Atmospheric Research 138 (2014) 414–426

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Atmospheric Research

j ourna l homepage: www.e lsev ie r .com/ locate /atmos

Ground-based GNSS ZTD/IWV estimation system for numericalweather prediction in challenging weather conditions

Witold Rohma,b,⁎, Yubin Yuan a, Bertukan Biadeglgne c, Kefei Zhang a, John Le Marshall c

a RMIT University, SPACE Research Centre, GPO Box 2476 Melbourne, VIC 3001, Australiab Wroclaw University of Environmental and Life Sciences, Institute of Geodesy and Geoinformatics, Grunwaldzka 53, 50-357 Wroclaw, Polandc Australian Bureau of Meteorology, Melbourne, VIC, Australia

a r t i c l e i n f o

⁎ Corresponding author at: Wroclaw University oLife Sciences, Institute of Geodesy and Geoinformat50-357 Wroclaw, Poland.

E-mail address: witold.rohm@up.wroc.pl (W. Rohm

0169-8095/$ – see front matter © 2013 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.atmosres.2013.11.026

a b s t r a c t

Article history:Received 2 August 2013Received in revised form 23 October 2013Accepted 30 November 2013

The Global Navigation Satellite Systems (GNSS) are one of the very few tools that can providecontinuous, unbiased, precise and robust atmosphere condition information. The extensive researchof GNSS space-based segment (e.g. available precise, real-time satellite orbits and clocks), unlimitedaccess to the ground-based Continuously Operating Reference Stations (CORS)GNSS networks alongwith thewell established data processingmethods provides an unprecedented opportunity to studythe environmental impacts on the GNSS signal propagation. GNSS measurements have beensuccessfully used in precise positioning, tectonic plate monitoring, ionosphere studies andtroposphere monitoring. However all GNSS signals recorded on the ground by CORS are subject toionosphere delay, troposphere delay, multipath and signal strength loss. Nowadays, the GNSS signaldelays are gradually incorporated into the numerical weather prediction (NWP)models. Usually theZenith Total Delay (ZTD) or IntegratedWater Vapour (IWV) have been considered as an importantsource of water vapour contents and assimilated into the NWP models. However, successfulassimilation of these products requires strict accuracy assessment, especially in the challengingsevere weather conditions.In this study a number of GNSS signal processing strategies have been verified to obtain the bestpossible estimates of troposphere delays using a selection of International GNSS Service (IGS) orbitand clock products. Three different severe weather events (severe storm, flash flooding, flooding)have been investigated in this paper. The strategies considered are; 1) Double Differenced (DD)network solution with shortest baselines, 2) DD network solution with longest baselines, 3) DDbaseline-by-baseline solution (tested but not considered), 4) Zero Differenced (ZD) Precise PointPositioning (PPP) based on ambiguity float solutions, all with precise orbits and clocks, and real timeclocks and predicted orbits. The quality of the estimates obtained has been evaluated againstradiosondemeasurements, AutomaticWeather Station (AWS) observations, NWP (assimilation stepwithout ground-based GNSS data) and ZTD estimates from the well established IGS processingcentre, the Center of Orbit Determination in Europe (CODE). It shows that the ZTD and IWVestimates from the DD short baseline solution are robust with usually a very small bias (−2.7 to−0.8 mm) and errors of less than 10 mm (7.6–8.5) (ZTD) or 3 mm (2.6–2.7) (IWV). The DD shortbaseline network solution was found to be the most reliable method in the considered case studies,regardless of the type of orbits and clocks applied.

© 2013 Elsevier B.V. All rights reserved.

Keywords:ZTD/IWV estimationGNSS meteorologyVerification

f Environmental andics, Grunwaldzka 53,

).

ll rights reserved.

1. Introduction

The successful assimilation of GNSS space-based observa-tions from Constellation Observing System for Meteorology,Ionosphere, and Climate (COSMIC) mission and other Low

415W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

Earth Orbiters (LEO) satellites in NWP models (Marshall etal., 2010) has significantly stimulated the interest of meteo-rological community in using ground-based GNSS observa-tions to improve weather forecasting. The ground-basedGNSS observations are collected by dense networks of CORSand processed by a central unit to obtain precise atmosphereinformation to improve the quality of satellite clocks andorbits and therefore improve positioning solutions. Theby-product of the CORS data processing is the tropospheredelay linked with the weather conditions (pressure, temper-ature and water vapour). The most important parameter insevere weather forecasting is the water vapour (WV) contentsince it is a WV induced phenomenon. The WV plays anactive role in energy exchange between climatic zones, and ina finer scale as a vertical channel of energy transfer (e.g. bylatent heat). Therefore, all major severe weather events thatare linked to the WV can be detected by GNSS signals.

However, the rapidly changing weather conditions such asthose presented before, during and after severe weather eventspose a big challenge for a successful data processing ofGNSS signals to achieve the required accuracy of troposphereconditions. The ZTD accuracy requirements imposed byNWP assimilation strategy as reported by (Barlag et al., 2004)are 10 mm, whereas the IWV should be delivered with anaccuracy better than 5 mm. This study is focused on identifyingpotential problems of GNSS data processing in challengingweather conditions, quantifying the magnitude of errors intro-duced by such phenomena and eventually removing theirimpacts. The ultimate goal of this study is to provide optimalstrategy to retrieve troposphere phase delay from GNSS groundbased observations for NWP assimilation algorithms.

The GNSS signal is bended, attenuated and delayed in theatmosphere, on two basic layers through which it propagatespredominately, troposphere and ionosphere. The signalbending effect, widely used in satellite-to-satellite GNSSdata processing, has negligible impact on the GNSS signalsrecorded by the ground-based receivers. The neutral refrac-tivity N0, a main cause of delay, could be split into thefollowing form (Thayer, 1974; Solheim et al., 1999):

N0 ¼ Nd þ Nv þ Nnon þ Ndiff ð1Þ

where Nd is the dry delay and Nv is the water vapour delay,whereas Nnon and Ndiff are linked with the non-gaseous partsof atmosphere (like dust) and hydrometeors, respectively.The last two elements of Eq. (1) have usually very limitedimpacts on refractivity and in practice they are not consid-ered in data processing strategies. The neutral refractivity iscalculated from the equation below:

N0 ¼ Zd−1 � k1

pdT

þ Zv−1 k2

eTþ k3

eT2

� �; ð2Þ

where pd is a dry pressure (the pressure of atmosphereexcluding water vapour partial pressure) and temperature T,water vapour partial pressure e coupled with temperature T.Zd

−1 is an inversion of dry compressibility factor and Zv−1 is

an inversion of wet compressibility factor (Owens, 1967).The k1, k2, and k3 parameters are atmospheric refractivityconstants given by (Kleijer, 2004).

