relating macroclimatic circulation patterns with characteristics of floods and droughts at the...

Journal of Hydrology (2007) 335, 109–123

ava i lab le a t www.sc iencedi rec t . com

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Relating macroclimatic circulation patternswith characteristics of floods and droughtsat the mesoscale

Luis Samaniego a,*, Andras Bardossy b

a Helmholtz-Centre for Environmental Research-UFZ, Permoserstrasse 15, 04318 Leipzig, Germanyb Institute of Hydraulic Engineering, University of Stuttgart, Pfaffenwaldring 61, 70550 Stuttgart, Germany

Received 20 June 2006; received in revised form 9 October 2006; accepted 10 November 2006

00do

*

KEYWORDSStatistical downscaling;Hydrological extremes;Land use/cover change;Generalized models;Heteroscedasticity

22-1694/$ - see front mattei:10.1016/j.jhydrol.2006.11

Correspondingauthor.Tel.:E-mail address: luis.saman

r ª 200.004

+493412iego@ufz

Summary The prediction of extreme hydrological events in mesoscale catchments hasbeen a main concern in hydrology because of their considerable societal impacts andbecause of the compelling evidence that anthropogenic activities significantly modifytheir occurrence likelihood. In this paper, nonlinear generalized models were used to pre-dict extreme runoff characteristics like the specific volume, the frequency of high-flows,and the total drought duration. Explanatory variables included many physiographic, landcover, and climatic characteristics such as mean slope, aspect, elevation, type of geolog-ical formations, shares of a given land cover type, and many composed indicators relatingantecedent precipitation index and atmospheric circulation patterns. All time-dependentvariables were estimated semiannually for each subcatchment. The proposed method wastested in 46 subcatchments belonging to the Upper Neckar River basin covering an area ofapproximately 4000 km2 during the period from 1961 to 1993. The results of this studyindicated that macro circulation patters derived from either subjective or operationalclassifications combined with other explanatory variables can be effectively used to pre-dict seasonal extreme runoff characteristics at the mesoscale. Moreover, the results indi-cated that most runoff characteristics exhibited a distributional element other thannormal and that the selection of nonlinear generalized models was an appropriate choiceto deal with the heteroscedasticity of model errors.ª 2006 Elsevier B.V. All rights reserved.

6 Elsevier B.V. All rights reserved

353971;fax:+493412353939..de (L. Samaniego).

Introduction

The quantification of the magnitude and duration of meteo-rological extremes, as well as their probability of occur-rence in a mesoscale catchment, has long been a main

.

mailto:[email protected]

110 L. Samaniego, A. Bardossy

concern in hydrology and related disciplines because theseanomalies might induce significant changes on severalwater-cycle-related state variables (e.g. soil moisture).These changes, in turn, might lead to the occurrence of eitherflood or drought spells (high- and low-flow regimes). Themag-nitude of the environmental degradation and the subsequentdemographic and economic impacts at regional level arestrongly dependent on the magnitude and duration of theseevents. Typical examples of the environmental degradationinduced by the shortage of water are forest fires, stress onthe supply side of the food chain, and soil erosion caused bythe combined effects of vegetative cover reduction and windaction. An excess of water, on the other hand, also createsenvironmental problems such as the destruction of the ende-mic flora and fauna, insect infestations, and soil erosioncaused by rill and gully erosion. Both extreme events entailsubstantial socioeconomic consequences such as heavy reduc-tion of agricultural production and power generation, dam-ages to the basic infrastructure and the manufacturingsector, as well as famines and people’s migration.

Moreover, there is compelling evidence (e.g. see Hough-ton et al. (2001)) that the anthropogenic disruptions of theenvironment are significantly modifying the likelihood ofoccurrence of these events in a given period. Consequently,it would be crucial to investigate how the magnitude andthe probability of occurrence of high- and low-flows mightbe affected by land use/cover and climatic changes.

Hydrological extremes occurring at the mesoscale arelargely dependent on the occurrence of particular macrocli-matic processes in the atmosphere, which are currentlymodeled by complex General Circulation Models (GCMs).GCMs, however, are not able to predict mesoscale hydro-logic extremes mainly because these models are conceivedto represent the main features of the atmospheric circula-tion rather than the regional climatic details. Moreover,GCM outputs depend on a given forcing scenario (e.g. CO2

emissions) and, therefore, are highly uncertain.In spite of that, it is possible to use their outputs, among

them upper level winds, geopotential heights, and sea levelpressure, as predictors of mesoscale observations such asprecipitation. This procedure, which is generally termedempirical downscaling, is carried out using methods likemultiple linear regressions, neural networks (Cannon andWhitfield, 2002), fuzzy rules (Bardossy et al., 2002), orregression tree approaches (Li and Sailor, 2000).

Another downscaling alternative is to use proxies for thestate of the atmosphere at a given location and time as pre-dictors of mesoscale variables. These proxies include: mac-roclimatic indexes such as the Pacific North America Index(PNA), the El Nino Southern Oscillation (ENSO), or the Euro-pean atmospheric Circulation Patterns (CP) (Hess andBrezowsky, 1969). This type of information is particularlyrelevant to assess the effects of macroclimatic changes inmesoscale catchments, especially in ungauged basins or inthose with very low-density of meteorological stations.For instance, Reddmont and Koch (1991), Bardossy andPlate (1992), and Shorthouse and Arnell (1997) used thisprocedure to link macroclimatic indices with the magnitudeand the spatial distribution of meteorological variables (e.g.precipitation, temperature). Alternatively, Dracup andKahya (1994), Piechota and Dracup (1996), and Stahl andDemuth (1999) linked them with stream flow characteristics

such as partial duration of floods or drought spells. To ourknowledge, however, there is no reference in the literature(excluding Samaniego (2003)) in which this approachhas been used to assess simultaneously the influences ofland use/cover and climate changes on hydrologicalextremes.

Two main types of CP classification techniques, subjec-tive and objective, can be distinguished in the literature.The main advantage of the subjective classification is thatthe meteorologist’s experience is applied on a daily basisin the classification. This advantage, however, entails ashortcoming for some practical applications such as mediumrange forecasting; namely, that the results of the classifica-tion can not be reproduced automatically (Yarnal, 1993).Objective classifications, on the contrary, operate on a givendata set and derive day-by-day classified CPs using auto-mated algorithms. The results of this kind of classificationare ideal for the integration with climate-change simulationsbecause they can be reproduced rapidly without humanintervention (Bardossy et al., 2002; Bardossy and Filiz, 2005).

In this study, low- and high-flow characteristics were re-lated to existing CP classifications. The stochastic downscal-ing method was subsequently tested in the Upper NeckarCatchment in Southern Germany.

