January 14, 2003 GPS Meteorology Workshop 1

Information from a Numerical Weather Model for Improving

Atmosphere Delay Estimation in GeodesyArthur Niell

MIT Haystack Observatory

Leonid PetrovNVI/GSFC

January 14, 2003 GPS Meteorology Workshop 2

Mapping Function

τZ

τ(ε)

m(ε) = τ(ε)/ τZ

January 14, 2003 GPS Meteorology Workshop 3

Background

Very Long Baseline Interferometry (VLBI) Preceded GPS Atmosphere modeling serious limitation No orbit, multipath, antenna modeling

problems below 10 degrees elevation Use all data down to 3 degrees

Used to evaluate NWM as input for atmosphere model

January 14, 2003 GPS Meteorology Workshop 4

Outline

What is a mapping function? How can it be parameterized to reflect

the real atmosphere? A new isotropic mapping function A different way to model the

asymmetric parts of the atmosphere Are the results any better?

January 14, 2003 GPS Meteorology Workshop 5

Summary Use of NWM improves mapping

functions significantly. Hydrostatic mapping function error is

more important than wet for repeatability except in the tropics.

Wet mapping function is more important than hydrostatic for seasonal variation.

A priori hydrostatic gradient allows more accurate wet gradient estimation.

January 14, 2003 GPS Meteorology Workshop 6

Why is the troposphere such a problem for geodesy?

( ) ( ) ( )i i i ig C a

Delay observable for ith satellite:

where g = geometric delay (antenna position,

orbits, Earth parameters) C = clock errors (receiver, satellite) a = atmosphere delay = elevation angle of observation

January 14, 2003 GPS Meteorology Workshop 7

Troposphere Delay Model( , ) ( ) ( ) ( , )

(P) ( ) ( )

[ cos( ) sin( )] ( )

ga h w tota

Z

l

Zh h

N E

w

g

wm

L

m

mL

, = elevation, azimuth P = surface pressure h

Z = zenith hydrostatic delay (~2 m) w

Z = zenith wet delay (~20 cm) LN = north gradient delay (total) LE = east gradient delay (total)mh, mw, mg = mapping functions

January 14, 2003 GPS Meteorology Workshop 8

Analytic mapping function

Determine coefficients a, b, c in terms of atmospheric parameters

e.g. ah, bh, ch as a function of latitude and the geopotential height of the 200 hPa level

11

1( )sin( )

sin( )sin( )

ab

cma

bc

January 14, 2003 GPS Meteorology Workshop 9

Numerical Weather Model Provides global distribution of information

Data every six hours Grid spacing 2.5° (NCEP) Geopotential height, specific humidity,

temperature

January 14, 2003 GPS Meteorology Workshop 10

Numerical Weather Model Hydrostatic mapping function parameter

z200 = geopotential height of 200 hPa surface Physical significance

z200 represents thickness of the troposphere corresponds to a height near the tropopause

a priori hydrostatic gradient given by (azimuth, zenith angle) of normal to z200

January 14, 2003 GPS Meteorology Workshop 11

Hydrostatic Gradientgradient ~0.02°

~10 km ~9.95 km~10.05 km

~200 km

200 hPa surface

January 14, 2003 GPS Meteorology Workshop 12

Numerical Weather Model

Wet mapping function parameter ~mw(3°)

2 2elev3.3

2 2elev90

3

e(s)k ds

T (s)smfw

e(z)k dz

T (z)

January 14, 2003 GPS Meteorology Workshop 13

Troposphere Delay Model using IMF

( , ) (P) ( ', ) ( , 3)

[ cos( ) sin( )] ( )

Za h

Zw

W WN E

h w

Wg

m z200 m smfw

mL L

´, = tilted elevation, azimuth P = surface pressure h

Z = zenith hydrostatic delay (~2 m) w

Z = zenith wet delay (~20 cm) LN

W = north gradient delay (wet) LE

W = east gradient delay (wet)mh, mw, mg

W = mapping functions

January 14, 2003 GPS Meteorology Workshop 14

IMF Implementation Obtain NCEP analysis after 6-hour update

geopotential height temperature specific humidity

Write out two files on same grid spacing (2.5°) geopotential height of 200 hPa surface value of smfw3 calculated at each grid point

Interpolate in time and latitude/longitude Calculate a, b, and c for hydro and wet Calculate mh( ´) and mW()

January 14, 2003 GPS Meteorology Workshop 15

Comparison with radiosonde-derived mapping functions

January 14, 2003 GPS Meteorology Workshop 16

Height Error (5° min. elevation)

January 14, 2003 GPS Meteorology Workshop 17

Height Uncertainty(mid-latitude)

January 14, 2003 GPS Meteorology Workshop 18

Evaluation usingVLBI data

2 2 2( ) ( ) ( )

21( )

2

IMF NMF

eV

WRMS L WRMS L WRMS L

RWRMS L

L

January 14, 2003 GPS Meteorology Workshop 19

Baseline Length Repeatability (CONT94)

January 14, 2003 GPS Meteorology Workshop 20

Repeatability Improvement with IMFg (CONT94)

January 14, 2003 GPS Meteorology Workshop 21

Repeatability Improvement with IMFg (1993-2002)

January 14, 2003 GPS Meteorology Workshop 22

Wet Gradient with/withoutapriori Hydrostatic Gradient

WVR wtd avg

January 14, 2003 GPS Meteorology Workshop 23

Annual Baseline Length(Westford-Wettzell)

January 14, 2003 GPS Meteorology Workshop 24

Annual Baseline Length(Kashima-Gilcreek)

January 14, 2003 GPS Meteorology Workshop 25

Summary Use of NWM improves mapping

functions significantly. Hydrostatic mapping function error is

more important than wet for repeatability except in the tropics.

Wet mapping function is more important than hydrostatic for seasonal variation.

A priori hydrostatic gradient allows more accurate wet gradient estimation.

January 14, 2003 GPS Meteorology Workshop 26

IMF or YAMF?

Isobaric Mapping Functionor

Yet Another Mapping Function

Thank you for your attention.