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GeoPlanning 
  Journal of Geomatics and Planning                                                                                                                   Vol. 8, No. 1, 2021     
 

Original Research 

Temperature Acquisition System for Real Time 

Application of First Velocity Correction by EDM 

(Electronic Distance Measurement) 

Felipe A. C. Rodriguez 1*, Luis A. K. Veiga 1, Wilson A. Soares 1 

1. Federal University of Paraná 

DOI: 10.14710/geoplanning.8.1.61-74  

Abstract 

The first velocity correction is used to correct the measured distance affected by the velocity variation of the electromagnetic 

wave propagation in a medium. This correction depends on the refractive index of the propagation medium and reference 

refractive index. The influence of the temperature in the medium refractive index is critical; some estimates establish that 

variation 1°C causes 1ppm of error in distances. In the measuring processes with total stations, the temperature is usually 

collected at only one point, for example, in the position where the measuring instrument is setup. However, the wave 

propagates in a medium of non-constant temperature, where the extremes of the line can present variations and thus this 

measurement in only one point could be non-representative. In this context, it was developed a low-cost real-time 

temperature acquisition system. This system provides the temperature values in different locations allowing their 

monitoring through the time. Experiments realized during the geodetic monitoring of a dam, show variations up to 8°C 

among geodetic points on the dam and around it. An analysis was development to evaluate the influence of temperature 

variations on monitoring distances and geodetic coordinate of a 2d network with different approaches (temperature 

modeling).  The results shows different values for distances (1.0 mm) and coordinates (0.5 mm) depending of the approach 

choose. 

Copyright © 2021 GJGP-Undip 

This open access article is distributed under a  

Creative Commons Attribution (CC-BY-NC-SA) 4.0 International license 

1. Introduction 

The accuracy of the distances obtained by electronic distances measurement (EDM) technique is a critical 

factor to some applications as geodetic network monitoring or geodetic control of structures (Brunner, 1984; 

Ussisoo, 1969;  Scaioni et al., 2014). The accuracy of EDM depends of two factors; the first, known as internal, 

is related with the manufacturing characteristics own of each instrument. On second case found the external 

factors that are more complex since depend mainly of the environmental conditions of the medium in which the 

electromagnetic wave propagates (Rüeger, 1990). According Brunner (1984); Rüeger (1990); Torge & Müller 

(2012) and Ogundare (2015) the principal effect that generate the medium is the variation of propagation velocity 

of the wave due to mainly density changes in their composition. This situation affect directly the distance 

compute and therefore their accuracy. 

According to Brunner (1984), the ideal situation to geodetic calculations it would be when the wave 

propagated in the vacuum, this supposes a homogeneous and constant medium however, the troposphere, 

medium of propagation associated to the terrestrial measurements, is constantly changing their composition 

(density). Rüeger (1990), define that the principal components of the troposphere that change their composition 

and affect the velocity propagations of wave in EDM instruments are the pressure, humidity and temperature. 

The correction of the effects which the atmospheric parameters of pressure, humidity and temperature cause on 

the wave velocity propagation are modeled through the refractive index, this is a factor that related the velocity 

e-ISSN: 2355-6544 
 
Received: 13 March 2020;  
Accepted: 1 January 2021;  
Published: 30 July 2021. 
 
Keywords:  
EDM, Refraction, Sensors 
 
*Corresponding author(s) email: 
felipe.carvajalro@gmail.com  
 
 

 

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mailto:felipe.carvajalro@gmail.com


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of light of propagation in a medium and in the vacuum. For EDM corrections, the refractive index is used to 

compute the first velocity correction, the last one provide the distance bias generated by the variation of the 

velocity of the electromagnetic wave due to the medium composition (Rüeger, 1990). The Equation 1 presented 

the first velocity correction: 

𝐾 = (𝑛𝑓 − 𝑛𝐿) ∙ 𝑑 (1) 

Where: 

𝐾 = the first velocity correction 

𝑛𝑓 = the reference refractive index 

𝑛𝐿 = group refractive index valid for atmospheric conditions described by t, p, e 

𝑑 = electronic distance or distance influenced by atmospheric parameters 

 

The refractive index of the medium depends on the frequency of the electromagnetic radiation propagating 

through it and the composition of the medium. In 1963, The International Union of Geodesy and Geophysics 

(IUGG) decided, in the XIIIth General Assembly, that the refractive index for light and NIR waves (employed 

in the electronic distance measurement) could be reduced to ambient conditions through the simplification of the 

formula proposed by Barrel e Sears 1939 (Rüeger, 1990). The Equation 2 shows how to obtain the refractive 

index. 

