that the elaborated model has a small inherent
error and adequately reflects the basic hydrological processes in river basins of the AltaiSayan mountain country.
7.6 Development of Hydrochemical
Runoff Model
In the same fashion as the balance WR model,
we developed the HCR model to calculate the
seasonal and long-term dynamics of seven HCR
components (NO
À
2 ; NO
À
3 ; NH
þ
4 , PO
3À
4 , ions,
total dissolved Fe, and suspended matter). The
input factors and variables of the model are as
follows: spatially generalized for the Altai-Sayan
mountain country normalized monthly precipitation and mean monthly air temperature; WR
estimated for individual landscapes in river
basins with the WR model; the cartographic
information on the area and average altitude of
the basins, the altitude of the outlet, the length of
river channels (between the river head and the
outlet), and the area of arable lands. The same 13
typological
geosystem
groups/landscapes
(Table 7.1) were applied to account for a landscape structure of river basins.
The target HCR is described by imitation
balance equations with due regard for calculated
WR, precipitation, lateral slope of the basin, and
arable land area:
for the first season (winter low water),
HR
i
¼
X
k
fa k Q
i
k Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ
 Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i
Þg þ bq
i
þ dS
i Q
i
ð7:4aÞ
and for each of the rest seasons,
HR
i ¼
X
k
fa k Q
i
k Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ
 Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i Þg þ bq
i þ d
ffiffiffiffi
S
i
p
Q
i ;
ð7:4bÞ
where HR
i is the seasonal average hydrochemical
runoff (HCR) from basin i; P is normalized
monthly precipitation averaged for preceding IXXI months (1st season) or for IV–VI, VII–VIII,
IX–XI months (second, third, fourth seasons); Q
i
k
is the calculated water runoff (WR) from k-th
landscape in basin i, k = 1–13, i = 1–34; a k are
parameters corresponding to a permanent seasonal analyte concentration in the calculated WR
for landscape k = 1–13; K
i is the average lateral
slope of basin i; b is the parameter characterizing
the permanent seasonal analyte concentration in
the calculated inflow (or outflow) of mean seasonal groundwater runoff q
i in basin i; S
i is the
relative area of arable land in basin i; d is the
parameter characterizing the dependence of the
analyte concentration on S
i in the calculated
runoff Q
i in basin i.
In the right part of Eqs. (7.4a and b), a cumulative contribution provided by surface, subsurface, and groundwater runoff of each geosystem
group to seasonal HCR is presented. Function
Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ characterizes the influence of precipitation P of the current hydrological
season, and Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i
Þ—lateral
slope K
i of river basin i. The influence of arable
land is expressed as area S
i . Power n = 1 of S
i for
the first hydrological season (winter low-water)
means the analyte inflow from the whole area of
arable land to groundwater and water in fractured
rock zones feeding the streams in winter. Power
n = 1/2 of S
i for the remaining hydrological seasons reflects the analyte inflow mostly due to the
surface and subsurface interflow. The contribution
bq
i reflects matter inflow or outflow under positive
or negative q
i calculated by the WR model. Thus,
seasonal and interannual dynamics of HCR for
each landscape and the entire basin is calculated
with the use of Eqs. (7.4a and b).
In Eqs. (7.4a and b), the average lateral slope
K
i of basin i is defined as the tangent of inclination angle of slopes relative to the horizontal.
To calculate it, we use the equation:
K
i ¼
h
1=2L
¼
ðaverage altitude of basin iÞ À ðoutlet altitudeÞ
1=2ðbasin areaÞ=ðriver bed lengthÞ
;
ð7:5Þ
7 System-Analytical Modeling of Water Quality …
93
error and adequately reflects the basic hydrological processes in river basins of the AltaiSayan mountain country.
7.6 Development of Hydrochemical
Runoff Model
In the same fashion as the balance WR model,
we developed the HCR model to calculate the
seasonal and long-term dynamics of seven HCR
components (NO
À
2 ; NO
À
3 ; NH
þ
4 , PO
3À
4 , ions,
total dissolved Fe, and suspended matter). The
input factors and variables of the model are as
follows: spatially generalized for the Altai-Sayan
mountain country normalized monthly precipitation and mean monthly air temperature; WR
estimated for individual landscapes in river
basins with the WR model; the cartographic
information on the area and average altitude of
the basins, the altitude of the outlet, the length of
river channels (between the river head and the
outlet), and the area of arable lands. The same 13
typological
geosystem
groups/landscapes
(Table 7.1) were applied to account for a landscape structure of river basins.
The target HCR is described by imitation
balance equations with due regard for calculated
WR, precipitation, lateral slope of the basin, and
arable land area:
for the first season (winter low water),
HR
i
¼
X
k
fa k Q
i
k Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ
 Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i
Þg þ bq
i
þ dS
i Q
i
ð7:4aÞ
and for each of the rest seasons,
HR
i ¼
X
k
fa k Q
i
k Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ
 Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i Þg þ bq
i þ d
ffiffiffiffi
S
i
p
Q
i ;
ð7:4bÞ
where HR
i is the seasonal average hydrochemical
runoff (HCR) from basin i; P is normalized
monthly precipitation averaged for preceding IXXI months (1st season) or for IV–VI, VII–VIII,
IX–XI months (second, third, fourth seasons); Q
i
k
is the calculated water runoff (WR) from k-th
landscape in basin i, k = 1–13, i = 1–34; a k are
parameters corresponding to a permanent seasonal analyte concentration in the calculated WR
for landscape k = 1–13; K
i is the average lateral
slope of basin i; b is the parameter characterizing
the permanent seasonal analyte concentration in
the calculated inflow (or outflow) of mean seasonal groundwater runoff q
i in basin i; S
i is the
relative area of arable land in basin i; d is the
parameter characterizing the dependence of the
analyte concentration on S
i in the calculated
runoff Q
i in basin i.
In the right part of Eqs. (7.4a and b), a cumulative contribution provided by surface, subsurface, and groundwater runoff of each geosystem
group to seasonal HCR is presented. Function
Hðc 1 ; c 1 ; 1; 1; c 2 ; c 3 ; PÞ characterizes the influence of precipitation P of the current hydrological
season, and Hðc 4 ; c 4 ; 1; 1; c 5 ; c 6 ; K
i
Þ—lateral
slope K
i of river basin i. The influence of arable
land is expressed as area S
i . Power n = 1 of S
i for
the first hydrological season (winter low-water)
means the analyte inflow from the whole area of
arable land to groundwater and water in fractured
rock zones feeding the streams in winter. Power
n = 1/2 of S
i for the remaining hydrological seasons reflects the analyte inflow mostly due to the
surface and subsurface interflow. The contribution
bq
i reflects matter inflow or outflow under positive
or negative q
i calculated by the WR model. Thus,
seasonal and interannual dynamics of HCR for
each landscape and the entire basin is calculated
with the use of Eqs. (7.4a and b).
In Eqs. (7.4a and b), the average lateral slope
K
i of basin i is defined as the tangent of inclination angle of slopes relative to the horizontal.
To calculate it, we use the equation:
K
i ¼
h
1=2L
¼
ðaverage altitude of basin iÞ À ðoutlet altitudeÞ
1=2ðbasin areaÞ=ðriver bed lengthÞ
;
ð7:5Þ
7 System-Analytical Modeling of Water Quality …
93