a result, we obtained the long-term monthly
dynamics of normalized temperature and precipitation, that is the same throughout the AltaiSayan mountain country (Kirsta 2011b).
The developed method of spatial generalization of climatic characteristics was applied to
calculate their dynamics using the data from 11
reference weather stations for 1951–2010, and,
thus, to work out the regional climate model. All
stations were outside the considered river basins
but had a continuous series of observations. The
found dynamics was expressed in percent/
fraction of three specified in situ long-term
averaged monthly values (January temperature
applied for X–IV months, July temperature for
V–IX months, and July precipitation for all
months of a year), and it does not depend on the
site coordinates and altitude. Such an independence of the altitude changing across the territory
allowed describing the dynamics of normalized
temperature and precipitation throughout each
basin with altitude difference as much as 2000 m,
and this was of great importance. Moreover, this
dynamics was identical for all river basins in the
Altai-Sayan mountain country. In the subsequent
SAM, the climate model is used for calculating
both 636 normalized values of average monthly
temperature and 636 normalized monthly precipitation over the period 1951–2003 as input
factors for WR/HCR models.
The adequacy of calculations of normalized
climatic characteristics in the climate model was
also assessed (Kirsta 2011b). In the case of
arbitrary (not reference) weather stations, a
comparison of the observed and calculated longterm data series according to criterion A in
Eq. (7.2) gave A = 0.5 for average monthly air
temperature and A = 0.66 for monthly precipitation. Hereafter we shall use these values of A in
evaluating the adequacy of WR/HCR models.
Note that in order to restore the long-term
monthly dynamics of temperature and precipitation in terms of °C and mm, correspondingly,
one should know only their monthly values
observed at the study site for 1–2 years. First, the
observed and normalized values are used to calculate the transition coefficients. Then, the calculated long-term monthly dynamics of both
normalized temperature and precipitation, which
is uniform throughout the Altai-Sayan mountain
country, is multiplied by these coefficients.
It should be noted that a sufficiently large
criterion A = 0.66 for spatial generalization of
precipitation, the dynamics of which is influenced by many random factors, has not prevented the execution of SAM. This value of
A corresponds to RSR = A
ffiffi ffi
2
p
=0.93 that usually
is not allowed for hydrological models (Koch
and Cherie 2013).
7.5 Development of Water Runoff
Model
Since the normalized air temperature and precipitation are among the input factors of the WR
model, the river streamflow values should be
normalized as well. For this purpose, the
observed streamflow values were divided by the
corresponding long-term mean seasonal values
for each basin. By this means, we passed from
streamflow measurements in m
3 /sec to dimensionless units of normalized streamflow. In a
similar manner, geosystem group areas (km
2 ) in
each basin were converted into percent/fraction
via division by the basin area (Table 7.1).
Like regression analysis rules, to use SAM
successfully, the array of actual data on the
process dynamics should exceed the number of
model equation parameters at least by a factor of
10 (Kirsta and Kirsta 2014). There are 5300
values of seasonal average river streamflow that
theoretically allows entering up to *500
parameters to the model or 500/4 *100 for each
of four hydrological seasons stated above.
However, the number of river basins comes to 34
resulting in three allowed parameters if we
describe the influence of the basin-specific
characteristics (e.g. area or altitude of landscapes) on streamflow. For example, when
describing (analytically or graphically) the relationship between WR and basin area or landscape altitude, we have only 34 pairs of
dependent and independent variables, and,
hence, cannot use more than three parameters for
this relationship in SAM. The limitation to three
88
Y. Kirsta and A. Puzanov
dynamics of normalized temperature and precipitation, that is the same throughout the AltaiSayan mountain country (Kirsta 2011b).
The developed method of spatial generalization of climatic characteristics was applied to
calculate their dynamics using the data from 11
reference weather stations for 1951–2010, and,
thus, to work out the regional climate model. All
stations were outside the considered river basins
but had a continuous series of observations. The
found dynamics was expressed in percent/
fraction of three specified in situ long-term
averaged monthly values (January temperature
applied for X–IV months, July temperature for
V–IX months, and July precipitation for all
months of a year), and it does not depend on the
site coordinates and altitude. Such an independence of the altitude changing across the territory
allowed describing the dynamics of normalized
temperature and precipitation throughout each
basin with altitude difference as much as 2000 m,
and this was of great importance. Moreover, this
dynamics was identical for all river basins in the
Altai-Sayan mountain country. In the subsequent
SAM, the climate model is used for calculating
both 636 normalized values of average monthly
temperature and 636 normalized monthly precipitation over the period 1951–2003 as input
factors for WR/HCR models.
The adequacy of calculations of normalized
climatic characteristics in the climate model was
also assessed (Kirsta 2011b). In the case of
arbitrary (not reference) weather stations, a
comparison of the observed and calculated longterm data series according to criterion A in
Eq. (7.2) gave A = 0.5 for average monthly air
temperature and A = 0.66 for monthly precipitation. Hereafter we shall use these values of A in
evaluating the adequacy of WR/HCR models.
Note that in order to restore the long-term
monthly dynamics of temperature and precipitation in terms of °C and mm, correspondingly,
one should know only their monthly values
observed at the study site for 1–2 years. First, the
observed and normalized values are used to calculate the transition coefficients. Then, the calculated long-term monthly dynamics of both
normalized temperature and precipitation, which
is uniform throughout the Altai-Sayan mountain
country, is multiplied by these coefficients.
It should be noted that a sufficiently large
criterion A = 0.66 for spatial generalization of
precipitation, the dynamics of which is influenced by many random factors, has not prevented the execution of SAM. This value of
A corresponds to RSR = A
ffiffi ffi
2
p
=0.93 that usually
is not allowed for hydrological models (Koch
and Cherie 2013).
7.5 Development of Water Runoff
Model
Since the normalized air temperature and precipitation are among the input factors of the WR
model, the river streamflow values should be
normalized as well. For this purpose, the
observed streamflow values were divided by the
corresponding long-term mean seasonal values
for each basin. By this means, we passed from
streamflow measurements in m
3 /sec to dimensionless units of normalized streamflow. In a
similar manner, geosystem group areas (km
2 ) in
each basin were converted into percent/fraction
via division by the basin area (Table 7.1).
Like regression analysis rules, to use SAM
successfully, the array of actual data on the
process dynamics should exceed the number of
model equation parameters at least by a factor of
10 (Kirsta and Kirsta 2014). There are 5300
values of seasonal average river streamflow that
theoretically allows entering up to *500
parameters to the model or 500/4 *100 for each
of four hydrological seasons stated above.
However, the number of river basins comes to 34
resulting in three allowed parameters if we
describe the influence of the basin-specific
characteristics (e.g. area or altitude of landscapes) on streamflow. For example, when
describing (analytically or graphically) the relationship between WR and basin area or landscape altitude, we have only 34 pairs of
dependent and independent variables, and,
hence, cannot use more than three parameters for
this relationship in SAM. The limitation to three
88
Y. Kirsta and A. Puzanov