Hydrological calculations in Siberia (the Russian Federation): the basic

and features
Dr. Savichev Oleg. G.
Tomsk, Russia
Tomsk Polytechnic University
Institute of Natural

Federation
The circuit of the
Ob river basin

hydrology which connects together the methods of hydrodynamics, mathematical statistics,

But it is necessary to understand that all water systems

Runoff of the last glaciation (by [Volkov, Kazmin, 2007]); a

water

the lack of stream flow in the most part of

tributary of the Ob River)

water resources (in Siberia or in whole Eurasia), then how

But always there is a problem - the repeated invention

the Earth surface, as well as in the thickness of

1. Briefly about the methods used in Russia

occurring changes such as Hydrological Regime, reflected in long-term, seasonal

research is the expert analysis of data.

In Russia the definition

involves:
- determination of qualitative and quantitative correlation between landscape elements

conditions of flow formation.

In the selection of analogues we

methods in Hydrological Calculations assumes preliminary random, homogeneous test of

three cases:
1) the presence of observational data; 2) at

1.3.1. Basis of Calculation in the presence of observational data

The method consists in selection and use of probability distribution function. For each type of construction objects exceeding probabilities are stipulated. Using these values and function of distribution we can find parameters of a flow.

of the correspondence analysis of the theoretical and empirical curves.

are Kritsky-Menkel distribution in any ratio Cs/Cv; Pearson distribution of

:
where ki =Qi/Qcp; Cv* and Cs* – biased estimates of

, (1.3.1.2)

, (1.3.1.3)

, (1.3.1.4)

to determine according to the formulas (1.3.1.3; 1.3.1.4) without the

is representative and the relative standard error of calculated hydrological

, r<0.5. (1.3.1.9)

, r ≥ 0.5.
(1.3.1.10)

autocorrelation coefficient.

If the relative standard error is more than the

of observational data insufficiency the calculations are realized by the

Rкр (0.7);
R/R  Акр,
k/k  Bкр,

where N' – the

data
When observational data are not available, the distribution parameters and

presence of observational data
The annual runoff is calculated by applying

commonly used method of flow calculation are applied: 1) the

, (1.4.1.2.1)

where Qn, Qna – means of hydrological characteristics for the study and analogue objects for joint observational period; QN, QNa – normal annual of runoff for N-period; sn, sna – standard deviations.

coefficient of variation Cv,N is determined by the formula:
,

where N,a – standard error of river-analogue for the N-year period.

regression dependencies, and then the distribution parameters are calculated.


Calculated

empirical dependencies of climate parameters and other factors.

In the

1.4.1.3. Determination in the absence of observational data

characteristics of the maximum river flow in snow melt flood

annual runoff, are determined on the basis of regression analysis:

1.4.2.2. Determination in insufficiency of observational data

main groups:
Reducing formulas reflect a decrease in runoff modulus

1.4.2.3. Determination in the absence of observ. data

, (1.4.2.3.1)

where W – volume of flow for the characteristic time;  – lag time.

of the maximum flow of the spring flood Qр% (m3/sec)

Aоz), (1.4.2.3.1.2)
where С – empirical coefficient. Average weighted rate of

, (1.4.2.3.1.3)

where Si – mirror lake area, km2; Ai – catchment area of a lake, km2. Coefficient 1 is determined by the formula:

, (1.4.2.3.1.4)

where n' – coefficient of reduction;  – empirical coefficient; Aл – relative area of forest. Coefficient 2 is determined by the formula:
2=1–∙lg(0.1∙Aб + 1), (1.4.2.3.1.5)
where  – empirical coefficient; Aб – relative area of swamp in the river basin (%).

of forest (I) and swamps (II) for the conditions in

small rivers in the spring floods is allowed to determine

, (1.4.2.3.1.6)

where Qmax,P – maximum water discharge with exceeding probability Р; Р – transition coefficient from water flow with exceeding probability 1%. The value of ncp can be defined as an average weighted value of surface roughness catchment ecosystem coefficients.

