To determine the flow of the river depending on the area of ​​the basin, the height of the sediment layer, etc. in hydrology, the following quantities are used: river flow, flow modulus, and flow coefficient.

River runoff call water consumption over a long period of time, for example, per day, decade, month, year.

Drain module they call the amount of water expressed in liters (y), flowing on average in 1 second from the area of ​​​​the river basin in 1 km 2:

Runoff coefficient call the ratio of water flow in the river (Qr) to the amount of precipitation (M) on the area of ​​the river basin for the same time, expressed as a percentage:

a - runoff coefficient in percent, Qr - annual runoff value in cubic meters; M is the annual amount of precipitation in millimeters.

To determine the runoff modulus, it is necessary to know the water discharge and the area of ​​the basin upstream of the target, according to which the water discharge of the given river was determined. The area of ​​a river basin can be measured from a map. For this, the following methods are used:

• 1) planning
• 2) breakdown into elementary figures and calculation of their areas;
• 3) measuring the area with a palette;
• 4) calculation of areas using geodetic tables

It is easiest for students to use the third method and measure the area using a palette, i.e. transparent paper (tracing paper) with squares printed on it. Having a map of the studied area of ​​the map on a certain scale, it is possible to make a palette with squares corresponding to the scale of the map. First, you should outline the basin of this river above a certain alignment, and then apply the map to the palette, on which to transfer the contour of the basin. To determine the area, you first need to count the number of full squares located inside the contour, and then add up these squares, partially covering the basin of the given river. Adding the squares and multiplying the resulting number by the area of ​​one square, we find out the area of ​​the river basin above this alignment.

Q - water consumption, l. For translation cubic meters in liters we multiply the consumption by 1000, S the area of ​​​​the pool, km 2.

To determine the river runoff coefficient, it is necessary to know the annual runoff of the river and the volume of water that has fallen on the area of ​​a given river basin. The volume of water that fell on the area of ​​this pool is easy to determine. To do this, you need to multiply the area of ​​​​the basin, expressed in square kilometers, by the thickness of the layer of precipitation (also in kilometers). For example, the thickness will be equal to p if precipitation in a given area was 600 mm per year, then 0 "0006 km and the runoff coefficient will be equal to:

Qr is the annual flow of the river, and M is the area of ​​the basin; multiply the fraction by 100 to determine the runoff coefficient as a percentage.

Determination of the river flow regime. To characterize the flow regime of the river, you need to establish:

a) what seasonal changes the water level undergoes (a river with a constant level, which becomes very shallow in summer, dries up, loses water in pores and disappears from the surface);

b) the time of high water, if any;

c) the height of the water during the flood (if there are no independent observations, then according to questionnaire data);

d) the duration of the freezing of the river, if it occurs (according to their own observations or according to information obtained through a survey).

Determination of water quality. To determine the quality of water, you need to find out whether it is cloudy or transparent, drinkable or not. The transparency of the water is determined by a white disk (Secchi disk) with a diameter of approximately 30 cm, summed up on a marked line or attached to a marked pole. If the disk is lowered on the line, then a weight is attached below, under the disk, so that the disk is not carried away by the current. The depth at which this disk becomes invisible is an indication of the transparency of the water. You can make a disk out of plywood and paint it in White color, but then the load must be hung heavy enough so that it falls vertically into the water, and the disk itself maintains a horizontal position; or plywood sheet can be replaced with a plate.

Determination of water temperature in the river. The temperature of the water in the river is determined by a spring thermometer, both on the surface of the water and at different depths. Keep the thermometer in water for 5 minutes. A spring thermometer can be replaced with a conventional wooden-framed bath thermometer, but in order for it to sink into the water at different depths, a weight must be tied to it.

You can determine the temperature of the water in the river with the help of bathometers: a bathometer-tachymeter and a bottle bathometer. The bathometer-tachymeter consists of a flexible rubber balloon with a volume of about 900 cm 3; a tube with a diameter of 6 mm is inserted into it. The bathometer-tachymeter is fixed on a rod and lowered to different depths to take water.

The resulting water is poured into a glass and its temperature is determined.

It is not difficult for a student to make a bathometer-tachymeter. To do this, you need to buy a small rubber chamber, put on it and tie a rubber tube with a diameter of 6 mm. The bar can be replaced with a wooden pole, dividing it into centimeters. The rod with the tachymeter bathometer must be lowered vertically into the water to a certain depth, so that the opening of the tachymeter bathometer is directed downstream. Having lowered to a certain depth, the bar must be rotated by 180 and held for about 100 seconds in order to draw water, and then again turn the bar by 180 °. runoff water regime river

It should be removed so that water does not spill out of the bottle. After pouring water into a glass, determine the temperature of the water at a given depth with a thermometer.

It is useful to simultaneously measure the air temperature with a sling thermometer and compare it with the temperature of the river water, making sure to record the time of observation. Sometimes the temperature difference reaches several degrees. For example, at 13 o'clock the air temperature is 20, the temperature of the water in the river is 18 °.

Study in certain areas on certain nature of the riverbed. When examining sections of the nature of the riverbed, it is necessary:

a) mark the main reaches and rifts, determine their depths;

b) when detecting rapids and waterfalls, determine the height of the fall;

c) draw and, if possible, measure the islands, shoals, middles, side channels;

d) collect information in which places the river is eroding and in places that are especially strongly eroded, determine the nature of the eroded rocks;

e) study the nature of the delta, if the estuarine section of the river is being investigated, and plot it on the visual plan; see if the individual arms correspond to those shown on the map.

General characteristics of the river and its use. At general characteristics rivers need to find out:

a) which part of the river is mainly eroding and which is accumulating;

b) degree of meandering.

