University of Athens School of Physics Atmospheric Modeling and Weather Forecasting Group

Transcription

1 University of Athens School of Physics Atmospheric Modeling and Weather Forecasting Group Data Assimilation in WAM System operations and validation G. Kallos, G. Galanis and G. Emmanouil

2 SUBJECTS TO BE DISCUSSED Operational use and code modifications of the new parallel version of WAM at the University of Athens Applications of Kolmogorov-Zurbenko (K-Z) filters on satellite data in order to: Remove high variability Quality control the measurements Use of Kalman filters for reconstructing missing satellite data constructing missing observations for assimilation purposes Evaluation of the system

3 Modifications and operational use of the new parallel version of WAM The UOA/AM&WFG has adopted a stand-alone version of the new WAM model (ECMWF version). The new model is recorded in FORTRAN95, is fully parallelized and further modified by our group in order to operate in Linux distributed memory environments. The model utilizes grided surface wind fields from global or limited area atmospheric models. It includes data assimilation systems that can utilize altimetry and spectra data from different satellites, like ENVISAT and JASON.

4 The new parallel version of WAM The assimilation methodology includes corrections by K-Z and Kalman filtering techniques for both near-surface winds and waves. Because of its capability to run on parallel it is possible to operate in high resolution even at its global configuration. The system is currently running in Mediterranean Sea with resolution 0.05x0.05 degrees. The global configuration runs with resolution of 0.5x0.5 degrees. The two operational configurations cover forecasting period of 3 and 7 days respectively. The model predictions are used in Sea routing and other applications.

5 The Global version (resolution 0.5 x 0.5 degrees, Forecasting horizon: 7 days)

6 The Mediterranean Sea (resolution 0.05 x 0.05 degrees, Forecasting horizon: 3 days)

7 Focusing on different local domains: Aegean Sea Central Aegean (Cyclades( Cyclades)

8 Focusing on different local domains: Adriatic Sea Black Sea

9 WAM predictions in sea routing applications: Optimization of fuel consumption during sea passage taking into account the vessel characteristics and the sea-weather conditions

10 Developments New Results I. Applications of Kolmogorov-Zurbenko (K-Z) filters on satellite and buoy data Assimilation systems for wave models are based on the combination of model forecasts and corresponding observations (mainly obtained by satellite or buoy measurements) However, this type of data are of different qualitative characteristics: The observations are point records, referring to instantly measured values and emerge increased variability. The forecasts of numerical prediction wave models are smoothed spatially and temporally according to the model horizontal resolution and time step. These differences affect the impact of assimilation systems and the quality of the final outcome.

11 K-Z Z Filter Model Forecasts and the corresponding observations. The increased variability of the satellite measurements makes them incompatible with the smoothed model results.

12 We propose: The observation series are smoothed by an appropriate K-Z filter before being utilized as assimilation input. KZ-filters are based on iterative moving averages and are able to remove high frequency variations from the available data : Initial values : First iteration : (2q+1 = the length of the filter window) These values become the input for the second iteration and so on. To filter all periods of less than P 0 x i x 1 q 1 0 i = xi+ j 2q + 1 j= q time steps, the following criterion has to be fulfilled: (2q+ 1) N P, N denoting the number of iterations. The appropriate choice of the involved parameters leads to smoothed observation time series that are comparable to corresponding forecasted values from the wave model and disposed from extreme values.

13 Raw data (before smoothing). Satellite data emerge increased variability while the model outputs are smoothed spatially K-Z filters on altimeter (I) K-Z smoothed data High frequency data have been removed and the two time series are of the same characteristics

14 K-Z filters on altimeter (I) Raw data (before smoothing). The two time series are of different qualitative characteristics. K-Z smoothed data The observational data are disposed from extreme values and can be combined with the corresponding forecasts.

15 K-Z Z filters on buoy data The initial model outputs and observations from buoys Filtered data where high frequency variability has been removed. The systematic error has not been affected and can be treated through Kalman filters or other methods

16 Development New Results II. Use of Kalman filters for the reconstruction of missing satellite data It is a common fact that satellite measurements often appear gaps due to quality controlled, filtered or unavailable data. This situation creates problems or even makes impossible the use of satellite data for assimilation or other purposes. A way out is proposed here: The use of Kalman filters for filling up missing data.

17 The Kalman filter It is the statistically optimal sequential estimation procedure for dynamic systems. Existing satellite data are recursively combined with recent forecasts, with weights that minimize the corresponding biases, in order to simulate the missing satellite values. Main advantages : Easy adaptation to any alteration of the observation or forecast type Only short series of background information are needed

18 A short description of the Kalman filter algorithm used Kalman filtering applies on direct model output m t and existing satellite values s t The main goal is the estimation of the deviations between them y t = m t -s t as a polynomial function of the forecasting model direct output: y t = x + x m + x m + x m + v The coefficients (x i,t ) are the parameters that have to be estimated by the filter and v t the Gaussian non systematic error The state vector of the filter is the one formed by the coefficients The observation matrix takes the form : 2 3 1,t 2,t t 3, t t 4, t t x t T = x1, t x2, t x3, t x4, t 2 3 H t = 1 m t m t m t t The system and observation equations, become: xt = xt 1 + wt, yt = H t xt + vt As soon as the deviations y t have been calculated, they are used for the estimation of missing satellite values.

