Prediction of First-Year Corrosion Losses of Carbon Steel and Zinc in Continental Regions

Dose-response functions (DRFs) developed for the prediction of first-year corrosion losses of carbon steel and zinc (K1) in continental regions are presented. The dependences of mass losses on SO2 concentration, K = f([SO2]), obtained from experimental data, as well as nonlinear dependences of mass losses on meteorological parameters, were taken into account in the development of the DRFs. The development of the DRFs was based on the experimental data from one year of testing under a number of international programs: ISO CORRAG, MICAT, two UN/ECE programs, the Russian program in the Far-Eastern region, and data published in papers. The paper describes predictions of K1 values of these metals using four different models for continental test sites under UN/ECE, RF programs and within the MICAT project. The predictions of K1 are compared with experimental K1 values, and the models presented here are analyzed in terms of the coefficients used in the models.


Introduction
Predictions of the corrosion mass losses (K) of structural metals, in general for a period not exceeding 20 years, are made using the power function: where K 1 represents the corrosion losses for the first year, g/m 2 or µm; τ is the test time in years; and n is a coefficient that characterizes the protective properties of corrosion products. The practical applications of Equation (1) for particular test locations in various regions of the world and the methods for n calculation are summarized in [1][2][3][4][5][6][7][8].
The power linear function that is believed to provide the most reliable predictions for any period of time and in any region of the world was suggested in [9,10]. Corrosion obeys a power law (Equation (1)) during an initial period and a linear law after the stationary stage starts. The total corrosion losses of metals for any period of time during the stationary stage can be calculated using Equation (2): where K st stands for corrosion losses over the initial period calculated by Equation (1), g/m 2 or µm; τ st is the year when stabilization begins; and α is the yearly gain in corrosion losses of metals during the stationary stage in g/(m 2 year) or µm/year. The differences in the predictions of corrosion losses by Equations (1) and (2) consist of different estimates of τ st , α, and n values for test locations with various corrosivity and atmosphere types. According to [10], τ st equals 20 years. The n values are given per atmosphere type, irrespective of the atmosphere corrosivity within a particular type. In [9], τ st = 6 years, and equations for n calculations based on the corrosivity of various atmosphere types are suggested. In [9,10], the α values are equal to the instantaneous corrosion rate at τ st .
Furthermore, various types of dose-response functions (DRFs) have been developed for long-term predictions of K; these can be used for certain territories or for any region of the world [11][12][13][14][15][16][17]. It should be noted that DRFs are power functions and have an advantage in that they provide predictions of first-year corrosion losses (K 1 ) based on yearly-average meteorological and aerochemical atmosphere parameters. The power-linear function uses K 1 values that should match the yearly-average corrosivity parameters of the test site atmosphere. The K 1 values can be determined by repeated natural yearly tests in each location, which require significant expense and ISO 9223:2012(E) presents equations for the calculation of K 1 of structural metals for any atmosphere types [18].
Recently, one-year and long-term predictions have been performed using models based on an artificial neural network (ANN) [19][20][21][22][23]. Their use is undoubtedly a promising approach in the prediction of atmospheric corrosion. The ANN "training" stage is programmed so as to obtain the smallest prediction error. Linear and nonlinear functions are used for K or K 1 prediction by means of an ANN. Using an ANN, the plots of K (K 1 ) versus specific corrosivity parameters can be presented visually as 2D or 3D graphs [19]. Despite the prospects of K prediction using ANNs, DRF development for certain countries (territories) is an ongoing task. The analytical form of DRFs is most convenient for application by a broad circle of experts who predict the corrosion resistance of materials in structures.
DRF development is based on statistical treatment, regression analysis of experimental data on K 1 , and corrosivity parameters of atmospheres in numerous test locations. All DRFs involve a prediction error that is characterized, e.g., by the R 2 value or by graphical comparison in coordinates of predicted and experimental K 1 . However, comparisons of the results on K 1 predictions based on different DRFs for large territories have not been available to date. Furthermore, the DRFs that have been developed assume various dependences of K on SO 2 concentration; however, the shape of the K = f (SO 2 ) function was not determined by analysis of data obtained in a broad range of atmosphere meteorological parameters.
The main purpose of this paper is to perform a mathematical estimate of the K = f (SO 2 ) dependence for carbon steel and zinc, popular structural materials, and to develop new DRFs for K 1 prediction based on the K = f (SO 2 ) dependences obtained and the meteorological corrosivity parameters of the atmosphere. Furthermore, we will compare the K 1 predictions obtained by the new and previously developed DRFs for any territories of the world, as well as analyze the DRFs based on the values of the coefficients in the equations.