The dynamics of the changes in WV content e andtemperature Twill result in substantial time and space variationsof the wet refractivity Nv in time and space (Eq. (2)). In severeweather conditions the changes in the wet refractivity aresignificant (Manning et al., 2012). Consequently, there areseveral important issues linked with GNSS data processingfor troposphere: 1) the azimuthal inhomogeneity of thetroposphere, 2) the unknown and variable correlation time ofthe troposphere conditions, and 3) a high value of stochasticparameter reflecting the variation of the troposphere conditions.

The propagation environment for GNSS signals arriving fromdifferent directions (both elevation angles and azimuths) varies,hence the functional model of phase propagation delay shouldreflect these inhomogeneities. Usually to resolve this issuetroposphere gradients are introduced. Another important factorrelated to the dynamics of the troposphere is the tropospheredelay parametrisation time step size. The linear parametrisation(Dach et al., 2007) assumes that the path delay is constantwithinthe time step within the specified a priori standard deviation.Therefore the stochastic modelling of signal phase delay shouldbe carefully considered, because the a posteriori ZTD error willreflect how the functional model fits into the data.

The GNSS signal propagation from a satellite to the receiverthrough the neutral atmosphere is subject to the changeof propagation speed expressed as a Slant Total Delay (STD)(δρR(zRS)) and given by the following equation:

δρR zSR� �

¼ 10−6 � ∫N0ds ¼ 10−6 � ∫Nddsþ ∫Nvds� �

: ð3Þ

A good approximation of STD can be expressed usually,as a first a priori value (δρapr,R), according to the followingformula:

δρapr;R zSR� �

¼ mapH zSR� �

� ZHDþmapW zSR� �

� ZWD; ð4Þ

where mapH(zRS) is the mapping function for the dry delay ZHDand mapW(zRS) is the mapping function for the wet delay ZWD.The STD is not related to the frequency of the GNSS signals,therefore the impact of troposphere, unlike the ionosphere,cannot be reduced by linear combinations of the signalfrequencies. Usually to derive signal's delay in the neutralatmosphere (Dach et al., 2007; Herring et al., 2010), correctionsat stations to the a priori model along with station coordinatesare estimated. The functional model adopted is as follows (Dachet al., 2007):

δρSR ¼ δρapr;R zSR

� �þ δhρR tð Þ �mapN zSR

� �þ δnρR tð Þ ∂mapN

∂z cosASR þ……

þ δeρR tð Þ∂mapN∂z sinAS

R;

ð5Þ

where, zRS is the zenith angle of satellite S as seen from station R,ARS is a satellite azimuth, δhρR(t) is a time t dependent delay in

zenith direction at a point R, mapN(zRS) is a mapping function,δnρR(t) is a time dependent gradient in north direction, andδeρR(t) is a time dependent gradient in east direction. However,the realization of this principle varies between data processingsoftware packages and processing strategies.

The stochastic of the troposphere parameter is rathersimple (Schüler, 2001). The absolute value of δρR can be

416 W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

constrained to an arbitrary value (absolute constraining), oralternatively the rate of change of troposphere delay at thestation δρR

δt could be kept fixed. The second option is to use amaximum correlation time. These stochastic parameters arelinked with troposphere conditions, therefore their empiricalevaluation is presented in the case study section. The ZWD, asa measure of WV content and temperature conditions in thetroposphere, is derived from the following equation:

ZWD ¼ δhρR tð Þ−ZHD: ð6Þ

The relation between ZWD and the WV content in theatmosphere is expressed by IWV and given by the followingequation (i.e. (Kleijer, 2004)):

IWV ¼ ZWD �k′2 þ k3

TM

� �−1

10−6 � Rw¼ ZWD � Q ð7Þ

where Rw = 461.525 ± 0.003 [J kg−1 K−1] is the specific gasconstant for water vapour, k2′ = 24 ± 11 [K hPa−1], andk3 = 3.75 ± 0.03 [105 K2 hPa−1] are refraction constants(Schüler, 2001) and TM ≈ 70.2 ± 0.72 ⋅ T0 is the weightedmeanwater vapour temperature of the atmosphere, and T0 is thesurface temperature (Mendes and Langley, 1999). AlternativelyTM value can be retrieved from the profile of temperature T andwater vapour partial pressure e according to the equation:

TM ¼ ∑eT

∑ eT2

: ð8Þ

This study focuses on the investigation of the most robustyet efficient method to derive ZTD and IWV in severeweather conditions. The challenging weather conditionswill presumably result in the following propagation effects:

1. Non-homogeneity of the horizontal distribution of theatmosphere masses. To account for this effect, the ZTDgradients are introduced in Eq. (5). The variation of thewet refractivity in the approach demonstrated in thisstudy is measured with a time autocorrelation function of

wet refractivity distribution in selected tropospherealtitude layers, in normal and storm prone conditions.

2. The increased ZTD estimation uncertainty as a response torapid changes in temperature and WV content and theparametrisation scheme with constant ZTD for the epochto be estimated. This effect is investigated by comparingthe estimation uncertainty of ZTD in normal conditions toZTD in the severe storm conditions.

3. Low observation signal-to-noise ratio during the stormactivity. The impact of atmospheric loss fluctuations onthe estimated parameters is challenging to quantify (Misraand Enge, 2001; Christian et al., 2004) and has not beendiscussed in this study.

4. In DD strategies, uneven weather conditions on both sides ofthe baseline increase the reliability of ZTD absolute estima-tion. This effect is discussed in the following sections.

