ORIGINAL ARTICLE

Using a regional numerical weather prediction model for GNSS
positioning over Brazil

Daniele Barroca Marra Alves1 • Luiz Fernando Sapucci2 •

Haroldo Antonio Marques3 • Eniuce Menezes de Souza4 •

Tayná Aparecida Ferreira Gouveia1 • Jackes Akira Magário1

Received: 8 October 2014 / Accepted: 14 July 2015 / Published online: 6 August 2015

� Springer-Verlag Berlin Heidelberg 2015

Abstract The global navigation satellite system (GNSS)

can provide centimeter positioning accuracy at low costs.

However, in order to obtain the desired high accuracy, it is

necessary to use high-quality atmospheric models. We

focus on the troposphere, which is an important topic of

research in Brazil where the tropospheric characteristics

are unique, both spatially and temporally. There are dry

regions, which lie mainly in the central part of the country.

However, the most interesting area for the investigation of

tropospheric models is the wet region which is located in

the Amazon forest. This region substantially affects the

variability of humidity over other regions of Brazil. It

provides a large quantity of water vapor through the

humidity convergence zone, especially for the southeast

region. The interconnection and large fluxes of water vapor

can generate serious deficiencies in tropospheric modeling.

The CPTEC/INPE (Center for Weather Forecasting and

Climate Studies/Brazilian Institute for Space Research) has

been providing since July 2012 a numerical weather pre-

diction (NWP) model for South America, known as Eta. It

has yield excellent results in weather prediction but has not

been used in GNSS positioning. This NWP model was

evaluated in precise point positioning (PPP) and network-

based positioning. Concerning PPP, the best positioning

results were obtained for the station SAGA, located in

Amazon region. Using the NWP model, the 3D RMS are

less than 10 cm for all 24 h of data, whereas the values

reach approximately 60 cm for the Hopfield model. For

network-based positioning, the best results were obtained

mainly when the tropospheric characteristics are critical, in

which case an improvement of up to 7.2 % was obtained in

3D RMS using NWP models.

Keywords Numerical weather prediction � Zenithal
tropospheric delay � GNSS � Positioning

Introduction

The global navigation satellite system (GNSS) has revo-

lutionized geodetic positioning by providing positioning

with centimeter accuracy in PPP and network-based posi-

tioning (Alves and Monico 2011; Marques et al. 2012). In

order to obtain this centimeter accuracy over long dis-

tances, a major difficulty is finding high-quality iono-

spheric and tropospheric models. With respect to the

& Daniele Barroca Marra Alves

danibarroca@fct.unesp.br

Luiz Fernando Sapucci

luiz.sapucci@cptec.inpe.br

Haroldo Antonio Marques

haroldoh2o@gmail.com

Eniuce Menezes de Souza

emsouza@uem.br

Tayná Aparecida Ferreira Gouveia

tayna.ppgcc@gmail.com

Jackes Akira Magário

jackes_magario@live.com

1 São Paulo State University - UNESP - Brazil, Roberto

Simonsen, 305, Presidente Prudente,

São Paulo State 19060-900, Brazil

2 INPE - Instituto Nacional de Pesquisas Espaciais, Rodovia

Presidente Dutra, km 40, Cachoeira Paulista,

São Paulo 12630, Brazil

3 UFPE - Universidade Federal de Pernambuco - Brazil, Rua

Academico Hélio Ramos, S/N, Cidade Universitária, Recife,

PE 5740-030, Brazil

4 Maringa State University - UEM - Brazil, Colombo Av.,

5790, Maringa, Parana State 87020-900, Brazil

123

GPS Solut (2016) 20:677–685

DOI 10.1007/s10291-015-0477-x

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troposphere, Brazil has a large territory with varying

characteristics. Dry regions exist mainly in the northeast

and central regions of the country. However, an interesting

study area is the northern region located over the Amazon

forest. This region is very wet and substantially affects the

variability of humidity over other areas of Brazil. It pro-

vides a large quantity of water vapor through the humidity

convergence zone, especially for the southeastern region.

The interconnection and large fluxes of water vapor in the

regions can generate serious deficiencies of the tropo-

spheric models.

