Calibration of ADJULES

Transcription

1 Calibration of ADJULES Tim Jupp University of Exeter June 10, 2010

2 Outline 1 Introduction 2 Calibration 3 Example 4 Conclusions

3 Outline 1 Introduction 2 Calibration 3 Example 4 Conclusions

4 Introduction With thanks to: Thomas Kaminski (FastOpt.com) Simon Blessing (FastOpt.com) Matt Pryor (Met Office, Wallingford) Eleanor Blyth (CEH, Wallingford)

5 Overview of adjoint model Used commercial software (FastOpt) to differentiate JULES v2.0 line by-line ADJULES is subroutine callable from within R for a parameter vector x : ADJULES finds cost function f (x) ADJULES finds derivative of cost function : f (x)

6 Use of ADJULES use R-routines for efficient search of parameter space start from initial parameter vector x 0 find best parameter vector x 1 most user decisions made at runtime works and ready for testing by JULES community licensing and future development?

7 Outline 1 Introduction 2 Calibration 3 Example 4 Conclusions

8 Calibration Validation of flux #2: H H Time point black observed red modelled with initial parameter vector x 0 blue modelled with final parameter vector x 1

9 Cost function ADJULES currently hardwired to calibrate against 3 fluxes: NEE t NEE t o t = H t LE t ; m t = H t LE t Cost function is weighted least squares f (x) = n (m t o t ) T w T w(m t o t ) t=1 where 3 by 3 weight matrix w can be chosen at runtime.

10 Flexibility in choice of w For example w w consider NEE only consider H only often choose w T w observed covariance when x = x 0

11 Full parameter space: x ADJULES currently has 50 parameters in the vector x: q10 leaf nl0 1 nl0 2 nl0 3 nl0 4 nl0 5 alpha 1 alpha 2 alpha 3 alpha 4 alpha 5 f0 1 f0 2 f0 3 f0 4 f0 5 tlow 1 tlow 2 tlow 3 tlow 4 tlow 5 tupp 1 tupp 2 tupp 3 tupp 4 tupp 5 lai 1 lai 2 lai 3 lai 4 lai 5 canht ft 1 canht ft 2 canht ft 3 canht ft 4 canht ft 5 satcon 1 satcon 2 satcon 3 satcon 4 b 1 b 2 b 3 b 4 cs rootd ft 1 rootd ft 2 rootd ft 3 rootd ft 4 rootd ft 5 Table: Parameters currently hardwired into ADJULES.

12 Procedure In practice, choose a subset z of full parameter vector x choose suitable weight matrix w rescale w so that f (z 0 ) = 1 ADJULES can evaluate f (z) and f (z) for any z Optimisation routines find local minimum: z 1 f (z 1 ) < f (z 0 ) = 1

13 Outline 1 Introduction 2 Calibration 3 Example 4 Conclusions

14 Example: Morgan Monroe data one year of hourly data 9000 data points calibrate against H and LE so w = 0 a b 0 0 c chose to optimise over 29 parameters in z optimisation takes 30 minutes on high end unix machine

15 Example: Morgan Monroe data Error correlations for fluxes H and LE with z=z0 [red], z=z1 [blue] errors in flux #3: LE errors in flux #2: H red modelled with initial parameter vector x 0. Used to define w. blue modelled with final parameter vector x 1

16 Example: Morgan Monroe data Slice through z0 cost function, f(z) (z_off + z)[6]: alpha_1

17 Example: Morgan Monroe data Slice through z0 cost function, f(z) (z_off + z)[12]: f0_2

18 Example: Morgan Monroe data Validation of flux #2: H H Time point

19 Example: Morgan Monroe data Validation of flux #3: LE LE Time point

20 Example: Morgan Monroe data Errors in flux #2: H with z=z0 [red], z=z1 [blue] H Time point

21 Example: Morgan Monroe data Errors in flux #3: LE with z=z0 [red], z=z1 [blue] LE Time point

22 Example: Morgan Monroe data Change in errors for flux #2: H errors when z = z errors when z = z0

23 Example: Morgan Monroe data Change in errors for flux #3: LE errors when z = z errors when z = z0

24 Example: Morgan Monroe data Slice through z1 cost function, f(z) (z_off + z)[6]: alpha_1

25 Example: Morgan Monroe data Slice through z1 cost function, f(z) (z_off + z)[12]: f0_2

26 Outline 1 Introduction 2 Calibration 3 Example 4 Conclusions

27 State of play find (locally) optimum parameters from within R successfully compiled under ifort and g95 get fortran source from me get Windows compatible executable from me get R from r-project.org

28 Issues for the future subject to LICENSING... what parameters should be added to x? what fluxes should be added? update version of JULES (currently 2.0)