State Space Models for Wind Forecast Correction

Transcription

1 for Wind Forecast Correction Valérie 1 Pierre Ailliot 2 Anne Cuzol 1 1 Université de Bretagne Sud 2 Université de Brest MAS /28/08

2 Outline 1 2 Linear Model : an adaptive bias correction Non Linear Model : bias and location correction 3 4

3 Outline 1 2 Linear Model : an adaptive bias correction Non Linear Model : bias and location correction 3 4

4 Accuracy of wind forecast Wind Energy Management Security and Rescue Forecast errors : intensity and position Satellite Forecast (same date) 2008/5/24 5h

5 Forecast and observations 2008/05/25-00 : /05/25-12 :

6 Weather forecast correction (state of art) Local Numerical Weather models Purely stochastic Y t = f(y t 1,, Y t k ; θ) + σɛ t Combined models Regression [Lange et al. (2006), von Bremen et al. (2007)] or Y obs t Y obs t = f(y for t = f(y for t, Z for t ; θ) + σɛ t, Y obs t 1,..., Y obs t k ; θ) + σɛ t Data Assimilation [Dee and da Silva (1998), Galanis et al. (2002)] based on state space models

7 Outline Linear Model Non Linear Model 1 2 Linear Model : an adaptive bias correction Non Linear Model : bias and location correction 3 4

8 First step : single location Linear Model Non Linear Model Position error phase error observation forecast 0 02/03 02/04 02/05 42 observed : -, forecast :

9 A first model Linear Model Non Linear Model Linear Gaussian spate-space model db t = α(b t µ)dt + σdw t Y true t Y obs t Error (hidden) = Y for t + B t "True" Y t (hidden) = Y true t + σ obs ɛ t Observed Y t W t : standard brownian motion, ɛ t Gaussian white noise Y t : observed at time t 1,, t K Inference Kalman filter : weighted mean between the predicted state and the observation

10 Need another model Linear Model Non Linear Model Location or phase error 2008/5/24 5h

11 Introduction of a phase correction Linear Model Non Linear Model Model d t = α ( t µ )dt + σ dv t db t = α B (B t µ B )dt + σ B dw t Y true t Y obs t = Y for t+ t + B t Phase error (hidden) Intensity error (hidden) "True" Y t (hidden) = Y true t + σ W ɛ(t) Observed Y t V t, W t : standard brownian motions, ɛ t Gaussian white noise Y t : observed at time t 1,, t K Inference Parameter estimation : EM algorithm (need smoothing) or maximum likelihood by a gradient algorithm [Robbins and Monroe, 1951] θ k = θ k 1 + γ k θ L T (θ) Monte Carlo approximation of L T (θ) and θ L T (θ) based on particular filtering [Coquelin et al., 2007] Breaks in the data due to the assimilations of the observations in the numerical weather model

12 Outline 1 2 Linear Model : an adaptive bias correction Non Linear Model : bias and location correction 3 4

13 Wind forecast correction Example of correction for Brest Obs For Nonlinear Phase Linear Reg Lin /03 02/04 02/05

14 Comparison Root Mean Square Errors EQM Linear Nonlinear Phase Numerical Stochastic Reg Lin time (day)

15 Outline 1 2 Linear Model : an adaptive bias correction Non Linear Model : bias and location correction 3 4

16 Correction of weather forecast by bias and phase correction with dynamic Phase correction does not improve the bias correction rmse Mean error Local phenomena Perspectives : Spatial model Local weather