contributions of the preceding and current seasons, correspondingly; but when calculating the
streamflow for the first season (winter low
water), these summands relate to the third and
fourth seasons of the previous year because snow
remains on the surface and does not affect the
streamflow in winter; parameters a k , b k characterize the contribution of k-th geosystem group in
relevant seasons, k = 1–13; S
i
k represents the
relative area of k-th geosystem group in basin i;
h
i
k is mean altitude of the same group in basin i,
m a.s.l.; P 1 , P 2 are normalized monthly precipitation averaged for a corresponding season; T 1 ,
T 2 are deviations of normalized air temperature
from 1 (1 is a long-term mean value of normalized characteristics) averaged for a corresponding
season; H is a piecewise linear function (see
Eq. 7.1); parameters c 1 ,…,c 9 reflect the influence
of temperature T 1 , T 2 and altitude h
i
k upon the
basin WR; parameter c 10 characterizes constant
replenishment (c 10 > 0) or depletion (c 10 < 0) of
WR into both free groundwater and water of rock
fracture zones. Thus, Eq. (7.3) includes 13
parameters a k , 13 parameters b k , and 10 parameters c i , i.e. 36 parameters for each hydrological
season are used to calculate WR.
On the right-hand side of Eq. (7.3), the individual contributions of geosystem groups into the
seasonal average streamflow Q
i of the basin i are
summed up. In the first summand, the contribution of k-th geosystem group refers to a delayed
WR formed by precipitation P 1 of the preceding
season. This process is specific to each group and
depends on (a) the peculiarities of water movement in soils and various losses of water before it
reaches a riverbed (parameter a k ), (b) the area S
i
k
occupied by the group, (c) evapotranspiration
features primarily dependent on temperature T 1 ,
(d) and the altitude of geosystem location h
i
k . The
contribution of k-th geosystem group in the
second summand is provided by precipitation P 2
of the current hydrological season and depends
on the above-listed factors, surface and subsurface flows (parameter b k ) and S
i
k ; T 2 ; h
i
k . Thus,
fairly simple Eq. (7.3) describes the formation of
river WR under the influence of six important
environmental factors: P 1 , P 2 , T 1 , T 2 , S
i
k and h
i
k .
In block 3, the inverse problem is solved to
determine 36 parameters for each season separately that give minimal discrepancy between the
calculated data according to Eq. (7.3) and the
observed WR. The problem is implemented with
the optimization procedures of a widely used
software package MATLAB (procedures
LSQNONNEG, LSQNONLIN are used to determine the initial and final values of parameters,
correspondingly). All 36 parameters in Eq. (7.3)
are computed simultaneously from the data
sample of observed Q
i , which characterizes the
individual season and includes 5300/4 *1300
normalized seasonal average values of river
streamflow. Hence, to calculate streamflow for
four seasons, the 36 Â 4 = 144 parameters are
identified. It is compatible with SAM requirement
on tenfold excess of actual data (5300) over the
number of model parameters (144). It should be
noted that 36 model parameters define the seasonal runoff of 13 geosystem groups (Table 7.1),
i.e. we use less than three (36/13 < 3) parameters
to characterize the seasonal peculiarities of
hydrological regime for each group/landscape.
This minimal number of parameters allows for the
impact of six environmental factors on hydrological processes. When describing these processes by differential equations with three
parameters, the achievement of similar results
will be extremely difficult.
