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SEPTEMBER 2001 DE PONDECA AND ZOU 1559 A Case Study of the Variational Assimilation of GPS Zenith Delay Observations into a Mesoscale Model MANUEL S. F. V. DE PONDECA* National Center for Atmospheric Research,1 Boulder, Colorado XIAOLEI ZOU Department of Meteorology, The Florida State University, Tallahassee, Florida (Manuscript received 7 August 2000, in ®nal form 5 February 2001) ABSTRACT Results from a case study of the four-dimensional variational assimilation of total zenith delay (TZD) ob- servations from a dense global positioning system (GPS) network into the Pennsylvania State University±National Center for Atmospheric Research Fifth-Generation Mesoscale Model are reported. TZD is made up of the rescaled pressure and precipitable water at the site of the GPS receiver. Pro®ler-wind and radio acoustic sounding system (RASS) virtual temperature observations are also included in the assimilation experiments. Four experiments are performed. The study targets the 12-h period from 0000 to 1200 UTC 6 December 1997, characterized by the passage of a frontal system that produced intense rainfall over southern California. Forecasts prior to data assimilation underestimate the observed 6- and 12-h accumulated rainfall for most of the domain. The (sole) assimilation of TZD observations is found to have a small but bene®cial impact on the short-range precipitation forecast. Measured against the control forecast, area-mean improvements of up to 33.15% and 25.08% are found in the 6- and 12-h accumulated rainfall in Los Angeles County. The inclusion of pro®ler-wind observations is found to have a signi®cant impact on the model precipitation, with improvements in the 6- and 12-h accumulated precipitation as high as 88.26% and 32.53%, respectively. However, these increments are noticeably reduced when the TZD data are excluded from the assimilation experiments. Further improvements are achieved when the TZD and pro®ler-wind data are assimilated along with the RASS virtual temperature data. Increases of up to 93.21% and 50.58% are found in the 6- and 12-h accumulated precipitation, respectively. Because the virtual temperature also contains information on the three-dimensional moisture ®eld, these ®ndings point to the potential bene®t that may result from the future assimilation of GPS slant-path delay data. 1. Introduction nals suffer as they propagate through the (electrically) neutral atmosphere. The delay re¯ects both bending and This is our second self-contained paper devoted to retardation and is measured with respect to propagation the assimilation of global positioning system (GPS) total under vacuum conditions. This work treats the delay zenith delay observations into a mesoscale model. GPS along the zenith direction, that is, the total zenith delay senses the atmospheric water vapor remotely with a very (TZD). Estimates of TZD are readily available from high spatial and temporal resolution (e.g., Bevis et al. signal phase measurements at ground-based GPS re- 1992). Precipitable water estimates are accurate at the ceivers. As shown in the literature (Saastamoinen 1972; millimeter level and can be superior to those from water Davis et al. 1985; Bevis et al. 1992; Janssen 1993), TZD vapor radiometers (e.g., Rocken et al. 1995 and Duan can be expressed as et al. 1996). The GPS technique exploits the delay that radio sig- Ap TZD 5 s (1 2 0.002 66 cos2l 2 0.000 28H) * Current af®liation: Department of Meteorology, The Florida State ek University, Tallahassee, Florida. 1 1026 k91 3 dz . (1) 1 The National Center for Atmospheric Research is sponsored by []E TT122 the National Science Foundation. Here, A 5 (2.2779 6 0.0024) and ps is the pressure (hPa) at the site of the GPS antenna. The latter is at Corresponding author address: Manuel De Pondeca, The Florida State University, Department of Meteorology, 404 Love Bldg., Tal- latitude l (rad) and height H (km) above the ellipsoid. lahassee, FL 32306-4520. Here, T is the temperature (K), e is the water vapor 21 E-mail: [email protected] pressure (hPa), k92 5 (17 6 10) K hPa , and k3 5 q 2001 American Meteorological Society Unauthenticated | Downloaded 10/02/21 09:38 PM UTC 1560 JOURNAL OF APPLIED METEOROLOGY VOLUME 40 (3.776 6 0.004) 3 105 K 2 hPa21. The geometrical co- els via the 4D-Var approach. We concluded that the ordinate z along the zenith path and TZD itself are given three-dimensional moisture pro®les retrieved from the in millimeters. The ®rst term on the lhs of (1) is the TZD data were comparable in accuracy to those re- hydrostatic zenith delay (HZD), and the second term is trieved from the PW data. We also found that the TZD known as the wet zenith delay (WZD). One can show data yield highly accurate retrievals of the vertically that WZD is proportional to the precipitable water PW integrated water vapor content, which lead to signi®cant (Davis et al. 