To determine the degree of meandering, you need to know the tortuosity coefficient, i.e. the ratio of the length of the river in the study area to the shortest distance between certain points in the study part of the river; for example, river A has a length of 502 km, and the shortest distance between the source and the mouth is only 233 km, hence the tortuosity coefficient:

K - sinuosity coefficient, L - river length, 1 - shortest distance between source and mouth

Meander study It has great importance for timber rafting and shipping;

c) Non-squeezing river fans formed at the mouths of tributaries or produce temporary flows.

Find out how the river is used for navigation and timber rafting; if the hand is not navigable, then find out why, it serves as an obstacle (shallow, rapids, are there waterfalls), are there dams and other artificial structures on the river; whether the river is used for irrigation; what transformations need to be done to use the river in the national economy.

Determining the nutrition of the river. It is necessary to find out the types of river nutrition: ground, rain, lake or swamp from melting snow. For example, r. Klyazma is fed, ground, snow and rain, of which ground supply is 19%, snow - 55% and rain. - 26 %.

The river is shown in Figure 2.

m 3

Conclusion: In the course of this practical lesson, as a result of calculations, the following values ​​were obtained, characterizing the flow of the river:

Drain module? = 177239 l / s * km 2

Runoff coefficient b = 34.5%.

28.07.2015

fluctuations river flow and criteria for its evaluation. River runoff is the movement of water in the process of its circulation in nature, when it flows down the river channel. River flow is determined by the amount of water flowing through the river channel for a certain period of time.
Numerous factors influence the flow regime: climatic - precipitation, evaporation, humidity and air temperature; topographic - terrain, shape and size of river basins and soil-geological, including vegetation cover.
For any basin, the more precipitation and less evaporation, the greater the flow of the river.
It has been established that with an increase in the catchment area, the duration of the spring flood also increases, while the hydrograph has a more elongated and “calm” shape. In easily permeable soils, there is more filtration and less runoff.
When performing various hydrological calculations related to the design of hydraulic structures, reclamation systems, water supply systems, flood control measures, roads, etc., the following main characteristics of the river flow are determined.
1. Water consumption is the volume of water flowing through the considered section per unit of time. The average water consumption Qcp is calculated as the arithmetic average of the costs for a given period of time T:

2. Flow volume V- this is the volume of water that flows through a given target for the considered period of time T

3. Drain module M is the flow of water per 1 km2 of catchment area F (or flowing from a unit catchment area):

In contrast to the water discharge, the runoff modulus is not associated with a specific river section and characterizes the runoff from the basin as a whole. The average multi-year runoff module M0 does not depend on the water content of individual years, but is determined only by the geographical location of the river basin. This made it possible to zonate our country in hydrological terms and to build a map of isolines of average long-term runoff modules. These maps are given in the relevant regulatory literature. Knowing the catchment area of ​​a river and determining the value M0 for it using the isoline map, we can determine the average long-term water flow Q0 of this river using the formula

For closely spaced river sections, the runoff moduli can be taken constant, i.e.

From here, according to the known water flow in one section Q1 and famous squares watersheds in these sections F1 and F2, the water discharge in another section Q2 can be established by the ratio

4. Drain layer h- this is the height of the water layer, which would be obtained with a uniform distribution over the entire basin area F of the runoff volume V for a certain period of time:

For the average multi-year runoff layer h0 of the spring flood, contour maps were compiled.
5. Modular drain coefficient K is the ratio of any of the above runoff characteristics to its arithmetic mean:

These coefficients can be set for any hydrological characteristics (discharges, levels, precipitation, evaporation, etc.) and for any periods of flow.
6. Runoff coefficient η is the ratio of the runoff layer to the layer of precipitation that fell on the catchment area x:

This coefficient can also be expressed in terms of the ratio of the volume of runoff to the volume of precipitation for the same period of time.
7. Flow rate- the most probable average long-term value of runoff, expressed by any of the above runoff characteristics over a multi-year period. To establish the runoff norm, a series of observations should be at least 40 ... 60 years.
The annual flow rate Q0 is determined by the formula

Since the number of observation years at most water gauges is usually less than 40, it is necessary to check whether this number of years is sufficient to obtain reliable values ​​of the runoff norm Q0. To do this, calculate the root mean square error of the flow rate according to the dependence

The duration of the observation period is sufficient if the value of the root-mean-square error σQ does not exceed 5%.
The change in annual runoff is predominantly influenced by climatic factors: precipitation, evaporation, air temperature, etc. All of them are interrelated and, in turn, depend on a number of reasons that are random in nature. Therefore, the hydrological parameters characterizing the runoff are determined by a set of random variables. When designing measures for timber rafting, it is necessary to know the values ​​of these parameters with the necessary probability of exceeding them. For example, in the hydraulic calculation of timber rafting dams, it is necessary to set the maximum flow rate of the spring flood, which can be exceeded five times in a hundred years. This problem is solved using the methods of mathematical statistics and probability theory. To characterize the values ​​of hydrological parameters - costs, levels, etc., the following concepts are used: frequency(recurrence) and security (duration).
The frequency shows how many cases during the considered period of time the value of the hydrological parameter was in a certain interval. For example, if the average annual water flow in a given section of the river changed over a number of years of observations from 150 to 350 m3/s, then it is possible to establish how many times the values ​​of this value were in the intervals 150...200, 200...250, 250.. .300 m3/s etc.
security shows in how many cases the value of a hydrological element had values ​​equal to or greater than a certain value. In a broad sense, security is the probability of exceeding a given value. The availability of any hydrological element is equal to the sum of the frequencies of the upstream intervals.
Frequency and availability can be expressed in terms of the number of occurrences, but in hydrological calculations they are most often defined as a percentage of total number members of the hydrological series. For example, in the hydrological series there are twenty values ​​of average annual water discharges, six of them had a value equal to or greater than 200 m3/s, which means that this discharge is provided by 30%. Graphically, changes in frequency and availability are depicted by curves of frequency (Fig. 8a) and availability (Fig. 8b).