Table 7.1 presents SAM-estimated values b k
in Eq. (7.3). They are related to the portion of
seasonal precipitation, which comes to river
streamflow from each geosystem group during
the current season. Apart from the landscape
features, the change of actual (not normalized)
precipitation with altitude is also taken into
account. For instance, rain precipitation increase
at altitudes of 1600–1900 m (Selegey and Selegey 1978) will enlarge the contribution from
geosystem groups peculiar to these altitudes to a
streamflow. In Table 7.1, we can immediately see
the small contribution of highlands into the river
streamflow in autumn (geosystem groups 1–3, 5
in season 4), where precipitation remains on the
surface as a snow cover. Besides, we see a
considerable contribution of forest and forest90
Y. Kirsta and A. Puzanov
streamflow for the first season (winter low
water), these summands relate to the third and
fourth seasons of the previous year because snow
remains on the surface and does not affect the
streamflow in winter; parameters a k , b k characterize the contribution of k-th geosystem group in
relevant seasons, k = 1–13; S
i
k represents the
relative area of k-th geosystem group in basin i;
h
i
k is mean altitude of the same group in basin i,
m a.s.l.; P 1 , P 2 are normalized monthly precipitation averaged for a corresponding season; T 1 ,
T 2 are deviations of normalized air temperature
from 1 (1 is a long-term mean value of normalized characteristics) averaged for a corresponding
season; H is a piecewise linear function (see
Eq. 7.1); parameters c 1 ,…,c 9 reflect the influence
of temperature T 1 , T 2 and altitude h
i
k upon the
basin WR; parameter c 10 characterizes constant
replenishment (c 10 > 0) or depletion (c 10 < 0) of
WR into both free groundwater and water of rock
fracture zones. Thus, Eq. (7.3) includes 13
parameters a k , 13 parameters b k , and 10 parameters c i , i.e. 36 parameters for each hydrological
season are used to calculate WR.
On the right-hand side of Eq. (7.3), the individual contributions of geosystem groups into the
seasonal average streamflow Q
i of the basin i are
summed up. In the first summand, the contribution of k-th geosystem group refers to a delayed
WR formed by precipitation P 1 of the preceding
season. This process is specific to each group and
depends on (a) the peculiarities of water movement in soils and various losses of water before it
reaches a riverbed (parameter a k ), (b) the area S
i
k
occupied by the group, (c) evapotranspiration
features primarily dependent on temperature T 1 ,
(d) and the altitude of geosystem location h
i
k . The
contribution of k-th geosystem group in the
second summand is provided by precipitation P 2
of the current hydrological season and depends
on the above-listed factors, surface and subsurface flows (parameter b k ) and S
i
k ; T 2 ; h
i
k . Thus,
fairly simple Eq. (7.3) describes the formation of
river WR under the influence of six important
environmental factors: P 1 , P 2 , T 1 , T 2 , S
i
k and h
i
k .
In block 3, the inverse problem is solved to
determine 36 parameters for each season separately that give minimal discrepancy between the
calculated data according to Eq. (7.3) and the
observed WR. The problem is implemented with
the optimization procedures of a widely used
software package MATLAB (procedures
LSQNONNEG, LSQNONLIN are used to determine the initial and final values of parameters,
correspondingly). All 36 parameters in Eq. (7.3)
are computed simultaneously from the data
sample of observed Q
i , which characterizes the
individual season and includes 5300/4 *1300
normalized seasonal average values of river
streamflow. Hence, to calculate streamflow for
four seasons, the 36 Â 4 = 144 parameters are
identified. It is compatible with SAM requirement
on tenfold excess of actual data (5300) over the
number of model parameters (144). It should be
noted that 36 model parameters define the seasonal runoff of 13 geosystem groups (Table 7.1),
i.e. we use less than three (36/13 < 3) parameters
to characterize the seasonal peculiarities of
hydrological regime for each group/landscape.
This minimal number of parameters allows for the
impact of six environmental factors on hydrological processes. When describing these processes by differential equations with three
parameters, the achievement of similar results
will be extremely difficult.
Table 7.1 presents SAM-estimated values b k
in Eq. (7.3). They are related to the portion of
seasonal precipitation, which comes to river
streamflow from each geosystem group during
the current season. Apart from the landscape
features, the change of actual (not normalized)
precipitation with altitude is also taken into
account. For instance, rain precipitation increase
at altitudes of 1600–1900 m (Selegey and Selegey 1978) will enlarge the contribution from
geosystem groups peculiar to these altitudes to a
streamflow. In Table 7.1, we can immediately see
the small contribution of highlands into the river
streamflow in autumn (geosystem groups 1–3, 5
in season 4), where precipitation remains on the
surface as a snow cover. Besides, we see a
considerable contribution of forest and forest90
Y. Kirsta and A. Puzanov