Abstract
In the present study, ice production in a natural river reach has been studied by means of the thermodynamic theory regarding the heat flux between ice, air, riverbed, and water. The heat transfer coefficient and equivalent total heat flux were determined for different periods during winter. The characteristics of variation and distribution of ice production in the Inner Mongolia Reach of the Yellow River (IMRYR) were studied in combination with the change of heat flux. A model for describing the temporal–spatial variation of ice production for the IMRYR has been developed. The ice production process of the IMRYR from 2017 to 2021 was simulated using the proposed model, and the simulation results were in good agreement with those of the measurements. Results of the analysis showed that when the total ice production in the Bayangaole gauging station reaches 3.18 × 107 m3, a freeze-up process in this river reach is likely to occur. The influence degree of each variable on the ice production was in the following descending order: water surface area, air temperature, radiation, and flow. Particularly, a change of 20% of the water surface area will lead to a 11.48% change in the final calculated result of ice production.
HIGHLIGHTS
Ice production in Inner Mongolia Reach of the Yellow River: At present, there are some related studies on the variation characteristics of ice situation and flow in the Inner Mongolia Reach of the Yellow River, but there is hardly any study regarding ice production in a natural river.
Thermodynamics: The water body heat exchange process and heat flux components of each part during winter were analyzed.
INTRODUCTION
During winter, a lot of ice appears in rivers in cold regions produced through the heat exchange process. Once an ice jam or ice dam is formed in the river, the flow capacity of the river is reduced. Consequently, the water level will be increased and the flow velocity under an ice jam may increase. It may cause an ice flood (Sui et al. 2002, 2005, 2006) and dramatical deformation of a riverbed under an ice jam (Sui et al. 2000). The Yellow River is one of the rivers with the most frequent ice floods in China. The main ice flood disasters are concentrated in the northernmost Inner Mongolia Reach and the downstream Hequ Reach of the Yellow River (Sui et al. 2002, 2005, 2006, 2007, 2008). According to incomplete statistical results from 1990 to 2019, more than 30 ice jam/ice dam events occurred in the Inner Mongolia Reach of the Yellow River (IMRYR) (Zhao et al. 2020).
Sufficient ice on the water surface is an essential condition for the formation of an ice jam or ice dam. When the ice discharge rate from upstream is greater than the ice transport capacity of the river reach, ice floes and frazil ice particles easily accumulate under an ice cover and form an ice jam or ice dam. The speed of the development of an ice cover or ice jam is related to the amount of ice production (Lees et al. 2021). Thus, the flow cross-sectional area decreases, and ultimately it leads to a decrease in the flow capacity, and an increase in the water level during an ice-jammed period. This will result in an increase in the ice jam thickness (Sui et al. 2002, 2005, 2008). The calculation results of ice production can provide support and guarantee for predicting the occurrence of an ice jam and the relationship between the flow and water level in a river, which has great importance for disaster prevention and mitigation (Wang et al. 2007, 2021).
