Journal of Hydrology 313 (2005) 48–57
www.elsevier.com/locate/jhydrol
Identification of flood producing atmospheric circulation patterns
András Bárdossy*, Fulya Filiz
Institut für Wasserbau, Universität Stuttgart, Pfaffenwaldring 61, 70550 Stuttgart, Germany
Received 18 February 2003; accepted 13 October 2004
Abstract
Floods in mesoscale catchments (with a size of a few hundreds to a few thousand square kilometers) are often related to
typical large scale weather phenomena which affect a large area in continental scale. The purpose of this paper is to develop a
methodology for the identification of flood producing daily atmospheric circulation patterns (CPs) from large-scale pressure
maps. The CPs are described by fuzzy rules which indicate the locations of the pressure centers—lows and highs. The flood
producing circulation patterns are identified using the positive increments of the observed discharge series. The rules are
assessed using a discrete optimization procedure based on simulated annealing. The goal of the optimization is to find CPs
corresponding to high discharge increments. The methodology is applied in two catchments: the Ardèche in France and the
Llobregat in Spain. In both cases typical flood producing CPs could be identified. The occurrence of these CPs does not
necessarily lead to floods, but most important floods were related to them.
q 2005 Elsevier B.V. All rights reserved.
Keywords: Flood; Circulation pattern; Fuzzy rules; Optimization
1. Introduction
Floods are frequently caused by unusual weather
situations. In the temperate climate zone, within
mesoscale catchments, high amounts of precipitation
falling in a short time period are responsible for floods.
The purpose of this paper is to investigate the
meteorological conditions leading to floods and to
identify typical large scale weather features related to
local floods.
It is obvious that there is a close relationship
between atmospheric circulation and climatic
* Corresponding author.
E-mail address: [email protected] (A. Bárdossy).
0022-1694/$ - see front matter q 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2005.02.006
variables. This has been investigated by a large
number of authors since the middle of the 20th
century. Bürger (1958) found a good correspondence
between atmospheric circulation patterns and daily
temperature, precipitation amounts measured for four
German cities (Berlin, Bremen, Karlsruhe and
Munich). Lamb (1977) stated that even the highly
varying precipitation is strongly linked to the atmospheric circulation. Recently, the regional forecasting
of the effects of climate change lead to the development of a large number of methods for downscaling.
There are several methods which link surface
weather variables (precipitation, temperature) to large
scale atmospheric variables such as sea level pressure
(SLP) or geopotential elevations or other derived
indices (vorticity, flow direction) on different time
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
scales (daily/monthly). Wilby et al. (1998a,b) give a
good overview of different techniques. In contrast
little has been done to investigate the relationship
between large scale atmospheric features and discharges (Duckstein et al., 1993). The only exceptions
are the studies investigating the relationship between
ENSO and floods (Waylen and Caviedes, 1989;
Galambosi et al., 1996; Pongracz et al., 2000;
Bartholy et al., 1996). These studies are not based
on daily observations, but relate floodings of a
selected season to El-Nino or La-Nina events.
On a daily time scale the relationship between
large scale features and discharge is difficult to find.
The main reasons for this are:
† the delayed reaction of catchment runoff due to the
concentration time;
† other influencing factors related to the state of the
catchment such as antecedent moisture or previous
rainfall, vegetation features;
† high discharges occur both in the rising as in the
falling limb of the discharge curve.
A possible advantage of considering discharge is
that it integrates the precipitation falling over a large
area, and thus is being less influenced by local
precipitation variability.
In Duckstein et al. (1993) the authors investigate the
occurrence of daily circulation patterns prior to floods
in Arizona. They conclude that there are CPs which
occur statistically significantly more frequently before
floods than on arbitrary other days. Caspary (1996)
investigated the link between the occurrence of floods
in south-west Germany and westerly circulations. He
found that in selected regions all winter floods were
related to zonal circulations. The purpose of this paper
is to investigate the link between CPs and floods and to
develop a methodology for the identification of floodproducing CPs from daily SLP fields.
