Annual Atmospheric Corrosion of Carbon Steel Worldwide. An Integration of ISOCORRAG, ICP/UNECE and MICAT Databases

In the 1980s, three ambitious international programmes on atmospheric corrosion (ISOCORRAG, ICP/UNECE and MICAT), involving the participation of a total of 38 countries on four continents, Europe, America, Asia and Oceania, were launched. Though each programme has its own particular characteristics, the similarity of the basic methodologies used makes it possible to integrate the databases obtained in each case. This paper addresses such an integration with the aim of establishing simple universal damage functions (DF) between first year carbon steel corrosion in the different atmospheres and available environmental variables, both meteorological (temperature (T), relative humidity (RH), precipitation (P), and time of wetness (TOW)) and pollution (SO2 and NaCl). In the statistical processing of the data, it has been chosen to differentiate between marine atmospheres and those in which the chloride deposition rate is insignificant (<3 mg/m2.d). In the DF established for non-marine atmospheres a great influence of the SO2 content in the atmosphere was seen, as well as lesser effects by the meteorological parameters of RH and T. Both NaCl and SO2 pollutants, in that order, are seen to be the most influential variables in marine atmospheres, along with a smaller impact of TOW.


Introduction
The economic impact of corrosion of metallic structures is a matter of great relevance throughout the world. The World Corrosion Organisation (WCO) currently estimates the direct cost of corrosion worldwide at between €1.3 and 1.4 trillion, which is equivalent to 3.8% of the global Gross Domestic Product (GDP). More than half of the considerable damage due to corrosion is a result of atmospheric impacts on materials, which is logical considering that most metallic equipment and structures operate in the atmospheric environment. For this reason, the action of the atmosphere on metals is one of the major issues in corrosion science.
In a perfectly dry atmosphere, metallic corrosion progresses at an extremely low rate, and for practical purposes can be ignored. However, on wet surfaces, corrosion can be quite severe, as the atmospheric corrosion process is the sum of the individual corrosion processes that take place whenever an electrolyte layer forms on the metal surface. However, for the corrosion rate to be really significant, the atmosphere must also be polluted. Of all atmospheric pollutants, chlorides from marine aerosol and sulphur dioxide (SO 2 ) mainly from the combustion of fossil fuels, are the most common aggressive agents in the atmosphere.
It is a well-known fact, which has been proven by practical experience with real structure behaviour and the results of numerous tests, that the corrosion rate of metals in the atmosphere can be tens or even hundreds of times higher in some places than in others. Thus, it is of great interest to understand the basic variables that operate in atmospheric corrosion and in order to establish a classification of the aggressiveness of an atmosphere. The best possible knowledge of the factors that affect atmospheric corrosivity would obviously help to plan anticorrosive measures for metals in a given environment.
In the 1980s, three different cooperative studies involving the participation of a large number of countries were carried out: • ISOCORRAG cooperative programme. This programme was designed by the Working Group/WG 4 of ISO 156 Technical Committee "Corrosion of metals and alloys", with the aim of standardising atmospheric corrosion tests) [1]. The Programme began in the year 1986 and, as a result of the efforts of WG 4, four international standards were developed: ISO 9223 [2,3], ISO 9224 [4], ISO 9225 [5] and ISO 9226 [6]. These standards were based on an extensive review of atmospheric exposure programmes carried out in Europe, North America, and Asia. The aim of drawing up these documents was to establish simple and practical guidelines for the technicians responsible for designing structures to be exposed to the atmosphere and for corrosion engineers responsible for adopting anticorrosive protection measures. ISO 9223 [2] provided a general classification system for atmospheres based either on 1-year coupon exposures or on measurements of environmental parameters to estimate time of wetness (TOW), sulphur dioxide concentration or deposition rate, and sodium chloride deposition rate. ISO 9224 provided an approach to calculating the extent of corrosion damage from extended exposures for five types of engineering metals based on application of guiding corrosion values (average and steady-state corrosion rates) for each corrosivity categories in ISO 9223. ISO 9225 provided the measurements techniques for the sulphur dioxide concentration or deposition rate, and sodium chloride deposition rate, needed as classification criteria in ISO 9223. ISO 9226 provided the procedure for obtaining one-year atmospheric corrosion measurements on standard coupons. • MICAT cooperative programme: "Ibero-American Atmospheric Corrosivity Map" [7]. The MICAT programme was launched in 1988 as part of the Ibero-American CYTED "Science and Technology for Development" international programme and ended after six years of activities. Fourteen countries participated in the programme, whose goals were: (i) to obtain a greater knowledge of atmospheric corrosion mechanisms in the different environments of Ibero-America; (ii) to establish, by means of suitable statistical analysis of the results obtained, mathematical models that allow the calculation of atmospheric corrosion as a function