Discriminant analysis of the freeze-up and break-up conditions in the Inner Mongolia Reach of the Yellow River

River ice formation affects the safety of residents living in the adjacent floodplain (Kovachis et al. 2017). In winter, 60% of the rivers in high latitudes are impacted by river ice formation (Rokaya et al. 2018). The evolution of ice formation and depletion is exceedingly complicated. As the temperature drops, rivers in high latitudes will successively experience frazil ice growth, freeze-up, and break-up processes. Each stage has its characteristics and governing laws. Frazil ice is the small ice particulates floating above the water surface. Frazil ice forms pans and eventually congregates to produce bigger ice floes. When the river is constrained by structures, the ice floes cause ice jams and pose flooding hazards when river break-up starts (Su et al. 1997; Beltaos 2012; De Munck et al. 2017; Kim et al. 2021). River freeze-up occurs when the formation of a continuous, immovable ice cover completely shuts down waterway transport. A break-up event is the opposite of a freeze-up event and occurs near the winter's end as temperatures rise. Freeze-up and break-up dates often mark the closing and re-opening of the navigation and boat traffic in winter, which is crucial for preserving ecohydrology and developing socioeconomics in cold regions such as Canada (Williams 1965; Lacroix et al. 2005).

Many scholars have attempted to simulate the river freeze-up and break-up processes. Adams (1976) established the relationship between surface heat loss and temperature drop and predicted the freeze-up of the upper reaches of the St. Lawrence River. The errors in the prediction of the freeze-up dates were within 2 days compared to the observed data. Ashton (1985) summarized the equations for heat exchange between the water surface and the atmosphere and between the ice cover and the atmosphere and revealed the ice melting mechanisms during the break-up stage by analyzing the influence of the surface energy budget on the ice cover temperature. Foltyn & Shen (1986) established a river freeze-up date forecast model using water temperature, air temperature, and flow velocity. When applied to the upper St. Lawrence River, the model results only showed 4.5 days error for 16 years of observed data. Palecki & Barry (1986) used regression analysis to determine the statistical relationship between the freeze-up dates and mean temperatures over different periods in 63 Finnish lakes and found a strong correlation (up to 88% for the proposed equations) between the mean temperatures of the months before the freeze-up event and the actual freez-up dates. Shen & Chiang (1984) and Shen & Wang (1995) analyzed measured data of Hequ Reach of the Yellow River and characterized the evolution of the ice jam regarding heat exchanges. The ice transport capacity was developed by analogizing with sediment transport, and numerical thermal-ice simulation models for natural channels were derived from their studies. Morales-Marín et al. (2019) coupled the hydrological and one-dimensional river temperature models into a new river ice modeling framework. This framework has been successfully applied to the Athabasca River Basin in Canada, and the simulated river break-up date was in good agreement with the hydrological station monitored data (e.g., R² = 0.91 for Fort McMurray station). Sun (2018) proposed a stacking ensemble tree model (STEM) framework that further enhances the freeze-up/break-up date prediction accuracy of the classification and regression tree (CART) and the modified version of the CART (M5) by 13.1 and 13.2%, respectively. With climate change becoming a heated debate topic, scholars have also examined how climate change may change the freeze-up/break-up processes. Sha et al. (2018) adopted a coupled model to the headwater reach of the Yalu River above the Balin Hydrological Gauge Station. They found that with earlier snowmelt peaks in spring, the total frozen days in winter would be reduced. The impacts of human activities on hydrological processes have also been studied by scholars considering multiple climate scenarios. Agashua et al. (2022) findings imply that the values for the post-impact (1967–2022) maximum flow rate dropped as the day advances in River Ikpoba. Garcia et al. (2022) investigated the effect of drought on the life cycle of barge transportation in Madeira River, Brazil. Their results demonstrated that during a drought, barge transportation is more detrimental to the environment.