A better understanding of the meteorological causes
of floods might contribute substantially to the debate on
whether only anthropogenic changes in catchments
have altered the magnitude and frequency of floods.
Further, it might explain changes in flood frequencies
in time and lead to a better design flood estimation.
The paper is organized as follows: the general
methodology is presented next. In Section 3 the
methods are demonstrated using the example of
49
a French catchment (Ardèche) and a Spanish catchment (Llobregat). Finally discussion and conclusions
are presented.
2. Methodology
Downscaling methods for precipitation and temperature are based on the fact that the surface weather
variables on a given day can be directly linked to the
atmospheric circulation on the same day. This is not
the case for discharge, as a high discharge is often the
result of weather on the previous days. A major
problem of linking discharges and atmospheric
circulation is that a high discharge might correspond
not only to a day with heavy rainfall, but also to a dry
day following a flood peak. Therefore, a direct link is
not possible. Instead of investigating the discharges,
daily discharge differences DQ(t) were considered:
DQðtÞ Z QðtÞ K Qðt K DtÞ
(1)
The time window Dt for determination of discharge
increment series depends on the catchment characteristics. For catchments with short concentration times,
Dt can be defined as one day. For catchments with
longer concentration times, Dt might correspond up to
a few days in order to include the lagged relationships.
An increase of the discharge (DQ(t)O0) is caused
by precipitation (or snowmelt). The decrease (DQ(t)!
0) is the natural reaction of the watershed to conduct
excess water out of the catchment. Therefore, for the
analysis of flood producing weather situations days
with (DQ(t)O0) are interesting. Introducing the
positive part of DQ(t) as new variable Z(t):
(
DQðtÞ; if DQðtÞO 0
(2)
ZðtÞ Z
0;
else
One can assume that Z(t) is the additional runoff
caused by weather and linked to the actual atmospheric
circulation. Fig. 1 shows the discharge series Q(t), the
corresponding DQ(t) series and the series of positive
differences Z(t) for the Ardèche at St Martin. The
problem of linking Z(t) to CPs is that in larger
catchments the effect of rainfall on a given day might
also be an increase of the discharge on the subsequent
day due to longer concentration times. However, if
mesoscale catchments with relatively short flow
50
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
The basis of the classification are the SLP or the
geopotential elevation fields. Suppose these data are
available on a regular grid in daily resolution. The
normalized anomalies g(i, t) are calculated from the
gridded SLP data h(i, t) as
gði; tÞ Z
Fig. 1. Daily discharge, discharge difference and positive discharge
difference for the Ardeche river at St Martin in 1983.
duration are considered, the approach is useful.
Further, CPs tend to prevail for a few days making
the identification of critical CPs easier. The advantage
of investigating discharge differences compared to
local precipitation is that they represent areal integrals,
therefore, less subject to local effects and thus can be
better linked to large scale features.
Existing CP classifications are developed for
climatic variables such as precipitation and temperature using subjective or objective (Goodess and
Palutikof, 1998; Jones et al., 1993) classification
methods. These CP types are not necessarily optimal
for the description of flood production. The reason for
this is that local high precipitation events (affecting
only a part of the catchment) might not lead to a
substantial increase of the discharge. Therefore, a
classification to identify CPs leading to high discharge
increases has been developed. The goal is to obtain
CPs which lead to large values of Z(t). The
classification method used is the fuzzy rule based
classification described in detail in Bárdossy et al.
(1995). The fuzzy rules are not identified by the
expert, but instead an optimization algorithm as
described in Bárdossy et al. (2002) is used.
Here only a brief description of the classification
and the optimization is given. The classification
consists of three steps:
1. data transformation,
2. definition of the fuzzy rules, and
3. classification of observed data.
tÞ
hði; tÞ K hði;
sði; tÞ
(3)
where iZ1,.,I are the gridpoints, tZ1,.,T is
tÞ is the mean annual
the time (in days), hði;
cycle (mean over the corresponding Julian date) and
s(i, t) is the standard deviation for the given date.
