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Tropospheric correction model in support of Precise Point Positioning
Jan Dousa, Michal Elias and Pavel VaclavovicGeodetic Observatory Pecny of the Research Institute of Geodesy, Topography and Cartography, Czech Republic [[email protected]]
IGS Workshop 2014 Pasadena, California, USA
AbstractNew tropospheric correction model was developed at the Geodetic Observatory Pecny (GOP) based on a) numerical weather data field and b) new concept of the zenith wet
delay modelling. The model provides parameters for precise calculation of zenih hydrostatic and wet tropospheric delays at the surface and at any altutude up to 10 km. The
correction model supports a flexible parametrization including benefit of in situ meteorological observations.
First, we demonstrate the performace of new ZWD approximations and analytical calculation when applying a closed loop with a numerical weather field considered as the
reference. Additionally, we compared numerical weather field with respect to results from GNSS final tropospheric product provided by IGS. Finally, we study a potential of
the model to support GNSS applications like kinematic Precise Point Positioning.
Enhanced Zenith Wet Delay (ZWD) model development based on Askne-Nordius modelASKNE-NORDIUS model (1987)
for ZWD analytical calculation
COLLINS - LANGLEY UNB3 model (1997)for ZWD vertical approximation
MODIFIED UNB3 model (2014)for ZWD vertical approximation
+ + +
DOUSA-ELIAS model (2014)for improved ZWD vertical approximation
DOUSA-ELIAS model (2014) enhanced ZWD calculation via ASKNE-NORDIUS model
+
Although developed in 1987, the analytical model of Askne and Nordius
remains one of the most precise models for calculating ZWD. New strategy
based on improved ZWD vertical approximation is described in Dousa and
Elias (2014). Here, we provide several remarks only:
•Askne-Nordius model is based on the knowledge of the temperature and
its lapse rate (beta) and partial water vapour pressure and its exponential
decay parameter (lambda).
•We introduced new ZWD vertical approximation (gamma), which follows
the definition of the water vapour decay parameter.
•Both parameters are fitted via full NWP or radiosonde profile using orig-
inal formula and Levenberg-Marquardt algorithm (1963).
•Optimal combination of both decay parameters was developed for im-
proving the ZWD model of Askne-Nordius (1987).
• Flexibility of the new model includes potential utilization of in situ ob-
served meteorological parameters.
New ZWD vertical approximation
0
2
4
6
8
10
0 1 2 3 4 5 6 7
he
igh
t [k
m]
water vapour pressure [hPa]
2005-06-05[00] lat/lon/hgt = +86deg/+10deg/+2m
datafit via Efit via ZWD
0
2
4
6
8
10
0 5 10 15 20 25
he
igh
t [k
m]
water vapour pressure [hPa]
2005-06-05[00] lat/lon/hgt = +42deg/+10deg/+63m
datafit via Efit via ZWD
0
2
4
6
8
10
0 20 40 60 80 100 120 140 160 180
he
igh
t [k
m]
zenith wet delay [mm]
2005-06-05[00] lat/lon/hgt = +42deg/+10deg/+63m
datafit via ZWDfit via e
Left figure shows water vapour profile (crosses) and approximation (line).
Right figures top right display water vapour and ZWD profiles at other
location showing a typical unfolding character of both approximations.
ZWD vertical approximations using: 1+2) original and modified UNB3
model; 3+4) new model as a function of pressure and height.
