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<front>
<journal-meta>
<journal-id journal-id-type="index">565</journal-id>
<journal-title-group>
<journal-title specific-use="original" xml:lang="es">Atmósfera</journal-title>
<abbrev-journal-title abbrev-type="publisher" xml:lang="es">Atmósfera</abbrev-journal-title>
</journal-title-group>
<issn pub-type="ppub">0187-6236</issn>
<issn pub-type="epub">2395-8812</issn>
<publisher>
<publisher-name>Universidad Nacional Autónoma de México</publisher-name>
<publisher-loc>
<country>México</country>
<email>claudio.amescua@atmosfera.unam.mx</email>
</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="art-access-id" specific-use="redalyc">56582679013</article-id>
<article-id pub-id-type="doi">10.20937/ATM.52966</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Sin sección</subject>
</subj-group>
</article-categories>
<title-group>
<article-title xml:lang="en">
<bold>Prediction of atmospheric corrosion from meteorological parameters:Case of the atmospheric basin of the Costa Rican Western Central Valley</bold>
</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name name-style="western">
<surname>Rodríguez-Yáñez</surname>
<given-names>Javier E.</given-names>
</name>
<xref ref-type="corresp" rid="corresp1"/>
<xref ref-type="aff" rid="aff1"/>
<email>jrodriguezy@uned.ac.cr</email>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Rivera-Fernández</surname>
<given-names>Erick</given-names>
</name>
<xref ref-type="aff" rid="aff3"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Alvarado-González</surname>
<given-names>Daniel</given-names>
</name>
<xref ref-type="aff" rid="aff5"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Abdalah-Hernández</surname>
<given-names>Mariela</given-names>
</name>
<xref ref-type="aff" rid="aff7"/>
</contrib>
<contrib contrib-type="author" corresp="no">
<name name-style="western">
<surname>Quirós-Quirós</surname>
<given-names>Rafael</given-names>
</name>
<xref ref-type="aff" rid="aff9"/>
</contrib>
</contrib-group>
<aff id="aff1">
<institution content-type="original">Urban Ecology Research Laboratory, Costa Rica Distance University, 474-2050, Mercedes de Montes de Oca, San José, Costa Rica.</institution>
<country country="CR">Costa Rica</country>
<institution-wrap>
<institution content-type="orgname">Urban Ecology Research Laboratory, Costa Rica Distance University</institution>
</institution-wrap>
</aff>
<aff id="aff3">
<institution content-type="original">School of Physics and Center for Geophysical Research, University of Costa Rica, 11501-2060, San Pedro de Montes de Oca, San José, Costa Rica.</institution>
<country country="CR">Costa Rica</country>
<institution-wrap>
<institution content-type="orgname">School of Physics and Center for Geophysical Research, University of Costa Rica</institution>
</institution-wrap>
</aff>
<aff id="aff5">
<institution content-type="original">Advanced Computing Laboratory, National High Technology Center, 1174-1200, Pavas, San José, Costa Rica.</institution>
<country country="CR">Costa Rica</country>
<institution-wrap>
<institution content-type="orgname">School of Physics and Center for Geophysical Research, University of Costa Rica</institution>
</institution-wrap>
</aff>
<aff id="aff7">
<institution content-type="original">Advanced Computing Laboratory, National High Technology Center, 1174-1200, Pavas, San José, Costa Rica.</institution>
<country country="CR">Costa Rica</country>
<institution-wrap>
<institution content-type="orgname">Advanced Computing Laboratory, National High Technology Center,</institution>
</institution-wrap>
</aff>
<aff id="aff9">
<institution content-type="original">School of Geography, University of Costa Rica, 11501-2060, San Pedro de Montes de Oca, San José, Costa Rica.</institution>
<country country="CR">Costa Rica</country>
<institution-wrap>
<institution content-type="orgname">School of Geography, University of Costa Rica</institution>
</institution-wrap>
</aff>
<author-notes>
<corresp id="corresp1">
<email>jrodriguezy@uned.ac.cr</email>
</corresp>
</author-notes>
<pub-date pub-type="epub-ppub">
<season>Enero</season>
<year>2023</year>
</pub-date>
<volume>36</volume>
<issue>1</issue>
<fpage>171</fpage>
<lpage>182</lpage>
<history>
<date date-type="received" publication-format="dd mes yyyy">
<day>26</day>
<month>08</month>
<year>2020</year>
</date>
<date date-type="accepted" publication-format="dd mes yyyy">
<day>20</day>
<month>04</month>
<year>2021</year>
</date>
</history>
<permissions>
<ali:free_to_read/>
</permissions>
<abstract xml:lang="en">
<title>Abstract</title>
<p>The assessment of atmospheric corrosion is currently based on the study of atmospheric basins (AB). Modeling atmospheric corrosion in many cases involves the measurement of several meteorological and atmospheric pollution parameters, specifically temperature, relative humidity, chloride, and sulfur dioxide, making the estimation process more complex. However, for the Western Central Valley (WCV) in Costa Rica, a low-pollution AB, it is possible to develop simplified atmospheric corrosion models based on a small number of atmospheric parameters. In this paper, the meteorological variables of the study region were analyzed in terms of their dependency on altitude and their applicability in the development of a simplified model to predict the corrosion rate (Vcorr). The output of the predictive model was compared with the standard model of ISO 9223:2012, showing a higher skill and giving reliable results for a wide interval of altitudes.</p>
</abstract>