At present, there are two typical methods for estimating ice production in a river. The first method for estimating ice production is to use the observed or calculated area of floating ice on the water surface multiplied by ice thickness to obtain the volume of ice production (Comiso et al. 2011). The second method for estimating ice production is to simulate the heat exchange process by establishing a thermodynamic model and calculate the volume of ice production (Cheng et al. 2017). The heat budget has an important influence on the river ice production in cold regions, and it is also an important part of developing a model for determining the ice production. The evolution of river ice along a river reach is influenced by the heat exchange process among the atmosphere, ice cover, flowing water in the river and riverbed, which is a key factor affecting and determining the change of water temperature and ice production (Maykut 1982; Tuo 2018). Untersteiner (1964) and Maykut & Untersteiner (1971) have been carrying out research work regarding the ice thermodynamics and modeling. Ashton (1985) summarized the heat exchange equation between the water surface and the atmosphere and between the ice cover and the atmosphere when studying the mechanism of ice cover melting. By analyzing the influence of heat budget on the temperature of an ice cover, Ashton revealed the melting process during the break-up period. Shen & Chang (1984) considered the heat exchange of the whole system at the interface of air–ice body, water surface, and riverbed, and proposed a thermodynamic model to simulate the generation and dissipation of river ice in a natural river. Using field observation data, based on other researchers’ models regarding solar radiation, long-wave radiation, evaporation, and convection, Yang (2021) developed a nonlinear thermodynamic model for heat flux in rivers, lakes, and the atmosphere. However, it is not easy to obtain necessarily meteorological data for calculating the heat exchange process by using the above-mentioned nonlinear thermodynamic model. The linear thermodynamic model is normally used to study river ice hydraulics due to its advantages of simple calculation and relatively fewer requirements on meteorological data. By analyzing the heat loss between water and the atmosphere, Paily et al. (1974) classified different linear thermodynamic models into three categories and proposed the heat transfer coefficient in linear thermodynamic models. For linear thermodynamic models, a correct selection of the heat transfer coefficient at the ice interface is often the key factor for assessing the melting process of an ice cover (Sarraf & Zhang 1996). Marsh & Prowse (1987) compared four different methods for calculating the heat transfer coefficient and claimed that the heat transfer coefficient calculated by the Colburn analogy method was more accurate and more suitable for determining the heat flux under an ice cover. At present, most thermodynamic models only consider the influence of heat flux between the atmosphere and water on the generation and dissipation of river ice. However, the heat transfer process of ice–water interface is often ignored or considered with simple parameterized methods. When there is an ice cover on the river surface, the ice cover separates the water from the atmosphere, and the heat exchange process mediated by the ice cover is clearly different from the heat exchange between the atmosphere and water. The heat transfer process at the ice–water interface affects the ice thickness and the water temperature under the ice cover, and the adoption of an inappropriate ice–water heat flux value will affect the accuracy of the simulation of ice generation and extinction process (Benson et al. 2012). Li et al. (2016) studied the heat transfer process between the water body and the ice cover and established a linear relationship between the ice–water heat transfer coefficient and flow discharge of water under the ice cover based on experimental data in a flume. Conceptually, the heat exchange phenomenon is not an independent process but an interactive process. A complete coupled model is required for simulation of this process (Launiainen & Cheng .1998). The heat exchange between the water body and the frozen riverbanks and riverbed is also an important factor affecting the ice production in a river. The heat exchange in rivers where water temperature varies greatly from day to night should not be ignored (Mao & Chen 1999). Considering the effect of the heat flux between the ice cover and the water body and between the riverbed/riverbanks and the water body on the production of river ice, to improve the accuracy in calculation of ice production, the Colburn analogy method is coupled with the principle for solid plate heat transfer and thermodynamic model.
To date, some studies have been conducted to assess the characteristics of the ice regimen and flow in the IMRYR. However, only few studies have been carried out to study the ice production, since the amount of ice production depends on the heat exchange process which is very complicated and closely related to air temperature, meteorology, flow, and other factors. To study the features of variation of ice production in the IMRYR, the water body heat exchange process and heat flux components at each hydrological station during winter were analyzed. Then, the ice production model has been established and the features of variation in ice production have been studied.
STUDY RIVER REACH AND DATA
The research area
Data
To date, during the ice-covered period along this river reach, long-term systematic observations along the entire IMRYR have not been conducted for collecting data regarding wind speed, solar radiation, atmospheric pressure, and other data. In the present study, some hydrological and meteorological data are available at the following four gauging stations along the IMRYR: Bayangaole, Sanhuhekou, Baotou, and Toudaoguai, as shown in Figure 1. These gauging stations are maintained by the Yellow River Water Conservancy Commission. The following hydrological and meteorological data during a period from 2017 to 2020 have been collected from these four gauging stations: air temperature (Ta), water temperature (Tw), wind speed (V6), flow discharge (Qw), flow velocity (V), and ice thickness (hi), with the data accuracy 0.1 °C, 0.1 m/s, 1 m³/s, 0.1 m/s, and 0.01 m, respectively. Data for river cross-sections and profile along the river reach from the upstream Bayangaole station to the downstream Toutaogai station measured in 2012 have also been collected.
