Estimation of atmospheric chloride deposition and its corrosion effect in the coastal region of China

2.1 Experimental information introduction

To investigate the distribution of atmospheric chloride deposition rate and its corrosion effect in coastal region, we established five experimental sites (S1–S5) in Hainan Province, China. These sites are situated at distances of 25 m, 95 m, 165 m, 235 m, and 305 m from the coast, respectively, as depicted in Figure 1. At these sites, we conducted atmospheric environment monitoring, atmospheric chloride deposition rate measurements, and natural environmental exposure tests on typical metals. Detailed descriptions of the experimental setup and procedures are provided below.

Figure 1:

Distribution of the five experimental sites (S1–S5).

2.2 Environmental features monitoring

Atmospheric environmental features were monitored using a high-precision unmanned automatic meteorological observation system, as shown in Figure 2(a). This system enabled automatic monitoring and data storage of meteorological factors, with functionalities including a stable solar power supply and remote data transmission. The environmental features collected included air temperature, relative humidity, wind speed, wind direction, and rainfall, totaling five key parameters. Additionally, previous research suggests that wave height is another crucial environmental feature influencing atmospheric chloride deposition rate in coastal region (Bresciani et al. 2014; Cole et al. 2009). Therefore, we obtained data of wave height for the coastal region of central and eastern Hainan Island from the National Marine Data Center (2024). We performed statistical analysis on the environmental data by calculating monthly averages to facilitate subsequent modeling analysis.

Figure 2:

Experimental setup. (a) Environmental features monitoring system. (b) Atmospheric chloride deposition rate monitoring system. (c) Natural exposure experiment for metal materials.

2.3 Atmospheric chloride deposition rate monitoring

The atmospheric chloride deposition rate was measured in accordance with the dry plate method outlined in the Chinese standard Standards China (2017). This method estimates the chloride deposition rate by quantifying the amount of chloride ions accumulated on a standardized surface over a defined period. It enables extended exposure to atmospheric conditions, thereby offering reliable data on chloride deposition. The dry plate method is particularly effective for long-term monitoring of atmospheric pollutant deposition rates. The experimental setup is depicted in Figure 2(b). During the experiment, each sampling plate was suspended in a location that was sheltered from direct rainwater exposure, well-ventilated, and positioned 1.5–2 m above ground level. The plates were oriented vertically, with the sampling surface facing the nearest open sea area. Sampling was conducted monthly, with three parallel samples collected each time, and each sampling period lasted for (30 ± 2) days. The average data from the three parallel samples were used to determine the atmospheric chloride deposition rate for that month. The timing of deposition rate collection was synchronized with the monitoring of environmental features. All five experimental sites adhered to a uniform sampling frequency and duration throughout the collection cycle, resulting in 1 year of accumulated deposition rate data.

2.4 Metal material corrosion measurement

The setup for the natural environment exposure experiment of typical metals is illustrated in Figure 2(c). The metal test specimens were positioned at a 45° angle to the ground, facing the direction of the open sea. Typical carbon steels (A3, CortenA) and aluminum alloys (L3M, LD2CS) were selected for this experiment. The chemical compositions of these four types of metal materials are detailed in Table 1.

Exposure tests for the four metals were conducted at the five experimental sites. Prior to testing, all samples were ground to 800 grits, degreased with acetone, and rinsed with distilled water. The samples were then mounted on test racks inclined at a 45° angle at the specified experimental sites. During the test period, the corrosion rate of the four metals was measured according to the standard Standards China (2018). The average corrosion depth was calculated by converting the weight loss of the test specimens due to corrosion. For carbon steel materials, the test period spanned 3 years, with sampling intervals at 0.5 years, 1 year, 2 years, and 3 years. For aluminum alloy materials, the test period spanned 1.5 years, with sampling intervals at 0.5 years, 1 year, and 1.5 years.

