The nonlinear impact of climate change on inland waterway transportation in the Upper Mississippi—Illinois River Region

The inland waterways system is vital for ensuring the efficient movement of U.S. agricultural goods from production areas to markets. In 2019, the U.S. inland waterways facilitated the transit of 514.9 million tons of waterborne cargo, accounting for approximately 14% of all intercity freight with a value of $134.1 billion. This makes the system the most cost-effective, safest, and environmentally friendly option with the lowest carbon footprint (Waterways Council 2023). Despite these advantages, the system has faced increased challenges from climate change due to its dependence on the availability and reliability of water resources.

For instance, drought can cause low water levels which may reduce the cargo-carrying capacity of vessels, increase transportation costs and affect the competitiveness of inland waterway transport (Vinke et al 2022). Jonkeren et al (2007) found that low water levels could reduce the load factors of vessels by up to 50% on some sections of the Rhine–Main–Danube corridor. In 2022, a severe drought significantly affected inland waterway transportation (IWT) in both the Rivne River in Europe and the Mississippi River in the U.S. Another major threat is flooding, which can suspend of navigation due to high water levels, causing delays, damage to infrastructure and property, and safety risks for people living near waterways. For example, Hurricane Harvey in 2017 caused widespread flooding and suspended navigation on several inland waterways in Texas. Similarly, a stalled weather system in 2015 caused record-breaking rainfall and flooding in South Carolina, affecting many inland waterways.

Although understanding the effects of climate change on IWT is crucial, given its significance for various regions and sectors, especially agriculture, the impact of climate change on the system remains inadequately explored. Most existing studies (Folga et al 2009, Oztanriseven and Nachtmann 2017, 2020) have focused on waterways utilizing diverse methods and scenarios but failed to consider the complex nonlinear influences of climate variables, hydrological processes, and navigation conditions on the performance of IWT. For instance, it is unclear to what extent changes in water levels such as reductions caused by droughts or increases due to flooding, impact barge shipping rates ¹ . Many existing studies rely on traditional statistical or simulation models that fail to capture the full range of uncertainties and dynamics inherent in the environment.

From an operational and planning practice perspective, it would be highly valuable to ascertain the environmental conditions under which substantial changes in barge shipping rates are likely to occur. This knowledge could help shippers optimize their shipping schedules, aiding barge transportation companies and lock and dam systems in preparing for potential disruptions. Ultimately, this proactive approach can mitigate the risk of losses and damage to agricultural commodity shipments, ensuring a more efficient and resilient transportation network.

This study aims to address these gaps by developing a novel evaluation framework using machine-learning methods to address the research question of the nonlinear impacts of climate change on the U.S. agricultural IWT system. The hypothesis is that climate change has significant nonlinear effects on the efficiency and reliability of the IWT system, impacting the transport of grain exports. Specifically, climate change is defined in this study as changes in temperature, precipitation patterns, and the frequency and severity of extreme weather events. The focus on the U.S. is motivated by its possession of one of the largest and most developed IWT networks globally, responsible for transporting approximately 60% of the country's grain exports. The study incorporates real-world historical data on barge shipping performance, weather information, water levels, and lock and dam operational data from various sources, including the National Oceanic and Atmospheric Administration (NOAA), the United States Geological Survey (USGS), the U.S. Army Corps Engineers and the United States Department of Agriculture (USDA). To analyze the data and generate predictions, the study utilizes the state-of-the-art machine-learning technique known as Gradient Boosting Decision Trees (GBDT). This technique offers several distinct advantages for data analytics, including exceptional predictive accuracy, the capability to reduce bias and variance, effectiveness in handling nonlinearity, missing data, and outliers, and the ability to conduct feature importance analysis, facilitating the interpretation of results (Ma et al 2017).

