Indicators of high and low inflow to Lake Baikal and the runoff of its main rivers

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1. Introduction

In the context of the river water availability, the criteria employed (high, low, average) are typically of a qualitative nature, despite the fact that hydrology has been utilizing a classification of river runoff values into different gradations (categories, classes) for a relatively long period of time based on their provision (P). One of the earliest classifications of water availability for annual river runoff, which allows for the allocation of high-water years (P<25%), medium-water years (P from 25 to 75%), and low-water years (P>75%), was proposed by the SHI (State Hydrological Institute) in the middle of the twentieth century (Kuzin, 1953). This was evidently insufficient for practice, and furthermore, the number of gradations in terms of water availability increased. In the work of Kochukova (1955), the number of gradations was increased to seven, with the high-water and low-water gradations divided into three additional classes. However, in spite of widespread use of runoff characteristics of estimated water provision in planning and constructive practice, there are still no unified criteria for determining quantitative indicators of high or low water availability of rivers in the normative-legal base of the Russian Federation on water resources. The necessity for different requirements regarding boundary water discharges can be attributed to the varying coverage domains and tasks to be solved. Furthermore, the discreteness of data presentation and their averaging must be considered, with annual, monthly, daily, and urgent averages being employed. Urgent averages are typically used for maximum and minimum water discharges corresponding to the highest or lowest water levels at the observation dates.

Hydrological calculations focus on critical values of river runoff that have a probability of occurrence of no more than 5-10% (SR (Set of Rules) 33, SR 115, SR 482). Capital objects are calculated for discharges and water levels of infrequent recurrence, defined as events that occur once in 100 or 1,000 years or more (with a probability of 1 or 0.1% or less). In the context of climate change, the probability of such events may significantly increase. To illustrate, the probability of a catastrophic flood in California, comparable to the megaflood of 1862, resulting from an increase in atmospheric water vapor and the replacement of a portion of the solid precipitation falling in mountainous regions by liquid precipitation due to warming is estimated to be several times greater (Huang and Swain, 2022).

For Lake Baikal, the problems of water availability indicators have been exacerbated since 2001 due to the restrictions of its level regulation limits. It is necessary to introduce normative-legal relations in the sphere of water resources using quantitative criteria of low-water or high-water periods to find a right solution. In this context, Abasov et al. (2017) considered the option of dividing the useful inflow values to Lake Baikal into five water availability gradations. In the work of Bolgov et al. (2018), the boundary values of inflow for water provision below 50% are estimated. Within the assignment of NRM (Natural Resources Ministry) on optimization of the level regime of Lake Baikal, the SHI proposed a scheme for dividing the useful inflow to Lake Baikal into seven water content gradations. Concurrently, it becomes evident that in order to enhance the efficacy of the regulation of lake runoff and its level, to safeguard the Baikal ecosystem, and to minimize the potential socio-economic risks in the region, quantitative water availability indicators should be based not only on inflow, but also on other characteristics of the water regime in the Baikal basin, and be enshrined in legislation. This paper is aimed at examining these factors in relation to the total surface water inflow to Lake Baikal and the runoff of its principal tributaries.

2. Materials and methods

The study was based on Roshydromet observations of monthly and annual volumes of total river water inflow from the Baikal catchment area and runoff of its main tributaries in the closing stations: the Selenga (Mostovoy Passage, basin area is 440,000 km²), the Upper Angara (Verkhnyaya Zaimka village, 20,600 km²) and the Barguzin (Barguzin village, 19,800 km²). In addition, for rivers, it is necessary to consider the significant differences in hydrological conditions within a year and the diverse interests of users. Consequently, several runoff characteristics are employed, including annual, monthly, maximum and minimum. The maximum runoff is considered in terms of the maximum spring flood and rainfall flood discharges, while the minimum runoff is considered in terms of the lowest winter and summer runoff values. In this case, for monthly river runoffs, the focus is on the most high-water or low-water months.