3.1 Deposition rate estimation model

In the previous study, we analyzed the holistic process of atmospheric chloride deposition and divided it into three subprocesses: production, transportation, and deposition (Chen et al. 2024b). In the coastal region of China, the environmental factors in the three processes can be simplified as shown in Figure 3. Each of these subprocesses is influenced by different environmental features, which collectively determine the atmospheric chloride deposition rate. We first analyzed the influencing features for each subprocess and then established quantitative descriptive models to accurately represent each stage.

Figure 3:

The holistic process of atmospheric chloride deposition in the coastal region.

3.2 Metal corrosion loss model

Atmospheric corrosion of metals is inherently a complex electrochemical process, influenced by various environmental factors such as air temperature, relative humidity, rainfall, and chloride deposition rate. Air temperature increases accelerate the electrochemical corrosion rate of metals, including both anodic and cathodic reactions. The acceleration effect of air temperature is often described using the Arrhenius model (Escobar and Meeker 2006), expressed as follows:

where A F T is a scaler representing the acceleration factor, T is the air temperature (unit, K), T 0 is the reference air temperature (unit, K), B = E a / K , E a is the activation energy of the reaction process, and K is the Boltzmann constant.

Relative humidity determines whether a water film forms on the metal surface. Higher humidity promotes the dissolution of salts and corrosive gases, forming an electrically conductive electrolyte solution that accelerates the corrosion process. The acceleration effect of relative humidity is typically characterized using a modified Peck model (Cai et al. 2020), expressed as follows:

where A F R H is a scaler representing the acceleration factor, R H is the relative humidity (unit, %), R H 0 is the reference relative humidity (unit, %), and C is a constant.

Rainfall can clean or flush the corroded surface of metals, thereby influencing the corrosion rate. The cleaning or flushing effect can be expressed as the ratio of rainfall amount W to the number of rainy days D , i.e.,  W / D . The effect of rainfall on corrosion is generally described using a power-law model (Corvo et al. 2005), expressed as follows:

where A F W / D is a scaler representing the acceleration factor and E is a constant.

Atmospheric chloride can damage the oxide film or protective layer on the metal surface, accelerating the corrosion process. The effect of chloride deposition rate on metal corrosion is typically characterized using a power-law model (Ji et al. 2021):

where A F C l is a scaler representing the acceleration factor, C l is atmospheric deposition rate (unit, mg · m − 2 · d − 1 ), C l 0 is the reference value of the chloride deposition rate (unit, mg · m − 2 · d − 1 ), and F is a constant.

In terms of time dimension, metal corrosion kinetics models are often described using a power-law model, which takes the following form:

where C t is the corrosion loss (unit, μ m ), C 1 is the corrosion loss in the first year (unit, μ m ), t is the corrosion time (unit, yr), and n is a constant.

The acceleration effect of environmental factors on metal corrosion is primarily reflected in the parameter. We analyzed the combined acceleration effects of the aforementioned environmental factors, examining the accuracy and generalizability of the corrosion process representation when considering different environmental factors. Ultimately, by integrating the influences of all the above environmental factors on corrosion acceleration, the proposed corrosion prediction model is proposed as follows:

where K represent corrosion loss, F , B , C , and E represent the acceleration effect parameters of chloride deposition rate, air temperature, relative humidity, and rainfall, respectively.

3.3 Spatial and temporal distribution map construction

Geographic information system (GIS) is a technological framework that integrates geographic spatial data with attribute data to collect, store, manage, analyze, and display geographic information (Santa et al. 2022; Slamova et al. 2012). To better incorporate the analysis of environmental spatiotemporal changes in coastal region, we proposed a two-stage workflow, as shown in Figure 4, inspired by GIS principles. This workflow was employed to construct distribution maps of atmospheric chloride deposition rate and its corrosion effect.

Figure 4:

Two-stage spatial and temporal distribution map construction.

