Modeling of maximum runoff characteristics of small rivers in the mountain permafrost zone

Zhunusova Oksana Radikovna ORCID: 0009-0004-0518-4029 Postgraduate student; Laboratory of Hydrological Processes Modeling; State Hydrological Institute Research laboratory assistant; Institute of Earth Sciences; St. Petersburg State University 199034, Russia, Saint Petersburg, Universitetskaya nab., 7-9 zhun.oksana@gmail.com Nesterova Nataliia Vadimovna ORCID: 0000-0003-0677-4982 PhD in Technical Science Researcher; Institute of Earth Sciences; St. Petersburg State University 199034, Russia, Saint Petersburg, Universitetskaya nab., 7-9 nnesterova1994@gmail.com

Makarieva Ol'ga Mikhailovna ORCID: 0000-0002-2532-4306 PhD in Technical Science Leading Researcher; St. Petersburg State University Leading Researcher; Northeastern State University 685000, Russia, Magadan region, Magadan, Portovaya str., 13 omakarieva@yandex.ru

Introduction

Global warming is affecting natural and anthropogenic systems all over the world. In different regions of Russia, there are changes in precipitation characteristics ^[1], the dynamics of soil moisture and temperature at different depths ^[2], the timing of snow cover establishment and descent, a decrease in the thickness of ice cover on rivers ^{[3, 4]}, and the degradation of permafrost soils ^[5]. These factors lead to significant changes in the regime of formation of dangerous hydrological phenomena and transformation of the elements of the water balance. In mountainous areas, which are characterized by a variety of landscapes and climatic conditions, as well as those that play a key role in the formation of water resources ^[6], OGW are formed especially often.

In recent decades, when climate change has become particularly noticeable, there has been a significant reduction in the network of hydrometeorological stations in the world. Over the past 40 years, the density of the hydrological monitoring network in Russia has decreased by more than one and a half times ^[7]. The lack of data on river flow affects the accuracy of forecasts of dangerous hydrological phenomena and calculations of flow characteristics in infrastructure planning.

Traditional methods of hydrological calculations are based on approaches created 40-50 years ago. They are based on observational data during the period of stable climate. However, the use of these techniques is not always advisable in a changing climate. Clarifying the parameters of calculation formulas based on statistical data is difficult for many regions due to a lack of information ^[8]. Therefore, the task of developing new approaches to calculating river flow characteristics is relevant. Such approaches may be based on the integrated use of mathematical modeling methods for hydrological processes.

In this paper, the authors consider one of the regions of the Far Eastern Federal District — the Magadan Region. The region, with significant reserves of natural resources, plays an important role in the Russian economy, ranking first in terms of gold reserves ^[9]. Floods caused by significant amounts of precipitation are recorded annually in the Magadan region. The most devastating floods of the last decade occurred in 2013, 2014 and 2019, causing damage to the region in the amount of 0.6, 0.7 and 1 billion rubles, respectively. Roads are regularly washed out and infrastructure is damaged.

The purpose of the study was to study the processes of formation and calculation of maximum water consumption in the Magadan region using pluviograph data and mathematical modeling.

Objects of research

The climate of the Magadan region is monsoon, sharply continental in the interior of the continent, and softens towards the coast of the Sea of Okhotsk. The average annual air temperature in the entire region has negative values and ranges from -2.7 °C on the coast to -12 °C in the mountains. In winter, an inversion is observed in mountainous areas - with increasing altitude, the air temperature rises. Due to the difficult terrain, precipitation varies greatly. The average annual precipitation is 250-600 millimeters. The average snow cover height is 50-70 cm, the highest values (90-100 cm) are observed in the valley of the middle course of the Kolyma River, the lowest (30-50 cm) in its upper reaches and on the coast of the Sea of Okhotsk ^[10].

In the mountainous relief of the Magadan region, the vertical belt of landscapes is clearly expressed. The upper belt is represented by loaches (rocky tali) and mountain tundra. In the continental part, this belt occupies heights of 1100-1200 m above sea level, and near the coast – above 400-450 m. The char belt is surrounded by a belt of cedar thickets (the height range is 900-1100 m in the continental part, 600-800 m in the coastal part). With decreasing altitude, it is replaced by sparse larch woodlands, the abundance of which increases downhill and in river valleys ^[11].