April, 2010)

flow in rain floods is chosen taking into account the

maximum flow of rain flood with given exceeding probability

in the presence of one or more river analogues has

is determined by the formula:
, (1.4.2.3.2.2)
where V – the maximum of

in catchment area less 200 km2 has the form:
, (1.4.2.3.2.4)
where q’1%

, (1.4.2.3.2.5)

This value is determined depending on the hydro-morphological characteristic of the channel Фp (1.4.2.3.2.6) and the length of the slope lag time ск;  – collecting runoff coefficient; H1% – the maximum diurnal depth of precipitation with exceeding probability P=1% (mm); determined by the data of nearest meteorological stations.

for lowland rivers is carried out by the formula:
,

where С2 – empirical coefficient; 0 – collecting coefficient for a conditional catchment with the area 10 km2.

of the minimum water discharges is carried out as annual

, (1.4.3.1.1)

where P1 – the probability of an element in a series of non-zero values; n1 and n2 – sample volumes with non-zero and zero values. For the calculations the minimum daily mean, monthly mean or 30-daily discharges (non-calendar) observed in winter and (or) summer-autumn seasons are used. Monthly minimum means are used if they do not exceed the 30-daily more than 10%.

same as in the case of runoff rate. Specificity is

1.4.3.3. Determination in the absence of observational data

Minimum water discharge in large and medium rivers is determined by interpolation between points of observation taking into account lateral inflow data and meteorological research. Minimum flow of small rivers QР% (m3/s) is calculated from:

km2; А1 – additional catchment area; 1 – coefficient of

of observational data
Determination of calculated calendar annual distribution of flow

years, three year groups are distinguished:
- wet years

for water year. It is based on the calculation of

Tugoyakovka River (the tributary of the Tom River)

the observed runoff values for water year, seasons and months

1.4.4.3. Determination in the absence of observational data

In the absence of hydrometric observational data the annual runoff distribution is determined by the river analogues according to the district schemes and regional dependencies.

presence of observational data
Highest water levels are determined by analytical

surface is produced within small areas along the lengths (1-3

, (1.5.1.1)

where Qр% – water discharge; kQ - winter rate.

Determination of maximum levels of lake water is carried out by exceeding probability level distribution curves using the same method as for the rivers.

of maximal levels is performed by using analytical functions of

water levels is performed by the curve Q = f(H)

, (1.5.3.1)

where  – area of channel or floodplain cross-section for level Н, m2; п – roughness coefficient, s/m0.33; h - average depth of water in the channel or floodplain, m; I – slope of the water surface. Curves  = f(H) and h = f(H) are plotted by the results of measurements. The coefficient n and slope I are found from special tables or they are measured.

of ice dams and jams, preliminary special research is required.

by the formula:
, (1.5.3.2)
where  – coefficient of ice dam

the Tom River in 2004
Definition of some terms:
ice

the humid area the following dependence is used:
, (1.5.3.4)
where DH

direction of current from the south to the north. In

1.5.4. An example of calculations of water level in the ice dam

After the rock the velocities decrease; and the sediments form

Tom' River near Tomsk city
The south part of Tomsk city
Rocky

Wide channel

utility bridge in 12.03.2010; I – water; II – frazil

=0.411; Кwint=0.41
Normal level

in April, 2010 (beginning of flooding)

near Tomsk in April, 2010 (peak of flooding)
Ice dam

Classification of river bed evolution
In accordance with the hydro-morphological theory

meters: 1 – ribbon ridge type (lг - step of

occurs in small and average lowland rivers (and the individual

, (1.6.1.1)

where Cg – velocity of ridges offset (m/s); V - average velocity of (m/s); Fr - Froude number.

process occurs in the lowland and submountain rivers formed of

type of channel process in lowland rivers. It usually develops

type; the Vasugan River

further development and complication of incomplete meandering. It is characterized

of the characteristics of suspended sediment runoff in the presence

1.6.2.2. Determination in insufficiency or absence of observational data

In case of observational data insufficiency and significant correlation, the charges of suspended sediment can be restored by observation data of water runoff. Restoration of series is similar to the corresponding calculation of water flow.