The calculation period includes 1961–2020 and reflects modern conditions of river runoff formation in the Baikal basin. However, when analyzing multiyear water availability conditions for rivers, a full series of observations is used, and for annual inflow, the data (Afanasyev, 1967) for 1901–1960 are used. The determination of the calculated provision of inflow to the lake and river runoff was carried out in accordance with the requirements and recommendations (Manual for determining..., 1984; SR-33-101-2003, 2004; Methodological Recommendations..., 2005; STO of the SHI, 2017). First, the distribution parameters of the considered series were calculated, namely the mean value (Q_o), coefficients of variation (C_v), and asymmetry (C_s). These parameters were then used to calculate the ordinates of the analytical distribution curves. Moreover, the last two parameters were subject to adjustment if the correlation coefficient (r1) between adjacent members of the series was equal to or greater than 0.3. The calculations of the indicators of the given security values were conducted using the Kritski-Menkel distribution. However, for series with rare C_s/C_v ratios (greater than 6 and less than –1), the binomial distribution was employed. The calculations were limited to 0.1 and 99.9% provisions.

The initial series were preliminary examined for homogeneity using Fisher and Student`s criteria, and in cases of heterogeneity of the data, the required curves were plotted according to the composite distribution, which was constructed from the distributions for each of the parts of the heterogeneous series. The accuracy of initial data on the inflow and water content of rivers corresponds to the accuracy of determining the runoff of rivers illuminated by hydrometric observations, which, according to the standard (Methodological Guidelines, 1987), is at the level of 6–10%. Using the averaged data (multiyear, annual, seasonal), the error of their determination is reduced more than twice, and even for rivers with unstable channels, the normative frequency of water discharge measurements is 4% (Karasev and Yakovleva, 2001). In addition, when estimating the parameters of multiyear runoff variability (if the methods of measurement and calculation remain unchanged), this error often becomes systematic and distorts the relative nature of fluctuations to a small extent.

The above-mentioned scheme of the SHI of seven classes depending on inflow or runoff provision is taken as a basis for water availability gradations. The first class corresponds to the catastrophically high water content (Р≤1%), the second one corresponds to moderately high (1%<Р≤10%), the third one corresponds to high (10%<Р≤40%), the fourth one corresponds to medium (40%<Р<60%), the fifth one corresponds to moderately low (60%≤Р<90%), the sixth one corresponds to low (90%≤Р<99%), and the seventh one corresponds to catastrophically low (Р≥99%).

Meanwhile, the terminology “low water availability” and “catastrophically low water availability” is obviously illogical for maximum river runoff (the same applies to high and catastrophically high water content for minimum water discharge and monthly low-water runoff), so in such cases, instead of defining classes, it is more correct to use their numbers (first class, second class, etc.).

3. Results and discussion

3.1. The surface water inflow into Lake Baikal

The main parameters of the inflow distribution and its boundary values of calculated provision for each calendar year and individual month (Table 1) allow differentiating river water inflow to Lake Baikal based on the availability of water into seven distinct classes.

Table 1. Distribution indicators and values of the annual and monthly inflow of the calculated probabilities

The data obtained indicate that the boundaries of water content classes naturally decrease from high water content to low water content. This is connected with essentially positive asymmetry of the considered series. The widest range of values of both annual and monthly inflow is typical for the second water availability class, and the narrowest is for the sixth. In the winter months, the boundaries of water content class decreases to 0.03-0.04 km³, with a low inflow. This is sufficient to attribute the differences in water availability to various gradations. In general, the range of classes for each of the series is in accordance with its distribution parameters, namely Q_o, C_v, and C_s.

The results of calculations indicate that the annual water inflow to the lake was catastrophically high approximately half a century ago (1973), reaching 92.2 km³ (Fig. 1). The maximum inflow observed was 98.7 km³ and was recorded in 1932. Additionally, a markedly low inflow was observed in Lake Baikal for an extended period, in 1903 and 1922. The occurrence of these events was not within the calculated period, and thus, their probability of occurrence was low. In particular, the observed decrease in inflow in 1903 to 32.2 km³ corresponds to the provision of more than 99.9%, or a recurrence less than once in 1,000 years. Since the beginning of the 21st century, the lowest water years were 2014-2017, with a minimum inflow of 42.5 km³ in 2015.