HEIGHT 0-1 km 1-2 km 2-3 km 3-4 km 4-5 km 5-6 km 6-7 km 7-8 km
Original 11.4 20.7 20.2 19.9 15.3 13.2 10.4 7.9
Modified 10.8 19.1 18.6 18.0 13.6 11.4 8.7 6.5
New f(P) 8.2 7.4 5.5 6.5 5.6 5.6 5.0 3.7
New f(H) 8.3 7.4 5.5 6.5 5.7 5.6 5.0 3.7
Improved ZWD calculation (global assessment)
−25
−20
−15
−10
−5
0
5
10
15
20
25
ZWD − ref.ZWD [mm]
−25
−20
−15
−10
−5
0
5
10
15
20
25
ZWD − ref.ZWD [mm]
−25
−20
−15
−10
−5
0
5
10
15
20
25
ZWD − ref.ZWD [mm]
−25
−20
−15
−10
−5
0
5
10
15
20
25
ZWD − ref.ZWD [mm]
Four figures show global ZWD
differences for ZWDs calcu-
lated using A-N model with
vertical approximations using:
a) water vapour pressure decay
parameter (lambda), b) ZWD
decay parameter (gamma), c)
combination of both decay pa-
rameters, Tm calculated (A-
N), d) combination of both
decay parameters, Tm inte-
grated.
Figure right shows ZWD accuracy in a latitudinal de-
pendence when using various vertical approximation
variants for the partial water vapour pressure and ZWD:
log-fitting, pow-fitintg and new combined approach. 0
10
20
30
40
50
60
-80 -60 -40 -20 0 20 40 60 80
ze
nith
we
t d
ela
y -
rm
s [
mm
]
latitude [degree]
pow-fit via E
log-fit via E
pow-fit via ZWD
log-fit via ZWD
pow-fit via E+ZWD
Model application - initial study for positioning
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00
2.28
2.30
2.32
2.34
2.36
2.38
2.40
2.42
N, E
, U [m
]
ztd
[m]
09-JAN-2012
ONSA [EST-KIN-NWM]
(c) GOP/RIGTC, 14-05-30 12:30
NorthEast
UpZTD
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00
2.28
2.30
2.32
2.34
2.36
2.38
2.40
2.42
N, E
, U [m
]
ztd
[m]
09-JAN-2012
ONSA [EST-KIN-NWM]
(c) GOP/RIGTC, 14-05-30 12:30
NorthEast
UpZTD
Plots above demonstrate PPP pseudo-kinematic positioning (ONSA) for two scenar-
ios: a) with simultaneously estimated coordinates and tropospheric parameters (left);
b) with coordinates estimated after introducing tropospheric parameters from the
global ERA Interim model (right). Left figure demonstrates a correlation between
height and troposphere which time-to-time significantly weakens the solution.
0.000
0.020
0.040
0.060
0.080
0.100
0.120
2012-01-01
2012-01-02
2012-01-03
2012-01-04
2012-01-05
2012-01-06
2012-01-07
2012-01-08
2012-01-09
2012-01-10
2012-01-11
2012-01-12
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2012-01-14
2012-01-15
2012-01-16
2012-01-17
2012-01-18
2012-01-19
2012-01-20
2012-01-21
2012-01-22
2012-01-23
2012-01-24
2012-01-25
2012-01-26
2012-01-27
2012-01-28
2012-01-29
2012-01-30
ST
D [
m]
DRES-2012-Jan: (EST-KIN)
NorthEast
Up
0.000
0.020
0.040
0.060
0.080
0.100
0.120
2012-01-01
2012-01-02
2012-01-03
2012-01-04
2012-01-05
2012-01-06
2012-01-07
2012-01-08
2012-01-09
2012-01-10
2012-01-11
2012-01-12
2012-01-13
2012-01-14
2012-01-15
2012-01-16
2012-01-17
2012-01-18
2012-01-19
2012-01-20
2012-01-21
2012-01-22
2012-01-23
2012-01-24
2012-01-25
2012-01-26
2012-01-27
2012-01-28
2012-01-29
2012-01-30
ST
D [
m]
DRES-2012-Jan: (NWM-KIN)
NorthEast
Up
0.000
0.020
0.040
0.060
0.080
0.100
0.120
2012-01-01
2012-01-02
2012-01-03
2012-01-04
2012-01-05
2012-01-06
2012-01-07
2012-01-08
2012-01-09
2012-01-10
2012-01-11
2012-01-12
2012-01-13
2012-01-14
2012-01-15
2012-01-16
2012-01-17
2012-01-18
2012-01-19
2012-01-20
2012-01-21
2012-01-22
2012-01-23
2012-01-24
2012-01-25
2012-01-26
2012-01-27
2012-01-28
2012-01-29
2012-01-30
ST
D [
m]
DRES-2012-Jan: (NWM-KIN)
NorthEast
Up
Figures above show monthly coordinate repeatabilities (DRES) demonstrating the
better performance for height with tropospheric delays introduced from the external
model and when compare to simultaneously estimated ZTDs and coordinates.
