Modeling of runoff formation processes with aufeis feed in mountain cryosphere of the north-east of Russia

Zemlianskova Anastasiia Aleksandrovna ORCID: 0000-0002-2249-5708 Laboratory assistant, Laboratory of Monitoring and Forecasting Climate Change and the Environment, North-Eastern State University, Magadan, Russia; Junior Researcher and Postgraduate Student of the Institute of Earth Sciences, St. Petersburg University 685017, Russia, Magadan region, Magadan, Portovaya str., 13 anastasiazemlanskova@gmail.com Other publications by this author

Makarieva Ol'ga Mikhailovna ORCID: 0000-0002-2532-4306 PhD in Technical Science Head of Laboratory of Monitoring and Forecasting Climate Change and the Environment, North-Eastern State University, Magadan, Russia; Leading Researcher of Earth Sciences, St. Petersburg University 685000, Russia, Magadan region, Magadan, Portovaya str., 13 omakarieva@yandex.ru Other publications by this author

Introduction

Ice is a specific form of seasonal glaciation characteristic of the mountainous conditions of permafrost ^[1-3]. The area of one object can be measured in tens of ^km2, and the ice thickness can reach 10-12 m ^[4]. Under conditions of global climate warming, there is a reduction in the size of glaciers ^{[5, 6]} and their migration, which affects the hydrological regime of rivers in the cryolithozone and geocryological conditions ^{[3, 7]}. The large size of the glaciers provides high identifiability of these objects in satellite images, which allows them to be used as qualitative indicators of water exchange transformation in vast, inaccessible and insufficiently studied territories of the North-East of Russia, where, according to recent estimates, there are at least 6,683 glaciers with a total area of about 4,500 ^{km2 [8]}.

Ice is a key element in the chain of water exchange processes in the permafrost zone. According to B. L. Sokolov's observations, in May-June up to 50-90% of the ice runoff falls into the river runoff, in July this share decreases to 30%, and in August — to 7%. The hydrological role of glaciers in the formation of river runoff can be comparable to such snow-ice phenomena as glaciers, which is confirmed by the results of many studies ^{[6, 9, 10]}. Observations of ice during the construction of the Baikal-Amur mainline have shown that the share of ice runoff in the annual river flow can reach 35% for catchments up to 500 ^km2. During the spring flood, this proportion ranges from 5 to 40%, and in the summer runoff does not exceed 10% ^[11].

Glaciers can play an important role in the water supply of arid regions ^{[2, 12]}. Despite the history of studying this natural phenomenon (more than 100 years) and the results achieved, there are no methods for predicting the development of ice processes, as well as hydrological models that take into account the share of ice nutrition in river runoff. At the moment, research is underway to create conceptual models of ice formation ^{[13, 14]}, which will allow for a better understanding of their nature. In well-known hydrological models, such as the HBV-Light model ^{[15, 16]}; PREVAH ^[17], etc. With the help of a system of equations, glacier destruction and glacial runoff are satisfactorily described, they can also be used in relation to ice by regulating the snow index, but this loses all physical meaning ^[18].

The problem of developing a mathematical apparatus that allows predicting the size and nature of ice processes, as well as taking into account their impact on river flow and other components of the natural environment lies in the fact that there is no state program for studying ice. Ground-based observations in Russia are carried out thanks to grant support [19-21 et al.] by separate scientific groups, the results of which are often not comparable with each other. A comprehensive program for studying ice at key sites in different regions is needed, which will take into account the peculiarities of climate, geological structure, relief, geocryological characteristics, and landscapes for the formation of ice. Satellite monitoring data will allow for a retrospective assessment of changes in their sizes ^{[5, 22]}. In the last century, on the icy areas of Samokit, Verina, Anmangynda, etc. Comprehensive observations of their water regime and the role of ice in the formation of river runoff were carried out. Therefore, it is these objects that are proposed to be considered primarily as key objects of the network of ice telemetry points.

In the basin of the Anmangynda River (Kolyma River basin), a long series of data was obtained (1962-1991) on the area, volume, thickness of giant ice in different seasons, as well as the hydrological regime of the river in the alignment below the ice (1962-1987) and on a large tributary stream. Olchan (1962-1978). Based on these materials, integral curves for reducing the morphometric characteristics of ice were obtained, which were used in calculations on other objects ^{[10, 23, 24]}.

