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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. NOAA GPSMet Network. GPS Meteorology. GPS Satellite in Mid-Earth Orbit. 20,200 km. Final Frontier.

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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


NOAA GPSMet Network


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


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


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


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


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.


Models currently assimilating TPW

CONUS West

CONUS East

  • LAPS – 3 km

  • NAM – 40 km

  • RAP – 13 km


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


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.


Why assimilate just signal delays?

Potentially Available

Currently Available


Assimilating GPS total delays in variational LAPS

Instead of assimilating retrieved TPW, variational LAPS directly assimilates GPS neutral (tropo) delays:

where


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


GPS delays assimilation

  • Ingest codes;

  • Forward operator,

  • Adjoint operator,

  • Connection to the variational cost function and

  • minimization process.


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.



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.


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