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CHAPTER – 1

INTRODUCTION

1.1 Importance of atmospherical vapor for the Climate !"stem

Water vapour is continually athletics through the atmosphere, evaporating from the surface, compressing to

create clouds and afterwards returning to the world as precipitation. Heat from the sun evaporates water and

this heat is free into the air once the water condenses into clouds and once it precipitates. The evaporation

condensation cycle is a crucial mechanism for transferring heat from the Earth's surface to its atmosphere

and in moving heat round the earth. thus atmospherical vapour is very important for the climate system and a

key to grasp the hydrological cycle.

Tren#s

Recent world estimates of long tropospheric water vapour changes show a rise in precipitate water

throughout the amount from 2! to 2"!. #argest trends will $e ascertained within the tropics with a rise of

concerning thirteen per decade. associate degree analysis of vapour trends higher than %orth &mericasupported radiosonde measurements from "( to 2"( reveals will increase in precipitate ta$le water over

all regions e)cept northern and *ap +anada wherever it fell slightly. Regions of wetness increase ar related to

regions of rising temperatures over identical amount, and also the regions of weakened wetness ar related to

falling temperatures. ne ma*or hindrance for associate degree improved information of the role of vapour within the climate system is *oined to data-$ased gaps that presently e)ist. ost studies primarily have

confidence radiosonde information. they need a fairly smart vertical, however a poor hori/ontal resolution.

1.$ The Role of %ater vapor in &P! 'eoph"sics an# Navi'ation

1.$.1 NA(!TAR &P!

%&01T&R 31 is funded and controlled $y the 4. 1. 5epartment of 5efense 6557 and consists of (

segments, the space, the management and also the user section. The house and also the user section ar

shortly e)plained here.

The 31 constellation consists of a minimum of twenty one satellites organi/ed in vi or$italnplanes with !!8

inclination associate degreed an altitude of twenty,2 klick higher than the Earth's surface. The or$ital

amount is concerning twelve hours, thus a 31 satellite is incessantly visi$le higher than the hori/on for concerning five hours. many varieties of 31 satellites are launched to date. ost of the satellites presently

in use ar 9lock :: and 9lock ::& satellites. The latter ar simply alittle modification of the initial style. 9lock :: satellites have a weight of ( kilo and a velocity of four km;s.

They transmit signals victimi/ation 2 fre<uencies, particularly #" 6f#2 = "!>!.?2 H/7 and #2 6f#2 =

"22>.@ H/7 and receive signals on a fre<uency of ">A(.>? H/. 9lock :: satellites carry four atomic

clocks - two atomic num$er (> and a couple of +s clocks - and have a design-lifetime of seven.! years. The

renewal satellites of kind 9lock ::R have the ne)t lifespan of ten years.

The user section contains the 31 receivers re<uired to decipher the transmitted signals. Bor tropospheric

delay estimation , high-<uality two-fre<uency receivers ar necessary so as to eliminate ionospheric

propagation delays properly.

1



1.$.$ Tropospheric Dela"s an# &P!

3recise 31 applications ar difficult $y atmospherical effects, particularly propagation delays within the

region and layer. &s so much $ecause the region cares, it's potential to compensate the primary order impact

given measurements on 2 totally different fre<uencies. Bor the delay caused $y the layer, no dispersion

effects ar gift and elimination isn't potential. The tropospheric delay will $e separated into ahydrostatic and a wet part. The hydrostatic part in celestial point direction is named CH5 6/enith hydrostatic

delay7. :t will $e e)actly determined $y surface pressure measurements. The CW5 6/enith wet delay7,

however, can not $e sufficiently modelled $y surface measurements thanks to the irregular distri$ution of

water vapour within the atmosphere. %e)t chapter can affect the main points of tropospheric delay

modelling.

The CH5 amounts to concerning two.( m, whereas the CW5 is simply within the vary of /ero."! m in worldaverage. though it's a lot of smaller than the hydrostatic part, the uncertainties in we tend tot tropospheric

delay modeling do place an e)cellent $urden on high e)actitude 31 applications if we recall that carrier

section measurements themselves have associate degree accuracy of a couple of milli meters and $ound

receiver makers even claim that they need reached noise levels within the su$-milli-meter vary.

&mong several e)amples in geophysics and navigation, %&:T D"A reports a few Fapanese network that

has $een esta$lished for deformation analysis and earth-<uake detection. The analysis of the measurementsshowed drifts within the coordinate solutions that apparently weren't thanks to plate motions, however

associated with associate degree light compensation of tropospheric delays. e)tra estimation of wet delays

inside the routine analysis ought to improve the case.

1.) vapor perceptive !"stems

& variety of platforms and sensors is out there to live atmospherical water vapour. Each system has $ound

$lessings and draw$acks. the su$se<uent summary is $ased on +G#ER and a$or. Bigure "-" shows a

num$er of these sensors and their characteristics ar summari/ed in Ta$le "-".

1.).1 Description of han#*pic+e# !ensors

round-$ased direct sensors, weather $alloons and craft were the sole tools offered to live precipita$le

vapour within the past. The radiosonde has $een one amongst the foremost vital devices and can actually still

$e a valua$le vapour detector within the future. Radiosondes ar $alloon-$orne instruments with radiotransmittal capa$ilities. They contain instruments capa$le of creating direct unaltered measurements of air

temperature, humidness and pressure with height, usually to altitudes of roughly thirty klick. These

ascertained information ar transmitted instantly to the $ottom station $y a sender. round-$ased radio

direction finding antenna instrumentality tracks the motion of the radiosonde throughout its ascent through

the ? n round-$ased 31 Tropospheric 5elay EstimationI air. The recorded elevation and &C info ar re$orn to wind speed and direction at numerous levels $y triangulation techni<ues.

Today, more remote sensors capa$le of taking vapour measurements over giant aras are offered. 1u$stantial

progress has $een created victimi/ation satellite o$servations to get total column water vapour and low-resolution vertical profiles from infrared and microwave sensors, however these satellite o$servations don't

give information underneath all atmospheric condition nor specially surfaces. typically speaking, they live

2



a$sorption lines within the radiation from the new $ackground provided $y the world. +onse<uently, clouds

could cause issues in addition $ecause the surface of land plenty. 9est results ar o$tained over oceanic

regions.