The Yellow River is one of the rivers experiencing the most frequent ice jams in China (Chang et al. 2016). The major ice jam disasters occurred in the northernmost part of the Inner Mongolia section. This section of the Yellow River has an inverted U shape, with a steep upstream slope and a gentle downstream slope, causing ice dams to occur frequently in winter and attributing to massive casualties and property losses (Zhao et al. 2020). Ice prediction is an effective means to prevent or mitigate ice-induced natural disasters. Wang et al. (2008) used the artificial neural network model based on feed-forward back-propagation improved by the Levenberg–Marquardt algorithm to forecast the ice situation of the Yellow River in Inner Mongolia. The measured values in winter are in good agreement with observed data (the calculated R² ranges from 0.96 to 0.98).

Chen & Ji (2005) proposed a fuzzy optimization neural network method adopting the correlation coefficient method to select governing factors. Applying their method to the Inner Mongolia Reach of the Yellow River, the predicted errors were equal to or less than 6 days in 27 out of 30 cases. Fu et al. (2014) applied the Yellow River Conservancy Commission River Ice Dynamic Model (YRIDM) to the Ningxia-Inner Mongolia section of the Yellow River and verified the accuracy of their model based on observed data. The root mean square error (RMSE) for Sanhuhekou station during the winter of 2008/2009 is 0.85, deemed acceptable by the authors. The model can simulate water level, flow, water temperature and ice cover thickness under unsteady flow conditions. The continuous improvement of field observation methods and related research provides convenience for more accurate prediction of the freeze-up/break-up dates. Zhao et al. (2021) used a combination of observation and remote sensing monitoring to explore the interaction between sediment transport at the river bends and the river freeze-up process. The results showed that due to the convex bank's shallow depth and low flow velocity, smooth ice covers first appeared near the bank and then continued to develop upstream to freeze the river completely. Zhang et al. (2021) proposed an ice evolution monitoring system using the channel extraction method based on sparse reconstruction (CE-SR), adaptive threshold segmentation (Th), and Fuzzy C-means (FCM) methods to monitor the ice regime of the Yellow River. The optimal combination of CE-SR + Th + FCM can achieve 90.65% on the accuracy assessment factor. Its performance is ideal for detecting changes in river ice.

In previous studies, the simulation of the freeze-up and break-up processes mainly adopted mathematical model frameworks, statistical regressions, and neural network computations. The mathematical model frameworks are based on the physical mechanism of river ice formation and evolution. Based on the equations of hydrology, thermodynamics, and river ice hydraulics, a mathematical model framework is established to simulate river ice-related processes. The field-monitored data from hydrological stations are used to validate the equations and predict the freeze-up and break-up dates (Bian et al. 2015). The statistical regression analysis screens the factors that affect the freeze-up and break-up dates, such as factors influencing the momentum and thermodynamics of the system. Statistical regression analysis techniques establish the connections between freeze-up/break-up dates and the factors examined (Qiao et al. 2013). The artificial neural network is formed by the interconnection of a large number of nodes. It is an abstract mathematical model that reflects the structure and function of the human brain. The artificial neural network uses a large amount of data for repeated learning and summarizes the internal correlation of the data (Chen & Ji 2004). However, neural network methods are insufficient to generalize from limited training data. Due to the complexity of mathematical model construction, upstream and downstream neuron data support is often insufficient. The simplification of some parameters and constraints in the calculation process reduces the accuracy of the neural network models. To the best of the authors' knowledge, the existing models consider thermal, hydraulic, terrain, and other influencing factors but not the impact of ice production. If the impact of ice production on the freeze-up/break-up dates is considered, it will be beneficial to further improve the river ice-water conversion process simulation accuracy.

Based on Hou et al.’s (2022) study of ice production in the Inner Mongolia section of the Yellow River, this paper innovatively considers both the ice production and the storage capacity of the channel to calculate the total storage potential. Considering the thermal, geomorphologic, and river ice hydraulic factors, an empirical equation was derived to assess the river freeze-up and break-up conditions. This study can provide a theoretical basis for determining an accurate river freeze-up and break-up forecast model to mitigate and/or prevent ice-induced disasters.