The empirical models and meteorological information

from a standard atmosphere, normally used to reduce the

impact of the tropospheric delay, are not able to capture the

spatial and temporal variability of the atmosphere. Con-

sequently, in high-accuracy GNSS applications, mainly in

real time, this kind of model is not adequate in places like

Brazil where the atmospheric conditions are unique.

Therefore, there is a need to employ models capable of

overcoming the described limitations. An interesting way

of obtaining the zenith total delay (ZTD) is a numerical

weather prediction (NWP) model, which is based on initial

conditions generated from a complete meteorological

database in a process known as data assimilation. This

methodology has been explored in previous research, and

good results have been reported. Rocken et al. (2001) using

numerical reanalysis model products obtained a significant

reduction in seasonal and latitudinal biases observed in

empirical models. Niell (2001) developed an atmospheric

mapping function, and Boehm and Schuh ( 2004; Boehm

et al. 2006a, b) developed the Vienna Mapping Function

(VMF) and the Global Mapping Function (GMF); both

developments are based on numerical weather model

(NWM). Other research has shown the benefits of inte-

grating NWM and GPS (Schüler et al. 2003; Jensen et al.

2002; Jupp et al. 2003). Strategies based on ray-traced

tropospheric slant delay corrections obtained from NWP

have been investigated, which demonstrated that small

improvements can be obtained with respect to the mapping

function approach (Hobiger et al. 2008). Hobiger et al.

(2010) showed the improvement obtained in the position-

ing solutions during extreme weather occurrences, when

the standard mapping function approach suffers from the

fact that the complex weather situation is not well modeled

by the gradient-like asymmetric contribution.

The CPTEC (Center for Weather Forecasting and Cli-

mate Studies) at INPE (Brazilian Institute for Space

Researches) makes available a regional model of the ZTD

for South America (http://satelite.cptec.inpe.br/zenital/).

The ZTD values are provided for all of South America in a

regular grid twice per day, with predictions for a period of

66 h (Sapucci et al. 2007). The first versions were tested

against the empirical Hopfield model. The results showed a

better performance for the NWP model with an improve-

ment of approximately 19 % (Alves et al. 2006; Alves and

Monico 2011).

Since June 2012, a new version of the regional NWP

model, called Eta, has been available (Chou et al. 2005;

Mesinger et al. 2012). Important improvements in the

horizontal, vertical, and temporal resolutions were imple-

mented in this version, including a horizontal resolution of

15 km, 42 vertical levels, and a ZTD forecast every 3 h.

Here, the main goal is to evaluate the Eta model for precise

point positioning (PPP). Using PPP, the model perfor-

mance will be tested in 5 different regions, with different

tropospheric characteristics. Additionally, the model will

be tested with regard to network-based positioning using

data from the GNSS-SP network. In both methods, data

from June 2012 to December 2013 were processed. The

theory involved with tropospheric modeling by using

NWP, and the Eta model will be described below. In

addition, we present the network and software configura-

tions and a description of the experiments and analyses

carried out to demonstrate the performance of the model.

Evaluation of tropospheric modeling

Atmospheric gases cause changes in direction and speed of

GPS electromagnetic waves while propagating through

different atmospheric layers. These changes cause the

actual path of the signal to be longer than the straight

geometric distance, resulting in a signal delay, also called

tropospheric delay. Mapping functions are used to model

these delay variations (Davis et al. 1985; Niell 1996).

These mapping functions permit the variations of the tro-

pospheric delay in any direction to be expressed as a

function of the ZTD, by considering the concentration of

gases in a vertical atmospheric column. In recent years,

significant progress has been made in improving mapping

functions, especially with the use of NWP products

(Boehm and Schuh 2004; Niell 2001).