In order to select the most appropriate approach, severalprocessing strategies (in Section 2) with final and real-timeIGS products (clocks and orbits) have been validated. InDD processing mode, three data processing scenarios areexamined, these include: 1) the network solution withshortest baselines, 2) the network solution with longestbaselines, and 3) baseline-by-baseline estimation withshortest baselines. The ZD phase observations (PPP) havealso been investigated in this study. Majority of thecomputing work has been performed using Bernese GPSSoftware version 5.0. However the methodology discussed inthis manuscript is equally applicable to any GNSS dataprocessing software package. The data used for control andvalidation (contained in Section 3) of results comprise:deterministic models Global Pressure and Temperature(GPT) (Boehm et al., 2007), UNB3m (Leandro et al., 2008),ground-based Automatic Weather Stations managed byAustralian Bureau of Meteorology (BoM), radiosonde obser-vations from 14 locations in Australia and AustralianCommunity Climate and Earth-System Simulator —Regional(ACCESS-R) outputs of analysis step. Section 4 contains theanalysis of three severe case studies. The case studies arecomposed of: 2010 severe storm that hit the Melbournemetropolitan area, 2011 flooding in Victoria and 2012 flashflooding in Victoria. The paper is concluded in Section 5.

2. ZTD estimation

The standard procedure to obtain high quality coordinates requires double differencing of phase observations to remove thesatellite and receiver clock errors and exploit the integer nature of ambiguities (Hofmann-Wellenhof et al., 2008). Usually the finalsolution is obtained on Ionosphere Free combination (L3) (Dach et al., 2007). Procedure adopted in this study in case of DDprocessingfollows (Bosy et al., 2003) withminor modifications. Precedence to the ZTD estimation, due to a large number of stations (e.g. 218 in2012), the normal equation set-up is separated into 3 regions. Within each region the same procedure is applied as follows:

• the reference station coordinates are propagated into observation epoch,• the Lagrange polynomials are fit into the discrete satellite positions,• the receiver clocks are synchronised using code-based standard positioning solution,• the single differencing of the phase observations is performed using predefined baselines (skeleton network only) and selecteddifferentiation strategy (shortest, longest),

• the phase observations undergo quality control including: cycle slip detection, marking and removing spurious observations,• the first estimation of float ambiguities on wide —lane (L5) wavelength is performed,• the second estimation of integer values of ambiguities on narrow —lane (L3) wavelength is obtained,• the previously estimated ambiguities are introduced to form and store normal equations.

417W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

This procedure is followed by steps common for the whole network:

• combination of daily normal equation files across the whole network into one file per network per day• estimation of weekly coordinates using constrained translation parameters based on velocities and coordinates of IGS referencestations,

• estimation of troposphere parameters (ZTD, and troposphere gradients) with daily normal equation files with minimum constraintconditions imposed on IGS stations' coordinate translation parameters.

The last item listed above contains several standardised steps and the procedure given below is equally valid for ZeroDifferenced (ZD)observations. According to Eq. (2) refractivity is in 80–90% linkedwith pressure of dry atmosphere pd, and in 10–20 % to the distributionof water vapour e and temperature T and consequently to the stations height, so the first step would be the determination of the totaldelay applying globally adopted mean of meteorological parameters with corrections to the stations height. Then, at each station ZTDwith gradient parameters is modelled as a correction to the a priori model given previously, according to Eq. (5).

The IGS Final orbits and clocks (PREC) are combined from a number of contributing IGS Analysis Centres, using six, largelyindependent, software packages (i.e. BERNESE, GAMIT, GIPSY, NAPEOS, EPOS and PAGES). The IGS Final orbit/clocks are usuallyavailable in two weeks after the last observation. The anticipated accuracies of final orbits and clock products are 1–2 cm and0.02–0.06 ns respectively (Kouba, 2009). The real-time clocks and orbits (PRED) are the outcomes of the IGS Real-time PilotProject (IGS-RTPP). The IGS real-time processing centre estimates and distributes high-resolution GPS corrections of broadcastorbits and high frequency clocks for PPP applications. The orbits used in this study are ultrarapid predictions from 8 processingcentres, the anticipated accuracy of these orbits is 5 cm. The clock product is estimated in the real time mode (Li et al., 2013) fromthe network of global IGS stations, the quality achieved is on the order of 0.10 ns (http://rts.igs.org/monitor/).

2.1. Double Difference processing

The standard equation for DD phase observations reads as follows (Hofmann-Wellenhof et al., 2008):

λ �ΦSTPR tð Þ ¼ δrSTPR þ λ � NST

PR þ δρSTPR þ λ � �STPR: ð9Þ

The final ZTD estimation step for DD case is conducted according to Dach et al. (2007), Kubo et al. (2012), and Strang and Borre(1997). The linearised Eq. (9) in amatrix form read:AX = lwhereA represents the designmatrix,X is the parameter to be estimated andl is a set of observations. The estimation of troposphere parameters is obtainedwith previously derived, integer ambiguitiesN, thereforein Eqs. (10)–(12) N values do not appear. The following is an example of two receivers, four satellites for a single epoch in DD case.

A ¼

aS1T2XPR

tð Þ aS1T2YPR

tð Þ aS1T2ZPR

tð Þ δmapN zS1T2PR

� �δ∂mapN

∂z cosAS1T2PR δ

∂mapN∂z sinAS1T2

PR

aS1T3XPR

tð Þ aS1T3YPR

tð Þ aS1T3ZPR

tð Þ δmapN zS1T3PR

� �δ∂mapN

∂z cosAS1T3PR δ

∂mapN∂z sinAS1T3

PR

aS1T4XPR

tð Þ aS1T4YPR

tð Þ aS1T4ZPR

tð Þ δmapN zS1T4PR

� �δ∂mapN

∂z cosAS1T4PR δ

∂mapN∂z sinAS1T4

PR

2666664

3777775

ð10Þ

X ¼

ΔXPRΔYPRΔZPR

δhρP tð ÞδnρP tð ÞδeρP tð ÞδhρR tð ÞδnρR tð ÞδeρR tð Þ

266666666666664

377777777777775

ð11Þ

l ¼λ �ΦS1T2

PR tð Þ−δrS1T2PR −Δδρapr;R zS1T2

PR

� �λ �ΦS1T3

PR tð Þ−δrS1T3PR −Δδρapr;R zS1T3

PR

� �λ �ΦS1T4

PR tð Þ−δrS1T4PR −Δδρapr;R zS1T4

PR

� �

26664

37775: ð12Þ

The troposphere parameter is estimated as a piecewise linear function with monotonic parameters in zenith direction δhρR(t)along with gradient parameters δnρR(t) and δeρR(t).

