simulation of the impacts of land use/cover and climatic changes on the runoff characteristics at...
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e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
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Simulation of the impacts of land use/cover and climaticchanges on the runoff characteristics at the mesoscale
Luis Samaniegoa,∗, Andras Bardossyb
a UFZ Centre for Environmental Research Leipzig-Halle GmbH, Permoserstraße 15, 04318 Leipzig, Germanyb Institute of Hydraulic Engineering, University of Stuttgart, Germany
a r t i c l e i n f o
Article history:
Received 30 June 2005
a b s t r a c t
The analysis of climatic and anthropogenic effects on mesoscale river basins has become
one of the main concerns for hydrologists, environmentalists, and planners during the last
Received in revised form11 January 2006
Accepted 30 January 2006
Published on line 23 March 2006
Keywords:
Monte Carlo simulation
Land use change
Runoff characteristics
Climate change
Downscaling
Master equation
decade. Many attempts at dealing with this issue have been proposed in the literature. In
most studies, however, the main components of the system have been isolated in order
to reduce the complexity of the system and its intrinsic uncertainty. In this paper, an at-
tempt to couple two realms of the water system at a mesoscale catchment, namely, the
hydrological behaviour of a catchment and the state of the land cover at a given point in
time, is presented. Here, instead of using a standard hydrological model, various nonlinear
models relating several runoff characteristics with physiographic, land cover, and meteoro-
logical factors were linked with a stochastic land use/cover change model. Then, using this
integrated model, the magnitude of the effects of the hydrological consequences of land
use/cover and climatic changes was assessed in a probabilistic way by a sequential Monte
Carlo simulation provided four different scenarios which take into account likely develop-
ments of macroclimatic and socioeconomic conditions relevant for a given study area. The
proposed methodology was tested in a river basin of approximately 120 km2 located to the
south of Stuttgart, Germany.
© 2006 Elsevier B.V. All rights reserved.
1. Introduction
A mesoscale river basin1 is an open, highly complex dynamicsystem with poorly controlled boundary conditions, whosecomplexity stems from the fact that it comprises a large num-ber of agents (e.g. people, firms, and government) and a num-ber of tightly coupled subsystems interacting in both spaceand time at various scales (Weidlich and Haag, 1983a; Bloschland Sivapalan, 1995; Allen and Strathern, 2003; Allen, 2004).These subsystems have very different characteristics but mostof them – if not all – exhibit intrinsic nonlinear relationships,delayed responses, feedback loops (Wu and Marceau, 2002;
∗ Corresponding author.E-mail address: [email protected] (L. Samaniego).
1 That is to say, those basins whose length ranges from 102 m toless than 105 m and with an area less than 5000 km2 (Dooge, 1988).
Porporato and Ridolfi, 2003) and, in some cases, stochastic be-haviours. As a result, the macrostates that emerge from sucha system may range from stochastic to chaotic – in the long-term – as was shown by Jayawardena and Lai (1994), Sivakumar(2000), and Sivakumar et al. (2002) among others. Moreover, itis recognised that there is a considerable uncertainty in ourknowledge of the component processes and the representa-tion of that knowledge when one builds predictive modelsfor such a system (Refsgaard, 1997; Beven, 2002; Young andParkinson, 2002).
Despite the intricacies of this system, remarkable progressin analysing it has been achieved during the past decades.
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2006.01.005
46 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
The main approach employed consists of subdividing it intosub-components which are, in turn, modelled as uncoupledsubsystems having no endogenous links to any other one.For example, land use models and river basin econometricmodels were not coupled with hydrological ones [e.g. Berry etal., 1996; Guise and Flinn, 1973, respectively] and, conversely,precipitation-runoff models neither consider models dealingwith the land use dynamics nor the economic development ofthe region [e.g. Leavesley et al., 1983 among others]. The mainshortcomings of the lack of integration are: (1) the loss of boththe synergy and the feedback effects among subsystems, and(2) the impossibility of estimating the degree to which a vari-able in a given subsystem may be changed due to the increaseor decrease of another one belonging to an exogenous subsys-tem.
