1

On the use of Numerical Weather Models

to Predict Neutral-Atmosphere Delays

Felipe G. Nievinski

2

The curse of tropospheric delay in GPS positioning

• One of main error sources in medium- to long-range kinematic applications.

• Estimation more challenging than in static app. – Due to, e.g., time-varying height.

• A better a priori prediction would be valuable.– Whether estimating or only correcting for

tropospheric delay.

3

Numerical Weather Models: a better picture of today’s weather?

• Typical tropospheric delay prediction models:(i) Climatological models

(ii) Surface-measured pressure, temperature, humidity

• NWM aims at representing(i) The daily weather

(ii) The entire 3-dimensional

weather field.Northern half of 3D refractivity (unitless) field on

Aug 16, 2004, 22:45 UTC (vertical scale 100x)

4

Methods

• 1. How to predict delays with NWM

• 2. How to test if the delays are not wrong

• 3. How to assess whether the delays improve GPS applications

5

• Numerical integration:

• Coordinate conversion:

• Interpolation:

• Refractivity calculation:

C

dN )(10 6

1232

11

wd

d ZT

eK

T

eKZ

T

PKN

},,{}{ GHyx

qpTYYHH

HHYY iG

iGi

Gi

G

i ,ln,,1

1

1

0 1 2 3 4 5 6 7 8

x 104

0

50

100

150

200

250

300

350

Slant distance (m)

Refr

activity

Predicting delays with NWM

6

Tropospheric corrections: NWM–radiosonde discrepancy

30 40 50 60 70 80 90

-2

0

2

30 40 50 60 70 80 90

-2

0

2

30 40 50 60 70 80 90

-2

0

2

Latitude (degrees)

Total(cm)

Hydro-static(cm)

Non-hydro-static(cm)

mean (cm) rms (cm) std (cm)

Total Delay 1.05 1.29 0.75

Hydrostatic Delay 1.15 1.18 0.25

Non-Hydrostatic Delay -0.1 0.69 0.69

Easting (km)

Nor

thin

g (k

m)

-2000 -1000 0 1000 2000 3000 4000

-5000

-4000

-3000

-2000

-1000

0

7

GPS positioning

• Two scenarios for kinematic processing:– Moving rover: on board ferry boat

– Stationary rover: one of two base stations

• In each scenario, test and reference solutions:

Moving rover Stationary rover

Test

Solutions

Individual baselines from each base station

to ferry boat

Baselines from one fixed base station to another base

acting as rover

Reference Solution

Multi-base station to ferry boat

5 day-long static PPP at each base station

8

Impact assessment

• 3 tropospheric prediction models assessed:– NWM

– UNB3m

– Saastamoinen with standard weather parameters

– uncorrected observations (no model)

• Criteria:– Discrepancy in rover position between test and

reference solutions

– RMS of observation residuals

9

Stationary rover:test–reference discrepancy

Height (cm) Latitude (cm) Longitude (cm) mean rms std mean rms std mean rms std

no model -7.8 25.2 23.9 8.2 13.7 11 2.6 17.2 17.0 Saastamoinen -2.6 6.7 6.2 0.2 3.7 3.7 1.2 4.1 4.0

UNB3m -2.5 6.0 5.4 0.2 3.2 3.2 1.2 2.7 2.4 NWM -0.9 5.0 4.9 0.0 3.2 3.2 1.1 2.5 2.3

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15

Longitude (cm)

Latit

ude

(cm

)

0 6 12 18 24

-20

-10

0

10

20

Time of the day (hours, GPST)

Hei

ght

(cm

)

Saastamoinen

UNB3m

NWM

10

Moving rover: discarding unreliable epochs

Saint John

Digby0 6 12 18 24

0

20

40

60

80

0 6 12 18 240

20

40

60

80

Dis

tanc

e to

nea

rest

ba

se s

tatio

n (k

m)

0 6 12 18 240

20

40

60

80

Time of the day (hours, GPST)

St. John

Digby

Multi-base

11

Moving rover (1): test–reference discrepancy

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15

Longitude (cm)

Latit

ude

(cm

)

0 6 12 18 24-30

-20

-10

0

10

20

30

Time of the day (hours, GPST)

Hei

ght

(cm

)

Saastamoinen

UNB3m

NWM

Height (cm) Latitude (cm) Longitude (cm) mean rms std mean rms std mean rms std

no model 10.2 16.1 12.5 -8.1 10.2 6.2 -0.8 6.4 6.3 Saastamoinen 2.4 10.5 10.2 -1.6 5.2 4.9 -2.8 5.1 4.3

UNB3m 4.3 8.0 6.8 -1.9 4.8 4.4 -1.3 3.1 2.8 NWM 1.5 5.8 5.6 -0.9 3.3 3.2 -0.8 2.8 2.6

12

Moving rover (2): test–reference discrepancy

Height (cm) Latitude (cm) Longitude (cm) mean rms std mean rms std mean rms std

no model 10.0 21.5 19.1 4.9 11.7 10.6 -5.6 11 9.4 Saastamoinen -1.9 5.9 5.5 0.3 4.1 4.1 1.0 2.3 2.0

UNB3m -0.5 8.4 8.4 -0.8 4.6 4.5 -1.5 4.0 3.7 NWM 0.9 9.2 9.1 -0.6 4.3 4.2 -1.5 3.8 3.5

-15 -10 -5 0 5 10 15-15

-10

-5

0

5

10

15

Longitude (cm)

Latit

ude

(cm

)

0 6 12 18 24-30

-20

-10

0

10

20

30

Time of the day (hours, GPST)

Hei

ght

(cm

)

Saastamoinen

UNB3m

NWM

13

Conclusions and future work

• NWM has only marginal improvement on

that particular 70 km baseline.• Validation: vertical coordinates in NWM

• Study how it is handled in data assimilation• Test it with GPS-equipped radiosondes

• Impact assessment: varying-length baselines• Kinematic processing at stationary rover• From 100 to 1,000 km

14

Publications

• Paper at ION AM 2005 in Boston, MA

• Poster at AGU Joint Assembly in Washington, DC

• Paper at ION GNSS 2006 in Fort Worth, TX

15

Thanks!

Questions?

Felipe G. Nievinski

16

• GPS signals are refracted in the Earth’s neutral atmosphere.– Hence timings (rangings)

are delayed (increased).– ~ 2.5 m at zenith direction,

~ 25 m at 5º elevation angle (for a station on the geoid)

satellite

receiver

≈ ρ+τ

ρ

Neutral-Atmosphere Delays

17

30 40 50 60 70 80 90

-2

0

2

30 40 50 60 70 80 90

-2

0

2

30 40 50 60 70 80 90

-2

0

2

Latitude (degrees)

Tropospheric corrections: NWM self-discrepancy

30 40 50 60 70 80 90

-2

0

2

Latitude (degrees)

NWM Ray-trace vs Radiosonde ray-trace

NWM Ray-trace vs NWM Saastamoinen

Hydro-static(cm)

Hydro-static(cm)