In hydrological calculations, the probability curve is more often used. It can be seen from this curve that the greater the value of the hydrological parameter, the lower the percentage of availability, and vice versa. Therefore, it is generally accepted that years for which the runoff availability, that is, the average annual water discharge Qg, is less than 50% are high-water, and years with Qg more than 50% are low-water. A year with a runoff security of 50% is considered a year of average water content.
The availability of water in a year is sometimes characterized by its average frequency. For high-water years, the frequency of occurrence shows how often years of a given or greater water content occur on average, for low-water years - of a given or less water content. For example, the average annual discharge of a high-water year with 10% security has an average frequency of 10 times in 100 years or 1 time in 10 years; the average frequency of a dry year of 90% security also has a frequency of 10 times in 100 years, since in 10% of cases the average annual discharge will have lower values.
Years of a certain water content have a corresponding name. In table. 1 for them the availability and repeatability are given.

The relationship between repeatability y and availability p can be written as follows:
for wet years

for dry years

All hydraulic structures for regulating the channel or flow of rivers are calculated according to the water content of the year of a certain supply, which guarantees the reliability and trouble-free operation of the structures.
The estimated percentage of provision of hydrological indicators is regulated by the "Instruction for the design of timber rafting enterprises".
Provision curves and methods of their calculation. In the practice of hydrological calculations, two methods of constructing supply curves are used: empirical and theoretical.
Reasonable calculation empirical endowment curve can be performed only if the number of observations of the river flow is more than 30...40 years.
When calculating the availability of members of the hydrological series for annual, seasonal and minimum flows, you can use the formula of N.N. Chegodaeva:

To determine security maximum spending water apply dependence S.N. Kritsky and M.F. Menkel:

The procedure for constructing an empirical endowment curve:
1) all members of the hydrological series are recorded in decreasing order in absolute value;
2) each member of the series is assigned a serial number, starting from one;
3) the security of each member of the decreasing series is determined by formulas (23) or (24).
Based on the results of the calculation, a security curve is built, similar to the one shown in Fig. 8b.
However, empirical endowment curves have a number of disadvantages. Even with a sufficiently long observation period, it cannot be guaranteed that this interval covers all possible maximum and minimum values river runoff. Estimated values ​​of runoff security of 1...2% are not reliable, since sufficiently substantiated results can be obtained only with the number of observations for 50...80 years. In this regard, with a limited period of observation of the hydrological regime of the river, when the number of years is less than thirty, or in their complete absence, they build theoretical security curves.
Studies have shown that the distribution of random hydrological variables most well obeys the type III Pearson curve equation, the integral expression of which is the supply curve. Pearson obtained tables for constructing this curve. The security curve can be constructed with sufficient accuracy for practice in three parameters: the arithmetic mean of the terms of the series, the coefficients of variation and asymmetry.
The arithmetic mean of the terms of the series is calculated by formula (19).
If the number of years of observations is less than ten or no observations were made at all, then the average annual water discharge Qgcp is taken equal to the average long-term Q0, that is, Qgcp = Q0. The value of Q0 can be set using the modulus factor K0 or the sink modulus M0 determined from the contour maps, since Q0 = M0*F.
The coefficient of variation Cv characterizes the runoff variability or the degree of its fluctuation relative to the average value in a given series; it is numerically equal to the ratio of the standard error to the arithmetic mean of the series members. The value of the Cv coefficient is significantly affected climatic conditions, type of river feeding and hydrographic features of its basin.
If there are observational data for at least ten years, the annual runoff variation coefficient is calculated by the formula

The value of Cv varies widely: from 0.05 to 1.50; for timber-rafting rivers Cv = 0.15...0.40.
With a short period of observations of the river runoff or in their complete absence the coefficient of variation can be established by the formula D.L. Sokolovsky:

In hydrological calculations for basins with F > 1000 km2, the isoline map of the Cv coefficient is also used if the total area of ​​lakes does not exceed 3% of the catchment area.
In the normative document SNiP 2.01.14-83, a generalized formula K.P. is recommended for determining the coefficient of variation of unstudied rivers. Resurrection:

Skewness coefficient Cs characterizes the asymmetry of the series under consideration random variable about its average value. The smaller part of the members of the series exceeds the value of the runoff norm, the greater the value of the asymmetry coefficient.
The asymmetry coefficient can be calculated by the formula

However, this dependence gives satisfactory results only for the number of observation years n > 100.
The coefficient of asymmetry of unstudied rivers is set according to the Cs/Cv ratio for analogue rivers, and in the absence of sufficiently good analogues, the average Cs/Cv ratios for the rivers of the given region are taken.
If it is impossible to establish the Cs/Cv ratio for a group of analogous rivers, then the values ​​of the Cs coefficient for unstudied rivers are accepted for regulatory reasons: for river basins with a lake coefficient of more than 40%

for zones of excessive and variable moisture - arctic, tundra, forest, forest-steppe, steppe

To build a theoretical endowment curve for the above three parameters - Q0, Cv and Cs - use the method proposed by Foster - Rybkin.
From the above relation for the modular coefficient (17) it follows that the average long-term value of the runoff of a given recurrence - Qp%, Mp%, Vp%, hp% - can be calculated by the formula

The modulus runoff coefficient of the year of a given probability is determined by the dependence

Having determined a number of any runoff characteristics for a long-term period of different availability, it is possible to construct a supply curve based on these data. In this case, it is advisable to carry out all calculations in tabular form (Tables 3 and 4).

