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Procedia Engineering 162 (2016) 145 – 152

International Conference on Efficient & Sustainable Water Systems Management toward Worth
Living Development, 2nd EWaS 2016

New method for estimation mean hydrological changes and question
of reliability in forecasting future hydrological regimes
Dejan Dimkiüa,*
a

Jaroslav ýerni Institute for the Development of Water Resources, Jaroslava ýernog 80, 12226 Belgrade, Serbia,

Abstract
Important hydrological changes are observed in Serbia, as well as in many parts of the world. Many national and international
projects and studies address climate change and its impact on water resources. Some focus solely on the impact of climate change,
while others also assess the impact of land use changes and/or changes in human use of water. Due to differences in climate change
and human activities, the different climate and hydrological trends are obtained for the different regions in Serbia.
This paper presents the past longterm temperature, precipitation and river discharge trends across Serbia. Second, more important
aim of the research, is to assess and forecast average relationships between an increase in air temperature and changes in river
discharges and precipitation. This relation could help us to find appropriate regional climate and hydrological models.
Even within a single catchment, depending on the regional models used, the initial and other assumptions made, and the impacts
assessed, the differences between the results can be small but often significant, too. The reliability of the projections receives little
or no consideration. This paper also discusses this topic and attempts to provide some guidelines.
©
by Elsevier
Ltd. This
is an open
access article under the CC BY-NC-ND license

©2016
2016Published
The Authors.
Published
by Elsevier
Ltd.
( />Peer-review under responsibility of the organizing committee of the EWaS2 International Conference on Efficient & Sustainable
Peer-review
underManagement
responsibilitytoward
of the organizing
committee
of the EWaS2 International Conference on Efficient & Sustainable
Water Systems
Worth Living
Development.
Water Systems Management toward Worth Living Development
Keywords: Trends; climate and hydrological changes; temperature; precipitation; reliability.

* Corresponding author. Tel.: +381-11-3906-478; fax: + +381-11-3906-481.
E-mail address:

1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

( />Peer-review under responsibility of the organizing committee of the EWaS2 International Conference on Efficient & Sustainable Water Systems
Management toward Worth Living Development

doi:10.1016/j.proeng.2016.11.030



146

Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

1. Introduction
Considerable pressures regarding future water supply security, like in many parts of the world [1], [2], are expected
in Serbia, given the imminent increase in water demand and decrease in discharge, to a different extent, of all rivers
and water resources in the region [3], [4], [5]. This paper considers just mean annual values for Temperature (T),
Precipitation (P) and River discharge (Q). In 20th and first decade of 21th century, Serbia’s rivers registered a negative
trend. This led to a large number of projects, studies and papers over the past ten years, which address the problem
and future expectations based on certain initial assumptions.
The question is reliability of such forecastings. Analysis of observed changes and some additional investigations,
presented here, could help us in finding answer to this question. Applied Methodology and Results are related to
Serbia, and the same could be done elsewhere. To be clearly, second (Methodology) and third (Results) sections of
this paper are divided in three parts:
x Observed climate and hydrological changes in Serbia
x Correlation between air temperature and river discharges and precipitation
x The reliability of the Regional climate and hydrology model’s projections
2. Methodology
2.1. Observed climate and hydrological changes in Serbia
For assessment of observed average annual changes, it is very important to find the period suitable for analysis.
Assessment of the spatial distribution of one of the three parameters (T, P, Q) required a sufficient data density (for
reducing the stochastic component, which is always present when the number of analyzed stations is small), such that
the selected period for analysis in this case was from 1949 to 2006. This period was convenient because it was
relatively long (58 years), data were available from numerous monitoring stations, and they exhibited a close similarity
to estimated long-term temperature and precipitation trends, and particularly river discharge trends in Serbia [4], [6],
[7].
To assess past climate and hydrological trends, 26 temperature, 34 precipitation and 18 hydrological stations were
selected. All the trend charts shown were generated using Surfer software, based on data recorded at analyzed stations,
removing the stochastic component by regional averaging [4], [5]. Trend for analyzed period (1949-2006) for T and

P was adjusted as follows:
For each given station, all other available stations at an air distance of up to 100 km were identified. Then the
distance was caluculated between each of these stations and the given station, for which the climate parameter
(temperature or precipitation) trend was to be adjusted. Finally, the trend of the given station was determined using
the formula:
ௌ
ܶ௞௢௥Ǥ
ൌ ܶ ௌ ή ሺͳ െ ‫ܭ‬ሻ ൅

భ
ೋ೔
భ
σ೔
ೋ೔

σ೔ ்೔ ή

ή‫ܭ‬

(1)

where:
Zi – distance of the i-th station from the given station;
Ti – (T or P) trend measured at the i-th station;
TS – (T or P) trend measured at the given station;
K – coefficient dependent on the number and distance of stations within a 100 km radius (0.4 ÷ 0.7)
TSkor – adjusted (T or P) trend of the given station.
Trend for river discharge is not adjusted, it is used as it is. Hydrological stations were selected in accordance with
written in section 3.1.



Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

2.2. Correlation between air temperature and river discharges and precipitation
Observed hydrological changes told us that there is a downward average annual riverflow trend in Serbia (part 3.1).
If temperature continues to increase, what is to be expected with regard to hydrological trends? Common approach
(RCM models) try with some scenarios to give us answer. In addition to common approach, the good way of arriving
at the answer to this question is to analyze what has happened in the past with average annual temperature vs. riverflow
levels, and it is also useful to establish the same type of correlation between temperature and precipitation [4], [5], [6].
The temperature and precipitation stations which are closest to the center of the Catchment Area (C.A.) of a
hydrological station were taken as reference stations. The analysis included 18 hydrological stations and their
associated meteorological stations.
Relative parameters were calculated for each C.A., for each years during the 1949-2006 period:
x Average annual riverflow at a given monitoring site, relative to the mean, Qrel;
x Annual precipitation sum recorded at a precipitation station close to the center of C.A., again relative to the mean
annual sum, Prel;
x Difference, ǻTav, between the average annual temperature and the mean temperature at that station.
To arrive at relationships, data were grouped into categories according to deviations of average annual temperatures
from the mean values for that station, at intervals of 0.5°C. Average values were then calculated for each category of
temperature deviation, and of the annual discharge and precipitation relative to their mean values, respectively. These
data were then used to construct graphs of the relationships between the derived values, displaying also the linear and
3rd degree polynomial fit to the composite data shown and the associated coefficient of determination R2.
Even though each of the studied C.A. exhibits specific features, there is no major difference between them: all
show the expected trend of an average decline in riverflow with increasing temperature and vice-versa. It is, therefore,
fully justifiable to synthesize all relevant data into a single data series. This enlarges the data series by 58 members,
of each of the analyzed series, to 58x18 = 1044, and decreases the effect of random, non-standard years, especially in
classes which otherwise have few data points. A synthesis of all data (part 3.2; Figure 2) yielded average values and
the derived trends can be considered highly representative for assessing the average temperature impact on river
discharges and precipitation in Serbia.
2.3. The reliability of the Regional climate and hydrology model’s projections

Apart from climate change (CC), the hydrologic regime of a river is affected by changes in land use (LU) within
the C.A. and changes in the extent and method of human use (HU) of water [8], [9], [10]. As a result, some of Serbia’s
rivers record a considerable decrease in discharge. The discharges of only a small number of rivers have increased,
largely due to water transfers from other river basins, which began in the 1970’s and 1980’s. All three components
are very important and the degree of significance varies very much from C.A. to C.A. Based on precipitation and
temperature trend distributions, the greatest negative trend changes were noted in eastern Serbia. But, for stations at
some other parts of Serbia, especially where changes in human use of water or in land use are significant, climate
change impact is often negligible. The same is valid for the future.
Most of the recent projects are based on different climate models and different scenarios that provide basic inputs
for hydrological models. A large number of studies based on regional climate-hydrological models address only the
first type of change (CC). Neither overestimate or underestimate the importance of particular projects, we have
reviewed 5 projects, and all available data on mean annual level from these projects were analyzed [11]. Five different
groups of experts have analyzed 10 different rivers at 15 different hydrological stations in Serbia and 54 different
cases (different scenarios or climate – hydrology model). In just few of them all three impacts on water resources (CC,
LU and HU) were analyzed. Detailed results are not reported here due to lack of space.

147


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Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

3. Results
3.1. Observed climate and hydrological changes in Serbia
The annual average temperature trend in Serbia was found to be about 0.6°C/100 years, while the average
precipitation trend was slightly negative. In the same period hydrological trend was about -30%/100 years. The spatial
annual distribution is shown in Figure 1 [4], [5], [12].
Serbia, especially its eastern part, experiences a downward riverflow trend. However, contrary to climate
parameters, it is difficult to spatially generalize because several factors affect these trends [13], [14] :

1. The size of the river,
2. The transfer of water, if any, between C.A.s upstream form a given hydrological station,
3. The volume of water used by man in a given C.A.,
4. The presence or absence of river reservoir(s) in the C.A.,
5. Land use changes (forest have been generally increased in Serbia last 60 years), and
6. Climate change (including differences associated with geographic locations within Serbia).