Method

Problem formulation

The purpose of this paper is to find robust cause–effectrelationships between a given runoff characteristic (i.e.one that accounts for a high-, or low-flow regime in a catch-ment) and a selected set of variables in given spatial andtemporal domains. These relationships relate a given runoffcharacteristic with a set of explanatory variables such as:(1) physiographical factors, (2) shares of land cover types,and (3) climatic or meteorological factors. These variablesare related to known physical processes that take place ina given catchment but are not the result of a physically-based analysis. The proposed method is consequently data-base driven and searches for significant signals within theavailable information. To apply this modeling approach,the following definitions are necessary.

Let Ytil denote the l runoff characteristics, related with

low- or high-flows, observed in basin i during year t, andfl(Æ) a nonlinear, differentiable, and monotonic functionrelating it to a set of explanatory variables fxti1; . . . ;xtij; . . . ; xting � fhMi

ti ; hUi

ti ; hGi

tig. Here j denotes the variable

index and n the total number of explanatory variables.Each vector hMiti , hUi

ti , and hGi

ti is composed of variables

that are evaluated at the mesoscale, which denote: (1) cli-matic or meteorological, (2) land cover, and (3) physio-graphical characteristics, respectively. The operator h Æ idenotes a vector composed by either the integral or a spa-tial statistic obtained from a set of variables defined on agiven spatial and temporal domain. Moreover, let b be avector of parameters to be calibrated and validated basedon historical records, and etil be an additive error term withzero mean but otherwise of undefined distribution. Based onthese definitions, the general form of the relationship canbe written as

Relating macroclimatic circulation patterns with characteristics of floods and droughts at the mesoscale 111

Ytil¼ fl hMiti ;hUi

ti ;hGi

ti ;b

� �þetil 8i¼1; . . . ;I t¼1; . . . ;T ð1Þ

where I and T denote the total number of basins, and the to-tal number of years of the calibration period respectively.

The variables required for Eq. (1) are based on the bestpossible information describing the relevant basin’s charac-teristics at the mesoscale. For example, one could use landcover classifications obtained from hyperspectral remotesensing data, physiographic characteristics of the basin de-rived from digital elevation models, soil types and theirrespective physical parameters together with geologic for-mations obtained from field campaigns and existing mapsat the mesoscale, or time series for discharge and climaticvariables. To account for macroclimatic changes one coulduse stochastic downscaling procedures to generate wetnessand dryness indices that could be linked with high- and low-flow regimes at the mesoscale. The derivation of such indi-ces is described next.

Downscaling circulation patterns

In the present study, the subjective CP classification pro-posed by Hess and Brezowsky (1969) and two objective CPclassifications developed by Bardossy and Filiz (2005) were

Table 1 European circulation patterns according to Hess and Br

Major type Sub-type Index k Descript

Zonal circulation W 1 West, an2 West, cy3 Southern4 Anglefor

Mixed circulation SW 5 Southwe6 Southwe

NW 7 Northwe8 Northwe

HM 9 Central10 Central

TM 11 Central

Meridional circulation N 12 North, a13 North, c14 North, Ic15 North, Ic16 British Is17 Central

NE 18 Northea19 Northea

E 20 Fennosc21 Fennosc22 Norwegi23 Norwegi24 Southea25 Southea

S 26 South, a27 South, c28 British Is29 Western

Unclassified U 30 Classific

employed to downscale the macroclimatic state of theatmosphere as predictors for several mesoscale runoffcharacteristics.

The subjective classification is a synoptic meteorologicalclassification defined for a large spatial domain (40�W, 30�Nand 60�E, 80�N). This index is usually referred to as theEuropean atmospheric circulation patterns and is currentlyused by the German Weather Service. This classification isbased on mean air pressure distribution over Europe andthe northern Atlantic Ocean and differentiates among threemajor circulation types called zonal, mixed, and meridio-nal. These major types are, in turn, further subdividedaccording to the direction of movement of frontal zones,location of high- and low-pressure areas, and cyclonic andanti-cyclonic rotation. As a result, there are 29 plus oneunclassified CPs as shown in Table 1.

The two objective classifications were optimized for aspecific spatial domain and are specific for low- and high-flows. The fuzzy rule-based optimization was carried outwith the method proposed by Bardossy et al. (2002). Thetechnique used for the classification of the high-flow relatedCPs was already reported in Bardossy and Filiz (2005). A sim-ilar technique, with the exception of the objective function,was used to derive low-flow related CPs.

ezowsky (1969)

ion Abbreviation

ticyclonic Waclonic Wz, West WSmed West WW

st, anticyclonic SWast, cyclonic SWzst, anticyclonic NWast, cyclonic NWzEuropean high HMEuropean ridge BMEuropean low TM

nticyclonic Nayclonic Nzeland high, anticyclonic HNaeland high, cyclonic HNzles high HBEuropean trough TRMst, anticyclonic NEast, cyclonic NEzandian high, anticyclonic HFaandian high, cyclonic HFzan Sea-Fennoscandian high, anticyclonic HNFaan Sea-Fennoscandian high, cyclonic HNFzst, anticyclonic SEast, cyclonic SEznticyclonic Sayclonic Szles low TBEurope trough TRW

ation not possible U


The purpose of the classification was to identify a se-lected number of classes so the members of these classes:

(1) Behaved similarly with respect to rainfall and/or dis-charges. This means that the classes should be ashomogeneous as possible.

(2) Behaved differently from the mean. This means thatthe classification should enable a distinction withrespect to the selected variable. A wet/dry situationhas to be identified.

The classification was based on the large scale atmo-spheric variables such as the Sea Level Pressure (SLP) orthe 500 hPa geopotential height anomaly obtained fromthe National Meteorological Center (NMC) gridpoint dataset for different windows over Europe with a grid resolu-tion of 5� · 5�. In this study the classification was per-formed by optimization using an objective function thatevaluated the performance of the classification and theSLP data. In this study, two kinds of objective functionswere considered.

For floods, positive increments of the discharges wereused to define the objective function

OFðRÞ ¼1

TD

XTt¼1

XDd¼1

zðCPtðdÞ ¼ kÞ�z

� 1

�� ð2Þ

where �z is the mean increase of the discharge on an arbi-

trary day at a given location i with (z > 0). zðCPtðdÞ ¼ kÞ isthe mean increase of the discharge on days t(d) with CP k(CPt(d) = k), and D the number of days of the year t. The rulesystem describing K CPs is represented by the matrix R–formore details please refer to Bardossy and Filiz (2005). Thisobjective measures the relative performance of the classifi-cation compared to no-classification. The value of OF islarge if there are CP types which lead regularly to high in-creases of discharge and others which do not. This measureis thus related to flood peaks and flood volumes.