of climate and pollution parameters; and (iii) to elaborate atmospheric corrosivity maps of the Ibero-American region. • ICP/UNECE cooperative programme [8]. Airborne acidifying pollutants are known to be one of the major causes of corrosion of different materials, including the extensive damage that has been observed on historic and cultural monuments. In order to fill some important gaps in the knowledge of this field, the Executive Body for the Convention on Long-Range Transboundary Air Pollution (CLRTAP) decided to launch an International Cooperative Programme within the United Nations Economic Commission for Europe (ICP/UNECE). The programme started in September 1987 and initially involved exposure at 39 test sites in 11 European countries and in the United States and Canada. The aim of the programme was to perform a quantitative evaluation of the effect of sulphur pollutants in combination with NOx and other pollutants as well as climatic parameters on the atmospheric corrosion of important materials. Figure 1 shows the countries participating in each one of these programmes. The atmospheric corrosion stations are basically located in Europe, America and Asia, covering a broad range of meteorological and pollution conditions. Though the three programmes, ISOCORRAG, ICP/UNECE and MICAT, each have their own particular characteristics, they nevertheless share a number of common objectives. The similarity of certain aspects of their methodologies allows a welcome meeting point between the three programmes, as was suggested by Morcillo in the 11th International Corrosion Congress held in Florence in April 1990, in the session on atmospheric corrosion where the three cooperative programmes were presented [9][10][11]. Such a meeting point would allow, for the first time, a worldwide perspective (38 countries) on the problem of atmospheric corrosion, covering a broad spectrum of climatological and atmospheric pollution conditions, never before considered in the abundant published literature on atmospheric corrosion. This idea was taken up at UNECE (Figure 2) by the "Working Group on Effects" of Executive Body for the Convention on Long-Range Transboundary Air Pollution [12]. programmes were presented [9][10][11]. Such a meeting point would allow, for the first time, a worldwide perspective (38 countries) on the problem of atmospheric corrosion, covering a broad spectrum of climatological and atmospheric pollution conditions, never before considered in the abundant published literature on atmospheric corrosion. This idea was taken up at UNECE (Figure 2) by the "Working Group on Effects" of Executive Body for the Convention on Long-Range Transboundary Air Pollution [12].  The statistical analysis of data obtained in atmospheric corrosion studies in order to obtain correlation equations that allow the estimation of annual corrosion rates from meteorological and pollution parameters is a matter of great interest. Such equations are known as damage or dose/response functions. They often incorporate the SO2 concentration, the chloride concentration in areas close to the sea, and a parameter representing the wetness of the metallic surface (relative humidity, number of days of rain per year, time of wetness, etc.). Models for predicting the corrosion  programmes were presented [9][10][11]. Such a meeting point would allow, for the first time, a worldwide perspective (38 countries) on the problem of atmospheric corrosion, covering a broad spectrum of climatological and atmospheric pollution conditions, never before considered in the abundant published literature on atmospheric corrosion. This idea was taken up at UNECE (Figure 2) by the "Working Group on Effects" of Executive Body for the Convention on Long-Range Transboundary Air Pollution [12].  The statistical analysis of data obtained in atmospheric corrosion studies in order to obtain correlation equations that allow the estimation of annual corrosion rates from meteorological and pollution parameters is a matter of great interest. Such equations are known as damage or dose/response functions. They often incorporate the SO2 concentration, the chloride concentration in areas close to the sea, and a parameter representing the wetness of the metallic surface (relative humidity, number of days of rain per year, time of wetness, etc.). Models for predicting the corrosion The statistical analysis of data obtained in atmospheric corrosion studies in order to obtain correlation equations that allow the estimation of annual corrosion rates from meteorological and pollution parameters is a matter of great interest. Such equations are known as damage or dose/response functions. They often incorporate the SO 2 concentration, the chloride concentration in areas close to the sea, and a parameter representing the wetness of the metallic surface (relative humidity, number of days of rain per year, time of wetness, etc.). Models for predicting the corrosion damage of metals in the atmosphere are useful when it comes to answering questions on the durability of metallic structures, determining the economic costs of damage associated with the degradation of materials, or acquiring knowledge about the effect of environmental variables on corrosion kinetics.
The purpose of this work is to bring together the three databases from the three international cooperative programmes (ICP/UNECE, MICAT and ISOCORRAG), carrying out a statistical analysis of the results they contain in order to establish mathematical expressions which allow an estimation of the extent of atmospheric corrosion of carbon steel during first-year exposure as a function of meteorological and pollution parameters.