Hygrometers and #:5&Rs will $e helpful for ela$orate native studies. measuring instrument is associate

degree form for lightweight detection and locomote, a vigorous remote sensing techni<ue that operates in an

e)ceedingly similar manner as echo sounder systemsJ & pulse of optical maser lightweight is emitted into the

sky and also the <uantity of come thanks to $reak up from the atmosphere is measured versus time. Withinformation of the speed of sunshine, the time is re$orn into altitude. The num$er of photons counted for

every altitude $in is proportional to the atmospherical density.

Bigure "-" - summary of water vapour measure platforms and sensors following +&RTER Water vapor sensors ar

carried on a spread of platforms as well as ground stations, weather $alloons, craft and satellites. %&01T&R 31

consists of a minimum of twenty one E satellites at associate degree or$it altitude of twenty, km.

atmospherical o$servance with 31 is feasi$le in 2 waysJ $y searching the atmosphere with facilitate of 31receivers on #E 6low-earth or$iting7 satellites, the supposed radio $reak techni<ue, or $y victimi/ation networks

of ground-$ased 31 receivers. in keeping with &9R D">, remotely piloted vehicles have nevertheless toreturn ancient, however supply a dou$tless long loiter time and high altitude ceiling.

1., O-ectives an# !trctre of this Thesis

The outstanding pro$lems in vapour analysis for meteorology ar printed $y +G#ER and divided into

theoretical, data-$ased and climate modelling pro$lems. To summari/e the primary 2 classes, an a$sence of

data as so much $ecause the role of vapour in influencing the radiation $udget of the world will $e declared.

identical is true for the processes decisive the distri$ution of vapour and its changes over time. Retrievals of

vapour shall $e improved and e)tended with special stress on long, continuous and world o$servations to

assist within the analytic thinking.

:n 31 geophysics and navigation, the first goal in modelling the tropospheric propagation delay is to cut

$ack the uncertainties associated with the wet part or, e<uivalently, to water vapour. Bor permanent 313



arrays, the e)tra estimation of celestial point wet delays reduces the impact of tropospheric modelling errors

and provides valua$le estimates of total atmospherical column water vapour for climate models and

meteorology. for several different 31 applications, tropospheric delay estimation isn't potential or

pro$lematic. & typical e)ample for this cluster are kinematic applications that commonly don't ena$le the

determination of such e)tra parameters and are thus su$*ect to improvement $y precise tropospheric

corrections e<uipped $y 31 permanent arrays and;or numerical weather models.

1.,.1 O-ectives of this Thesis

:n order to take advantage of the potential of 31 receivers as water vapour sensors, a tropospheric analysis

system is to $e developed that's a$le to e)actly filter celestial point wet delays and integrated water vapour

from 31 section measurements. This platform independent process package ought to $e opera$le in semi-

automatic and totally automatic mode as well as non-interactive information writing. computer file in

commonplace formats should $e supported and also the analysis results got to $e hold on in normally united

commonplace formats, too. 1pecial stress is to $e arranged on the responsi$ility of the results, and also thenetwork performance is to $e mechanically analy/ed and, if necessary, to $e altered 6i. e. e)clusion of

suspicious receivers7 and re-analy/ed conse<uently. The computer code shall $e a$le to analy/e multi-station

networks with long $aselines 6more than one thousand km7 with enough accuracy. The temporal resolution

is to $e chosen ade<uately and shall meet potential desires for high-fre<uency information.

The overall goal is to estimate wet delays and integrated water vapour whereas the <uality output of complete 31 information analysis will solely encompass neutral 6or total7 delays. this suggests that e)tra

meteorologic information ar re<uired like surface pressure for modeling the hydrostatic part and

temperature for the conversion of wet delays into precipita$le;integrated water vapour. Therefore, the

analysis system should give all necessary interfaces to access these e)tra information. &s a matter of reality,

the supply of in place meteorologic measurements at 31 monitor stations is e)tremely restricted. &s a

conse<uence, algorithms got to $e developed to e)tract the re<uired info from numerical weather models.thanks to the world si/e of 31 following we$ works *ust like the :1 net, weather models of worldwide

e)tend are favora$le to accomplish this task.

The efforts to e)tract tropospheric info from numerical weather models shall not $e restricted to the support

of the 31 information analysis with reference to meteorology and meteorology, however shall even $e

assessed in terms of their relevance to 31 navigation and geophysics. &n open, memory-efficient and

gridded format shall $e developed that carries all information analy/ed within the three-5 numerical weather

models that ar re<uired to work out hydrostatic , wet and neutral delays at anyplace on the world. These

gridded tropospheric correction information shall $e suited to kinematic 31 process and may con*ointlyfunction a carrier for gridded integrated water vapour information. correct ways for hori/ontal interpolation

and vertical reduction of the delays are to $e developed and valid.

Binally, the on an irregular $asis distri$uted tropospheric delays calcula$le at the 31 sites shall $e

com$ined with the gridded information of the tropospheric correction files that are derived from numerical

weather models. during this manner, the 31 and also the less correct %W delays are li<uified along and

also the outcome are associate degree improved, additional correct answer for the gridded information sets.appropriate algorithms for this mi) shall $e

investigated with special concentrate on random improvement.

4



&ll algorithms ar to $e documented and mentioned. This doesn't solely discuss with the special tasks of 31

tropospheric delay estimation, however con*ointly includes a full summary of the components which will $e

referred to as KconventionalK 31 processing, i. e. those algorithms that ar essential for 31 information

analysis, al$eit not primarily associated with 31 tropospheric delay estimation. The dominant error sources

shall $e analy/ed and their impact is to $e evaluated with facilitate of sensi$le e)periments. &ll (

cornerstones, particularly 6:7 the filtering of celestial point wet delays and integrated water vapour from 31

measurements, 6::7 the meteorologic information e)traction from numerical weather fields and its application

to 31 meteorology, and 6:::7 the suita$leness of the gridded tropospheric correction information fromweather fields in addition $ecause the com$ined 31;%W answer fields ought to $e valid.