Each circulation pattern is defined through a fuzzy
rule. This means that to each gridpoint i a fuzzy set
membership function is assigned. Five different
possibilities are considered as follows: the anomaly
at the location is:
1.
2.
3.
4.
5.
large positive,
medium positive,
medium negative,
large negative, and
arbitrary.
While the first four classes describe the locations of
the pressure centers, the fifth indicates locations
whose anomalies are irrelevant for the CP. These
five possible classes of anomalies appear to be
adequate to describe the main CP features. Thus, the
kth CP is described with the fuzzy rule k represented
by a vector v(k)Z(v(1, k),.,v(I, k)). Here, v(i, k) is
the index (1–5) corresponding to gridpoint i for CP k.
The rule system describing K CPs can be represented
by the matrix V:
0
B
V Z@
vð1; 1Þ
«
/ vðI; 1Þ
«
1
C
A
(4)
vð1; KÞ / vðI; KÞ
The v(i, k)s are the indices (1,.,5) of the
membership function corresponding to the selected
locations. The classification of the SLP map of a given
day t is done as follows:
1. The daily SLP map is transformed to a daily
anomaly map;
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
2. For each rule the degree of fulfillment (DOF) is
calculated as follows
!1=pm
4
X
X
1
pm
DOFðk; tÞ Z
m ðgði; tÞÞ
Nk;m vði;kÞZm m
mZ1
(5)
where Nk,m is the number of gridpoints which are
assigned to class m in rule k. mm is the membership
function of the anomalies corresponding to the five
previously defined cases. The exponents pm are
used to account for possible small differences in
the exact location of the anomalies. Their role and
choice is discussed in Bárdossy et al. (1995).
3. The rule k0 with the highest DOF(k, t) is selected,
and the corresponding index k0 is assigned as CP of
the day.
In order to find the optimal rules for the
description of flood producing weather situations,
the performance of the classification has to be
defined. Several different functions can be introduced to measure the performance of the classification with regard to flood prediction. Two
measures are used in this paper, the occurrence of
positive increments and a wetness index. The
performance regarding the probability of the occurrence of a positive increment (a day with increasing
discharge) can be measured with
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
T
u1 X
O1 ðVÞ Z t
(6)
ðpðz0 ðCPðtÞ Z iÞÞ K p z0 Þ2
T tZ1
where p is the probability of an increase of the
discharge exceeding a given limit z0R0 on an
arbitrary day. p(z(CP(t)Zi)) is the probability of an
increase of the discharge exceeding a given limit
z0R0 on a day with CP of class i (CP(t)Zi). The
value of O1 is large, if there are circulation patterns
which often lead to higher than z0 increases of the
discharge Oz0 and others which seldom or never
lead to a high increase of the discharge. Thus this
measure is related flood occurrences. The second
measure is to describe the magnitude of an increase
O2 ðVÞ Z
T
1 X
jzðCPðtÞ Z iÞ z K 1j
T tZ1
(7)
51
where z is the mean increase of the discharge on an
arbitrary day with (zO0). zðCPðtÞZ iÞ is the mean
increase of the discharge on days t with CP i
(CP(t)Zi). This objective measures the relative
performance of the classification compared to no
classification. The value of O2 is large if there are
CP types which lead regularly to high increases of
discharge and others which do not. This measure is
thus related to flood peaks and flood volumes.
The objective of the classification is to identify a rule
system V which maximizes the two above objective
functions. For this purpose a weighted sum of the two
objectives is used as a single objective function where
the weights are defined subjectively assigning higher
weight to O2 since floods peaks and volumes are of
higher interest for us than flood occurrences.
OðVÞ Z w1 O1 ðVÞ C w2 O2 ðVÞ
(8)
The optimization is done over the set of all possible
rule matrices V. Due to the complexity of the problem,
an algorithm based on simulated annealing is used.