ICP/UNECE Programme
Twenty-four countries participated in the exposure programme with a total of 55 exposure sites. These sites included industrial, urban and rural atmospheres. Marine atmosphere exposures were not included. A list of the sites together with their code is given in Table 1.
Exposure always started in the autumn, typically from October of one year to September of the following year. The test site network originally consisted of 39 sites, which were all part of the original eight-year exposure between 1987 and 1995. Subsequently, in a four-year exposure programme carried out between 1997 and 2001, only part of the original sites were kept and eight new test sites were added. Since then, new sites have joined.  Figure 3 shows a diagram of the exposure schedule. For each exposure and site, three identical flat samples were exposed. Average corrosion values for these three panels were obtained. A detailed description of the material and methods for measuring environmental parameters and the evaluation of corrosion attack is provided in Reference [8]. Abundant literature has been published on these models and damage functions. For instance, for long-term prediction of carbon steel atmospheric corrosion, mention may be made of the work of Benarie and Lipfert [13], Pourbaix et al. [14], Feliu et al. [15,16], Knotková and Barton [17], Kucera [18], Mc Cuen and Albrecht [19], Albrecht and Hall [20], Panchenko et al. [21,22], Melchers [23,24], etc. Recent reviews on corrosion models for long-term prediction of atmospheric corrosion has been made by Morcillo et al. [25] and Adikari and Munasinghe [26].
The purpose of this work is to bring together the three databases from the three international cooperative programmes (ICP/UNECE, MICAT and ISOCORRAG), carrying out a statistical analysis of the results they contain in order to establish mathematical expressions which allow an estimation of the extent of atmospheric corrosion of carbon steel during first-year exposure as a function of meteorological and pollution parameters.

ICP/UNECE Programme
Twenty-four countries participated in the exposure programme with a total of 55 exposure sites. These sites included industrial, urban and rural atmospheres. Marine atmosphere exposures were not included. A list of the sites together with their code is given in Table 1.  Figure 3 shows a diagram of the exposure schedule. For each exposure and site, three identical flat samples were exposed. Average corrosion values for these three panels were obtained. A detailed description of the material and methods for measuring environmental parameters and the evaluation of corrosion attack is provided in Reference [8].

ISOCORRAG Programme
Fourteen countries participated in the exposure programme with a total of 53 exposure sites. These sites included industrial, urban, rural, marine and costal locations in temperate, tropical and arctic zones. A list of the sites together with their code is given in Table 2.
Flat carbon steel specimens were exposed in triplicate, fixing their size and thickness in accordance with the provisions of standard ISO 8565 [27]. A detailed description of the exposed material is provided in Reference [1].
A set of specimens was initially exposed for one-year exposure at each site. After six months, another set of specimens was exposed for one-year exposure. After one year, the first set of one-year exposed specimens was removed and another set of one-year specimens was exposed. Every six months, this process was repeated until six sets of specimens had been exposed for one year. Figure 4 shows a diagram of the exposure schedule. The original exposure was planned to begin in the autumn of 1986, but several delays occurred at various sites.
A detailed description of the material and methods for measuring environmental parameters and the evaluation of corrosion attack is provided in Reference [1].

MICAT Programme
Fourteen countries participated in the exposure programme with a total of 75 exposure sites. These sites included industrial, urban, rural and marine atmospheres. A list of the sites together with their code is given in Table 3.
Flat carbon steel panels were exposed in triplicate. A detailed description of the exposed material can be found in the book published with all the results of the project [7]. Figure 4 shows a diagram of the exposure schedule. The original exposure was planned to begin in 1989, but several delays occurred at various sites.

MICAT Programme
Fourteen countries participated in the exposure programme with a total of 75 exposure sites. These sites included industrial, urban, rural and marine atmospheres. A list of the sites together with their code is given in Table 3. Flat carbon steel panels were exposed in triplicate. A detailed description of the exposed material can be found in the book published with all the results of the project [7]. Figure 4 shows a diagram of the exposure schedule. The original exposure was planned to begin in 1989, but several delays occurred at various sites.
A detailed description of the material and methods for measuring environmental parameters and the evaluation of corrosion attack is provided in Reference [7].