Bigure "-2 - 1tructure of this thesis. +hapters two to four will $e thought of $ecause the theoretical

half descri$ing the modelling ways and algorithms of 31 tropospheric delay estimation andinformation e)traction from numerical weather fields. sensi$le results ar $estowed in chapters five to

seven and a summary is given in chapter eight.

5



Chapter *$

Principles of &P! processin'

Tropospheric delay estimation needs careful modelling of the 31 measurements. Bor this reason, the

principles of 31 processing ar printed here within the initial place $efore the matter of tropospheric

propagation delays is self-addressed within the chapter three well. %ote that the su$se<uent sections aren't

meant as a general introduction into 31 process, however concentrate on the ways enforced within thetropospheric analysis computer code Trop &+ on that the results $estowed in chapters five, vi and seven are

$ased mostly. Bor a general description, the interested reader could discuss with 1EE9ER and

HBB&%%-WE##E%HB et al. D"(, as an e)ample.

$.1 process smmar"

The main process steps will $e divided into pre-processing, network filtering and post-filter process. These (

stages ar shortly mentioned $elow. #inks to the corresponding sections are given.

$.1.1 Pre*Processin'

&t the pre-processing stage, the re<uired information ar scan, checked and corrected. The measurements like

code ranges and carrier section o$servations ar scan from R:%EL files. +arrier phases need some e)tracorrections, e. g. the synchroni/ation downside has got to $e self-addressed if 6single or7 dou$le variations

shall $e shaped, the orientation downside will $e relevant for e)tended $aselines, elevation-dependent

antenna section center corrections should $e applied. Binally, ionospheric and tropospheric delays ar

foreseen. oreover, typical issues like cycle slip detection and repair in addition as multipath detection

con*ointly $elong to the tasks of the pre-processor.

Bigure 2-" - a*or modules of the Trop &+ permanent array filter computer code and their

interrelations. The pre-processor for the 31 information is named 3&BM3RE3 and prepares all

re<uired information for Galman filtering. %etwork filtering is allotted with the modules 3&BMB:#T,

3&BMTR3 or 3&BMR&%. 3rogram 3&BME is interface to the numerical weather models and

3&BM+9 is ready to com$ine often gridded tropospheric information sets from the weather fields

and also the on an irregular $asis distri$uted 31 estimates.

6



$.1.$ Net%or+ /ilterin'

The pre-processed information are filtered for the unknowns, particularly ground station coordinates 6and in

special cases con*ointly satellite or$it $iases7, celestial point wet delays and am$iguities. Bor this purpose, a

Galman filter is employed. though pre-processing ought to have removed suspicious information, the filter

itself is capa$le of $lunder detection and should even perform a post-fit residual analysis and tell on the

previous answer if necessary. &s throughout the pre-processing steps, the network is checked for poorly

playacting sites another time ensuing in an e)ceedingly new filter run if such stations are found.

$.1.) Post*/ilter process

&t the post-filter stage, $ound computations are allotted that don't $elong on to the Galman filter method, e.

g. the derivation of mean ground station coordinate estimates, the information transformation of networks in

addition $ecause the creation of free network answers $y similarity transformation and also the method of

melting network partitions to associate degree overall solution file.+ertainly, troposphere-related *o$s *ust like the conversion of celestial point wet delays into integrated water

vapour $elong to the present process stage, too.

Name of

Module

Purpose

TR3&+

uidance programN user interface to simplify access to the program system generation

of $atch-files, scheduling of processes, visuali/ation.

3&BMR9:

Trop&+ normally uses precise or$its from the :1 analysis centers which are provided

in the 13(-format defined $y the %ational eodetic 1urvey 6%1, 41&7, seeRE--%5 O D"A, "" for details on this format. 9roadcast or$its are less accurate and

given in a different format 6R:%EL %&0 files7. This module allows to created 13(-

files from one or more R:%EL navigation files.

3&BME

The meteorological module of Trop&+. :t allows to e)tract meteorological data from

numerical weather models provided in R:9-format. 1everal data can $e e)tracted likesurface pressure, temperature and humidity. TR3EL files can $e generated and ray-

tracing can $e performed.

3&BM+9

The tropospheric com$ination module. :t allows to com$ine 31-derived tropospheric

delays with those integrated in numerical weather fields.

3&BM3RE3

The 31 pre-processor for static networks. This module prepares all needed data for

the filter processJ 31 measurements are read and filtered, or$its are interpolated,

dou$le differences are formed and synchroni/ed, cycle slips are detected and repaired,

tropospheric delays are predicted and, finally, a $inary network file is created

containing all necessary information for the filter engine.

3&BMB:#T

The Galman filter engine $ased on dou$le-difference phase measurements. The state

vector of this filter consists of ( coordinate components for each site and - optionally -

of one /enith wet delay per site modeled as random walk stochastic process. oreover,

or$it rela)ation can $e applied. The am$iguity parameters are dynamically allocated inthe state vector. This module equals PAF_FILT except for the fact that it does ot estimate

!



PAF_T"#P coordiates$ This reduces the um%er of u&o's ad speeds up

processi($

$.$ O-servations an# O-servation E0ations

31 o$servations? principally comprise pseudo-range and carrier section measurements. section

measurements have a amplitude of a couple of millimeters and are terri$ly precise compared to code rangesthat are solely correct to a couple of meters or some decimetres at their $est. Bor this reason, carrier phasesare the first and most vital kind of o$servation for high-precision parameter estimation. the aim of pseudo-

ranges is primarily associated with the pre-processing stages. :n distinction to carrier phases, code ranges

aren't am$iguous and might thus $e simply applied to sight section $reaks, as an e)ample, and serve for

several different functions as are mentioned within the following sections.

