Let us consider the prospects of using the
differential equations of liquid and gas motion in
modeling the mountain river WR. Their construction is based on well-known physical laws,
including the continuity of the simulated continuum, conservation of its mass and momentum,
physical force influence; however, after the 50year efforts, the mathematical models of 3D fluid
flow (e.g. past 3D objects of relatively simple
shape) have still many unresolved problems and
require time-consuming experiments. The question is how many years it will take to develop
adequate differential equations for mountain river
WR. They should describe concurrently streamflow in channels of a very complex profile, flow
around various bars (rapids, waterfalls, changing
thickness of channel gravel), surface, subsurface
and groundwater runoff, changing water phase
states (solid, liquid, gaseous) under daily and
seasonal temperature changes. Obviously, even
after the creation of such a hypothetical system of
hydrological/hydrodynamical equations, it would
require a huge amount of experimental data to
determine the parameters and specify initial and
boundary conditions. The second question arises
whether it is essential to describe the mountain
river WR by using differential equations calling
for a detailed specification of the processes.
All the previously mentioned is true for river
HCR. A system approach with appropriate
methods for modeling complex natural systems
can be a feasible solution to the problem. One of
such methods is the application of single-valued
functions with multiple arguments analytically
defined on specified time intervals. The system
approach and the functions were used as a basis
for proposed system-analytical modeling of
WR/HCR.
We have chosen the whole Altai-Sayan
mountain country (50–56° N and 83–100° E)
for our investigation. Its territory is interesting
for WR/HCR analysis since its climate undergoes some destabilization responsible for
increasing the number of catastrophic hydrometeorological events. Such a destabilization was
corroborated by spatial clustering of continental
meteorological fields (Kirsta et al. 2014). The
analysis of the interannual dynamics of surface
air temperature and precipitation allowed us to
define the areas with the largest deviations from
the evolutionary developed statistical regularities
of these factors. Two types of spatial clusters
with a relatively stable and destabilized climate
were detected in Eurasia (Figs. 7.1 and 7.2). The
first one is formed at the stabilizing influence of
natural vegetation, whereas the second—because
of resonant human impact.
The territory of the Altai-Sayan mountain
country represents a part of the world watershed
between the humid zone of the Arctic Ocean and
the arid drainless area of Central Asia (AltaiSayan 1969). In the Altai, the mountain ridges
reach 3500–4500 m above sea level, while in the
Sayan—3000–3500 m. The climate is extremely
continental with cold winters and cool summers
(Sevast'yanov 1998). Atlantic cyclones freely
penetrate the region. The distribution of precipitation in the Altai-Sayan mountains has not been
adequately explored. According to observations
of rare weather stations, its annual amount varies
very widely. For instance, the northern slopes at
altitudes over 3000 m get 1200–2500 mm of
precipitation per year, the middle parts of the
slopes—up to 600 mm, and the bottom ones—
about 200 mm. In all rivers, the largest WR is
observed during a warm season and accounts for
up to 80–90% of the annual one. The flow
regime depends mainly on snowmelt in springtime and the amount of precipitation during
summer and autumn periods. The share of snow
water in the annual flow is not less than 50%.
Glacier melting in river basins also contributes to
the river flow (Revyakin et al. 1979).
7.2 System-Analytical Modeling
The method of system-analytical modeling
(SAM) (Kirsta 2006a; Kirsta and Kirsta 2014)
allows to avoid the abovementioned problems
and to create the simulation models having an
adequate description of real physical, hydrological and chemical processes. Following Beven
(2002), adequacy is conformity of the model to
physical principles and laws completed by
appropriate assumptions. Unlike Refsgaard
7 System-Analytical Modeling of Water Quality …
81
differential equations of liquid and gas motion in
modeling the mountain river WR. Their construction is based on well-known physical laws,
including the continuity of the simulated continuum, conservation of its mass and momentum,
physical force influence; however, after the 50year efforts, the mathematical models of 3D fluid
flow (e.g. past 3D objects of relatively simple
shape) have still many unresolved problems and
require time-consuming experiments. The question is how many years it will take to develop
adequate differential equations for mountain river
WR. They should describe concurrently streamflow in channels of a very complex profile, flow
around various bars (rapids, waterfalls, changing
thickness of channel gravel), surface, subsurface
and groundwater runoff, changing water phase
states (solid, liquid, gaseous) under daily and
seasonal temperature changes. Obviously, even
after the creation of such a hypothetical system of
hydrological/hydrodynamical equations, it would
require a huge amount of experimental data to
determine the parameters and specify initial and
boundary conditions. The second question arises
whether it is essential to describe the mountain
river WR by using differential equations calling
for a detailed specification of the processes.
All the previously mentioned is true for river
HCR. A system approach with appropriate
methods for modeling complex natural systems
can be a feasible solution to the problem. One of
such methods is the application of single-valued
functions with multiple arguments analytically
defined on specified time intervals. The system
approach and the functions were used as a basis
for proposed system-analytical modeling of
WR/HCR.
We have chosen the whole Altai-Sayan
mountain country (50–56° N and 83–100° E)
for our investigation. Its territory is interesting
for WR/HCR analysis since its climate undergoes some destabilization responsible for
increasing the number of catastrophic hydrometeorological events. Such a destabilization was
corroborated by spatial clustering of continental
meteorological fields (Kirsta et al. 2014). The
analysis of the interannual dynamics of surface
air temperature and precipitation allowed us to
define the areas with the largest deviations from
the evolutionary developed statistical regularities
of these factors. Two types of spatial clusters
with a relatively stable and destabilized climate
were detected in Eurasia (Figs. 7.1 and 7.2). The
first one is formed at the stabilizing influence of
natural vegetation, whereas the second—because
of resonant human impact.
The territory of the Altai-Sayan mountain
country represents a part of the world watershed
between the humid zone of the Arctic Ocean and
the arid drainless area of Central Asia (AltaiSayan 1969). In the Altai, the mountain ridges
reach 3500–4500 m above sea level, while in the
Sayan—3000–3500 m. The climate is extremely
continental with cold winters and cool summers
(Sevast'yanov 1998). Atlantic cyclones freely
penetrate the region. The distribution of precipitation in the Altai-Sayan mountains has not been
adequately explored. According to observations
of rare weather stations, its annual amount varies
very widely. For instance, the northern slopes at
altitudes over 3000 m get 1200–2500 mm of
precipitation per year, the middle parts of the
slopes—up to 600 mm, and the bottom ones—
about 200 mm. In all rivers, the largest WR is
observed during a warm season and accounts for
up to 80–90% of the annual one. The flow
regime depends mainly on snowmelt in springtime and the amount of precipitation during
summer and autumn periods. The share of snow
water in the annual flow is not less than 50%.
Glacier melting in river basins also contributes to
the river flow (Revyakin et al. 1979).
7.2 System-Analytical Modeling
The method of system-analytical modeling
(SAM) (Kirsta 2006a; Kirsta and Kirsta 2014)
allows to avoid the abovementioned problems
and to create the simulation models having an
adequate description of real physical, hydrological and chemical processes. Following Beven
(2002), adequacy is conformity of the model to
physical principles and laws completed by
appropriate assumptions. Unlike Refsgaard
7 System-Analytical Modeling of Water Quality …
81