This study offers several key research highlights compared to previous work in this field. Firstly, it provides a comprehensive and systematic assessment of the impact of climate change on the agricultural IWT system with a focus on the key locks and dams system in the IMR-IR, considering multiple dimensions, such as water levels, discharge volume, different extreme weather events, and system disruptions ² . Secondly, it employs machine-learning techniques to handle large and diverse datasets, capturing complex relationships between factors and barge shipping rates as well as productivity. Furthermore, the application also has the potential to provide probabilistic and scenario-based predictions, enabling more evidence-based planning and operational decision-making in the context of climate change. Thirdly, it captures the non-linear and dynamic nature of the system through path-dependent plots, revealing potential tipping points or thresholds that may lead to abrupt changes in barge shipping costs. Understanding these threshold effects of various environmental conditions may help develop specific strategies to make the IWT resilient to future climate change induced disruptions.

In sum, this study contributes to the literature on climate change adaptation and mitigation in the transport sector by providing new insights and evidence to understand the non-linear impact of climate change on IWT. It offers valuable information and guidance for policymakers, planners, operators, shippers, farmers, researchers, and other stakeholders involved in IWT, enabling them to understand current and future challenges and opportunities under different climate scenarios. Moreover, it helps identify potential adaptation strategies to enhance the resilience and sustainability of IWT in a changing climate.

The rest of the paper is organized as follows: section 2 provides a summary of relevant literature and identifies research gaps. Sections 3 and 4 introduce the data and methodology, respectively. Section 5 discusses the empirical results of the analysis, while section 6 concludes by outlining implications for planning and policy decision-making.

Climate change's impacts on transportation systems can have significant economic, social, and environmental implications. This review focuses on the impacts of climate change on the transportation system's performance and operation, with a special emphasis on the impacts on the US agricultural inland waterway system. The review is organized into four subsections, namely the impact of climate change on transportation system, the impact of climate change on barge transportation for agricultural commodities, the application of machine-learning, and research gaps.

2.1. Impact of climate change on transportation systems

2.2. Impact of climate change on barge transportation for agricultural commodities

2.3. The application of machine-learning

2.4. Research gaps

3.1. Region of investigation and data collection

To address the existing research gaps and refine our understanding while boosting predictive capabilities, we focused on examining the impacts of climate change on the performance of the IWT system. Our focal point lies within the Upper Mississippi River—Illinois River (UMR-IR) region, encompassing seven major locks and dams illustrated in figure 1. These specific locks and dams—MISS 15, MISS 25, MISS 26, MISS 27, ILL 8, OHIO 52, and ARK 1—were selected based on two criteria. First, these infrastructure points are critical components of the UMR-IR navigation system but face challenges stemming from aging structures and severe shifts in environmental conditions. Second, our choice was influenced by data availability, as the USDA provides comprehensive data on barge volume and weekly rate monitoring solely for these seven locks.

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Studying this region is essential due to its role in transporting a significant portion of the nation's agricultural commodities, particularly grain exports. The UMR-IR waterways are heavily utilized and are vital to the national and global food supply chains. Additionally, the region's susceptibility to climate change-induced fluctuations, such as droughts and floods, makes it imperative to understand how these environmental changes impact navigation and operational efficiency. Insights gained from this study can help develop adaptive strategies to ensure the resilience and reliability of the waterway system, thereby safeguarding economic and operational viability.

The dataset used in this study has previously been employed to assess the regional economic consequences of disruptions in the inland waterway system, as demonstrated by Chen and Cheng (2024). A notable limitation of the earlier study is its reliance on conventional spatial econometric models that assume a linear statistical relationship to estimate the impacts of environmental factors on barge rate variations. This approach is inherently limited, as it does not account for the complexity and nonlinearity of environmental influences.

In this study, we leverage the same dataset to further investigate the nonlinear implications of climate change on the functionality of selected locks and dams in the UMR-IR region. By quantifying the functional relationships between environmental metrics and barge operation/shipping rates, we aim to improve the methodology through the application of nonlinear machine-learning techniques. This approach enhances our understanding of the intricate relationships between barge performance and environmental conditions, providing a more realistic and comprehensive perspective. Such an understanding is critical for planning and policy development, as it allows for the creation of more targeted and effective strategies to address the multifaceted impacts of environmental changes on barge transportation.