<trans-abstract xml:lang="es">
<title>Resumen</title>
<p>La evaluación de la corrosión atmosférica se basa actualmente en el estudio de las cuencas atmosféricas (AB, por sus siglas en inglés). La modelización de la corrosión atmosférica implica en muchos casos la medición de varios parámetros meteorológicos y de contaminación atmosférica, concretamente la temperatura, la humedad relativa, el cloruro y el dióxido de azufre, lo que hace más complejo el proceso de estimación. Sin embargo, para el Valle Central Occidental (WCV, por sus siglas en inglés) de Costa Rica, un AB de baja contaminación, es posible desarrollar modelos simplificados de corrosión atmosférica, basados en un pequeño número de parámetros atmosféricos. En este trabajo se analizaron las variables meteorológicas de la región de estudio en cuanto a su dependencia de la altitud y su aplicabilidad en el desarrollo de un modelo simplificado para predecir la tasa de corrosión (Vcorr). El resultado del modelo de predicción se comparó con el modelo estándar de la norma ISO 9223:2012, mostrando una mayor habilidad y dando resultados fiables para un amplio intervalo de altitudes.</p>
</trans-abstract>
<kwd-group xml:lang="en">
<title>Keywords</title>
<kwd>atmospheric basin</kwd>
<kwd>corrosion</kwd>
<kwd>meteorological parameters</kwd>
<kwd>basic modeling</kwd>
</kwd-group>
<counts>
<fig-count count="6"/>
<table-count count="4"/>
<equation-count count="9"/>
<ref-count count="44"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>redalyc-journal-id</meta-name>
<meta-value>565</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro">
<title>
<bold>1. Introduction</bold>
</title>
<p>The Costa Rican Western Central Valley (WCV) is limited to the northwest by the Central Volcanic mountain range, to the east by the hills of Ochomogo, and to the southwest by the foothills of the Talamanca mountain range. The average altitude of the WCV is about 1000 m above sea level (m.a.s.l.), with values up to 2000 m.a.s.l. in some places (<xref ref-type="bibr" rid="redalyc_56582679013_ref18">IMN, 2008</xref>).</p>
<p>The region’s average annual precipitation is 2300 mm, with two clearly marked seasons: a rainy season from May to November and a dry season from December to April. During the rainy season, a relative minimum of precipitation occurs in July-August, known as the <italic>veranillo</italic> or mid-summer drought (<xref ref-type="bibr" rid="redalyc_56582679013_ref23">Magaña et al., 1999</xref>). Temperature and relative humidity show small changes, with average values of 20 ºC and 75 %, respectively, varying with altitude and the time of the year (<xref ref-type="bibr" rid="redalyc_56582679013_ref41">Solano and Villalobos, 2000</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref18">IMN, 2008</xref>). The predominant winds are the trade winds that blow from the northeast to the southwest. The Central Volcanic mountain range allows the passage of trade winds over the mountains or through mountain passes (mainly the gaps of La Palma and Desengaño). The seasonal variation of wind intensity, associated with the Caribbean low-level jet, determines most of the climatic changes in the WCV (<xref ref-type="bibr" rid="redalyc_56582679013_ref30">Muñoz et al., 2002</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref3">Amador, 2008</xref>). Another characteristic pattern of the wind in the WCV is related to mountain-valley circulations. These are generated by temperature differences between both geographic landforms during the day, causing the wind to move from the mountain to the valley in the morning and in the opposite direction in the afternoon (<xref ref-type="bibr" rid="redalyc_56582679013_ref44">Zárate, 1978</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref6">Barrantes et al., 1985</xref>). Due to the climatic and orographic conditions of the WCV, this area can be considered an Atmospheric Basin (AB). Here the climatic variability, circulation, and dispersion of air pollutants are driven mainly by the prevailing direction of winds and orography (<xref ref-type="bibr" rid="redalyc_56582679013_ref45">Zárate, 1980</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref30">Muñoz et al., 2002</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref7">Caetano and Iniestra, 2008</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref14">García-Reynoso et al., 2009</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref16">Herrera et al., 2012</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref39">SEMARNAT-INECC, 2016</xref>).</p>
<p>Metallic materials are thermodynamically unstable under atmospheric conditions, which causes their deterioration, giving rise to the atmospheric corrosion phenomenon. A usual way to evaluate this process is by obtaining the loss of material in a fundamental state with respect to the time of exposure to the environment. This way allows the corrosion rate estimation as a loss of mass per unit area (mg m<sup>–2 </sup>y<sup>–1</sup>) or as a loss of sheet thickness (µm y<sup>–1</sup>) during the exposure time. Low carbon steel is the most common material for visualizing corrosión, similar to ASTM A36/A36M-19 (<xref ref-type="bibr" rid="redalyc_56582679013_ref5">ASTM International, 2019</xref>).</p>