For droughts, this approach is not optimal, as small or nodischarge changes are not necessarily related to low-flowsor droughts. Therefore rainfall data measured at differentstations were used to define the objective function as

ODðRÞ ¼1

TDM

XTt¼1

XDd¼1

XMm¼1

lnzmðCPtðdÞ ¼ kÞ

�zm

!�� ð3Þ

In this case, �zm is the mean precipitation at location m and

zmðCPtðdÞ ¼ kÞ is the mean precipitation at location m ondays t(d) with CP k (CPt(d) = k), and M is the number of mea-surement locations considered. The logarithmic transforma-tion ensures that CPs with lower than normal precipitationare considered stronger than in the case of the linear typeevaluation used in Eq. (2).

Both classifications were calibrated and validated for aspecific region and are composed of twelve categories(K = 12) ranging from CP1 to CP12 and one unclassified onecalled CP13. The procedure used in this study to downscalethe proposed CPs is described next.

The first step was to cluster the CPs into two or threegroups denoted as wet, normal and dry periods, using forthis purpose a seasonal wetness index Wk (Bardossy, 1993)estimated as follows:

Wk ¼1P

Pt

Pd2Stp

tðdÞk

1T

Pt

Pd2Stu

tðdÞk

ð4Þ

with

ptðdÞk ¼ hpitðdÞ if CPtðdÞ ¼ k ^ d 2 St

0 otherwise

(ð5Þ

utðdÞk ¼ 1 if CPtðdÞ ¼ k ^ d 2 St

0 otherwise

�ð6Þ

P ¼Xt

Xd2SthpitðdÞ ð7Þ

and wherehpit(d) is the expected daily precipitation at the study

area X. The operator h Æ i denotes the integral ofthe daily precipitation p over the domain X occur-ring during the day d of the water yeart 2 {1, . . . ,T}.

CPt(d) is the atmospheric circulation pattern indexaccording to Hess and Brezowsky for a given dayd of the water year t.

St is a set indicating whether a the day d belongs tosummer or winter. St takes the values {1, . . . ,dw}and {dw + 1, . . . ,D} for winter and summer, respec-tively. If t denotes a leap year, then dw = 182 andD = 366; otherwise dw = 181 and D = 365.

P is the total summer or winter precipitation withinX during the calibration period in millimeter.

k is a CP-type index whose equivalence is either gi-ven in Table 1 or defined automatically by the clas-sifier.

The wetness index defined in Eq. (4) represents the ratiobetween the relative amount of precipitation in summer orwinter occurring during those days with the CP-type k andthe relative frequency of such CP. Using Wk, the CPs canbe grouped into three categories by applying the followingrules:

if

Wk 6 s1 ) k 2 fDry=seasongs1 < Wk 6 s2 ) k 2 fNormal=seasongWk > s2 ) k 2 fWet=seasong

8><>: ð8Þ

If only dry and wet periods–in any season–are required thenthe thresholds s1 and s2 must be equal.

The second step consisted of defining the following indi-ces based on the previous classification, namely:

xtij ¼XD

d¼dwþ1#tðdÞij j ¼ 1; 2 ð9Þ

xtij ¼Xdwd¼1

#tðdÞij j ¼ 3 ð10Þ

with

#tðdÞij ¼

1 if j ¼ 1 ^ xtðdÞi4 � xtðd�1Þi4 < 0

CPtðdÞ 2 fDry=summerg

(

1 if j ¼ 2 ^ xtðdÞi4 P Fcðx4ÞCPtðdÞ 2 fWet=summerg

(1 if j ¼ 3 CPtðdÞ 2 fWet=winterg0 otherwise

8>>>>>>>>>><>>>>>>>>>>:ð11Þ


and

xtðdÞi4 ¼XCc¼0ðtÞchpitðd�cÞ ð12Þ

wheret is the recession constant, commonly ranging within

the interval 0.85 < t < 0.98 (Chow, 1964).Fc(x) is a threshold value representing the cth percentile

of variable x.c is a time index denoting the precipitation occurred

c days before the event t(d). A common range for cis from 15 to 120 days.

The variable x1 obtained with Eq. (9) is aimed at finding arelationship between the occurrence of ‘‘dry’’ circulationpatterns and low-flows–i.e. YtðdÞ

i 6 F10ðYiÞ–occurring dur-ing summer. Hence, it tallies the total number of occur-rences of CPs clustered as ‘‘dry periods’’ for a givencatchment i during summer of a year t which have simulta-neously a decreasing API (i.e. days where d

dtx4 < 0).

Variables x2 and x3 in Eq. (10), on the contrary, are in-tended to analyze relationships for peak flows–i.e.YtðdÞ

i P F95ðYiÞ. The former counts the number of days insummer on which both the occurrence of ‘‘wet’’ circulationperiods and an antecedent precipitation index greater thana given threshold occur simultaneously. In other words, thisindex assumes that a flood may be expected if a certain cli-matic condition and a given amount of precipitation duringa continuous period have already occurred. The latter tal-lies simply the number of occurrences of wet circulationperiods during winter.

Modeling high- and low-flow characteristics

Modeling extreme runoff characteristics–here denoted bythe variable Y–is, in general, a challenging task becauseof their highly skewed probability density functions (PDF).Empirical studies carried out with extreme runoff charac-teristics have shown that the error term of multivariatemodels–represented by e in Eq. (1)–has a PDF other thanthe normal, or in other words, it is heteroscedastic (Sama-niego, 2003). Consequently, standard methods such as mul-tivariate linear or nonlinear regression generally fail toproduce unbiased and acceptable fits if the common Gauss-ian assumption is not relaxed (i.e. the error term e should benormally distributed with zero mean and a constantvariance).

There are currently many possibilities to address thisproblem: (1) To introduce variable transformations as inMontgomery and Peck (1982) or to weight the residualsin the objective function according to their reliability asproposed in Gentleman (1974) and Draper and Smith(1981); (2) To use multivariate copulas to establish thedependence among the marginals of many random vari-ables (Schweizer and Wolff, 1981; Favre et al., 2004); or(3) To use a generalized model to deal with the varianceof a given random variable in a proper manner (Clarke,1994; Lindsey, 1999. In this paper, the latter approachwas adopted.

In general, the structure of a generalized model is com-posed of three elements:

(1) The deterministic element, also called the predictor,gt

i, which is a suitable function of the explanatory vari-ables xt

i, thus

gtil ¼ flðxt

i ; bÞ ð13Þ

(2) The distributional element, which indicates that thevariance of the response Y t

ij is an explicit function ofthe expectation at each observation denoted by lt

il,hence

E½Ytil� ¼ lt

il ð14Þvar½Yt

il� ¼ jVðltilÞ ð15Þ

and that Ytil is h distributed with distributional param-

eters a.(3) The link function g(Æ), which is a nonlinear, monotone,

and differentiable function that establishes a linkbetween the deterministic and the stochastic part ofthe model, so that

gðltilÞ ¼ gt

il ð16Þ

where xti is a vector of observed variables at the basin i and

point in time t, j denotes a dispersion parameter, a are thefitted parameters of the probability density function h(Æ),and V(Æ) is a variance function.