1985). We recall that PW is, by de®nition, improvements in short-range precipitation forecasts. the amount of water vapor overlying the receiver ex- The geographical region targeted in PZ was southern pressed in terms of an equivalent column of water. When California, where there is a network of ground-based expressed in the same units of length, WZD is approx- GPS receivers, known as the ``Southern California In- imately 6.4 times PW (e.g., Bevis et al. 1992). This tegrated GPS Network'' (Bock and Williams 1997). In relationship is accurate to better than 1.5% in our me- this paper, we use the 4D-Var method to assimilate TZD soscale model. This means | WZDmodel 2 6.4 3 observations from that network and to investigate their PWmodel |/|WZDmodel | , 0.015, where WZDmodel and impact on the model initial conditions and short-range PWmodel are the model wet zenith delay and precipitable precipitation forecasts. This study also includes the as- water at any location in the model domain. Precipitable similation of pro®ler-wind and radio acoustic sounding water is a powerful constraint in both synoptic analysis system (RASS) virtual temperature observations from and numerical weather prediction, because PW provides seven different sites. In connection with the model rain- an estimate of the available moisture that fuels convec- fall patterns, we present a few hypotheses on the chang- tion and thunderstorms. Using PW observations for the es in the ¯ow behavior brought about by the data as- central United States from the special soundings of the similation process. However, we defer the detailed pre- Severe Environment Storms and Mesoscale Experiment, sentation of the ¯ow kinematics, which we deem very 1979, Kuo et al. (1996) demonstrated the feasibility of important, to a future paper. assimilating PW observations into a mesoscale model Section 2 contains the model description, details on via the four-dimensional variational (4D-Var) approach. the 4D-Var system, and an overview of the synoptic Their results showed an effective recovery of the ver- situation. Section 3 contains the experimental design. tical structure of water vapor and an improvement in The numerical results are in section 4, and the discussion the quality of the moisture analysis. Furthermore, when and concluding remarks are in section 5. assimilated together with wind and temperature data, the PW observations lead to improved short-range pre- cipitation forecasts. Guo et al. (2000) used a 4D-Var 2. Model description and case selection system based on a mesoscale model to assimilate GPS- a. The model and the 4D-Var system derived PW observations and found a positive impact of these data on short-range rainfall prediction. Their In this work, we use the Pennsylvania State Univer- study targeted a September 1996 squall line over the sity±National Center for Atmospheric Research central United States with intense embedded convection. (NCAR) Fifth-Generation Mesoscale Model (MM5) Xiao et al. (2000) found the 4D-Var assimilation of Adjoint Modeling System described by Zou et al. Special Sensor Microwave Imager±derived PW obser- (1997). MM5 is a primitive equation, ®nite-difference± vations into a mesoscale model to improve signi®cantly based nonhydrostatic mesoscale model (Anthes and the prediction of the January 1989 explosive Atlantic Warner 1978; Dudhia 1993; Grell et al. 1994). The ter- cyclone studied in the Experiment on Rapidly Intensi- rain-following vertical sigma coordinate of this model fying Cyclones over the Atlantic fourth intensive ob- is de®ned in terms of a time-invariant reference pres- serving period. These authors obtained improved cy- sure. The model includes moisture and planetary bound- clone track, cyclone-associated frontal structure, and ary layer processes. In our study, the state vector com- precipitation along the front. prises all gridpoint values of the three components of Estimating PW from TZD requires an independent the wind ®eld, the temperature, the perturbation pres- measurement of the station pressure ps and a weighted sure, that is, the deviation from the reference pressure, vertical mean temperature. The latter enters the coef- the speci®c humidity, cloud water, and rainwater. MM5 ®cient of proportionality between WZD and PW (Davis is a model with nested capability that can be run in two et al. 1985) and correlates very well with the surface different modes: one-way and two-way. Unlike the for- temperature (Bevis et al. 1992). In practice, and espe- mer, the latter mode is one in which the nested domains cially in dense GPS networks, pressure measurements are allowed to interact. As discussed by Dudhia (1993), might not be available for a large number of GPS sta- nonhydrostatic models have the advantage over hydro- tions. This motivated the study presented in our ®rst static models of allowing more localized studies, par- paper (De Pondeca and Zou 2001, hereinafter PZ).