A new statistical-dynamical downscaling technique

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1 A ew statistical-dyamical dowscalig techique Yosvay Martiez Wei Yu Hai Li Meteorological Research Brach Eviromet Caada

2 Outlie Backgroud ad Motivatio Methodology Applicatios Discussio Future Work Page 2 July-4-12

The activities o eergy compaies are strogly aected by temperature coditios: heatig ad coolig degree days are requetly used as a measure o

3 Backgroud ad Motivatio Daily time series o temperature Temperature coditios have a importat impact o may aspects o agricultural productio such as pest maagemet, platig date, ad harvestig date Kadioglu et al The activities o eergy compaies are strogly aected by temperature coditios: heatig ad coolig degree days are requetly used as a measure o eergy demads Johso et al Daily time series o wid speed Importat or the wid eergy idustry to determie the wid resource ad the deploymet o wid turbies or the geeratio o electricity Page 3 July-4-12

4 Backgroud ad Motivatio Techiques or time series costructio Stochastic weather geerators: Ca simulate may realizatios ad thus ca provide a wide rage o easible weather situatios Semeov et al. 1998; Hase ad Driscoll 1977; Youg 1994; Gregory et al. 1993; Katz ad Parlage 1993 Pricipal Compoet Aalysis PCA Dowscalig techiques Statistical empirical: Derive statistical relatios betwee large-scale ad regioal-scale aomalies Heye et al. 1996; Beestad 2001; Huth Dyamical or Nestig: Uses a mesoscale model to dowscale the global data to a certai regio Rie et al. 2010; Hahma et al Statistical-dyamical: Liks global data with mesoscale model simulatios usig statistics about large-scale weather classes Frey-Buess et al. 1995; Frak ad Ladberg 1997; Yu et al Page 4 July-4-12

5 Objectives Itroduce a ew statistical-dyamical dowscalig techique based o the Empirical Orthogoal Fuctio EOF aalysis o large-scale data Applicatios to the geeratio o regioal time series o temperature ad wid Applicatios to the estimatio o the wid resource. Wid atlas mappig Validate the method usig observatios ad previous results rom other authors Page 5 July-4-12

6 Methodology Preparatio o the dataset ad observatios - Basic states computatio historic mea 0 - Disturbaces, t 0 + ', t ' T = Z - Itroduce geographical + variable weightig - Prepare the observatio dataset or uture validatios =, T, H, U, V Perorm EOF aalysis o large-scale data - Flow decompositio ', t = a t + e, t - Costruct covariace matri 1 T C ij = ' i, tk ' j, tk N k - Solve the eigeproblem ad id EOFs ad PCs: C = l Page 6 July-4-12

7 Methodology Costruct the large-scale atmospheric patters to drive the mesoscale model w w = 0 + s is the -th large-scale atmospheric weather patter s the stadard deviatio correspodig to the -th PC Note: Here the orderig o w is i terms o the statistical variace eplaied by idividual EOFs Coduct mesoscale simulatios to adapt the basic state 0 ad the large-scale atmospheric compoet patters w to high-resolutio terrai ad surace roughess Costruct the regioal time series usig the ormula: w - 0, t = 0 + a t = 0 + a t s Page 7 July-4-12

8 Methodology Costruct regioal time series o wid speed 2 sp, t = U, t + V, t Take the time average o the wid speed time series to geerate wid maps 2 Use observatios to validate results - Compute absolute mea error or idividual statios ad globally - Compute correlatio coeiciets betwee estimated ad observed time series Page 8 July-4-12

Applicatios Page 9 July-4-12 NCEP Reaalysis data - 6 hourly temperature, geopotetial height, zoal ad meridioal wids, speciic humidity - 1958-2003 45 yrs - 2.5 2.

9 Applicatios Page 9 July-4-12 NCEP Reaalysis data - 6 hourly temperature, geopotetial height, zoal ad meridioal wids, speciic humidity yrs degrees horizotal grid poits i the horizotal - 9 pressure levels: 1000., 925., 850., 700., 500., 300., 200., 100., 50., 20. mb Observatio data - 29 masts - Temperature at 30 m - wid speed at 40 m - 6 hourly - 5 yrs observatios

10 PCs ad variace spectra -First 10 EOF modes eplai almost 80 % o the total variace. - Diural, syoptic ad aual time cycles - Statistical iormatio is compressed ito a ew domiat weather patters which represet ad advatage over previous techiques that use several hudreds o weather situatios Page 10 July-4-12

11 NCEP time series recostructio 3 modes 5 modes 7 modes 34 modes w 0 Time samplig 6 h rom 1 Jauary Page 11 July-4-12

12 NCEP time series recostructio 3 modes 5 modes 7 modes 34 modes Time samplig 6 h rom 1 Ja Page 12 July-4-12

13 Numerical itegratios GEM-LAM versio Model coiguratio similar to Yu et al km grid space - Domai size height o model lid 20 km - 28 uevely spaced model vertical levels - 10 levels iside the PBL below 1500 m - time step 120 s - umber o time step durig which moutai grows The model is drive irst by the large-scale basic state ad the by the atmospheric compoet patters w - The model is ru util a steady state is reached appro. 4 h Page 13 July-4-12

14 Page 14 July-4-12 Regioal time series geeratio - + = + = w t a t a t s, modes 3 modes 5 modes 34 modes

15 Regioal time series geeratio The Global Mea Absolute Error GMAE is o-mootoic Page 15 July-4-12

16 Page 16 July-4-12 Regioal EOFs - + = + = w t a t a t s, 0 0 0

17 Page 17 July-4-12 Regioal EOFs - + = + = w t a t a t s, 0 0 0

Numerical wid atlas Numerical wid atlas - Similar to the wid map geerated i Yu et al. 2006 - Similar value o GMAE appro. 0.

18 Numerical wid atlas Numerical wid atlas - Similar to the wid map geerated i Yu et al Similar value o GMAE appro m/s - The wid speed estimate or the mast i regio B high terrai is better compared with the estimate or the same mast i Yu et al Page 18 July-4-12

19 Summary The homogeeous geostrophic wid ad hydrostatic balace costraits used by previous method have bee elimiated allowig the use o larger domais to perorm the computatios A umerical wid map is geerated as accurate as the wid map obtaied i Yu et al or the same regio. The ew method, however, is computatioally cheaper. The ew method allows or the geeratio o highly accurate regioal time series Page 19 July-4-12

20 THANK YOU!

21 Basic states Page 21 July-4-12

22 Basic states Page 22 July-4-12

23 Large-scale EOF mode mb Page 23 July-4-12

24 Large-scale EOF mode mb Page 24 July-4-12

Lecture 2: Monte Carlo Simulation

Lecture 2: Monte Carlo Simulation STAT/Q SCI 43: Itroductio to Resamplig ethods Sprig 27 Istructor: Ye-Chi Che Lecture 2: ote Carlo Simulatio 2 ote Carlo Itegratio Assume we wat to evaluate the followig itegratio: e x3 dx What ca we do?