Atmospheric Corrosion in the Tropics: The Costa Rican Central Valley Case

Abstract

The Western Central Valley (WCV) of Costa Rica is an area of interest, due to its high concentration of population and economic activity, presenting itself as a tropical monsoon-type atmospheric basin (AB), with well-defined climatic seasons (dry and rainy). The present study proposes the assessment of low carbon steel (CS) atmospheric corrosion, based on ISO 9223 (2012) and associated standards. A general analysis of the atmospheric basin effect was initially performed on these data, followed by the basic modeling of air pollutants and meteorological parameters. The WCV is an area of low contamination, which corresponds to a C2 or C3 category, according to ISO 9223. It mainly shows significant climatic seasons (dry and rainy) effects on the initial corrosion rates, but obtaining similar annual corrosion results for them. The ISO 9223 annual atmospheric corrosion model overestimated the actual obtained corrosion values, whereas linear or logarithmic models gave better results, especially when time and/or time of wetness (TOW) were considered as variables.

Full text

J. Rodriguez-Yáñez et al. / Portugaliae Electrochimica Acta 40 (2022) 409-424
409
Atmospheric Corrosion in the Tropics:
The Costa Rican Central Valley Case
J. Rodriguez-Yáñez1*, R. Brenes-Brenes2, R. Jiménez-Salas2,
M. Abdalah-Hernandez3 and J. Sanabria-Chinchilla4
1Laboratory of Urban Ecology, Distance State University, P.O. Box 474-2050,
San José, Costa Rica. ORCID. https://orcid.org/0000-0001-5539-3153
2Corrosion research center, Technological Institute of Costa Rica,
P.O. Box 10032-1000, Cartago, Costa Rica. ORCID
3National Co-laboratory of Advanced Computing- National Center
of High Technology, Pavas, San José, Costa Rica. ORCID
4Center of Electrochemistry and Organic Chemistry, University of Costa Rica,
P.O. Box 11501-2060, San José, Costa Rica, ORCID
*Corresponding author: jrodriguezy@uned.ac.cr
Received 09/09/2021; accepted 20/11/2021
https://doi.org/10.4152/pea.2022400602
Abstract
The Western Central Valley (WCV) of Costa Rica is an area of interest, due to its high
concentration of population and economic activity, presenting itself as a tropical monsoon-
type atmospheric basin (AB), with well-defined climatic seasons (dry and rainy). The present
study proposes the assessment of low carbon steel (CS) atmospheric corrosion, based on ISO
9223 (2012) and associated standards. A general analysis of the atmospheric basin effect was
initially performed on these data, followed by the basic modeling of air pollutants and
meteorological parameters. The WCV is an area of low contamination, which corresponds to
a C2 or C3 category, according to ISO 9223. It mainly shows significant climatic seasons
(dry and rainy) effects on the initial corrosion rates, but obtaining similar annual corrosion
results for them. The ISO 9223 annual atmospheric corrosion model overestimated the actual
obtained corrosion values, whereas linear or logarithmic models gave better results,
especially when time and/or time of wetness (TOW) were considered as variables.
Keywords: low CS, mathematical modeling, monsoonal climate, air pollutants, rain, TOW,
ISO 9223 and ISO 9225.
Introduction
The basic metals production is a minor economic activity in Costa Rica. The majority
of these materials are obtained by importation. Therefore, it can be set as convenient
for the country to know the corrosion mechanisms of basic metallic materials, in order
to consider their effects on its economy. Corrosion losses are estimated to be about
3% of the country's gross domestic product (GDP). Much of this impact can be
avoided with appropriate protective measures. The main losses in a tropical country