<p>Previous research by <xref ref-type="bibr" rid="redalyc_56582679013_ref26">Morcillo et al. (2011)</xref> and the guidelines of the ISO 9223:2012 standard state that temperature (T), relative humidity (RH), chlorides (Cl<sup>-</sup>), and sulfur oxides (SO<sub>2</sub>) are the primary agents that contribute to corrosion. Temperature and relative humidity provide enough conditions for the material oxidation process, while pollutants modify the oxides formed on steel surfaces, producing distortion in the crystalline network and structural weakness. Consequently, materials turn more labile and porous, becoming more susceptible to corrosive attacks (<xref ref-type="bibr" rid="redalyc_56582679013_ref12">Feliu et al., 1993</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref28">Morcillo et al., 2013</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref11">Díaz et al., 2018</xref>).</p>
<p>Temperature and relative humidity variables are obtained from meteorological data, and the deposition of both chlorides and sulfur oxides is measured or estimated by air pollution evaluation methods. These parameters permit the characterization of the effects of pollution variation on the corrosion rate in the WCV (<xref ref-type="bibr" rid="redalyc_56582679013_ref25">Morcillo et al., 1998</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref36">Roberge et al., 2002</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref27">Morcillo et al., 2012</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref37">Robles, 2013</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref15">Garita-Arce et al., 2014</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref38">Rodríguez-Yáñez et al., 2015</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref2">Alcántara et al., 2015</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref29">Morcillo, 2017</xref>).</p>
<p>
<xref ref-type="bibr" rid="redalyc_56582679013_ref15">Garita-Arce et al. (2014)</xref> proposed a series of models for obtaining corrosion rates depending on the available information. For Costa Rica, maps of applicability of the corrosion models are based on the work of <xref ref-type="bibr" rid="redalyc_56582679013_ref38">Rodríguez-Yáñez et al. (2015)</xref>. These maps present an increasing complexity, starting from the Brooks deterioration index to the ISO 9223 (<xref ref-type="bibr" rid="redalyc_56582679013_ref20">ISO, 1992</xref>) standard and using linear equations to model corrosion rate. The updated ISO 9223:2012 (<xref ref-type="bibr" rid="redalyc_56582679013_ref21">ISO, 2012a</xref>) standard includes a new model for estimating corrosion. It considers the annual corrosion as a function of climatic and pollution variables.</p>
</sec>
<sec sec-type="materials|methods">
<title>
<bold>2. Data and methods</bold>
</title>
<p>Hourly meteorological data for several stations within the WCV were provided by the National Meteorological Institute and the Costa Rican Electricity Institute (IMN and ICE, respectively, by their Spanish acronyms). <xref ref-type="fig" rid="gf1">Figure 1</xref> shows the location of the area of study. The analysis period was from 2010 to 2019 (<xref ref-type="table" rid="gt1">see Table I</xref>). Only meteorological stations with less than 5 % of missing data were considered. From these data, the variables of interest were T and RH. The time of wetness (TOW), defined as the fraction of hours per year where T is greater than 0 ºC and RH is greater than or equal to 80 %, was also obtained.</p>
<p>
<fig id="gf1">
<label>
<bold>Fig. 1</bold>
</label>
<caption>
<title>Location of the WCV and the weather stations used for data collection.</title>
</caption>
<alt-text>Fig. 1 Location of the WCV and the weather stations used for data collection.</alt-text>
<graphic xlink:href="56582679013_gf2.png" position="anchor" orientation="portrait">
<alt-text>Fig. 1 Location of the WCV and the weather stations used for data collection.</alt-text>
</graphic>
</fig>
</p>
<p>
<table-wrap id="gt1">
<label>Table I</label>
<caption>
<title>Location of the meteorological stations available in the WCV.</title>
</caption>
<alt-text>Table I Location of the meteorological stations available in the WCV.</alt-text>
<alternatives>
<graphic xlink:href="56582679013_gt2.png" position="anchor" orientation="portrait"/>
<table id="gt2-526564616c7963">
<thead style="display:none;">
<tr style="display:none;">
<th style="display:none;"/>
</tr>
</thead>
<tbody>
<tr>
<td>Name</td>
<td>North latitude</td>
<td>West longitude</td>
<td>Altitude (m.a.s.l)</td>
<td>Start date</td>
<td>End date</td>
</tr>
<tr>
<td>RECOPE, Ochomogo</td>
<td>09º 53’ 40.2”</td>
<td>83º 56’ 19.4”</td>
<td>1546</td>
<td>01/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>CIGEFI</td>
<td>09º 56’ 11.0”</td>
<td>84º 02’ 43.0”</td>
<td>1210</td>
<td>01/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>IMN, Aranjuez</td>
<td>09º 56’ 16.6”</td>
<td>84º 04’ 10.8”</td>
<td>1181</td>
<td>01/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>Juan Santamaría International airport</td>
<td>09º 59’ 26.5”</td>
<td>84º 12’ 52.9”</td>
<td>913</td>
<td>01/01/2010</td>
<td>15/02/2018</td>
</tr>
<tr>
<td>Fraijanes lake</td>
<td>10º 08’ 14.4”</td>
<td>84º 11’ 36.6”</td>
<td>1720</td>
<td>01/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>RECOPE, La Garita</td>
<td>10º 00’ 19.0”</td>
<td>84º 17’ 45.0”</td>
<td>740</td>
<td>12/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>West Pavas, near to airport</td>
<td>09º 57’ 26.3”</td>
<td>84º 08’ 51.6”</td>
<td>997</td>
<td>01/01/2010</td>
<td>05/03/2015</td>
</tr>
<tr>
<td>Santa Bárbara</td>
<td>10º 02’ 00.0”</td>
<td>84º 09’ 57.0”</td>
<td>1070</td>
<td>01/01/2010</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>Belén</td>
<td>09º 58’ 30.0”</td>
<td>84º 11’ 08.0”</td>
<td>926</td>