Methods for calculating modular coefficients. To solve many water management problems, it is necessary to know the distribution of runoff by seasons or months of the year. The intra-annual distribution of runoff is expressed in the form of modular coefficients of monthly runoff, representing the ratio of the average monthly flow Qm.av to the average annual Qg.av:

The intra-annual distribution of runoff is different for years of different water content, therefore, in practical calculations, the modular coefficients of monthly runoff are determined for three characteristic years: a high-water year with 10% supply, an average year for water content - 50% supply, and a low-water year - 90% supply.
Monthly runoff modulus coefficients can be established based on actual knowledge of average monthly water discharges with observational data for at least 30 years, on an analogous river or on standard tables of monthly runoff distribution, which are compiled for different river basins.
The average monthly water consumption is determined based on the formula

(33): Qm.cp = KmQg.sr

Maximum water consumption. When designing dams, bridges, lagoons, measures to strengthen the banks, it is necessary to know the maximum water flow. Depending on the type of river feeding, the maximum flow rate of spring floods or autumn floods can be taken as the calculated maximum discharge. The estimated security of these costs is determined by the class of capital size of hydraulic structures and is regulated by the relevant regulatory documents. For example, timber rafting dams of class Ill of capitality are calculated for the passage of a maximum water flow of 2% security, and class IV - of 5% security, bank protection structures should not collapse at flow rates corresponding to the maximum water flow of 10% security.
The method for determining the value of Qmax depends on the degree of knowledge of the river and on the difference between the maximum discharges of the spring flood and the flood.
If there are observational data for a period of more than 30 ... 40 years, then an empirical security curve Qmax is built, and with a shorter period - a theoretical curve. The calculations take: for spring floods Cs = 2Сv, and for rain floods Cs = (3...4)CV.
Since observations of the regime of rivers are carried out at water-measuring posts, the supply curve is usually plotted for these sites, and the maximum water discharges in the sites of the location of structures are calculated by the ratio

For lowland rivers maximum flow of spring flood water given security p% is calculated by the formula

The values ​​of the parameters n and K0 are determined depending on natural area and categories of relief according to the table. 5.

Category I - rivers located within hilly and plateau-like uplands - Central Russian, Strugo-Krasnenskaya, Sudoma uplands, Central Siberian plateau, etc .;
II category - rivers, in the basins of which hilly uplands alternate with depressions between them;
Category III - rivers, most of the basins of which are located within the flat lowlands - Mologo-Sheksninskaya, Meshcherskaya, Belarusian woodland, Pridnestrovskaya, Vasyuganskaya, etc.
The value of the coefficient μ is set depending on the natural zone and the percentage of security according to Table. 6.

The hp% parameter is calculated from the dependency

The coefficient δ1 is calculated (for h0 > 100 mm) by the formula

The coefficient δ2 is determined by the relation

The calculation of the maximum water discharges during the spring flood is carried out in tabular form (Table 7).

The levels of high waters (HWL) of the calculated supply are established according to the curves of water discharges for the corresponding values ​​of Qmaxp% and calculated sections.
With approximate calculations, the maximum water flow of a rain flood can be set according to the dependence

In responsible calculations, the determination of the maximum water flow should be carried out in accordance with the instructions of regulatory documents.

INTRODUCTION

Tasks of hydrological calculations and their role in the development of the country's economy. Connection of hydrological calculations with other sciences. History of the development of hydrological calculations: the first works of foreign scientists in the 17th-19th centuries; works of Russian scientists of the late 19th - early 20th centuries; the first textbook of hydrology in Russia; Soviet period of development of hydrological calculations; All-Union hydrological congresses and their role in the development of methods for calculating river runoff; post-Soviet period of development of hydrological calculations. The main characteristics of river flow. Three cases of determining hydrological characteristics.

METHODS FOR ANALYSIS OF RIVER FLOW CHARACTERISTICS.

Genetic analysis of hydrological data: geographic and hydrological method and its special cases - methods of hydrological analogy, geographic interpolation and hydrological and hydrogeological. Probabilistic-statistical analysis: method of moments, maximum likelihood method, quantifier method, correlation and regression analysis, factor analysis, principal component method, discriminant analysis method. Methods of analysis of computational mathematics: systems of algebraic equations, differentiation and integration of functions, partial differential equations, Monte Carlo method. Mathematical modeling of hydrological phenomena and processes, classes and types of models. System analysis.

METHODS FOR GENERALIZING HYDROLOGICAL CHARACTERISTICS.

Runoff contour maps: construction principles, runoff determination reliability. Hydrological zoning of the territory: concept, boundaries of application, principles of zoning and approaches to zoning, methods for determining the boundaries of regions, homogeneity of regions. Graphic processing of hydrological data: rectilinear, exponential and exponential graphic dependences.

FACTORS OF RIVER FLOW FORMATION.

The importance of understanding the mechanism and degree of influence of physical and geographical factors on the regime and magnitude of river runoff. River basin water balance equation. Classification of river runoff formation factors. Climatic and meteorological factors of river runoff: precipitation, evaporation, air temperature. Influence of factors of the river basin and its underlying surface on the runoff: geographical position, size, shape of the river basin, relief, vegetation, soils and rocks, permafrost, lakes, swampiness, glaciers and ice within the basin. Influence economic activity on river runoff: creation of reservoirs and ponds, redistribution of runoff between river basins, irrigation of agricultural fields, drainage of marshes and wetlands, agroforestry activities in river catchment areas, water consumption for industrial and domestic needs, urbanization, mining.

STATISTICAL PARAMETERS OF RIVER FLOW.

RELIABILITY OF INITIAL HYDROLOGICAL INFORMATION.

The flow rate and the principles of its calculation. River runoff variability, its relative (coefficient of variation) and absolute (standard deviation) expression, connection with meteorological factors. Variability of intra-annual distribution of runoff, maximum runoff of spring floods and rain floods, minimum winter and summer runoff. Asymmetry coefficient. Degree of reliability of hydrological input information. Causes of errors in regime hydrological information.

FORMATION CONDITIONS AND CALCULATIONS OF ANNUAL FLOW RATE.

Annual runoff of rivers as the main hydrological characteristic. Conditions for the formation of annual runoff: precipitation, evaporation, air temperature. Influence of lakes, swamps, glaciers, ice floes, basin area, watershed height, forest and its clearing, creation of reservoirs, irrigation, industrial and municipal water consumption, drainage of swamps and wetlands, agroforestry measures on the formation of annual river flow. The concept of the representativeness of a series of hydrological data. Elements of cyclic fluctuations in runoff. Synchronicity, asynchrony, in-phase, out-of-phase fluctuations of the drain. Calculations of the annual flow rate in the presence, insufficiency and absence of observational data. Distribution of annual runoff across the territory of Russia.