𝑛𝐿 = 1 +
𝑛𝑔 − 1

1 + 𝛼 ∙ 𝑡
∙

𝑝

1013.25
−

4.125 ∙ 10−8

1 + 𝛼 ∙ 𝑡
∙ 𝑒 

 

(2) 

Where: 

𝑛𝐿 = group refractive index valid for atmospheric conditions described by t, p, e 

𝑛𝑔= group refractive index 

𝑡 = dry bulb temperature of air (°C) 

𝑝 = atmospheric pressure (mb) 

𝛼 = coefficient of expansion of air (= 0.003661 per °C) 

𝑒 = partial water vapor pressure (mb) 

 

Other simplification was proposed by Kohlrausch (1955), cited by Rüeger (1990). In this case the 

coefficient of the air expansion varies slightly doing α = 1/273.15. With this modification, through Equation 3 

the refractive index is obtained: 

(𝑛𝐿 − 1) = (𝑛𝑔 − 1) +
273.15 ∙ 𝑝

(273,15 + t) ∙ 1013.25
∙

11.27 ∙ 10−6

(273.5 + t)
∙ 𝑒 

(3) 

The error in the refractive index due to pressure, temperature and humidity parameters can be estimated 

by the partial differentials of the Kohlrausch formulate. In Rüeger (1990) and Ogundare (2015) are presented 

examples that shows that, for the refractive index of light, the temperature is critical for the determination of 

the refractive index. According to the authors, for a temperature of 15°C, a pressure of 1007 mb, a partial water 

vapor pressure of 13 mb and a group refractive index of 1.0003045, a pressure variation of 1.0mb generates an 

error of 0.3 ppm in the distance determination, humidity variation of 1mb produces 0.04 ppm of error in the 

distance, meanwhile, the temperature variation of 1°C results in an error of 1ppm in the distance determination. 

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The measurement of atmospheric parameters is a typical procedure to land surveys engineers before to 

staring a measurement. Torge & Müller (2012) present gradients of -0.0065°C/m,  -0.12hPa/m, -0.0035hPa/m, 

to temperature, pressure e humidity respectly. From these values is posibile conluding that the temperature 

presents more variation in function to changes in the altitude. Rüeger (1990) and  Angus-Leppan & Brunner 

(1980), postulate that the average between the measurement of the pressure and humidity parameters at both 

terminal of a line are sufficient to achieve the representative value, however for the temperature parameter the 

average is not always representative, since the temperature gradients in the lower atmosphere are unstable. The 

principal cause for this is the different heat absorption and emission capacities of the Earth's surfaces. In this 

context Brunner (1984), postulate that the development of instrument solutions to measure the atmospheric 

parameters can be provide information that permit the modeling of this parameters, therefore obtain a better 

estimation of refractive index and of the first velocity correction. 

Actually, the total stations have a microprocessor to automatic compute of the refractive index and first 

velocity correction, for this, the user should be to insert the atmospheric values, and the correction is made. In 

this case, the use of external atmospheric sensors are necessary. In addition, some total stations have internal 

sensors to measure the atmospheric parameters.  For both cases, the measure is made in one place; therefore, this 

not considered the variations of atmospheric parameters around it, mainly the temperature. The problem of the 

representative of these values has led to the development of an atmospheric monitoring system as well as 

estimation models from the data provide by these systems. An example is a sensor development by Solarić et al. 

(2012), this sensor provides atmospheric data to calculate the atmospheric corrections on the EDM calibration 

baseline, this system permits measure the data on the each pillar of the baseline. Artese & Perrelli (2018), 

Proposed a method using the climatic data and a digital terrain model (DTM) of a landslide area, in this case the 

model is done to entire area. The next step after collected of data, it is the modeling of parameters, in this context 

Robertson (1977); Brunner & Fraser (1977); Angus-Leppan & Brunner (1980); Fraser (1981) and Brunner & 

Rüeger (1992), presented mathematical models to atmospheric parameters estimation.  To apply each of these 

models, the measurements of atmospheric parameters are necessary. 