Details of the algorithm are described in Bárdossy et al.
(2002).
3. Application
The above described methodology was applied to
two different catchments: the Ardèche in France
which is a Rhone tributary with a catchment area of
2240 km2 at St Martin, and the Llobregat at Martorell
in Spain, with a catchment area of 4561 km2 flowing
to the Mediterranean through an industrial area to the
south of the city of Barcelona.
Fig. 2 shows the locations of the catchments.
In both catchments, intense rainfall causes a fast
increase of the discharge and leads to occasional
floods. The concentration times of the basins are short
and both rivers flow naturally without being under
considerable artificial influences. Water management
activities usually do not cause sudden substantial
increases of the discharge, thus do not have a major
effect on our analysis.
Daily discharge series for both catchments were
used and DtZ1 day was selected.
On Fig. 1 the discharge series (Q(t)) for the
Ardèche and the corresponding series of discharge
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A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
Fig. 2. Locations of the Ardeche and Llobregat catchments.
changes (DQ(t)) were shown. One can clearly observe
in the figure a few sudden dramatic increases followed
by a fast decrease. In the most part of the year the
discharge changes remain insignificant. The positive
part of the series is the result of precipitation falling,
which can be considered as random process. The
negative changes are due to the mostly deterministic
reaction of the catchment to excess water.
Fig. 3 shows the location of the gridpoints of
the SLP data were used for the classification. The
gridded sea level pressure data that represent the
observations originate in the National Center for
Environmental Research (NCEP) analysis provided
by National Center for Atmospheric Research
(NCAR, USA). The resolution of data is 5!58.
SLP data were used to produce long CP—time
series. The daily SLP data set is available for the
time period 1899–2003.
The classification of weather conditions is done
specifically for each catchment. For the Ardèche
catchment IZ84 gridpoints in total were used and
KZ10 rules leading to 10 CPs were assessed whereas
for the Llobregat catchment, KZ12 rules were
determined leading to 12 CPs.
The performance of the classification was
measured using a split sampling approach. Ten
Fig. 3. Locations of the gridpoints used for SLP classification.
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
53
Table 1
Statistics of Z(t) for different CPs for the Ardèche catchment
Ardèche St Martin (October–April)
CP
Frequency (%)
Probability of
increase (%)
Contribution
(%)
Wetness
index(K)
Mean (m3/s)
Standard deviation
(m3/s)
CP01
CP02
CP03
CP04
CP05
CP06
CP07
CP08
CP09
CP10
Unclassified
7.33
2.27
5.20
8.55
1.57
3.93
15.04
21.11
11.11
19.84
4.04
51.13
31.71
29.43
47.95
43.53
23.94
28.10
25.44
29.07
26.79
34.25
31.82
2.56
1.47
33.73
4.25
1.97
5.94
4.98
4.23
7.03
2.01
4.34
1.13
0.28
3.95
2.71
0.50
0.39
0.24
0.38
0.35
0.50
113.8
47.7
12.9
110.3
83.4
28.0
18.8
12.4
17.5
17.7
19.5
224.6
189.4
26.2
216.4
121.7
53.0
52.7
36.1
50.6
44.3
40.3
years of discharge data (1981–1990) were used in
the optimization algorithm to identify the matrix V.
Then, the rule system was applied to a control
period (1951–1980) to see, whether the rule system
captured the main features correctly. The objective
function values for this control period were
compared to those of the learning period. In all
cases, there were no significant differences between
the statistics corresponding to the learning and the
validation period.
Table 1 shows the results for the Ardèche
catchment for the time period from October to
April. All considerable flood events occurred in that
time period of the year, therefore, the evaluation is
also restricted to this time interval.
