Direct assimilation of GPS signal delays into Variational LAPS (STMAS) and GSI

1. Direct assimilation of GPS signal delays into Variational LAPS (STMAS) and GSI Seth Gutman and Yuanfu Xie Forecast Applications Branch, NOAA ESRL/GSD, Boulder, CO USA

2. NOAA GPSMet Network

3. GPS Meteorology GPS Satellite in Mid-Earth Orbit 20,200 km Final Frontier GPS Signals in Space 480 km Thermo GPS Signals in the Ionosphere Dispersive Geometric path length 80 km Meso 50 km GPS Signals in the lower (neutral) atmosphere Stratosphere Neutral Excess path length 9-16 km Tropo GPS Receiver on Ground

4. GPS Meteorology GPS Satellite in Mid-Earth Orbit 20,200 km Signal Delay <=> Excess Path Length Final Frontier GPS Signals in Space 480 km GPS Signals in the Ionosphere Thermo Dispersive Geometric path length 80 km • Iono delay ≈ 15-30 m • Tropo delay ≈ 2.5 m @ msl • Hydro delay αPsta≈ 90% total delay • ≡ dP • TPW = Meso 50 km Stratosphere GPS Signals in the lower (neutral) atmosphere Neutral Excess path length 9-16 km GPS Receiver on Ground Tropo

5. GPS Meteorology Excess path length = measured path length - expected path length Caused by the total refractivity (N) of the atmosphere along the path of the radio signal N = refractivity ≡ 106 (n-1) ne = electron number density f = wavelength (e.g. L1, L2, L5) Pd = total atmospheric pressure T = temperature Pv = water vapor pressure

6. GPS PW retrieval uncertainty • Forward model = GAMIT double difference • 3-dimensional antenna position error ~ 1 cm • GPS orbit error < 10 cm • ZTD uncertainty < 0.5 cm • Pressure sensor error < 1 hPa • Horizontal distance from antenna < 50 km • Vertical distance from antenna < 0.1 km • Temperature sensor error ~ 1o K • ZHD estimation: Saastamoinen, 1972 • Wet delay transfer function: Bevis et al., 1994

7. GPS PW estimation uncertainty MOHAVE 2009 0.5 mm in winter 1.0 mm in summer O+R ≈ 0.24 mm  0.43 mm Leblanc et al. 2011: Measurements of Humidity in the Atmosphere and Validation Experiments (MOHAVE)-2009: overview of campaign operations and results, Atmos. Meas. Tech., 4, 2579-2605, doi:10.5194/amt-4-2579-2011.

8. Models currently assimilating TPW CONUS West CONUS East • LAPS – 3 km • NAM – 40 km • RAP – 13 km

9. NWP Analysis errors w.r.t. GPS 2nd 4th 1st 3rd Green identifies those NOAA models that currently assimilate GPS PW Red identifies a NOAA model that does not yet assimilate GPS observations

10. Why assimilate just signal delays? • It’s the only recourse we have when we can’t reliably retrieve PW from the GPS signal delay. • This occurs when the Wx sensors needed to parse the total delay into its wet and “dry” components are not in close proximity to the GPS antenna. • This forces us to exclude: • About 50% of the usable GPS receivers in the U.S., • About 75% of the GPS receivers in the developed world, • About 90% of the rest of the GPS receivers around the world.

11. Why assimilate just signal delays? Potentially Available Currently Available

12. Assimilating GPS total delays in variational LAPS Instead of assimilating retrieved TPW, variational LAPS directly assimilates GPS neutral (tropo) delays: where

13. GPS delays assimilated a proper multigrid level Long waves Short waves Sequence of 3-4DVARs with proper humidity balances Similar to LAPS analysis with less requirement of covariance Standard 3-4DVAR With a band covariance The variational GPS analysis does not require surface temperature obs, which is not available for 2/3 of GPS sites. Possible ensemble Filter application

14. GPS delays assimilation • Ingest codes; • Forward operator, • Adjoint operator, • Connection to the variational cost function and • minimization process.

15. Potential GPS delay impact GPS delay assimilation should bring down the RMS error comparing to TPW. Why? Because ZTD has 3-degrees of freedom, while PW has only one.

16. GPS delays capture CI process ~2h

17. Summary • The ability to directly assimilate GPS signal delays will provide us with reliable and low cost access to all weather local-to-global scale moisture information in near real-time for: • Improved severe weather warnings and forecasts; • Cal/Val of in situ (raob and aircraft) and satellite remote sensing observations over land and from fixed platforms in the open ocean; • Improved atmospheric corrections for space geodetic observations used to monitor earthquakes, tsunamis, subsidence, volcanic activity, etc.