This formulation differs from the standard GeneralizedLinear Model (GLM) in one respect only, namely: that thefunction fl(Æ) can be assumed either linear or nonlinear. Bydoing so, there is more flexibility to handle the intertwinedrelationships between the predictors and the predictand.

Model selection and parameter estimation

The model selection was done in two steps: (1) a prioriselection of a functional form for the Eq. (1) according toa parsimonious criterion and/or available knowledge onthe relationships between some of the related variables,and (2) the selection of the most robust model once a func-tional relationship is given.

In the present study, once a nonlinear relationship wasselected, a constrained multi-objective optimization prob-lem–whose solution space comprised all feasible combina-tions of given explanatory variables–was then solved. Bydefinition, a feasible combination consisted only of statisti-cally significative variables in which each subcategory musthave at least one variable, i.e. hMiti , hUi

ti , hGi

ti 6¼ ;. Here,

the significance of each variable was assessed by a nonpara-metric test (Efron, 1982).

Among all competing models, the most robust model isthat which is least sensitive to the selection of the estima-tor. In the present study two estimators were used for theselection of the most robust model structure (i.e. variablecomposition), namely: L1 and L2. The former denotes thesum of the absolute residuals whereas the latter denotesthe sum of the squares of residuals. These two estimatorswere selected a priori. Other possibilities are conceivabletoo, e.g. two different likelihood functions. Consequently,the best model should simultaneously surpass the others intwo predefined objectives:

Uo ¼XI

i¼1

XTt¼1

Ytil � eY t

ilðLoÞ� �2

o ¼ 1; 2 8l ð17Þ


where Uo is a jackknife statistic (Quenouille, 1949) found byminimizing the estimator Lo with o = 1,2. For the estimationof each eY t

il, the vector xti was sequentially excluded from

the data set. Subsequently, model parameters were cali-brated with the rest of the sample and finally eY t

il was eval-uated for xt

i . This procedure was repeated "i,t. To improvethe performance of the optimization algorithm and ease thecomparison between the objective functions all variables(i.e. both the input and output ones) were transformed(scaled) to the interval (0,1]. The jackknife statistics werenot normalized as shown in Eq. (17).

Once both the functional form and the model structurewere selected, the estimation of model parameters b wascarried out by maximizing the log-likelihood function ‘(Æ)whose general form for the explained variable Yt

il is

maxb

‘ðbÞ ¼Xi;t

ln hðYtiljxt

i ; a; bÞ ð18Þ

and, its corresponding goodness of fit was assessed by theAkaike’s Information Criterion AIC (Akaike, 1973) as follows:

AIC ¼ �2‘ðbÞ þ 2p� ð19Þ

where hðYtiljxt

i ; a; bÞ denotes the probability density function(PDF) of Yt

il assuming that all observations are independent,and p* is the number of parameters used to define the modelfl(Æ). It should be noted that minimizing the estimator L2 im-plies that the explained variable and the residuals are as-sumed normal distributed. The maximum likelihoodmethod was used here to introduce a given distributionalelement. For more details on this approach please refer toSamaniego (2003) and Samaniego and Bardossy (2005).

Application

The study area and information available

The proposed method was tested in the upper catchmentof the Neckar River upstream of the Plochingen gauging

Figure 1 Location of the study area within the state of Baden-Wuralso displayed.

station covering an area of approximately 4000 km2

(Fig. 1). The data concerning this Study Area were ob-tained from several sources as indicated in Table 2. Allvariables described in Eq. (1) were integrated both inspace, at subcatchment level, and in time, at semiannualintervals. The spatial domain of each subcatchment com-prised the drainage area of 46 gauging stations (I = 46) lo-cated in the Study Area, whose area ranged from 4 km2 to4000 km2. With respect to the time domain, the gaugeddischarge was aggregated from event scale (day) duringthe period from 1960.11.01 to 1993.10.31, into semiannualintervals termed summer or winter to minimize theexisting autocorrelation, hence T = 33. To validate thesedata, an annual water balance for each subcatchmentwas calculated and all those observations exceeding athreshold value were excluded as outliers (Samaniego,2003). Every predictor and explained variable listed inTable 2 were estimated for each subcatchment and timeinterval based on data provided by several German StateAgencies, as is indicated in the same table.

A priori structures of the model

In the present study, four types of functional relationshipsfl(Æ) were selected to represent presumed relationships be-tween the explanatory variables and the predictor, there-fore, they should be seen as hypotheses rather thanmodels. The configuration of the predictor was based on cri-teria such as simplicity of model structure and parsimony ofparameters. They, however, should help to reveal the kindof linkage that may exist among the system’s processes rep-resented here by the observables listed in Table 2. Conse-quently, four combinations of variables mixing linear and/or nonlinear functions were investigated, namely: (1) amultilinear (ML), (2) a potential (POT), and (3) two multi-linear-potential (MLP1, MLP2) relationships. Formally, theserelationships can be written as

ttemberg, Germany. The location of subcatchments A and B are

Table 2 Explained variables, selected predictors, and data sources used in this study

Source Variable Description

Time series of mean daily flows from 1961 to 1993(Institute for Environmental ProtectionBaden-Wurttemberg, LfU)

Y1 Specific volume of high flows in winter (mm)Y2 Specific volume of high flows in summer (mm)Y3 Total duration of high flows in winter (day)Y4 Total duration of high flows in summer (day)Y5 Frequency of high flows in winter (year�1)Y6 Frequency of high flows in summer (year�1)Y7 Total drought duration in summer (day)Y8 Cumulative specific deficit in summer (mm)

European Circulation Patterns according toHess and Brezowsky,and precipitation time series (GermanMeteorological Service, DWD)

x1 A dryness index tallying the total No. of ‘‘dry periods’’with decreasing API in summer (day)

x2 Total number of ‘‘wet periods’’ occurring,simultaneously with an API greater than a giventhreshold in summer (day)

x3 Total number of ‘‘wet periods’’ in winter (day)

Time series of daily precipitation and temperature for288 meteorological stations in Baden-Wurttemberg from1961 to 1993 (LfU and DWD). Each day was interpolatedwith External Drift Kriging to a spatialresolution of 300 m · 300 m

x4 Antecedent precipitation index (API) (mm)x5 Cumulative winter precipitation (mm)x6 Cumulative summer precipitation (mm)x7 Mean winter precipitation (mm)x8 Mean summer precipitation (mm)x9 Mean temperature in January (K)x10 Mean temperature in July (K)x11 Maximum temperature in January (K)