Due to the behavior of atmospheric gases, the ZTD is

divided into two components: the zenith wet delay (ZWD),

formed by the influence of water vapor, and the zenith

hydrostatic delay (ZHD). The ZHD component depends on

the atmospheric air density. Consequently, if the supposi-

tion of the hydrostatic balance is true, values with good

quality can be estimated from pressure measurements at the

surface P0, taking into consideration the latitude u and the

altitude h0 of the location. This relationship can be

expressed by following equation (Davis et al. 1985):

ZHD ¼ ð2:27683157� 10�3ÞP0

ð1� 0:0026 cos 2u� 0:00028h0Þ
ð1Þ

The ZWD values can be obtained by following equation

(Davis et al. 1985):

678 GPS Solut (2016) 20:677–685

123

http://satelite.cptec.inpe.br/zenital/


ZWD ¼ 10�6

Z1

h0

k02
e

T
Z�1
w þ k3

e

T2
Z�1
w

� �
dh; ð2Þ

where e is the partial pressure of the water vapor and T is

temperature, both of which vary as a function of altitude h.

Additionally, Z�1
w is the inverse of the constant of com-

pressibility of the water vapor, k02 = 22.10 K hPa-1 and

k3 = 373900 K2 hPa-1, which are constants for the

atmospheric refractivity (Bevis et al. 1994). Although the

influence of ZHD is smaller than the hydrostatic compo-

nent, which is approximately 10 % of the ZTD, the tem-

poral and spatial variation is much larger, changing by

20 % in a few hours (Spilker 1996).

Numerical weather prediction models applied

in tropospheric modeling

There is a consensus in the scientific community that the

NWP models can contribute significantly to the modeling

of the ZTD. The approach involves an atmospheric general

circulation model (AGCM), which meticulously accounts

for the interactions of the physical phenomena in the ter-

restrial atmosphere via a complex system that demands

high computational capacity (Richardson 1922). This sys-

tem is constantly fed with and corrected by observations of

atmospheric variables, which are provided by various types

of sensors. Consequently, the NWP is able to generate ZTD

forecasts of better quality than those of the available

mathematical models, such as Hopfield and Saastamoinen

models.

The principle involved in the NWP model is relatively

simple: Knowing the evolution laws of the atmosphere

state, the future state can be predicted in the instant t, if the

initial state is known at the instant t0. The ZWD forecast

can be obtained by applying the profiles of temperature and

humidity predicted by the NWP model using numeric

integration of (2). In a similar way, the ZHD forecast is

obtained by applying the values of the atmospheric pres-

sure at the surface predicted by model and the coordinates

of the respective point in (1). Adding both components

yields the forecasts of the ZTD for each individual point

belonging to model domain. Interpolation methods can be

used to obtain ZTD values for any other internal point of

the model domain, which makes it possible to analyze the

seasonal ZTD variability over South America.

Eta model with a 15 km horizontal resolution

The Eta model is a descendent of the earlier HIBU (Hy-

drometeorological Institute and Belgrade University)

model (Mesinger and Janjic 1974). The code has been

upgraded to the Arakawa-style horizontal advection

scheme of Janjic (1984), then rewritten to use the Eta

vertical coordinate (Mesinger et al. 1988), and subse-

quently, at NCEP, supplied with an advanced physics

package (Janjic 1990; Mesinger and Lobocki 1991).

One of the most significant differences between Eta and

other NWP models is the vertical coordinate, which was

defined by Mesinger (1984) and which provides the name

of this model. Using this vertical coordinate defines quasi-

horizontal coordinate surfaces and thus prevents pressure-

gradient force errors due to steep topography that can occur

with terrain-following coordinates (Mesinger 1984). This

feature is particularly useful for regions with steep orog-

raphy such as South America because of the presence of

the Andes Cordillera (Chou et al. 2005). The Eta coordi-

nate at an atmospheric point with pressure P is defined by

the following expression:

g ¼ p� pT

pS � pT

� �
pREFðzÞ � pT

pREFð0Þ � pT

� �
ð3Þ

where the indices S and T refer to the terrestrial surface and

the top of the model atmosphere, respectively. The index

REF refers to a prescribed reference atmosphere, and z is

the surface height. The model prognostic variables are as

follows: surface pressure, horizontal wind components,

temperature, specific humidity, turbulent kinetic energy,

and cloud hydrometeors.