Data collection for this study involved gathering weekly barge transportation data spanning from 2013 to 2021 at the seven locks and dams. The data was obtained from the Grain Transportation Report datasets, made available by the Agricultural Marketing Services of the USDA. The collected dataset comprises information on the weekly total barge grain movement, measured in 1000 tons, passing through each lock and dam. In addition, the dataset includes the weekly barge freight rate, which represents the average shipping cost per ton from the nearby areas of each lock and dam to New Orleans. We measure barge service performance using labor productivity, which indicates the number of agricultural commodities transported per barge employee. This metric is adopted because it is a standard and widely recognized measure of transportation system performance (Meyer and Gomez-Ibanez 1980, Chen et al 2016, Vu and Hartley 2022).

Figure 2 illustrates the fluctuations in gage height alongside changes in barge rate and productivity, utilizing lock 27 as an illustrative example. In figure 2(a), a negative correlation is evident between gage heights and alterations in barge rates. This indicates that lower gage heights correspond to relatively higher barge shipping rates. Notably, during specific weeks—9/29/2014, 10/2/2017, and 10/18/2021—the barge rates surged to unprecedented levels concurrently with lower gage heights. These low gage heights correspond with high barge shipping rates, suggesting the negative impacts of drought, which cause water levels to drop, forcing ships to reduce their loading capacity and thereby increasing shipping rates.

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Figure 2(b) illustrates the relationship between gage height fluctuations and barge labor productivity over the period from January 2013 to December 2020. The green line represents the gage height at MISS 27, while the blue line depicts the barge labor productivity measured in thousand tons per barge employee. Unlike figure 2(a), which focus on barge rates, this figure highlights a discernible pattern where changes in gage height appear to correspond with variations in barge labor productivity. Specifically, periods of increased gage height generally coincide with higher productivity levels, whereas lower gage heights tend to align with reduced productivity. This correlation suggests that riverine conditions, as indicated by gage height, have a notable impact on the efficiency of barge operations. High water levels likely facilitate better navigation and loading conditions, thereby enhancing productivity, while low water levels may impede these operations, reducing overall efficiency.

3.2. Factors influencing barge rate and productivity

Different from conventional statistical analysis using panel regression models, the GBDT method was adopted to examine the non-linear association between climate change-related factors and barge system performance. GBDT is a powerful machine learning technique that has gained popularity in various domains due to its ability to model complex relationships and handle non-linear patterns in data (Wu et al 2019, Tao et al 2020). It combines the strengths of decision trees and boosting algorithms to create an ensemble of weak learners, gradually improving their predictive performance (Tao et al 2020).

In the context of evaluating the non-linear impact of inland waterway system failure on a panel dataset, the GBDT method offers several advantages (Ma et al 2017). Firstly, it can effectively capture non-linear relationships between predictor variables (Elith et al 2008) (such as the changes in barge shipping rates) and the response variable (various economic and environmental factors). This is crucial as the impact of different variables on IWT performance may not follow a simple linear trend. For instance, the performance of IWT may not be affected until the water level or river discharge volume exceeds certain safety levels. According to the National Weather Service, the Army Corps requires that year-round target water levels are between 11.5 and 12.2 feet for a safe navigation of barge system in Mississippi River near the city of Louisiana ³ . Hence, the GBDT method excels in capturing complex interactions and non-linear patterns, enabling a more accurate representation of the underlying dynamics.

Secondly, the GBDT method is suited for panel datasets, which consist of observations over multiple time periods for a set of entities (e.g. regions, cities, or industries). Panel datasets often exhibit within-entity correlations and individual heterogeneity, and the GBDT algorithm can account for such characteristics to capture the temporal dynamics and heterogeneity of the data, as well as handle missing values and high-dimensional features. GBDT can also perform feature selection by ranking the features by importance or by using a group testing procedure, which helps us better identify the relatively important factors affecting the performance of the outcome variable (Friedman 2001).

Furthermore, the GBDT method can handle missing data and automatically handle variable selection, making it robust and efficient for analyzing large and complex datasets (Tao et al 2020). This is particularly important when dealing with real-world data, where missing values and redundant variables are common challenges.

By employing the GBDT method on a panel dataset, we can gain insights into the nonlinear impact of climate change on IWT performance variation. The ability of GBDT to capture complex relationships and accommodate panel dataset characteristics makes it a valuable tool for uncovering the nuanced effects of system failure and informing decision-making processes related to inland waterway infrastructure management and policy interventions. The model specifications were introduced in Appendix 2.