Field observation of a river's ice regime is the preliminary step for studying the initiation and development of river ice cover, during which the researchers can monitor the whole process intuitively. In strict accordance with the Specification for Observation of Ice Regime in Rivers SL 59-2015 (Ministry of Water Resources of the People's Republic of China 2015), the Yellow River Institute of Hydraulic Research (YRIHR) conducted fixed-point observations of the entire Inner Mongolia Reach of the Yellow River in winter. The observed data from four gauging stations (Bayangaole, Sanhuhekou, Baotou, and Toudaoguai) were evaluated in the study. The assessed hydrological and meteorological data include cross-section data, freeze-up/break-up dates, air temperatures, water temperatures, wind speed, discharge, velocity, and ice thickness.

Mathematical frameworks that combine the governing thermodynamic and hydraulic equations and consider the influence of river channel morphology can better simulate the actual physical process of ice evolution during the freeze-up and break-up of a river. The total storage potential of the channel is divided into ice formed on the river surface and the water storage capacity under the ice cover. Considering the available data for parameters used in previous research (e.g., Chen & Ke 1994; Ke et al. 2001; Wang et al. 2021; Hou et al. 2022) that examined the influence of thermal processes, hydraulic processes, topography, and ice production of the river, the derivation of the empirical equation for freeze-up/break-up determinations is indicated below.

Observatory data were analyzed regarding the freeze-up dates, break-up dates, and total frozen days of the four selected stations in the Inner Mongolia Reach of the Yellow River in winter from 2017 to 2020. The results are shown in Tables 1–3. It can be seen from Table 1 that the freeze-up order of the selected gauging stations is Toudaoguai, Baotou, Sanhuhekou, and Bayangaole, indicating that the water surface in the study reach gradually freezes from the downstream to the upstream. It is worth noting that the freeze-up date at Baotou station in 2016–2017 was 2 days later than that of Sanhuhekou, and the freeze-up date of Toudaoguai in 2018–2019 was 4 days later than that of Baotou, which is inconsistent with the identified trend. Further research is required to investigate these anomalies.

It can be observed from Table 2 that the break-up order of the four selected stations is Bayangaole, Sanhuhekou, Baotou, and Toudaoguai, indicating that the stationary ice cover gradually breaks up from the upstream to the downstream. In the winter of 2016–2017, ice cover at Baotou and Toudaoguai shared the same break-up date. Similarly, in the winter of 2018–2019, break-up events occurred concurrently at Sanhuhekou and Baotou.

Table 3 indicates that the number of total frozen days in the lower reaches is greater than in the upper reaches, reflected by the descending order of Toudaoguai, Baotou, Sanhuhekou, and Bayangaole. Similar to the river freeze-up date statistics, the total freezing days in Toudaoguai in 2018–2019 were 2 days less than in Baotou. Freeze-up and break-up events happened simultaneously at Baotou and Toudaoguai in 2016–2017. The exact coincidence occurred for Sanhuhekou and Baotou in 2018–2019.

It is worth noting that Baotou and Toudaoguai had the same freeze-up date in 2016 (November 25th) and break-up date in 2017 (March 16th). Sanhuhekou and Baotou stations also recorded same-day freeze-up events in 2018 (December 7th) and break-up occurrences in 2019 (March 16th). In the Inner Mongolia Reach of the Yellow River, the upstream is closely connected to the downstream as an integrated water body between hydraulic stations. Under specific temperature and flow conditions, the freeze-up and break-up events of the upstream and downstream stations are very likely to occur on the same day within hours. For example, when the water in the upstream hydraulic station radically freezes up after the drastic temperature drop, the downstream flow will be reduced immediately following the upstream freeze-up occurrence. Therefore, the freeze-up of the downstream station will also be noticed under the consolidated influences of the temperature drop and the flow reduction. Contrarily, the upstream break-up occurs when the temperature rise, which increases the downstream flow, and the downstream ice cover will continue to thaw under the impacts of temperature rise and flow increase. If the weather and hydraulic conditions are ideal for fast thawing of the ice cover, same-day break-up can be expected between the upstream and downstream stations.

The Inner Mongolia Reach of the Yellow River is gradually freezing from the downstream to the upstream. Later, the ice cover broke up progressively from the upstream to the downstream. The number of freezing days in the downstream exceeds that in the upstream. These patterns are comparable with data from studies in other Yellow River tributaries (Ke et al. 2001; Qiao et al. 2013; Wang et al. 2021).