Topographic map 1:25 000 for 1961 (State SurveyingAgency Baden-Wurttemberg, LVA) and LANDSATscenes from 1975, 1984, and 1993

x12 Fraction of forest cover (–)x13 Fraction of impervious cover (–)x14 Fraction of permeable cover (–)

DEM 30 m · 30 m (LVA) x15 Area of a given catchment (km2)x16 Trimmed mean slope F(15)–F(85) (�)x17 Mean slope in floodplains (�)x18 Drainage density (1/km)x19 Fraction of north-facing slopes (–)x20 Mean elevation of the catchment (m)x21 Difference between max. and min. elevation (m)x22 Fraction of saturated areas (–)

Soil map 1:200 000 and Geological map 1:600 000 (LfU)x23 Mean field capacity (mm)x24 Fraction of karstic formations (–)


gtil ¼ b0 þ

Xj

bjxtij ð20Þ

gtil ¼ b0

Yj

xtij

� �bjð21Þ

gtil ¼ b0 þ

Xj2G[U

bjxtij þ bJ�

Yj2M

xtij

� �bjð22Þ

and

gtil ¼ b0 þ

Xj2U

bjxtij þ bJ�

Yj62U

xtij

� �bjð23Þ

Furthermore, to fulfil the model requirements describedin ‘‘Modeling high- and low-flow characteristics’’, thesepredictors were combined with several variance andlink function alternatives shown in Tables 3 and 4,respectively.

Results and discussion

CP classifications

Based on the hydrological data available for the StudyArea, the subjective and objective atmospheric circula-tion patterns were classified into two or three categoriesusing parameters s1 and s2 as shown in Table 5. Theadopted values for the recession constant t were 0.95and 0.85 for winter and summer, respectively. Additionalparameters required for this classification were the per-centile level c = 0.80, and the maximum range of c, whoseadopted values for winter and summer were c = 30 andc = 120 days, respectively. It is worth noting that accord-ing to the classification rules proposed for the subjectiveclassification, most of the dry-CPs in this region are

Table 3 Probability distributions employed in this study and their relevant characteristics

Distribution Ytil � hðaÞ Expectation E½Yt

il� Variance function VðltilÞ Dispersion parameter j

Normal Nðltil;rÞ lt

il 1 r2

Poisson PðltilÞ lt

il ltil 1

Gamma Gða;btilÞ ltil ¼ abtil ðlt

ilÞ2 a�1

Weibull Wða;btilÞ ltil ¼ btilCð1þ a�1Þ ðlt

ilÞ2 Cð1þ2a�1Þ

C2ð1þa�1Þ � 1

Note: a and btil denote the shape and the scale parameters of the PDF, respectively, and C(Æ) is the gamma function.

Table 4 Link functions used in this study

Name Function ltil ¼ g�1ð�Þ

Identity gtilLogit 1

1þexpðgtilÞ

Log expðgtilÞReciprocal ðgtilÞ

�1


anticyclonic. This result confirms the adequateness of theadopted classification parameters since warmer and drierair masses in an anticyclone tend to suppress convectiveprecipitation, which, in turn, leads to a reduction of therelative humidity. Most of the wet-CPs are, on the con-trary, cyclonic.

Visualizing possible effects of land cover change onhydrological extremes

Two subcatchments labeled A and B (Fig. 1) were selectedto illustrate the evolution of some explanatory variablesover time and the possible effects of land use/coverchange. These subbasins have approximately the same ex-tent (123 km2 and 126 km2, respectively) but differ largelyon their main land cover type. Their average elevationabove sea level is 630 m and 385 m, respectively.

Table 5 Classification of circulation patterns (CPs) for winter aStudy Area during the period from 1961 to 1993

Classification type s1 s2 Category CP winter

Subjective 0.6 1.0 Dry BM, HB, HFa, HM,HNa, HNFa, NEa,NWa, Sa, SEa, SEz,SWa, Wa

Normal HNFz, NEz, Sz, TBWet HFz, HNz, Na, NWz,

Nz, SWz, TM, TRM,TRW, U, Ws, WW, W

Objective high-flows 1.1 1.1 Dry CP1, CP3, CP4, CP7,CP9, CP12,

Wet CP2, CP5, CP6, CP8,CP10, CP11, CP13

Objective low-flows 0.8 0.8 Dry –Wet –

The number of CPs and their total frequency of occurrence in percen

During the period from 1961 to 1993, subcatchment Aexhibited slightly growing shares of forest and imperviouscover whereas subcatchment B endured a steady land usetransition from grassland (permeable land cover) to settle-ment (impervious land cover) and a steady decline of forestsince the mid 70 s. As a result of that, in 1993, the formerwas mainly covered by forest (48%) whereas the latter wasextensively urbanized (56%) and hence mainly covered byimpervious surfaces.

The behavior of these two subcatchments is depicted onthe left and right panel of Fig. 2, respectively. Total droughtduration in summer (Y7), for instance, exhibited a remark-able decrement in the largely urbanized catchmentalthough the total precipitation in the same half year as wellas the mean air temperature in July did not reveal any sig-nificant trend. Moreover, the index x1 showed a completelydifferent behavior depending on the shares of land cover.This fact suggests that the combination of a rapid growthof impervious cover accompanied by a decline of forestmay have led to a rapid shrink of the total drought dura-tions. In contrast, slightly growing shares of forest andimpervious areas may have led to an increase of totaldrought durations. Moreover, for a given meteorologicaldrought, the effect on the runoff characteristic varied con-siderably. These facts are illustrated in Fig. 2 by the rectan-gles drawn with a dashed line. The frequency of high-flowsin winter (Y5) and the index x3 also revealed different

nd summer seasons according to the wetness index Wj in the

No. q [%] CP summer No. q [%]

13 41 BM, HB, HFa, HM, HNa, NEa,NWa, Sa, SEa, SWa, Wa

11 44

4 6 HNFa, Na, Sz, U 4 4

z

13 53 HFz, HNFz, HNz, NEz, NWz,Nz, SEz, SWz, TB, TM, TRM,TRW, WS, WW, Wz

15 52

6 61 CP1, CP3, CP4, CP6, CP7,CP9, CP12

7 69

7 39 CP2, CP5, CP8, CP10,CP11, CP13

6 31

CP3, CP5, CP8, CP11, CP13 5 35CP1, CP2, CP4, CP6, CP7,CP9, CP10, CP12

8 65

tage (q) for each category are also indicated.

Table 6 Summary of the composition of the calibrated hydrological models (1 denotes that a variable is included in the model,otherwise it is omitted)

RunoffCharacteristic

g(Æ) h(Æ) Variable xi (i) N

1 2 3 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Y3 POT N 1 1 1 1312Y4 MLP2 N 1 1 1 1318Y5 POT P 1 1 1 1 1 1 1 1 1 1247Y6 MLP2 W 1 1 1 1 1 1 1 1 977Y7 MLP2 W 1 1 1 1 1 1 1263

Additionally, the sample size N as well as the type of predictor and distribution functions employed in each model are shown.