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0 10 20 30 40 50
RM
S Z
TD
[m
]
HOUR [#5-minutes ]
Comparing of RMS errors:ONSA-Jan-2012
IGS - NWM
*smt - *flt
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0 10 20 30 40 50
RM
S Z
TD
[m
]
HOUR [#5-minutes ]
Comparing of RMS errors:ONSA-Jan-2012
IGS - NWM
*smt - *flt
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0 10 20 30 40 50
RM
S Z
TD
[m
]
HOUR [#5-minutes ]
Comparing of RMS errors:ONSA-2012
IGS-PPPIGS-NWM
Last plots compare ZTD accuracies during the PPP initialization (ONSA) and ZTD
accuracies from the ERA Interim model. Note the results are from the winter period;
ZTD accuracy of ERA Interim can be double worse.
ERA Interim ZTD assessment
2
2.1
2.2
01/07/12 01/14/12 01/21/12 01/28/12-0.04
-0.02
0
0.02
0.04
ZT
D [m
]
Diffe
rence [m
]
EPOCH [#5-minutes ]
ANKR-2012-Jan: ZTD (IGS-NWM)
Diff IGS NWM
2
2.1
2.2
01/07/12 01/14/12 01/21/12 01/28/12-0.04
-0.02
0
0.02
0.04
ZT
D [m
]
Diffe
rence [m
]
EPOCH [#5-minutes ]
ANKR-2012-Jan: ZTD (IGS-NWM)
Diff IGS NWM
2.1
2.2
2.3
07/07/12 07/14/12 07/21/12 07/28/12-0.04
-0.02
0
0.02
0.04
ZT
D [m
]
Diffe
rence [m
]
EPOCH [#5-minutes ]
ANKR-2012-Jul: ZTD (IGS-NWM)
Diff IGS NWM
2.1
2.2
2.3
07/07/12 07/14/12 07/21/12 07/28/12-0.04
-0.02
0
0.02
0.04
ZT
D [m
]
Diffe
rence [m
]
EPOCH [#5-minutes ]
ANKR-2012-Jul: ZTD (IGS-NWM)
Diff IGS NWM
Comparison of ERA Interim global numerical weather data field and IGS final tro-
pospheric products. Plots display ZTDs (and ZTD differences) between IGS final
product and ZTDs calculated from the ERA Interim numerical weather data field
during two months (seasons): January and July, 2013.
Reference
1. Askne J, Nordius H (1987) Estimation of tropospheric delay for microwaves from
surface weather data, In: Radio Science, 22(3):379–386
2. Collins JP (1997) Assessment and Development of a Tropospheric Delay Model
for Aircraft Users of the Global Positioning System, M.Sc.E. thesis, Department
of Geodesy and Geomatics Engineering Technical Report No. 203, University of
New Brunswick, Fredericton, New Brunswick, Canada, 174 pp.
3. Dousa J, Elias M (2014) An improved model for calculating tropospheric wet
delay, Geophysical Research Letters (accepted on 6 June, 2014)
4. Marquardt, D. (1963) An algorithm for least-squares estimation of nonlinear pa-
rameters, J Soc Ind Appl Math, 11(2):431–441
Acknowledgement: The model development was supported by the ESA ProjectTrop4LAS and the Czech Science Foundation (P209/12/2207). We acknowledge
the ERA Interim data provided by the European Centre for Medium-Range Weather
Forecasts (ECMWF).