The performance of the IWT was described using two variables, including the weekly barge shipping rate (UnitRate) and barge labor productivity. Other variables, such as the year trend (yeartrend), the dummy variable representing the periods of trade tension between China and the US (tradewar) and the duration of lock/dam disruptions (tdistruption) were treated as control variables. In total, two sets of GBDT models were developed to investigate the nonlinear relationships between changes of the waterway environment and variations in barge rate and productivity, respectively.

To prevent overfitting resulting from increasing model complexity, we utilized a five-fold cross validation method and reported the root mean square error (RMSE) and the number of iterations for the best performing model under cross-validation (CV), as shown in figure 3. Our analysis demonstrates that the mean squared error (MSE) decreases and stabilizes as the number of iterations increases across all five models. The green line indicates the MSE for the testing dataset under CV, while the black line shows the MSE for the training dataset. The vertical blue dashed line marks the iteration point where the model achieves its optimal performance.

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To determine and quantify the contribution or impact of different variables in the GBDT model, we generated relative importance diagrams for two groups of analyses using the gbm package in R. As shown in figure 4, it becomes evident that several key factors exert significant influence over variations in barge rates. These primary factors include gage height, discharge volume, temperature, year trend, and the duration of lock and dam system disruptions. In particular, the gage height variable presents over 25% of relative influence on the model's predictability, suggesting the pivotal role of water level as the crucial environmental factor affecting barge rates.

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Figure 5 presents a similar pattern, examining the relative influences of factors in predicting barge labor productivity, although with a slightly different ranking of the aforementioned variables. For instance, discharge volume, gage height, and temperature emerge as the top three variables with the highest relative influences.

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Figure 6 presents partial path dependent plots highlighting the influential variables' impact on barge rate changes and productivity ⁴ . Specifically, figure 6(a) shows the relationship between gage height and barge shipping rates. When the median gage height of the Mississippi River ranges from 12 to 25 feet, the barge shipping rate stabilizes around 330 units. However, if the gage height drops below approximately 12 feet, the shipping rate is expected to increase by 120 units, representing a 36% increase, reaching approximately 450 units. Conversely, as the gage height rises to around 30 feet, the rate decreases to its lowest level at around 100 units, indicating a 70% reduction. Further increases in gage height lead to a rebound in the shipping rate to approximately 300 units. These results emphasize the complex, nonlinear relationship between gage height and barge rates, with critical thresholds that significantly influence outcomes.

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The diagram further highlights the presence of a nonlinear relationship between gage height and productivity. Specifically, when the median gage height is below 12 feet, there is a notable upward trend in productivity with increasing gage height. However, as the gage height continues to rise, reaching around 40 feet, productivity experiences a significant decline, dropping from 14 to just 2. Beyond this point, any further increase in gage height appears to have no discernible impact on the variation in barge productivity, as it remains consistently low. This nonlinear pattern underscores the complex and nonlinear relationship between gage height and productivity, with clear inflection points where the effect of gage height on productivity undergoes distinct changes.

Figure 6(b) reveals a negative association between median river discharge volume and barge shipping rates. When the weekly median river discharge volume exceeds 200 000 cubic feet per second, the barge rate remains below 300 units. However, when the volume falls below 200 000 cubic feet per second, the rate experiences an exponential increase by 50%, surpassing 450 units. This result indicates that lower discharge volumes, often associated with drought conditions, have severe implications for barge rate changes.

In terms of its impact on barge productivity, figure 6(b) unveils a noteworthy positive correlation between the median riverine discharge volume and productivity. As the volume remains below 600 000 cubic feet per second, there is a substantial increase in productivity. Interestingly, as the volume continues to rise beyond the 600 000 cubic feet per second threshold, productivity maintains a relatively high level. This outcome not only underscores the existence of a nonlinear relationship between the median riverine discharge volume, the barge shipping rate, and productivity but also emphasizes that the median river discharge volume exerts a different influence on the barge shipping rate and productivity.