The Eta model became officially operational at CPTEC

in 1996. During the last few years, CPTEC has signifi-

cantly enlarged the computational capacity and conse-

quently the spatial resolution of its models. The Eta model

began with a horizontal resolution of 80 km; currently, it

has a resolution of 15 km. The function of the regional

model is complementary to the forecast generated by the

global model by providing a detailed forecast of phenom-

ena associated with fronts, orography, marine breezes, and

severe storms (Chou et al. 2005). Such systems, in a fine

temporal scale, exhibit nonlinear behavior; consequently,

the period of reasonable forecast accuracy is smaller and

the forecast periods are frequently shorter. The forecasts

operationally extend to 72 h. Eta covers a large part of

South America and adjacent oceans (longitudes from 25�W
to 90�W and latitudes from 12�N to 45�S), and its forecast

are available twice per day. It will be evaluated using only

data from the Brazilian territory.

Hopfield model

The Hopfield (1969) model assumes that atmospheric

refractivity N is a function of temperature T0, humidity e0,

and pressure P0 measurement at the surface and of the

height of the atmospheric layers involved in the hydrostatic

and wet components of the ZTD, which are labeled here by

HH and HW, respectively. This model is based on equations

GPS Solut (2016) 20:677–685 679

123



presented by Smith and Weintraub (1953), Hopfield

(1969), and contributions by Seeber (1993), generating the

following algorithm:

ZHD ¼ 1552� 10�7 P0

T0
HH ð4Þ

ZWD ¼ 1552� 10�7 4810e0

T2
0

HW ð5Þ

HH ¼ 40:136þ 14; 872ðT0 � 27; 316Þ ð6Þ
HW ¼ 11:000 ð7Þ

mhðEÞ ¼ ðsinðE2 þ 6:25Þ1=2Þ�1 ð8Þ

mwðEÞ ¼ ðsinðE2 þ 2:25Þ1=2Þ�1 ð9Þ
ZTD ¼ ZHDmhðEÞ þ ZWDmwðEÞ ð10Þ

where mh and mw are mapping functions for hydrostatic

and wet ZTD components, respectively. The term E is the

elevation angle of the GPS satellite.

GNSS network of Brazil

The continuous GNSS network RBMC (Rede Brasileira de

Monitoramento Contı́nuo—Continuous Monitoring

Brazilian Network, http://www.ibge.gov.br/english/geo

ciencias/geodesia/rbmc/rbmc.shtm) covers all of Brazil. It

currently consists of about 110 reference stations that are

not uniformly distributed, featuring a lower density of

stations across certain regions such as the Amazon forest.

Figure 1 (green symbols) shows the distribution of the

RBMC stations.

Unfortunately, the RBMC cannot support high-precision

network-based positioning due to the sparse station spacing.

This limitation can be lessened for users in São Paulo State

who can access data from the GNSS-SP network (GPS

Active Network of São Paulo State). The main objectives of

this network are to increase the number of active GNSS

stations and to support research on the atmosphere, network-

based positioning, and related fields. The data are available

in real time through the Internet using the NTRIP (Net-

worked Transport of RTCM via Internet Protocol) or for

post-processed applications (http://www.fct.unesp.br/#!/

pesquisa/grupos-de-estudo-e-pesquisa/gege//home/).

The GNSS-SP network is maintained by UNESP (Sao

Paulo State University), and it is composed of approxi-

mately 20 receivers. Currently, the distance between the

stations ranges from 100 to 200 km. All receivers stream

data to a central facility at UNESP Presidente Prudente, SP,

where the data are stored and distributed to the users.

Figure 1 (red symbols) shows the distribution of the sta-

tions in the São Paulo State region and its borders.

Methodology

The focus is on PPP results using the NWP and Hopfield

models for stations from the RBMC where the ground-truth

coordinates are available for comparison. Additionally, the

network-based positioning will be tested. In both methods,

we obtained the daily solution from static mode using

NWP and Hopfield models. The results were evaluated in

terms of discrepancies, standard deviations (SD), and root

mean squares (RMS).

PPP

Experiments were carried out in the static PPP mode by

using the in-house software called RT_PPP, which is

capable of processing data in real time and also in post-

processed mode (Marques et al. 2012). The RT_PPP allows

the processing of dual-frequency GPS data by employing a

Kalman filter and the DIA method (detection, identifica-

tion, and adaptation) for quality control (Teunissen 1998).