Currently, low-cost technology has allowed the development of programmable sensors, microcontrollers 

like Arduino or Raspberry, communication modules like Xbee or LoRA. In this context, we present a temperature 

acquisition system to monitoring and collect the temperature data, critical parameter to compute the refraction 

index. This system was developed through the concept of real time wireless sensor network (RWSN), with open-

source hardware and software and low-cost sensors. Two experiment was presented with objective of evaluate 

the operation of this system and the temperature monitoring, also was presented an example to evaluate the 

incidence of the variations of this parameter on a 2D topographic network. 

 

2.  Data and Methods 

For the proposed temperature acquisition system was selected different devices, and in some cases 

evaluated and configured them as it will be shown later. For the communication, the Zigbee protocol was chosen; 

through radio frequency Xbee S2C devices, this protocol provides wireless communication. In the case of the 

control system, the microcontroller Arduino Uno allowed the configuration of parameters used to send data and 

temperature measurements and with which frequency. Finally, it was evaluated the digital temperature sensor 

DS18B20 (classic and waterproof version) and the TMP36 analog temperature sensor. This allowed choosing 

the one that was more suitable for this work. Below each step developed is detailed. 

2.1. DS18B20 and TMP36 temperature sensors 

The evaluation applied to DS18B20 and TMP36 sensor seeks to choose the more suitable sensor for this 

work. The TMP36 sensor is analog and provides voltage differences that can be converted in temperature 

through a scale factor (Devices, 2020). The D18B20 is a digital sensor with two versions; classical, not 

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encapsulated, and waterproof, both versions provide directly temperature values (Maxim, 2020). The main 

characteristics are presented in the Table 1. 

Table 1.  Main characteristics of both sensors. 

 Sensor  TMP36 DS18B20 

Operating system Analog Digital 

Precision  ±2°C ±0,5°C 

Operation range - 40°C to 125°C - 10°C to 85°C 

 

2.2. Comparison between DS18B20, TMP36 temperature sensors and the standard thermometer 

It was compared both DS18B20 (classical version) and TMP36 sensors, related to a standard glass 

mercury thermometer of 0.1°C nominal precision, defined as the reference of the response in temperature range. 

This experiment was developed in the physics laboratory at Federal University of Paraná. The experiment 

consisted in inducing temperature values through a thermostatic bath that permits to heat one solution from the 

7°C to 100°C range. Figure 1, shows that the thermometer and sensors were submerged in water. 

 

 
 Figure 1. Thermostatic bath and experiment configuration 

 

 

The circuit shown in Figure 2 is composed by an Arduino Uno microcontroller, DS18B20 and TMP36 

sensors, and provides automatically the temperature. The temperature values from the thermometer correspond 

to analogic measurements. 

 

 
Figure 2. DS18B20 and TMP36 circuit for comparative experiment 

 

 

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The results of this experiment are shown in the Figure 3, in this case it were realized 73 temperature 

measurements. The approximate range of these values is 10°C to 45° C. 

 

 
Figure 3. Evolution temperature during of experiment. 

 

For evaluating the differences between temperature series of DS18B20, TMP36 sensors and the reference 

thermometer, it was used the Pearson’s Chi-squared statistical test with a 95% confidence interval (Agresti, 

2007). In this case, the expected values (E) correspond to the reading of the glass reference thermometer; the 

observed values (O) correspond to the measurements of the sensors TMP36, DS18B20, and n correspond to the 

number of sample elements. 

𝜒𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑
2 = ∑

(𝑂𝑖 − 𝐸𝑖)2

𝐸𝑖

𝑛

𝑖

 
 

(4) 

The degrees of freedom are defined by: 

𝑣 = (𝑟 − 1) ∙ (𝑘 − 1) (5) 

Where: 

v: degrees of freedom 

r: number of  rows 

k: number of columns 

 

Two hypotheses were proposed, H0 the samples are homogeneous and H1 the samples are not 

homogeneous. Table 2 shows the results: 

Table 2. The Pearson’s Chi-squared statistical test for TMP36 and DS18B20 sensors 

Sensor v 𝝌𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅
𝟐  𝝌𝒑−𝒗𝒂𝒍𝒖𝒆

𝟐  

TMP36 72 114.908 47.857 

DS18B20 72 3.488 47.857 

 

Considering the results obtained in the experiment, it is possible to conclude that the better adherence of 

the results were obtained with the DS18B20 sensor in comparison with the results obtained by the TMP36 

sensor, so the hypothesis H0, for the sensor DS18B20, was accepted, however for the sensor TMP36 it was not. 