Analysis of Data Properties
Before statistically analysing all the data collected from the various sources (data mining), data screening has been carried out. There follows a description of the criteria governing this screening:

1.
Extremely cold stations, with annual average temperatures below 0 • C, have been removed from the statistical analysis. Such is the case of the stations at Svanvik (Norway), Murmansk and Ojmjakon (USSR), Jubany (Argentina), Marsch (Chile) and Artigas (Uruguay), the latter three being Antarctic scientific bases. Low temperatures cause the metallic surface to be covered with an ice layer for long time periods during the year, considerably impeding the development of corrosion processes. This ice layer reduces oxygen access to the metallic surface and its time of wetness, decreasing corrosion rates to extremely low values [28][29][30][31].

2.
In stations characterised as rural environments where SO 2 and Cl − deposition rates have not been determined due to being insignificant, values have been estimated for both pollutants. The figures indicated in Tables 4-6 correspond to the average value of the 0-3 mg Cl − /m 2 .d range (level S 0 ) and the 0-4 mg SO 2 /m 2 .d range (level P 0 ) according to standard ISO 9223 [3].
In those cases where both pollutants have been estimated, an average of the corrosion data from available annual series has been made.

3.
For test stations located in non-rural environments, all corresponding annual series data, or even the entirety of the available information, have been removed in those cases where, for some reason, meteorological or pollution data are not included. 4.
Chloride ion pollution data have not been determined for stations in the ICP/UNECE programme, which only considers non-marine test sites, unlike the other two exposure programmes (ISOCORRAG and MICAT). Therefore, the annual corrosion rate data and meteorological and SO 2 deposition rate obtained are only included in the statistical analysis for non-marine environments.
In this respect, the criteria adopted has been to remove from the ICP/UNECE database all stations located at a distance of less than 2 km from the seashore, supposing in these cases a chloride ion deposition level of more than 3 mg/m 2 .d (lower level S 1 according to standard ISO 9223 [3]). Bilbao station (Spain), despite being characterised by high SO 2 values, has been removed because of its location very close to the port.
On the other hand, a series of anomalous values have been observed at stations characterised as marine environments (ISOCORRAG and MICAT databases). Figure 5a shows the relationship between the variables of corrosion (µm/y) and salinity (mg Cl − /m 2 .d) in both databases. In this figure it is possible to see a cloud of points with very high salinity values (above 200 mg Cl − /m 2 .d) which does not seem to agree with the relatively low carbon steel corrosion values found (50-100 µm). It is also seen that a considerable rise in the marine chloride deposition rate (from 200 to 650 mg Cl − /m 2 .d) does not result in greater first-year corrosion of carbon steel, which is contradictory to the abundant literature on this matter recently reviewed by Alcántara et al. [32].These data have therefore been considered to be anomalous, and have been removed from the database. The corrosion stations removed for this reason are: Saint Remy (France), Tannanger (Norway) and Kvarnvik (Sweden). Figure 5b shows the linear relationship between these two variables after removing the aforementioned testing stations.  [3]. In those cases where both pollutants have been estimated, an average of the corrosion data from available annual series has been made. 3. For test stations located in non-rural environments, all corresponding annual series data, or even the entirety of the available information, have been removed in those cases where, for some reason, meteorological or pollution data are not included. 4. Chloride ion pollution data have not been determined for stations in the ICP/UNECE programme, which only considers non-marine test sites, unlike the other two exposure programmes (ISOCORRAG and MICAT). Therefore, the annual corrosion rate data and meteorological and SO2 deposition rate obtained are only included in the statistical analysis for non-marine environments. In this respect, the criteria adopted has been to remove from the ICP/UNECE database all stations located at a distance of less than 2 km from the seashore, supposing in these cases a chloride ion deposition level of more than 3 mg/m 2 .d (lower level S1 according to standard ISO 9223 [3]). Bilbao station (Spain), despite being characterised by high SO2 values, has been removed because of its location very close to the port.
On the other hand, a series of anomalous values have been observed at stations characterised as marine environments (ISOCORRAG and MICAT databases). Figure 5a shows the relationship between the variables of corrosion (µm/y) and salinity (mg Cl − /m 2 .d) in both databases. In this figure it is possible to see a cloud of points with very high salinity values (above 200 mg Cl − /m 2 .d) which does not seem to agree with the relatively low carbon steel corrosion values found (50-100 µm). It is also seen that a considerable rise in the marine chloride deposition rate (from 200 to 650 mg Cl − /m 2 .d) does not result in greater first-year corrosion of carbon steel, which is contradictory to the abundant literature on this matter recently reviewed by Alcántara et al. [32].These data have therefore been considered to be anomalous, and have been removed from the database. The corrosion stations removed for this reason are: Saint Remy (France), Tannanger (Norway) and Kvarnvik (Sweden). Figure 5b shows the linear relationship between these two variables after removing the aforementioned testing stations.