1960 1970 1980 1990Year

0

5

10

Y5 [

y-1

]

0

40

80

120

Y7 [d

ay

]

0

50

100

x 1[d

ay]

0

25

50

Land

Cov

er[%

]

250

500

750

Sum

mer

Pre

c.[m

m]

10

15

20

25

Tem

p. J

uly

[˚C

]

0

25

50

x 3 [

da

y]

Impervious cover

Forestn= 33

0

5

10

0

40

80

120

0

50

100

0

25

50

250

500

750

10

15

20

25

0

25

50

Variable

5-year moving average

Basin A

1960 1970 1980 1990Year

Basin B

Figure 2 Time series and trends (by means of a 5-year running average) of selected variables, namely: the frequency of high flowsin winter (Y5), the total drought duration in summer (Y7), indices x1 and x3 based on the subjective CP classification, summerprecipitation (x6), mean temperature in July (x10), and fractions of land cover (x12 and x13) for two subcatchments (A and B) depictedin Fig. 1. Additionally, it is also shown how the same climatic phenomenon (i.e. a sequence of dry years highlighted by a dashed line)have produced different outcomes depending on the land cover and morphological situation within the catchment.


atedhyd

rologica

lmodels

(theclim

atic

indicesarebasedonthesubjectiveclassifica

tion)

1112

1314

1516

1718

19

20

21

22

23

24

0.05

9

[�0.]

02 4]

0.10

5

[�0.]

0.05

8

[0.018

]

�0.13

1

[�0.]

�0.16

6

[�0.]

�0.63

70.556

0.225

[0.015]

�0.005

[�0.]

0.01

2

[0.032

]

�0.82

5

[0.010

]

�1.136

[0.004]

�0.289

[0.002]

0.486

[0.064]

�0.006

[0.024]

0.01

7

[0.045

]

�0.07

5

[�0.]

�0.71

1

[�0.]

�2.126

[�0.]

0.236

[0.016]


behavior depending on the main land cover type. Subcatch-ment B, for instance, exhibited a clear positive trendwhereas subcatchment A did not. A more detailed analysisof probable causal relationships is presented in ‘‘Modelparametrization and performance’’.

Consequently, these observations seemed to indicatethat although the explained variables were mainly governedby macroclimatic conditions, they might be significantlyattenuated or enhanced by the land cover conditions as wellas by morphological characteristics of the catchment.

Model parametrization and performance

The most robust models were selected by the method de-scribed in ‘‘Model selection ans parameter estimation’’.The composition of these models and their correspondingcalibrated parameters are shown in Tables 6 and 7, respec-tively. Models for the runoff characteristics Y1, Y2, and Y8were not estimated because they are highly correlated withcharacteristics Y3, Y4, and Y7, whose pairwise Pearson’s cor-relation coefficients were 0.87, 0.89, and 0.71, respectively.For the remaining runoff characteristics, the best resultswere obtained with the identity link function, but, in anycase, the predictor function appears to be multilinear.

To select among the several functional relationshipsconsidered in this study (MLP1, MLP2 and POT), a scatter-plot (Fig. 3) of the performance indices U1 and U2 was used.Since these performance indices denote Jackknifestatistics-errors, the smaller the performance index, thehigher the robustness of the model fit. In the exampleshown in Fig. 3, for instance, model type MLP2 was betterthan POT, and this, in turn, was better than model typeMLP1. The performance indices for the ML type model donot appear in this graph because their corresponding valueswere greater than the maximum values shown in this graph.Similar results were obtained for the other characteristics.This finding indicated that the nonlinearity of the described

Table

7Param

eterestim

atesan

dtheir

respectivep-valuesforeac

hoftheca

libr

Runoff

Param

eter

b i(i)[p-value]

Char.

0J *

12

35

89

10

Y3

1.41

90.95

1

[�0.]

�0.11

6

[�0.]

Y4

0.88

93.36

51.14

3

[�0.]

�0.5

[0.02

Y5

0.02

40.16

0

[�0.]

0.76

1

[�0.]

Y6

0.10

04.92

30.45

4[�

0.]

1.09

8

[�0.]

Y7

�0.26

914

.658

0.86

9

[�0.]

5.2 5.6 6 6.4 6.8

5.4

5.6

5.8

6

6.2

6.4POTMLP1MLP2

Figure 3 Performance of three models types (MLP1, MLP2and POT) used to predict total drought duration in summer (Y7).U1 and U2 are Jackknife statistics calculated by minimizing theL1 and L2 estimators, respectively.


system stemmed mainly from the meteorological and/orphysiographic variables.

The model summary presented in Table 6 shows that withthe exception of Y3 and Y4, the remaining runoff character-istics exhibited a distributional element other than normal.This means that the runoff characteristics Y5, Y6, and Y7 aswell as their associated additive error term (Eq. (1)) are het-eroscedastic, or in other words, that they exhibit a non-sta-tionarity variance either along time, or along some of thepredictors, or both.

The goodness of the fit (r), bias, and the root of meansquare error obtained for each calibrated model using boththe subjective and objective CP classifications are summa-rized in Table 8. In general, these results indicated thatthe objective classification was as efficient as the synopticone proposed by Hess and Brezowsky (1969). In the caseof the low-flow characteristic (Y7), the results obtainedfor both the r and the RMSE were significantly better thanthose obtained with the subjective classification. Thisimportant result showed an additional advantage of the

Table 8 Correlation coefficient (r), bias (BIAS), and root of me(AIC) obtained for the calibration period from 1961 to 1993 with

Runoff characteristic Subjective CP classification

BIAS RMSE r

Y3 �0.1 3.3 0.94Y4 +0.0 2.3 0.94Y5 +0.0 1.5 0.77Y6 +0.2 1.1 0.87Y7 +0.0 13.3 0.86

Figure 4 Spatial distribution of the correlation coefficient r of thtotal drought duration in summer (Y7, right panel). In the particular0.92 for the Y7, respectively.

objective classification, namely: that the learning (optimi-zation) algorithm employed to find the fuzzy-rule classifica-tion system (see Bardossy et al. (2002)) can be fine-tunedfor a specific purpose, say predicting drought events atthe mesoscale.

From all modeled characteristics, total drought durationin summer Y7 exhibited the highest RMSE (13 days and 9 daysdepending of the classification used), which can be seen asan overall indicator of uncertainty associated with the esti-mation of this variable. In this case, the use of a ‘‘fine-tuned’’ objective CP classification (i.e for low-flows) led toa 30% reduction in the uncertainty of the predicted variable.

