1. Observational Error Estimation of FORMOSAT-3/COSMIC GPS Radio Occultation Data SHU-YA CHEN AND CHING-YUANG HUANG Department of Atmospheric Sciences, National Central University, Jhongli, Taiwan YING-HWA KUO University Corporation for Atmospheric Research, and National Center for Atmospheric Research, Boulder, Colorado SERGEY SOKOLOVSKIY University Corporation for Atmospheric Research, Boulder, Colorado

2. LEO GPS L1(1.57542GHz) L2(1.22760GHz) Introduction The GPSRO technique has emerged as a robust global observing system that provides valuable data to support operational numerical weather prediction (Healy and The´paut 2006; Cucurull et al. 2007; Anthes et al. 2008; Cucurull and Derber 2008; Healy 2008).

3. L1 and L2 phase excess data Doppler-shifted frequencies f d1, f d2 Bending angles and impact parameters Index of refraction n Abel transform Refractivity N Temperature and pressure T, p Auxiliary meteorological data Introduction Observations retrieved form GPSRO can be used in data assimilation (Kuo et al. 2000).

4. Introduction GPS RO refractivity is typically modeled at the ray perigee point by a ‘‘local refractivity operator’’ in a data assimilation system. local refractivity operator does not take the horizontal gradients into account.

5. Introduction A new observable (linear excess phase), defined as an integral of the refractivity along some fixed ray path within the model domain, has been developed in earlier studies to account for the effect of horizontal gradients (Sololovski et al. 2005a)

6. Introduction Representativeness errors are the errors related to discrete representation of continuous meteorological fields by an atmospheric model. It arise from two sources: 1) The limited resolution of the NWP model 2) the inability of the observation operator to derive a perfect measurement from a perfect model state

7. Methodologies and Experiment Design Apparent errors, observation errors, and forecast errors : Apparent error. It is equivalent to (O-B) : Observation error : Forecast error

8. Methodologies and Experiment Design Prediction Model and Preprocessor WRF model Ver. 2.1.2 A Preprocessor is used to map the model variables (T, P, Q) from WRF forecast grid fields to time and location of observation. Winter month: 15 JAN ~ 15 FEB 2007 Summer month: 15 AUG ~ 15 SEP 2007

9. Methodologies and Experiment Design Observation operators (linear excess phase) Observation approachModel approach -L-LL0 dl -L-LL0

10. Methodologies and Experiment Design Data Processing 1. lat, lon, geomH, azimuth, N -- from atmPrf 2. define the mean model vertical grid 3. interpolate observation to mean model vertical grid 4. lat, lon, azimuth, logN to midpoint

11. Methodologies and Experiment Design Model Settings and Calculation Steps 151×151 ~ 45km, 31 model vertical levels, TOM at 50hPa

12. Methodologies and Experiment Design Model Settings and Calculation Steps 1. initial condition: NCEP AVN at 00, 06, 12, 18 2. using NMC method to calculate the forecast error, 3. calculating N and S 4.

13. Observational Error Estimation The Fractional Error

14. Observational Error Estimation The Fractional Error FIG. 2. Fractional differences between the observations (S obs or N obs ) and model forecasts (S fst or N fst ) at each model level for (a),(c) linear excess phase and (b),(d) refractivity in the (a),(b) winter and (c),(d) summer month. Angle brackets (<>) indicate the mean of the observations at each model mean height. The data before and after the criterion check are shown by the black lines and red lines, respectively.

15. Observational Error Estimation The Fractional Error FIG. 3. Fractional standard deviations of the apparent error (thick solid lines), forecast error (dotted lines), and observational error (thin solid lines) for (a),(c) linear excess phase and (b),(d) refractivity in the (a),(b) winter and (c),(d) summer months. The counts of GPS RO soundings are presented by circles. S N W S

16. Observational Error Estimation Latitudinal Dependence FIG. 4. Fractional standard deviations of the observation errors of linear excess phase (solid lines) and refractivity (dashed lines) to the south (thin lines) and to the north (thick lines) of 30°N in the (a) winter and (b) summer months.

17. Observational Error Estimation Latitudinal Dependence FIG. 5. Fractional standard deviations of the observational errors stratified in different latitudinal bins (color lines) for (a),(c) linear excess phase and (b),(d) refractivity for the (a),(b) winter and (c),(d) summer months.

18. Observational Error Estimation Latitudinal Dependence FIG. 6. As in Fig. 5, but for 12-h forecast errors.

19. Observational Error Estimation Latitudinal Dependence FIG. 7. The monthly zonally averaged specific humidity of 12-h WRF forecasts in different latitudinal bins (color lines) in the (a) winter and (b) summer months. (c),(d) As in (a),(b), respectively, but for the standard deviation of the forecast errors (24-h forecast minus 12-h forecast).

20. Observational Error Estimation Latitudinal Dependence FIG. 8. The estimated (dashed lines) and fitted (solid lines) fractional standard deviations of the observational errors stratified in different latitudinal bins for (a) linear excess phase and (b) refractivity in the winter month. (c),(d) As in (a),(b), but for the estimated (dots) and fitted (red lines) observational errors in the summer month.

21. Observational Error Estimation Latitudinal Dependence

22. Conclusions Observational errors of refractivity and linear excess phase retrieved from FORMOSAT-3/COSMIC RO data for two months: one month (15 January– 15 February 2007) in the winter and the other (15August–15 September 2007) in the summer, are investigated. Fractional standard deviations of observational errors for refractivity and linear excess phase both show a roughly linear decrease with height in the troposphere and a slight increase above the tropopause. The observational errors of refractivity demarcated by 30°N in this study are comparable with those in Kuo et al. (2004). The latitudinal dependence of both observational errors (refractivity and linear excess phase) is stronger in the winter month and weaker in the summer month. The latitudinal dependence of the observational error is found to be influenced by the variations of the atmospheric moisture.