Development of DRFs for Continental Territories
To develop DRFs, we used the experimental data from all exposures for a one-year test period in continental locations under the ISO CORRAG international program [24], the MICAT project [11,25], the UN/ECE program [12,14], the Russian program [26], and the program used in [19]. The test locations for the UN/ECE program and the MICAT project are presented in Table 1. The corrosivity parameters of the test site atmospheres and the experimental K 1 values obtained in four one-year exposures under the UN/ECE program are provided in Table 2, those obtained in three one-year exposures under the MICAT project are given in Table 3, and those obtained in the RF program are provided in Table 4. Cai et al. [19] report a selection of data from various literature sources. Of this selection, we use only the experimental data for continental territories that are shown in Table 5. The test results under the ISO CORRAG program [24] are not included in this paper because they lack the atmosphere corrosivity parameters required for K 1 prediction. We used them simply to determine the K = f (SO 2 ) dependences for steel and zinc.   Table 3. Atmosphere corrosivity parameters of test locations, first-year corrosion losses of carbon steel and zinc (K 1 , g/m 2 ) under the MICAT program and those reported in [20], and numbers of test locations in the order of increasing K 1 . Adapted from [20], with permission from © 2000 Elsevier.   [20]; ** the values reported in [20] are shown in parentheses.

Predictions of First-Year Corrosion Losses
To predict K 1 for steel and zinc, we used the new DRFs presented in this paper (hereinafter referred to as "New DRFs"), in the standard [18] (hereinafter referred to as "Standard DRFs"), in [13] (hereinafter referred to as "Unified DRFs"), and the linear model [20] (hereinafter referred to as "Linear DRF").
The Standard DRFs are intended for the prediction of K 1 (r corr in the original) in SO 2 -and Cl − -containing atmospheres in all climatic regions of the world. The K 1 values are calculated in µm.
For carbon steel, Equation (3): For zinc, Equation (4): where f Zn = 0.038 × (T − 10) at T ≤ 10 • C; f Zn = −0.071 × (T − 10) at T > 10 • C, where T is the temperature ( • C) and RH (%) is the relative humidity of air; P d and S d are SO 2 and Cl − deposition rates expressed in mg/(m 2 day), respectively. In Equations (3) and (4), the contributions to corrosion due to SO 2 and Cl − are presented as separate components; therefore, only their first components were used for continental territories.
Unified DRFs are intended for long-term prediction of mass losses K (designated as ML in the original) in SO 2 -containing atmospheres in all climatic regions of the Earth. It is stated that the calculation is given in g/m 2 .
For carbon steel, Equation (5): For zinc, Equation (6): where T is the temperature ( • C) and RH (%) is the relative humidity of air; [SO 2 ] is the concentration of SO 2 in µg/m 3 ; "Rain" is the rainfall amount in mm/year; [H + ] is the acidity of the precipitation; and τ is the exposure time in years.
To predict the first-year corrosion losses, τ = 1 was assumed.
The standard DRFs and Unified DRFs were developed on the basis of the results obtained in the UN/ECE program and MICAT project using the same atmosphere corrosivity parameters (except from Rain[H + ]). If τ = 1, the models have the same mathematical form and only differ in the coefficients. Both models are intended for K 1 predictions in any regions of the world, hence it is particularly interesting to compare the results of K 1 predictions with actual data.
The linear model was developed for SO 2 − and Cl − -containing atmospheres. It is based on the experimental data from the MICAT project only and relies on an artificial neural network. It is of special interest since it has quite a different mathematical form and uses different parameters. In the MICAT project, the air temperature at the test sites is mainly above 10 • C (Table 3). Nevertheless, we used this model, like the other DRFs, also for test locations with any temperatures.
The first-year corrosion losses of carbon steel (designated as "Fe" in the original) are expressed as Equation (7): where b 0 = 6.8124, b 1 = −1.6907, b 2 = 0.0004, b 3 = 0.0242, and b 4 = 2.2817; K 1 is the first-year corrosion loss in µm; Cl − is the chloride deposition rate in mg/(m 2 ·day); P is the amount of precipitation in mm/year; RH is the air relative humidity in %; TOW is the wetting duration expressed as the fraction of a year; and [SO 2 ] is the SO 2 concentration in µg/m 3 . The prediction results for the first year are expressed in µm.
To predict K 1 in continental regions, only the component responsible for the contribution to corrosion due to SO 2 was used.
The K 1 values in µm were converted to g/m 2 using the specific densities of steel and zinc, 7.8 and 7.2 g/cm 3 , respectively. Furthermore, the relationship P d,p mg/(m 2 ·day) = 0.67 P d,c µg/m 3 was used, where P d,p is the SO 2 deposition rate and P d,c is the SO 2 concentration [18].
The calculation of K 1 is given for continental test locations at background Cl − deposition rates ≤2 mg/(m 2 ·day) under UN/ECE and RF programs and MICAT project. The R 2 values characterizing the prediction results as a whole for numerous test locations are not reported here. The K 1 predictions obtained were compared to the experimental values of K 1 for each test location, which provides a clear idea about the specific features of the DRFs.