METHODOLOGY
Ice production in a river is mainly affected by the net heat flux per unit area of the river surface. The heat budget along a river reach consists of heat exchange between water and the atmosphere, heat exchange between water and riverbed, heat caused by friction between the water body and riverbed, heat flux of snow falling on the water surface, local heat flowing into the river, etc. (Shen & Ruggles 2010). When the heat transferred from local inflows such as tributaries or groundwater is small along a river reach, the influence of the heat from local inflows on the heat budget along a river reach can be ignored. The heat generated by friction between the water body and riverbed along a short reach can be also ignored. In this paper, to study ice production along the IMRYR, only the flux of heat exchange between ice, air, riverbed, and water body is considered.
The process of ice accumulation in the IMRYR can be divided into the following three stages: the ice floating period, the river freeze-up period, and the river break-up period. During the ice floating period, the water surface normally loses heat and produces frazil ice particles. Frazil ice particles emerge to the water surface. A vast amount of frazil particles collide and gradually form a lot of ice pans floating on the water surface. With the increase in the coverage rate of the water surface by ice pans, the flow velocity of the water surface decreases. If the air temperature is low enough, part of the water surface becomes frozen. As a consequence, if the flow velocity is not high enough, an ice cover will develop toward the upstream of this river reach, namely the river freeze-up period. The break-up period is a period when the ice cover on the water surface becomes broken up and melts. The river break-up process normally happens in the spring season, although it often happens during an ice-covered period due to high flow velocity with high energy.
During the ice floating period, ice covers start to grow along riverbanks or regions with the low flow velocity. The presence of the ice cover on the water surface separates the flowing water body from the atmosphere and reduces the energy exchange between the water body and the atmosphere. Thus, the heat exchange between the water body and the atmosphere needs to be carried out through the ice cover (Smits et al. 2021). Therefore, the heat budget due to heat exchanges in the presence of an ice cover on the water surface (partially covered along riverbanks) is the most complicated issue during the river freeze-up period. During the river freeze-up period, three heat exchange processes should be considered simultaneously, namely the heat exchanges between the atmosphere and the water body, between the ice cover and the water body, and between the water body and riverbed (including riverbanks).
To determine the heat flux between the atmosphere and the water body, between the ice cover and the water body, as well as between the riverbed and the water body, the following methods are used, respectively.
Heat flux between the atmosphere and the water body
Heat flux between the ice cover and the water body
The heat loss between the ice cover and the water body results in the decrease in the temperature of the water body, and thus freeze-up process of the water surface, as well as the thickening process of the ice cover provided the temperature is low enough. The ice production in the river will also be affected during the process of convective heat transfer and heat conduction.
Heat flux between the riverbed and the water body
VARIATION OF ICE PRODUCTION
Variation of ice production with time
Based on hydrological and meteorological data during winter periods (from November 2 to April 15) from 2017 to 2020 collected at the Bayangaole gauging station, the characteristics of variation of the temperature difference between the daily water temperature and air temperature, heat flux, and ice production during winter in the Bayangaole station of the next year have been analyzed.
Variations of the temperature difference between the daily water temperature and air temperature.
Variations of the temperature difference between the daily water temperature and air temperature.
The cumulative change of the total heat flux with the temperature difference.
The cumulative heat flux, total ice production, and cumulative temperature difference between water temperature and air temperature at the Bayangaole gauging station during each winter from 2017 to 2020 have been statistically analyzed. Results of the statistical analysis are shown in Table 1. Results indicated that when the total heat flux reaches 7,388.58 W/m2, the total ice production reaches 3.18 × 107m3, and the T value reaches 472.92 °C, the Yellow River at the Bayangaole station will easily become ice-covered.
River freeze-up date and total ice production at the Bayangaole station during the winter period
Year . | 2016–2017 . | 2017–2018 . | 2018–2019 . | 2019–2020 . | Average value . |
---|---|---|---|---|---|
Freeze-up date | 2017/1/16 | 2018/1/6 | 2019/1/11 | 2020/1/11 | |
ϕT (W/m2) | 7,683.08 | 7,201.77 | 7,222.64 | 7,446.83 | 7,388.58 |
QT (107m3) | 3.175 | 3.143 | 3.152 | 3.250 | 3.180 |
T (°C) | 402.40 | 370.20 | 577.70 | 541.40 | 472.92 |
Year . | 2016–2017 . | 2017–2018 . | 2018–2019 . | 2019–2020 . | Average value . |
---|---|---|---|---|---|
Freeze-up date | 2017/1/16 | 2018/1/6 | 2019/1/11 | 2020/1/11 | |
ϕT (W/m2) | 7,683.08 | 7,201.77 | 7,222.64 | 7,446.83 | 7,388.58 |
QT (107m3) | 3.175 | 3.143 | 3.152 | 3.250 | 3.180 |
T (°C) | 402.40 | 370.20 | 577.70 | 541.40 | 472.92 |
Changes of effective daily ice production at the Bayangaole station during the winter of 2019–2020.