Fig. 1. Recorded annual trends in Serbia (1949-2006), based on (a) T-26, (b) P-34 and (c) Q-18 stations

1.
Small rivers are much more stochastic in nature and sensitive to water withdrawal for human consumption,
while large international rivers (the Danube, the Sava and the Tisa) often do not adequately reflect what happens
within one country or region, in this case Serbia. As such, medium-size rivers are the most reliable representatives of
the overall trend in a particular area (including climate change and human activity), provided that Factor 2 – water
transfer between C.A.s – is not significant.
2.
Factor 2 is dominant at many hydrological stations and such stations need to be excluded from analyses, in
order to derive relevant results.
3.
Factor 3 is significant, and the degree of significance ranges from negligible (small volumes of water
withdrawn from large rivers) to dominant (large volumes withdrawn from small rivers), within the framework of the
recorded trend. A favorable circumstance from a trend analysis perspective is that much more water is used in Serbia
for drinking water supply (where relatively accurate data are available), than irrigation (where there are only rough
estimates).
4.
The existence of a river reservoir upstream of a given hydrological station is generally a negligible or has a
small contribution to the overall hydrological trend. Exceptions are small rivers, or large river reservoirs relative to
the surface area of the C.A.
5.
Land use changes diver from negligible to very significant.



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Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

6.
Climate change is often the most important contributor to the overall hydrological trend. Climate change has
to date had the greatest impact and resulted in the most distinct recorded downward precipitation and riverflow trends
in Eastern Serbia. Conversely, only minor change has been noted in Southwestern Serbia, where many rivers exhibit
near-zero trends as a result of an upward precipitation trend, but also an upward evapotranspiration trend due to a
slightly higher temperature increase in that region.
An approximate geographical distribution of the downward average annual riverflow trend in Central Serbia is
shown in Figure 1, compiled based on the trends recorded at 18 selected river monitoring stations, where Factors 3
and 4 were assessed as having an acceptable degree of impact, and where Factor 2 was either absent or negligible. It
should be kept in mind that the above hydrological results are given in terms of averages, while the discharge trends
for specific C.A.s can be significantly different, both up and down, due to differences in human activities (factors 3,
4 and especially 2).
We can see that the direction of the discharge changes in Serbia (decline trend from west to east) is generally in
accordance with the forecasts based on IPCC scenario A1B [15], like in many parts of the world [1], [16], [17]. For
the same period (1949-2006), for Temperature and Precipitation, trend results were checked by Mann-Kendal test.
Results are grouped depending of the part of the country (Table 1), and it could be seen that they are generally in line
with graphs on Figure 1.
Table 1. Results of Mann-Kendal test: Trend description for Temperature and Precipitation for different regions in Serbia
Serbia’s region ĺ

North Serbia

West part of Central
Serbia


Central part of Central
Serbia

East part of Central
Serbia

Temperature

clearly increasing

clearly increasing

negligible

between unclear and
slightly positive

Precipitation

between unclear and
slightly positive

clearly increasing

between unclear and
slightly negative

clearly decreasing


Temperature deviation
category (°C)
ǻT av < -1.0°C
-1.0 < ǻT av < -0.5
-0.5 < ǻT av < 0.0
All data for 18 C.A.
0.0 < ǻT av < 0.5
0.5 < ǻT av < 1.0
1.0°C < ǻTav

Relative discharge
(average)
1.27
1.11
1.04
1.00
0.96
0.90
0.72

Relative precipiTemperature
tation (average) difference (average)
1.09
-1.22
1.05
-0.72
1.00
-0.24
1.00
0.00

1.00
0.22
0.99
0.70
0.88
1.36

1,60

1,60

y = -0,0508x 3 + 0,0141x 2 - 0,1313x + 0,9981
R2 = 0,9986

1,50
1,40

1,40
1,30

Prel

Qrel

1,20

1,10
1,00
0,90
0,80

0,70

0,40
-2,0

y = -0,0348x 3 - 0,0021x 2 - 0,0243x + 1,0055
R2 = 0,9703

1,50

1,30
1,20

0,60
0,50

Number of data
points (years)
74
148
327
1044
278
123
94

1,10
1,00
0,90
0,80

0,70

y = -0,1997x + 1,0033
R2 = 0,9809

-1,5

-1,0

0,60
0,50

-0,5

0,0

0,5

ǻT av ( °C )

1,0

1,5

2,0

0,40
-2,0

y = -0,0728x + 1,0015

R2 = 0,9032

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

ǻT av ( °C )

Fig. 2. Average annual riverflow and precipitation, relative to the average, as a function of temperature deviation (all 18 C.A.s).