DRF Development
Corrosion of metals in continental regions depends considerably on the content of sulfur dioxide in the air. Therefore, development of a DRF primarily requires that this dependence, i.e., the mathematical relationship K = f (SO 2 ), be found. The dependences reported in graphical form in [20,27] Tables 2-4 are presented as "Ins." (Insignificant), ≤1, 3, 5 µg/m 3 , which indicates that there is no common technique in the determination of background concentrations. For SO 2 concentrations of "Ins." or ≤1 µg/m 3 , we used the value of 1 µg/m 3 , whereas the remaining SO 2 concentrations were taken from the tables.
In finding the K = f (SO 2 ) relationship, we used the actual test results of all first-year exposures under each program rather than the mean values, because non-linear functions are also used.
The K = f (SO 2 ) relationships obtained for each program are shown in Figure 1 for steel and in Figure 2 for zinc. In a first approximation, this relationship can be described by the following function for experimental K 1 values obtained in a broad range of meteorological atmosphere parameters: where K 1 • are the average corrosion losses over the first year (g/m 2 ) in a clean atmosphere for the entire range of T and RH values; and α is the exponent that depends on the metal.  Tables 2-4 are presented as "Ins." (Insignificant), ≤1, 3, 5 μg/m 3 , which indicates that there is no common technique in the determination of background concentrations. For SO2 concentrations of "Ins." or ≤1 μg/m 3 , we used the value of 1 μg/m 3 , whereas the remaining SO2 concentrations were taken from the tables.
In finding the K = f(SO2) relationship, we used the actual test results of all first-year exposures under each program rather than the mean values, because non-linear functions are also used.
The K = f(SO2) relationships obtained for each program are shown in Figure 1 for steel and in Figure 2 for zinc. In a first approximation, this relationship can be described by the following function for experimental K1 values obtained in a broad range of meteorological atmosphere parameters: where K1° are the average corrosion losses over the first year (g/m 2 ) in a clean atmosphere for the entire range of Т and RH values; and α is the exponent that depends on the metal.  [20] for TOW ranges in accordance with the data in Tables 2-5. -model [20] for TOW ranges in accordance with the data in Tables 2-5. The K1° values corresponding to the mean values of the parameter range of climatic conditions in clean atmospheres were found to be the same for the experimental data of all programs, namely, 63 and 4 g/m 2 , while α = 0.47 and 0.28 for carbon steel and zinc, respectively. A similar K1° value for carbon steel was also obtained from the Linear DRF, Equation (6). In fact, at background SO2 concentrations = 1 μg/m 3 in РЕ4 test location (Table 3) at TOW = 26 h/year (0.002 of the year), the calculated K1° is to 53 g/m 2 , while for СО2 test location at TOW = 8760 h/year (entire year) it is 71 g/m 2 ; the mean value is 62 g/m 2 .
Based on Equation (8), it may be accepted in a first approximation that the effect of [SO2] on corrosion is the same under any climatic conditions and this can be expressed in a DRF by an [SO2] α multiplier, where α = 0.47 or α = 0.28 for steel or zinc, respectively. The K1° values in Equation (8) depend on the climatic conditions and are determined for each test location based on the atmosphere meteorological parameters.
In the development of New DRF, the K1 values were determined using the DRF mathematical formula presented in the Standard DRF and in the Unified DRF, as well as meteorological parameters T, RH, and Prec (Rain for warm climate locations or Prec for cold climate locations). The complex effect of T was taken into account: corrosion losses increase with an increase in T to a certain limit, Тlim; its further increase slows down the corrosion due to radiation heating of the surface of the material and accelerated evaporation of the adsorbed moisture film [12,28]. It has been shown [29] that Тlim is within the range of 9-11 °С. Similarly to Equations (3)-(6), it is accepted that Тlim equals 10 °C. The need to introduce Prec is due to the fact that in northern RF regions, the K1 values are low at high RH, apparently owing not only to low T values but also to the small amount of precipitation, including solid precipitations. The values of the coefficients reflecting the effect of T, RH and Prec on corrosion were determined by regression analysis. for carbon steel was also obtained from the Linear DRF, Equation (6). In fact, at background SO 2 concentrations = 1 µg/m 3 in PE4 test location (  (8), it may be accepted in a first approximation that the effect of [SO 2 ] on corrosion is the same under any climatic conditions and this can be expressed in a DRF by an [SO 2 ] α multiplier, where α = 0.47 or α = 0.28 for steel or zinc, respectively. The K 1 • values in Equation (8) depend on the climatic conditions and are determined for each test location based on the atmosphere meteorological parameters.
In the development of New DRF, the K 1 values were determined using the DRF mathematical formula presented in the Standard DRF and in the Unified DRF, as well as meteorological parameters T, RH, and Prec (Rain for warm climate locations or Prec for cold climate locations). The complex effect of T was taken into account: corrosion losses increase with an increase in T to a certain limit, T lim ; its further increase slows down the corrosion due to radiation heating of the surface of the material and accelerated evaporation of the adsorbed moisture film [12,28]. It has been shown [29] that T lim is within the range of 9-11 • C. Similarly to Equations (3)-(6), it is accepted that T lim equals 10 • C. The need to introduce Prec is due to the fact that in northern RF regions, the K 1 values are low at high RH, apparently owing not only to low T values but also to the small amount of precipitation, including solid precipitations. The values of the coefficients reflecting the effect of T, RH and Prec on corrosion were determined by regression analysis.
The New DRFs developed for the prediction of K 1 (g/m 2 ) for the two temperature ranges have the following forms: for carbon steel: and for zinc:

Predictions of K 1 Using Various DRFs for Carbon Steel
Predictions of K 1 were performed for all continental test locations with chloride deposition rates ≤2 mg/(m 2 ·day). The results of K 1 prediction (K 1 pr ) from Equations (3)- (7), (9), and (10) (5)), the K 1 pr of carbon steel in RF territory [30] had low values. It was also found that the K 1 pr values are very low for the programs mentioned above. Apparently, the K 1 pr values (Equation (5)) were calculated in µm rather than in g/m 2 , as the authors assumed. To convert K 1 pr in µm to K 1 pr in g/m 2 , the 3.54 coefficient in Equation (6) and for zinc:

Predictions of K1 Using Various DRFs for Carbon Steel
Predictions of K1 were performed for all continental test locations with chloride deposition rates ≤2 mg/(m 2 ·day). The results of K1 prediction (K1 pr ) from Equations (3)-(7), (9), and (10) are presented separately for each test program. To build the plots, the test locations were arranged by increasing experimental K1 values (K1 exp ). Their sequence numbers are given in Tables 2-4. The increase in K1 is caused by an increase in atmosphere corrosivity due to meteorological parameters and SO2 concentration. All the plots are drawn on the same scale. All plots show the lines of prediction errors δ = ±30% (the 1.3 K1 exp -0.7 K1 exp range). This provides a visual idea of the comparability of K1 pr with K1 exp for each DRF. The scope of this paper does not include an estimation of the discrepancy between the K1 pr values obtained using various DRFs with the K1 exp values obtained for each test location under the UN/ECE and RF programs. The scatter of points is inevitable. It results from the imperfection of each DRF and the inaccuracy of experimental data on meteorological parameters, SO2 content, and K1 exp values. Let us just note the general regularities of the results on K1 pr for each DRF.
The results on K1 pr for carbon steel for the UN/ECE program, MICAT project, and RF program are presented in Figures 3-5, respectively. It should be noted that according to the Unified DRF (Equation (5)), the K1 pr of carbon steel in RF territory [30] had low values. It was also found that the K1 pr values are very low for the programs mentioned above. Apparently, the K1 pr values (Equation (5)) were calculated in μm rather than in g/m 2 , as the authors assumed. To convert K1 pr in μm to K1 pr in g/m 2 , the 3.54 coefficient in Equation (6) [20] are different for some test locations (Table 3). In fact, for B6, the [SO2] value for all exposures is reported to be 28 μg/m 3 instead of 67.2; 66.8 and 48.8 μg/m 3 . Figure 4е presents K1 pr for the Linear DRF with consideration for the parameter values reported in [20]. Naturally, K1 pr for B6 decreased considerably in comparison with the values in Figure 4d but remained rather overestimated with respect to K1 exp . Furthermore, for the Linear DRF (Figure 4d) Figure 4е); ○-experimental K1 data under the assumption that they were expressed in g/m 2 rather than in μm.
Thin lines show the calculation error (±30%). The numbers of the exposure sites are given in accordance with Table 3.  Table 4.
If all DRFs give underestimated K1 pr values for the same locations, this may result from an inaccuracy of experimental data, i.e., corrosivity parameters and/or K1 exp values. We did not perform any preliminary screening of the test locations. Therefore, it is reasonable to estimate the reliability of  Figure 4e); -experimental K 1 data under the assumption that they were expressed in g/m 2 rather than in µm. Thin lines show the calculation error (±30%). The numbers of the exposure sites are given in accordance with Table 3.
(e)  Figure 4е); ○-experimental K1 data under the assumption that they were expressed in g/m 2 rather than in μm.
Thin lines show the calculation error (±30%). The numbers of the exposure sites are given in accordance with Table 3.  Table 4.
If all DRFs give underestimated K1 pr values for the same locations, this may result from an inaccuracy of experimental data, i.e., corrosivity parameters and/or K1 exp values. We did not perform any preliminary screening of the test locations. Therefore, it is reasonable to estimate the reliability of   The reason for potentially overestimated K 1 exp values being obtained is unknown. It may be due to non-standard sample treatment or to corrosion-related erosion. It can also be assumed that the researchers (performers) reported K 1 in g/m 2 rather than in µm. If this assumption is correct, then K 1 pr values would better match K 1 exp (Figure 4). Unfortunately, we cannot compare the questionable K 1 exp values with the K 1 exp values rejected in the study where an artificial neural network was used [20].
We believe that, of the K 1 exp values listed, only the data for the test locations up to No. 26 in Figure 4 can be deemed reliable.
For the RF program, the K 1 pr values determined by the New DRF and the Standard DRF are pretty comparable with K 1 exp , but they are considerably higher for the Unified DRF ( Figure 5).
The presented figures indicate that all DRFs which have the same parameters but different coefficients predict K 1 for same test locations with different degrees of reliability. That is, combinations of various coefficients in DRFs make it possible to obtain K 1 pr results presented in Figures 3-5. In view of this, the analysis of DRFs in order to explain the principal differences of K 1 pr from K 1 exp for each DRF appears interesting.