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are due to the atmospheric corrosion of structural materials, such as low CS or
galvanized steel [1, 2].
Costa Rica main urban areas are located away from the coast line, inside the
geographic region known as WCV. WCV concentrates most of the country population
(50%) and economic activities (60%). Hence, this sector is of great interest for the
assessment of the basic metals deterioration [3-5].
WCV is considered an AB, surrounded by the volcanic mountain range to the north,
and the foothills of the Talamanca mountain range to the south and the east. It has an
average altitude of 1000 m above the sea level (m.a.s.l.), with elevations exceeding the
2500 m. The climate is monsoonal, with an average annual rainfall of 2300 mm/m-2,
mainly between the months of May and November (rainy season). The temperature (T)
ranges from 20 to 25 ºC, while the relative humidity (RH) varies from 70 to 90%,
depending on the altitude and the time of the year. Winds have a main direction
associated with the Alisios or Trade winds, in the NE towards the SW direction,
according to the orography and seasonality [6-8].
In Costa Rica, atmospheric corrosion studies are generally associated to externally
funded or company projects with specific purposes, both in terms of the selected
location and the used materials. Some of them present only general information about
WCV, for low steel alloys and galvanized Fe, without considering the climatic
variability in that area [9, 10].
Atmospheric corrosion in WCV was proposed as a mild rural or light urban type of
corrosion, with low levels of contamination, and mainly dependent on the
meteorological parameters, especially RH, or its equivalent in terms of corrosion, and
TOW. This is related to the C2 or C3 corrosion levels, as stated by ISO 9223 [9-13].
None of the studies mentioned any difference in the seasonality effect on corrosion.
Meanwhile, Garita et al. (2014) performed a basic corrosion modeling estimate with
atmospheric parameters, for WCV [14].
In this work, low CS corrosion was studied to evaluate if there was a seasonal effect,
after the metal short exposure in WCV, and to examine different mathematical models
for corrosion data estimation.
Methodology
The studied area is shown in Fig. 1. The study was conducted with low CS. Low CS
composition before analysis is detailed in Table 1, and compared with that stated by
the American Society for Testing and Materials (ASTM) for A36 CS, which is
commonly used as a standard [15-17]. CS composition was evaluated by optical
emission spectrometry (OES), using a Leco model GDS500A spectrometer.
Table 1. Low CS composition and comparison with that stated by ASTM for A36 CS.
Material
Fe
%
C
%
Mn
%
Si
%
S
%
P
%
Cu
%
Exposed
CS
99.5
0.055
0
.
266
0
.
031
0
.
007
0
.
011
0
.
006
ASTM - A36 CS >99 Max. 0.25 - Max. 0.4 Max. 0.05 Max. 0.04 Min. 0.2

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Figure 1. Location map of WCV in Costa Rica.
The low CS samples were cut into 100 mm x 50 mm x 1.5 mm coupons. They were
initially cleaned with soap and water, to remove grease and dirt. Then, they were
polished with wet sandpaper of increasing grades, up to 600 grit. Later, the specimens
were cleaned in an ultrasonic bath, and rinsed with distilled water and acetone, before
being dried in air. All the coupuns were weighed and prepared for the exposure test
[17-19].
Corrosion monitoring stations were built based on ASTM G50-20 and G92-20
standards [17, 20]. Their installation sites are shown in Table 2. These stations were
located across WCV, in the main direction of the wind flow, from NE towards SW
(see Fig. 1).
Table 2. Corrosion monitoring station installation sites.
Site
North latitude
West longitude
Altitude
(m.a.s.l.)
CIGEFI
*
09º 56' 11"
84º 02' 43"
1210
San Luis 10° 00' 54" 84° 01' 36" 1341
Santa Ana 09° 52' 54” 84° 11' 14" 1772
* Centro de Investigaciones Geofísicas (Research Center in Geophysics, University of Costa
Rica).
For the corrosive atmospheric classification proposed by ISO 9223, climate
parameters were evaluated based on meteorological data provided by the National
Meteorological Institute (IMN) and the Costa Rican Institute of Electricity (ICE), at
stations near the sampling sites. The considered parameters were T, RH, rainfall (R)
and wind (W). TOW was estimated according to ISO 9223, by counting the number
of hours when RH was greater than or equal to 80%, and T was higher than 0 ºC [13].
Atmospheric pollutants were evaluated following ISO 9225 (2012), using humidity
candles for chlorides (Cl), and passive monitoring, such as Passam AG (2012), for
sulfur dioxide (SO2), ozone (O3) and nitrogen oxides (NOx) [21, 22].
Public volcanological data, on the dispersion of contaminants emitted by nearby
volcanoes (Irazú, Turrialba, in the SE, and Poás, in the North of WCV), provided by