Several, more specific strategies were tested in the processing case studies and are listed below.

2.1.1. Baseline-by-baseline solutionThe investigation of baseline length impact has been performed using baseline-by-baseline processing. In that case, for each

shortest baseline, as given by Bernese GPS Software (Dach et al., 2007), design matrix A has been setup for whole day, covering

418 W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

satellites and two stations. The shortest baseline strategy produces vectors of the mean distance of 70 km. The ZTDs' distancedependent correlation coefficients (from PPP solution), for baselines shorter than 100 km in flat lowlands (station MOBS 41 m),are above 0.95. If the highest point in the network would be considered (station HOTH 1774 m), then for the same interstationdistance correlation coefficient would be above 0.90. Hence there are similar troposphere conditions on both ends of the baseline.Therefore the last 3 columns of matrix A (10) are close to 0, which produces a high uncertainty of solutions and amplification oferrors presented in the observations. The mean discrepancy between reference data and outcomes of this strategy is 9 mmand 31 mm in terms of bias and standard deviation, respectively. The maximum outliers reach up to 400 mm. Thereforebaseline-by-baseline solution has not been regarded as an appropriate strategy for troposphere estimation and is not presented inour figures or tables.

2.1.2. Shortest baselines network solutionThe other approach, routinely adopted to derive precise coordinates and velocities of national and regional reference networks

(Bosy et al., 2009), requires setting up a network of n − 1 independent shortest baselines (n is the number of points) (Dach et al.,2007). The matrix A (10) previously used to obtain troposphere solutions for one baseline (PR) is converted to a stacked matrix As

covering the whole network. Observation matrix ls is composed of all observations in the time span considered (usually a day)across all baselines. The vector of unknown Xs consists of coordinates, zenith delays and gradient parameters in the north and eastdirections. Therefore, the number of unknowns is limited to: 3 ⋅ nst number of baselines in the network (one for each coordinate),plus nztd times the interval length of ZTD estimation plus one (extra term in the beginning or in the end of the observationwindow) and ngrad times interval length of the ZTD gradient estimation (usually much lower then nztd). The key issue of allWeighted Least Squares (WLS) (Strang and Borre, 1997) estimation is covariance matrix C. The mathematical correlation betweenDD observations (Schüler, 2006) has been considered (Dach et al., 2007), as well as correlations between baselines(Hofmann-Wellenhof et al., 2008). In addition, minimum constraints have been applied on translation parameters and anelevation � dependent weighting σ0(�) function has been applied. The campaigns discussed in this study have been processed byapplying ZTD relative constraints (σrelZTD) with maximum time constraints. The values associated with relative constraints are setbased on the empirical tests using ZTD autocovariance. In the Bernese GPS software, constraints are introduced as fictitiousobservations (Dach et al., 2007) yfictitious = H ⋅ x where H is a matrix of ones or zeros when an observation add 1 or not 0. Allstatistical considerations given above translate into variance covariance matrix Cs of the following form (Hofmann-Wellenhof etal., 2008; Schüler, 2006):

CDD ¼ σ0 �ð Þ �

4 2 2 2 1 12 4 2 1 2 12 2 4 1 1 22 1 1 4 2 21 2 1 2 4 21 1 2 2 2 4

26666664

37777775

ð13Þ

Fig. 1. Longest baseline selection scheme. Boxes in red represent the selected stations in set A; boxes in green represent the selected stations in set B; boxes in blue representthe stations to be selected in set B.

419W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

CS ¼

CDD 0 0 0 0 0 0 00 σX 0 0 0 0 0 00 0 σY 0 0 0 0 00 0 0 σZ 0 0 0 00 0 0 0 σ relZTD 0 0 00 0 0 0 0 σ relZTD 0 00 0 0 0 0 0 σδn 00 0 0 0 0 0 0 σδe

266666666664

377777777775: ð14Þ

The covariance matrix CS is inverted to obtain the weighting matrix P. The DD network solution discussed in thisparagraph considers full correlation matrix (Eq. (14)) between baselines and within double difference observations(Eq. (13)). This extensive correlation modelling and the CORS network size, spanning thousands of kilometres fromAdelaide (South Australia) to Townswille (North Queensland) lead to absolute delay estimation, regardless of the baselinelength.

2.1.3. Longest baselines network solutionThe longest baseline solutions are also evaluated to investigate the best solution for GNSS data processing. In this study the

testing approach used for the longest baselines is demonstrated in Fig. 1 using the following steps:

Step 1 All the n stations are located in set Bwhile the selected stations consist of set Awhich is originally empty (with zero valueelements);

Step 2 We start from selecting one random station A[0]. Distances between A[0] and the other n − 1 stations are compared. Thestation with the longest baseline is where A[0] will be selected next. After this step there are A[0] and A[1] in set A whilethe rest n − 2 stations are still in set B;

Step 3 Similar to Step 2, the length of baselines between A[1] and the stations in set B is compared. This step is repeatediteratively until no stations are left in set B;

Step 4 The set B is re-ordered as set A in which two adjacent stations form a baseline. This strategy creates the baselines of900 km average length.

In this strategy the baseline lengths are significantly longer (usually 10 times) than those in the network shortest solution.However the mathematical observation models remain unchanged (10, 11, 12). The most significant differences are threefold:1) the last columns of matrix A (10) contains coefficients that are uncorrelated (distance approx. 500 km); 2) as aconsequence, the estimation of ambiguities is more challenging, due to the shortest common observation window; and3) different ionosphere conditions on both ends of the baseline. Therefore, the number of the longest baseline solutionbenefits (no correlation of troposphere conditions) are outnumbered by disadvantages linked with station separation(ambiguities fixing problem, lower number of observations). The network solution regardless of the configuration (shortest orlongest) shows actually the same performance in terms of estimating troposphere conditions, which has been proved in thecase study section.