Integration of ICP/UNECE, ISOCORRAG and MICAT Databases
Tables 4-6 present the databases finally considered for the ICP/UNECE, ISOCORRAG and MICAT programmes for statistical analysis after the screening mentioned in the preceding section. ICP/UNECE: Table 4 presents the corrosion data obtained at the different testing stations along with the corresponding annual average values for the meteorological and pollution parameters measured in the programme: temperature (°C), precipitation (mm/y), relative humidity (%) and SO2 deposition rate (mg/m 2 .d).
ISOCORRAG: Table 5 presents the corrosion data obtained at the different testing stations along with the corresponding annual average values for the meteorological and pollution parameters measured in the programme: temperature (°C), relative humidity (%) (only for stations in the Czech Republic), time of wetness (annual fraction), SO2 deposition rate (mg/m 2 .d) and chloride ion deposition rate (mg/m 2 .d).
MICAT: Table 6 presents the average corrosion value obtained at the different testing stations along with the annual average values for the meteorological and pollution parameters measured in the programme: temperature (°C), relative humidity (%), time of wetness (annual fraction), precipitation (mm/y), SO2 deposition rate (mg/m 2 .d) and chloride ion deposition rate (mg/m 2 .d).
There follows an indication of the similarities and differences between the experimental methods used in the three collaborative programmes and how this has affected the integration of the three databases for statistical analysis:

Integration of ICP/UNECE, ISOCORRAG and MICAT Databases
Tables 4-6 present the databases finally considered for the ICP/UNECE, ISOCORRAG and MICAT programmes for statistical analysis after the screening mentioned in the preceding section. ICP/UNECE: Table 4 presents the corrosion data obtained at the different testing stations along with the corresponding annual average values for the meteorological and pollution parameters measured in the programme: temperature ( • C), precipitation (mm/y), relative humidity (%) and SO 2 deposition rate (mg/m 2 .d).
ISOCORRAG: Table 5 presents the corrosion data obtained at the different testing stations along with the corresponding annual average values for the meteorological and pollution parameters measured in the programme: temperature ( • C), relative humidity (%) (only for stations in the Czech Republic), time of wetness (annual fraction), SO 2 deposition rate (mg/m 2 .d) and chloride ion deposition rate (mg/m 2 .d).
MICAT: Table 6 presents the average corrosion value obtained at the different testing stations along with the annual average values for the meteorological and pollution parameters measured in the programme: temperature ( • C), relative humidity (%), time of wetness (annual fraction), precipitation (mm/y), SO 2 deposition rate (mg/m 2 .d) and chloride ion deposition rate (mg/m 2 .d).
There follows an indication of the similarities and differences between the experimental methods used in the three collaborative programmes and how this has affected the integration of the three databases for statistical analysis: (e) Measurement of Cl deposition rate according to ISO 9225 [5]. The ICP/UNECE programme does not consider marine atmospheres.     Over the years, many models have been developed to assess the corrosion of carbon steel in the atmosphere. The specialised literature offers a large range of damage functions that relate atmospheric corrosion of carbon steel with environmental data. However, most of them are of limited applicability as they were obtained with minimal variations in meteorological parameters (small geographic areas). Special mention should be made of the efforts of Benarie and Lipfert [13] to develop universal corrosion functions in terms of atmospheric pollutants, meteorological parameters and the rain pH, as well as the work of Feliu et al. [15] compiling a comprehensive literature survey of worldwide atmospheric corrosion and environmental data that were statistically processed to establish general corrosion damage functions in terms of simple meteorological and pollution parameters. Reviews on this subject can be found in [7,26].
In recent decades, several international exposure programmes (ISOCORRAG [1], ICP/UNECE [8], and MICAT [7]) have been carried out with the aim of more systematically obtaining relationships (dose/response functions) between atmospheric corrosion rates and pollution levels in combination with climate parameters. Integration of the databases obtained in these three exposure programmes may make it possible to obtain universal damage functions based on a worldwide variety of meteorological and pollution conditions. This has been the chief aim of the work reported here.
The data have been fitted to the following linear equation: C = a 1 + a 2 RH + a 3 P + a 4 T + a 5 TOW + a 6 SO 2 + a 7 Cl, This equation is quite simple. Other combinations between the different variables or other more sophisticated statistical treatments would likely yield better fits, but the aim of this work has been to use as simple as possible a relation. According to this model, the dependent variable C (carbon steel annual corrosion in µm) is interpreted as a linear combination of a set of independent variables: RH, annual average relative humidity, in per cent; T, annual average temperature, in • C; P, annual precipitation, in mm; TOW, time of wetness, annual fraction of number of hours/year in which RH > 80% and T > 0 • C [3]; SO 2 , SO 2 pollution, in mg/m 2 .day; and Cl, chloride pollution, in mg/m 2 .day. Each independent variable is accompanied by a coefficient (a 2 -a 7 ) which indicates the relative weight of that variable in the equation. The equation also includes a constant a 1 .
The minimum-quadratic regression equation is constructed by estimating the values of coefficients a 1 -a 7 from the regression model. These estimates are obtained trying to keep the squared differences between the values observed and the forecast values to a minimum. In order to know the model's fitting quality in relation to the experimental data, the statistic R 2 is used, i.e., the square of the multiple correlation coefficient. R 2 expresses the proportion of variance of the dependent variable which is explained by the independent variables.
There are different methods to select the independent variables that a regression model must include. The most widely accepted is the stepwise regression model. With this method, the best variable is firstly selected (always with a statistical criterion); then the best of the rest is taken; and so on, until no variables that fulfil the selection criteria remain. A great change in R 2 when a new variable is inserted in the equation indicates that this variable provides unique information on the dependent variable that is not supplied by the other independent variables.
The study has been carried out with the assistance of a commercial computer programme (SSPS) [33]. Statistical processing has been carried out considering marine and non-marine atmospheres separately. The variability of the corrosion and environmental data is shown in Table 7.