Based on the results obtained in this statistical test it was chosen as the best option for the development of this 

work the DS18B20 sensor (Soares, 2006; De Rubeis et al., 2017). 

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2.3. DS18B20 sensor correction 

The next step was the calibration of DS18B20 sensor, in this case it was used the waterproof version 

because this has a more resistant structure. It was applied the same test of the previous experiment. The Figure 

4 shown the temperature curve of the DS18B20 sensor and thermometer 

 

 Figure 4. Thermometer and DS18B20 temperature evolution 

 

For this experiment, it was realized 79 temperature measurements. The approximate range of these values 

is 22 °C to 60°C, maximum thermometer graduation. Two hypotheses were proposed, Ho the samples are 

homogeneous and H1 the samples are not homogeneous. Table 3 shown the results: 

 

Table 3. The Pearson’s Chi-squared statistical test for DS18B20 waterproof sensor 

Sensor v 𝝌𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒅
𝟐

 𝝌𝒑−𝒗𝒂𝒍𝒖𝒆
𝟐

 

DS18B20 78 0.346 51.910 

 

The Figure 5, shows the temperature difference between DS18B20 sensor and the reference thermometer. 

In addition, a trend line adjusted by a second-degree polynomial, calculated from difference values between the 

thermometer and DS18B20 sensor, provides the correction function for temperature sensor measurements, the 

calibration function is: 

 

Figure 5. Temperature differences between DS18B20 sensor and thermometer, trend-line and correction 

function 

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The estimated temperature for the DS18B20 sensor used is: 

𝑡𝑐 = 𝑡𝑠 + (−0.001177 ∙ 𝑡𝑠
2 + 0.096833 ∙ 𝑡𝑠 − 1.470066) 

 

(6) 

Where: 

𝑡𝑐=Correction temperature values 

𝑡𝑠= DS18B20 temperature values 

 

2.4. Arduino and Xbee configuration 

The Xbee devices were configured with the API (application programming interface) operating mode; this 

mode is available for the operation of the Zigbee protocol, used in this case, and permits the Xbee coordinator to 

receive wireless data packets from multiple Xbee devices, identifying each remote device. This characteristic is 

fundamental to associate each Xbee device with a geographic location. We used the star topology in this Zigbee 

network, configuring a coordinator and router devices. With an Arduino Uno board, it was possible to control 

the data to be sent to the network and the temperature measurement frequency, for this, two sketches control 

the transmission and reception of data in nodes and in coordinator respectively. For those Arduino Uno boards 

integrated with the remote devices, the format of the data is the principal function since the sensor measurement 

must be sent as well as its identification. In the case of coordinator, the Arduino Uno board must interpret the 

data packet received. 

The network is composed of five nodes and one coordinator. Each node has a DS18B20 temperature 

sensor, Xbee S2C module, and an Arduino Uno microcontroller. For the coordinator, the configuration is the 

same, but the DS18B20 is not used. Figure 6 shows the configuration of the coordinator and the node. 

 

 

Figure 6. Coordinator and node structure for the wireless network. 

 

For the coordinator, the energy power was provided by the USB port connection. For the nodes, due to 

their characteristic of being positioned in different positions on the ground, it was used a solar panel-based power 

and batteries, the latter being used as a reserve, if there are any problems in the power supply from the solar 

panels. Figure 7 shows the configuration of node energy system 

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Figure 7. Configuration of node energy system 

 

The configuration of this power source considers a 5.5-volt solar panel, a one-way diode; a lithium battery 

charger, a lithium battery, and a voltage lift to keep this parameter constant during its use. The node and 

coordinator are shown in Figure 8. 

 

 

Figure 8. Coordinator and nodes of network 

 

The upper part of the module has two functions: the first is protecting the temperature sensor from the 

direct incidence of the sunrays and, secondly, it supports the solar panel. This part can be rotated for better 

positioning of the solar panel. Figure 9 shows the wireless network diagram, in this case, the nodes were 

configured to send the temperature values each 1 minute to the coordinator. The coordinator controls the data 

flow and a sketch in python language save the information 

 

Figure 9. Network operation diagram 

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The collected temperature data, received by the coordinator node, were transmitted to the computer that 

was connected to the total station. One program developed in C # language receives this information and, using 

a user-selected interpolation model, determined the temperature value to be used for the correction of the first 

velocity. This program automatically sets the temperature and pressure values for the total station.  