The first-order ionospheric effects were corrected by

applying the ionospheric-free linear combination. When C1

observable is available, we apply the DCB (P1-C1) to align

the observations. When L2C (C2) is available, it is used

instead of P2, applying DCB (P2-C2). The troposphere

delay can be corrected from the Hopfield model or from

CPTEC numerical weather forecast model (ZTD/CPTEC)

and also by applying troposphere wet component estima-

tion. The software also applies final satellites orbits and

clocks corrections from IGS, absolute PCV (phase center

variation) for receivers and satellites, phase windup, rela-

tivity effects, OTL (ocean tide loading), and EBT (Earth

Fig. 1 RBMC stations SAGA, RNNA, CUIB, PPTE, and UFPR

(yellow) used in the PPP tests and GNSS/SP stations (red) applied in

network-based positioning

680 GPS Solut (2016) 20:677–685

123

http://www.ibge.gov.br/english/geociencias/geodesia/rbmc/rbmc.shtm
http://www.ibge.gov.br/english/geociencias/geodesia/rbmc/rbmc.shtm
http://www.fct.unesp.br/%23!/pesquisa/grupos-de-estudo-e-pesquisa/gege//home/
http://www.fct.unesp.br/%23!/pesquisa/grupos-de-estudo-e-pesquisa/gege//home/


body tide) among others. The ambiguities are estimated as

float solutions, and when a cycle slip is detected, the

ambiguity parameter is reinitialized.

GPS data from five Brazilian stations (Fig. 1—yellow

symbols) during the period of June 2012 to December 2013

were processed in the static PPP mode with daily coordi-

nate estimates. These stations were chosen to evaluate the

Eta model in various regions of Brazil, considering dif-

ferent climatic characteristics and data availability.

All PPP corrections were applied, and the troposphere

was modeled in the PPP processing via two different

strategies, i.e., application of the Hopfield model and the

ZTD from NWP/CPTEC. The Hopfield model has an

implicit mapping function, and, in case of NWP/CPTEC,

the global mapping function (GMF) was applied (Boehm

et al. 2006a, b). Furthermore, pressure and temperature

values for Hopfield model were obtained from GPT (global

pressure and temperature) function (Boehm et al. 2007).

Data were processed by taking into account an elevation

cutoff of 10� and adopted observation precisions as 0.8, 1,

0.008, and 0.001 m for C1, P2, phase L1, and phase L2,

respectively. The estimated coordinates were compared

with ground-truth coordinates to analyze the accuracy

reached when considering the two troposphere correction

strategies. The results and analysis can be seen in the next

sections.

Zenithal wet delay

The ZWD was estimated in the RT_PPP as a random walk

stochastic process in the Kalman filter with a priori spectral

density equal to 5 mm per hour. In this case, the GMF is

applied and the hydrostatic component comes from Hop-

field model. Considering the ZWD estimated in each epoch

during the daily solution, a ZWD daily average was com-

puted; Fig. 2 shows the time series for stations SAGA,

RNNA, CUIB, PPTE, and UFPR. Additionally, we also

present in the same figure the daily average of ZWD

obtained by the NWP and Hopfield models. It is possible to

note that ZWD obtained by the NWP model is similar to

the estimated solution.

Network-based positioning

At São Paulo State University, an in-house software system

is under development for generating network-based cor-

rections using the VRS concept. In the proposed method,

atmospheric models are used to generate network correc-

tions. Details about the software methodology can be found

in Alves and Monico (2011). This software was used to

generate the VRS data.

Data from the GNSS/SP network (Fig. 1—red symbols)

were used to perform the network-based positioning. VRS

data were generated using the subnetwork west of São

Paulo State (symbols with an inner circle). Station PPTE

(yellow symbol with inner circle) was used as the base

station because it is closest to the VRS position (blue

symbol). The VRS was generated approximately 40 km

from PPTE station.

To accomplish the experiments, we generated VRS data

for the same period of the PPP solutions, i.e., from June

2012 to December 2013. Additionally, VRS data were

generated using the Hopfield and NWP/CPTEC models.

The next step was to evaluate the VRS data quality. Here,

we used the RT_PPP software and PPP static mode.

