Observational Error Estimation of FORMOSAT-3/COSMIC GPS Radio Occultation Data

Abstract

The Global Positioning System (GPS) radio occultation (RO) technique is becoming a robust global observing 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 (midJanuary 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, regardless 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.

Estimating observation and model error variances using multiple data sets

“…The largest variability and largest error estimates occur at Guam which uses a different radiosonde, which is thought to have large dry and wet water vapor biases due to sensor 30 malfunctions (Vömel 2017, personal communication). (5) The magnitudes of the estimated RO error variances are supported by previous published studies, including Kuo et al (2004) and Chen et al (2011). 35 (6) The estimated error profiles are smallest for the ERA-Interim model data set, which is a reasonable result since ERA uses an excellent model and data assimilation system, using many independent, quality checked observations.…”

“…Finally, the ERA error variance (analogous to the forecast error) is obtained by subtracting VAR(RO) from MS(RO-ERA) using Eq. (10) The results shown in Figure 5 are quite similar to those from Kuo et al (2004, Figure 13) and Chen et al (2011, Figure 3d) 5 who used different models and different data sets. The STD of normalized RO refractivity errors are a maximum of between 2.0 and 2.5% near the surface, decreasing to about 0.5% at 10 km.…”

“…We note that the apparent errors are the same as the (O-B) (observation minus background) or innovations as used in data assimilation methods and studies (Chen et al, 2011).…”

“…As discussed by Kuo et al (2004) and Chen et al (2011), the forecast error variance can be estimated by two alternative 20 methods, the "NMC method" (Parrish and Derber, 1992) or the Hollingsworth and Lönnberg (1986) method. Kuo et al (2004) used both methods to estimate the observational errors of RO refractivity using the NCEP AVN model.…”

“…We first compute the estimated error variance for RO refractivity using GFS and ERA data for comparison with the Kuo et al (2004) and Chen et al (2011) estimates of RO error variance to illustrate the three cornered hat method. In an analogy to the apparent error Eq.…”