Figure 6(c) depicts the relationship between mean temperature and barge rate changes. Generally, when the temperature is below 62 degrees Fahrenheit, the barge rate increases as the temperature rises. However, once the temperature surpasses 62 degrees, the rate significantly declines. In addition, figure 6(c) also presents the relationship between mean temperature and productivity. Generally, this pattern reflects the sensitivity of barge operations to temperature variations, with higher temperatures potentially reducing barge efficiency and increasing costs.

Regarding the influence of precipitation, figure 6(d) demonstrates that changes in precipitation levels influence barge rate and productivity, particularly when the median weekly precipitation volume falls below 0.5 inches. Lower precipitation typically denotes dry weather or limited rainfall, leading to notable fluctuations in barge rates. When the weekly precipitation volume exceeds 0.5 inches, the barge rates stabilize, indicating that moderate to high precipitation level may provide more consistent conditions for barge operation.

This phenomenon can be attributed to several factors. Firstly, moderate precipitation over the period likely contributes to maintaining optimal water levels, facilitating smoother and more predictable barge navigation. Additionally, higher precipitation reduces the variability in water conditions, thereby minimizing disruptions and operational uncertainties. However, it is also important to consider potential limitations and noise in the data. The model's capacity to capture these patterns accurately might be influenced by the quality and resolution of the precipitation data. Furthermore, the observed stabilization might reflect a broader trend within the dataset, indicating that barge operations benefit from more stable environmental conditions provided by consistent rainfall. Overall, these insights underscore the importance of considering environmental factors in transportation planning and policymaking, highlighting the nuanced ways in which different levels of precipitation can impact inland waterway operations.

International trade policies can significantly affect barge shipping rates. The impact of a trade war on these rates can vary depending on several factors, including the countries involved, specific trade policies implemented, and the duration and intensity of the trade war. In the case of the United States and China, an escalating trade dispute unfolded starting in June 2018. China, in response to US tariffs, announced its own tariffs on $50 billion worth of U.S. goods on June 16 (Chengying et al 2022). The targeted industries included agriculture, automobiles, and energy. Subsequently, on June 29, as a countermeasure to increased tariffs on Chinese goods, China further intensified the trade war by imposing tariffs on a wide range of U.S. products, such as soybeans, pork, and automobiles.

To examine the extent to which the barge shipping rate was influenced before and after the U.S.-China trade war, a dummy variable was created. Figure 6(e) illustrates the relationship between barge rate and productivity variations pre- and post-trade war. The trade war was found to have a negative impact on the barge shipping rate, and a positive impact on productivity. On average, the shipping rates were 7 units lower after the initiation of the trade war and the productivity was about 0.7 units higher after the initiation of the trade war. The observed decrease in barge shipping rates can be attributed to multiple factors. Firstly, it is possible that the reduction in rates is a consequence of the diminished demand for agricultural commodities resulting from the influence of the trade war. Secondly, trade wars have the potential to disrupt established supply chains and trade relationships. As major agricultural importers, countries like China may seek alternative trading partners or adjust their import/export strategies, leading to shifts in the transportation patterns of specific commodities. Consequently, these shifts can affect the demand for certain goods and subsequently impact barge shipping rates. Thirdly, the decrease in rates could also be attributed to the economic uncertainty and market volatility generated by the trade war.

Figure 6(f) illustrates the relationship between the duration of lock and dam system disruptions and corresponding changes in barge shipping rates and productivity. The productivity reveals a decreasing trend as the disruption duration increases, reaching its lowest point at 8.7 when the disruption period spans approximately 3.5 d. An intriguing observation is that the shipping rate exhibits a declining pattern as the disruption duration increases, reaching its lowest point at 322 when the disruption period spans approximately 1.5 d. However, as the duration of disruptions extends further, the shipping rate displays a continuous increase.

This trend can be attributed to several factors. In the initial phase of a short disruption, the barge shipping rate may decrease due to concerns surrounding a potential decrease in service supply. The temporary disruption raises apprehensions among shippers, leading to a cautious approach and a reduction in shipping rates. However, as the disruption duration prolongs, the mounting concerns of potential barge service disruptions among shippers may trigger a panic buying behavior. This phenomenon arises from the fear of further disruptions and a desire to secure transportation services, driving an increase in shipping rates.