Stage 1 involves the construction of the atmospheric chloride deposition rate distribution map. This process begins with defining both the temporal and spatial resolutions, followed by grid division. Utilizing existing environmental monitoring data, the Kriging interpolation method is applied to compute the environmental features for the selected area. The specific details of the interpolation algorithm are provided in Text S1. Subsequently, these environmental features are input into the prediction model proposed in Section 3.1 to generate the spatiotemporal distribution map of atmospheric chloride deposition rates. Stage 2 focuses on constructing the metal corrosion map. The inputs for this stage include the predicted atmospheric chloride deposition rate distribution results from Stage 1, corrosion time, and metal type. Based on the metal corrosion model proposed in Section 3.2, the corrosion spatiotemporal distribution maps for typical metal materials are then produced.

4.1 Statistical analysis of raw monitoring data

The monthly average results of the five environmental features monitored during the experimental period, along with the collected wave height data, are presented in Figure 5. Comprehensive statistical information is provided in Table S1.

Figure 5:

Environmental features monitoring result in the experimental period.

Figure 5 illustrates significant variations in the environmental features throughout the year, with most exhibiting clear seasonal patterns. Air temperature peaked during the summer months, displaying a sinusoidal pattern in monthly averages. Relative humidity remained consistently high, with averages exceeding 80 % throughout the year. Rainfall showed marked peaks during the summer and autumn seasons, with notable fluctuations. Wind speed was higher in the autumn and winter seasons, while lower in the spring and summer. Wind direction predominantly featured southeasterly winds in the spring and summer, shifting to northeasterly winds in the autumn and winter. Wave height data indicated higher values during the winter months, with December recording the highest values, whereas wave height was relatively lower during the other seasons.

Figure 6(a) presents the monitoring results of atmospheric chloride deposition rates measured at each site during the experimental period. The figure indicates that the deposition rate exhibited seasonal variations, generally higher in the autumn and winter seasons and lower in the spring and summer seasons, consistent with the observed patterns in wind speed and wave height data from the environmental monitoring results. Additionally, Figure 6(b) shows the variation of deposition rates with the distance from the coast, with vertical lines indicating standard deviations. The figure demonstrates that the deposition rate decreased rapidly with increasing distance from the coast, and the standard deviation of the data also gradually decreased. These findings align with the conclusions drawn from previous research (Davies and Crosbie 2018; Pongsaksawad et al. 2021).

Figure 6:

Atmospheric chloride deposition rate monitoring data. (a) Monthly average deposition rates at each site. (b) Variation of deposition rates with distance from the coast.

4.2 Data correlation analysis

We used Pearson correlation analysis, Spearman correlation analysis, and Kendall correlation analysis to examine the relationship between atmospheric chloride deposition rate and environmental features. The results are shown in Figure 7. The lower left part of each subplot represents the correlation coefficients between variables, while the upper right part indicates the results of the significance tests for the correlations.

Figure 7:

Correlation matrix of the atmospheric chloride deposition rate and the environmental features. Significant correlations are denoted as “*” (p < 0.05) and “**” (p < 0.01).

The analysis reveals that the three environmental features with the greatest influence on atmospheric chloride deposition rate were distance from the coast, wave height, and air temperature, with the effects of the first two factors being significant. Wave height and effective wind speed had a positive impact on deposition rates, while distance from the coast and air temperature had a negative impact. Among the remaining environmental features, air temperature exhibited relatively high correlations with other features, likely due to the influence of temperature variations on coastal air currents, which subsequently affect other environmental features. Furthermore, wave height and effective wind speed were positively correlated, consistent with the mechanism of atmospheric chloride production.

For the correlation analysis among environmental features, the correlations among environmental features were all below 0.7, with most correlations below 0.3, indicating relatively low multicollinearity issues. Given that each environmental feature is an important influencing factor in the holistic process, all these features were retained in the modeling process.

4.3 Atmospheric chloride deposition estimation

4.3.2 Model estimation result analysis

Based on the monitoring deposition rate data and environmental features from the five sites in coastal region of China, we conducted a modeling evaluation for the aforementioned models. Parameters were estimated using nonlinear least squares. The prediction performance and performance metrics for each model are presented in Figure 8.