By inspection of Table 7 some hydrological interpretationof the empirical models is presented. Results obtained fortotal duration of high-flows in winter and summer (Y3 andY4, respectively) indicated that these runoff characteristicshave a very strong correlation with the macroclimatic situ-ation represented by the variables x3 and x9 in winter and x2and x10 in summer, respectively. Morphological variableswere irrelevant in these cases but land cover variables

an square error (RMSE) and the Akaike Information Criteriumyearly time steps

Objective CP classifications

AIC BIAS RMSE r AIC

2919 �0.2 3.9 0.91 32661538 +0.0 2.8 0.88 24034327 �0.0 1.5 0.76 43301372 �0.1 1.3 0.79 16938751. �0.3 9.3 0.92 7021.

e total duration of high flows in winter (Y3, left panel), and thecase of basins A and B, r were 0.71 and 0.73 for Y3; and 0.98 and


(x12 and x9) were found to be statistically dependent andsignificant, although their contribution to the total ex-plained variance was quite small. In both cases, mean tem-perature was inversely related to the total duration of high-flows, which is plausible since the higher the temperature,the larger the evapotranspiration, and thus the lower thedischarge.

The frequency of high-flows (Y5) in winter appeared asdirectly dependent on the meteorological conditions, espe-cially the total precipitation (x5), the maximum tempera-ture in January (x11) and the composed indicator of wetcirculation patterns (x3). Thus, the wetter a given yearwas, the higher the likelihood that a flood event wouldarise. Moreover, if the winter temperature in January washigh, then the frequency of high-flows tended to increasesince the thawing process would be faster, which, in turn,may have increased discharge. The same direct relationshipapplied to the fraction of north-facing slopes (x11) and theaverage field capacity (x23). The former could be explaineddue to a reduced evapotranspiration and hence higher run-off (i.e. the conservation of mass principle that is implicit inthe water balance of a basin). The shares of forest and per-meable areas (x12 and x14, respectively) are inversely re-lated variables, all perfectly plausible relationships from

1960 1970 1980 1990

Year

0

40

80

120

Y7

= T

ota

l Dro

ugh

t Du

ratio

n -

Su

mm

er [

d]

1960 1970 1980 1990Year

0

2

4

6

8

10

Y5 =

Fre

que

ncy

Hig

h F

low

s -

Win

ter

[y-1

]

Basin A

Calculated Basins A/B

Observed

a

b

Figure 5 Observed and calculated time series for the total droughflows in winter [Y5, panel (b)] for basins A and B, respectively.

the hydrological point of view because land cover types withlarger roughness coefficients tended to increase the time ofconcentration within a basin and hence reduce the likeli-hood of peak events. Causal relationships for the other vari-ables were not quite clear, which indicates that they mayrepresent artifacts found in the sample. During summer,the frequency of high-flows (Y6) also exhibited a direct rela-tionship with the mean precipitation (x8) and the composedindex for wet circulation patterns (x1), the share of satu-rated areas (x5), and the share of impervious areas withina catchment (x13).

Based on the data available, the total drought durationin summer (Y6) appeared to have a complex nonlinear rela-tionship with the predictors. For instance, it exhibited anonlinear relationship with the macroclimatic conditionsrepresented by the variable (x1), which not only dependson the circulation patterns but also on the antecedent pre-cipitation index. The latter, which is a proxy of the aver-age soil moisture, was, in turn, directly related to theshare of forest within a catchment (x12) and inversely re-lated to the share of impervious areas (x13). Furthermore,x12 appeared as a linear predictor of Y6 too. These rela-tionships are also consistent with the catchment’s waterbalance, as during a summer dry spell, the evapotranspira-

1960 1970 1980 1990

Year

0

40

80

120

Basin B

1960 1970 1980 1990Year

0

2

4

6

8

10

t duration in summer [(Y7), panel (a)] and the frequency of high


tion from forest reaches the higher annual values, which,implies no recharge of the subsurface storage occurs,and, therefore, there should be less discharge intostreams. The area of the basin (x15) appeared to be inver-sely related to Y6. In other words, the larger the basin’sarea, the larger its storage capacity, and hence, the longer

0 10 20 30

x

x

0

20

40

60

80

100

120

140

Y7 (

obs,

cal)

[day

]Y

7 (ob

s,ca

l) [d

ay]

0 10 20 300

20

40

60

80

100

120

140

Qobs

QcalLine: magnitud of the std. dev.Circle / square: mean

n= 74 8a

b

Figure 6 Variation of the dispersion of the observed and calculaindex x1. The only difference between panels (a) and (b) is the kindthus, the error term: On the panel (a), Y7 is assumed normal distribdistributed. Both continued and dashed lines represent the magnrepresent the mean values at each level of predictor.

the basin’s baseflow can be kept above a given threshold.This, in turn, implies fewer days per year accounting forwater deficits.

Based on the results shown in Table 8 and Fig. 5, it canalso be inferred that the selected models perform rela-tively well because they were able to explain between

40 50 60 70

1 [day]

1 [day]40 50 60 70

ted total drought duration in summer (Y7) as a function of theof distribution function assumed for the explained variable, anduted, whereas on the panel (b) the variable is assumed Weibullitude of the standard deviation whereas dots and rectangles


59% and 88% of the observed variance. This efficiency ofthe models, however, was not constant over space butexhibited considerable spatial-temporal variability withinthe studied area. For example, variability in Y3 and Y7(Fig. 4), depended not only on the season (i.e. winterand summer) but also on the kind of hydrological regime(i.e. high- and low-flows) that was analyzed. In the presentcase, the lack of predictability seems to be associated withmorphological characteristics such as the fraction of kar-stic formations underneath a given basin and its status asa headwater basin. In general, headwater subbasins per-formed better than those which are not. This is probablyrelated with the number regulation structures (e.g. weirsand barrages) located along the courses of non-headwaterbasins. Moreover, subcatchments with lower fraction ofkarstic formations performed better than those with largerfractions of karstic fractions. The reason for that could bethe unaccounted sources of water caused by size differ-ences between surface and underground catchments,which, in turn, might alter the water budget accounting(particularly with respect to the baseflow) at a given gaug-ing location.

Effects of the distributional element on thesimulated variance

The correct selection of the distributional element whenmodeling highly heteroscedastic time series is a decidingfactor on the model’s quality, especially regarding the var-iance of the explained variable. This is clearly illustratedin Fig. 6, where the the total drought duration was mod-eled using two distributional elements as null hypothesisnamely: (1) the normal distribution which is symmetricaland has a constant mean and variance; and (2) a skeweddistribution like the Weibull which has a variance that de-pends on the value of the mean. For the sake of compar-ison, in both cases the a priori adopted function of thepredictor, the sample size, and the explanatory variableswere kept equal. Based on the results depicted in Fig. 6,it can be concluded that, under these assumptions, bothmodels were able to predict relatively well the expectedvalue of Y7; but that the model based on the normal distri-bution completely underestimates the observed variabilityof Y7 which largely depends on the index x1. The modelbased on the Weibull distribution, on the contrary, exhib-ited a significant increase of the estimated variance alongthe abscissa, and, in this respect, performed much betterthan the former.