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the Volcanological and Seismological Observatory of Costa Rica (OVSICORI) and
the Environmental Observatory of the National University, with the support of IMN
and the Laboratory of Chemistry of the Atmosphere (LAQAT), were also analyzed.
The influence of tropical storms was also considered [23].
CS samples corrosion assessment was performed through the weight loss (WL)
gravimetric technique, by chemical pickling, according to ASTM G1 (2003), using
the 3.35 method [18].
Two series of samples were exposed to the corrosion process in the rainy (from
September 2018 to September 2019) and dry seasons (from March 2019 to April
2020), respectively.
The 2, 6 and 12-month-old samples were additionally analyzed by Scanning
Electronic Microscopy (SEM) and X-ray Diffraction (XRD). The SEM microscope
was a Carl Zeiss Sigma 300 model, and the diffractometer was a Bruker XDS D8
Focus model.
Corrosion models
The annual values gravimetrically obtained were compared with those established by
the model given in ISO 9223 [13] for low CS, according to the climatic and pollution
parameters for each site, as per the formula:
𝑉𝑐𝑜𝑟𝑟 = 1.77 𝑃
.𝑒𝑥𝑝 (0.020 𝑅𝐻 + 𝑓
) + 0.102 𝑆
. 𝑒𝑥𝑝 (0.033 𝑅𝐻 + 0.040 𝑇) (1)
𝑓
 = 0.150 × (𝑇 − 10), 𝑖𝑓 𝑇 ≤ 10
𝑓
 = −0.054 × (𝑇 − 10), 𝑖𝑓 𝑇 > 10
N = 128 R2 = 0.85
where Vcorr = corrosion rate in the first year (µm y-1), fst = factor for steel (due to the
change of T effect on atmospheric corrosion from a critical temperature near to10 ºC),
T = annual average temperature (°C), RH = annual average relative humidity, %Pd =
annual average SO2 deposition (mg/m-2/d-1) and Sd = annual average Cl- deposition
(mg/m-2/d-1).
Some authors [14, 24-26] proposed a corrosion model based on time, where the most
simplified equation corresponds to:
𝐿𝑜𝑔 𝐶𝑜𝑟𝑟 = 𝐴 + 𝑛 𝐿𝑜𝑔 𝑡 (2)
where Corr = corrosion accumulated in time (µm), t = accumulated time (in years)
and n = slope, which is inversely associated with the protection level of the oxide
surface. The A constant is equivalent to Log (Corr), where Corr is the corrosion in the
first year.
Other applicable models are lineal, logarithmic or bi-logarithmic [26-30] equations,
which are stated as:
𝐶𝑜𝑟𝑟 = 𝑎 + 𝑏 𝐶𝑙 + 𝑐 𝑆𝑂+ 𝑑 𝑇𝑂𝑊 + 𝑒 𝑅 (3a)
𝐶𝑜𝑟𝑟 = 𝑎 + 𝑏 𝐿𝑜𝑔 𝐶𝑙 + 𝑐 𝐿𝑜𝑔 𝑆𝑂+ 𝑑 𝐿𝑜𝑔 𝑇𝑂𝑊 + 𝑒 𝐿𝑜𝑔 𝑅 (3b)
log 𝐶𝑜𝑟𝑟 = 𝑎 + 𝑛 log 𝑡 + 𝑏 𝐶𝑙 + 𝑐 𝑆𝑂+ 𝑑 𝑇𝑂𝑊 + 𝑒 𝑅 (4)