In this paper, using the example of the Anmangynda River basin, it is proposed to study the hydrological regime, and also, using a long series of data using mathematical modeling methods, to develop a method for accounting for ice nutrition.

The object of the study

The catchment area of the Anmangynda River (flows into the Detrin River, a tributary of the Kolyma River), for which the calculation is carried out, is 376 ^km2. The study area belongs to the zone of continuous permafrost distribution, its thickness reaches 300 m, decreases to 80-100 m in river valleys and is interrupted in talik zones ^[25]. The geological structure is represented by sedimentary rocks of the Upper Triassic, Jurassic and Cretaceous. According to ^[26], the depth of zero heat turns is 11.5 and 13.5 m at an altitude of 712 and 1027 m, respectively.

The height of the catchment area of the Anmangynda river ranges from 700 to 1850 m.  The river valley at the ice formation site (Fig. 1) has a trapezoidal shape with gentle slopes. The length of the ice glade is about 6-7 km, with an absolute height of 700-770 m. The slopes are covered with larch forest on a moss-lichen litter, in places cedar elfin and patches of open tundra. The soils are mountainous, podzolic, tundra and mountain tundra.

Fig. 1. The Anmangynda ice.

The valley floor is composed of alluvium, in the upper part it is poorly covered with shrubs and moss cover. In areas where the ice has been lying for a long time, a hummock is formed, as well as dense willow. Ice is formed annually, in the modern period its area can reach 5.4 km2 (2000), and the historical maximum was 6.8 ^km2 (1978). The average volume of ice for the period 1963-1991 was 8.5 million ^m3, which is 22.6 mm of annual runoff layer. Modern estimates show a significant decrease in the total size of the Anmangynda ice ^[27], so in 2000-2022 the maximum volume according to estimated estimates did not exceed 8.2 million ^m3, and on average is 7 million ^m3.

The water regime of the Anmangynda River is characterized by data from a hydrological post located below the ice. Year-round runoff is observed in the area of the polynya above the ice and in the middle part of the ice glade.

The climate of the studied area is sharply continental, the average annual temperature at the Ust-Omchug station (576 m above sea level) for the period 1967-2022 was -9.8 °C (in July +14.5 ° C, in January -33.4 °C). In the coldest months (December-January), the temperature drops to -57?, and in the warmest months it rises to +33.6? (July). The average annual precipitation is 341.2 mm (m/s Ust-Omchug).

Snow cover in the mountains is established at the end of September, and throughout the basin in mid-October. According to field research data from 2021-2023, the snow height in different parts of the catchment at the end of March ranges from 48 to 84 cm, whereas at the Ust-Omchug m/s it is 25 cm.

Materials and methods of research

Historical data

The materials of the Kolyma Department of the Hydrometeorological Service were collected, digitized and analyzed for the period 1962-1991. They included information about the dynamics of the area, volume, and thickness of ice in different seasons of the year. The analysis and results are described in detail in ^{[27, 28]}. It is noted that over the past 60 years, the maximum ice sizes have decreased by 15 and 17% for the area and volume, respectively (on average from 5.5 to 4.7 ^km2, from 8.5 to 7.0 million ^m3).

Information on the hydrological regime was obtained for the lower reaches of the Anmangynda River (1962-1987) ^[29].

A modern series of observations

The assessment of the current ice area was carried out based on the analysis of satellite images of Landsat (TM, ETM+ and OLI sensors) and Sentinel-2 (MSI sensor) satellites for the period 1999-2022 and 2016-2022, respectively. The accuracy of determining the area of ice from the images depends on its resolution, the deviation from the actual size of the ice can be up to 15%.

Satellite image data does not allow us to estimate the volume of ice, so the calculation formula (1) is used:

W=0,364*S^1,167, (1)

where W is the volume of ice (thousand ^m3), S is the area of ice, thousand ^m2, the coefficients a and n were proposed in ^[27]. For the historical period (1963-1990), the formula showed satisfactory results. The deviation of the calculated values from the observed values was 0.01—2.09 million ^m3 or 0-5 mm of runoff.