<td>01/01/2010</td>
<td>02/11/2017</td>
</tr>
<tr>
<td>Burio hill, Aserrí</td>
<td>09º 50’ 25.3”</td>
<td>84º 06’ 45.6”</td>
<td>1811</td>
<td>14/11/2012</td>
<td>12/10/2017</td>
</tr>
<tr>
<td>Altos Tablazo, Higuito</td>
<td>09º 50’ 12.4”</td>
<td>84º 03’ 18.1”</td>
<td>1660</td>
<td>28/06/2012</td>
<td>31/05/2017</td>
</tr>
<tr>
<td>Chitaria hill, Santa Ana</td>
<td>09º 53’ 30.1”</td>
<td>84º 11’ 37.3”</td>
<td>1717</td>
<td>01/03/2011</td>
<td>11/10/2017</td>
</tr>
<tr>
<td>Poás volcano lake</td>
<td>10º 11’ 21.0”</td>
<td>84º 13’ 55.2”</td>
<td>2598</td>
<td>05/09/2011</td>
<td>12/02/2018</td>
</tr>
<tr>
<td>Cedral hill, Escazú</td>
<td>09º 51’ 41.1”</td>
<td>84º 08’ 45.2”</td>
<td>2255</td>
<td>29/08/2012</td>
<td>12/10/2017</td>
</tr>
<tr>
<td>School of Agricultural Sciences, Santa Lucía, Heredia</td>
<td>10º 01’ 22.8”</td>
<td>84º 06’ 42.4”</td>
<td>1257</td>
<td>19/11/2013</td>
<td>31/01/2018</td>
</tr>
<tr>
<td>West Tobías Bolaños airport, Pavas</td>
<td>09º 57’ 26.3”</td>
<td>84º 08’ 51.6”</td>
<td>981</td>
<td>05/03/2015</td>
<td>10/10/2017</td>
</tr>
<tr>
<td>San Luis</td>
<td>10º 00’ 54.0”</td>
<td>84º 01’ 36.0”</td>
<td>1341</td>
<td>01/09/2018</td>
<td>31/9/2019</td>
</tr>
<tr>
<td>Colima</td>
<td>09º 57’ 09.0”</td>
<td>84º 05’ 24.2”</td>
<td>1145</td>
<td>01/01/2010</td>
<td>12/31/2017</td>
</tr>
</tbody>
</table>
</alternatives>
</table-wrap>
</p>
<sec>
<title>
<bold>
<italic>2.1 Atmospheric conditions and air pollution</italic>
</bold>
</title>
<p>Within the studied period, the number of both warm (El Niño) and cold (La Niña) phases of the El Niño-Southern Oscillation (ENSO) is similar (<xref ref-type="bibr" rid="redalyc_56582679013_ref32">NOAA, 2019</xref>). ENSO episodes are linked to inter-annual variations in circulation and precipitation patterns over Costa Rica (<xref ref-type="bibr" rid="redalyc_56582679013_ref13">Fernández et al. 2013</xref>).</p>
<p>On the other hand, the volcanic activity was low and spaced in time. It was mainly associated with eruptions of the Poás and Turrialba volcanoes in 2015. During most of these eruptive events, winds were not blowing toward the WCV (<xref ref-type="bibr" rid="redalyc_56582679013_ref34">OVSICORI, 2015</xref>). Under these conditions, several authors have shown that pollution levels of chlorides and sulfur oxides in the WCV are about 5 mg m<sup>–2 </sup>d<sup>–1 </sup>and 10 mg m<sup>–2</sup> d<sup>–1</sup>, respectively (<xref ref-type="bibr" rid="redalyc_56582679013_ref37">Robles, 2013</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref17">Herrera-Murillo et al., 2014</xref>). These levels correspond to a low polluted atmosphere.</p>
<sec>
<title>
<bold>
<italic>2.2 Corrosion models</italic>
</bold>
</title>
<p>According to the results of <xref ref-type="bibr" rid="redalyc_56582679013_ref15">Garita-Arce et al. (2014)</xref> for the low carbon steel, an estimation curve of the corrosion rate at the WCV can be derived from meteorological parameters, specifically RH and TOW. Corrosion rate (Vcorr) for the WCV is a linear function of TOW or RH, as given by the following equations:</p>
<p>
<disp-formula id="e1">
<label>(1)</label>
<graphic xlink:href="56582679013_ee2.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>
<disp-formula id="e2">
<label>(2)</label>
<graphic xlink:href="56582679013_ee3.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>where,</p>
<p>Vcorr: corrosion rate, µm y<sup>–1</sup>,</p>
<p>TOW: fraction average annual hours of wetness, dimensionless,</p>
<p>RH: average annual relative humidity, %.</p>
<p>The above equations were determined for an altitude of 1108 m.a.s.l. in the La Sabana sector of San José, Costa Rica.</p>
<p>The ISO 9223:2012 standard contains guidelines to determine Vcorr. One of them is to utilize the corrosion categories listed in <xref ref-type="table" rid="gt2">Table II</xref>. A second alternative is to obtain it by employing model equations. In this standard, the set of equations to calculate the corrosion of carbon steel is:</p>
<p>
<disp-formula id="e3">
<label>(3)</label>
<graphic xlink:href="56582679013_ee4.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>where,</p>
<p>
<italic>f</italic>
<sub>st</sub>: factor of Steel</p>
<p>Vcorr: corrosion rate in the first year, µm y<sup>–1</sup>,</p>
<p>T: annual average temperature, ºC,</p>
<p>RH: annual average relative humidity, %,</p>
<p>P<sub>d</sub>: annual average SO<sub>2</sub> deposition, mg m<sup>–2</sup> d<sup>–1</sup>,</p>
<p>S<sub>d</sub>: annual average Cl<sup>-</sup> deposition, mg m<sup>–2</sup> d<sup>–1</sup>.</p>
<p>
<table-wrap id="gt2">
<label>Table II</label>
<caption>
<title>Corrosion rate for different corrosivity categories for low carbon steel.</title>
</caption>
<alt-text>Table II Corrosion rate for different corrosivity categories for low carbon steel.</alt-text>
<alternatives>
<graphic xlink:href="56582679013_gt3.png" position="anchor" orientation="portrait"/>
<table id="gt3-526564616c7963">
<thead style="display:none;">
<tr style="display:none;">
<th style="display:none;"/>
</tr>
</thead>
<tbody>
<tr>
<td>Corrosion category</td>
<td>Corrosion rate (µm y<sup>–1</sup>)</td>
<td>Corrosivity level</td>
</tr>
<tr>
<td>C1</td>
<td>≤ 1.3</td>
<td>Very low</td>
</tr>
<tr>
<td>C2</td>
<td>1.3 to 25</td>
<td>Low</td>
</tr>
<tr>
<td>C3</td>
<td>25 to 50</td>
<td>Medium</td>
</tr>
<tr>
<td>C4</td>
<td>50 to 80</td>
<td>High</td>
</tr>
<tr>
<td>C5</td>
<td>80 to 200</td>
<td>Very High</td>
</tr>
<tr>
<td>CX</td>
<td>200 to 700</td>
<td>Extreme</td>
</tr>
</tbody>
</table>
</alternatives>