be estimated by analyzing the equation of channel deformation, which

, (1.6.2.2.1)

where G1 – runoff by the flow of sediment;
G2 – bottom or rising up;
m0 – relative density of soils and sediments;
B - width of the river, m;
x - coordinate of the longitudinal displacement;
z - elevation bottom; t - coordinate time.

can be calculated by the method of A.V. Karaushev: G2=(u.+ku)∙Se–ku∙Sv, (1.6.2.2.2)
where u

, (1.6.2.2.3)

where Г - hydro-mechanical parameter of sediment, calculated for the i-fraction of sediment :
Гi=БiФi, (1.6.2.2.4)
Function Бi and Фi are defined by the Karaushev method depending on the hydraulic size of sediment u, the vertical fluctuations vz, the average flow velocity, and the values of Chezy coefficient СCh.

(1.6.2.2.6)
, (1.6.2.2.7)
where h – average depth of

, (1.6.2.2.8)

Se at the end of the element x is determined

where Sb – average turbidity of water in the beginning of part x, g/m3; Q - water flow, m3/sec.

,(1.6.2.2.10)

data
In the presence of observational data Bed Load Runoff (G1)

1.6.3.2. Determination in insufficiency or absence of observational data

In case of insufficiency or absence of observational data, Bed Load Runoff G1 can be calculated by different methods. Further the methods of I.I. Levi, G.I. Shamov, V.N. Goncharov are presented.

for rivers, sediments which are sand and gravel, should be

, (1.6.3.2.1)

where d – average diameter of sediment, m; v0(L) – velocity of not washing.

where d90 – diameter of particles with probability 90%.

, (1.6.3.2.2)

in cases of the sandy and sandy-gravelly sediment is recommended

, (1.6.3.2.3)

where k - coefficient taking into account the heterogeneity of the load; parameter v0 is determined by the formula:

. (1.6.3.2.4)

with the diameter from 0.2 to 10 mm is advisable

, (1.6.3.2.5)

where  – parameter of turbulence determined by the special tables of V.N. Goncharov; parameter v0(G) is determined by the formula:

, (1.6.3.2.6)

where d5 – diameter of particles with probability 5 %; w and G – density of water and sediment.

melt flood

of observational data
Vertical Riverbed Deformations are determined on the basis

, (1.6.4.1.1)

where g – depth measurement error in the riverbed shooting; n – error of depth determination on the plan; сo – error of cross-channel profile combination (g =0.3 м; n=0.5∙0, where 0 – step between isobaths, m; сo(м)= 0.5∙MB/1000, where MB – scale of the profile. If z>0.5 znp, then z=znp+2∙z).

absence of measurements an important characteristic of vertical deformations is

basis of maps and topographical comparison in view of an

, (1.6.5.1)

where M – scale coefficient of combined plans; с – error of channel planned measurement; np – errors of reduction of maps to the one scale; сo – error of map overlapping; ob – measurement error of the coast line displacement on the combined plans. Average errors of the planned survey is usually taken as 0.5 mm in the plan scale.

(in millimeters of the reduced scale) should be equal:
,

where nM – the ratio of the biggest scale coefficient to the smallest; 0.5 mm – the average error of the characteristic length. Combined survey should lead to a larger scale. The error of map overlapping сo is taken equal to 1 mm in the plan scale in presence of common and time constant benchmarks in the maps.

of vertical deformations of channel of the Tom' River near

from the river mouth (from 74.8 km to 58.3 km)

part 74.8-58.3 km from the mouth; Q=6860 m3/s (average maximum)

on part 74.8-58.3 km from the mouth; Q=472 m3/s (low

River on the part 74.8-58.3 km from the mouth; Q=6860

River on the part 74.8-58.3 km from the mouth; Q=1090

in Siberia
Features of mathematical modeling and hydrological computations in Siberia

body boundaries on the territory are possible up to several

the Chaya River

information in Russia.

11. The rivers of Siberia are often characterized