FORMATION FACTORS AND CALCULATION

INTRA-ANNUAL DISTRIBUTION OF RIVER FLOW.

The practical significance of knowledge about the intra-annual distribution of runoff. The role of climate in the distribution of runoff during the year. Underlying surface factors that correct the intra-annual distribution of runoff: lakes, swamps, river floodplains, glaciers, permafrost, icing, forest, karst, river basin size, catchment shape. Influence of the creation of reservoirs and ponds, irrigation, agroforestry activities and drainage on the intra-annual distribution of river flow. Calculation of the intra-annual distribution of runoff in the presence, insufficiency and absence of observational data. Calculation of the daily distribution of runoff. Curves of duration of daily expenses. Coefficient of natural runoff regulation. Coefficient of intra-annual runoff unevenness.

FEATURES OF FORMATION AND CALCULATION OF THE MAXIMUM

RIVER FLOW DURING THE SPRING FLOOD PERIOD.

The concept of "catastrophic flood (flood)". Practical and scientific significance of a reliable assessment of the statistical parameters of floods. Causes of catastrophic floods. Genetic groups of maximum water flow rates. Estimated availability of maximum water flow rates depending on the capitalization class of a hydraulic structure. Quality of initial information on maximum water discharges. Conditions for the formation of flood runoff: snow reserves in the river basin and water reserves in the snow cover, evaporation losses from snow, intensity and duration of snowmelt, loss of melt water. Underlying surface factors: relief, slope exposure, dimensions, configuration, dissection of the basin, lakes and swamps, soils and soils. Anthropogenic factors in the formation of the maximum flow of floods. Genetic theory of formation of maximum runoff. Reduction of the maximum flow. Calculations of the maximum spring runoff in the presence, insufficiency and absence of observational data. Mathematical and physico-mathematical models of the processes of formation of melt water runoff.

MAXIMUM RIVER FLOW DURING RAIN FLOOD PERIOD.

Areas of distribution of high rain maxima. Difficulties in researching and generalizing the characteristics of rain runoff. Types of rain and their components. Features of the formation of rain floods: the intensity and duration of rain, the intensity of infiltration, the speed and time of rainwater runoff. The role of underlying surface factors and types of economic activity in the formation of rain runoff. Calculations of the maximum water discharges of rain floods in the presence, insufficiency and absence of observational data. Simulation of the runoff of rain floods.

FORMATION CONDITIONS AND CALCULATIONS OF THE MINIMUM SUMMER
AND WINTER DRAIN OF RIVERS.

The concept of low-water period and low-water runoff. The practical significance of knowledge about the minimum flow of rivers. The main design characteristics of the minimum and low flow of rivers. The duration of the winter and summer or summer-autumn low-water periods on the rivers of Russia. Types of low water and low water periods of Russian rivers. Factors of formation of the minimum runoff: precipitation, temperature, evaporation, connection of waters of the aeration zone, ground water, karst and artesian waters with the river, geological and hydrogeological conditions in the basin, lakes, swamps, forest, dissection and height of the terrain, river floodplain, depth of the erosional incision of the river bed, areas of surface and underground watersheds, slope and orientation of the watershed, irrigation of agricultural lands, industrial and domestic consumption of river water, drainage, use groundwater, creation of reservoirs, urbanization. Calculations of the minimum low-water runoff for different volumes of initial hydrological information.

4. PRACTICAL WORKS.

PRACTICAL WORK No. 1.

CALCULATIONS OF ANNUAL RUNOFF OF RIVERS
WITH INSUFFICIENCY AND ABSENCE OF OBSERVATION DATA.

TASK 1: Select a river basin with a catchment area of ​​at least 2000 km² and not more than 50000km ² within the Tyumen region and extract from the publications of the WRC for this basin a number of observations of average annual discharges.

TASK 2: Determine the statistical parameters of the curve for the average annual flow of the selected river using the methods of moments, maximum likelihood, graph-analytical.

TASK 3: Determine the annual flow of the river with a security of 1%, 50% and 95%.

TASK 4: Calculate the average annual runoff of the same river using the isoline map of the module and runoff layer and evaluate the accuracy of the calculation.

THEORY: In the presence or insufficiency of observational data, the main statistical parameters of river runoff are determined by three methods: the method of moments, the maximum likelihood method, and the graphical analytical method.

METHOD OF MOMENTS.

To determine the parameters of the distribution curveQo, Cv and Cs by the method of moments, the following formulas are used:

1) average long-term value of water consumption

Qо = ΣQi /n, where

Qi – annual values ​​of water consumption, m³/s;

n is the number of years of observations; for observation series of less than 30 years, instead of n, take (n - 1).

2) coefficient of variation

Cv \u003d ((Σ (Ki -1)²) / n)½, where

Ki - modular coefficient calculated by the formula

Ki \u003d Qi / Qo.

3) coefficient of asymmetry

Cs \u003d Σ (Ki - 1)³ / (n Cv³).

Based on the Cv and Cs values, the Cs/Cv ratio and the calculation errors of Qo, Cv and Cs are calculated:

1) Qo error

σ = (Cv /n½) 100%;

2) Cv error should be no more than 10-15%

Έ = ((1+Cv²) / 2n)½ 100%,

3) Cs error

έ = ((6/n)½ (1+6Cv²+5Cv ( ½ / Cs) 100%.

Maximum likelihood method .

The essence of the method is that the most probable value of the unknown parameter is considered to be at which the likelihood function reaches its maximum possible value. In this case, the members of the series, which correspond to a larger value of the function, have a greater influence. This method is based on the use of statistics λ 1 , λ 2 , λ 3. Statistics λ 2 and λ 3 are connected with each other and their ratio changes from the change in Cv and the ratio of Cs / Cv. Statistics are calculated using the formulas:

1) statistics λ 1 is the arithmetic mean of a series of observations

λ 1 = ΣQi / n;

2) statistics λ 2

λ 2 \u003d Σ IgKi / (n - 1);

3) statistics λ 3

λ 3 = Σ Ki· IgКi /(n – 1).