Continuous permafrost is observed in the continental part of the Magadan Region, and its distribution on the coast is intermittent and insular. The depth of the seasonally thawed layer varies from 0.1 to 5 m ^[10].

The watersheds of small rivers with areas from 8.4 to 932 ^km2 and maximum heights up to 2,139 m, provided with observations over a long period, were selected for the study. The characteristics of the catchments and the main indicators of river flow are presented in Table 1. The location of the studied catchments is shown in Fig. 1. River hydrographs are characterized by the absence of winter runoff, high spring flooding and pronounced summer floods.

Table 1. Characteristics of the studied catchments.

S is the catchment area, ^km2; H/Hmax is the average and maximum height of the catchment, m; W is the average slope of the catchment, °; Qd_max is the maximum daily water consumption, ^m3/s; Q_max is the maximum urgent water consumption, ^m3/s.

Fig. 1. Location of selected river catchments.

Materials and methods

Hydrological model "Hydrograph"

The basis of the study was the distributed deterministic hydrological model "Hydrograph" ^[12]. Since its launch requires a limited set of meteorological data (air temperature and humidity, precipitation), it is suitable for use in poorly studied catchments ^{[7, 12, 13]}.

Schematization and parameterization of the model is carried out by identifying conditionally homogeneous natural zones (runoff-forming complexes, SPCs), which can be described by a single set of model parameters, assuming that within the SPCs the process of runoff formation is fairly uniform, and its quantitative characteristics can be averaged ^[12].

In the horizontal projection, the so-called "representative" points (RT) are allocated on the catchment area, which evenly cover the catchment area and are located at the same distance from each other. Each RT has its own terrain characteristics, such as the height, slope and exposure of the slope, as well as the running time. The RT characteristics are assumed to be representative of the entire area of the "subcommand" hexagon. In vertical section, the model is a soil column with at least 3 layers. The heat and water balance are calculated for each layer.

The model basically takes into account that any catchment area can include different basin reservoirs (underground, soil, surface) with their characteristic expiration time and volume. Conceptually, moisture exchange rates are set for each tank in the model, which can reach tens and hundreds of years.

The calculated interval of the model ranges from minutes to one day ^{[8, 14]}.

The parameterization of the model was carried out on the basis of data from the Kolyma Water Balance Station (KVBS) (1947-1997) ^[15] and the hospital of Suntar Khayat ^[13]. It was previously noted that parameter sets developed in the studied watersheds can be transferred to unexplored basins with similar types of underlying surfaces without calibration ^[16].

Hydrological and meteorological data

Daily information on temperature, humidity, and precipitation from two meteorological stations was used as the initial meteorological data (Table 2). To use these data in mountainous conditions, we adjusted the daily values in accordance with the altitudinal gradients of precipitation and air temperature. To calculate these gradients, information on average annual precipitation and air temperature at meteorological stations over the entire observation period was used.

Table 2. Characteristics of meteorological stations.

To model outstanding floods in the intraday interval, events were selected for which both data on maximum water consumption and pluviograph data on the intraday course of precipitation were available. The pluviograph data is borrowed from the database of pluviographs of the Magadan region, developed on the basis of digitized meteorological monthly journals published in the USSR ^[17] and observation materials for 1947-1997 of the Kolyma Water Balance Station ^[18]. The database includes data from 72 stations for a period of 47 years (1950-1997) for the range of absolute heights from -8 to 1200 meters and has more than 70 thousand values ^[19]. To verify the results of river flow modeling, data on daily water consumption and maximum emergency water consumption for outstanding floods were used.

Parameterization of the model

Using the ArcGIS program and data from the USSR Landscape Map ^[20], as well as Landsat satellite images, the main types of landscapes in the catchment areas were identified and the SPCs were identified: char (rocky talus), mountain tundra, thickets of cedar elderberry, larch woodlands and burnt vegetation. A regular RT grid has been developed for each catchment area. The schematization of the catchments is shown in Fig. 2. The parameters of the Hydrograph model were borrowed from ^{[13, 21-23]}.

The parameters of soils, vegetation, slope, and groundwater runoff were set for each SFK. All soil sections have 20 calculated soil layers, each 10 cm thick. The parameters of the vegetation cover are also accompanied by the indication of four phenological dates: the beginning of vegetation development, its reaching its maximum level, and the beginning and end of the wilting period.

Fig. 2. Schemes of catchments (a – stream Krivulya, b – R. Ambardakh, c – R. Susuman).