Fig.1. Dynamics of the annual inflow and runoff of rivers with delineation of water availability class boundaries.

In the intra-annual distribution of inflow, the maximum inflow of river water into the lake occurs in June, which is associated with the spring flooding in the rivers of the Baikal basin at this time. Although the rainfall flood runoff is generally higher than in the spring flood, in different years it falls at different months (June-September), due to which the inflow in June on average is predominant. However, the absolute maximum of inflow with a repeatability of once every 100 years can be observed in August and reach 20.4 km³/month. For 1950–2020 (no monthly data are available for earlier years), the maximum inflow was 20.7 km³ and was observed in August 1973. It is typical that in the same year, the inflows in June, July and September also reached their highest levels.

During the winter months, the inflow of surface water to the lake is significantly reduced, with an average of less than 1 km³ observed in February and March. The lowest monthly inflow of 0.58 km³ was recorded in February 1973, corresponding to the seventh class of water availability (P > 99 %).

3.2. The annual and monthly river runoff

The Selenga, Upper Angara, and Barguzin rivers, the main tributaries of Lake Baikal, provide on average 2/3 of the surface water inflow to the lake from the territory comprising about 80% of its total catchment area (Sinyukovich and Chernyshov, 2017). Besides, each of these rivers has an extremely important independent significance. In the areas where they runoff into the lake, they contribute to the formation of the most biologically productive areas, including the Selenga shallow water, Verkhneangarsky Sor, and Barguzinsky Bay. The functioning of these biotopes directly depends on the water regime of the feeding rivers.

The distribution parameters and boundary water discharges of the three rivers are significantly influenced by their long-term dynamics. With regard to the Selenga, it is noteworthy that two deep low-water events should be included in the calculation period: the first occurring between 1976 and 1981 and the second spanning from the end of the twentieth century to 2018 (Fig. 1).

This indicates that the discharge values of the Selenga calculated provision may be underestimated. The calculated data (Table 2) indicate that the average annual runoff of the Selenga may exceed 1,500 m³/s (twice the mean annual runoff) once in 100 years, or alternatively, be below 385 m³/s. Within the year, the lowest runoff of the river on average is in February (about 1% of the annual water availability) and the highest in August (18%). According to the different flows in these months, to be classified in the first water content category, the runoff in August should be at least 4,160 m³/s, while in February it can be a little more than 200 m³/s.

Table 2. Distribution parameters and boundary values of the runoff for calendar years and individual months of the main Baikal rivers for seven water provision gradations

For the entire observation period (1934-2020), the most high-water year on the Selenga was 1973 (1,470 m³/s) and almost corresponded to class 1, or catastrophically high water content, and the lowest-water year was 2002 (505 m³/s, moderately low water content). The highest monthly runoff was recorded in August 1993 reaching 4,360 m³/s (water class 1), while the lowest one was observed in February 1936, at 34.7 m³/s (water class 7).

In the Upper Angara, significant runoff fluctuations occurred only in the 21st century with high-water years 2004-2008 and low-water years 2013-2017 (see Fig. 1). Since the beginning of observations (1939), the annual river runoff has varied from 172 (2016, water class 6) to 404 m³/s (2006, water class 1). Differences between neighboring water content classes are not as contrasting as in the Selenga, which is explained by both the lower water content of the Upper Angara and the lower variability of its runoff (C_v is 0.18).

Within the year, the highest river runoff is in June, when, with a probability of 1%, it can reach 1,370 m³/s. In fact, in 2006, the runoff was very close to this limit (1,360 m³/s), but corresponded only to water content class 2. The lowest discharge in June (340 m³/s, water content class 7) was observed in 2013. The most low-water month in the Upper Angara is March, the runoff of which varies little from year to year (C_v is 0.14). For all years of observations, the average March water discharge varied from 48.1 m³/s (1969) to 86.2 m³/s (2006). Despite the relatively small difference, in the first case, water availability corresponded to the 6th class, and in the second case, it corresponded to the first class.