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where TOW = accumulated time of wetness (in h), SO2 = accumulated SO2 deposition
(mg/m-2), Cl = accumulated Cl- deposition (mg/m-2) and R = accumulated rain (mg/m-2).
These equations were contrasted in different seasons, for each site, and by group.
Modeling control parameters
Three possible relationships between the experimental and modeling results were
considered as control parameters: the Pearson's correlation coefficient (PR2), which
should be greater than 0.7, to be taken as acceptable; the residual sum of squares
(RSS), a performance evaluator, which is expected to be minimum; and the Fisher's
index (F) that should be higher than 100 [31-33].
Prior to the iterative modeling process, Principal Component Analysis (PCA) and
basic statistic tests (U Mann Whitney, Kruskal Wallis and Pearson's correlations
factors) were initially carried out to determine the main factors [31, 32]. Based on
this, the models of the equations 3 and 4 were developed, considering that they must
had more data than variables to be modeled.
Model fitting and parameter determination were performed in Python programming
language, using the Pandas software library, for data management, and the stat models
package, for parameters estimation and control parameters calculation.
Results and discussion
Corrosion and associated parameters
Corrosion assessment, at the sampling sites, and the meteorological and
contamination data are shown in Tables 3 and 4, for rainy and dry seasons,
respectively. All parameters are expressed in a cumulative form.
Table 3. Corrosion data and accumulated parameters for the first series (rainy season).
Sites Time
(days)
Corr
(µm)
R
(mm/m-2)
Cl
(mg/m-2)
SO2
(mg/m-2)
TOW
(h)
CIGEFI
30
3.
6
305.4
109.
3
199.
1
540
CIGEFI 60 6.5 384.2 299.7 519.9 1054
CIGEFI 123 8.5 404.0 534.4 1659.3 1738
CIGEFI 179 11.6 404.0 819.6 2208.1 2272
CIGEFI 273 15.3 1077.2 1354.5 3157.2 3544
CIGEFI 368 16.7 1640.6 1408.7 3678.9 4992
San Luis 30 2.1 241.8 20.7 448.1 645
San Luis
60
5.0
294.4
26.8
667.8
1284
San Luis 123 7.7 354.3 174.8 2160.6 2489
San Luis 179 10.6 381.5 249.7 2637.8 3297
San Luis 273 14.0 717.8 658.5 3772.6 5147
San Luis 364 17.5 1113.3 1311.7 4906.5 7117
Santa Ana
32
2.
1
496.8
50.
8
205.9
685
Santa Ana 62 8.4 573.0 56.3 456.3 1270
Santa Ana
125
10.
2
591.6
49
9
.
0
1632.
4
2058
Santa Ana 184 14.2 613.2 926.5 2404.6 2683
Santa Ana
275
14.7
1728.1
1314.
5
3279.6
4168
Santa Ana
369
17.
3 2205.4
1458.3
3916.
5
5855