Results and discussion

Verification of the model on a daily basis

The verification of the Hydrograph model was carried out based on a comparison of the simulation results using the developed set of parameters of daily hydrographs for the periods 1966-1994 for the Krivulya stream and 1966-1987 for the Susuman and Ambardakh rivers with the observed values. Currently, there are no runoff observations at these facilities, which does not allow for verification of the simulation for later time intervals. The Nash-Sutcliffe coefficient (NSE) was chosen to evaluate the effectiveness of hydrological modeling ^[24]. Correction coefficients were introduced for each watershed to increase the convergence of calculated and observed hydrographs.

Table 3 shows the calculated annual values of the water balance (precipitation, evaporation, runoff), as well as the average, median, maximum and minimum values of the Nash-Sutcliffe criterion (NSE). Figure 3-5 shows a comparison of the calculated and observed daily hydrographs of water flow with the average NSE value for each watershed.

Table 3. Characteristics of the water balance and the NSE criterion.

Yo and Ys are the observed and calculated average annual runoff layer, mm; P is precipitation, mm; E is evaporation, mm; Qo and Qs are the maximum observed and calculated flow rate, ^m3/s; av and m are the average and median NSE values; max and min are the maximum and minimum NSE values.

Fig. 3. Calculated (red line) and observed (black line) hydrograph of water flow with an average value of NSE (NSE = 0.38) for Krivulya Creek, 1977.

Fig. 4. Calculated (red line) and observed (black line) hydrograph of water flow with an average value of NSE (NSE = 0.61) for the Susuman River, 1980.

Fig. 5. Calculated (red line) and observed (black line) hydrograph of water flow with an average value of NSE (NSE = 0.55) for the Ambardakh river, 1973.

For the period 1966-1994, the calculated average annual runoff layer for the Krivulya Creek watershed is on average 2% higher than the observed one. For the basins of the Susuman and Ambardakh rivers in the period 1966-1987, there was an excess of the calculated average annual runoff layer by 5 and 9%, respectively.

The median NSE value for daily water consumption is pp. Krivulya, Susuman and Ambardakh vary from 0.52 to 0.61. The maximum average NSE value of 0.61 is typical for the watershed of the Susuman River. The maximum NSE values for all pools vary within a small range of 0.86-0.90. The Ambardakh River catchment has the lowest average NSE (0.07) among all catchments, which is mainly due to the influence of the extremely low NSE value (-7.71) for 1974.

The amount of evaporation from the catchment area of the stream. The curvature was 147 mm, the Susuman River was 124 mm, and the Ambardakh River was 112 mm. The difference in the amount of evaporation between catchments is due to the different percentage of SPF in the catchment area. Thus, according to ^[15], the area of char, which evaporates least from its surface, increases in a number of streams. Krivulya (4.5%) — R. Susuman (18.5%) — R. Ambardakh (24.2%).

Although in some years there are extremely low NSE values (up to -7.71), the median NSE values for daily expenses on all rivers range from 0.52 to 0.61, and the maximum values range from 0.86 to 0.90. Therefore, according to generally accepted criteria ^[25], the modeling results can mainly be assessed as satisfactory. The lower NSE values are explained by the fact that data from only one meteorological station was used in the modeling for all basins. The weather stations are located outside the catchment areas and are located at altitudes that are 200-400 m below the average height of each facility. For example, the average height of a stream's watershed. The curvature is 880 m, the maximum is 1,282 m, and the nearest Kulu weather station was located at an altitude of 668 m. It was shown in ^[14] that the quality of modeling runoff hydrographs in mountain basins critically depends on the number of meteorological stations used. It is necessary that at least two are located in the mountainous part of the basin.

Despite the low NSE values observed in some years, the calculated runoff hydrographs are in satisfactory agreement with the observational data in both phases and absolute values. The factors causing the error can be recognized as the insufficiency of input meteorological data ^[8], as well as the possible influence of the mining industry on the processes in the riverbeds under study, which was not taken into account when modeling the processes of runoff formation.