Analysis of the gauging statistical data demonstrates that the freeze-up date, break-up date, and total frozen days of the study reach constantly change every year. Thermal factors determine the process of ice generation and melting in the river. Hydraulic factors determine the ice transport capacity of the river. River regime and whether there are any in-stream structures determine the ice jam initiation location. Furthermore, the ice production amount in a river determines the thickness and shape of the formed ice jam.

River regime and in-stream structures also contribute to the formation of ice jams and ice dams in the river. Ice jams in the Inner Mongolia section of the Yellow River mainly occur in river sections where the gradient of the river channel changes from steep to slow and where river bends or in-stream structures exist. The upper reach Bayangaole section of the Inner Mongolia Reach of the Yellow River has a wider river body, with many shoals and bends. In contrast, the downstream Baotou section becomes gentler, with more numbers of large bends. The unique morphology and channel bed slope make it easier for ice to accumulate in places where the flow velocity is slow. Ice accumulation causes ice floes to build and leads to river freeze-up. The circulation formed at the bend or hydraulic structures such as bridge piers hinders the transport of ice, which will also decrease the probability of ice jams. In recent years, with the development of China's economy, many new bridges have been built in the Inner Mongolia Reach of the Yellow River (Wu & Hui 2021). The flow velocity around the bridges decreases, thus triggering an earlier freeze-up of the reach.

The peak time of ice production in the channel is often close to the freeze-up date, and the reduction in ice production is closely related to ice melting and the break-up of the river. During the field observation of the Yellow River, frazil ice density was selected to reflect the ice production process. Frazil ice density is defined as the ratio of the ice floe area to the total channel surface area. The winter observation results from 2017 to 2020 show that the channel experienced freeze-up events when the frazil ice density reached 0.6–0.9. Therefore, the river freeze-up process is not only determined by the timing of the peak ice production but also related to the ice transport capacity of the river channel impacted by other factors such as terrain and discharge. The break-up process is divided into gradual break-ups, rapid break-ups, and moderate break-ups. Due to different dominant influencing factors, the speed of break-up events will also vary. The temperature increase and the ice production decrease dominate the tranquil break-up events. The rapid break-up is dominated by the discharge surge and the river's steep bed slope. The moderate break-up is dominated by the combined effects of tranquil and violent break-up events.

As extreme events associated with climate change become more prevalent in watersheds around the world, it is critical to understand how river freeze-up and break-up dates can be predicted to better regulate channel navigation. This study found that the Inner Mongolia Reach of the Yellow River is gradually frozen from the downstream to the upstream. Later, the ice cover gradually broke up from the upstream to the downstream. The total number of frozen days in the downstream is greater than in the upstream. These trends are consistent with findings from other reaches of the Yellow River. The influence of thermal factors, hydraulic factors, topography, and ice production process all have a significant effect on the dates when freeze-up and break-up will occur, with a strong correlation between the amount of ice formed in the channel and the water storage beneath the ice. The results imply that when the proportion of ice formed in the channel is high, and the proportion of water storage is low, freeze-up is prone to occur. Greater ice thickness, higher temperatures, and greater discharges are often required to facilitate the break-up of a river better.

The current discriminant study on the freeze-up and break-up conditions in the Inner Mongolia Reach of the Yellow River can provide a certain reference for the determination of the time of freeze-up and break-up in a year, but it can only assess the critical situation. Future study on the determination of freeze-up and break-up dates should focus on gaining an integrated understanding of the whole ice production process. Furthermore, while the current study examines the observed data of the freeze-up dates, break-up dates, and total frozen days of four gauging stations at the Inner Mongolia Reach of the Yellow River in winter from 2017 to 2020, more statistical analysis are needed to gain a better understanding of trends over break-up and freeze-up dates in a longer time span – for example, how the ice formation processes have evolved before and after the construction of any in-stream hydraulic structures.

This research is funded by the Joint Funds of the National Natural Science Foundation of China, grant number U2243239 and the National Key Research and Development Program of China, grant number 2022YFC3202500. The authors are grateful for the financial support.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.