Analysis of DRFs for Carbon Steel
The DRFs were analyzed by comparison of the coefficients in Equations (3), (5) and (9). Nonlinear DRFs can be represented in the form: where A × e k1·RH × e k2·(T−10) × e k3·Prec = K 10 . The values of the coefficients used in Equations (3), (5) and (9) are presented in Table 7.  (8)  The K 1 pr values are strongly overestimated at high values of these parameters (Figure 4c,d). That is, the Linear model has a limited applicability at combinations of TOW and [SO 2 ] that occur under natural conditions. Furthermore, according to the Linear DRF, the range of K 1 pr in clean atmosphere is 53-71 g/m 2 , therefore the K 1 pr values in clean atmosphere lower than 53 g/m 2 (Figures 3d and 4d,e) or above 71 g/m 2 cannot be obtained. Higher K 1 pr values can only be obtained due to [SO 2 ] contribution.
The underestimated K 1 pr values in comparison with K 1 exp for the majority of test locations (Figure 3d) are apparently caused by the fact that the effects of other parameters, e.g., T, on corrosion are not taken into account. Figure 6 compares K = f (SO 2 ) for all the models with the graphical representation of the dependence reported in [20] (for [SO 2 ], mg/(m 2 ·d) values were converted to µg/m 3 ). The dependence in [20] is presented for a constant temperature, whereas the dependences given by DRFs are given for average values in the entire range of meteorological parameters in the test locations. Nevertheless, the comparison is of interest. Below 70 and 80 µg/m 3 , according to [20], K has lower values than those determined by the New DRF and Standard DRF, respectively, while above these values, K has higher values. According to the Unified DRF, K has extremely low values at all [SO 2 ] values, whereas according to the Linear DRF (TOW from 0.03 to 1), the values at TOW = 1 are extremely high even at small [SO 2 ].  [20]. ▬▬plot according to [20], ▬▬ by the New DRF; ▬ ▬ by the Standard DRF; ▬•▬ by the Unified DRF; --by the Linear DRF [20].
To perform a comparative estimate of k1 and k2, let us use the value Тlim = 10 °C accepted in the DRF, i.e., where the temperature dependence changes. Furthermore, it is necessary to know the K1 value in clean atmosphere at Тlim and at the RH that is most common at this temperature. These data are unknown at the moment. Therefore, we'll assume that at Тlim = 10 °C and RH = 75%, K = 63 g/m 2 . The dependences of K on Т and RH under these conditions and with consideration for the corresponding k1 and k2 for each DRF are presented in Figure 7.
The nearly coinciding k1 values (0.020 for the Unified DRF and Standard DRF, and 0.024 for the New DRF, Table 8) result in an insignificant difference in the RН effect on K (Figure 7а).   [20]. plot according to [20], by the New DRF; by the Standard DRF; • by the Unified DRF; by the Linear DRF [20].
To perform a comparative estimate of k 1 and k 2 , let us use the value T lim = 10 • C accepted in the DRF, i.e., where the temperature dependence changes. Furthermore, it is necessary to know the K 1 value in clean atmosphere at T lim and at the RH that is most common at this temperature. These data are unknown at the moment. Therefore, we'll assume that at T lim = 10 • C and RH = 75%, K = 63 g/m 2 . The dependences of K on T and RH under these conditions and with consideration for the corresponding k 1 and k 2 for each DRF are presented in Figure 7.
The nearly coinciding k 1 values (0.020 for the Unified DRF and Standard DRF, and 0.024 for the New DRF, Table 8) result in an insignificant difference in the RH effect on K (Figure 7a).  [20]. ▬▬plot according to [20], ▬▬ by the New DRF; ▬ ▬ by the Standard DRF; ▬•▬ by the Unified DRF; --by the Linear DRF [20].
To perform a comparative estimate of k1 and k2, let us use the value Тlim = 10 °C accepted in the DRF, i.e., where the temperature dependence changes. Furthermore, it is necessary to know the K1 value in clean atmosphere at Тlim and at the RH that is most common at this temperature. These data are unknown at the moment. Therefore, we'll assume that at Тlim = 10 °C and RH = 75%, K = 63 g/m 2 . The dependences of K on Т and RH under these conditions and with consideration for the corresponding k1 and k2 for each DRF are presented in Figure 7.
The nearly coinciding k1 values (0.020 for the Unified DRF and Standard DRF, and 0.024 for the New DRF, Table 8) result in an insignificant difference in the RН effect on K (Figure 7а).   The temperature coefficient k 2 has a considerable effect on K.  (Table 4) and K pr = 42 g/m 2 ( Figure 5). In A3 test location, at T = 20.6 • C and RH = 76%, K 1 exp = 44.5 g/m 2 (Table 4), while due to A and other parameters, K 1 pr = 86.2 g/m 2 , Figure 4c.
In the Standard DRF, the k 2 values are higher than in the Unified DRF: 0.150 and −0.054 for T ≤ 10 • C and T > 10 • C, respectively, so a greater K decrease is observed, especially at T ≤ 10 • C, Figure 7b. At low T, the K values are small, e.g., K~2 g/m 2 at T = −12 • C. In K 1 pr calculations, the small K are made higher due to A, and they are higher in polluted atmospheres due to higher α = 0.52. As a result, K pr are quite comparable with K exp , Figure 3b. However, let us note that K pr is considerably lower than K exp in many places. Perhaps, this is due to an abrupt decrease in K in the range T ≤ 10 • C. This temperature range is mostly met in test locations under the UN/ECE program. In the New DRF, k 2 has an intermediate value at T ≤ 10 • C and the lowest value at T > 10 • C, whereas A has the lowest value. It is more difficult to estimate the k 2 value with similar k 2 values in the other DRFs, since the New DRF uses one more member, i.e., e k3·Prec . The dependence of K on Prec is presented in Figure 7c. The following arbitrary values were used to demonstrate the possible effect of Prec on K: K = 7.8 g/m 2 at Prec = 632 mm/year. For example, in location PE5 (UN/ECE program) with Prec = 632 mm/year, K = 7.8 g/m 2 at T = 12.2 • C and RH = 67%. The maximum Prec was taken as 2500 mm/year, e.g., it is 2144 mm/year in NOR23 (UN/ECE program) and 2395 mm/year in B8 (MICAT project). It follows from the figure that, other conditions being equal, K can increase from 5.4 to 22.6 g/m 2 just due to an increase in Prec from 0 to 2500 mm/year at k 3 = 0.00056 (Table 7).
Thus, it has been shown that the coefficients for each parameter used in the DRFs vary in rather a wide range. The most reliable K 1 pr can be reached if, in order to find the most suitable coefficients, the DRFs are based on the K = f (SO 2 ) relationship obtained.