For the Barguzin, the boundaries of the water content classes are even smaller. The minimum difference between the annual runoff of classes 3 and 5 is only 14 m³/s, and for March, which is the lowest-water month, it is only 3.5 m³/s. Over the observation period since 1933, the highest annual runoff was 213 m³/s (1949, water content class 1), while the lowest was 67.2 m³/s (2015, water content class 6). As for August, which is the most high-water month, the maximum discharge reached 653 m³/s in 1973. This was a catastrophically high water content. However, a higher runoff of 710 m³/s was observed in June 1936. This maximum is outside the calculation period. The minimum runoff in August (87.4 m³/s) occurred in 1987 and was almost at the boundary of water content classes 6 and 7.

In March, the highest river runoff was observed in 1996 (43.5 m³/s) and corresponded to water content class 2. The minimum one was observed in 2020 (15.3 m³/s) and corresponded to the class 6.

3.3. Maximum and minimum runoffs

The characteristics of extreme runoff and calculated provision of the studied rivers (Fig. 2) give an idea of the scale of possible fluctuations in their water runoff in different phases of the water regime. For the Selenga, with a 1% probability, the runoff can vary from 41.2 m³/s during the winter low water period to 7,300 m³/s during rainfall floods. The actual range of runoff fluctuations was even more pronounced with values varying from 29.9 m³/s in winter 2012 to 7,620 m³/s (water content class 1) in the flood of 1936. A slightly lower flood maximum was observed in 1973 (7,210 m³/s), which was already of the water content class 2. It is important to note that, in certain years, the intensity of flooding may be relatively low. For example, in 2004, the maximum runoff was only 1,200 m³/s.

Fig.2. Boundaries of the water availability classes for maximum and minimum river runoffs.

During the flood season, the Selenga water runoff is significantly lower than during high water periods (see Figure 2), which is also reflected in the observation data. The maximum spring flood runoff on the Selenga (4,200 m³/s) was observed in 1951 and was considerably lower than the flood season, and during the lowest flood, which occurred in 2007, it decreased to 874 m³/s. The minimum runoff rates of the Selenga River during the open channel period and in winter differ even more significantly. The absolute summer minimum runoff was 459 m³/s, which is an order higher than the winter minimum.

In the Upper Angara, the maximum annual runoff recorded in the spring snowmelt period differs from that observed in the Selenga. The highest runoff of 2,570 m³/s was recorded in 2007, while the highest flood, which occurred in 1951, resulted in a runoff of 1,860 m³/s. The lowest river runoff of 40.5 m³/s was recorded in winter 1980. During the free channel period, the minimum water runoff is considerably higher ranging from 91 to 419 m³/s. In accordance with the noted seasonal extremes of the Upper Angara runoff, the absolute amplitude of their fluctuations is 2,530 m³/s.

For the Barguzin, all runoff indices were significantly lower than for the Upper Angara, despite the similar sizes of their catchments. Water runoffs from rainfall floods on the Barguzin River are generally higher than in floods, but during the period of observations since 1933, the maximum river runoff reached 1,110 m³/s and was recorded in the flood of 1936, while in the highest flood it was only 909 m³/s. The calculated parameters of flood runoff distribution for the period 1961–2020 indicate the possibility of high meltwater runoff with a probability of 0.01%, which would occur once every 10,000 years.

It is important to note that a flood of comparable magnitude occurred in 1933 (848 m³/s), with a recurrence interval of less than once in 500 to 600 years. Such a low theoretical probability of this extremum is associated, as in the case of the river runoff in June 1936, with the absence of similar values in the calculation period. A similar situation is common for the minimum runoff of the Barguzin River, especially in winter, the lowest value of which (12.4 m³/s) falls at 1945, also not included in the calculation period. Nevertheless, the indicated minimum corresponds to a theoretical recurrence, approximately once every 100 years due to the presence of several close values in the 1961-2020 data.

During the summer runoff low period, the river runoff is considerably higher than during the rest of the year. For the entire period of observations, the river runoff varied from 52.5 m³/s (1933) to 268 m³/s (1949). Consequently, both extremums were not involved in the calculations of the runoff distribution and the results of determining the boundary values of runoff may be not correct enough.

