VARIATIONAL BIAS CORRECTION FOR RADIOSONDE TEMPERATURE

1. VARIATIONAL BIAS CORRECTION FOR RADIOSONDE TEMPERATURE P ? P, Q, … … F.G. DEP Marco Milan, Leopold Heimberger Reading 10/09/2013

2. MOTIVATION/OUTLINE • Changes bias due to: • Change of radiosonde • Change of locations for the same radiosonde • Other equipment changes • We want to predict the radiosonde bias! • Predictand => radiosonde bias • Predictors => every available quantity which bias depends on • Develop a regression model for one sonde type • Offline – using available background departure statistics • Apply the regression model • Offline – using available background departure statistics • Online – applying VAR-BC on IFS • Results

3. VARIATIONAL BIAS CORRECTION • Standard 4DVAR cost function: • The minimization of the cost function produces an adjustment to the model background based on all used observations • Errors in the input [y-h(xb)] arise from: • Errors in the actual observations • Errors in the model background • Errors in the observation operator • The bias can be computed using the average of the background departure: • Split the observation constraint in a bias one and in a bias corrected one Background constraint Observational constraint

4. VARIATIONAL BIAS CORRECTION • The observations are considered biased, a linear predictor model is used as observation operator in the 4DVAR equations: • Introduction of a “bias term” in the variational cost function • With xb and bba priori estimations of model state and bias control parameters • A large Bballows the parameter estimates to respond more quickly to the latest observation, a sensitivity test is needed. • The adjustment of the radiosondes depends on the resulting fit of the analysis to all other OBS, given the background from the model.

5. VARIATIONAL BIAS CORRECTION • Bias in observations can change during the time • Seasonal and daily variations in bias exist • The bias model : PREDICTORS must be chosen according to observations and physical origins of the bias. • We assume the model unbiased, the presence of model bias attributes a wrong bias to the observations where there are not enough observations to correct the analysis

6. CHOICE OF PREDICTORS OFFLINE • Assumption => BIAS equal to the mean of first guess (FG) departure • Goal => approximation of the FG departure • Predictors determination • Multiple linear regression using the predictors and the FG departures of the output of the operational version of IFS as predictand (data from Hans Hersbach - ECMWF) • Previous test using ERA-INTERIM data. • Optimal fit derived from RMSD between fit and the data (search of minimum), using the possible lowest number of predictors ONLINE (in doing) • Implementation of the clustering method based on the sound type • Apply the optimal predictors to the VAR-BC • Evaluation of the Bias

7. PRESSURE DEPENDENT PREDICTORS • Radiosonde temperature FG departure depends on pressure. • Three constant predictors for: • 10-50 hPa (Pred3) • 50-150 hPa (Pred2) • 150-700 hPA (Pred3) • 700+ hPa (Pred4) • (pred4) Value 1 in the range [850, 1000] hPa, interpolation from 1 to 0 in the range [ 700,850] • (pred1) value 1 in the range [300,700] hPa, interpolation in the ranges [700,850] and [200,300] • …

8. SOLAR ELEVATION DEPENDENT PREDICTORS • Radiosonde temperature FG departure in the stratosphere depends on solar elevation value. • Find a polynomial function and compute RMSD with the FG departure. • Compute RMSD for all sonde_type with more than 10000 values between 2000 and 2010 • We decide for an order 3, 3 new predictors (Q,Q²,Q3), in the stratosphere.

9. LOG PRESS DEPENDENT PREDICTORS • We tested also a predictor function of the pressure but with a logarithmic behaviour with p0 the soil pressure

10. OFFLINE EVALUATION OF PREDICTORS • With the data of ERA-INTERIM check the predictors and their combinations, fit using a linear regression • Fix predictors are the four pressure dependent (linear) • Add: • Log press • Log press only on the stratosphere • Three predictors depending on solar elevation in the stratosphere. • Check using all data

11. OFFLINE EVALUATION OF PREDICTORS BIAS MODELS • LINEAR • LINER + LOG • LINEAR + SOLAR ELEVATION (only in the stratosphere) • LINEAR + SOLAR ELEVATION + LOG • LINEAR + SOLAR ELEVATION + LOG. STRAT.

12. OFFLINE EVALUATION OF PREDICTORS • Apply the parameters gained from linear regression to the data with solar elevation in the ranges: • Q< -7.50 • Q ]-7.50 , 7.50] • Q ]7.50 , 22.50] • Q>22.5 • Check the behaviour of the predictors for different solar elevations

13. OFFLINE EVALUATION OF PREDICTORS • Mean of RMSD between linear regression and first guess departure over all sonde types. • Check also for different solar elevation ranges. • Pressure less than 850hPa and in the stratosphere • The four linear predictors give results comparable to the other setup of predictors (for all data) • Some improvements using solar elevations

14. CONCLUSIONS AND OUTLOOK • Offline fit useful to find the optimal predictors before assimilation • First results with predictors combination have good results • Varbc answer to the predictors (not shown) is also promising • Varbc online with linear predictors and solar elevations predictors • New predictors to test, one using a tropopause layer • Clustering

15. THANK YOU FOR YOUR ATTENTION Courtesy of ElkeRustemeier

16. QUESTIONS • Definition of the matrix Bb • RMS • ERA-INTERIM

17. DEFINITION OF Bb • We do not know the actual error covariances of b (Bb) • We use Bb to control the adaptivity of the bias parameters: • Increase Bb for faster bias adjustments; decrease for slower adjustments • We take diagonal Bbrelated to the diagonal of R: for i=1,…,Nj number of predictors for the variable j • In this way the part in the cost function related to the bias parameter background constraint for the variable j has the same weight as Mj new observations.

18. RMS firstguessdepartureT Night Q< -7.5° • The negative departures do not counteract the positive departures • RMS give more weight to the larger first guess departure • The Russian stations has larger RMS in the upper levels and near 200 hPa • Japanese’s stations RMS in the upper levels larger for higher solar angles • USA stations better than Russian’s and Japanese’s for Q > 22.5° • Groups for different stations are desirable Q > 22.5°

19. OFFLINE EVALUATION OF PREDICTORS • Mean of RMSD between linear regression and first guess departure over all sonde types. • Check also for different solar elevation ranges. • Pressure less than 850hPa and in the stratosphere • The four linear predictors give results comparable to the other setup of predictors (for all data) • Some improvements using solar elevations for particular solar ranges