$.$.1 Pse#o*Ran'es

3seudo-ranges are non-am$iguous measurements. though they need the ne)t amplitude than section

measurements, they will serve an honest *o$ for the detection of multipath, the parado) resolution methodand also the derivation of appro)imate station coordinates. oreover, code ranges play a key-role for the

determination of the signal transmission epoch and facilitate to synchroni/e the $aselines!. Bollowing

WP99E%& simplified o$servation e<uation for radio radiation #" will $e e)pressed asJ

P"iA)L1* = + A)L1* + c ⋅ ,δtA − δti - + δ+i A)I#./L1* + δ+A)T"#P* + εP"

1i &J geometric distance $etween receiver antenna & and satellite i

+ J speed of light 6in vacuum, c = 2 >2 ?!A m;s7dt& J receiver clock error dti J satellite clock error d1i& D:%J ionospheric propagation delayd1i&DTR3J tropospheric propagation delaye3RJ noise term

$.$.$ Carrier Phase easrements

3recise positioning and filtering of tropospheric delays is carried out using carrier phase measurements. Theo$servation is the so-called carrier $eat phase.

Φ i& ,tR )= Φ RE+ ,tR -−Φ REB ,tR -= Φ i ( tT )− Φ RE+ t,#"-

tR J time of signal receipttTJ time of signal transmissionΦ i

&J carrier phase measurement, carrier $eat phaseΦ RE+J received carrier phase from satellite i at receipt time tR

Φ iJ carrier phase of satellite i at signal transmission time tT

Φ REBJ phase of reference signal generated $y the receiver & at receipt time tR

$.$.$.1 Do-le Differences

0



The original carrier phases are not used for filtering $ecause these measurements are corrupted $y receiverand satellite clock errors. :nstead, dou$le differences are derivedJ :n a first step, single differences@ areformed, i. e. phase differences $etween two ground stations & and 9 which $oth have satellite i in view. :n asecond step, the same is done with those measurements to satellite *. The difference $etween the two singledifferences is computed and yields the dou$ly differenced phase o$servation

∇∆Θi*

&9D#" = (Θ *

9D#" − Θ i

&D#" )− Θ i

9D#" − Θ i

&D#"

$.$.$.$ !"nchroni2ation Pro-lem

5ue to the presence of receiver clock errors, care must $e taken to refer the measurements to the correctepoch. Bollowing the definitions given $y WP99E%&, the receiver time tQ at the measurement epochdeviates from the true 31 time t $y the receiver clock error δt& in the following wayJ

t′ΟR = t ΟR + δt ⇔ t ΟR = t′ ΟR − δtA

t#" true P+ time of si(al receipt at receier site A

t#" receier time of si(al receiptδtA schroiatio error/ receier cloc& error

$.$.$.) Antenna Orientation #o%nsi#e

+ircularly polari/ed magnetic attraction waves are transmitted from the 31 satellite's antenna to the

receiving antenna. +onse<uently, the ascertained carrier section measurements rely upon the orientation of

the receiver and transmitter antennas and also the direction of the road of sight. :f the orientation $etween the

transmittal and also the receiving antenna changes, a amendment will $e measured within the ascertained

section. Bor static networks, such changes in orientation are caused $y the moving 31 satellites. W4 et al.D"( incontesta$le that the correction thanks to antenna orientation is negligi$le for $rief $aselines,

however could reach a magnitude of up to four cm for $aselines as long as ? kms.

The formula given here permits a general description of the matter and might even $e applied for kinematic

31 process. However, angle and &C info is re<uired in such cases as a result of the orientation of the

antenna dipoles should $e renowned and should actually vary within the case of moving antennas. The

effective dipole of the receiving antenna is found to $e

dA = e7 − ei

A ⋅ ,ei

A ⋅ e7 - + ei

A × e 8d&J effective dipole vector of the receiving antenna at site & referring to satellite ieLJ E+EB unit vector in direction of the )-dipole element of the receiving antennaeOJ E+EB unit vector in direction of the y-dipole element of the receiving antennaei

&J E+EB unit vector from receiving to transmitting antenna.

where all vectors ar e)pressed within the world, philosopher E+EB system. Bor static networks with the

$ottom antennas $eing properly aligned to northward direction, the native level unit vectors of the 2 antenna

dipole parts ar outlined as

" e) = eO = - "

9



"

e)J native level orientation vector of )-dipole component

eLJ E+EB orientation vector of )-dipole component

2.2.4.1 initial Order impact :

Gnowledge of the negatron content is enough so as to model the primary order ionospheric impact. :n mostcases, solely the primary order delay is taken into consideration as a result of it's out and away the foremost

dominant a part of the ionospheric propagation delay.

I#. : 1; <2 =f 2 : 1;<$.e

%eJ negatron density in Delectrons;mS

+J constantN + = forty.2A DmS;s

%ow, the ionospheric propagation delay in celestial point direction will $e integrated victimi/ation thenegatron density

%e. Bor carrier section measurements this correction in celestial point direction is

δ1:%C=

: ∫hA

∞C 2

f 2 =

C

f 2 . ∫hA

∞

N

e 6h7.dh = C

f 2 $>T?<

1@



CHAPTER *)

o#ellin' an# Estimatin' Tropospheric Propa'ation Dela"s

The primary purpose of the Trop&+ analysis system is to estimate wet tropospheric delays which will $e

re$orn into integrated vapour and there$y function a valua$le input into numerical weather and climatemodels. Bor this reason, a whole chapter is dedicated to tropospheric delay modelling and estimation.

).1 temporar" smmar" of the 3o%er Atmosphere

The atmosphere may $e a mi)ture of dry gases that primarily contri$ute to the hydrostatic delay and water

vapour that is answera$le for the wet delay. 13:#GER states that the dry atmosphere is uniform anduncomplicat- -ed in modelling whereas the wet half is erratically distri$uted. The vertical profiles of the

foremost vital meteorologic <uantities ar planned in Bigure (-2 for associate degree at random chosen day at

:1 monitor station $erpfaf fenhofen .