Predictions of K 1 Using Various DRFs for Zinc
The results on K 1 pr for zinc for the UN/ECE program, MICAT project, and RF program are presented in Figures 8-10, respectively. In the UN/ECE program, the differences between the K 1 pr and K 1 exp values for zinc are more considerable than those for carbon steel. This may be due not only to the imperfection of the DRFs and the inaccuracy of the parameters and K 1 exp , but also to factors unaccounted for in DRFs that affect zinc. For all the DRFs, the K 1 pr values match K 1 exp to various extent; some of the latter exceed the error δ (±30%). Let us estimate the discrepancy between K 1 pr and K 1 exp for those K 1 pr that exceed δ. For the New DRF ( Figure 8a) and the Standard DRF (Figure 8b) Table 2.
With regard to the MICAT project, the New and Unified DRFs (Figure 9а,с) give overestimated K1 pr at low K1 exp , but the Standard DRF gives K1 pr values comparable to K1 exp (Figure 9b)  With regard to the MICAT project, the New and Unified DRFs (Figure 9a,c) give overestimated K 1 pr at low K 1 exp , but the Standard DRF gives K 1 pr values comparable to K 1 exp (Figure 9b)  The numbers of the exposure sites are given in accordance with Table 3.
For the RF program, the K1 pr values calculated by the New and Unified DRFs are more comparable to K1 exp than those determined using the Standard DRF ( Figure 10). The numbers of the exposure sites are given in accordance with Table 3.
For the RF program, the K 1 pr values calculated by the New and Unified DRFs are more comparable to K 1 exp than those determined using the Standard DRF ( Figure 10). The numbers of the exposure sites are given in accordance with Table 3.
For the RF program, the K1 pr values calculated by the New and Unified DRFs are more comparable to K1 exp than those determined using the Standard DRF ( Figure 10). The numbers of the exposure sites are given in accordance with Table 4.

Analysis of DRFs for Zinc
As for steel, DRFs were analyzed by comparison of their coefficients. The nonlinear DRFs for zinc can be represented in the form: The values of the coefficients used in Equations (4), (6), and (10) are presented in Table 8. Let us assume for a comparative estimate of k1 and k2 that K = 4 g/m 2 in a clean atmosphere at Тlim = 10 °C and RH = 75%. Figure 11 demonstrates the plots of K versus these parameters under these starting conditions. The Standard DRF (k1 = 0.46) shows an abrupt variation in K vs. RH. According to this relationship, at the same temperature, the K value should be 0.5 g/m 2 at RH = 30% and 12.6 g/m 2 at RH = 100%. According to the New DRF and Unified DRF with k1 = 0.22 and 0.18, respectively, the effect of RH is weaker, therefore K = 1.5 and 1.8 g/m 2 at RH = 30%, respectively, and K = 6.9 and 6.4 g/m 2 at RH = 100%, respectively. The numbers of the exposure sites are given in accordance with Table 4.