Non-Marine Atmospheres
The three databases have been analysed together: ICP/UNECE database (Table 4) (all corrosion stations), and ISOCORRAG (Table 5) and MICAT (Table 6) databases (only those stations with a chloride ion deposition rate of Cl − < 3 mg/m 2 .d).
The meteorological and pollution parameters common to all three databases and which have been included in the treatment are: temperature, relative humidity and SO 2 pollution, though relative humidity is only available in the ISOCORRAG database for stations in the Czech Republic [34]. The stepwise method has been used to select what independent variables are included in the treatment and which are significant. Statistically all the variables are significant, with SO 2 being the variable that contributes with an extremely high percentage (R 2 = 0.671) in the total recorded variance (R 2 = 0.725). RH and T also contribute, raising the R 2 by 0.037 and 0.017 units, respectively. The where N is the number of data. The model explains 72.5% of the dependent variable. This is the regression equation with non-standard coefficients, partial regression coefficients which define the regression equation at direct scores. Figure 6 shows the relationship between predicted and observed carbon steel corrosion values by applying Equation (2). The standardised partial regression coefficients are the coefficients that define the regression equation when it is obtained after standardising the original variables, i.e., after converting the direct scores into typical scores. These coefficients make it possible to evaluate the relative importance of each independent variable within the equation. The regression equation with standardised coefficients is shown in Equation (3) Great caution must be used when making corrosion predictions with independent variable values that are much larger or smaller than those used to derive these equations (see Table 7).
The goodness of the fit is slightly higher than the damage function developed by ICP/UNECE for this type of atmospheres using a more sophisticated mathematical model (Table 8), with a notably lower number of data (N = 148) used in the statistical treatment.
If, instead of RH, time of wetness (TOW) were to be considered (No. of hours in which RH > 80% and T > 0 • C, and therefore less precise than RH), taking into consideration the ISOCORRAG and MICAT databases the resulting regression equation would be: C = 6.58 + 0.75 SO 2 + 20.85 TOW; (R 2 = 0.684) (N = 138), with a slightly lower regression coefficient than Equation (2). In this case, the temperature is a non-significant variable and the greatest specific weight again corresponds to SO 2 , which contributes to the total recorded variance with an R 2 = 0.646 of a total R 2 = 0.684. Considering another related parameter, such as precipitation (P) (in mm/y), instead of RH, the following regression equation would be obtained: C = −29.26 + 0.87 SO 2 + 0.51 RH + 0.49 T − 0.003 P; (R 2 = 0.625) (N = 315), (5) in which the resulting regression coefficient decreases even more. Non marine ICP/UNECE (for weathering steels)