Therefore, the observed pattern of decreasing rates followed by an eventual increase can be understood because of the interplay between short-term concerns about service availability and a relative long-term apprehension regarding prolonged disruptions. These dynamics influence the decision-making of shippers, ultimately shaping the fluctuation in barge shipping rates during different durations of lock and dam system disruptions.

To understand how barge shipping rate may vary due to different types of disruptions caused by different events, we also generated the path dependent plots based on four major types of events: flooding, fog, snow and ice, and system failure. As illustrated in figure 7(a), as the duration of lock and dam closure increases, both the barge shipping rate and productivity are likely to experience a substantial decrease especially in the first two days of closure. As the period of disruption further extends, the magnitude of shipping rates reduction and productivity reduction tend to be decreased as well, until it stabilizes.

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Regarding fog-related disruptions, figure 7(b) shows that overall, the influence of fog has a relatively mild effect on fluctuations in barge shipping rates and productivity. Nevertheless, there may be instances of notable fluctuations during the initial disruption, typically occurring over a half-day period. Similarly, the impact of lock and dam disruptions caused by snow and ice is also observed to be relatively minor, as indicated in figure 7(c). This could be attributed to the proactive measures taken by various industries and businesses during the winter season to adapt to potential disruptions. These measures include adjustments to shipping schedules and the implementation of winter maintenance practices.

While the earlier discussion of the results focused on deterministic estimates, figures 6 and 7 also incorporate confidence intervals, which provide valuable insights into the uncertainty of these estimates. These intervals delineate the range within which the true values are likely to fall, thus highlighting the reliability and precision of the model's predictions. For instance, the wider confidence intervals observed at extreme values of precipitation, trade war effects, fog delays, and system failure-related delays suggest a higher degree of uncertainty. This indicates that predictions in these ranges should be interpreted with caution.

Furthermore, the presentation of results with narrower confidence interval reflects the inherent variability in the data and the model's precision of predictivity given the different inputs. The use of these figures ensures a balance between precision and readability, acknowledging the model's accuracy without overstating the exactness of the results. This level of precision is particularly important in practical applications, as overly precise estimates might convey a false sense of certainty.

This study focused on estimating the nonlinear impact of climate change on the U.S. agricultural IWT system using the innovative approach of GBDT machine-learning method. By examining the relationship between barge shipping rates, productivity, and various environmental factors, we aimed to fill the research gap regarding the effects of climate change on inland waterway operations.

Our findings provide valuable insights into the nonlinear associations between environmental conditions and variations in barge rates and productivity. The GBDT analysis revealed that factors such as water levels, temperature, and disruptions to lock and dam systems have significant impacts on barge shipping rates. We observed threshold effects, where small changes in environmental conditions resulted in minimal rate fluctuations, while larger changes caused substantial rate changes. Moreover, such threshold effect varies across various inland waterway operational indicators (e.g. barge shipping rates and productivity). This reveals that different and specific strategies may be required to cope with different weather variations to achieve different transportation operational goals.

To gain a deeper insight into the interplay among barge shipping rates, productivity changes, and different disruption types, figure 6 elucidates critical thresholds that delineate distinct relationships between barge performance indicators and environmental condition factors. Our analysis identifies the 29 ft gage height as a pivotal threshold influencing barge rate changes; rates tend to rise as the gage height decreases. However, surpassing this threshold can also lead to increased shipping rates. Conversely, a decrease in gage height from 41 ft to 11 ft is associated with heightened barge operational productivity, likely due to improved navigation system safety during flooding events. However, when the gage height falls below 11 ft, productivity experiences a further reduction. From a shipper or barge operational standpoint, these threshold levels offer valuable guidance for adjusting shipping arrangements under diverse environmental conditions.

For instance, when the gage height is below 11 ft, the analysis suggests a high disruptive impact on the barge operation supply chain, characterized by both increased rates and decreased productivity. Hence, shippers may consider alternative shipping options, such as changing the mode of transportation if the goal is to deliver the goods to the destination on time. Of course, the reality of the decision-making can be more complicated given the consideration of costs.