</table-wrap>
</p>
<sec>
<title>
<bold>
<italic>2.3. Data processing</italic>
</bold>
</title>
<p>Annual averages of RH, T, and TOW were obtained for each location with the corresponding standard deviation. A relatively high correlation between these parameters and altitude (A), in m.a.s.l., was found. The determination correlation coefficient (R<sub>2</sub>) is a useful statistic for testing linearity. An acceptable value of R<sub>2</sub> must be higher than 0.75 (<xref ref-type="bibr" rid="redalyc_56582679013_ref43">Wilks, 2011</xref>).</p>
<p>General data analysis was performed with Python. The corrosion rate was determined and represented in two maps. One was generated with a simplified model, and the other with the new method formulated by the ISO 9223:2012 standard. Contour lines for the WCV were taken from the Atlas of Costa Rica with a spatial resolution of 10 m (<xref ref-type="bibr" rid="redalyc_56582679013_ref33">Ortiz-Malavasi, 2015</xref>), and the maps were created with ArcGIS software.</p>
<p>The simplified and the ISO 9223:2012 models were compared between them and against experimental measurements. The latter were obtained according to the procedures in the ISO 9223:2012, ISO 9225:2012, and ASTM G1-03 (<xref ref-type="bibr" rid="redalyc_56582679013_ref21">ISO, 2012a</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref22">ISO, 2012b</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref4">ASTM International, 2017</xref>) standards.</p>
</sec>
</sec>
</sec>
</sec>
<sec sec-type="results|discussion">
<title>
<bold>3. Results and discussion</bold>
</title>
<sec>
<title>
<bold>
<italic>3.1. Meteorological parameters</italic>
</bold>
</title>
<p>Most stations were located below 1500 m.a.s.l. and inside the valley. There were less data points in medium- altitude locations a (1500 m.a.s.l. to 2000 m.a.s.l.), and only three in the most elevated parts (above 2000 m.a.s.l.). The geographical distribution of the meteorological observations was not homogeneous. Data points were scarce in the northern section of the WCV, particularly around the foothills of the Barva volcano.</p>
<p>
<xref ref-type="fig" rid="gf2">Figures 2</xref>, <xref ref-type="fig" rid="gf3">3</xref>, and <xref ref-type="fig" rid="gf4">4</xref> represent the relations between temperature, relative humidity, and time of wetness with altitude and their standard deviation.</p>
<p>
<fig id="gf2">
<label>
<bold>Fig. 2</bold>
</label>
<caption>
<title>Variation of (a) annual average and (b) standard deviation of temperature with altitude.</title>
</caption>
<alt-text>Fig. 2 Variation of (a) annual average and (b) standard deviation of temperature with altitude.</alt-text>
<graphic xlink:href="56582679013_gf3.png" position="anchor" orientation="portrait">
<alt-text>Fig. 2 Variation of (a) annual average and (b) standard deviation of temperature with altitude.</alt-text>
</graphic>
</fig>
</p>
<p>
<fig id="gf3">
<label>
<bold>Fig. 3</bold>
</label>
<caption>
<title>Variation of (a) annual average and (b) standard deviation of RH with altitude.</title>
</caption>
<alt-text>Fig. 3 Variation of (a) annual average and (b) standard deviation of RH with altitude.</alt-text>
<graphic xlink:href="56582679013_gf4.png" position="anchor" orientation="portrait">
<alt-text>Fig. 3 Variation of (a) annual average and (b) standard deviation of RH with altitude.</alt-text>
</graphic>
</fig>
</p>
<p>
<fig id="gf4">
<label>
<bold>Fig. 4</bold>
</label>
<caption>
<title>Variation of (a) annual accumulated average and (b) standard deviation of time of wetness with altitude.</title>
</caption>
<alt-text>Fig. 4 Variation of (a) annual accumulated average and (b) standard deviation of time of wetness with altitude.</alt-text>
<graphic xlink:href="56582679013_gf5.png" position="anchor" orientation="portrait">
<alt-text>Fig. 4 Variation of (a) annual accumulated average and (b) standard deviation of time of wetness with altitude.</alt-text>
</graphic>
</fig>
</p>
<p>Based on the information presented in <xref ref-type="fig" rid="gf2">figure 2</xref>, the equation that describes the temperature variation between 700 m.a.s.l. and 2600 m.a.s.l. is:</p>
<p>
<disp-formula id="e4">
<label>(4)</label>
<graphic xlink:href="56582679013_ee5.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>where,</p>
<p>T: annual average temperature, ºC,</p>
<p>A: altitude, m.a.s.l.</p>
<p>The value of the vertical temperature gradient in the WCV from equation (4) is remarkably similar to the global mean value of –6.5 ºC km<sup>–1</sup> in the lower atmosphere <xref ref-type="bibr" rid="redalyc_56582679013_ref40">Sendiña-Nadal and Pérez-Muñuzuri, 2006</xref>). The standard deviation tends to increase with altitude at a rate of 2 % for every 1000 m. This behavior is possibly related to a more significant seasonal variability of temperatures in mountainous regions of the WCV (<xref ref-type="bibr" rid="redalyc_56582679013_ref41">Solano and Villalobos, 2000</xref>). Usually, the standard deviation of temperature in the WCV is less than 0.5ºC.</p>
<p>In <xref ref-type="fig" rid="gf3">figure 3</xref>, it can be observed that relative humidity increases linearly with an altitude between 700 m.a.s.l. and 2600 m.a.s.l. This relation is expressed as:</p>
<p>
<disp-formula id="e5">
<label>(5)</label>
<graphic xlink:href="56582679013_ee6.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>(5)</p>
<p>where,</p>
<p>RH: annual average relative humidity, %,</p>
<p>A: altitude, m.a.s.l.</p>