Marine Atmospheres
As in the previous case, the stepwise method has been used to select what independent variables are included in the statistical treatment and are significant. In this case, given that the ICP/UNECE programme did not measure the Cl ion deposition rate as it only considered non-marine testing stations, only stations from the ISOCORRAG and MICAT databases have been considered, taking as independent variables the chloride deposition rate (Cl), SO 2 pollution, temperature and time of wetness. As has been noted above, data on relative humidity are not available for ISOCORRAG stations.
In this case Cl is the variable that contributes with the highest percentage (R 2 = 0.411) to the total recorded variance (R 2 = 0.474). SO 2 also contributes, raising the R 2 by 0.041 units. TOW is also a significant variable but raises the R 2 by only 0.022 units. Temperature is excluded as a significant variable.
The resulting regression equation is: Cl and SO 2 , in this order, are the variables with the greatest weight in the carbon steel corrosion rate. Figure 7 shows the relationship between predicted and observed carbon steel corrosion values by applying Equation (6).  The goodness of this fit is slightly lower than in the MICAT programme and notably lower than those obtained in the ISOCORRAG programme (Table 8). On the other hand, the number of data used in the statistical treatment to obtain the damage function (Equations (6) and (7)) is somewhat higher.
Replacing the TOW variable with RH, information that is available in MICAT and perhaps in ISOCORRAG records, could possibly have improved the fitting quality achieved.
It would be also helpful to make new fits using more sophisticated mathematical models, and we encourage experts in statistics to do this. For this purpose, a good starting point could be the perfected broad database that are presented in this work (Tables 4-6).

Contribution of the Information Supplied for Each International Programme
Having established the integrated database, it is of interest to compare the damage functions and correlation coefficients obtained using the combined information of the three programmes (Equations (3) and (7)) with those obtained separately using the information supplied each individual programme. In this way, it may be possible to determine the contribution of each programme to the general damage functions. The results obtained with this treatment of the information are shown in Table 9.  The goodness of this fit is slightly lower than in the MICAT programme and notably lower than those obtained in the ISOCORRAG programme (Table 8). On the other hand, the number of data used in the statistical treatment to obtain the damage function (Equations (6) and (7)) is somewhat higher.
Replacing the TOW variable with RH, information that is available in MICAT and perhaps in ISOCORRAG records, could possibly have improved the fitting quality achieved.
It would be also helpful to make new fits using more sophisticated mathematical models, and we encourage experts in statistics to do this. For this purpose, a good starting point could be the perfected broad database that are presented in this work (Tables 4-6).

Contribution of the Information Supplied for Each International Programme
Having established the integrated database, it is of interest to compare the damage functions and correlation coefficients obtained using the combined information of the three programmes (Equations (3) and (7)) with those obtained separately using the information supplied each individual programme. In this way, it may be possible to determine the contribution of each programme to the general damage functions. The results obtained with this treatment of the information are shown in Table 9. The goodness of this fit is slightly lower than in the MICAT programme and notably lower than those obtained in the ISOCORRAG programme (Table 8). On the other hand, the number of data used in the statistical treatment to obtain the damage function (Equations (6) and (7)) is somewhat higher.
Replacing the TOW variable with RH, information that is available in MICAT and perhaps in ISOCORRAG records, could possibly have improved the fitting quality achieved.
It would be also helpful to make new fits using more sophisticated mathematical models, and we encourage experts in statistics to do this. For this purpose, a good starting point could be the perfected broad database that are presented in this work (Tables 4-6).