19 Filling of missing satellite data (I) The Kalman filter uses the existing satellite data and the wave model forecasts (solid lines) in order to estimate missing values on the orbit line. Area of the test case: Mediterranean Sea

20 Filling of missing satellite data (I) The obtained new data follow the variability of the existing satellite values and keep the same behavior comparing with model outputs.

21 Development New Results III. Use of Kalman filters for the construction of missing observations for assimilation purposes The majority of wave assimilation systems have a limited, in time, ability of affecting the final wave prediction, especially that of long forecasting period systems. This is mainly due to the fact that after closing the assimilation window the wave model continues to run without any external information. Therefore, if a systematic deviation from the observations appeared, this will be established again and only a limited portion of the forecasting period will be practically affected.

22 Development New Results III. Use of Kalman filters for constructing missing observations for assimilation purposes A way of encountering this drawback is proposed here: A combination of two different statistical tools - K-Z and Kalman filters is employed so to eliminate any systematic error of (a first run of) the wave model results at specific locations where continuous flow of data is available. The obtained forecasts are then used as reconstructed observations that can be assimilated to a follow up model run inside the forecasting period.

23 The assimilation system used for altimeter data The analysis scheme is based on a modification of the traditional successive correction methods It is analogous to the statistical optimal interpolation The method is based on the following two iterative equations for SWH: N A A O A i + = i + ij j j j= 1 SWH ( k 1) SWH ( k) a ( SWH SWH ( k)), N A A O A x + = x + xj j j j= 1 SWH ( k 1) SWH ( k) a ( SWH SWH ( k)), where a = ( m + d ) / M, a = m / M ij ij ij j xj xj j Subscripts i, j refer to observation points, x to grid points, superscripts O, P, T and A to observed, first guess, true and analyzed value, N is the number of observations and k an iteration counter. m ij and d ij are model error and observation error covariances respectively. M j is a function of m ij and d ij chosen so that the above equation converge.

24 The application of the assimilation system leads to a limited in time impact on model forecasts: In both test cases the model forecasts are improved only for a limited time period. After this, the initially emerged discrepancies are established again Test case: California, USA

25 The use of reconstructed observations Apart from the real observations assimilated (blue solid line) within the assimilation window, the improved, via the filters, forecasts of the model (dashed line) are assimilated inside the forecasting period as reconstructed observations. The assimilation impact is extended to the whole forecasting period. Test case: California, USA

26 The use of the constructed observations The classical assimilation procedure creates cycles in which the forecast fluctuates between accurate and biased values The utilization of the constructed observations by the proposed methodology leads to a constant improvement of the final predictions for the forecasting period.

27 Evaluation of the proposed techniques A first evaluation of the proposed techniques refers to a 3-month period run of the system at an open sea area (SW USA, Pacific Ocean) for SWH forecasts using WAM and six different buoys as observational stations The study area

28 Evaluation of the proposed techniques Buoy A Buoy B Buoy C WAM WAM2 WAM3 WAM WAM2 WAM3 WAM WAM2 WAM3 Bias RMSE Nbias Buoy D Buoy E Buoy F WAM WAM2 WAM3 WAM WAM2 WAM3 WAM WAM2 WAM3 Bias RMSE Nbias Statistics for the 6 buoys on three different runs: WAM : The wave model runs without any assimilation system WAM2 : The classical assimilation scheme is activated using available observations WAM3 : The system assimilates real (for the assimilation window) and reconstructed (for the whole forecasting period) observations

29 Evaluation of the proposed techniques Average values over all buoys Impovement (%) against WAM1 WAM2 WAM1 WAM2 WAM3 Bias 0,68 0,35 0, RMSE 0,83 0,62 0, Nbias 0,57 0,35 0, It is important to notice: the almost vanished bias values (88 % improvement against the classical assimilation scheme), the substantial decrement of RMSE and Normalized Bias. the 31% improvement of the RMSE in contrast to WAM2-case is totally due to the application of the proposed new technique and to the utilization of artificial assimilated data inside the forecasting period. There was no way of capturing this by the use of an assimilation system only.

30 Evaluation of the proposed techniques Bias RMSE Averaged Statistics for the three different methods and for all buoy used

31 Final Remarks WAM is running operationally on a global scale and in Mediterranean Sea. Data assimilation from altimeter and SAR instruments is used. New techniques employing KZ filters as well as Kalman filters are used in order to improve the quality of wave forecasts for longer period than the classical assimilation schemes. The Statistical analysis performed showed a significant contribution of K- Z and Kalman filters on: The extension of the impact of assimilation temporally and spatially. The improvement of the quality and quantity of satellite data in use.

32 Future plans The statistical methods presented have been employed so far on altimeter and buoy data for testing purposes. It is planned to be applied also on SAR measurements.