2.2. Precise Point Positioning processing

The last method considered in this study is based on PPP processing, of ZD phase observations. The flow is similar to DDprocessing, already discussed in great detail in the previous section. In the Bernese GPS Software the ambiguities of ZDobservations are not fixed to the integer values. Studies show (Sunil Bisnath—personal communication, this paper) that PPP floatambiguities processing of long GNSS observation session will have the same accuracy of troposphere estimates as the one withfixed ambiguities. Similar to the DD processing, the float ambiguity N are estimated and removed from processing priori to theZTD estimation, therefore N values are omitted in Eqs. (16)–(18). The ZD phase observation model is slightly different to the DDone (Eq. (9)), the commonly adopted model follows (Dach et al., 2007) and it reads as follows:

λ �ΦSR tð Þ ¼ δrSR þ λ � NS

R þ δρSR þ c � �R tð Þ: ð15Þ

The comparison of the PPP fundamental Eq. (15) and the DD basic Eq. (9) reveals an extra term c ⋅ �R(t) that is linked with thereceiver clock error (Eq. (15)). The satellite clock bias (PREC and PRED product) is used to correct the phase observations(Eq. (15)). The time series of this parameter exhibits short-term variations super imposed over a long-term trend (Collins et al.,2010). It is also important to note that all quantities given in Eq. (15), unlike in DD model (Eq. (9)) (including ambiguities) areabsolute values. Therefore any biases presented in the orbits (Douša, 2010) and satellite clocks will have strong signature in the

Fig. 2. The scheme presenting the ZTD/IWV evaluation process using AWS, RS and NWP.

420 W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

troposphere values obtained. Eq. (15) is linearised and (in the case of four satellites in one epoch) it reads as follows l = A ⋅ Xwhere:

A ¼

a1XRtð Þ a1YR

tð Þ a1ZR tð Þ 1 mapN zS1R� � ∂mapN

∂z cos AS1R

∂mapN∂z sinAS1

R

a2XRtð Þ a2YR

tð Þ a2ZR tð Þ 1 mapN zS2R� � ∂mapN

∂z cos AS2R

∂mapN∂z sinAS2

R

a3XRtð Þ a3YR

tð Þ a3ZR tð Þ 1 mapN zS3R� � ∂mapN

∂z cos AS3R

∂mapN∂z sinAS3

R

a4XRtð Þ a4YR

tð Þ a4ZR tð Þ 1 mapN zS4R� � ∂mapN

∂z cos AS4R

∂mapN∂z sinAS4

R

26666666664

37777777775

ð16Þ

X ¼

ΔXRΔYRΔZR

c � �R tð ÞδhρS tð ÞδnρS tð ÞδeρS tð Þ

2666666664

3777777775

ð17Þ

l ¼

λ �ΦS1R tð Þ−δrS1R −δρapr;R zS1R

� �λ �ΦS2

R tð Þ−δrS2R −δρapr;R zS2R� �

λ �ΦS3R tð Þ−δrS3R −δρapr;R zS3R

� �λ �ΦS4

R tð Þ−δrS4R −δρapr;R zS4R� �

26666664

37777775: ð18Þ

The essential difference between parameter vector X in PPP (Eq. (17)) and in DD (Eq. (17)), is that the number of estimatedparameters in the case of PPP is larger by at least one parameter per epoch, which is the receiver clock term c�R(t). Hence thedesign matrix A in PPP (Eq. (16)) has one column more than matrix A in DD (Eq. (10)) case. The unwanted correlation betweencolumns of A will not occur, unlike in the DD case, because matrices A (Eq. (16)) and l (Eq. (18)) contains observations fromindependent satellites.

3. Validation of ZTD and IWV

The data processed in this study were validated againstreference GNSS troposphere and meteorological products, forboth ZTD and IWV. The verification process follows thescheme presented in Fig. 2.

3.1. GNSS reference data

The data processed by the Center for Orbit Determinationin Europe (CODE) Astronomical Institute University of Bern(AIUB) has been used as a reference, mainly final troposphere

Table 1The validation results for three severe weather events (2010STORM —severestorms [864 reference CODE observations, 144 reference RS observations],2011FLOOD —flooding [720 reference CODE observations, 192 reference RSobservations], 2012FLASH—flash flooding [720 reference CODE observations,192 reference RS observations]) in terms of ZTD and IWV (both in [mm]).Three data processing strategies were investigated: SHORT —shortest baselinenetwork solution, LNG —longest baseline network solution, and PPP —ZDsolution. The missing data for 2011FLOODLNG and 2012FLASHLNG PRED is aconsequence of limited number of common observations on two sides oflong baselines. PREC term refers to the precise orbits and clocks, whereas thePRED points out to the predicted orbits and real-time clocks.

CODE REF [mm] RS REF [mm]

PREC PRED PREC PRED

ZTD μZTD σZTD μZTD σZTD μZTD μZTD2010STORMSHORT −0.6 9.0 −1.1 8.5 −15.2 −9.12011FLOODSHORT −2.3 7.4 −2.4 7.7 −14.2 −13.12012FLASHSHORT 0 7.6 0 7.6 −10.1 −9.82010STORMLNG −3.3 7.8 0.8 13.3 −12.2 −12.22011FLOODLNG – – – – – –

2012FLASHLNG −7.1 7.4 – – −21.0 –

2010SSTORMPPP −1.7 10.9 −3.5 15.4 −10.2 −7.22011FLOODPPP −1.1 7.2 −2.7 16.4 −6.4 −9.22012FLASHPPP −0.6 6.8 −0.5 13.5 −4.3 −12.4

IWV μIWV σIWV μIWV σIWV μIWV μIWV

2010STORMSHORT −2.5 3.1 −1.9 2.6 −2.7 −1.92011FLOODSHORT −2.2 2.8 −2.2 2.6 −2.4 −2.2

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solutions for Australian stations. The processing strategyapplied is summarised as follows1:

Step 1 The basic observable is GPS/GLONASS carrier phase;code is only used for receiver clock synchronisation,elevation angle cutoff is 3 degrees, sampling rate is3 minutes,

Step 2 continuous parameterisation of troposphere ZTD andhorizontal gradient parameters, allowing for connec-tion of the parameters at day boundaries,

Step 3 a priori model for troposphere Saastamoinen-basedhydrostatic (using GPT) mapped with the dry-GMF,

Step 4 zenith delay corrections are estimated based on thewet Global Mapping Function (GMF) (Boehm et al.,2006) in 2 h intervals. N– and E–W horizontal delayparameters are solved for every 24 h,

Step 5 both zenith and gradient parameters are treated ascompletely unconstrained,

Step 6 ITRF2005/ITRF2008 reference frame for fiducial IGSstations and orbits,

Step 7 Datum definition: 3 no-net translation conditions, 3no-net rotation conditions, geocenter coordinatesconstrained nominally to zero values.