The determination of the coefficient of variability Cv and the ratio Cs / Cv is carried out according to nomograms (see in the textbook. Practical hydrology. L .: Gidrometeoizdat, 1976, p. 137) in accordance with the calculated statistics λ 2 and λ 3 . On the nomograms, we find the point of intersection of the values ​​of the statistics λ 2 and λ 3 . The Cv value is determined from the vertical curve closest to it, and the Cs / Cv ratio is determined from the horizontal curve, from which we proceed to the Cs value. The error Cv is determined by the formula:

Έ = (3 / (2n(3+ Cv²)))½ 100%.

GRAPH-ANALYTICAL METHOD .

With this method, the statistical parameters of the analytical endowment curve are calculated by three characteristic ordinates of the smoothed empirical endowment curve. These ordinates are Q

On the semi-logarithmic fiber of probabilities, the dependence Q = f (P) is built. To construct a smoothed empirical supply curve, it is necessary to build a series of observations in descending sequence and for each ranked value of water consumption Q ub . assign the value of security P, calculated by the formula:

P \u003d (m / n + 1) 100%, where

m is the serial number of a member of the series;

n is the number of members of the series.

Provision values ​​are plotted along the horizontal axis, the corresponding Q kill The intersection points are indicated by circles with a diameter of 1.5-2 mm and fixed with ink. A smoothed empirical security curve is drawn over the points with a pencil. Three characteristic ordinates Q are taken from this curve 5% ,Q 50% and Q 95% availability, due to which the value of the coefficient of skewness S of the supply curve is calculated according to the following formula:

S = (Q 5% + Q 95% - 2 Q 50% ) / (Q 5% - Q 95% ).

The skew factor is a function of the skewness factor. Therefore, according to the calculated value of S, the value of Cs is determined (see Appendix 3 in the textbook. Practical Hydrology. L .: Gidrometeoizdat, 1976, p. 431). According to the same application, depending on the obtained value of Cs, the difference of normalized deviations (Ф 5% - F 95% ) and normalized deviation Ф 50% . Next, calculate the standard deviation σ, the average long-term runoff Qо´, and the coefficient of variation Cv using the following formulas:

σ \u003d (Q 5% - Q 95% ) / (F 5% - F 95% ),

Qo ´ \u003d Q 50% - σ F 50%,

Сv = σ / Q´.

The analytical endowment curve is considered to be sufficiently consistent with the empirical distribution if the following inequality is satisfied:

IQo - Qo´I< 0,02·Qо.

The root mean square error Qо´ is calculated by the formula:

σ Qo´ = (Сv / n½) 100%.

Coefficient of variation error

Έ = ((1+ Сv²) / 2n)½ 100%.

CALCULATION OF THE EXPENSES OF A GIVEN SECURITY .

The consumption of a given security is calculated by the formula:

Qр = Кр·Qо, where

Кр - modular coefficient of the given security p%, calculated by the formula

Kp \u003d Fr Cv + 1, where

Fr - normalized deviations of a given security from the average value of the ordinates of the binomial distribution curve, determined according to Appendix 3 of the training manual. Practical hydrology. L .: Gidrometeoizdat, 1976, p. 431.

Recommended for further hydrological calculations and design work statistical parameters for the river basin and its secured costs are obtained by calculating the arithmetic mean of those obtained by the above three methods Qo, Cv, Cs, Q 5% ,Q 50% and Q 95% security.

DETERMINATION OF THE VALUES OF AVERAGE ANNUAL RIVER FLOW

CARDS.

In the absence of observational data on the runoff, one of the ways to determine it is the maps of the isolines of the modules and the runoff layer (see Fig. tutorial. Practical hydrology. L.: Gidrometeoizdat, 1976, pp. 169-170). The value of the modulus or runoff layer is determined for the center of the catchment area of ​​the river. If the center of the watershed lies on the isoline, then the average value of the runoff of this watershed is taken from the value of this isoline. If the watershed lies between two isolines, then the runoff value for its center is determined by linear interpolation. If the watershed is crossed by several isolines, then the value of the runoff module (or runoff layer) for the center of the watershed is determined by the weighted average method according to the formula:

Мср = (М 1 f 1 + М 2 f 2 +…М n f n ) / (f 1 + f 2 +…f n ), where

M 1, M 2 ... - average runoff values ​​between adjacent isolines crossing the watershed;

f1, f2… - catchment areas between contour lines within the catchment area (in km² or in scale divisions).

Intra-annual runoff distribution

Systematic ( daily) observations of water levels were started in our country around 100 years back. Initially, they were conducted in a small number of points. At present, we have data on the flow of rivers for 4000 hydrological posts. These materials are of a unique nature, making it possible to trace changes in runoff over a long period, and are widely used in calculating water resources, as well as in the design and construction of hydraulic and other industrial facilities on rivers, lakes and reservoirs. To solve practical issues, it is necessary to have observational data on hydrological phenomena for periods of time from 10 before 50 years and more.

Hydrological stations and posts located on the territory of our country form the so-called state hydrometeorological network. It is administered by Roskomgidromet and is designed to meet the needs of all industries. National economy according to the data on the regime of water bodies. For the purpose of systematization, observation materials at posts are published in official reference publications.

For the first time, hydrological observation data were summarized in the State Water Cadastre USSR (GVK). It included guides to water resources USSR (regional, 18 volumes), information about water levels on rivers and lakes USSR(1881-1935, 26 volumes), materials on the regime of rivers ( 1875-1935, 7 volumes). FROM 1936 materials of hydrological observations began to be published in hydrological yearbooks. Currently, there is a unified nationwide accounting system for all types of natural waters and their use on the territory of the Russian Federation.