The frequencies of the different CPs, the conditional frequency of discharge increases on days with
a given CP, the relative contribution of the CP to the
total discharge increases are given in Table 1. The
wetness index of a CP is the ratio of the relative
contribution of a CP to the increases by the frequency
of the CP. The higher this index, the more the increase
is caused by the CP (wetness index !1 indicates a dry
CP; wetness indexZ1 neutral; wetness index O1 wet
CP). The conditional mean and the standard deviation
of Z(t) are also given. According to the table three
CPs; CP01, CP04, and CP05 cause stronger discharge
increases than normal. By comparing the frequency
and the wetness index of these CPs, it can be
concluded that CP01 and CP04 are more important
Table 2
Statistics of Z(t) for different CPs for the Llobregat catchment
Privas (October–April)
CP
Frequency (%)
Probability of
increase (%)
Contribution
(%)
Wetness index
(K)
Mean (mm)
Standard deviation
(mm)
CP01
CP02
CP03
CP04
CP05
CP06
CP07
CP08
CP09
CP10
Unclassified
7.32
2.27
5.18
8.46
1.57
3.95
15.10
21.24
11.08
19.78
4.06
70.78
36.59
38.43
62.75
64.71
35.51
19.41
16.32
28.45
22.74
45.00
27.13
3.70
3.45
22.70
5.02
3.94
6.71
5.97
5.69
11.84
3.87
3.71
1.63
0.66
2.68
3.20
1.00
0.44
0.28
0.51
0.60
0.95
15.06
12.82
4.98
12.30
14.23
8.09
6.58
4.95
5.19
7.57
6.09
18.92
15.63
9.55
16.21
17.64
11.27
9.48
8.84
8.54
10.19
10.00
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A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
Fig. 4. Mean SLP anomalies corresponding to the circulation pattern CP01 for the Ardèche catchment—a pattern causing most of the floodings.
Dashed lines show negative solid lines positive anomalies.
than CP05. They contribute to 70% of all discharge
increases. CP01 is extremely wet causing 434%
increase compared to a normal day. Due to the fact
that CPs might cause precipitation leading to a
discharge increase on the following day, the contribution of days following CP01 or CP04 was also
calculated. These days bring 10% of the total increase,
so 80% of the total increase can be considered as a
consequence of CP01 and CP04.
In order to see the precipitation behavior of the
region conditioned on the CPs, the statistics corresponding to the station Privas in the Ardèche
catchment were calculated. The results are shown in
Table 2.
Obviously, the same patterns cause high precipitation as discharge increases. The relative contribution of patterns CP01 and CP04 deviates slightly
less from normal for precipitation than for discharge
increase. A possible explanation for this outcome is
that precipitation might also occur on days with other
CPs without causing considerable changes in
discharge.
Fig. 4 shows the normalized anomalies of the SLP
for the circulation pattern CP01 in the Ardèche. A low
pressure anomaly on the Atlantic north–west from
the Iberian peninsula and a high pressure anomaly
over the eastern Mediterranean region characterize
this CP. As shown in Table 1 this pattern is
Fig. 5. Observed annual maxima of discharges for the Ardeche at St
Martin and the weather patterns responsible for the increase.
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
55
Table 3
Statistics for Z(t) for days with CP01, 1 days after CP01, and 2 days after CP01 occurrences
Llobregar–Martorell (September–May)
CP
CP01
1 day after CP01
2 days after
CP01
Other days
Probability of
increase (%)
Contribution (%)
Wetness index
(K)
Mean (m3/s)
Standard deviation (m3/s)
7.32
5.11
4.53
35.23
29.41
16.77
46.61
16.01
3.11
6.37
3.13
0.69
27.2
16.0
6.2
73.4
29.4
10.8
83.04
15.38
34.27
0.41
4.0
10.0
Frequency (%)
responsible for most of the discharge increases, and
thus leading to floods. In order to see to what extent
the wettest CPs might explain floods the series of
annual discharge maxima was investigated. CPs prior
to the maxima corresponding to the major increase of
discharge were identified. Fig. 5 shows the observed
annual maxima with the corresponding return periods
and CPs. One can see that only three of the annual
maxima of the period 1955–1997 were not caused
preceded by CP01 and CP04. Two of the three were
related to CP05, which was also identified as a wet
pattern. Only the 1955 event which ranks 14th was
caused by a different CP, namely CP10.