With the help of an unmanned aerial vehicle, an ice clearing was photographed in 2021 and 2022. Based on the results of the work, orthophotoplanes were built, the area and volume of ice was determined ^[30], as well as the change in ice thickness. The accuracy of volume determination depends on many factors — camera stabilization, number of control points, lighting, etc. A comparison of ground-based observations with UAV data showed that the ice thickness error in the warm season ranged from 0.04 to 1.70 m. In case of gross errors, the materials were not used in the analysis. Thus, the accuracy of determining the volume varied from 0.02 to 0.46 million ^m3 (5-13%), which is from 0 to 1.5 mm of runoff for the Anmangynda River basin.

The Hydrograph model

The mathematical model "Hydrograph" with distributed parameters combines both physically sound and conceptual methods, which allows achieving a balance between the complexity of calculations and the availability of parameterization of the model ^[31]. It was used to calculate the flow of rivers in the Kolyma River basin, where permafrost rocks are common ^{[32, 33]}, and the results were accepted as satisfactory. The calculations did not assess the contribution of ice nutrition to river runoff, although in the North-East of the country it may amount to 0.2-11.0% during the spring flood (May-June, the Kolyma River basin) ^[8].

In the previously developed version of the Hydrograph model, when calculating the processes of runoff formation in the permafrost zone, the share of the contribution of ice nutrition to river runoff was not taken into account. The authors of the work proposed the calculation block "Ice", describing the processes of destruction of ice and accounting for ice nutrition in the formation of river runoff. As part of the adaptation of the algorithm and the program of the model, both the calculation schemes and the interface were modified.

To use the Hydrograph model, the schematization of the river basin is carried out. Two systems are used — 1) a set of representative (calculated) points (RT) representing the centers of the cells of the hexagonal grid, and 2) a system of flow-forming complexes (SFCs) determined by the type of landscape, soil, vegetation, altitude zone.  

The block "Ice" is a calculation algorithm for an array of ice, timed to a specific RT. For each ice within the RT area, information about its characteristics and location is set - geographical coordinates (latitude, longitude, altitude), maximum area (S _max) and the volume (W _max) of ice (determined according to field research data or using calculation formulas), the average thickness of ice (D _max), as a quotient of the volume and area of ice. Input meteorological data, namely effective temperature (Temp _ef) and the humidity deficit (Def _ef) of the air are calculated taking into account the absolute height of the ice.

The "Ice" block was based on the method of B. L. Sokolov, which is based on the dynamics of reducing the area of ice during the warm period, the beginning of which is associated with the date of transition of the average daily air temperature through zero towards positive values ^[10]. The volume of ice varies depending on the melting coefficient. When developing the method, B. L. Sokolov used a number of data on the dynamics of ice phenomena in the Anmangynda ice, which currently do not meet modern climatic conditions. Therefore, according to satellite monitoring data for the period (2000-2022), the regional curve of destruction of the relative area of the Anmangynda ice was clarified.

To calculate the ice runoff, two factors affecting the destruction of ice are taken into account – the effect of solar radiation (Abl _i) and thermal erosion processes, when, under the influence of river and groundwater runoff, ice blocks break off from the main body of ice and quickly (in the proposed algorithm – instantly) collapse in the water flow. This was proposed for the first time, previously block destruction was either not taken into account, or a solution of several equations was proposed ^[10]. The melting coefficient (k _t) was calculated according to field research data from 2020-2023 on the Anmangynda ice, it was found that for this object it averages 1 mm/?·day and varies from 0.1 to 4.2 mm/?·day depending on the month. In the model, it is set to be the same for the entire calculated time interval. The coefficient of evaporation from ice (m/mbar·s) is also introduced. The minimum size of the ice for which the calculation is carried out is 0.6 km ².

The estimated time interval (RIV) in the Hydrograph model can be any (but not more than a day), depending on the availability of data. In this work, an interval of a day is proposed, so for each day it is determined how the area and volume of ice have changed as a result of the action of solar radiation and thermal erosion destruction, taking into account evaporation from the ice surface. The thickness of the ice decreases evenly over the entire area of the ice, depending on the effective air temperature and the melting coefficient of the ice (solar radiation block). The volume of broken ice is calculated as the change in area multiplied by the average thickness of the ice (block thermomechanical destruction of ice). The total loss of ice volume on the RIVE is recalculated into a layer and a hydrograph of the ice runoff. Also, for each REEVE, the area, volume and average thickness of the ice are determined, as well as the layer, volume and flow rate of the ice runoff, the evaporation layer from the ice, which are used for further calculation. Below are the formulas used in the "Ice" block (Fig. 2).