The primary processing of data on daily water levels given in the Hydrological Yearbooks consists in performing an analysis of the intra-annual distribution of runoff and constructing a graph of water level fluctuations for the year.

The nature of the change in runoff during the year and the regime of water levels due to these changes mainly depend on the conditions for feeding the river with water. According to B.D. Zaikova rivers are divided into three groups:

With spring floods, formed as a result of snow melting on the plains and low mountains;

With high water in the warmest part of the year, arising from the melting of seasonal and perpetual mountain snows and glaciers;

With rainfall.

The most common are rivers with spring floods. This group is characterized by the following phases water regime: spring flood, summer low water, period of autumn water rise, winter low water.

During the period spring flood in the rivers of the first group, due to the melting of snow, the flow of water increases significantly, and its level rises. The amplitude of fluctuations in water levels and the duration of floods on the rivers of this group differ depending on the factors of the underlying surface and factors of a zonal nature. For example, the Eastern European type of intra-annual runoff distribution has a very high and sharp spring flood and low water discharges in the rest of the year. This is explained by the insignificant amount of summer precipitation and strong evaporation from the surface of the steppe basins of the Southern Trans-Volga region.

Western European type distribution is characterized by a low and extended spring flood, which is a consequence of a flat relief and severe waterlogging West Siberian lowlands. The presence of lakes, swamps and vegetation within the boundaries of the drainage basin leads to the equalization of the flow throughout the year. This group also includes the East Siberian type of runoff distribution. It is characterized by relatively high spring floods, rain floods in the summer-autumn period, and extremely low winter low water. This is due to the influence permafrost on the nature of the feeding of the river.

The amplitude of fluctuations in water levels at medium and big rivers Russia is quite significant. She reaches 18 m on the upper Oka and 20 m on the Yenisei. With such filling of the channel, vast areas of river valleys are flooded.

The period of low levels that change little over time during the summer is called the period summer low water when groundwater is the main source of river nutrition.

In autumn surface runoff increases due to autumn rains, which leads to water rise and education summer-autumn rain flood. The increase in runoff in autumn is also facilitated by a decrease in evaporation during this period of time.

Phase winter low water in the river begins with the appearance of ice and ends with the beginning of the rise in water levels from spring snowmelt. During the winter low water in the rivers, a very small flow is observed, since from the moment of the onset of stable negative temperatures, the river is fed only by groundwater.

The rivers of the second group are distinguished Far Eastern and Tien Shan types of intra-annual runoff distribution. The first of them has a low, strongly stretched, comb-like flood in the summer-autumn period and a low runoff in the cold part of the year. The Tien Shan type is distinguished by a smaller amplitude of the flood wave and a secure runoff in the cold part of the year.

Near the rivers of the third group ( Black Sea type) rain floods are evenly distributed throughout the year. The amplitude of fluctuations in water levels is strongly smoothed near rivers flowing from lakes. In these rivers, the boundary between high water and low water is hardly noticeable, and the volume of runoff during high water is comparable to the volume of runoff during low water. For all other rivers, the main part of the annual flow passes during the flood.

The results of observations over the levels for the calendar year are presented as level fluctuation chart(Fig. 3.5). In addition to the course of levels, the graphs show the phases of the ice regime with special symbols: autumn ice drift, freeze-up, spring ice drift, as well as the values ​​of the maximum and minimum navigational water levels.

Usually, the graphs of fluctuations in water levels at a hydrological post are combined for 3-5 years on one drawing. This makes it possible to analyze the river regime for low-water and high-water years and to trace the dynamics of the onset of the corresponding phases of the hydrological cycle for a given period of time.

Characteristics of the annual runoff

Runoff is the movement of water over the surface, as well as in the thickness of the soil and rocks during its cycle in nature. In calculations, runoff is understood as the amount of water flowing from the catchment for any period of time. This amount of water can be expressed as a flow rate Q, a volume W, a modulus M, or a runoff layer h.

Runoff volume W - the amount of water flowing from the catchment for any period of time (day, month, year, etc.) - is determined by the formula

W \u003d QT [m 3], (19)

where Q is the average water consumption for the calculated period of time, m 3 / s, T is the number of seconds in billing period time.

Since the average water discharge was calculated earlier as the annual flow rate, the flow volume of the r. Kegets per year W \u003d 2.39 365.25 24 3600 \u003d 31764096 m 3.

Runoff module M - the amount of water flowing from a unit catchment area per unit time - is determined by the formula

М=103Q/F [l/(sqm2)], (20)

where F is the catchment area, km 2.

Drain module Kegets М=10 3 2.39/178 = 13.42 l/(sqm 2).

Runoff layer h mm - the amount of water flowing from the catchment for any period of time, equal to the thickness of the layer, evenly distributed over the area of ​​this catchment, is determined by the formula

h=W/(F 10 3)=QT/(F 10 3). (21)

The runoff layer for the river basin. Kegets h = 31764096/ (178 10 3) = 178.44 mm.

The dimensionless characteristics include the modulus factor and the runoff factor.

The modular coefficient K is the ratio of the runoff for any particular year to the runoff rate:

K \u003d Q i /Q 0 \u003d W i / W 0 \u003d h i / h 0, (22)

and for r. Kegets for the period under consideration K changes from K = 1.58 / 2.39 = 0.66 for the year from minimum consumption up to K = 3.26 / 2.39 = 1.36 for maximum flow.

Runoff coefficient - the ratio of the volume or layer of runoff to the amount of precipitation x that fell on the catchment area, which caused the occurrence of runoff:

The runoff coefficient shows how much of the precipitation goes to the formation of runoff.

AT term paper it is necessary to determine the characteristics of the annual runoff for the considered basin, taking the runoff rate from the section

Intra-annual runoff distribution

The intra-annual distribution of river runoff takes important place in the issue of studying and calculating runoff, both in practical and scientific terms, being at the same time the most challenging task hydrological research /2,4,13/.