Analysis of DRFs for Zinc
As for steel, DRFs were analyzed by comparison of their coefficients. The nonlinear DRFs for zinc can be represented in the form: The values of the coefficients used in Equations (4), (6) and (10) are presented in Table 8.
To compare the α values, K 1 = 4 g/m 2 at [SO 2 ] = 1 µg/m 3 was used for all DRFs. Let us note that the value K 1 = 4 g/m 2 was obtained during the estimation of K = f (SO 2 ) for the development of the New DRF. The plots for all the programs are presented in Figure 2. For the New DRF, the line at α = 0. 28  Let us assume for a comparative estimate of k 1 and k 2 that K = 4 g/m 2 in a clean atmosphere at T lim = 10 • C and RH = 75%. Figure 11 demonstrates the plots of K versus these parameters under these starting conditions. The Standard DRF (k 1 = 0.46) shows an abrupt variation in K vs. RH. According to this relationship, at the same temperature, the K value should be 0.5 g/m 2 at RH = 30% and 12.6 g/m 2 at RH = 100%. According to the New DRF and Unified DRF with k 1 = 0.22 and 0.18, respectively, the effect of RH is weaker, therefore K = 1.5 and 1.8 g/m 2 at RH = 30%, respectively, and K = 6.9 and 6.4 g/m 2 at RH = 100%, respectively.
The effect of temperature on K is shown in Figure 11b. In the New DRF, k 2 = 0.045 at T ≤ 10 • C has an intermediate value; at T > 10 • C, k 2 = −0.085 has the largest absolute value, which corresponds to an abrupt decrease in K with an increase in temperature. In the Unified DRF, k 2 = −0.021 at T > 10 • C, i.e., an increase in temperature results in a slight decrease in K. As for the effect of A, this also contributes to higher K 1 pr values despite the small α value. The effect of temperature on K is shown in Figure 11b. In the New DRF, k2 = 0.045 at Т ≤ 10 °С has an intermediate value; at Т > 10 °С, k2 = −0.085 has the largest absolute value, which corresponds to an abrupt decrease in K with an increase in temperature. In the Unified DRF, k2 = −0.021 at Т > 10 °С, i.e., an increase in temperature results in a slight decrease in K. As for the effect of A, this also contributes to higher K1 pr values despite the small α value.
In the Standard DRF, the value А = 0.0929 (g/m 2 ), which is ~8 times smaller than in the New DRF, and a small k2 = −0.71 at Т > 10 °С were taken to compensate the K1 pr overestimation due to the combination of high values, α = 0.44 and k1 = 0.46. In the Unified DRF, the high А value that is ~2 times higher than in the New DRF is not compensated by the combination of the low values, α = 0.22 and k2 = −0.021 at Т > 10 °С. Therefore, the K1 pr values are mostly overestimated, Figures 8с and 9с for trusted test locations. However, small K1 pr values were attained for low Т at k2 = 0.62, Figure 10с.
The effect of Prec on K at k3 = 0.0001, which is taken into account only in the New DRF, given under the assumption that K = 0.65 in a clean atmosphere at Prec (Rain) = 250 mm/year, Т = 15 °C and RH = 60% (e.g., location Е5 in the MICAT project), is shown in Figure 11с. Upon an increase in Prec (Rain) from 250 to 2500 mm/year, K can increase from 0.65 to 0.81 g/m 2 .
As for carbon steel, the above analysis of coefficients in the DRFs for zinc confirms that the coefficients can be varied to obtain reliable K1 pr values. The New DRF based on K = f(SO2) gives the most reliable K1 pr values for zinc.

Estimation of Coefficients in DRFs for Carbon Steel and Zinc
Let us first note that the starting conditions that we took to demonstrate the effect of various atmosphere corrosivity parameters on K of carbon steel and zinc (Figures 7 and 11) may not match In the Standard DRF, the value A = 0.0929 (g/m 2 ), which is~8 times smaller than in the New DRF, and a small k 2 = −0.71 at T > 10 • C were taken to compensate the K 1 pr overestimation due to the combination of high values, α = 0.44 and k 1 = 0.46. In the Unified DRF, the high A value that is~2 times higher than in the New DRF is not compensated by the combination of the low values, α = 0.22 and k 2 = −0.021 at T > 10 • C. Therefore, the K 1 pr values are mostly overestimated, Figures 8c and 9c for trusted test locations. However, small K 1 pr values were attained for low T at k 2 = 0.62, Figure 10c.
The effect of Prec on K at k 3 = 0.0001, which is taken into account only in the New DRF, given under the assumption that K = 0.65 in a clean atmosphere at Prec (Rain) = 250 mm/year, T = 15 • C and RH = 60% (e.g., location E5 in the MICAT project), is shown in Figure 11c. Upon an increase in Prec (Rain) from 250 to 2500 mm/year, K can increase from 0.65 to 0.81 g/m 2 .
As for carbon steel, the above analysis of coefficients in the DRFs for zinc confirms that the coefficients can be varied to obtain reliable K 1 pr values. The New DRF based on K = f (SO 2 ) gives the most reliable K 1 pr values for zinc.