Contribution of the Information Supplied for Each International Programme
Having established the integrated database, it is of interest to compare the damage functions and correlation coefficients obtained using the combined information of the three programmes (Equations (3) and (7)) with those obtained separately using the information supplied each individual programme. In this way, it may be possible to determine the contribution of each programme to the general damage functions. The results obtained with this treatment of the information are shown in Table 9.
Considering non-marine atmospheres, it is seen that the greatest volume of information (81%) is supplied by the ICP/UNECE programme, which establishes SO 2 , RH and T as the most significant variables, the former with the greatest weight. The contribution of the ISOCORRAG programme (R 2 = 0.867), which incorporates a relatively small amount of data as only the Czech Republic testing stations supplied information on these three variables, makes only a slight improvement to the general correlation coefficient (0.725) in relation to R 2 supplied by the ICP/UNECE programme (0.674). With regard to the information provided by the MICAT programme, the low correlation coefficient obtained (0.398) may be an indication of poorer data quality than in the other programmes, perhaps due to the participation in MICAT of countries with little or no prior experience in the field of atmospheric corrosion [7]. In this respect, it should not be overlooked that one of the MICAT research programme's main aims was precisely to promote the development of this line of research in some of the participating countries [11].
Considering marine atmospheres, information has been supplied only by the ISOCORRAG and MICAT programmes, with a similar amount of data in each case. These data show the important effect of Cl and SO 2 pollutants (in this order) on the magnitude of the atmospheric corrosion of carbon steel. The greatest contribution to the general damage function seems to correspond to the ISOCORRAG programme, which includes TOW as an also significant variable. The joining of data from the two programmes, whose individual damage functions have only low correlation coefficients, yields a combined damage function with an even lower correlation coefficient. Table 9. D/R functions for first-year corrosion of carbon steel. Contribution of the information supplied by each of the international programmes to the overall D/R functions (Equations (3) and (7)) using the integrated database.

Goodness of the Fits
As we have seen, the environmental parameters considered in this work only partly explain the corrosion data. The goodness of fit of experimental data to a proposed model is often measured by the statistical R 2 , i.e., the square of the correlation coefficient (R) between the observed values of the dependent variable and those predicted from the fitted line.
In previous work [15,16], the authors noted a series of causes that may affect the goodness of the fit obtained:

•
Oversimplification of the mathematical model. In this sense, the best fits obtained in the ISOCORRAG programme, including or excluding the MICAT databases and data from Russian sites in frigid regions [1] (see Table 8), may have been at least partly due to considering interactions between the meteorological and pollution variables. One example of complex interactions involves the RH (or TOW), which in addition to its effect on the wetting of the metal surface, plays a major role in the mechanisms whereby air pollutants take part in corrosion.

•
The lack of quality in corrosion and environmental data. • Probable occurrence of other variables with marked effects on corrosion that were not considered in the statistical treatment. For instance, besides sulphur dioxide and chlorides, other pollutants not considered in the study may have played an important role in the corrosion data. In this sense, mention should be made of the effort made by ICP/UNECE to consider in the new damage functions (for the multi-pollutant situation) other important pollutants in terms of their effect on the corrosion of weathering steel [18]. • Many effects that have not been considered. To mention just a few: The magnitude of diurnal and seasonal changes in meteorological and pollution parameters, the frequency, duration and type of wetting and drying cycles, and the time of year when exposure is initiated.
Finally, it would be desirable, as noted by Leygraf et al. [36], to develop models on the basis of mechanistic considerations instead of statistical considerations, and recent work has attempted to take this into account [37][38][39]. Nevertheless, there is still a very long way to go to reach this desired goal. As Roberge et al. [40] note, the results obtained with mechanistic models reveal why statistical schemes have only a limited accuracy. There are many variables that can change from site to site which are not accounted for in the standard set of environmental variables. According to this researcher, a single transferable and comprehensive environmental corrosivity prediction model is yet to be published, and may ultimately not be possible due to the complexity of the issues involved.

Conclusions
The following may be considered the most relevant conclusions of this study:

•
A highly complete and perfected database has been obtained from published data from the ISOCORRAG, ICP/UNECE and MICAT programmes.

•
The number of data used in the statistical treatment has been much higher than that used in other damage functions previously published by the different programmes.

•
The statistical treatment carried out has differentiated between two types of atmospheres: non-marine and marine, which may represent a significant simplification for persons with little knowledge of the atmospheric corrosion process who wish to estimate the corrosion of carbon steel exposed at a given location. Moreover, having considered a highly simple polynomial function (Equation (2)) in the work may also be an advantage in this sense. where SO 2 is the variable of greatest significance. The inclusion of TOW (or precipitation) instead of RH leads to lower regression coefficients. The goodness of the fit obtained (R 2 ) is slightly higher than that obtained in the ICP/UNECE programme with a more sophisticated function. where Cl and SO 2 , in this order, are the most significant variables. The goodness of the fit is slightly lower than that obtained in the MICAT programme, which uses a similar type of function, and notably lower than that obtained in the ISOCORRAG programme using a more sophisticated type of function.