3.2. Meteorological data

The set of meteorological sensors and models includes:

• TheAWS, operated by theBureau ofMeteorology, are designedto provide real-time data for weather forecasting and warningas well as high quality data for climate applications. AWSmeasure and report meteorological variables such as temper-ature TAWS, humidity RHAWS, pressure pAWS, wind and rainfall.Only the first three parameters are used in this study. Theselection of useful stations was based on the distance to GNSSstation. In this study a 50-km radius has been adopted.

• The radiosonde (RS) vertical profile measurements from 17stations across eastern Australia are provided every 12 or 24 h.However, only 14 stations have been used, due to the 100 kmseparation limit between RS and GNSS station. The verticalprofiles comprise: pressure on the mandatory and significantlevels, temperature, dew point temperature (humidity equiv-alent), height, wind speed and wind direction. Only thepressure, temperature and dew point temperature frommandatory levels have been utilised in this study.

• The NWP analysis outputs from the Australian CommunityClimate and Earth System Simulator (ACCESS-A) model wereused to validate the GNSS data. The NWP model outputs(analysis run) with the time resolution of 6 h (for base time:00, 06, 12, 18 UTC) using a centred 6 hour observational datawindow. Themodel covers a spatial outline from− 45.0 ° S to4.73 ° N and 95oE to 169.9 ° E. The ACCESS system is based ontheUKMeteorological office UnifiedModel, and uses a numberof data sources to produce forecasts (e.g., AIRS radiances,COSMIC, radiosondes, pilot and profiler winds, ATVOS radi-ances, scatterometer winds, AMDAR, land surface stations)(Marshall et al., 2010). The model in the horizontal plain

1 http://igscb.jpl.nasa.gov/igscb/center/analysis/archive/code_20080528.acn.

contains 229nodeswith the grid spacing of 0.11 ° (12 km) andin the vertical direction it utilises terrain following hybrid(pressure/height) coordinates with 48 levels. The model'sforecast and analysis covers a number of meteorologicalparameters such as zonal wind speed, meridonal wind speed,cloud cover, temperature, precipitation etc. This study howev-er, considers only pressure, temperature and water vapourpartial pressure (given as a mixing ratio).

• The 3Dwet refractivities, outputs of tomographymodelling, for6 days in March 2010, were used to investigate spatial andtemporal correlations of weather conditions. The spatialresolution is 55 km with 17 varying thickness (exponentiallyincreasing) of horizontal layers. Themodel temporal resolutionis 10 min. The tomography retrieval is based on AWATOS2model (Perler et al., 2011) that is fedwith observations fromallGPSNet stations; no external data were introduced. TheAWATOS2 uses vertical and horizontal constraints as well as3D spline parametrisation of troposphere refractivity. Theresults of tomography processing, compared against radio-sonde profiles, agree within 8 ppm (mm/km) in terms of wetrefractivity (Manning et al., 2012).

3.3. ZHD and ZWD calculations

In order to compute the ZTD, meteorological parameterswere converted to the troposphere impacts onGNSS signal usingSaastamoinen model (Saastamoinen et al., 1972). The MSLheights from AWS station measurements are converted to theelipsoidal heights by calculating the geoidal undulation Nobtained from a global gravimetric geoid model (Boehm et al.,2007). Pressure values are then corrected for the difference Δh

2012FLASHSHORT −2.2 2.6 −2.5 2.7 −2.4 −2.42010STORMPPP −1.8 2.0 −1.2 3.5 −1.7 −1.32011FLOODPPP −2.1 2.1 −1.1 2.5 −0.8 −1.12012FLASHPPP −2.0 1.8 −2.4 10 −1.3 −2.5

10

20

30

40

50

60

AP

OL

BA

CC

BA

LL

CL

AC

CR

ES

EP

SO

GE

EL

KY

NE

MO

BS

PK

VL

ST

AR

δZTD normal conditionsδZTD storm conditions

δZT

D /

δT [

mm

/h]

Fig. 4. The troposphere rate of change in normal and severe weatherconditions for CORS stations affected by the storm.

422 W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

between AWS sensor elevation and GNSS antenna elevationusing the following equation (Berg, 1948):

pAWS@GNSS ¼ pAWS � 1−0:0000226 � Δhð Þð Þ5:225: ð19Þ

The WV and temperature are not interpolated to thelocation of the receiver. The assumption made in this study isthat 50 km radius weather conditions do not change.

The radiosonde pressure observations pRAOBS (2D data)are processed (Eq. (19)) using a procedure similar to thepoint observations pAWS. Therefore, the ground pressurereading from the radiosonde is interpolated to the height ofthe receiver. The pressure value is an input for ZHDcalculation using the Saastamoinen model (Saastamoinen,1973). Another approach was applied for WV and tempera-ture. These parameters were interpolated to the horizontallayers of fixed height above the ground. There are twoassumptions: 1) meteorological conditions (WV and temper-ature) at the interpolation layer are similar for GNSS signaland for radiosonde, and 2) the troposphere above the highestlayer (in this study 16 km) has negligible impacts onGNSS signal propagation. In order to obtain ZWD, the wetrefractivity Nv (Eq. (2)) has been calculated at eachhorizontal layer and multiplied by the separation distancebetween layers.

