MARCH 2011 C H E N E T A L . 853 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 (Manuscript received 26 October 2009, in final form 20 August 2010) ABSTRACT The Global Positioning System (GPS) radio occultation (RO) technique is becoming a robust global ob- serving system. GPS RO refractivity is typically modeled at the ray perigee point by a ‘‘local refractivity operator’’ in a data assimilation system. Such modeling does not take into account the horizontal gradients that affect the GPS RO refractivity. 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. In this study, the error statistics of both observables (refractivity and linear excess phase) are estimated using the GPS RO data from the Formosa Satellite 3–Constellation Observing System for Meteorology, Ionosphere and Climate (FORMOSAT-3/COSMIC) mission. The National Meteorological Center (NMC) method, which is based on lagged forecast differences, is applied for evaluation of the model forecast errors that are used for estimation of the GPS RO observational errors. Also used are Weather Research and Forecasting (WRF) model forecasts in the East Asia region at 45-km resolution for one winter month (mid- January to mid-February) and one summer month (mid-August to mid-September) in 2007. Fractional standard deviations of the observational errors of refractivity and linear excess phase both show an approximately linear decrease with height in the troposphere and a slight increase above the tropopause; their maximum magnitude is about 2.2% (2.5%) for refractivity and 1.1% (1.3%) for linear excess phase in the lowest 2 km for the winter (summer) month. An increase of both fractional observational errors near the surface in the summer month is attributed mainly to a larger amount of water vapor. The results indicate that the fractional observational error of refractivity is about twice as large as that of linear excess phase, re- gardless of season. The observational errors of both linear excess phase and refractivity are much less latitude dependent for summer than for winter. This difference is attributed to larger latitudinal variations of the specific humidity in winter. 1. Introduction and The´paut 2006; Cucurull et al. 2007; Anthes et al. 2008; Cucurull and Derber 2008; Healy 2008). Several The Global Positioning System (GPS) radio occulta- observables, retrieved from GPS RO measurements, tion (RO) technique has emerged as a robust global which range from raw excess phases to retrieved mois- observing system that provides valuable data to support ture and/or temperature profiles, can be used in data operational numerical weather prediction (e.g., Healy analysis and assimilation (Kuo et al. 2000). Such an observable as the bending angle, defined as the angle between the incoming and outgoing directions of a GPS- Corresponding author address: Ching-Yuang Huang, Dept. of Atmospheric Sciences, National Central University, 300 Jhongda transmitted electromagnetic ray (Kursinski et al. 2000), Rd., Jhongli City, Taoyuan County 32001, Taiwan. can be retrieved under the assumption of spherical sym- E-mail: [email protected] metry of refractivity. The refractivity can be retrieved DOI: 10.1175/2010MWR3260.1 Ó 2011 American Meteorological Society 854 MONTHLY WEATHER REVIEW VOLUME 139 from the bending angle (using Abel inversion) and as- In this study we estimate observational errors of refrac- signed to the occultation (ray tangent) point. In the tivity and linear excess phase based on FORMOSAT-3/ past, many studies on the assimilation of Abel-retrieved COSMIC data over East Asia and the western Pacific refractivity and bending angle data demonstrated pos- for one winter and one summer month (referring to the itive impacts on regional as well as global weather pre- Northern Hemisphere). We investigate latitudinal de- diction (Kuo et al. 1998; Zou et al. 1999, 2000, 2004; Liu pendence of both refractivity and linear excess phase and Zou 2003; Huang et al. 2005; Healy et al. 2005; observational errors by stratifying the observations into Healy and The´paut 2006; Cucurull et al. 2006, 2007; different latitudinal bins. A brief introduction of the Healy 2008; Poli et al. 2009; Chen et al. 2009; Huang methodologies (including the observational error, local et al. 2010). and nonlocal operators, and the WRF model) and the In most of the regional data assimilation studies, a lo- experiment design is given in section 2. The estimated cal refractivity observation operator is used to represent observational errors are discussed in section 3. Section 4 the GPS RO Abel-retrieved refractivity as local refrac- concludes this study. tivity. This introduces certain representativeness errors because the Abel-retrieved refractivity derived from 2. Methodologies and experiment design GPS RO observation is influenced by the atmosphere along the ray