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Table 4. Corrosion data and accumulated parameters for the second series (dry season).
Sites Time
(days)
Corr
(µm)
R
(mm/m-2)
Cl
(mg/m-2)
SO2
(mg/m-2)
TOW
(h)
CIGEFI
35
3.7
17.8
358.4
441.0
319
CIGEFI 64 6.1 244.8 418.5 853.1 769
CIGEFI 126 9.1 816.0 541.6 1081.7 1754
CIGEFI 189 12.2 1236.6 589.1 1470.8 2720
CIGEFI 274 14.1 1803.2 825.3 2748.3 4079
CIGEFI 399 17.9 1883.6 1083.7 3765.1 5328
San Luis 35 2.2 47.5 230.5 582.7 552
San Luis 64 4.4 190.5 344.9 1039.8 1145
San Luis
126
9.5
492.8
809.
3
1480.7
2488
San Luis 185 11..8 728..7 1062.0. 2268.7 3747
San Luis
274
15.
1
1261.4
1611.
9
3463.3
5686
San Luis 399 16.5 1402.1 1835.2 4630.0 8164
Santa Ana 32 2.8 226.5 363.5 299.6 338
Santa Ana 61 4.2 622.2 413.7 639.0 870
Santa Ana 123 8.4 1203.7 466.4 968.5 2034
Santa Ana 185 11.4 1592.2 563.0 1511.9 3172
Santa Ana 271 15..8 2402..0 867.6 2839.9 4830
Santa Ana
396
20.
4
2505.9
1239.
6
4413.
7
6414
Note: The final time for the second series is longer than a year, because, on March 2020, the COVID-
19 pandemics caused mobilization restrictions in Costa Rica.
Table 5 shows the annual mean values of Cl, SO2, RH and T, while Table 6 presents
the average W, NOx, and O3 data for the studied sites.
Table 5. Annual mean values of Cl, SO2, RH and T, for each season.
Site Cl
(mg/m-2/day-1)
SO2
(mg/m-2/day-1)
RH
(%)
T
(ºC)
Rainy
Dry
Rainy
Dry
Rainy
Dry
Rainy
Dry
CIGEFI 3.8 2.7 10.0 9.4 80.2 76.5 20.4 20.5
San Luis
3.6 4.6 13.5 11.6 87.5 90.1 17.8 18.2
Santa Ana
3.9
3.1
10.6
11.2
84.4
83.9
17.6
17.6
Table 6. Average annual W, NOx and O3 values at each site.
Site Wind
direction
Wind speed
(m/s-1)
O3
(µg/m-3)
NOx
(µg/m-3)
Rainy
Dry
Rainy
Dry
Rainy
Dry
CIGEFI NE 2.0 2.0 28.4 30.9 13.5 16.0
San Luis ENE 3.0 3.0 27.2 30.8 7.1 7.7
Santa Ana N (*) 3.0 3.1 33.2 41.7 4.6 5.8
Note: (*) The station has an orographic effect that causes the wind to move in a preferential N
direction, instead of the usual NE route associated with the Alisios winds.
The average annual values for Cl and SO2 are low. These were defined, by ISO 9223,
as S1 and P0, respectively. In a similar manner, the O3 and NOx values were found to
be in the low contamination level, as stated by ISO 9223. All pollutant parameters
measured for WCV indicate a rural or light urban atmosphere [13].

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415
The analysis of the accumulated SO2 levels, as a function of time, shows a steady
increase in them. The small differences between stations are associated to the volcanic
activities wind dispersion effects. Regardless of that, the Cl levels are very dependent
on the site and season of the year, and influenced by the seasonal wind speed.
The principal wind direction is the expected, and mostly affected by the strength of
the Alisios wind (from the NE) in each season, and by orographic effects that produce
a small increase in O3 in the Santa Ana site [34].
The mean RH value is relatively high, and usually above 80%, while T is above 17 ºC,
being both relatively independent of the seasons. The accumulated R decreases from NE
to SW, in WCV, almost equally in both seasons, with lower values than the historical
mean in the San Luis and CIGEFI sites [6, 8].
The annual TOW values are mainly in the range of 5, with more than 5000 h, a
considerably high figure [13, 35]. The Corr values measured in both campaigns
(started in the rainy or dry seasons) correspond to the C2 category in ISO 9223 [13],
in the range from 15 to 18 µm per year. This result is consistent with the concept of
rural or light urban atmosphere and high TOW values [9, 14, 36, 37].
Volcanic activity and tropical storms
The volcanic activity during the studied period was low, mainly originated in the
Turrialba volcano, as a result of eruptive emissions between September and December
2018, and in April 2019. The general SW wind direction (Alisios winds) transports
most of the Turrialba emissions far from WCV, located to the NW. Part of these
emissions were directed to WCV, in November and December, due to prevalent
winds, but did not have a significant influence on the overall values. There were also
slight emissions from the Poás volcano, between November and December 2018, but
the main direction was towards other areas located in the WCV west side [23].
No tropical storms have affected WCV during the course of this work [38, 39].
a) b)
c)
Figure 2. Vcorr values in both seasons (rainy: circles with full line; and dry: triangles with
dashed line), in the stations of: a) Santa Ana, b) CIGEFI and c) San Luis, respectively.
0
20
40
60
0 90 180 270 360
Vcorr (µm y-1)
Time (days)
0
10
20
30
40
0 90 180 270 360
Vcorr (µm y-1)
Time (days)
0,00
20,00
40,00
60,00
0 90 180 270 360
Vcorr (µm y-1)
Time (days)

