Similar to A' in (7.6), RSR' is equal to RSR
obtained via using the randomly mixed values of
the input factor instead of initially ordered ones.
Criterion FS is a close analog of determination
coefficient R
2 known in the variance analysis. In
accordance with the variance sum law, value
S
0
dif
À Á 2 is greater by two variances S fac
ð Þ
2 than
S obs
ð
Þ
2 . The first S fac
ð Þ
2 results from the contribution of real variations of the input factor to
observed values of the output variable, and the
second S fac
ð Þ
2 is due to the contribution of artificially created random variations of the input
factor (by entangling its observed values) into the
calculated output variable. For adequate models,
S dif
ð Þ
2 will be free of both variances S fac
ð Þ
2
because of subtracting the calculated contribution
of the input factor from the observed one. At the
same time, the variance derived from observational errors of the input factor (or errors of
spatial generalization of meteorological factors)
will be present both in S
0
dif
À Á 2 and S dif
ð Þ
2 and,
therefore, its values in (7.6) will be subtracted
from each other. Thus, FS evaluates the model
sensitivity solely to input factor variations,
except for observational errors. Based on this
sensitivity to individual environmental factors,
one can assess their relative importance to the
model. Since FS is expressed in proportion of
S obs
ð
Þ
2 , it can be expressed in percent via multiplying by 100.
The estimated sensitivity of WR/HCR models
to the input factors via the use of randomly
mixed values of the target input factor and its
original pattern is shown in Table 7.5. Take, for
example, the second season (spring–summer
flood). We see a consecutive reduction of WR
sensitivity to precipitation (22%), temperature
(16%), landscape structure of river basins (6%),
and landscape altitude a.s.l. (0.2%). As expected,
the WR model shows its maximum sensitivity to
precipitation and air temperature, and the minor
sensitivity to landscape altitude. The latter means
the high adequacy of meteorological condition
description for all 34 river basins by virtue of
using the spatially generalized normalized precipitation and air temperature (see Sect. 7.4) in
the model. Due to the normalization to the corresponding average long-term values, the
dynamics of these factors is the same throughout
the Altai-Sayan mountain country and properly
accounts for their change with altitude. In
Table 7.5, the FS abrupt jump >100% for PO
3À
4
runoff is due to two-order difference of landscape
areas in some river basins. During random mixing, such a difference leads to multiplying the
large WR of certain landscapes by the large
PO
3À
4 concentrations in WR of other landscapes,
and consequently in abrupt increase in S fac
ð Þ
2 in
Eq. (7.6).
The series of factors with consecutive reduction of their importance for the runoff formation
can be outlined from Table 7.5, thus ensuring
efficient water quality management. These series
are the same for 34 river basins and, therefore,
for any basin of the Altai-Sayan mountain
country.
7.8 Results and Discussion
The combined models of normalization and
spatial generalization of mean monthly temperature and monthly precipitation, as well of WR
and HCR, allow us to estimate seasonal and
long-term dynamics of water and seven analyte
runoff for any river basins of the Altai-Sayan
mountain country. Values of model parameters
are the same for 34 river basins in spite of their
marked orographic and climatic diversity. Thus,
the elaborated model package is universal and
applicable to any river basin in the investigated
mountainous area, including river basins, for
which experimental hydrometeorological and/or
hydrochemical data are not available.
Using the sensitivity data (Table 7.5), a
comprehensive component analysis of residual
variance S dif
ð Þ
2 of WR and HCR models (i.e.
variance of difference between the calculated and
observed runoff) was carried out (Kirsta 2016).
This analysis made possible to estimate the
contribution from the input factors of models and
the errors of the model equations themselves to
96
Y. Kirsta and A. Puzanov
obtained via using the randomly mixed values of
the input factor instead of initially ordered ones.
Criterion FS is a close analog of determination
coefficient R
2 known in the variance analysis. In
accordance with the variance sum law, value
S
0
dif
À Á 2 is greater by two variances S fac
ð Þ
2 than
S obs
ð
Þ
2 . The first S fac
ð Þ
2 results from the contribution of real variations of the input factor to
observed values of the output variable, and the
second S fac
ð Þ
2 is due to the contribution of artificially created random variations of the input
factor (by entangling its observed values) into the
calculated output variable. For adequate models,
S dif
ð Þ
2 will be free of both variances S fac
ð Þ
2
because of subtracting the calculated contribution
of the input factor from the observed one. At the
same time, the variance derived from observational errors of the input factor (or errors of
spatial generalization of meteorological factors)
will be present both in S
0
dif
À Á 2 and S dif
ð Þ
2 and,
therefore, its values in (7.6) will be subtracted
from each other. Thus, FS evaluates the model
sensitivity solely to input factor variations,
except for observational errors. Based on this
sensitivity to individual environmental factors,
one can assess their relative importance to the
model. Since FS is expressed in proportion of
S obs
ð
Þ
2 , it can be expressed in percent via multiplying by 100.
The estimated sensitivity of WR/HCR models
to the input factors via the use of randomly
mixed values of the target input factor and its
original pattern is shown in Table 7.5. Take, for
example, the second season (spring–summer
flood). We see a consecutive reduction of WR
sensitivity to precipitation (22%), temperature
(16%), landscape structure of river basins (6%),
and landscape altitude a.s.l. (0.2%). As expected,
the WR model shows its maximum sensitivity to
precipitation and air temperature, and the minor
sensitivity to landscape altitude. The latter means
the high adequacy of meteorological condition
description for all 34 river basins by virtue of
using the spatially generalized normalized precipitation and air temperature (see Sect. 7.4) in
the model. Due to the normalization to the corresponding average long-term values, the
dynamics of these factors is the same throughout
the Altai-Sayan mountain country and properly
accounts for their change with altitude. In
Table 7.5, the FS abrupt jump >100% for PO
3À
4
runoff is due to two-order difference of landscape
areas in some river basins. During random mixing, such a difference leads to multiplying the
large WR of certain landscapes by the large
PO
3À
4 concentrations in WR of other landscapes,
and consequently in abrupt increase in S fac
ð Þ
2 in
Eq. (7.6).
The series of factors with consecutive reduction of their importance for the runoff formation
can be outlined from Table 7.5, thus ensuring
efficient water quality management. These series
are the same for 34 river basins and, therefore,
for any basin of the Altai-Sayan mountain
country.
7.8 Results and Discussion
The combined models of normalization and
spatial generalization of mean monthly temperature and monthly precipitation, as well of WR
and HCR, allow us to estimate seasonal and
long-term dynamics of water and seven analyte
runoff for any river basins of the Altai-Sayan
mountain country. Values of model parameters
are the same for 34 river basins in spite of their
marked orographic and climatic diversity. Thus,
the elaborated model package is universal and
applicable to any river basin in the investigated
mountainous area, including river basins, for
which experimental hydrometeorological and/or
hydrochemical data are not available.
Using the sensitivity data (Table 7.5), a
comprehensive component analysis of residual
variance S dif
ð Þ
2 of WR and HCR models (i.e.
variance of difference between the calculated and
observed runoff) was carried out (Kirsta 2016).
This analysis made possible to estimate the
contribution from the input factors of models and
the errors of the model equations themselves to
96
Y. Kirsta and A. Puzanov