Results and analysis

This section presents the results obtained by PPP and

network-based positioning. We also illustrate the daily

ZWD estimated during PPP processing and ZWD obtained

using Hopfield and NWP models.

Zenithal wet delay

Analyzing Fig. 2 is possible to verify that the values

obtained by estimated ZWD and NWP models are quite

similar, but that the Hopfield model presents fairly constant

results and is, therefore, not able to capture the temporal

variability of ZWD values.

Ppp

Figure 3 presents the horizontal and vertical RMS values

obtained for station SAGA using the PPP static mode and

the Hopfield and NWP Eta models. Figure 4 presents 3D

RMS obtained for stations SAGA, RNNA, CUIB, PPTE,

Fig. 2 Daily ZWD obtained by NWP and Hopfield models and

estimated during PPP processing for stations SAGA, RNNA, CUIB,

PPTE, and UFPR

GPS Solut (2016) 20:677–685 681

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and UFPR. For SAGA and RNNA stations, some gaps can

be seen in these figures due to lack of RINEX observation

files.

With regard to the SAGA station, Figs. 3 and 4 show

that the RMS values for the Hopfield model are larger than

those for the NWP model. The most important result from

these stations is the high accuracy of the ZTD modeling

using NWP, which captures the seasonal oscillation during

the annual cycle. The Hopfield model exhibits poor accu-

racy during the summer, whereas the results obtained by

the Eta model feature lower RMS values and are seasonally

independent. Using the NWP model, the values are less

than 10 cm for all 24 h of data, whereas the values reach

approximately 60 cm for the Hopfield model.

By evaluating the time series for station RNNA in

Fig. 4, it is possible to note large RMS values associated

with the Hopfield model. The errors reach 80 and 20 cm for

the Hopfield and NWP models, respectively. This station is

located near the sea, where humidity is also relevant.

The station CUIB is located in a dry central region of

Brazil. The figure shows that, in general, the NWP model

presented the best results. Better results were obtained for

the summer season (December to March), which is the

wettest period of year, and the rain events are more

frequent.

Although station PPTE is located far from the coast, it

receives humidity from the Amazon forest when the South

Atlantic convergence zone (SACZ) is active, which is very

common during the period from November to March. The

figure shows that the behavior of the NWP model is better,

especially during the SACZ occurrence period. Using this

model, the 3D RMS values are less than 15 cm, but when

Hopfield model is used, the 3D RMS values reach 70 cm.

Station UFPR is located in the south of Brazil. The

analysis of the 3D RMS values shows that the Hopfield

results are larger than those of NWP. While the Hopfield

RMS values reach almost 60 cm, the NWP results are

approximately 10 cm. Similar to the other stations, the

horizontal discrepancies of this station are minor between

the two models, and the largest difference exists in the

altitude component.

In Table 1, we evaluate the median absolute error

(MAE) and the median absolute deviation (MAD) statistics

from the time series presented in Figs. 3 and 4. These

statistics are robust measures for non-normal distributed

data and insensitive to outliers. We also calculate the error

reduction factor (RF) when NWP is used instead of the

Hopfield tropospheric model (HOP/NWP).

In the evaluation of time series, the mean level is not an

adequate representation when trend or cycle effects are

present. This can be seen in Table 1 from MAD, which

represents not only the bias reduction but also the absolute

deviation around the median of the daily estimated coor-

dinates. For the Hopfield model, the greatest problem is

that the daily 3D value can be very good one day, with few

millimeters of discrepancy, but as large as 80 cm on

another days. Furthermore, as expected, the reduction

factor shows that the improvements were more relevant for

the vertical coordinates (3D relative to horizontal results),

reaching a reduction factor of about 9 in the MAE for

station SAGA. The 3D MAD errors were in general 3 times

larger for the HOP tropospheric model than for NWP.