The NWP model pressure outputs (3D data) are interpo-lated to the station locations using the method developed byBosy et al. (2010) that takes interpolation values from theeight closest NWP model nodes (4 above and 4 below theGNSS station). The pressure value is an input for the ZHDcalculation using the Saastamoinen model (Saastamoinen,1973). The temperature and WV values are interpolated tothe 3D grid, similar to the tomography model structure(Rohm and Bosy, 2011). The model horizontal resolution is100 km, while its vertical resolution is 300 m in the lowertroposphere to 2 km near the tropopouse. In each columnabove the receiver, ZWD is calculated in a similar way to thatemployed for radiosonde data. The coarse 3D grid horizontalresolution was chosen to account for radiosonde GNSSreceiver distance and satisfy the assumption of similarweather conditions on both ends of this baseline.

3.4. IWV calculation

Conversion between ZTD and IWV requires two types ofinformation: 1) pressure values to remove the dry delay from

Australia

Fig. 3. The radar image showing the storm passage over Melbou

the ZTD to retrieve the ZWD (Eq. (6)) and 2) factor Q(Eq. (7)) that translates ZWD (a signal dependent value) toIWV(a water vapour dependent value). The ZWD value isobtained using the ZHD derived from the NWP modeloutputs according to the methodology presented in thesubsection above. To derive factor Q, the water vapourtemperature gradient is required (Kleijer, 2004). Usually aglobal value for mean temperature is employed (Schüler,2001). It is, however, advised to use local troposphereparameters if available. In this study NWP derived Q factorhas been applied, the value of TM is calculated as a quadraticmean of vertical layers (Eq. (8)).

4. Severe weather case studies

The severe weather events are often related to excessiveamounts of WV present in the troposphere. As such it isanticipated that the WV should be detectable by the GNSSCORSnetwork. Certainly similar studies conducted all around theworld confirm that GNSS is capable of detecting passages of allkinds of severe events, such as multi-cell storms (Choy et al.,2013), tropical storms (Seco et al., 2009) and thunderstorms(Seko et al., 2004). Within the scope of this paper three severeweather instances were selected for future assimilation into theACCESS-A model. Hence, each severe weather event is onlyshortly introduced as the aim of this study is to provide anoptimal troposphere estimates for NWP models. The CORSnetwork used in each case study has a slightly different networkextent and the number of receivers. However, there are 3 CORSstations processed within each case study that; 1) are part oftroposphere global solution at CODE, 2) are collocated with aradiosonde and 3) are in the NWP model domain. Thismanuscript only contains figures for the station MOBS, however

rne, 06.03.2010 3:00 UTC to 06.03.2010 4:30 UTC (BoM).

ZTD (m m)

Fig. 5. The ZTD evolution of weather conditions from GNSS observations, using 127 CORS stations 5.03.2010 to 6.03.2010.

423W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

numerical statistics are also available for other two stations(HOB2 and TOW2). The overall statistics for each case study aregiven in Table 1 at the end of this section. The case studies arecomposed of: 2010 severe storm that hit the Melbournemetropolitan area, 2011 flooding in Victoria and 2012 flashflooding in Victoria, respectively. The first case study will bediscussed in great detail and the last two will be used as asupplementary example of GNSS ground-based troposphereestimation robustness.

Fig. 6. Comparison of ZTD time series from a number of data sources (GPT, UNB3m, Dand clocks were used.

The 2010 March severe storm in Melbourne (BoM, 2010)started on 6 March, initiated by a developing low pressuresystem and low pressure trough to the west of the south eastAustralia, developing showers and thunderstorms in the westof the Victoria during the morning. The thunder stormsspread eastward and intensified during the first couple ofhours of daytime. This thunderstorm developed to thenorthwest of the Melbourne Metropolitan area (Fig. 3) andmoved through the most suburbs of the city from early

GPT M.

D GNSS, PPP, AWS, NWP and radiosondes). In GNSS processing precise orbits

PPP

Fig. 7. The time series of IWV as derived from number of data sources and GNSS with real-time orbits and clocks.

424 W. Rohm et al. / Atmospheric Research 138 (2014) 414–426

afternoon progressing to the east and then into the south-eastern part of Victoria later in the afternoon.

The microwave signal propagation conditions wereassessed by means of autocorrelation function (20) of wetrefractivities Nv:

R t0; t1ð Þ ¼ E Nvt0−μ t0ð Þ Nvt1−μ t1ð Þ½ �σ t0 � σ t1

: ð20Þ

The E is an expectation operator, Nvt0 and Nvt1 are the wetrefractivity in epochs t0 and t1 respectively, and μt0 and μt1are the mean values of wet refractivity in the selected epochs(0 and 1). The R(t0, t1) in storm and non-storm conditionswas calculated at significant levels of troposphere: boundarylayer 0.3 km, mid-troposphere 3.0 km and top troposphere8.5 km. The decrease of correlation to the threshold value of0.5 (50%) for severe weather case has been achieved in about30 min, whereas the normal conditions result in the samethreshold value in about 1 h and 15 min.

Consequently the δρRδt parameter (Fig. 4) characterising the rate

of change of the troposphere delay in the Melbourne metropol-itan region is also significantly different from normal conditions.The storm and non-storm ZTD observations were separatedbased on the radar images and the δtwas set to 1 h. The relativeconstraining scheme σrelZTD (13) should adapt to the weatherconditions and take the 2 ⋅ σrelZTD value in case of severeweather conditions (i.e. 40 mm instead of 20 mm). The formalerrors of ZTD obtained using standard relative constraints(the same for severe weather and non-severe weather) showan increase of 0.3 − 0.5 mm across all storm-affected stationsin all 3 case studies.

TheGNSS observations during this severeweather event (3rdof March to 9th of March 2010) were collected at all 127Australian CORS stations. That is 66 stations operating withinGPSNet in Victoria, 41 stations from CORSnet-NSW and 10stations operated by Geoscience Australia. The data wereprocessed according to the strategy described in Section 2. Thelast processing step covers normal equation inversion and

estimation of unknowns, in Bernese GPS Software ADDNEQ2module (Dach et al., 2007) is used to manipulate and invert setof normal equations. ZTD parameters were estimated withan hourly time resolution in the final ADDNEQ2 run usingminimum constraints imposed over the translation parametersof CORS stations' weekly coordinates and troposphere relativeconstraints.