<p>At higher elevations, the air usually reaches the saturation point, and clouds may form. In the WCV, relative humidity was near the 100 % value at 2600 m.a.s.l. (<xref ref-type="bibr" rid="redalyc_56582679013_ref31">Murphy and Hurtado, 2013</xref>). Above this altitude, <xref ref-type="disp-formula" rid="e5">equation (5)</xref> is not applicable.</p>
<p>The standard deviation of RH is usually less than 5 %, with a slight tendency to decrease with altitude. In the lowest areas of the valley, the seasonal variability of RH is usually determined by the differences between dry and rainy seasons (<xref ref-type="bibr" rid="redalyc_56582679013_ref1">Abdalah-Hernández et al., 2019</xref>).</p>
<p>
<xref ref-type="bibr" rid="redalyc_56582679013_ref8">Campos and Castro (1992)</xref> explained that RH could quickly vary from 20 % to 100 % at higher elevations of the eastern part of the WCV. This variation is due to dry upper troposphere air and the transport of humid air masses through the mountain pass from the Caribbean region. According to these authors, RH fluctuations decrease at lower elevations.</p>
<p>The relation between time of wetness and altitude from 700 m.a.s.l. to 2600 m.a.s.l., as shown in <xref ref-type="fig" rid="gf4">figure 4</xref>, is as follows</p>
<p>
<disp-formula id="e6">
<label>(6)</label>
<graphic xlink:href="56582679013_ee7.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>where,</p>
<p>TOW: average fraction of annual hours of wetness per year, dimensionless,</p>
<p>A: altitude, m.a.s.l.</p>
<p>The TOW increases while the deviation standard decreases with altitude (<xref ref-type="bibr" rid="redalyc_56582679013_ref38">Rodríguez-Yáñez et al., 2015</xref>). This proportionality is due to more saturated air at higher elevations, where RH increases and gets close to 100 %.</p>
<p>The variance of the TOW in the lower valley is associated with changes between the dry and rainy seasons. There is also greater homogeneity in the TOW at higher elevations since the RH values tend to be above 80 % for extended periods.</p>
<sec>
<title>
<bold>
<italic>3.2. Estimation of Vcorr using the linear and ISO models</italic>
</bold>
</title>
<p>Using the linear relationships from the previous section (<xref ref-type="disp-formula" rid="e4">equations 4</xref> to <xref ref-type="disp-formula" rid="e6">6</xref>) is possible to calculate the variation of Vcorr with altitude by only considering meteorological variables (<xref ref-type="disp-formula" rid="e1">equations 1</xref> and <xref ref-type="disp-formula" rid="e2">2</xref>). The derived equations for corrosion rate, based on RH and TOW, are:</p>
<p>
<disp-formula id="e7">
<label>(7)</label>
<graphic xlink:href="56582679013_ee8.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>
<disp-formula id="e8">
<label>(8)</label>
<graphic xlink:href="56582679013_ee9.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>In both cases, the estimated R<sup>2</sup> values are greater than 0.75 and therefore acceptable.</p>
<p>A similar process is applied to the ISO 9223:2012 equation (<xref ref-type="disp-formula" rid="e3">equation 3</xref>). The factors P<sub>d</sub> and S<sub>d</sub> are estimated by <xref ref-type="bibr" rid="redalyc_56582679013_ref16">Herrera et al. (2012)</xref> approximation. In this case:</p>
<p>
<disp-formula id="e9">
<label>(9)</label>
<graphic xlink:href="56582679013_ee10.png" position="anchor" orientation="portrait">
<alt-text/>
</graphic>
</disp-formula>
</p>
<p>The simplified equation of ISO 9223:2012 is governed by the effect of RH and increases exponentially with the altitude.</p>
<sec>
<title>
<bold>
<italic>3.3. Model output comparison</italic>
</bold>
</title>
<p>Field corrosion data was collected from September 2018 to September 2019. <xref ref-type="table" rid="gt3">Table III</xref> shows the location and altitude of the measurement sites, as well as the annual average of the atmospheric variables and pollutants at each point. Atmospheric corrosion, from observations and models (<xref ref-type="disp-formula" rid="e1">equations 1</xref> to <xref ref-type="disp-formula" rid="e3">3</xref> and <xref ref-type="disp-formula" rid="e7">7</xref> to <xref ref-type="disp-formula" rid="e9">9</xref>), is shown in <xref ref-type="table" rid="gt4">Table IV</xref>.</p>
<p>
<table-wrap id="gt3">
<label>Table III</label>
<caption>
<title>Annual mean atmospheric parameters and levels of pollutants in three different sites.</title>
</caption>
<alt-text>Table III Annual mean atmospheric parameters and levels of pollutants in three different sites.</alt-text>
<alternatives>
<graphic xlink:href="56582679013_gt4.png" position="anchor" orientation="portrait"/>
<table id="gt4-526564616c7963">
<thead style="display:none;">
<tr style="display:none;">
<th style="display:none;"/>
</tr>
</thead>
<tbody>
<tr>
<td>Site</td>
<td>North latitude</td>
<td>West longitude</td>
<td>A (m.a.s.l.)</td>
<td>RH (%)</td>
<td>TOW (fraction)</td>
<td>T (ºC)</td>
<td>Cl<sup>–</sup> (mg m<sup>–2</sup> d<sup>–1</sup>)</td>
<td>SO<sub>2</sub> (mg m<sup>–2</sup> d<sup>–1</sup>)</td>
</tr>
<tr>
<td>CIGEFI</td>
<td>09º 56’ 11”</td>
<td>84º 02’ 43”</td>
<td>1210</td>
<td>79.92</td>
<td>0.5701</td>
<td>20.29</td>
<td>3.82</td>
<td>6.06</td>
</tr>
<tr>
<td>San Luis</td>
<td>10º 00’ 54”</td>
<td>84º 01’ 36”</td>
<td>1341</td>
<td>90.19</td>
<td>0.8126</td>
<td>18.36</td>
<td>3.52</td>
<td>8.58</td>
</tr>
<tr>
<td>Santa Ana</td>
<td>09º 52’ 54”</td>
<td>84º 11’ 14”</td>
<td>1772</td>
<td>83.46</td>
<td>0.6643</td>
<td>17.41</td>
<td>4.00</td>
<td>7.02</td>
</tr>
</tbody>
</table>
</alternatives>
</table-wrap>
</p>
<p>