The results for the Llobregat catchment are similar.
There one single CP is responsible for most of the
discharge increases. All others are causing smaller
increases than normal. The statistics for days with
CP01 and on days following CP01 (1 day and 2 days
after CP01) in Table 3 show that the influence of wet
CP (CP01) decreases rapidly since the catchment
reaction is fast. Fig. 6 shows the anomaly map
corresponding to the wettest CP for the Llobregat. The
catchment is influenced by a low anomaly centered
Fig. 6. Mean SLP anomalies corresponding to the circulation pattern CP01 for the Llobregat catchment—a pattern causing most of the
floodings. Dashed lines show negative solid lines positive anomalies.
56
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
Fig. 7. Observed annual maxima of discharges for the Llobregat
(1912–1990) and the corresponding weather patterns.
over the western part of Mediterranean Sea, east from
the Spanish coast.
The annual discharge maxima in the Llobregat
basin between 1912 and 1990 can be seen in Fig. 7.
One can conclude that all the big floods in the basin
were related to the wet CP. On the other hand not all
days and time periods with the wet CP are related to
large floods. This means that the occurrence of CP01
can be regarded as a necessary but not as a sufficient
condition for floods. For the two catchments in 10–
15% of the cases the occurrence of the CP was related
to a flood event.
4. Discussion and conclusions
A methodology to identify flood producing CPs in
mesoscale catchments was developed.
The results show that positive increments of the
daily discharge can be used in mesoscale catchments
as a useful indicator to identify flood producing
circulation patterns. This type of approach works
reasonably well in catchments with fast reactions to
precipitation. For larger catchments with slower
reactions, discharge increments have to be related to
more than one days weather in order to consider
the delayed hydrological response of the basin. This
time lag can be involved in the classification of CPs
within the optimization of the fuzzy rules. The rules
are optimized by measuring the performance of
the classification regarding the probability of the
occurrence of a positive increment within the time lag,
which is catchment specific. Further, artificial factors
which might affect the river flow can be considered in
case if their consequences are significant for the
investigation of floods.
The automatic derivation of fuzzy rules led to
meteorologically reasonable CPs. The CPs derived
from discharge increments can be used to describe the
precipitation behavior of the catchments. A split
sampling approach shows that CPs can be derived
from using 10 years of observed discharge and SLP
anomalies. Most of the annual discharge maxima were
preceded by one or two critical CPs.
Beyond SLP data, the differentiation of significant
changes in flow from insignificant ones can be
achieved by using geopotential elevations, specific
humidity and derived indices like vorticity and flow
direction. However, in this study, the preference was
given to SLP data due to its availability since the
beginning of 19th century.
The above developed methodology can be used
to investigate long series of CP occurrences with
respect to flooding in selected catchments. This way
possible non-stationarities of the series of extremes
can be investigated and detected. The understanding
of flood producing circulation might have an
influence on extreme value statistics, as different
mechanisms might produce different extremes.
Further research is needed to investigate this
possibility in detail.
This methodology can be used in catchments
without an important influence of ice and snow. The
reason for that is catchments with snow-melting have a
different precipitation-discharge characterization. The
increases in discharge during snow-melting are not
necessarily corresponding to wet CPs, but warming
temperatures. Therefore, a different approach is
needed to link discharge and CP in this case.
The approach might also be applied for reconstructing pre-instrumental flood frequencies and to
downscale future flood events from future GCM
output.
A. Bárdossy, F. Filiz / Journal of Hydrology 313 (2005) 48–57
Acknowledgements
EU SPHERE: This research has been carried
out as part of the EU funded SPHERE project
(Systematic Palaeoflood and Historical data for the
improvEment in flood Risk Estimation), contract no.
EVG1-CT-1999-00010.
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