The following layers ar to $e distinguishedJ The layer ranges from water level 6U /ero m7 to a height of

concerning twelve klick and is characterised $y a comparatively linear temperature decrease. The layer may

$e a little

$oundary layer $etween twelve and si)teen klick wherever the temperature remains some constant at tier of -@ to -A 8+ and within the layer 6"@ to fifty km7, a slow temperature increase happens. &s so much $ecause

the wetcomponent cares, the lower layer is of ma*or interest whereas the hydrostatic part is influenced up to the

stratopause. 13:#GER mentions that concerning one <uarter of the entire delay is caused $y gases higher

than the layer. ost of the vapour contents, however, is targeted at a height right $elow four klick and higher

than twelve klick, nearly no additional vapour is gift.

11



Figure 3-1 +chematic of the tropospheric ad stratosphericlaers ad the tropopause after B#<CL?" )1995*$ The meaertical distri%utio of temperature ad 'ater apor mixi(ratio ,lo(arithmic scale- are sho'$

).1.1 Pressre

The sea level pressure is concerning ""( h3a in average, a worth that's utili/ed in most traditional

atmosphere models. Bigure (-2 shows that the pressure decreases e)ponentially with increasing altitude. Thelayer height is reached at a pressure $etween three hundred h3a at the poles and seventy h3a at the e<uator

and a worth of roughly one h3a will $e declared at the stratopause height.

).1.$ Temperatre

The temperature shows a linear decrease up to the layer, however note that this linear trend will $e

significantly distur$ed within the initial few hundred meters higher than the surface thanks to inversion

layers. The supposed temperature lapse rate is within the vary of -! to -> G;km $elow the layer height. &t the

layer itself, the temperature remains some constant and slowly will increase within the layer.

).1.) %ater vapor

The ratio diagram in Bigure (-2 indicates that not solely the hori/ontal distri$ution, however con*ointly the

vertical distri$ution of water vapour within the layer can not $e e)pected to $e uniform. the e)planation for

this is often *oined to the fast turnover of water within the air in addition on the variation of temperature with

height and location", see +G#ER .

&lthough there ar apprecia$le variations, Bigure (-" con*ointly implies that there ar $ound trendsJ water

vapour decreases <uickly with height $ecause the atmosphere gets colder. %early DVfr" the entire water within the air is found $etween water level and concerning one.! klick higher than water level. $ut five-@

12



of the water is gift higher than ! klick, and fewer than a hundred and twenty fifth is found within the layer.

ratio shown in Bigure (-2 con*ointly tends to decrease with height, from a mean price of concerning @-A

at the surface to 2- four-hundredth at three hundred h3a 6 km7.

).$ o#elin' of Tropospheric Dela"s

The following sections shortly define the principles on that tropospheric delay modeling is predicated.

meteorologic inputs that ar necessary for the delay models, their vertical distri$ution and also the relations

$etween them ar treated in chapter four in addition.

:t ought to $e emphasised that the term tropospheric propagation delay is employed here despite the actual

fact that the hydrostatic part is additionally influenced $y gases higher than the layer.

).$.1 &enerali2e# practical Description

The geometrical distance differs from the particular ray path $y the distinction

δ1i&D%E4 =

n (s ) .ds−¿

∫ ATM

❑

¿ ∫VAC

❑

ds

d1i&D%E4J total;neutral slant path delay from receiver antenna & to satellite i

nJ inde) of atmospherical refraction

dsJ differential increment in distance with reference to the road of sight

&TJ ray path passing from antenna in direction to satellite through the atmosphere

0&+J virtual path of a ray passing from antenna in direction to satellite through vacuum.

δ+iA).?D* : δ+i

A)E8* ; δ+iA)G?T*

δ+)E8* hdrostatic slat path dela

δ+)G?T* ohdrostatic or 'et slat path dela

a hydrostatic and a non-hydrostatic part. The latter is commonly referred to as wet part that isn't too wrong

$ecause it is especially caused $y the vertical distri$ution of water vapour within the layer and also the initial

part is additionally referred to as dry delay that is partially dishonest . a comparatively new side in

tropospheric delay modeling is to any distinguish $etween the a/imuthally rhom$ohedral delay and unevencomponents.

δ+iA).?D* : δ+i

A)E8/+8BB* ; δ+iA)E8/+8BB* ; δ+i

A)G?T/+8BB*; δ+iA)G?T/+8BB*

δ+)+8BB* tropospheric dela term uder the assumptio of smmetr i aimuth$

δ+)A+8BB* tropospheric correctio term ta&i( asmmetric eHects ito accout$

where the uneven parts ar typically determined $y application of a hori/ontal tropospheric gradient model.+onse<uently, the total notation for the neutral delay is

13



δ1i&D%E4 = m ε i

&DHO5.CH5&Xm ε¿

i&7D&C:,HO5.D&D%,O5. cos ∝ i

a;A)?/E8*$si ∝ iA *$

m,ε- mappi( fuctioCH5J celestial point hydrostatic delay

CW5J celestial point wet delay

D%J gradient in northward direction

DEJ gradient in eastward direction

).$.1 o#elin' celestial point Dela"s

Bollowing TH&OER , the neutral celestial point path delay will $e derived from the radio inde) of refraction

of the air

% =G ".

P d

T .C-"d X G 2.

e

T .C-"w XG (.

e

T 2

.C-"

w

n6s7J inde) of refraction as operate of the space 's'

%J reduced inde) of tropospheric refraction

k"..(J refraction constants

Cd;w-"J inverse softness factors for dry and wet air

pdJ dry pressureN metallic element = p - e with p $eing the entire pressure 6measured <uantity7

eJ partial water vapour pressure

piJ pressure of perfect gas i

TJ temperature

0J volume

mJ mass

iJ molar mass of gas i

RiJ specific universal gas constant

RJ universal gas constantN R = eight.("?(? DF mol-" G-"

ρi desit of (as i

pi = ρi ⋅"i ⋅ T ⋅ i

CiJ softness issue of gas i .

).$.1.1 celestial point h"#rostatic Dela"

14



Three hydrostatic delay models are $estowed during this section. The Hopfield and also the 1aastamoinen

model ar mentioned well and compared with one another. moreover, the 31 model that doesn't want any

meteorologic measurements as input is delineated .