2,0


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Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

3.2. Correlation between air temperature and river discharges and precipitation
Results of correlation between air temperature and river discharges and precipitation is shown on Figure 2.
It should be noted that the coefficient of determination is very high in both graphs, leading to the conclusion that a

deviation of the average annual temperature by +1°C has an inversely proportional effect on the average annual
precipitation levels of about 7%, and on the average annual riverflow of about 20%. The results differ from C.A. to
C.A., but in most cases this variation is not great. If these linear and 3rd degree polynomial trends are extrapolated to
+2°C, values derived for relative riverflow and relative precipitation are shown in Table 2 (mean annual level).
Table 2. Relative riverflow and relative precipitation as a function of Temperature increasing
ǻTav ( °C )
Relative riverflow (Qrel)
Relative precipitation (Prel)

ĺ

0.5

1.0

1.5

2.0
0.60

Linear trend

0.90

0.80

0.70

3rd degree polynomial trend


0.93

0.83

0.66

0.39

Linear trend

0.97

0.93

0.89

0.86

3rd degree polynomial trend

0.99

0.94

0.85

0.67

This methodology could be basis for the most probable average river discharge assessment (decline) for the near
future (30 years) in Serbia, in dependence of the average yearly temperature increasing. The same methodology could

be applied for many countries and regions, especially for those where the negative annual trend for precipitation is
recorded.
3.3. The reliability of the Regional climate and hydrology model’s projections
An analysis of the results obtained from regional models led to the conclusion that the results vary considerably,
even for the same river, especially with regard to the distant future. If hydrologic predictions result in a broad range
of possible discharges of the same river (extremes of +20% and -40%), clearly the reliability (probability) of the
predictions needs to be examined. This requires either the selection of certain criteria for assessing the probability of
the prediction, which is theoretically possible (e.g. probability of adopted climate prediction multiplied by the
probability of correctly selected hydrological model), which is rather cumbersome and highly questionable, or expert
judgment of the study (project) analyst, which is certainly debatable.
Instead, we can use the relation explained in the part 2.2 and results shown in the part 3.2 of this paper. An important
characteristic of this approach is that it takes into account all three changes: CC, LU and HU. In order to be applied
to individual catchments, it might be useful to produce the same models for a number of catchments and try to arrive
at an average for the analyzed region (in this case central Serbia) that is similar to the values of the correlations given
on Figure 2.
4. Conclusions
The recorded average river discharge trends are about -30%/100 years, and depend on a large number of factors.
Climate change is only one of the factors that impact water resources. The impact of climate change has been noted
at all gauging stations, but its significance varies. In eastern Serbia, based on precipitation trend distributions, it is
generally dominant. In some parts of the country it is often not of primary concern, and elsewhere it is minor given
the magnitude of other impacts [4], [9].
If the average annual temperature were to increase by 2ºC, based on the correlations established to date between
average annual river discharges and average annual temperatures, one could expect, on average, approximately half
the amount of water in rivers whose C.A.s largely lie within Serbia.
Even though uncertainty (the consequently unreliability) is inherent in any projection, it is quite certain that it
grows with the period of time for which the projection is made. Considering all the above, the author believe that all
projections that pertain to the distant future (50 or more years) should be deemed purely “academic” and the focus of
professional circles and society as a whole should remain on the near future (about the next 30 years), as the average
decrease in water resource availability is not only probable but to an extent measurable. It is recommended that one



Dejan Dimkić / Procedia Engineering 162 (2016) 145 – 152

of the future projects that assess the impact of climate change on water resources in the near future (max. increase in
average annual temperatures by 1 to 2°C) should include a larger number of national river catchments and seek out
climate scenarios and hydrological models that produce average dependencies between river discharges and
temperatures at mean annual levels, according to the correlation shown in Figure 2.
Who can perhaps benefit from the outcomes of this research? Apart from Serbia, it is believed that the presented
results will be of interest to the entire region of Southeast Europe, particularly eastern and southern part of Balkan
peninsula. Further, the results indicate that an in-depth study of all observed data (above all temperature, precipitation
and hydrological data) should be undertaken before a regional model is produced. Ultimately, the proposed
methodology for the assessment of average temperature impact on average river discharge and precipitation could
certainly be applied in many parts of the world, especially in regions where a decreasing precipitation trend is recorded.
Some general, but in the case of paper’s subject very important remarks are emphasized in closing:
¾ Observed data are extremely important [12], as is continued systematic monitoring in the future.
¾ Regional integration is extremely important [3], SEE or the Danube River Basin in the case of Serbia, as is the use
of the same approach to produce various maps.
¾ Exchange of knowledge, experience and ideas between countries and regions that share the same problem is
important (e.g. regions that record downward precipitation trends, or sub-arid regions, etc.).
¾ It is important to apply various methods to assess past and predict future climate and hydrological developments.
If predictions for the near future under RCMs for numerous C.A.s and through correlation and extrapolation of
observed data do not differ to a large extent, the reliability of such predictions is quite high.

Acknowledgements
This paper is an outcome of the scientific project “Assessment of Climate Change Impact on Water Resources in
Serbia” (TR37005), funded by the Ministry of Education and Science of the Republic of Serbia.
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