Fig. 2. Block diagram "Ice".

1) Solar radiation — the change in the average thickness of ice per RIVE is calculated as a result of the arrival of solar energy.

If (if the melting layer under the influence of solar radiation exceeds the thickness of the ice).

2)    Thermomechanical destruction of ice — the change in the area and volume of ice due to block destruction is calculated.

3) Balance — the total volume of ice loss in the I-th RIVE is calculated due to evaporation, block destruction and melting under the influence of solar radiation.

The approbation of the method for calculating the area and volume of ice for each REEVE (Fig. 3) showed that the deviation of the obtained values on average does not exceed 10% of the maximum characteristics of the ice, and the largest deviation for a particular day was 24% (Table. 1), which is considered satisfactory. The maximum calculation error is observed in the period July—August, when the size of the ice is on average less than 10% of the area and volume values before melting.

Fig. 3. Approbation of the method for calculating the area and volume of ice based on ground—based observations (1) and materials from an unmanned aerial vehicle (3). Curve (2) is the result of using the "Ice" block.

Table 1. Deviation of calculated values of ice characteristics from those observed for each year.

R is the deviation from the maximum value (%).

Parameterization of the Hydrograph model and the data used

In order to parameterize the model, a map of permafrost landscapes of the Anmangynda river basin (Fig. 4), compiled in 2022, was used to isolate runoff-forming complexes (SFCs) ^[34]. Previously developed schematizations of soil and vegetation cover and model parameters published in ^{[32, 33, 35]} were used for each SFK.

Data from the Ust-Omchug meteorological station (1967-2022, Table 2) were used as input information. When interpolating meteorological elements, own field materials (2020-2023) were taken into account, including series of meteorological data obtained in various high-altitude zones of the Anmangynda basin.

Fig. 4. The scheme of the catchment area of the Anmangynda river.

Symbols: 1 — mountain tundra; 2 — mountain-slope; 3 — rare larch forest; 4 — river valley; 5 — stone scree; 6 — ice; 7 — river; 8 — hydrological post; 9 — settlement points; 10 — settlement point in the ice zone; 11 — basin boundary R. Anmangynda.

Table 2. Materials used in the study.

Results

Continuous modeling of the flow of the Anmangynda River was carried out during the period of observations of the hydrological regime (1967-1987), which was used to assess the applicability of the Hydrograph model, as well as for 2000-2022 to trace possible changes in the region. The result of the simulation is the daily hydrographs of water runoff and the values of the elements of the water balance in the formation of the Anmangynda River, taking into account the ice runoff. In ^[33], the "Hydrograph" model has already been used for this object, but without the "Ice" block. Then the results showed that the average deviation of the calculated annual flow hydrograph from the observed one is 18%, and the Nash-Sutcliffe criterion (NS) varies from -0.94 to 0.72 in different years.

When using the Ice block, the difference between the annual calculated and observed runoff layers averaged 36 mm or 13%. The median values of the NS criterion are on average 0.57, which is 0.16 higher than without using the "Ice" block (Table 3). Figure 5 shows an example of the result of calculating runoff using the "Hydrograph" model. The share of ice runoff during the high water period varied from 5 to 36%, and over the year — from 4 to 12% (from 15.4 to 31.1 mm).

Fig. 5. Calculated and observed hydrographs of the flow of the Anmangynda river, 1983-1985.

The maximum value of the NS criterion was 0.82 in 1983. The annual flow of the Anmangynda River during this period was 253 mm, the size of the ice was 5.2 km ² and 7.2 million ^m3 in area and volume, respectively. Thus, the ice supply of the river for this year amounted to 19.1 mm or 7.6% of the river flow.

Table 3. Annual water balance and modeling quality criteria in the Anmangynda river basin for the period 1966-1987. according to the author and the data of the dissertation work of N. V. Nesterova.

Yo and Ys are the observed and calculated average annual annual runoff layer, mm; P is precipitation, mm; A is the ice runoff layer, mm; E is evaporation, mm; Ro and Rs are the deviation of the runoff value, in mm and %, respectively; NS is the Nash—Sutcliffe criterion (for daily values), b/r; K is the correlation coefficient (for daily values), b/r.

