93 69.0% Method 2 36 3.32% 8.8% 2.92% 10.9% 3.92 68.5% Null met. (= orig. data) 6.30% 20.9% 5.08% 15.8% 8.33 All values correspond to RMSE from the (fixed) set of 50 resampled runs Average values from 13 pairs of reference/target series DD number of wind direction bins "Null method means the application of original short-term (1 year) data Linear regression good simulation of average values, does not simulate variability Method of ratios similar to linear regression, less accurate for average values Variance ratio simulation of variability on expense of average values prediction "Matrix analog" methods good in average wind speed and variability; prediction of individual values handicapped by included variability of simulated data

Comparison: methods method DD average wind speed power density speed distribution wind rose freq. KSI individual values Method of ratios 1 4.19% 31.6% 13.54% 57.4% Method of ratios 12 4.03% 26.1% 10.88% 53.8% Method of ratios 36 4.08% 25.8% 10.65% 53.8% Linear regression 1 3.68% 42.7% 22.94% 53.8% Linear regression 12 3.33% 34.6% 18.32% 49.9% Linear regression 36 3.28% 32.9% 17.45% 49.9% Variance ratio 1 4.74% 12.3% 4.80% 60.4% Variance ratio 12 4.47% 12.0% 4.02% 56.8% Variance ratio 36 4.60% 14.2% 4.04% 57.1% Method 1 1 3.58% 9.8% 3.24% 35.4% 13.66 74.8% Method 1 12 3.36% 8.8% 2.91% 15.6% 4.33 69.0% Method 1 36 3.32% 9.1% 2.91% 10.8% 4.06 68.5% Method 2 1 3.58% 9.9% 3.27% 14.7% 7.40 74.9% Method 2 12 3.37% 8.8% 2.94% 11.0% 3.93 69.0% Method 2 36 3.32% 8.8% 2.92% 10.9% 3.92 68.5% Null met. (= orig. data) 6.30% 20.9% 5.08% 15.8% 8.33 All values correspond to RMSE from the (fixed) set of 50 resampled runs Average values from 13 pairs of reference/target series DD number of wind direction bins Binning by wind direction improves results. Binning by 36 sectors not clearly better than binning by 12 sectors (except of wind rose - Matrix analog Method 1).

Comparison: reference and target series reference series target series Doksany Kopisty B-Tuřan O-Porub P-Libuš Kuchař. P-Ruzyn Č.Buděj. Cheb Luká K.Mysl. Mileš. Doksany 7.68% 8.97% 5.16% 3.98% 5.27% 4.07% 5.83% 7.97% 5.64% 4.58% 4.11% 5.75% Kopisty 9.72% 11.29% 6.17% 7.33% 7.87% 7.38% 8.10% 8.64% 9.06% 8.81% 7.20% 8.32% B-Tuřany 8.51% 6.61% 5.16% 3.73% 2.97% 4.29% 4.43% 4.07% 3.88% 5.71% 3.95% 4.85% O-Poruba 10.73% 6.41% 7.75% 6.06% 6.40% 6.87% 7.06% 6.69% 7.08% 8.46% 6.26% 7.25% P-Libuš 5.79% 5.52% 6.12% 3.97% 2.99% 1.27% 3.33% 4.86% 3.90% 4.19% 2.45% 4.04% Kuchařovice 6.79% 5.65% 5.32% 4.34% 2.55% 3.14% 3.79% 4.77% 3.51% 4.22% 3.33% 4.31% P-Ruzyně 5.59% 5.36% 6.23% 3.70% 1.11% 2.97% 3.16% 4.90% 3.82% 3.97% 2.16% 3.91% Č.Buděj. 7.33% 4.91% 5.80% 4.86% 2.27% 3.04% 2.63% 4.35% 3.97% 4.24% 2.66% 4.19% Cheb 9.64% 5.99% 5.57% 5.66% 4.35% 4.39% 4.92% 4.41% 5.05% 6.55% 4.56% 5.55% Luká 6.98% 5.74% 5.45% 4.74% 2.51% 2.94% 3.01% 3.81% 4.97% 4.59% 2.77% 4.32% K.Myslová 5.61% 6.44% 7.36% 4.66% 2.65% 3.28% 2.94% 4.03% 6.95% 3.83% 2.34% 4.55% Milešovka 7.23% 5.61% 6.83% 3.61% 2.36% 3.08% 2.18% 4.03% 5.39% 4.52% 4.20% 4.46% nc_925g 6.95% 5.01% 6.36% 4.62% 1.73% 1.62% 1.77% 3.17% 4.75% 3.11% 3.71% 1.38% 3.68% nc_925w 6.41% 5.10% 6.86% 4.24% 1.83% 2.18% 1.74% 3.17% 5.59% 3.70% 3.53% 1.48% 3.82% era_1000w 5.92% 5.59% 4.96% 3.23% 1.24% 1.45% 1.11% 3.41% 5.21% 2.49% 3.97% 1.60% 3.35% era_925g 6.77% 5.03% 5.68% 3.56% 1.40% 1.92% 1.51% 3.76% 5.23% 3.12% 4.05% 1.18% 3.60% era_925w 6.52% 5.23% 5.87% 3.44% 1.73% 1.97% 1.69% 3.28% 4.89% 2.89% 3.86% 1.32% 3.56% me_10m 6.51% 5.50% 5.64% 3.54% 1.26% 1.65% 1.37% 2.98% 5.13% 2.55% 3.78% 1.35% 3.44% avg. 7.24% 5.73% 6.59% 4.39% 2.83% 3.29% 3.05% 4.22% 5.55% 4.24% 4.85% 2.95% 4.61% Null method 11.20% 7.17% 7.58% 5.78% 5.45% 5.22% 6.91% 6.48% 6.59% 6.81% 6.45% 5.41% 6.76% Method 1, 36 directions, RMSE of average wind speed prediction. Red color = distance >100 km. target series: better results for open sites and vice versa avg.