Figure 8:

Comparison of different model prediction values with true values.

The red line in Figure 8 represents the best-fit line. When the predictions align closely with this line, the model achieves optimal performance, with R² equal to 1 and MAPE equal to 0. From the figure, it can be observed that among the six models, the proposed PTD model demonstrated the best predictive performance, with predicted values evenly distributed around the red line.

The MLR model, however, exhibited a tendency to underpredict high deposition rate and overpredict low deposition rate, indicating that a linear relationship does not adequately capture the complex relationship between deposition rates and the various environmental features.

The Keywood model showed a reasonable prediction trend for deposition rates, but since it only considered the distance from the coast, it failed to account for variations in environmental features in the production and deposition processes at the same location. Consequently, the prediction results exhibited a stratified pattern.

The Gustafsson model performed well in predicting deposition rates in areas with high values. However, as the distance from the coast increased, the predictions gradually deviated from the red line, with predicted values significantly exceeding the actual values. Similarly, the simplified Meira model, due to the lack of detailed analysis on the wind speed threshold, exhibited a predictive trend akin to that of the Gustafsson model.

The Hao model, which considered only the single influencing feature of distance from the coast, also displayed a stratified prediction pattern. Moreover, compared to the Keywood model, it appears that the exponential model form is more suitable than the power-law model for describing the decay trend in deposition rates.

Table 2 presents the quantitative analysis results of parameter estimation and model prediction performance for each model. Examining the parameters of the proposed PTD model, the coefficients for the two production environmental features, wave height and effective wind power, were greater than 0, indicating a positive effect on the deposition rate. The coefficient for the distance from the coast in the transportation process was less than 0 and relatively large, indicating a significant negative impact on the deposition rate. The coefficients for air temperature and relative humidity in the deposition process were negative, while the coefficient for rainfall was positive, indicating their respective negative and positive effects on the deposition rate. These coefficients had relatively small values, suggesting that these features act as adjustment factors for the deposition rate. The analysis results of environmental features were consistent with previous studies, validating that the PTD model correctly identifies the patterns of atmospheric chloride production, transportation, and deposition.

Table 2:

Model parameter estimation results and quantitative evaluation metrics.

Model	Parameter estimation result	R 2	RMSE	MAPE
PTD	D = 1632.33 e 1.06 w H + 0.11 E v − 14.42 d · 1 − 0.019 T − 0.0045 R H + 0.001 Pr	0.8814	95.720	0.5795
MLR	D = 216.58 w H − 2.28 E v − 1849.47 d − 22.3 T − 6.3 R H + 0.067 Pr	0.5729	181.64	4.0744
Keywood	D = 9239.89 e − 169.28 d + 577.69 e − 11.08 d	0.5441	187.67	1.1570
Gutaffson	D = 15.79 e 0.0001 v · d 0.76 − 0.1 v	0.6360	167.67	1.8283
Meira	D = 2197.96 e − 172.33 + 175.65 e 0.001 v · e − 36.14 x / v − 1	0.6118	173.17	2.1518
Hao	D = 16.50 d − 0.96	0.5327	189.99	2.0063

The impact of each feature on the deposition rate in the MLR model was generally consistent with the proposed PTD model, with the distance from the coast being assigned the highest weight. The Keywood model exhibited significant differences in the parameters of the two exponential terms. In the coastal region, the model was primarily determined by the first part, which validated the rationality of the simplified transportation process in the proposed PTD model. In the Gustafsson model, the coefficient of wind speed in the exponential part was relatively small, suggesting that its influence could be neglected. Thus, the model could be simplified to a power-law model, while wind speed still affected the decay rate. In the Meira model, the first term in the exponential was essentially constant, possibly due to the limited data collected in our study, lacking an analysis of wind speed thresholds. The second term indicated the positive and negative effects of distance from the coast and wind speed on the deposition rate.