3.4. Abnormally rare water availability indices

In general, the probability of the maximum and minimum values of the considered indicators occurring within the specified calculation period of 60 years has provision 1-2% and 98-99%, respectively. This corresponds to the recurrence of these extremes once every 50-100 years. However, as was seen above, the annual inflow to the lake decreased according to Afanasyev (1967) to 32.2 km³ in 1903, and it increased to 98.7 km³ in 1932. The probability of occurrence of such a low-water event as in 1903, for example, is 0.1%, i.e., it can occur only once every 1,000 years. First of all it should be noted that evaluating the reliability of these extremes, these are calculated values because the observations of the runoff of the large Baikal rivers had not been made at that time. To reconstruct the inflow data for 1901-1932, A.N. Afanasyev used the correlation between the annual runoff of the Angara River at the source and annual inflow calculated for 1933-1958 and characterized by a correlation coefficient of 0.997. Despite this, the reliability of the reconstructed data requires reconsideration using modern concepts of the runoff formation in the Lake Baikal basin and involvement of additional sources of information.

A similar phenomenon can be observed in the maximum spring flood season of the Barguzin River, which reached 1,110 m³/s in 1936. Theoretically, the river runoff can increase to such values only once every 10,000 years. In 1936, the river experienced extremely abnormal conditions of snow accumulation and snowmelt, which may have contributed to this phenomenon. Taking into account that instrumental measurements of water runoff in such cases are most often impossible, the reliability of the observed extremum also requires additional verification. Concurrently, particular focus should be placed on the transformation of runoff formation conditions, which have been subject to anthropogenic transformation (deforestation and land plowing) in the river basin since the 1950s.

When planning important water management measures, the noted rare hydrological events should be taken into account with repeated calculations of distribution parameters in case of confirmation of their reliability.

4. Conclusion

The obtained results enabled us to estimate the parameters of long-term variability and peculiarities of the distribution of surface water inflow to Lake Baikal and the runoff of its main tributaries for a single calculation period (1961–2020), grouping the studied parameters depending on their provision into seven water content classes. This differentiation enables the operation with numerical values of high or low water availability criteria, thereby eliminating ambiguity in their interpretation. During the observation period, the classes of catastrophically high or low water content in annual and monthly inflow values, as well as the runoff characteristics of the Selenga, Upper Angara, and Barguzin rivers, were observed on only a few occasions. Concurrently, for preceding years not included in the calculation period, inflow values and river runoff of less frequent occurrence are observed. In particular, the low inflow into Lake Baikal in 1903 and the spring flood season of the Barguzin River in 1936 correspond to the recurrence of once every 1,000 years and less frequently. Such cases require special examination to verify the reliability of the observed extremes and to make decisions on the expediency of extending the calculation period and performing repeated calculations.

The range of fluctuations in river inflow and runoff within individual classes is determined by the accepted provision boundaries, which define the division into classes of different water content, as well as by sample parameters of the distribution of the used series. The asymmetric distribution inherent to the runoff realization results in the narrowing of the boundaries of certain classes as the water content class decreases.

For practical use of the obtained results, it is obviously necessary to study other variants with different boundaries and number of water content gradations, because when considering a specific problem, an individual solution variant, including different period of averaging of initial data, may be optimal. For some watercourses, in this respect, it is expedient to involve in the analysis the characteristics of maximum and minimum runoff, which makes it possible to assess the absolute amplitude of fluctuations in river water discharge and a more objective approach to the choice of one or another variant of water content gradation allocation.

Acknowledgements

The study is carried out within the State Assignment of LIN SB RAS № 0279-2021-0004.

Conflict of Interest

The author declares no conflicts of interest.

About the authors

V. N. Sinyukovich

Author for correspondence.
Email: sin@lin.irk.ru
ORCID iD: 0000-0001-9135-3159
Russian Federation, Ulan-Batorskaya Str., 3, Irkutsk, 664033

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2. Fig.1. Dynamics of the annual inflow and runoff of rivers with delineation of water availability class boundaries.

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3. Fig.2. Boundaries of the water availability classes for maximum and minimum river runoffs.

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