).$.1.1.1Hopfiel# h"#rostatic Dela" o#el

The e<uation for hydrostatic e<uili$rium follows from the $est gas laws of 9oyle- ariotte and physicist

and might $e e)pressed in differential type as

dpJ differential amendment in pressure

g J gravity, assumed to $e constant, esp. with height

ρ J density of dry air, assumed to $e constant

dHJ differential amendment tall

and the density can even $e e)pressed $y

and ends up in the e<uation3 J pressure

T J temperature

RdJ specific universal gas constant of dry air.

&s already mentioned, the vertical evolution of the temperature within the layer will $e appro)imated $y a

linear trend victimi/ation the temperature lapse rate

TJ temperature as operate of altitude 'f6h7'TJ temperature at surface 6or antenna7 height h = /ero m

βJ temperature lapse rate

HJ height higher than water level

and is employed as model for the complete atmosphere. The e<uation $ecomes

15



k"J hydrostatic deflection constant 6k" = seventy seven.@ h;h3a7RJ universal universal gas constant 6R = eight.("?(? F mol-" G-"7

ρJ total density

dJ molar weight of dry air 6d = twenty eight.@?? kg;kmol7

Bor a default temperature lapse rate of $ = [email protected]" G;km, a molar weight of dry air of d = twenty eight.@??

kg;kmol, a universal universal gas constant of R = eight.("?(? DFYmol-"YG-" and a mean gravity

acceleration of g = nine.A@ m;s the e)ponent $ecomes h = four.2 U four that's adopted for the Hopfield

two-<uartic model. &nother modification is formed $y su$stitution of d

β temperature lapse rate i )C=&m*TJ surface;antenna temperature in DG

tJ surface;antenna temperature in D8+

HdJ effective height of the dry atmosphere higher than the surface in Dkm

HdJ effective height of the dry atmosphere for a temperature of /ero 8+ in Dkm

with the inverse negative height Hd that is that the effective height for the hydrostatic part and was o$tained

$y a work of worldwide radiosonde information to.

16



The celestial point hydrostatic delay of the Hopfield model will currently $e written in closed type as

and can $e computed with information of surface temperature and pressure(. &s has $ecome clear, variety of appro)imations cause this easy formula. with the e)ception of the actual fact that the air is treated as a

perfect gas that isn't too essential, the idea of a continuing temperature lapse rate is one vital appro)imation

that ought to $e stressed in addition $ecause the incontroverti$le fact that the gravity isn't sculptured withdependence on the peak. consecutive model $estowed can overcome this disadvantage.

).$.1.1.) OP! h"#rostatic Dela" o#el

:f no meteorologic information ar offered, the 31 tropospheric formula will $e applied. This approach

uses commonplace meteorologic information o$sessed on latitude and takes differences due to the season

into consideration. Birst, the latitude-dependent mean meteorologic parts are taken from Ta$le (-2 and

afterwards denoted as ). $eginning with one Fanuary, the day of year 5oO has got to $e computed so as to

account for seasonal changes and also the corresponding values are to $e taken from Ta$le (-( and denotedas 5).

Latitude |

φ |

p !"Pa# $ !%# e !"Pa#β

!%&m#λ

!&#

Z"!8

""(.2! 2.@! 2@.(" .@( 2.>>

3@J1@1!$25 294$15 21$!9 @$@@6@5 3$15

45J 1@15$!5 203$15 11$66 @$@@550 2$5!

6@J 1@11$!5 2!2$15 6$!0 @$@@539 1$013

>

'() 1@13$@@ 263$65 4$11 @$@@453 1$55

).$.1.$ celestial point 4et Dela"

1!



Cenith wet delays ar full of the distri$ution of water vapour. it's terri$ly tough to derive e)tremely correct

models victimi/ation solely surface measurements for this part, however it's potential to estimate celestial

point wet delays.

as e)tra parameters throughout network filtering. This issue are coated $y section three.?. yet, some

approaches for the appro)imation of celestial point wet delays ar given here which will serve to predict wet

delays so as to initiali/e the Galman filter.

).$.$ proecte# celestial point Dela"s into !lant Direction

The tropospheric delay is shortest in celestial point direction and can $ecome larger with increasing celestial

point angle. 3ro*ection of celestial point path delays into slant direction is performed $y application of a

mapping operate or o$li<uity issue that's outlined as

δ+).?D* eutral=total dela i slat directio. eith eutral delaB mappi( fuctio eith a(le from (roud statio to P+ satellite

for the neutral part, as an e)ample, and is well found to $e

+. slat eutral dela/ idetical 'ith δ+).?D*

10



CHAPTER * ,

&P! (ali#ation E5periments

1everal hand-picked 31 validation e)periments ar mentioned during this chapter. &ll tropospheric

parameters were calcula$le with the analysis system Trop&+ shaft that was developed as a part of this study.&s so much $ecause the tropospheric delays ar involved, ( levels of comparison ar potential.

The first level is that the comparison of celestial point neutral delays. %ote that total delays aren't calcula$le

$y the Trop &+ analysis computer code, however the celestial point wet delays. However, the hydrostatic

delay is sculptured with facilitate of surface pressure and thus, it's not tough to derive the neutral delay.

. = G+ E

C%5 J celestial point neutral 6total7 delay

CH5 J celestial point hydrostatic delay 6modelled;predicted $y pre-processor7

CW5J celestial point wet delay 6estimated $y Galman filter7

19



$ut mind the error $udgetJ The variance for the neutral delay should $e smaller than the variance of the wet

delay

σ

ΖΝ

D 6σ

Ζ

4D 7σ$8HD

$ecause 31 alone is not a$le to sense wet delays. :nstead, the hydrostatic component must $e derived frome)ternal information including additional measurement and modelling uncertainties. 0alua$le reference data

for this validation level come from the :1 analysis centers that provide a com$ined tropospheric product.These com$ined data sets are total delays in /enith direction that are derived as the weighted mean of theindividual solutions of the particular analysis centers.