reference series Comparison: reference and target series target series Doksany Kopisty B-Tuřan O-Porub P-Libuš Kuchař. P-Ruzyn Č.Buděj. Cheb Luká K.Mysl. Mileš. Doksany 7.68% 8.97% 5.16% 3.98% 5.27% 4.07% 5.83% 7.97% 5.64% 4.58% 4.11% 5.75% Kopisty 9.72% 11.29% 6.17% 7.33% 7.87% 7.38% 8.10% 8.64% 9.06% 8.81% 7.20% 8.32% B-Tuřany 8.51% 6.61% 5.16% 3.73% 2.97% 4.29% 4.43% 4.07% 3.88% 5.71% 3.95% 4.85% O-Poruba 10.73% 6.41% 7.75% 6.06% 6.40% 6.87% 7.06% 6.69% 7.08% 8.46% 6.26% 7.25% P-Libuš 5.79% 5.52% 6.12% 3.97% 2.99% 1.27% 3.33% 4.86% 3.90% 4.19% 2.45% 4.04% Kuchařovice 6.79% 5.65% 5.32% 4.34% 2.55% 3.14% 3.79% 4.77% 3.51% 4.22% 3.33% 4.31% P-Ruzyně 5.59% 5.36% 6.23% 3.70% 1.11% 2.97% 3.16% 4.90% 3.82% 3.97% 2.16% 3.91% Č.Buděj. 7.33% 4.91% 5.80% 4.86% 2.27% 3.04% 2.63% 4.35% 3.97% 4.24% 2.66% 4.19% Cheb 9.64% 5.99% 5.57% 5.66% 4.35% 4.39% 4.92% 4.41% 5.05% 6.55% 4.56% 5.55% Luká 6.98% 5.74% 5.45% 4.74% 2.51% 2.94% 3.01% 3.81% 4.97% 4.59% 2.77% 4.32% K.Myslová 5.61% 6.44% 7.36% 4.66% 2.65% 3.28% 2.94% 4.03% 6.95% 3.83% 2.34% 4.55% Milešovka 7.23% 5.61% 6.83% 3.61% 2.36% 3.08% 2.18% 4.03% 5.39% 4.52% 4.20% 4.46% nc_925g 6.95% 5.01% 6.36% 4.62% 1.73% 1.62% 1.77% 3.17% 4.75% 3.11% 3.71% 1.38% 3.68% nc_925w 6.41% 5.10% 6.86% 4.24% 1.83% 2.18% 1.74% 3.17% 5.59% 3.70% 3.53% 1.48% 3.82% era_1000w 5.92% 5.59% 4.96% 3.23% 1.24% 1.45% 1.11% 3.41% 5.21% 2.49% 3.97% 1.60% 3.35% era_925g 6.77% 5.03% 5.68% 3.56% 1.40% 1.92% 1.51% 3.76% 5.23% 3.12% 4.05% 1.18% 3.60% era_925w 6.52% 5.23% 5.87% 3.44% 1.73% 1.97% 1.69% 3.28% 4.89% 2.89% 3.86% 1.32% 3.56% me_10m 6.51% 5.50% 5.64% 3.54% 1.26% 1.65% 1.37% 2.98% 5.13% 2.55% 3.78% 1.35% 3.44% avg. 7.24% 5.73% 6.59% 4.39% 2.83% 3.29% 3.05% 4.22% 5.55% 4.24% 4.85% 2.95% 4.61% Null method 11.20% 7.17% 7.58% 5.78% 5.45% 5.22% 6.91% 6.48% 6.59% 6.81% 6.45% 5.41% 6.76% Method 1, 36 directions, RMSE of average wind speed prediction. Red color = distance >100 km. reference series: ERA Interim 1000 hpa & surface MERRA generally the best avg.

"Improvement rate" = ratio between error of prediction of avg. wind speed by matrix-analog MCP and Null method 'Improper' ref. sites are Doksany, Kopisty, O-Poruba and Cheb. They lay in valleys or basins, so that their wind regime is given by local orography or is isolated from largescale wind regime. Except of these bad reference stations, MCP improves results even in case of low correlation between reference and target wind speed series

Conclusions Matrix-analog approach enables reliable simulation of complete longterm wind climatology including wind speed distribution and wind rose. Its performance is very good compared to simple MCP approaches. Serious comparison with more complex MCP methods (e.g. artificial neural networks, commercial software) would be interesting! Methods based on matrix-analog approach can be individually refined. For example, optimized generation of "merged" bins may probably lead to further improvement of results, inclusion of stability etc... Performance of any MCP method strongly depends on the data used. When the training data do not contain enough information or the longterm series is inhomogeneous, no MCP method can work well. If no perfect near-by reference site is available, then using reanalyses is safer bet. I hope will make a paper soon...

Thank You for Your attention hanslian@ufa.cas.cz