Analyzing the performance evaluation metrics, the proposed PTD model exhibited the best performance compared to the other models, with an R² of 0.88, RMSE of 95.72, and MAPE of 0.57. Compared to the best-performing model among the other five models, the PTD model showed improvements of 37.50 % in R², 42.91 % in RMSE, and 50.86 % in MAPE. These quantitative metrics indicated that the proposed model achieved an accurate estimation of the deposition rate in the coastal region of China.

4.4 Metals corrosion loss estimation

The corrosion loss of the four metal materials exposed to the natural environment at the experimental sites is shown in Figure 9. As depicted in the figure, the corrosion loss of the four metals increased gradually with corrosion time. Additionally, there was a consistent and rapid decrease in corrosion loss with increasing distance from the coast. The corrosion loss at 25 m was significantly higher compared to that at 305 m, indicating a strong correlation between the corrosion loss of metals and their geographical location.

Figure 9:

Corrosion experimental results of the 4 metal materials.

Using corrosion loss data for four materials in coastal region, we applied nonlinear least squares (NLS) to estimate the parameters of the above model. The performance of models was evaluated using R², RMSE, and MAPE. The model parameter estimation results and quantitative evaluation metrics are presented in Tables 3–6. In the table, the units are as follows: t is in years, Cl is in mg/m²/d, RH is in %, T is in K, W is in mm, and D is in days. The corrosion loss of A3 steel and CortenA steel is in mm, while the corrosion loss of L3M and LD2CS aluminum alloys is in μm.

As shown in the table, the performance of model significantly improved after incorporating the chloride deposition rate, compared to the single corrosion kinetics model. For the two types of carbon steel, the corrosion process in coastal region is primarily determined by the chloride deposition rate, with the introduction of temperature, relative humidity, and rainfall resulting in a slight improvement in model evaluation. Specifically, due to the narrow range of air temperature and relative humidity variations in coastal region, the acceleration effect parameters for both temperature and relative humidity tend to zero. For the more severely corroded A3 steel, the acceleration effect parameter for rainfall is 0.0565, indicating that rainfall accelerates corrosion. In contrast, for CortenA steel, the acceleration effect parameter for rainfall is −0.4506, suggesting that rainfall inhibits corrosion.

Compared to carbon steel materials, aluminum alloys exhibit greater corrosion resistance, with the corrosion acceleration process being primarily governed by chloride deposition rate and influenced by a combination of air temperature, relative humidity, and rainfall. According to the parameter estimation results, the temperature acceleration effect parameters for the two aluminum alloys are 281.7414 and 278.1758, respectively, suggesting that temperature plays a promoting role in metal corrosion. The acceleration effect parameters for relative humidity are 0.3792 and 0.2036 for the two aluminum alloys, indicating that relative humidity also accelerates corrosion. The acceleration effect parameters for rainfall are −0.4984 and −0.5422, which suggests that the cleansing effect of rainfall reduces the chloride ion deposition rate on the metal surface, thereby inhibiting corrosion of the aluminum alloys.

The proposed model integrated various environmental factors, including chloride deposition rate, air temperature, relative humidity, and rainfall, along with corrosion time, effectively representing the metal corrosion process. A comparison between the predicted and actual values is shown in Figure 10. The figure demonstrates that the proposed model accurately captures the corrosion loss variation trends for the four metals. For all four metal materials, the model’s R² values exceed 0.92, confirming the model’s accuracy and generalizability.

Figure 10:

Corrosion loss prediction results of 4 metal materials.

4.5 Spatial and temporal distribution map

4.5.1 Atmospheric chloride deposition rate map

This section analyzes the spatial and temporal distribution of atmospheric chloride deposition rate in the coastal region. Geographically, we selected a study area of 3 km × 3 km near the experimental sites, with a spatial resolution of 0.001° × 0.001°. The study area was divided into grids to examine the spatial distribution patterns of the deposition rates. Temporally, we divided the year into four seasons: spring (March–May), summer (June–August), autumn (September–November), and winter (December–February) to investigate seasonal variations in deposition rates.