Changes of effective daily ice production at the Bayangaole station during the winter of 2019–2020.
Ice production at different locations
Table 2 shows calculation results of ice production at the following four gauging stations along the IMRYR during winter periods from 2016 to 2020: Bayangaole, Sanhuhekou, Baotou, and Toudaoguai gauging stations (note: each winter period starts from 2 November to 15 April of next year). As shown in the table, the highest annual ice production occurred at the Bayangaole station and the lowest annual ice production happened at the Toudaoguai station. Clearly, the average annual ice production decreased from the upstream Bayangaole station to the downstream Toudaoguai station of the IMRYR.
Results of the statistical analysis of total ice production during winter (107 m3)
. | Winter period . | ||||
---|---|---|---|---|---|
Station . | 2016–2017 . | 2017–2018 . | 2018–2019 . | 2019–2020 . | Average . |
Bayangaole | 9.336 | 11.280 | 7.902 | 7.624 | 9.036 |
Sanhuhekou | 5.187 | 5.311 | 6.029 | 5.192 | 5.430 |
Baotou | 2.290 | 5.079 | 4.093 | 3.659 | 3.780 |
Toudaoguai | 2.402 | 4.431 | 2.875 | 2.223 | 2.983 |
. | Winter period . | ||||
---|---|---|---|---|---|
Station . | 2016–2017 . | 2017–2018 . | 2018–2019 . | 2019–2020 . | Average . |
Bayangaole | 9.336 | 11.280 | 7.902 | 7.624 | 9.036 |
Sanhuhekou | 5.187 | 5.311 | 6.029 | 5.192 | 5.430 |
Baotou | 2.290 | 5.079 | 4.093 | 3.659 | 3.780 |
Toudaoguai | 2.402 | 4.431 | 2.875 | 2.223 | 2.983 |
Daily heat flux during the winter of 2017–2018 at different stations.
Relationship between the cumulative temperature difference and the total heat flux during the winter of 2017–2018.
Relationship between the cumulative temperature difference and the total heat flux during the winter of 2017–2018.
Sensitivity analysis
The key factors affecting ice production are thermal factor and hydraulic factor, including the air temperature, radiation, flow discharge, and water surface area. The air temperature, radiation intensity, and flux change affect the magnitude of heat flux. The water surface area not only affects the heat flux, but also affects the amount of ice production. Based on the values of primary variables in the ice production model, only one variable value is adjusted each time to assess the change of calculation results, and then to analyze the influence of each factor on the calculation results by using the ice production model.
Through the analysis of measured data, the variation range of variables is within 20%, and the changed variables are still in line with the actual situation of natural rivers. In order to clearly compare the influence of various variables on the calculation results, the variation range of sensitivity analysis is selected as 20% in consideration of the actual situation of measured data of the Yellow River. Considering the characteristics of each variable in the ice production model, the following adjustments on each influencing variable have been made based on the actual situation of the IMRYR, as shown in Table 3. One can see from Table 3, with the same amount of adjustment in percentage for each variable, the change (in percentage) of the final testing result is different. Results showed that the influence degree of each variable on the ice production was in a descending order as follows: water surface area, air temperature, radiation, and discharge. Comparing to the variation range of the calculated ice production, the ice production model is sensitive to the variation of the water surface area and air temperature. Particularly, when the value of the water surface area is adjusted by 20%, 11.48% of the final calculated result of ice production will be affected. Thus, the accurate measurement of the water surface area is very important for determining the ice production in a river.