Examining the interaction between temperature and barge performance in figure 8 reveals that when the temperature exceeds 80 degrees, barge productivity is likely to decrease, accompanied by a reduction in barge rates. This suggests that high temperatures could negatively affect barge operations, possibly due to increased maintenance requirements or reduced efficiency of barge crews working in hotter conditions. Additionally, elevated temperatures can exacerbate water level reductions due to increased evaporation, further complicating navigation and potentially leading to higher operational costs.

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The findings highlight the varying rates and extents of barge productivity responses under different weather or system conditions. Generally, barge rate changes appear more sensitive to disturbances of various types, as their lower threshold for initial change is less than that of productivity.

These insights are particularly relevant for future risk management of IWT given the understanding of the interplay between climate change conditions and the system performance. For example, expected higher temperatures due to climate change may affect barge rates and productivity by increasing the frequency of low water levels, necessitating more frequent load adjustments and increasing maintenance costs. Similarly, changes in precipitation patterns, resulting in either more intense droughts or floods, could further impact barge operations by either limiting navigability or causing damage to infrastructure.

The analysis also reveals that the relationship between environmental conditions and barge performance, as measured by barge rates and productivity, is inherently nonlinear. This finding contrasts with earlier work by Chen and Cheng (2024), which assumed a linear relationship. Our study demonstrates that ignoring the nonlinear nature of these interactions can potentially lead to misleading outcomes, particularly when estimating the macroeconomic impact of IWT disruptions caused by water level changes. This underscores the practical relevance and necessity of applying nonlinear models to accurately capture the complexities of environmental influences on barge transportation.

Understanding the threshold effects of environmental conditions on inland waterway operations is crucial for decision-makers. This knowledge can aid in the development of adaptive strategies to mitigate future risks and consequences arising from climate change-induced disruptions. Policymakers may also benefit from these findings to develop more effective policies for future infrastructure investments that enhance the resilience of the US inland waterway system.

Despite the robust findings, there are limitations to this analysis. Firstly, the analysis focused on the selected locks and dams in the UMR-IR region, and the findings may not be directly applicable to other regions. Secondly, the reliance on median and mean values for aggregation might overlook short-term fluctuations that could be relevant in specific contexts. Thirdly, there may be other variables not considered in our analysis that could influence barge rates.

In terms of the methodology, while the use of GBDT allows for the capture of nonlinear relationships and interactions among variables that simpler models might overlook, it is essential to recognize the potential disadvantages of using such sophisticated models, including the risk of overfitting and the challenges associated with model interpretability. In addition, GBDT models can be susceptible to biases if the training data is not representative of the broader context.

To mitigate the risk of overfitting, it is important to employ techniques such as cross-validation, regularization, and pruning within the model-building process. Furthermore, ensuring a robust and representative dataset is crucial for enhancing the generalizability of the model's findings. Issues related to data quality, such as aggregation and noise, can affect the accuracy and reliability of the results. Addressing these data quality issues through preprocessing and validation steps is essential for improving model performance.

Conversely, one may also note that simpler methods, while potentially less capable of capturing nonlinearities, can offer more straightforward interpretations and may be useful for identifying broad trends. These methods can serve as complementary tools to complex models, providing a baseline for comparison and validation of findings.

Future research should consider expanding the scope of the study to encompass a wider range of regions and factors. Incorporating additional variables, such as economic indicators or infrastructure conditions, could provide a more comprehensive understanding of the complex dynamics within the IWT system. Additionally, conducting scenario-based analyses to assess the potential impacts of future climate change scenarios on barge rates would further enhance our understanding and enable more informed decision-making. Such efforts would contribute to a more holistic view of the system and its vulnerabilities, ultimately supporting more resilient infrastructure planning and policy development.

An earlier version of this paper was presented at the 70th Annual North American Meetings of the Regional Science Association International. The authors would like to thank the conference participants and the two anonymous reviewers for their constructive comments, which greatly helped improve this paper. All remaining errors and mistakes are the responsibility of the authors.

The data that support the findings of this study are openly available at the following URL/DOI:https://agtransport.usda.gov/stories/s/Barge-Dashboard/965a-yzgy/.