Assessment of the characteristics of the maximum flow using pluviograph data

After verification of the hydrological model at the diurnal step, outstanding floods were selected for modeling in the intraday time interval, for which pluviograph data on intraday precipitation dynamics are available. For the Susuman and Ambardakh rivers, the historical flood of August 16, 1986 was chosen with the maximum observed urgent expenditures of 393 and 74.7 ^m3/s, respectively; for the Krivulya stream, the flood of July 26, 1984 was chosen with the maximum urgent expenditure of 14.2 ^m3/s. For the manual. The selected floods are the highest during the observation periods at the hydrological posts of these rivers (Krivulya Creek, 1942-1994; Susuman River, 1941-1988). For the Ambardakh river, the date of the largest expenditures differs from the chosen one — 06/26/1965 (107 ^m3/s), since there are no pluviograph data for this year.

When preparing hourly meteorological data for modeling, pluviograph data on the precipitation layer and their duration were used, and in their absence, daily data were interpolated. In the absence of data on the duration of daily precipitation, the ratio was used:

T = a∙H^b, (1)

where H is the daily precipitation layer (mm), a is the rain duration parameter (min/mm), and b is the degree indicator (b/r). The parameter values are set as follows: a = 50 and b = 0.84 ^[26].

The interpolated urgent data from meteorological stations was also used as hourly data on air temperature and humidity. The results of modeling individual floods on an hourly basis are shown in Table 4 and Figure 6.

Table 4. Simulation results of outstanding floods.

Qd_max — observed maximum daily water flow, ^m3/s; Q_max — observed maximum urgent water flow, ^m3/s; Qd_sim — calculated daily flow, ^m3/s; Qd_sim_pl — calculated average daily flow according to pluviographs, ^m3/s; Qh_max — calculated maximum hourly flow, m ³/sec.

Fig. 6. Flood simulation results.

During flood modeling, maximum flow rates were obtained for all rivers, which were 5-16% higher than those observed. For the Krivulya stream, this value is higher by 16% (calculated — 16.5 ^m3/s, observed — 14.2 ^m3/s), for the Susuman River – by 7% (calculated — 420 ^m3/s, observed — 393 ^m3/s), for the Ambardakh river – by 5% (calculated — 78.5 ^m3/s, observed — 74.7 ^m3/s). According to the yearbook, the maximum urgent expenses for the villages of Ambardakh and Susuman are estimated with an error of 20%. The contribution of the factors described in the model verification section should be taken into account in the error of the calculated values.

To analyze the cost data obtained from daily precipitation data and pluviograph data, precipitation intensities were compared. The average precipitation intensity based on daily precipitation data was calculated as the ratio of precipitation to its duration.

Based on the pluviograph data, the average precipitation intensity that caused the outstanding floods was 0.03 and 0.04 mm/min for the Susuman and Kulu meteorological stations, respectively. Although these values do not significantly differ from the average intensity calculated based on formula (1) for daily precipitation amounts (0.04 mm/min for both stations), the pluviograph data show an uneven distribution of precipitation and intensity during the flood period with maximum precipitation intensity equal to 0.11 mm/min and 0.12 mm/min for the Susuman and Kulu (Table 5). At Kulu station, the most intense precipitation was observed on July 25 from 4 a.m. to 10 a.m., when 30.4 mm of precipitation fell in 6 hours. At the same time, an important factor in the formation of the flood was that these precipitation fell on already moistened soil as a result of precipitation on the previous day, July 24, when a total of 13.6 mm fell. The precipitation schedule of Susuman station has two peaks, on August 15 at 9 a.m. and on August 16 after 7 a.m., when 16.1 mm of precipitation fell in 3 hours. At the same time, precipitation amounts according to pluviographs and daily data are similar: daily data — 58.7 mm, pluviograph data — 55.2 mm at the Kulu weather station; and 48.1 mm and 45.4 mm at the Susuman weather station. Due to the fact that precipitation interpolation in the Republic of Tatarstan takes into account an increase in precipitation with slope height, in Table 5 the precipitation layer for the flood is represented not by the value obtained at the meteorological station, but by the total average layer that fell in the catchment area.

Table 5. Characteristics of the water balance and precipitation regime of outstanding floods.

I is the average precipitation intensity, mm/min, I_max is the maximum precipitation intensity, mm/min; T is the duration of precipitation, min; P is the precipitation layer, mm; H is the runoff layer per event, mm.

In general, the modeling results are considered satisfactory and confirm the possibility of using deterministic hydrological modeling methods to estimate urgent maximum costs according to pluviograph data in the mountain cryolithozone.