Network-based positioning

Figure 5 shows the 3D RMS values obtained with the VRS

data files generated using the NWP and Hopfield tropo-

spheric models. By evaluating the time series presented in

the figure, it is clear that the results obtained by both

Fig. 3 Horizontal and vertical RMS values obtained by PPP static

mode for station SAGA using the NWP and Hopfield tropospheric

models

Fig. 4 PPP static mode results obtained by stations SAGA, RNNA,

CUIB, PPTE, and UFPR and NWP and Hopfield tropospheric models

682 GPS Solut (2016) 20:677–685

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tropospheric models are quite similar, yielding a 2.8-cm

RMS on average. Considering the network-based posi-

tioning methodology and the network used, the results are

acceptable. In network-based positioning, the errors are

computed in a relative mode, which attenuate the results.

Additionally, the GNSS-SP network is located in a dry

region.

There are certain periods, mainly when the troposphere

characteristics are critical, that the NWP model has a better

performance. This occurs, for example, in June where the

humidity is very low in this region. Figure 6 shows the

horizontal and vertical RMS values for this period. The

figures show that the NWP model yields the best results.

The average 3D RMS values are 2.98 and 3.22 cm for the

NWP and Hopfield models, respectively, an improvement

of 7.2 %.

In Table 2, we can evaluate the MAE, MAD, and the

error reduction factor when NWP is used instead of the

Hopfield tropospheric model from the time series presented

in Figs. 5 and 6. The table shows that the improvements

were much smaller than in PPP. When all periods are

considered, the results obtained by both models are quite

similar. In a critical month, like July, the results of the

NWP model are better.

Conclusions

We presented a new NWP tropospheric model available in

Brazil, known as the Eta model. Although this model has

yielded satisfactory results with improvement of the spatial

resolutions over South America in comparison with

empirical models (Alves et al. 2006; Alves and Monico

2011), it still had not been evaluated with regard to GNSS

positioning. In order to do this verification, this new NWP

tropospheric model was applied in PPP and network-based

Table 1 Median absolute error

(MAE) and the median absolute

deviation (MAD) for the

horizontal and 3D time series in

PPP static positioning using the

NWP and Hopfield tropospheric

models

Stations Horizontal (cm) 3D (cm)

MAE MAD MAE MAD

HOP NWP RF HOP NWP RF HOP NWP RF HOP NWP RF

CUIB 1.82 2.13 0.85 0.52 0.5 1.04 31.54 7.8 4.04 12.66 3.52 3.60

PPTE 0.95 0.94 1.01 0.46 0.42 1.10 18.42 8.82 2.09 10.23 3.92 2.61

RNNA 1.55 1.51 1.03 0.68 0.6 1.13 21.78 5.3 4.11 10.06 2.74 3.67

SAGA 3.16 1.44 2.19 1.84 0.6 3.07 38.32 4.35 8.81 5.12 1.99 2.57

UFPR 1.02 1.07 0.95 0.41 0.41 1.00 16.33 5.84 2.80 10.48 3.38 3.10

Fig. 5 PPP static mode results obtained by the VRS data files

generated using the NWP and Hopfield tropospheric models

Fig. 6 Horizontal and vertical RMS values obtained by PPP static

mode for the VRS data files generated using the NWP and Hopfield

tropospheric models for July 2012

Table 2 Median absolute error

(MAE) and the median absolute

deviation (MAD) for horizontal

and 3D time series obtained by

PPP static mode for the VRS

data files generated using the

NWP and Hopfield tropospheric

models

Period Horizontal (cm) 3D (cm)

MAE MAD MAE MAD

HOP NWP RF HOP NWP RF HOP NWP RF HOP NWP RF

All periods 1.89 1.83 1.03 0.39 0.39 1.00 2.89 2.8 1.03 0.54 0.5 1.08

July 2012 2.19 2.06 1.06 0.29 0.26 1.12 3.14 2.89 1.09 0.26 0.27 0.96

July 2013 2.03 1.74 1.17 0.25 0.31 0.81 3.45 3.21 1.07 0.37 0.38 0.97

GPS Solut (2016) 20:677–685 683

123



positioning and the obtained results are presented and

discussed here.