The severe meteorological conditions (BoM, 2010) result-ed in rapid changes of the ZTD parameter. Time derivative ofZTD evolution is shown in Fig. 5. The figure presents thedifferences between ZTD estimates at starting time 10:00UTC on the 5th of March 2010 and following epochs (every3 h) up to 10:00 UTC on the 6th of March 2010. The cold frontapproaching from the west is sweeping the moist and warmair in the advancing edge of the front, creating highlyunstable conditions and developing strong thunderstorms.

The point GNSS ZTD observations show (Fig. 6) signatureof highly unusual troposphere conditions. The typical pointobservations from station MOBS show a drastic increase of ZTDwhile moist air was approaching from the north and then asudden drop of ZTD just before the storm (Fig. 5 second row, firstand second from the left), followed by high and variable ZTDvalues. To assess the amount ofWV that has played an importantrole in the formation of this severe weather event ZTDobservations have been converted to the IWVpoint observations(Fig. 7) by applying formulas (6) and (7). The Q parameter hasbeen derived from NWP output profiles.

By comparing Fig. 6 with Fig. 7 it is clear that both timeseries closely match. This implies that this is a purely WVinduced phenomenon, without large pressure variations.

Detailed studies of ZTD/IWV response to severe weather(Champollion et al., 2004; Brenot et al., 2006; Choy et al., 2013),including this one, show that before catastrophic rainfalls IWVincreases to the unnoted values of 40–50 mm(Fig. 7 64DOY). Asthe severe weather approaches/develops, high variability ofretrieved parameters is observed (Fig. 7 DOY 65–66), followedby drop in the total value and significant IWV oscillation as thesystem dissipates (Fig. 7 DOY 67).

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The final part of this study is to assess the impact of real timeclocks and orbits on troposphere estimates. The effect is visibleespecially in the PPP data, which is a direct effect of thezero-difference observations solutions, and therefore no reduc-tion of satellite clocks and orbit errors is possible. The impactof real-time satellite clocks and orbits on DD processing isnegligible. Table 1 shows mean accuracy measures as indicatedby comparing with CODE reference (CODE REF) data andradiosonde measurements (RS REF).

The obtained solutions in terms of ZTD/IWV quality is inline with works of other authors (e.g. Karabatić et al. (2011),Jade et al. (2005), Gutman and Benjamin, (2001), andTregoning et al. (1998)), the expected ZTD retrieval qualityshould be on the level of 10–15 mm. The biases and standarddeviations are in cm-level when compared with radiosondesdata or reference ZTD estimates. It is evident that in all casestudies the SHORT baseline DD network solution performsbest, and the decrease of accuracy between the precise(PREC) and the predicted (PRED) IGS orbits is actuallynegligible. However this impact starts to be significant inthe case of PPP observations, both bias and standarddeviation increases. The estimates start to be noisier. TheIWV inherits this property which leads to a decreasedaccuracy between the precise products and real timeproducts. Surprisingly the bias of IWV is larger than ZTD,we believe that this is attributed to the pressure, temperatureand water vapour information from NWP model that areintroduced to retrieve the IWV. The data assimilation processshould not be affected by this bias since it is relative to theGNSS CODE data and not to the radiosonde data. Overallaccuracy, regardless of the data processing strategy, is wellwithin the required accuracy of 5 mm with respect to theradiosondes.

5. Summary and conclusion

This study is an initial part of a large project aimed atutilising GNSS ground-based troposphere estimation for en-hancing NWP models forecasts in Australia. Other applicationssuch as nowcasting using GNSS ZTD data in Australia werediscussed in (Choy et al., 2013). It is anticipated that the groundbased GNSS data will contribute to increased to 80% (from 40%)improvement in the intensive rainfall forecast (de Haan, 2013).This paper is focused on the GNSS ZTD and IWV processing inchallengingweather conditions that caused the increase of ZTDestimation error and signal noise. Several GNSS signal process-ing strategies have been investigated including; 1) DD (shortbaselines network solution, long baselines network solution,baseline-by-baseline solution —run but not considered) and2) PPP (float ambiguity). The final ZTD/IWV product for dataassimilation in NWP is going to be delivered to the BoM innear-real time. Therefore the impact of the predicted orbits andclocks on the estimated ZTD values needs to be quantified.Broadly speaking using DD or PPP in conjunction with preciseIGS orbits and clocks is of an acceptable quality (IWV errorbelow 3 mm, ZTD error below 15 mm), even in challengingweather conditions. It has to be noted however, that the DDestimates with short baseline formulation are slightly moreconsistent with reference values than PPP and other strategiesconsidered. The longest baseline strategy that was consideredto be the most appropriate one (decorellation of height and

troposphere conditions) for lower atmosphere, was notperforming exceptionally well. The standard short baselinestrategy with network solution was proved to be the mostreliable one in the DD strategies family. The PPP approach hasconfirmed to be robust and reliable with high precision clocksand orbits. However, PPP solution with real-time clocks andpredicted orbits is not performing as accurate as the DDsolution. From our experiments we concluded that (at leastfor investigated case studies): 1) severe weather conditions donot interfere with the ability of the CORS network to providehigh quality troposphere estimates for NWP data assimilation,2) the DD and PPP strategies are of equal accuracy in terms ofZTD estimation while using precise orbits and clocks, and 3) inthe near real time, and the real timemode the DD solution willperform better.

Acknowledgements

This research was supported by the Australian SpaceResearch Program project endorsed to a research consortiumled by K. Zhang at RMIT University. The GPS ground-based datawas retrieved from the GPSNet (owned and operated by theDepartment of Environment and Primary Industries, Victoria),CORSnet-NSW (owned and operated by the Department ofLand and Property Information, New SouthWales), Asia-PacificReference Frame (operated by Geoscience Australia) andSmartNET Australia. The meteorological data were kindlyprovided by the Australian Bureau of Meteorology. Fruitfuldiscussions with B. Carter and J. Bosy are kindly acknowledged.

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