Discussion

Many scientific studies are devoted to the analysis of catastrophic floods and floods on the rivers of Siberia and the Far East ^{[27, 28, 29, 30, 31]}. These works mainly describe these phenomena based on available hydrometeorological information. There are also methodological developments concerning the calculation and modeling of flood formation processes, as well as short-term forecasting of flood runoff for the European part of Russia ^{[32, 33, 34]}. The study ^[35] provides a detailed overview of runoff forecasting methods used abroad, however, without taking into account the features of runoff formation in cryolithozone conditions.

In the permafrost zone, the vast majority of work on intraday runoff modeling concerns large river basins with significant run-up time ^[36]. Only a few studies ^{[28, 29, 37, 38]} are devoted to modeling the flow of small rivers, to which this work also applies.

The results of our work, despite the scarcity and limited input meteorological data, indicate the practical potential of using methods of deterministic hydrological modeling in the intraday interval. Earlier studies have already presented satisfactory results of flood modeling based on pluviograph data and Hydrograph models on small mountain rivers such as the Magadanka River in the Far East ^[29], as well as rivers of the Black Sea coast of the Caucasus ^{[8, 14, 38]}.

However, the main problem for mountainous areas still remains the lack of data on the distribution of precipitation, its duration and intensity. Here, the use of meteorological models becomes a promising solution. Studies ^{[28, 29, 38]} show that combining information from weather stations and meteorological model data makes it possible to effectively model the characteristics of hazardous hydrological phenomena. This approach is especially relevant in the context of the reduction of the hydrometeorological observation network. The availability of open access to data from modern models opens up great prospects for using the Hydrograph model in the tasks of calculating runoff and developing an operational forecasting system with a lack of hydrometeorological information.

Conclusion

The study presents the results of modeling hydrographs of river runoff on a daily calculation interval and historical floods on an hourly calculation interval, conducted in three small catchments of the mountain cryolithozone with an area of 8.4 to 932 ^km2, located in the Kolyma River basin.

On the basis of a digital relief model, a landscape map and satellite images, the schematization of catchments was carried out, a set of parameters of the hydrological model Hydrograph was developed, and the results of modeling based on daily hydrometeorological data were verified. Analysis of the modeling results of daily runoff hydrographs and annual elements of the water balance, the Nash-Sutcliffe criterion showed that the previously developed set of model parameters based on data from the Kolyma water Balance station satisfactorily describes the hydrological regime. The median values of the Nash-Sutcliffe efficiency for diurnal hydrographs were 0.52 for the Krivulya River (1966-1994), 0.55 for the Ambardakh River (1966-1987), and 0.61 for the Susuman River (1966-1987).

Pluviograph data on the dynamics of rainfall for the meteorological stations Susuman and Kulu were used as input data for calculating the maximum water flow during the passage of historical floods (see Ambardakh and Susuman, 1986; manual. Krivulya, 1984) with an hour interval. Based on the simulation results, the assessment of urgent and daily expenses for each event under consideration was carried out, as well as their comparison with the observed data. The calculated maximum hourly costs were 16.5, 78.5 and 420 ^m3/s for pp. Crooked. Ambardakh and Susuman, respectively.

The results of the study confirm that the method of deterministic hydrological modeling can be used to calculate the maximum water consumption in the presence of detailed precipitation data. Currently, due to the limited information on precipitation, modeling methods are not used for mass calculations of runoff characteristics. However, pluviograph data is useful for analyzing the causes of catastrophic floods and further developing mathematical modeling methods. Climate models are a potential source of precipitation information. Using their forecasts as input meteorological data in the runoff formation model will make it possible to evaluate and predict the maximum characteristics of the runoff.

Methods and a system of short-term forecasts of dangerous hydrological phenomena in modern climatic conditions have not been developed for most regions of the Far Eastern Federal District. Historically, these regions are the least provided with data from standard hydrometeorological measurements. Climate change causes non-linearity of the reaction and transformation of the cryolithozone hydrological cycle under the influence of permafrost degradation processes and anthropogenic landscape changes. These factors make it difficult to develop short-term forecasting methods and make it impossible to apply simple (for example, regression) models of runoff characteristics.

The results of the study can be useful in the tasks of studying the regime of formation of catastrophic floods in modern climatic conditions, assessing the characteristics of runoff during hydrological calculations, and developing a system for operational forecasting of dangerous hydrological phenomena in the region under study.