The environmental features at grid points were obtained using the kriging interpolation method. For detailed implementation, please refer to Text S1. The interpolated environmental features were then input into the PTD model estimated in Section 4.3. The resulting spatial and temporal distribution maps of atmospheric chloride deposition rates in the coastal region are shown in Figure 11.

Figure 11:

Distribution maps of atmospheric chloride deposition rate (unit mg · m − 2 · d − 1 ).

Analyzing the distribution pattern of atmospheric chloride deposition rates based on Figure 11, we observe that spatially, the deposition rates in spring, summer, autumn, and winter all exhibited a rapid decrease with increasing distance from the coast. However, distance from the coast alone did not entirely dictate the distribution. Environmental features such as effective wind power and wave height also influenced the spatial distribution, resulting in variations. Temporally, the deposition rates during spring and summer were lower compared to those in autumn and winter. This difference is attributed to higher wave heights and wind speeds during the autumn and winter seasons.

4.5.2 Metals corrosion loss map

Using the atmospheric chloride deposition rate distribution map as input, we constructed maps depicting the distribution of corrosion loss for the four metal materials, employing the corrosion prediction models estimated in Section 4.4. The spatial resolution of the corrosion distribution maps was consistent with that of the deposition rate distribution map. Temporally, we set the time intervals at 1 year, 2 years, and 3 years. The average corrosion depth distribution maps for the four metals in the first year are shown in Figure 12. Besides, the average corrosion depth distribution maps for the 2 years and 3 years can be found in Figures S1 and S2.

Figure 12:

Distribution maps of first-year corrosion losses for four metal materials.

The corrosion distribution maps were consistent with the experimental corrosion results for each metal. The corrosion loss, from highest to lowest, was A3, CortenA, L3M, and LD2CS. Spatially, the variation patterns of corrosion loss for the four metal materials mirrored the distribution patterns of atmospheric chloride deposition rates. Similarly, the severity of corrosion increased rapidly as the distance from the coast decreased. The results from the corrosion distribution maps indicate that the degradation of metal products in coastal region is highly correlated with their placement location.

5.1 Analysis of deposition rate estimation model

The atmospheric chloride deposition rate estimation model (PTD model) proposed in this study incorporates various environmental features of the holistic process. Compared to existing models, the PTD model demonstrates superior accuracy and generalization performance. However, it also has some potential limitations that need to be addressed. Firstly, due to the flat geographical environment of the experimental area, factors such as elevation and terrain were not included in the model. Considering the deposition mechanism of atmospheric chloride, elevation remains an important environmental feature (Meira et al. 2017). Therefore, for analyzing deposition rate distribution in larger geographical areas, it may be beneficial to incorporate elevation. Furthermore, while the proposed PTD model is suitable for estimating deposition rates in coastal region, adjustments are necessary when considering areas further inland. Specifically, the model needs to account for deposition rate variations during the transportation stage. Based on existing research, segmented models could be considered as an alternative modeling approach for such scenarios.

5.2 Analysis of metal corrosion loss model

The corrosion effect model proposed for coastal region considered environmental factors such as chloride deposition rate, air temperature, relative humidity, and rainfall. The accuracy of the model had been validated using experimental data from four typical metal materials. However, there are still potential areas for improvement in the model, particularly in the following two aspects. On the one hand, the study currently analyzes the accelerated effects of environmental factors using averages, but the temporal dynamic changes of the environment during the actual service life of metals cannot be ignored. Incorporating dynamic temporal environmental changes into the metal corrosion degradation modeling process is one of the key ways to improve the accuracy of corrosion modeling. Research in this area needs to set higher demands for corrosion monitoring, increase monitoring frequency, and gather more data on corrosion degradation processes. In addition, the corrosion processes of different types of metals vary greatly, and their corrosion mechanisms lead to distinct corrosion kinetics models. Research in this area needs to conduct more detailed corrosion kinetic analyses for different types of metals. For long-term corrosion processes in metal materials, there is often a trend of stage-wise degradation, and using stage-based modeling methods is also an important way to improve the precision of corrosion modeling.