path. In a grossly simplified approximation, a. Apparent errors, observational errors, the Abel-retrieved refractivity is similar to a density- and forecast errors weighted average over the horizontal path of about Observational errors include measurement errors and 300 km, centered at the ray perigee point. There can be representativeness errors (Daley 1991; Kuo et al. 2004; significant inhomogeneity in the horizontal along the Sokolovskiy et al. 2005a). While the observational errors 300-km averaging path. To reduce this representative- can be estimated theoretically, this is a very difficult task ness error, Sokolovskiy et al. (2005a) suggested a new and commonly they are estimated by comparing to other observable, a linear excess phase, which is defined as observations with uncorrelated error characteristics. In the integrated amount of refractivity along a fixed (e.g., this study we use the model forecast. Then the variance straight line) ray path, to account for the nonlocal nature 2 of the apparent error sa is related to the variances of the of the Abel-retrieved refractivity. This follows from the 2 2 observational and forecast errors so and sf as follows: smaller apparent errors normalized by the standard de- 2 2 2 viations of the weather-induced variations of the excess sa 5 so 1 s f . (1) phase than those of the refractivity, as was shown by Sokolovskiy et al. (2005b). Because the nonlocal obser- Note that the apparent errors are the total errors, de- vation operator can achieve better accuracy at reasonable fined as the differences between the model forecast and computational expenses, it has been implemented in the observation. This is equivalent to observation minus data assimilation system of the Weather Research and background (O 2 B), or the innovation, as defined in Forecasting (WRF; e.g., Liu et al. 2008; Chen et al. 2009) standard data assimilation literature (e.g., Daley 1991). and National Centers for Environmental Prediction Given the apparent errors, observational errors can be (NCEP) Gridpoint Statistical Interpolation (e.g., Ma determined once forecast errors have been calculated. et al. 2009). Forecast errors can be estimated using the National The Formosa Satellite 3–Constellation Observ- Meteorological Center (NMC) method (Parrish and Derber ing System for Meteorology, Ionosphere and Climate 1992) based on lagged forecast differences, or by calculating (FORMOSAT-3/COSMIC) mission is now providing the correlation between innovations with uncorrelated substantially more RO soundings (around 2000 sound- observational errors (Rutherford 1972; Hollingsworth and ings per day) with better penetration and smaller mea- Lo¨nnberg 1986). The Hollingsworth and Lo¨nnberg (H-L) surement errors in the lower troposphere (with the method needs complementary observations (e.g., radio- use of the open-loop tracking technique) than other sondes), whereas the NMC method does not. However, relevant missions such as Challenging Minisatellite the NMC method tends to underestimate model forecast Payload (CHAMP), which uses a phase-locked loop errors because of the partial cancellation of the repre- tracking technique [see Anthes et al. (2008)]. To ap- sentativeness errors. In this study, the NMC method was propriately assimilate the FORMOSAT-3/COSMIC used since over the ocean, where error estimates are im- GPS RO data, using either the local refractivity op- portant, there is an insufficient amount of radiosonde data erator or the nonlocal linear excess phase operator, to apply the H-L method. The differences between the one needs the observational error statistics based on forecasts at two different times, 24 h and 12 h, for the these two operators. WRF model are used in the NMC method in this study. MARCH 2011 C H E N E T A L . 855 FIG. 1. The geographical distributions of 2999 GPS RO soundings from COSMIC within the WRF model domain in the winter month (15 Jan–15 Feb 2007). The model grid indices are also shown at the left and bottom sides of the figure. The observational error covariance matrix is used the error covariance matrix is a diagonal matrix. This in the minimization of the cost function. To reduce the diagonal error covariance matrix is constructed from computational cost, in the WRF three-dimensional vari- the fractional standard deviations (i.e., the standard ational data assimilation (3DVAR) it is assumed that deviations normalized by the mean observables). In this the observational errors are only autocorrelated and thus study, the observational errors of the two observables TABLE 1. The numbers of the soundings for linear excess phase (EPH) and refractivity (REF) for both the winter and summer months in different latitudinal zones, and the differences (Diff) in the sets of data that do not pass the criterion (less than 5 standard deviations of the apparent errors).