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Relationship between seasons
In all sites, accumulated Corr general trend was found to be logarithmic, while Vcorr
had an exponential decay, which can be seen in Fig. 2, for all sites. Corr was dependent
on the site characteristics, but not on the onset season, while Vcorr was affected by the
onset season in the first months of corrosion.
The relation of Corr with each season is relatively linear, according to the equation
which states that Corr (dry) = a Corr (rainy) + b, where the slope is near to 1 (see
Table 7).
Table 7. Linear fit for the correlation between Corr dry vs. Corr rainy.
Sites
a
b
R
2
Santa
Ana
1
.
0162
0
.
0124
0
.
9751
CIGEFI
0
.
9833
0
.
5789
0
.
9633
San Luis 1.1374 -2.1735 0.8470
Vcorr values do not present peaks in the first months, for the Santa Ana site, while, on
the other sites, this situation is observed, especially in the rainy season. The initial
Vcorr values in the rainy season increase when the wind is moving from SW to NE, in
WCV (see Fig. 2). CIGEFI and San Luis sites are clearly affected by R and RE effects,
possibly because the decrease in the intensity of the Alisios winds brings moisture
from the Pacific coast that concentrates in the WCV center and north side, due to the
higher altitude of the volcanic mountain range [6-8].
SEM and DRX
The basic oxide composition is associated to goethite (G) and lepidocrocite (L), in
proportions of 35 and 65%, respectively, for the one-year analysis. The values at 2
and 6 months show a similar composition and proportion, with a little trend towards
a decrease in L values and an increase in G values, with time. This process is related
to the oxide surface stabilization.
The annual corrosion process is similar in all sites, with a homogeneous penetration
edge, and SEM observation of typical L and G structures. Fig. 3 shows the typical
structure of the obtained oxide.
Figure 3. SEM image of the typical oxide structure in the CS sample from Santa Ana site.

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Data models
The values obtained for the different models, considering the climatic season and
sampling sites, are presented below.
ISO model (equation 1) and measured values
The equation 1 values from ISO 9223 always present higher results than the measured
values obtained for WCV (Table 8). This is consistent with the tropical conditions and
low contamination levels in WCV. In this situation, the equation is not so
representative, because it is mostly originated from subtropical data that reflect
different climacteric conditions [9, 14, 28, 36, 37, 40, 41].
Table 8. Annual Vcorr values (µm/y-1) from ISO 9223 (eq. 1), and those measured in each
site.
ISO 9223
Measured
values
A (m.a.s.l.)
Site
Rainy
Dry
Rainy
Dry
1210
CIGEFI
24
.
1
20
.3
16
.
7
17
.9
1341 San Luis 34.1 35.3 17.5 16.5
1717 Santa Ana 29.5 28.7 17.3 20.4
Note: actual dry season values were calculated for the sampling time.
Corr vs. time model (equation 2)
Table 9 shows the correlations associated with equation 2, for the stations, in the
different seasons, where Log (Corr) is the experimental value related to A, obtained
at each site.
Table 9. Parameters of equation 2, in the rainy and dry seasons.
Rainy
season
Dry season
Sites
A
n
PR
2
Log Corr
A
n
PR
2
Log Corr
CIGEFI
1.2656
0.8183
0.9824
1.2194
1.2444
0.6364
0.9920
1.213
7
San Luis 1.2427 0.6093 0.9850 1.2445 1.2759 0.8517 0.9595 1.1799
Santa Ana
1.3173
0.7764
0.8392
1.2323
1.2923
0.8138
0.9968
1.2740
General 1.2753 0.7346 0.8998
1.2711 0.7683 0.9590
The sites show correlations with PR2 values generally higher than 0.9, regardless of
the season. Parameter A has, in general, a good correspondence with Log (Corr) of
real values in one year, and it is similar in all equations.
The n constant has values in the range from 0.60 to 0.85, with an average of 0.73 to
0.76, for the general equations. These values imply corrosion moderate or partial
attenuation by the oxides surface formation, which tends to stabilize Vcorr over time,
in areas such as WCV [14, 26].
While the general equations by season are similar, they provide a general way for
estimating low CS corrosion over time, for WCV. In these equations, the correlation
in the dry season is more stable in the early stages, and less dependent on the
conditions of each site, thus presenting a better PR2. The global equation based in
equation 2, for WCV, is:

J. Rodriguez-Yáñez et al. / Portugaliae Electrochimica Acta 40 (2022) 409-424
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Log Corr = 1.2729 + 0.7505 Log t PR2= 0.9277 (5)
Equation 2 usually provides a good fit for low CS in less contaminated media, over
short to medium time periods (1 to 5 years) [9, 14, 24-30, 42-46].
Lineal and logarithmic models (equations 3 and 4)
Pearson’s correlation coefficients for each parameter, in relation to corrosion, were
calculated (p > 0.01). The values, for all parameters, have a good correlation (more
than 0.7). SO2 and TOW have the best correlations, followed by Cl and R (see Table
10).
Table 10. Pearson's correlation coefficient between variables.
Corr
(µm)
R
(mm/m-2)
Cl
(mg/m-2)
TOW
(h)
SO2
(mg/m-2)
Corr
1
0
.
788
0
.
827
0
.
949
0
.
903
Rain
1 0.671 0.765
0.771
Cl 1 0.853
0.842
TOW
1 0.952
SO2 1
Comparisons between seasons (U Mann Witney, p > 0.05) and sites (Kruskal Wallis,
p > 0.05) show no significant differences.
Since there are no significant seasonal differences, the modeling was globally
considered by site, and in WCV, with different numbers of variables. As stated in the
methodology, the control parameters to evaluate the quality of models were PR2, RSS
and F.
The best results for equation 3, in its lineal and logarithmic forms, were:
Corr = 2.708 + 2.828 E-3 SO2 + 1.283 E-3 Cl – 4.603 E-4 TOW+ 2.663 E-3 R (6)
PR2 = 0.9213 RSS = 77.68 F = 90.77
and
Corr = -30.63 + 1.496 Log SO2 + 0.911 Log Cl + 2.432 Log TOW + 0.919 Log R (7)
PR2 = 0.9193 RSS = 79.65 F = 88.33
There was no substantial improvement when using the linear form. Similar equations
were obtained for tropical environments, by other authors [10, 14, 26-30, 36, 37, 40,
41, 43-46].
The most basic equations with one parameter are the ones that include TOW,
expressed as a logarithmic regression. TOW is usually the most important parameter
to control the corrosion processes in tropical environments, especially far from the
coast, and with low levels of pollutants [9, 11, 14, 26, 35-37, 41-46].
Corr = 12.793*Log TOW – 32.20 (8)
PR2= 0.881 RSS= 117.99 F= 250.5