Estimation of Coefficients in DRFs for Carbon Steel and Zinc
Let us first note that the starting conditions that we took to demonstrate the effect of various atmosphere corrosivity parameters on K of carbon steel and zinc (Figures 7 and 11) may not match the real values. However, the plots obtained give an idea on K variations depending on the coefficients in the DRFs.
For continental test locations under all programs, the K 1 exp values are within the following ranges: for carbon steel, from 6.3 (Oimyakon, RF program) to 577 g/m 2 (CS3, UN/ECE program); for zinc, from 0.65 (E5, MICAT project) to 16.41 g/m 2 (CS3, UN/ECE program). That is, the difference in the corrosion losses is at least~10-35 fold, the specific densities of these metals being nearly equal. Higher K 1 pr values for steel than for zinc are attained using different coefficients at the parameters in the DRFs.
In the New DRFs, A is 7.7 and 0.71 g/m 2 for carbon steel and zinc, respectively, i.e., the difference is~10-fold. Higher K 1 pr values for steel than for zinc were obtained chiefly due to the contribution of [SO 2 ] α at α = 0.47 and 0.28, respectively. The values of RH and Prec affect the corrosion of steel more strongly than they affect zinc corrosion. The coefficients for these parameters are: k 1 = 0.024 and 0.022; k 3 = 0.00056 and 0.0001 for steel and zinc, respectively. However, the temperature coefficients (k 2 = 0.095 and −0.095 for steel; k 2 = 0.045 and −0.085 for zinc) indicate that, with a deviation of T from 10 • C, the corrosion process on steel is hindered to a greater extent than on zinc.
In the Standard DRF, A is 1.77 and 0.0129 µm for carbon steel and zinc, respectively, i.e., the difference is~137-fold. The α value for steel is somewhat higher than that for zinc, i.e., 0.52 and 0.44 respectively, which increases the difference of K 1 pr for steel from that for zinc. As shown above, the difference should not be greater than 35-fold. This difference is compensated by the 2.3-fold higher effect of RH on zinc corrosion than on steel corrosion (k 1 = 0.046 and 0.020 for zinc and steel, respectively). Furthermore, the temperature coefficient k 2 at T ≤ 10 • C for steel is 3.95 times higher than that for zinc. This indicates that steel corrosion slows down abruptly in comparison with zinc as T decreases below 10 • C. At T > 10 • C, the k 2 values for steel and zinc are comparable. Taking the values of the coefficients presented into account, the K 1 pr values for steel are 15-fold higher, on average, than those for zinc at T ≤ 10 • C, but~60-fold at T > 10 • C. Of course, this is an approximate estimate of the coefficients used in the Standard DRF.
In the Unified DRF, A is 3.54 and 0.188 µm for carbon steel and zinc, respectively, i.e., the difference is~19-fold. The α value for steel is lower than that for zinc, i.e., 0.13 and 0.22 respectively, which decreases the difference of K 1 pr of steel from that of zinc. Conversely, the RH value affects steel corrosion somewhat more strongly than that of zinc (k 1 = 0.020 and 0.018 for steel and zinc, respectively). The k 2 values for steel and zinc are comparable in both temperature ranges. The ∆K [H+] component was introduced only for zinc, which somewhat complicates the comparison of the coefficients in these DRFs. All the presented DRFs are imperfect not only because of the possible inaccuracy of the mathematical expressions as such, but also due to the inaccuracy of the coefficients used in the DRFs. The K 1 pr values obtained using the New DRF match K 1 exp most accurately. However, while the α values that were assumed to be 0.47 and 0.28 for carbon steel and zinc, respectively, may be considered as accurate in a first approximation, the other coefficients need to be determined more accurately by studying the effect of each atmosphere corrosivity parameter on corrosion, with the other parameters being unchanged. Studies of this kind would allow each coefficient to be estimated and DRFs for reliable prediction of K 1 in atmospheres with various corrosivity to be created.

Conclusions
1. K = f (SO 2 ) plots of corrosion losses of carbon steel and zinc vs. sulfur dioxide concentration were obtained to match, to a first approximation, the mean meteorological parameters of atmosphere corrosivity.

2.
Based on the K = f (SO 2 ) relationships obtained, with consideration for the nonlinear effect of temperature on corrosion, New DRFs for carbon steel and zinc in continental territories were developed.

3.
Based on the corrosivity parameters at test locations under the UN /ECE and RF programs and the MICAT project, predictions of first-year corrosion losses of carbon steel and zinc were given using the New DRF, Standard DRF, and Unified DRF, as well as the linear model for carbon steel obtained in [20] with the aid of an artificial neural network. The predicted corrosion losses are compared with the experimental data for each DRF. It was shown that the predictions provided by the New DRFs for the first-year match the experimental data most accurately.

4.
An analysis of the values of the coefficients used in the DRFs for the prediction of corrosion losses of carbon steel and zinc is presented. It is shown that more accurate DRFs can be developed based on quantitative estimations of the effects of each atmosphere corrosivity parameter on corrosion.