<table-wrap id="gt4">
<label>Table IV</label>
<caption>
<title>Atmospheric corrosion in three different sites, using<xref ref-type="disp-formula" rid="e1"> equations 1</xref> to <xref ref-type="disp-formula" rid="e3">3</xref>, <xref ref-type="disp-formula" rid="e7">7</xref> to <xref ref-type="disp-formula" rid="e9">9</xref>, and actual values, in µm y<sup>–1</sup>. Values in <italic>italics</italic> correspond to overestimations of the corrosion rate compared to actual measurements (bold black quantities). Other modeled corrosion rates showing small differences (less than 5 %) with respect to observations are underlined.</title>
</caption>
<alt-text>Table IV Atmospheric corrosion in three different sites, using equations 1 to 3, 7 to 9, and actual values, in µm y–1. Values in italics correspond to overestimations of the corrosion rate compared to actual measurements (bold black quantities). Other modeled corrosion rates showing small differences (less than 5 %) with respect to observations are underlined.</alt-text>
<alternatives>
<graphic xlink:href="56582679013_gt5.png" position="anchor" orientation="portrait"/>
<table id="gt5-526564616c7963">
<thead style="display:none;">
<tr style="display:none;">
<th style="display:none;"/>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="3">Site</td>
<td>Vcorr</td>
<td>Vcorr</td>
<td>Vcorr</td>
<td>Vcorr</td>
<td>Vcorr</td>
<td>Vcorr</td>
<td>Vcorr</td>
</tr>
<tr>
<td>model <italic>
<italic>RH</italic>
</italic>
</td>
<td>model <italic>
<italic>TOW</italic>
</italic>
</td>
<td>ISO 9223</td>
<td>Observed</td>
<td>model <italic>
<italic>RH</italic>
</italic>
</td>
<td>model <italic>
<italic>TOW</italic>
</italic>
</td>
<td>ISO 9223</td>
</tr>
<tr>
<td>(eq. 1)</td>
<td>(eq. 2)</td>
<td>(eq. 3)</td>
<td/>
<td>(eq. 7)</td>
<td>(eq. 8)</td>
<td>(eq. 9)</td>
</tr>
<tr>
<td>CIGEFI</td>
<td>
<italic>
<italic>19.2</italic>
</italic>
</td>
<td>
<italic>
<italic>20.8</italic>
</italic>
</td>
<td>
<italic>
<italic>20.8</italic>
</italic>
</td>
<td>
<bold>
<bold>17.4</bold>
</bold>
</td>
<td>16.7</td>
<td>
<italic>
<italic>18.6</italic>
</italic>
</td>
<td>
<italic>
<italic>23.8</italic>
</italic>
</td>
</tr>
<tr>
<td>San Luis</td>
<td>
<italic>
<italic>28.9</italic>
</italic>
</td>
<td>
<italic>
<italic>26.5</italic>
</italic>
</td>
<td>
<italic>
<italic>30.0</italic>
</italic>
</td>
<td>
<bold>
<bold>17.3</bold>
</bold>
</td>
<td>18.2</td>
<td>
<italic>
<italic>19.6</italic>
</italic>
</td>
<td>
<italic>
<italic>25.2</italic>
</italic>
</td>
</tr>
<tr>
<td>Santa Ana</td>
<td>
<italic>
<italic>22.5</italic>
</italic>
</td>
<td>
<italic>
<italic>22.9</italic>
</italic>
</td>
<td>
<italic>
<italic>24.9</italic>
</italic>
</td>
<td>
<bold>
<bold>16.6</bold>
</bold>
</td>
<td>
<italic>
<italic>23.4</italic>
</italic>
</td>
<td>
<italic>
<italic>23.2</italic>
</italic>
</td>
<td>
<italic>
<italic>31.0</italic>
</italic>
</td>
</tr>
</tbody>
</table>
</alternatives>
</table-wrap>
</p>
<p>Pollutant levels were similar to those utilized for the approximations with <xref ref-type="disp-formula" rid="e7">equations 7</xref> to <xref ref-type="disp-formula" rid="e9">9</xref>; however, RH and TOW did not follow the expected tendency with altitude. The reason for this behavior is probably the position of the stations in the WCV since they were located under the influence of different climatic conditions. Particularly, the station in San Luis is constantly influenced by humid air masses transported from the Caribbean region (<xref ref-type="bibr" rid="redalyc_56582679013_ref8">Campos and Castro, 1992</xref>).</p>
<p>
<xref ref-type="fig" rid="gf5">Figure 5</xref> illustrates the predicted corrosion from <xref ref-type="disp-formula" rid="e7">equations 7</xref> to <xref ref-type="disp-formula" rid="e9">9</xref> and their comparison with actual measurements.</p>
<p>
<fig id="gf5">
<label>
<bold>Fig. 5</bold>
</label>
<caption>
<title>Vcorr vs. Altitude, for a model using a) <xref ref-type="disp-formula" rid="e7">equation 7</xref> (RH, dotted line), b) equation 8 (TOW, dashed line), c) <xref ref-type="disp-formula" rid="e9">equation 9</xref> (ISO 9223, solid line). Actual measurements are represented by cross markers (+).</title>
</caption>
<alt-text>Fig. 5 Vcorr vs. Altitude, for a model using a) equation 7 (RH, dotted line), b) equation 8 (TOW, dashed line), c) equation 9 (ISO 9223, solid line). Actual measurements are represented by cross markers (+).</alt-text>
<graphic xlink:href="56582679013_gf6.png" position="anchor" orientation="portrait">
<alt-text>Fig. 5 Vcorr vs. Altitude, for a model using a) equation 7 (RH, dotted line), b) equation 8 (TOW, dashed line), c) equation 9 (ISO 9223, solid line). Actual measurements are represented by cross markers (+).</alt-text>
</graphic>
</fig>
</p>
<p>The Vcorr values from the simple linear models based on RH and TOW (<xref ref-type="disp-formula" rid="e7">equations 7</xref> and <xref ref-type="disp-formula" rid="e8">8</xref>, respectively) increased rapidly with altitude and corresponded to C2 and C3 corrosivity categories, according to the ISO 9223:2012 standard (<xref ref-type="table" rid="gt2">Table II</xref>). The corrosion in the ISO 9223:2012 model shows a more significant increase with altitude. This increase is due to the exponential behavior of <xref ref-type="disp-formula" rid="e9">equation 9</xref>, governed by the RH variable. The difference between observed values and the ISO 9223:2012 equation is around 20 % at medium altitudes. In the mountain (Santa Ana), this contrast reaches the order of 100 %.</p>
