190
P. Jokiel and P. Tomalski
The method for GMO construction indicates that in the absence of flow seasonality
(identical mean flow for all months of the year), its value is 8.3. When the flow
happens for only one month (maximum seasonality) the coefficient equals 100.
It should be emphasized, however, that all the above mentioned characteristics
have some specific disadvantages. While defining them, we assume that a hydrological year is a “closed” time unit in which daily or monthly flows are independent of
the previous ones and would not affect those occurring after them. Considering large
flow inertia that is due to, e.g. retention, this assumption is not true, and it should be
constantly kept in mind [4].
To assess different types of changes in the vectors of resulting seasonality
measures, we used basic tools of statistical data analysis, including time series analysis, correlation, and regression, as well as simple tests and statistical diagrams. The
calculations were performed with EXCEL and STATISTICA packages.
10.5 Changes in Flow Seasonality Along Both Rivers
Average multiannual flow in the Oder along its nearly 680 km
2 length ranges from
42 m
3 · s
−1 to over 535 m
3 · s
−1 . In the Vistula, the flow increase along the river
course reaches over 1000 m
3 · s
−1 (Tables 10.2 and 10.3). Half of the annual flow
is released from the upper Oder catchment (TPO) between 21 and 25 April, and in
the lower section, this time is two weeks earlier and falls between 11 and 12 April.
Average flow concentration date (PK) for the Oder gauges follows a similar pattern.
In the upper section, it falls between 27 and 30 April and in the lower between 3 and 6
April – three weeks earlier. TPO changes along the Vistula course are of an analogous
character. In its upper section half of the annual flow is released from 28 to 30 April
and in the lower section two weeks earlier, i.e. from 15 to 16 April. Importantly, half
of the annual water resources of the Vistula, both in its middle and lower section,
is released by 4–5 days later than half of the annual water resources of the Oder.
The difference is small but stable along both rivers (except for their upper sections).
Concentration date coefficients (PK) do not show similar regularities. Their dates in
both rivers fell from the end of April (upper sections) until the beginning of April
(lower sections). The difference between the rivers is about 30 days.
In the Vistula and the Oder, there is a clear relationship between the concentration
date (PK) and half-flow date (TPO). It is of a linear character, and the rise in PK
accompanying the rise in TPO is markedly slower for the Vistula (red points in
Fig. 10.2) than for the Oder (blue points in Fig. 10.2). At the same time, the strength
of the relationship between the two parameters is greater and the spread of points
is smaller for the Oder than for the Vistula (Fig. 10.2). For the same concentration
dates (PK), the half-flow dates (TPO) on the Vistula gauges fall later than on the
Oder gauges. This difference disappears rapidly as TPO and PK decrease with a
growing area of both basins.
Comprehensive measures of flow seasonality (GMO and IS) change significantly
as the area of both river basins increases. For the Oder, mean GMO and IS drop
P. Jokiel and P. Tomalski
The method for GMO construction indicates that in the absence of flow seasonality
(identical mean flow for all months of the year), its value is 8.3. When the flow
happens for only one month (maximum seasonality) the coefficient equals 100.
It should be emphasized, however, that all the above mentioned characteristics
have some specific disadvantages. While defining them, we assume that a hydrological year is a “closed” time unit in which daily or monthly flows are independent of
the previous ones and would not affect those occurring after them. Considering large
flow inertia that is due to, e.g. retention, this assumption is not true, and it should be
constantly kept in mind [4].
To assess different types of changes in the vectors of resulting seasonality
measures, we used basic tools of statistical data analysis, including time series analysis, correlation, and regression, as well as simple tests and statistical diagrams. The
calculations were performed with EXCEL and STATISTICA packages.
10.5 Changes in Flow Seasonality Along Both Rivers
Average multiannual flow in the Oder along its nearly 680 km
2 length ranges from
42 m
3 · s
−1 to over 535 m
3 · s
−1 . In the Vistula, the flow increase along the river
course reaches over 1000 m
3 · s
−1 (Tables 10.2 and 10.3). Half of the annual flow
is released from the upper Oder catchment (TPO) between 21 and 25 April, and in
the lower section, this time is two weeks earlier and falls between 11 and 12 April.
Average flow concentration date (PK) for the Oder gauges follows a similar pattern.
In the upper section, it falls between 27 and 30 April and in the lower between 3 and 6
April – three weeks earlier. TPO changes along the Vistula course are of an analogous
character. In its upper section half of the annual flow is released from 28 to 30 April
and in the lower section two weeks earlier, i.e. from 15 to 16 April. Importantly, half
of the annual water resources of the Vistula, both in its middle and lower section,
is released by 4–5 days later than half of the annual water resources of the Oder.
The difference is small but stable along both rivers (except for their upper sections).
Concentration date coefficients (PK) do not show similar regularities. Their dates in
both rivers fell from the end of April (upper sections) until the beginning of April
(lower sections). The difference between the rivers is about 30 days.
In the Vistula and the Oder, there is a clear relationship between the concentration
date (PK) and half-flow date (TPO). It is of a linear character, and the rise in PK
accompanying the rise in TPO is markedly slower for the Vistula (red points in
Fig. 10.2) than for the Oder (blue points in Fig. 10.2). At the same time, the strength
of the relationship between the two parameters is greater and the spread of points
is smaller for the Oder than for the Vistula (Fig. 10.2). For the same concentration
dates (PK), the half-flow dates (TPO) on the Vistula gauges fall later than on the
Oder gauges. This difference disappears rapidly as TPO and PK decrease with a
growing area of both basins.
Comprehensive measures of flow seasonality (GMO and IS) change significantly
as the area of both river basins increases. For the Oder, mean GMO and IS drop