The second level is the comparison of /enith wet delays which are an output of the Trop &+ software.Reference data can $e taken from radio sonde launches, for instanceJ The wet, vertical refractivity profile isintegrated and yields /enith wet delays.

Binally, the third level of comparison is the most interesting one for meteorology and climate research, $ecause it focuses on integrated water vapour 6:W07 or precipita$le waterJ

PG precipita%le 'aterK coersio factor to trasform eith 'et delas ito precipita%le 'ater ad ice ersa

The uncertainty of the conversion factor [ is an additional contri$utor to the total error $udget of precipita$le water, $ut in most cases of minor concern. Water vapour radiometers can supply reference datafor water vapor comparisons.

3on'*term E5periment

The long-term e)periment was conducted for a period of appro)imately half a year. The $asic characteristicsand o$*ectives are given in Ta$le @-" and a network plot with the nominal $aseline configuration is given inBigure @-". The primary o$*ective of this e)periment was to validate the tropospheric /enith delays that are

filtered in routine, automatic processing mode. Bor this reason, the standard configuration settings wereapplied. &part from accuracy considerations ,the availa$ility of the o$servation data and the relia$ility of themeasurements are addressed in the following sections.

2@



CHAPTER*9

!OPAC

The 1cripps r$it and 3ermanent &rray +enter 613&+7 is located at the +ecil H. and :da . reen:nstitute of eophysics and 3lanetary 3hysics 6:337, 1cripps :nstitution of ceanography 61:7, 4niversityof +alifornia, 1an 5iego 64+157 in #a Folla, +alifornia. 13&+'s primary scientific role is to support high

precision geodetic and geophysical measurements using lo$al 3ositioning 1ystem 6317 satellites, particularly for the study of earth<uake ha/ards, tectonic plate motion, plate $oundary deformation, andmeteorological processes. 13&+ investigators also conduct research on the implementation, operation andscientific applications of continuously monitoring 31 arrays and 1ynthetic &perture Radar 61&R7interferometry.

13&+ is a ma*or participant in the :nternational 31 1ervice 6:17, serving as a lo$al 5ata +enter and alo$al &nalysis +enter. 13&+ is the archive for the 2!-station 1outhern +alifornia :ntegrated 31

%etwork 61+:%7, as well as an analysis center and a data retrieval facility. 13&+ maintains an archive of

regional continuous 31 data for 4%&0+, :nc. focusing on the Western %orth &merica plate $oundaryand is developing a seamless archive interface for 4%&0+. 13&+ performs research and providesoperational support for %&&'s Borecast &pplications 9ranch 6B&97 real-time 31 meteorology pro*ect for

21

http://igpp.ucsd.edu/


http://sio.ucsd.edu/


http://www.ucsd.edu/


http://igscb.jpl.nasa.gov/

http://www.scign.org/

http://www.unavco.org/

http://esrl.noaa.gov/gsd/fab/



http://igscb.jpl.nasa.gov/


http://www.unavco.org/

http://esrl.noaa.gov/gsd/fab/




short-term weather forecasting. 13&+ also provides essential infrastructure support for the +alifornia1patial Reference +enter 6+1R+7, a partnership with the %ational eodetic 1urvey 6 %17.

13&+ provides precise, rapid, ultra-rapid, and hourly or$its for the :nternational 31 1ervice 6:17 and %&&'s Borecast 1ystems #a$oratory 6B1#7. any 31-related services and tools are availa$le from the13&+ We$ site, such as 1+4T 6an :TRB +oordinates eneratorN "! minute turnaround time7, 1ite:nformation anager 61:7, and a utility to check for unused ?-character site codes. 13&+ archives 2?-hour R:%EL data from a$out A continuous 31 sites from more than 2 scientific networks around the

world, including the 2!-station 1outhern +alifornia :ntegrated 31 %etwork 61+:%7. 13&+ also helpsmaintain the operational center for the +alifornia 1patial Reference +enter 6+1R+7. The +1R+ provides+alifornia's geodetic framework for scientific, surveying, engineering, and geographical information systemsin partnership with the %ational eodetic 1urvey and +altrans. 13&+ also collects and archives high-rate6" H/7, low latency 6"-2 seconds7 31 data from stations in +alifornia.

+H&3TER -@

14&RO &%5 +%+#41:%

2.11 OBSERVATION DATA G (GPS) RINEX VERSION / TYPEteqc 2015Jun2 !"#$"# 20151105 00%10%0&'TPG / R'N BY / DATE*+nu, 2.-.212.E*#"O"te$n!cc #t3t+c*+nu, ,4&&-67 OENTBIT 2 O8 **I 8*AGS DATA O**ETED 'NDER A/S ONDITION OENTIIS AR9ER NAE220&002 AR9ER N'BERGGN AS OBSERVER / AGENY:R52001402 AS;TE; ':12 <00 RE = / TYPE / VERSR&2005-402 AS;01>-5E NONE ANT = / TYPE 1>&.-550 &001.12&1 1-24&.452 APPROX POSITION XY: 0.040 0.0000 0.0000 ANTENNA% DE*TA ;/E/N 1 1 ?AVE*ENGT; 8AT *1/2 *1 *2 P1 P2 1 S1 S2 = / TYPES O8 OBSERV 0.0000 INTERVA*

OENTT@+# 3t3 +# "$+e 3# 3 "uC+c #e+ce C NASA/JP*. OENTN$ F33nt +# e,"e##e $ +"+e e!3+n! #u+t3C++t OENT