<p>Model outputs in comparison with observations presented notable differences. When the atmospheric parameters are used (<xref ref-type="disp-formula" rid="e1">equations 1</xref> and <xref ref-type="disp-formula" rid="e2">2</xref>), the deviations are greater in places with high values of <italic>RH</italic> (RH &gt; 80 %) or <italic>TOW </italic>(TOW &gt; 0.6), for example, in San Luis. When considering the simple models with altitude dependency (equations 7 and 8), there is generally a good estimation of Vcorr in the region between 1000 m.a.s.l. and 1400 m.a.s.l. Overestimation greater than 10% occurs at altitudes higher than 1500 m.a.s.l. It is important to consider that most of the population of the WCV lives within the 900 m.a.s.l to 1400 m.a.s.l altitude range (<xref ref-type="bibr" rid="redalyc_56582679013_ref19">INEC, 2011</xref>).</p>
<p>The model-based of ISO 9223:2012 (<xref ref-type="disp-formula" rid="e3">equations 3</xref> and <xref ref-type="disp-formula" rid="e9">9</xref>) presented higher values with respect to observations. This problem was already pointed out in some studies carried out in the tropical atmosphere (<xref ref-type="bibr" rid="redalyc_56582679013_ref10">Correa-Bedoya et al., 2007</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref9">Corvo et al., 2008</xref>, <xref ref-type="bibr" rid="redalyc_56582679013_ref27">Morcillo et al., 2012</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref28">Morcillo et al., 2013</xref>, <xref ref-type="bibr" rid="redalyc_56582679013_ref15">Garita-Arce et al., 2014</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref35">Rios et al., 2017</xref>; <xref ref-type="bibr" rid="redalyc_56582679013_ref42">Vera et al., 2017</xref>).</p>
<p>In <xref ref-type="fig" rid="gf6">figure 6</xref>, the shown maps complement each other. It is possible to apply both the RH- and the TOW-based models (<xref ref-type="fig" rid="gf6">Fig. 6a</xref> or <xref ref-type="fig" rid="gf6">6b</xref>, respectively) in the central region of the WCV (from 900 m.a.s.l to 1400 m.a.s.l.) and the ISO 9223:2012 model (<xref ref-type="fig" rid="gf6">Fig. 6c</xref>) overestimated the corrosion in all altitudes.</p>
<p>
<fig id="gf6">
<label>
<bold>Fig. 6</bold>
</label>
<caption>
<title>Map of Vcorr using the a) RH, b) TOW, and c) ISO models.</title>
</caption>
<alt-text>Fig. 6 Map of Vcorr using the a) RH, b) TOW, and c) ISO models.</alt-text>
<graphic xlink:href="56582679013_gf7.png" position="anchor" orientation="portrait">
<alt-text>Fig. 6 Map of Vcorr using the a) RH, b) TOW, and c) ISO models.</alt-text>
</graphic>
</fig>
</p>
</sec>
</sec>
</sec>
</sec>
<sec sec-type="conclusions">
<title>
<bold>4. Conclusions</bold>
</title>
<p>Simple models based on RH, TOW, and the ISO standard were used to determine Vcorr in the WCV. The measurements indicated intermediate (C2) levels of Vcorr in the region, with values ranging from 16.6 to 17.4 µm y<sup>–1</sup>. Almost all the proposed models presented a level of Vcorr within the C2 category.</p>
<p>The linear equations dependent on atmospheric parameters only (equations 1 and 2) always overestimated the value of Vcorr with differences between 10 % and 70 %. Conversely, the altitude-dependent models (equations 7 and 8), presented a more realistic estimation, between 1000 m.a.s.l and 1400 m.a.s.l.</p>
<p>The equation of the ISO 9223:2012 standard (<xref ref-type="disp-formula" rid="e3">equation 3</xref>) and its simplified form based on the altitude (<xref ref-type="disp-formula" rid="e9">equation 9</xref>) showed an exponential behavior governed by the increase of RH with altitude.</p>
<p>The results demonstrated that linear equations with regular parameters, such as RH, are more practical for determining Vcorr at low altitudes in the WCV, specifically in the range of 1000 m.a.s.l to 1400 m.a.s.l., where most of the population of the WCV lives. Vcorr calculations out of this range showed larger discrepancies with respect to observations (more than 10 %).</p>
<p>The ISO model overestimated the Vcorr values in the WCV for all altitudes. In some cases, the differences were greater than 20 %.</p>
<p>The WCV is not a climatically uniform region, as it shows significant spatial and temporal variations. This variability suggests the need for more assessments considering these factors, given the dependency of corrosion with RH. Future analyses should encompass mountain profiles, climatic sub-regions, and climatic periods (for example, dry and rainy seasons).</p>
</sec>
</body>
<back>
<ack>
<title>Acknowledgments</title>
<p>Special thanks to the National Meteorological Institute and the Costa Rican Electricity Institute for providing the meteorological data of the Western Central Valley. The actual corrosion data was obtained from measuring sites located at facilities of the National Power and Light Company and the Ministry of Security. This study was funded by the National Council of University Presidents (CONARE) of Costa Rica as part of a collaborative project among the State Distance University (UNED-VINVES-6-10-50), the University of Costa (UCR-VI-805-B8-650), the National High Technology Center (CeNAT-VI-269-2017), the National University (UNA- SIA: 0600-17), and the Costa Rica Institute of Technology (ITCR-VIE 1490-021).</p>
<p>Rodríguez-Yáñez acknowledges the support of the Innovation and Human Capital for Competitiveness Program (PINN) of the Ministry of Science, Technology, and Telecommunications (MICITT) of Costa Rica.</p>
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