First, PPP was carried out at five different Brazilian

stations with different tropospheric characteristics. The

best results were obtained by the NWP model for all sta-

tions. In high-humidity regions, which include the SAGA

station, the improvements were more significant. For this

station, improvements of about a factor of 3 were obtained

for both horizontal and 3D MAD. In an additional analysis,

we evaluated the network-based positioning using data

from the GNSS/SP network. In these tests, the results

presented by both models were quite similar when con-

sidering the entire period. The NWP exhibited the best

results only in months that featured critical tropospheric

characteristics, such as July. Ideally, we should be able to

use data from a network located very the Amazon forest or

the coast, where the humidity is very high. However, in

Brazil, this is not possible because of sparse station spac-

ing. This might be possible in the future.

Considering these results, we can conclude that the

NWP Eta model yields high-quality tropospheric predic-

tions. Consequently, it is possible to use this model instead

of empirical models to obtain a noticeable improvement in

GNSS positioning.

Acknowledgments The authors would like to thank FAPESP and

CNPq for the financial support provided to this research (FAPESP

research project—process number 2012/19906-7; CNPQ research

scholarship—process number 303079/2011-8).

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Daniele Barroca Marra Alves
is an Assistant Professor at

UNESP and Researcher from

National Council for Scientific

and Technological Develop-

ment (CNPq). She received her

BSc degree in Mathematics in

2001, MSc in 2004, PhD in

2008, and post-doctorate in

2011, all of them in Carto-

graphic Science, from São Paulo

State University. Her research

interests are on network-based

positioning and atmospheric

modeling.

Luiz Fernando Sapucci is a

researcher in the Group on Data

Assimilation Development of

the Center for Weather fore-

casting and Climate Studies

from INPE. He has underground

in Math and holds a MSc and

PhD degree in Cartographic

Science from São Paulo State

University in Presidente Pru-

dente, Brazil. He has worked

extensively with the GPS recei-

vers (spatial based and ground

based) in meteorological pur-

poses and tropospheric model-

ing for geodesic positioning over South American using NWP

products.

Haroldo Antonio Marques re-

ceived his BSc degree in Car-

tographic Engineering in 2005,

MSc in Cartographic Science in

2008, and PhD in Cartographic

Science in 2012 at Sao Paulo

State University (UNESP),

Presidente Prudente in Brazil.

Since 2011, he is an Adjunct

Professor at the Department of

Cartographic Engineering, Fed-

eral University of Pernambuco

(UFPE) at Recife in Brazil,

where he is lecturing and

researching topics related to

Geodesy and Adjustment, especially those related to GNSS, survey-

ing, and atmospheric sciences.

Eniuce Menezes de Souza is a

professor at Statistical Depart-

ment, Maringa State University

(UEM), and a researcher from

National Council for Scientific

and Technological Develop-

ment (CNPq). She received her

BSc degree in Mathematics in

2001 and her MSc degree

(2004) and PhD in Cartographic

Science (2008) from São Paulo

State University (UNESP). Her

research involves GNSS multi-

path and scintillation mitigation,

multiscale wavelet analysis, and

applied statistics, mainly, time series modeling.

Tayná Aparecida Ferreira
Gouveia received her BSc in

Mathematics at Sao Paulo State

University (FCT-UNESP),

Presidente Prudente in 2008,

Master in Cartographic Science

in 2013, and now she is a PhD

student, both in FCT-UNESP.

Her research activities involve

global geodetic positioning with

emphasis on troposphere mod-

eling mainly NWP models.

Jackes Akira Magário is a

Technical Training Fellow from

São Paulo State University in

Presidente Prudente, Brazil. He

received his BSc degree in

Analysis and Systems Develop-

ment from Technology College

(FATEC) in Presidente Pru-

dente, Brazil. He has worked on

a project called ‘‘Experiments

and analyses of atmospheric

models in Network-Based Posi-

tioning’’ using his knowledge to

improve network-based system.

GPS Solut (2016) 20:677–685 685

123


	Using a regional numerical weather prediction model for GNSS positioning over Brazil
	Abstract
	Introduction
	Evaluation of tropospheric modeling
	Numerical weather prediction models applied in tropospheric modeling
	Eta model with a 15 km horizontal resolution
	Hopfield model

	GNSS network of Brazil
	Methodology
	PPP
	Zenithal wet delay
	Network-based positioning


	Results and analysis
	Zenithal wet delay
	Ppp
	Network-based positioning

	Conclusions
	Acknowledgments
	References