J. Rodriguez-Yáñez et al. / Portugaliae Electrochimica Acta 40 (2022) 409-424
419
Table 11 presents equation 4 coefficients for the best correlations with a different
number of global variables, in the whole WCV.
Equation 4 is an extension of equation 2. The high correlation of corrosion with time
limits the improvement obtained with the addition of new variables. This is seen in a
somewhat higher PR2 value, with respect to equation 5, even when there is a decrease
in the number of variables (Table 11) [14, 43].
The most influential variable on corrosion, in equation 4, over time, is SO2. Even so,
equation 4 does not improve corrosion estimation, being more complex than equations
2 and 3.
Table 11. The best correlation obtained for WCV, in general, for equation 4.
Log t
Cl
SO
2
TOW
R
P
R
2
RSS
F
#
variables
a n b c d e
5
1.5435
1.0130
6.99E
-
06
-
6.89E
-
05
3.28E
-
06
-
3.17E
-
05
0.9427
1.71E
-
0
1
98.80
4 1.5421
1.0119
-6.48E-05 8.00E-06 ND -2.99E-05 0.9427
1.71E-01
127.54
3
1.5442
1.0136
ND
-
6.31E
-
05
ND
-
2.93E
-
05
0.9427
1.71E
-
01
175.40
2 1.4926
0.9650
ND -6.13E-05
ND ND 0.9408
1.76E-01
262.19
Early mathematical models of atmospheric corrosion were based on equations 2 and
3. These were used both cumulatively, and for sites comparison on annual corrosion
[9, 11, 14, 24-29, 46-49]. From these models, the main parameters to be considered
for atmospheric corrosion, according to the environment, were established.
For the case of rural or light urban atmospheres, the environmental factors were more
important than the pollutants, obtaining better relationships with time and TOW.
Subsequent studies in rural tropical bionetworks showed the strong influence of
environmental factors, with higher corrosion rates than those of other subtropical-eco-
systems under the same ecological conditions [9, 10, 14, 24, 36, 37, 40, 43, 45, 46,
48, 50-56].
For WCV, equation 2 is presented as a model with a very good correlation between
Corr and time, according to equation 5, while equation 3 generates a complex model
of which simplification in rural tropical environments tends to be a function of t, RH
and/or TOW [14, 28, 36, 37, 43, 45, 50-54]. This agrees, in this case, with the result
proposed for WCV, in equation 8.
Equation 4 arises within the process of improving corrosion modeling, by proposing
a combination between equations 2 and 3. This equation improves the results, when
the contamination effect is more important than time dependence. For WCV, there
was no substantial improvement in the corrosion evaluation, and the dependence was
associated with time and SO2 [14, 26-30, 33, 50, 55, 56].
In a similar way, equation 1, stated in ISO 9223, arises from worldwide corrosion
evaluations. In this one, there are few tropical data within rural environments, so, it
usually gives overestimated values, as in the WCV case [14, 27, 28, 41, 46, 48, 52,
55, 56].
Tropical corrosion assessments in rural environments do not show significant
differences in relation to seasonality. However, they do show initial corrosion rates

J. Rodriguez-Yáñez et al. / Portugaliae Electrochimica Acta 40 (2022) 409-424
420
dependent on the onset corrosion time, and in relation to TOW levels [37, 50, 51].
This is consistent with the results obtained for WCV.
Conclusions
The final low CS Corr values, after one year of exposure, did not show significant
differences with the starting climatic season, or with the monitoring site at WCV. On
the other hand, the initial corrosion values, during the first six months, were dependent
on the site climatic conditions. Vcorr values were higher when atmospheric corrosion
started during the rainy season and the sites had less rainfall, although there were high
TOW values. Because of the above, the modeling was reduced to a single environment
independent of the climatic season. While low pollution decreases the influence of
these parameters on complex models, making simplified models using time or TOW
produces adequate and less complex results. The ISO 9223 equation estimation for
annual corrosion is very high, possibly because it is based on measurements in non-
tropical environments.
Acknowledgements
Special thanks to the National Meteorological Institute and the Costa Rican Electricity
Institute, for providing the WCV meteorological data. The actual corrosion data were
obtained from the measurement of the sites located at the 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 Rica (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).
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.
Authors’ contributions
J. Rodriguez-Yáñez: conceived and designed the analysis; collected the data;
inserted the data or analysis tools; performed the analysis; wrote the paper. R. Brenes-
Brenes: conceived and designed the analysis; collected the data; inserted the data or
analysis tools; reviewed the paper. R. Jiménez-Salas: conceived and designed the
analysis; collected the data; wrote the paper. M. Abdalah Hernandez: inserted data
or analysis tools; performed the analysis; wrote the paper; made language revision. J.
Sanabria-Chinchilla: conceived and designed the analysis; collected the data;
performed the analysis; reviewed the paper.
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