Sensitivity analysis of variables in the ice production model
. | Variable . | Original value . | Adjusted value . | Difference (%) . | Test results (107m3) . | Change in results (%) . |
---|---|---|---|---|---|---|
Test 0 | / | / | / | 0 | 4.920 | 0 |
Test 1 | Air temperature (°C) | −15.9 | −12.72 | +20 | 4.689 | −4.69 |
Test 2 | Air temperature (°C) | −15.9 | −19.08 | −20 | 5.168 | 5.05 |
Test 3 | Discharge (m³/s) | 573 | 687.6 | +20 | 4.768 | −3.09 |
Test 4 | Discharge (m³/s) | 573 | 458.4 | −20 | 4.768 | 3.09 |
Test 5 | Radiation (W/m2) | 180.99 | 217.18 | +20 | 5.146 | −2.29 |
Test 6 | Radiation (W/m2) | 180.99 | 151.19 | −20 | 4.807 | 4.59 |
Test 7 | Surface area (m2) | 500 | 600 | +20 | 5.382 | 9.39 |
Test 8 | Surface area | 500 | 400 | −20 | 4.355 | −11.48 |
. | Variable . | Original value . | Adjusted value . | Difference (%) . | Test results (107m3) . | Change in results (%) . |
---|---|---|---|---|---|---|
Test 0 | / | / | / | 0 | 4.920 | 0 |
Test 1 | Air temperature (°C) | −15.9 | −12.72 | +20 | 4.689 | −4.69 |
Test 2 | Air temperature (°C) | −15.9 | −19.08 | −20 | 5.168 | 5.05 |
Test 3 | Discharge (m³/s) | 573 | 687.6 | +20 | 4.768 | −3.09 |
Test 4 | Discharge (m³/s) | 573 | 458.4 | −20 | 4.768 | 3.09 |
Test 5 | Radiation (W/m2) | 180.99 | 217.18 | +20 | 5.146 | −2.29 |
Test 6 | Radiation (W/m2) | 180.99 | 151.19 | −20 | 4.807 | 4.59 |
Test 7 | Surface area (m2) | 500 | 600 | +20 | 5.382 | 9.39 |
Test 8 | Surface area | 500 | 400 | −20 | 4.355 | −11.48 |
CONCLUSIONS
To calculate the ice production in a natural river, the heat flux between the ice cover and the water body and between the riverbed and water must be considered. The Colburn analogy method is coupled with the heat transfer principle of solid plate and the thermodynamic model. Based on this method, the ice production model has been established. The variation trend of the daily ice production was consistent with that of the ice cover thickness. Results of analysis during river freeze-up periods from 2017 to 2020 showed that when the total ice production in the Bayangaole gauging station reaches 3.18 × 107m3, river freeze-up is likely to occur.
The characteristics of ice production in the IMRYR indicate that the daily heat flux is closely related to the river freeze-up and ice cover thickness. The effective ice production has been determined based on the difference between the daily heat flux and the mean value of the daily heat flux before the period of river freeze-up. When effective ice production is much higher than 0, the ice cover thickness begins to increase. When the effective ice production is much less than 0, the ice cover thickness begins to decrease. When the effective ice production is about 0, the ice cover thickness basically keeps unchanged, and no new ice cover will be developed. Results showed that the highest annual ice production occurred at the Bayangaole station, and the lowest annual ice production happened at the Toudaoguai station. Clearly, the average annual ice production decreased from the upstream Bayangaole station to the downstream Toudaoguai station of the IMRYR. The cumulative temperature difference between the water temperature and air temperature has a strong correlation with the total heat flux. The sensitivity analysis of the variables in the ice production model and ice production has been carried out. The degree of influence of each variable on the ice production was in the following order: water surface area, air temperature, radiation, and discharge.
The present study has been carried out based on the limited field data collected from four gauging stations. Only the heat flux along the study river reach has been considered. The ice production from the upstream section of the study river reach has not been considered. Clearly, long-term systematic observations along the entire IMRYR during the ice-covered period should be conducted to obtain more comprehensive field data for further improving the accuracy of the model for ice production.
ACKNOWLEDGEMENT
This research is supported by the National Natural Science Foundation of China (Grant Numbers: 51879065 and U2243221). The authors are grateful for the financial support.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.