 

3. Result and Discussion 

The system was designed to be used primarily in monitoring works of large engineering structures. Thus, 

it was tested in a dam 67 meters (220 ft) high, 1,100 meters (3,600 ft) long, that has a geodetic network built for 

monitoring purposes. The Salto Caxias Hydroelectric power plant is located between the municipalities of 

Capitão Leônidas Marques and Nova Prata do Iguaçu, 650 km far from Curitiba, Brazil (Figure 10). 

 

 

Figure 10. The location of Salto Caxias hydroelectric plant 

 

In this dam there is an external monitoring network (Figure 11) composed of six forced centering pillars 

(fixed points) and several prisms fixed on the upstream face of the dam (object points). In addition, there is an 

internal monitoring network, used to measure points in the inspection-galleries of the dam 

 

Figure 11.  External control geodetic network 

 

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The observation of external network provides the geodetic control for the galleries. Figure 12, the position 

of the point EGE05 allows the connection of both networks through observation to the point EG21 that 

correspond to the inner geodesic station closest to the outside of the gallery. For this connection, the total station 

was set up at point EGE05 and is realized the back sight at point EGE04 (inclined distance of approximately 

116 meters) and foresight at point EGI21 (approximately 37 meters). 

 

Figure 12. Gallery geodetic network, adapted (Zocollotii Filho, 2005) 

 

The sensors were installed at the EGE04 point (sensor S5455), EGE05 (sensor S5451) and EGI21 (sensor 

S6579). Figure 13, 14 and 15 show the localization of the sensors 

 

Figure 13. EGE05 temperature sensor installation 

 

Figure 14. EGE04 temperature sensor installation 

 

Figure 15. EGI21 temperature sensor installation 

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The sensors provided a temporal temperature series of two hours approximately. Figure 16 shows the 

temperature variations during the experiment. 

 

Figure 16. The temperature variation in EGI21, EGE05 and EGE04 

This experiment seeks to present the behavior of the temperature around the dam. For this, in EGE03 

pillar one sensor provides temperature at the total station position. Near the downstream prisms line, the other 

four sensors provided the temperature near these object points. These sensors were placed at different heights. 

Figure 17 shows the sensors distribution. The distance from the EGE03 point to the prisms and the sensors was 

approximately 280 meters. 

 

Figure 17. Sensors distribution in the dam for the second test 

In this experiment, the five sensors provided a temporal series about 50 minutes of collected temperature 

values. Figure 18 shows the temperature variations during the experiment 

 

Figure 18. Temperature values of five sensors located in Salto Caxias dam 

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The Figure 18 show variations around 8°C between the different places where the temperature sensor was 

installed. An analysis was made comparing the precision of electronic distances and the refractive index, the last 

one was computed using the maximum difference of temperature during the second experiment (8°C).  For the 

refractive index was used Equation 3, with pressure and humidity measured on where the total station was 

installed. For electronic distance precision was used the Equation 7 

 

 

Where 𝜎𝑖
2 and 𝜎𝑡

2 miscentering error for instrument and reflector respectively, 𝑎 and b are specific 

accuracies and D is distance (Ghilani, 2017). To perform the analysis we choose a high precision electronic 

distance meter (1 + 0.5ppm) and the EGE03 – Dam distance (280m approximately). For the compute the distance 

precision, we inconsiderate miscentering error for instrument and reflector since both are fixed in the pillar for 

monitoring and in the body of dam respectively. Results are presented in Table 4. 

 

Table 4. Comparison between index refraction and electronic distance precision 

Approximate distance Index refraction influence on distance 

(first velocity correction) (m)  

distance precision (68% interval 

confidence) (m) 

EGE03 – Dam (280m) 0.002 0.001 

 

The results show that the variation in meters generated when considering the difference between the 

refractive indices is greater than the precision provided by the instrument for the distance used. Considering 

that the pressure and humidity parameters were considered fixed, the temperature and its variations affect the 

performance of the instrument. 