In 1981, the share of ice runoff in the annual flow of the river was 22.7 mm (12.3%), and during the spring flood (May–June) — 19.2 mm or 33%. Figure 6 shows the role of ice in the formation of the flow of the Anmangynda River, so we note that in low-water years during high water and summer autumn, almost all runoff is the result of the destruction of ice. During the spring flood, icy waters flow over the river ice.

Fig. 6. Calculated total and ice runoff of the Anmangynda river during the high water period, 1981. Regions 1 and 2 — the share of ice runoff is almost 100%.

For the modern period, using the example of 2016, it is also noted that the destruction of ice occurs earlier than river runoff is observed (Fig. 7). The river runoff layer this year was 251 mm, the contribution of ice to the annual flow of the river was 9%, and during the spring flood up to 19%.

Fig. 7. Calculated total and glacial runoff of the Anmangynda river during high water, 2016

According to the Hydrograph model, there is a significant change in the values of the water balance of the Anmangynda River basin in 2000-2022 compared with the period 1967-1987. This may be due to the observed transformation of the hydrological regime of the rivers of the North-East of the country under the influence of climate warming ^[37]. It is noted that in the modern period, the annual flow of the Anmangynda River increased on average from 294 mm (1967-1987) to 353 mm (2000-2022), and the maximum and minimum values reached 600 and 251 mm (Table. 4), previously they were at the level of 459 and 163 mm (Table. 3), respectively.

In particular, there is a decrease in the role of ice runoff in the formation of the water balance of the Anmangynda River. In 2000-2022, the amount of ice runoff varied from 13.4 to 22.6 mm, which amounted to 4 to 9% of the annual flow of the river, and during the spring flood, nutrition due to ice waters did not exceed 23%.

Table 4.Calculated annual water balance (mm) in the Anmangynda river basin for the period 2000-2022

Conclusion

The effect of ice on the natural environment has not yet been sufficiently studied due to the lack of long-term series of observations. For the same reason, methods for forecasting and accounting for ice in the water balance of rivers have not been developed, although on some rivers their contribution is comparable to glacial runoff. In this study, an algorithm for calculating ice runoff is proposed, which depends on the maximum size of the ice (before its melting), melting and evaporation coefficients, effective temperature and humidity deficiency, as well as the relative magnitude of the reduction in ice area over time. The algorithm was named the "Ice" block and was implemented into the "Hydrograph" model, which was repeatedly used to calculate the flow of rivers in the mountain cryolithozone, both provided and not provided with observational data.  

The expansion of the functionality of the Hydrograph model due to the introduction of a new Ice block made it possible to take into account the influence of ice phenomena on river flow in the daily interval, which is important for understanding the processes of water exchange in the cryolithozone. The algorithm was tested for R. Anmangynda. It was found that when using it, the error in calculating the annual flow of the river was 13%, having decreased by 5% (previously 18%). The Nash-Sutcliffe criterion improved and averaged 0.57 (previously 0.41).

The results of numerical calculations carried out using the updated version of the Hydrograph model revealed changes in the contribution of the Anmangynda ice to the river flow in different periods. Thus, in 2000-2022, due to a reduction in the maximum size of ice and an increase in river runoff, there is a decrease in the influence of ice on runoff, which is important for understanding the dynamics of water resources in the cryolithozone. The proposed algorithm makes it possible to detail the water balance, which is important for more accurate calculations of hydrological characteristics and prediction of dangerous hydrological phenomena.

Finally, it is worth noting that, despite the insignificant amount of ice runoff, its role in the ecosystem during the summer autumn in dry years can become critical. This circumstance underlines not only the importance of the conducted studies from the point of view of hydrology, but also their contribution to understanding ecological processes in regions where permafrost rocks are common. Nevertheless, a detailed understanding of the formation, distribution and influence of glaciers requires a comprehensive study, including data on the climate, hydrography and geology of a particular region.

Thanks

The authors sincerely thank Denis Anatolyevich Revutsky, Head of the Tenkinsky Municipal District of the Magadan region, for his help in conducting research and ensuring the work of the scientific group in the district.

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