Conclusions

Based on the results of this study, some general conclusionscan be drawn:

• The indices derived from either the objective or the sub-jective CP classifications were equally effective atexplaining a large proportion of the variance of the pro-posed runoff characteristics. Consequently, objectiveclassifications could become an efficient alternative inthose cases where automated operational forecasts arerequired.

• The proposed dryness index (dry circulation patternsoccurring with a decreasing antecedent precipitationindex) exhibits a completely different behavior depend-ing on the fraction of land cover within a catchmentwhile almost constant seasonal-mean precipitation andtemperature have been observed. Moreover, the drynessindex is highly correlated with total drought duration.

• The proposed compounded wetness indexes also explaina large fraction of the observed variance of the totalduration and the frequency of high-flows in winter andsummer.

• The fraction of forest and/or impervious areas seem tohave played–in the Study Area–a significative role inthe hydrological extremes at mesoscale level.

• The large fraction of the observed variance of allextreme runoff characteristics is, however, explainedby indices related to macroclimatic indices and

• The heteroscedasticity of the observed variables couldonly be acceptably simulated using nonlinear generalizedmodels that assume non-gaussian distributions.

Acknowledgement

The authors appreciated the helpful comments from Prof.E. Zehe, Dr. J. Calabrese, and one anonymous reviewer.

References

Akaike, H., 1973. A new look at the statistical model identification.IEEE Transactions on Automatic Control 19, 716–723.

Bardossy, A., 1993. Stochastische Modelle zur Beschreibung derraum-zeitlichen Variabilitat des Niederschlages, Vol. 44. Institutfur Hydrologie und Wasserwirtschaft der Universitat Karlsruhe,Karlsruhe.

Bardossy, A., Filiz, F., 2005. Identification of flood producingatmospheric circulation patterns. Journal of Hydrology 313, 48–57.

Bardossy, A., Plate, E., 1992. Space–time model for daily rainfallusing atmospheric circulation patterns. Water ResourcesResearch 28, 1247–1259.

Bardossy, A., Stehlik, J., Caspary, H.-J., 2002. Automated objectiveclassification of daily circulation patterns for precipitation andtemperature downscaling based on optimised fuzzy rules.Climate Research 23, 11–22.

Cannon, A., Whitfield, P., 2002. Downscaling recent streamflowconditions in british columbia, canada using ensemble neuralnetwork models. Journal of Hydrology 259, 136–151.

Chow, V. (Ed.), 1964. Handbook of Applied Hydrology: a Compen-dium of Water Resources Technology. McGraw-Hill, New York.

Clarke, R., 1994. Statistical Modelling in Hydrology. Wiley,Chichester.

Dracup, J.A., Kahya, E., 1994. The relationships between USstreamflow and La Nina events. Water Resources Research 30(7), 2133–2141.

Draper, N.R., Smith, H., 1981. Applied Regression Analysis, seconded. Wiley, New York.

Efron, B., 1982. The Jackknife, the Bootstrap and Other ResamplingPlans. Society for Industrial and Applied Mathematics VII,regional conference series in applied mathematics, 38.

Favre, A., Adlouni, S.E., Perreault, L., Thiemonge, N., Bobee, B.,2004. Multivariate hydrological frequency analysis using copulas.Water Resources Research 40, W01101. doi:10.1029/2003WR00245.

http://dx.doi.org/10.1029/2003WR00245

http://dx.doi.org/10.1029/2003WR00245


Gentleman, W.M., 1974. Basic procedures for large, sparse orweighted linear least squares problems. Applied Statistics 23,448–454.

Hess, P., Brezowsky, H., 1969. Katalog der großwetterlageneuropas. berichte des deutschen wetterdienst. Tech. Rep.113(15), Selbstverlag des Deutschen Wetterdienst, Offenbacha. Main, 2 neu bearbeitete und erganzte Aufl.

Houghton, J.T., Ding, Y., Griggs, D., Noguer, M., van der Linden, P.,Dai, X., Maskell, K., Johnson, C. (Eds.), 2001. Climate Change2001: The Scientific Basis. Cambridge University Press <http://www.grida.no/climate/ipcc_tar/wg1/index.htm>.

Li, X., Sailor, D., 2000. Application of tree-structured regression forregional precipitation prediction using general circulation modeloutput. Climate Research 16 (1), 17–30.

Lindsey, J.K., 1999. Applying Generalized Linear Models. Springer,New York.

Montgomery, D.C., Peck, E.A., 1982. Introduction to LinearRegression Analysis. Wiley, New York.

Piechota, T., Dracup, J., 1996. Drought and regional hydrologicvariations in the United States: associations with the El Nino-southern oscillation. Water Resources Research 32 (5), 1359–1373.

Quenouille, M., 1949. Approximate tests of correlation in timeseries. Journal of the Royal Statistical Society 11B.

Reddmont, T., Koch, R., 1991. Surface climate and stream flowvariability in the Western United States and their relationship tolarge-scale circulation indices. Water Resources Research 17,2381–2399.

Samaniego, L., 2003. Hydrological Consequences of Land Use/LandCover Change in Mesoscale Catchments. Institute of HydraulicEngineering, University of Stuttgart, Faculty of Civil Engineering,Stuttgart, Ph.D. dissertation No. 118, ISBN 3-9337 61-21-2. URL<http://elib.uni-stuttgart.de/opus/volltexte/2003/1437/>.

Samaniego, L., Bardossy, A., 2005. Robust parametric models ofrunoff characteristics at the mesoscale. Journal of Hydrology303 (1–4), 136–151. doi:10.1016/j.jhydrol.2004.08.02.

Schweizer, B., Wolff, E.F., 1981. On nonparametric measures ofdependence for random variables. Annals of Statistics 9, 879–885.

Shorthouse, C., Arnell, N., 1997. Spatial and temporal variability ineuropean river flows and the north atlantic oscillation.FRIEND’97: International Association of Hydrological SciencePublications 246, 77–85.

Stahl, K., Demuth, S., 1999. Linking streamflow drought to theoccurrence of atmospheric circulation patterns. HydrologicalSciences Journal 44 (3), 467–482.

Yarnal, B., 1993. Synoptic climatology in environmental analysis.Studies in Climatology Series. Belhaven Press, London.

http://www.grida.no/climate/ipcc_tar/wg1/index.htm

http://www.grida.no/climate/ipcc_tar/wg1/index.htm

http://elib.uni-stuttgart.de/opus/volltexte/2003/1437/

http://dx.doi.org/10.1016/j.jhydrol.2004.08.02

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