For evaluation the influence of temperature on coordinate precision, we simulated a 2D topographic 

network (Figure 19) with two-control point (A, D), two unknown points (B, C) and five distances (continuous 

lines). To obtain the coordinates and their precisions we used trilateration technique and parametric least squared 

method (Ghilani, 2017). The refraction index was compute with the temperature data set from the acquisition 

system presented in the section 3.5 during the second experiment. With these values, we developed two 

mathematical models to temperature determination. In the first approach, we used the temperature value 

measured in the place where the total station was installed (classic approach), while that the second approach 

was obtained through the mean temperature value from the five sensors used in the previous experiment. For 

the pressure and humidity parameters, we used the values measured with external sensors on the total station 

position during the experiment presents in the section 4.1, for this simulation these parameters are considering 

invariants. 

 

Figure 19. The simulated network 

𝜎𝐷 = √(𝜎𝑖
2 + 𝜎𝑡

2 + 𝑎2 + (𝐷 ∙ 𝑏 𝑝𝑝𝑚)2) 
 

(7) 

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The refraction index values for the first and second approaches are 18.49 ppm and 17.38 ppm respectively. 

With these values, the first velocity and their distance precision were computed to each distance on the simulated 

network. The precision of B and C points are presented in Table 5: 

Table 5. Precision coordinates B and C 

Temperature approach  B (68% interval confidence) C (68% interval confidence) 

 X (m)  Y (m) X (m) Y (m) 

 One sensor 0.0052 0.0086 0.0072 0.0054 

 Mean (5 sensors) 0.0049 0.0081 0.0068 0.0051 

 

For the confidence interval used, the precisions reached through the use of an mean of temperature are 

better than those obtained in the traditional way. This may be because the second approach provides a more 

representative temperature value of the region. 

For the first experiment, the temperature values presented differences in the EGI21, EGI21, EGI21 

control points (maximum value of 12°C). These differences could be originated by different factors such as the 

temperature dissipated by the structure or environmental conditions around the dam. Both factors can create 

different thermal conditions in each control point, with irregular variations. In the geodetic monitoring context, 

the external network is used as reference for the displacement analysis of internal network, the latter, provides 

relevant information about the health of the structure. For the deformation analysis of internal network it is 

necessary the connection between networks, this is made through angles and distance measurement, 

consequently the temperature values provides by the developed system and the differences found should be 

considered in the distance measurement. In the second experiment, the temperature sensors were installed on 

the top and around the dam. Were collected temperature values during the geodetic monitoring of points on the 

downstream. The results show that temperature values decreasing with increasing the height, however the 

decreasing it is not regular. Some of the possible factors that influence the temperature values are the heat 

dissipation of the structure and the water mass influence on the points that are on the dam top. In both 

experiments, the temperature values have an irregular comportment during the geodetic monitoring. These 

variations can be affecting the correct determination of first velocity correction, thus the distances obtained by 

EDM. 

The uncertainties generated by the temperature differences were obtained thought the first velocity 

correction, for this, the highest temperature difference found in these experiments (8°C) was used. This difference 

was obtained between the pillar EGE03 and a monitoring point on the top of the dam. The approximate distance 

between them is 280 meters and uncertainties are 2.0 mm approximately. The comparison between the 

uncertainties generated by the refractive index variations and the distance precision (1 mm) show that the 

temperature value is determinant to obtain precise distances by electromagnetic wave propagation. 

For the coordinate precision values, the 2D simulate network show that the precisions of coordinates 

provide by the least square method are better where the refractive index was calculated with the mean 

temperature of sensors. Thus, the modeling of temperature is necessary for the geodetic monitoring of structures, 

where the correct determination of distances is relevant to the coordinate compute and deformation analysis. 

 

4. Conclusion 

The system development for temperature acquisition provides in real-time values in multiple locations. 

This characteristic permits temperature monitoring during the observation of a geodetic network or in other 

related activities. The temperature values obtained in the dam experience and their variations in different 

locations around to dam can affect the calculation of the first velocity correction. Considering that variation on 

1°C affect distances in 1ppm and that it was found in both experiments, differences up to 8°C, to work in 

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DOI: 10.14710/geoplanning.8.1.61-74 

 

74 

temperature modeling for this correction is necessary. The experiments carried out show the importance of 

temperature both in determining distances and in coordinate precision of a topographic network, in this context, 

the developed system allows to collect data for modeling and provide a more representative temperature value. 

 

5. Acknowledgments 

The authors would like to thank Copel - Companhia Paranaense de Energia for allowing the tests to be 

carried out at the Salto Caxias plant. The authors also thank for the scholarship given. 

 

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