22

http://csrc.ucsd.edu/

http://www.ngs.noaa.gov/

http://sopac.ucsd.edu/checkSiteID.shtml



http://www.dot.ca.gov/


http://csrc.ucsd.edu/

http://www.ngs.noaa.gov/






$ u#e. 8$ ut@e +n$3t+$nH c$nt3ct% OENTD3e St$Fe#H NASA/JP* /# 24&00 OENT-400 O3 G$e D+eH P3#3en3 A >110> 'SA OENT OENT8$ce $u$ Dec+3t+$n t$ 0 #ec$n# OENT SNR +# 3""e t$ RINEX #n 3! 3ue 0>K OENT *1 L *2% +n(3,(+nt(#nB;M/&)H 0)H >) OENT"#eu$3n!e #$$t@+n! c$ect+$n# n$t 3""+e OENT 2015 11 - 0 0 0.0000000 GPS TIE O8 8IRST OBS END O8 ;EADER 15 11 - 0 0 0.0000000 0 G0&G0G24G1G0G1G02 204524>.0&5-> 1&20>5.502-4 20>510.&10- 20>515.1>4- 20>510.0 5-.000- 50.000- 144-4--0.--&-> 1-&&&115.>>-4 20>1-110.0-0- 20>1-11-.1>- 20>1-110.11 5-.000- 50.000- 1104-5.4>0-4 4&0-0>2.5>- 22221.20- 2222.2- 22221.>- ->.000- -5.000- &52-.50>- &0-251.25-& 20&&1.2-- 20&&.154- 20&&1.5> -&.000- -1.000- 455&4.22- &10&-.24- 22>40>0.4- 22>40>2.0&-- 22>40>1.05 -&.000- -2.000- 110110-.-1-4 101-40>>.524-4 21>-->05.1>-- 21>-->05.>2- 21>-->0-.>4&

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1.0 OPAT RINEX 8ORAT RINEX VERS / TYPERNX2RX e.-.0.& 12N$15 1%-5 RINEX PROG / DATE 2.11 OBSERVATION DATA G (GPS) RINEX VERSION / TYPEteqc 2015Jun2 !"#$"# 20151105 00%10%0&'TPG / R'N BY / DATE*+nu, 2.-.212.E*#"O"te$n!cc #t3t+c*+nu, ,4&&-67 OENT

BIT 2 O8 **I 8*AGS DATA O**ETED 'NDER A/S ONDITION OENTIIS AR9ER NAE220&002 AR9ER N'BERGGN AS OBSERVER / AGENY:R52001402 AS;TE; ':12 <00 RE = / TYPE / VERSR&2005-402 AS;01>-5E NONE ANT = / TYPE 1>&.-550 &001.12&1 1-24&.452 APPROX POSITION XY: 0.040 0.0000 0.0000 ANTENNA% DE*TA ;/E/N 1 1 ?AVE*ENGT; 8AT *1/2 *1 *2 P1 P2 1 S1 S2 = / TYPES O8 OBSERV 0.0000 INTERVA* OENT

T@+# 3t3 +# "$+e 3# 3 "uC+c #e+ce C NASA/JP*. OENTN$ F33nt +# e,"e##e $ +"+e e!3+n! #u+t3C++t OENT$ u#e. 8$ ut@e +n$3t+$nH c$nt3ct% OENTD3e St$Fe#H NASA/JP* /# 24&00 OENT

23



-400 O3 G$e D+eH P3#3en3 A >110> 'SA OENT OENT8$ce $u$ Dec+3t+$n t$ 0 #ec$n# OENT SNR +# 3""e t$ RINEX #n 3! 3ue 0>K OENT *1 L *2% +n(3,(+nt(#nB;M/&)H 0)H >) OENT"#eu$3n!e #$$t@+n! c$ect+$n# n$t 3""+e OENT 2015 11 - 0 0 0.0000000 GPS TIE O8 8IRST OBS END O8 ;EADERL15 11 - 0 0 0.0000000 0 G0&G0G24G1G0G1G02

L204524>0&5 L1&20>5502 L20>510&10 L20>5151>4 L20>5100 L5-000L50000 ->-4- - - -L144-4--0--& L1-&&&115>> L20>1-1100-0 L20>1-11-1> L20>1-11011 L5-000L50000 ->-4- - - -L1104-54>0 L4&0-0>25> L2222120 L22222 L22221>- L->000L-5000 -4-- - - -L&52-50> L&0-25125 L20&&12- L20&&154 L20&&15> L-&000L-1000 --&- - - -L455&422 L&10&-24 L22>40>04 L22>40>20&- L22>40>105 L-&000L-2000 --- - - -L110110--1 L101-40>>524 L21>-->051>- L21>-->05>2 L21>-->0->4& L52000L-4000 -4-4- - - -

L54>&-502 L-5->>>5& L22>024&5-> L22>024&&>& L22>024&&> L-000L-2000 --- - - -

+H&3TER ->

:i-lio'raph"• 1+H4E#ER, T., . W. HE:%, and 9. E:11BE##ER D2$, Towards an ptimal 1trategy for 31 Wet 5elay Galman Biltering, 3roceedings of :&:% 2;:% &nnual eeting, 1an5iego, +atamaran Hotel, 2@-2A Fune 2

• 1+H4E#ER, T., . W. HE:%, and 9. E:11BE##ER D2c, :mproved Tropospheric 5elayodeling 4sing an :ntegrated &pproach of %umerical Weather odels and 31,3roceedings of :% 31 2, The :nstitute of %avigation, 1alt #ake +ity, 4tah, 41&,"-22 1eptem$er 2

• 1EE9ER, . D"AN 1atellitengeod\sie, 0erlag de ruyter, 9erlin - %ew Oork, "(1EE9ER, . D"(, 1atellite eodesy - Boundations, ethods, and &pplications; 9erlinN

%ew OorkJ de ruyter, "(, :19% (-""-"2>!(-

24



• 1E#&, F. . D"A, 1pectral odeling at the %ational eteorological +enter, onthlyWeather Review, 0ol. "A, pp. "2>-"22, 1eptem$er "A1#9R:, 3. D2, 4ntersuchungen ]$er die %ut/ung numerischer Wettermodelle /ur

• Wasserdampf$estimmung mit Hilfe des lo$al 3ositioning 1ystems, 5iploma Thesis,:nstitute of eodesy and %avigation, 4niversity B&B unich, ermany, Be$. 213:#GER, F. F. D"@, Tropospheric Effects on 31, inJ 13:#GER and 3&RG:%1% 6eds.7,

31 Theory and &pplicationsN 0ol. :, 3rogress in &stronautics and &eronautics, 0ol."@(, pp. !">-!?@, "@

term paper

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