The main factors that determine the intra-annual distribution of runoff and its total value are climatic. They determine the general nature (background) of the distribution of runoff in the year of a particular geographical area; territorial changes in runoff distribution follow climate change.

The factors influencing the distribution of runoff during the year include lakes, forest cover, swampiness, watershed sizes, the nature of soils and soils, the depth of groundwater, etc., which to a certain extent should be taken into account in the calculations both in the absence and in the presence of observational materials.

Depending on the availability of hydrometric observation data, the following methods for calculating the intra-annual runoff distribution are used:

in the presence of observations for a period of at least 10 years: a) distribution by analogy with the distribution of a real year; b) the method of arranging the seasons;

in the absence or insufficiency (less than 10 years) of observational data: a) by analogy with the distribution of the runoff of the studied analogue river; b) according to regional schemes and regional dependences of the parameters of the intra-annual distribution of runoff on physical and geographical factors.

The intra-annual flow distribution is usually calculated not by calendar years, but by water management years, starting from the high-water season. The boundaries of the seasons are assigned the same for all years, rounded to the nearest month.

The estimated probability of flow exceeding for a year, limiting the period and season, is assigned in accordance with the tasks of the water management use of the river flow.

In the course work, it is necessary to perform calculations in the presence of hydrometric observations.

Calculations of the intra-annual distribution of runoff by the layout method

The initial data for the calculation are the average monthly water consumption and, depending on the purpose of using the calculation, the given percentage of supply P and division into periods and seasons.

The calculation is divided into two parts:

inter-seasonal distribution, which is of the greatest importance;

intra-seasonal distribution (by months and decades, established with some schematization.)

Interseasonal distribution. Depending on the type of intra-annual distribution of runoff, the year is divided into two periods: high water and low water (low water). Depending on the purpose of use, one of them is assigned limiting.

The limiting period (season) is the most stressful in terms of water use. For drainage purposes, the limiting period is high water; for irrigation, energy-shallow water.

The period includes one or two seasons. On rivers with spring floods for irrigation purposes, the following are distinguished: a high-water period (aka season) - spring and a low-water (limiting) period, which includes seasons; summer-autumn and winter, and the limiting season for irrigation is summer-autumn (winter for energy use).

The calculation is carried out according to hydrological years, i.e. for years beginning with a high-water season. The dates of the seasons are assigned the same for all years of observations, rounded up to the nearest whole month. The duration of the high-water season is assigned so that the high water is placed within the boundaries of the season as in the years with the most early term offensive, and with the most late deadline endings.

In the task, the duration of the seasons can be taken as follows: spring - April, May, June; summer-autumn - July, August, September, October, November; winter - December and January, February, March next year.

The amount of runoff for individual seasons and periods is determined by the sum of average monthly discharges (Table 10). AT last year the costs for December are added to the costs for three months (I, II, III) of the first year.

When calculating according to the layout method, the intra-annual distribution of runoff is taken from the condition of equality of the probability of exceeding the runoff for the year, the runoff for the limiting period, and within it for the limiting season. Therefore, it is necessary to determine the costs of the security specified by the project (in the task P = 80%) for the year, the limiting period and season. Therefore, it is required to calculate the parameters of the supply curves (О 0 , С v and С s) for the limiting period and season (for the annual runoff, the parameters are calculated above). Calculations are made by the method of moments in Table. 10 according to the scheme outlined above for the annual flow.

You can determine the estimated costs using the formulas:

annual flow

Orasgod \u003d Kr "12Q 0, (26)

limiting period

Оrasinter \u003d KpQ0inter, (27)

limiting season

Oraslo \u003d Kr "Qlo (27)

where Kp", Kp, Kp" are the ordinates of the curves of the three-parameter gamma distribution, taken from the table, respectively, for C v - annual runoff. C v low flow and C v for summer-autumn.

Note. Since the calculations are based on average monthly expenses, the estimated expense for the year must be multiplied by 12.

One of the main conditions of the layout method is the equality

Orasgod = Orases. However, this equality will be violated if the calculated runoff for non-limiting seasons is also determined from the supply curves (due to the difference in the parameters of the curves). Therefore, the estimated runoff for a non-limiting period (in the task - for the spring) is determined by the difference

Orasves = Orasgod - Orasmezh, (28)

and for a non-limiting season (in the task-winter)

Oraszim = Orasmezh. - Qlo (29)

The calculation is more convenient to perform in the form of a table. ten.

Intra-seasonal distribution - is taken averaged over each of the three water content groups (high-water group, including years with runoff per season Р<33%, средняя по водности 33<Р<66%, маловодная Р>66%).

To identify the years included in separate water content groups, it is necessary to arrange the total costs for the seasons in descending order and calculate their actual supply. Since the calculated availability (Р=80%) corresponds to the low-water group, further calculation can be made for the years included in the low-water group (Table 11).

For this c. in the column "Total flow" write down the expenses by seasons, corresponding to the provision P> 66%, and in the column "Years" - write down the years corresponding to these expenses.

Arrange the average monthly expenses within the season in descending order, indicating the calendar months to which they relate (Table 11). Thus, the first will be the discharge for the most wet month, the last - for the low-water month.

For all years, summarize the costs separately for the season and for each month. Taking the amount of expenses for the season as 100%, determine the percentage of each month A% included in the season, and in the column "Month" write the name of the month that repeats most often. If there are no repetitions, write out any of those encountered, but so that each month included in the season has its own percentage of the season.

Then, multiplying the estimated discharge for the season, determined in terms of the inter-seasonal distribution of runoff (Table 10), by the percentage of each month A% (Table 11), calculate the estimated discharge for each month.

Horac v = Horaces A % v / 100% (30)

The data obtained are entered in table. 12 “Estimated costs by months” and on graph paper, an estimated hydrograph R-80% of the river under study is built (Fig. 11).

Table 12. Estimated costs (m3/s) by months