The former is evident when one tries to assess the mostlikely impacts that land use/cover and climatic changes wouldinduce on the runoff characteristics (e.g. total discharge inwinter or frequency of high flow in summer) at the mesoscale(Samaniego, 2003). In order to deal with this problem properly,a holistic formal system (Casti, 1984) – or model – that mimicsa number of links (most of them nonlinear) among the rel-evant processes (e.g. macroclimatic conditions, soil type dis-tribution, hydrological regime) and the driving forces behindland use/cover change should be formulated. There are sev-eral studies reported in the literature dealing with the integra-tion of land use/cover change and hydrological models, for in-
describe the evolution of a complex natural system like theEarth’s climate is, however, a lost cause for science as wasshown by Lorenz (1994) and then corroborated by many oth-ers. There are many reasons for such analytical intractability(Wilks, 2000) – some of them were already pointed out in Sec-tion 1 – but a detail analysis of them is out of the scope of thispaper. This analytical conundrum implies that in order to dealwith the deep uncertainty associated with the future states ofthe system, a pragmatic solution has to be found.
Relevant literature in related disciplines shows us that thisproblem has been addressed in different ways in the past.For example, in disciplines like climatology or hydrology re-searchers have commonly applied the Ensemble Forecastingtechnique (Leith, 1974) and/or the Scenario Approach (Smith andHulme, 1998) to forecast probable trajectories for the evolu-tion of some variables of interest (e.g. state variables) undergiven initial conditions. In this case, models are assumed tocapture relatively well the inner mechanisms of the system,and thus, regarded valid to be used under future conditions.Since the initial state of the system will always remain un-certain an ensemble of initial conditions is required. In socialsciences, on the contrary – where inputs are more uncertain –researchers have tended to use models to generate a numberof realisations (sometimes also called scenarios), all consis-tent with the information available and then to test planningstrategies rather than to make predictions. This technique isusually called Exploratory Modelling (Bankes, 1993; Lempert et
stance those of Bronstert et al. (2002) and Niehoff et al. (2002).In those studies, however, the treatment of the land use/coverchange model did not follow a stochastic framework.
This paper presents an attempt to develop a simple butrobust integrated model to address this problem, as well asthe main assumptions therein, and to propose suggestions forfuture improvements. The proposed approach is illustrated bya case study carried out in a river basin in Germany.
2. Method
Building an integrated model for an environmental system re-quires trade-offs between the level of complexity and the de-gree of coupling among the various subsystems. The formeris determined by the number of state variables and parame-ters as well as their spatio-temporal scales, whereas the latteris given by the number and complexity of the coupling func-tions and/or interface variables (Walter and Liossatos, 1979).The model, however, should (1) provide a sufficiently good re-semblance of the observed “reality” – normally based on timeseries of observations, e.g. the annual total discharge – and (2)preserve the system’s adaptability and creativity (Allen, 1997).
There have been as many attempts as paradigms in thepast decades to address these challenges, for example: (1) cel-lular automata (CA) (von Neumann and Burks, 1966), (2) spa-tial dynamic modelling (Baker, 1989; Perez-Trejo, 1993; Allen,1997), (3) Monte Carlo simulation (MCS) (Hammersley andHandscomb, 1964), (4) fuzzy-rule based modelling (Bardossyand Duckstein, 1995), (5) multi-agent systems (see Wooldridge,1999; Barreteau and Bousquet, 2000, and references therein),and (6) Bayesian belief networks (Varis and Kuikkab, 1999;Cain, 2001). Moreover, finding a deterministic model able to
al., 2003).It should be noted however, that each technique presents
advantages and disadvantages, hence, compromises have tobe found to address a given problem. The selection of one ofthese approaches, or the combination of some of them, de-pends on the problem formulation, its research goals, and –very important – the data availability. In this paper, the intrin-sic uncertainty of the system will be addressed with a combi-nation of standard techniques, namely:
(1) the scenario definition,(2) the land use/cover change (LUCC) model,(3) the quantification of hydrological consequences of LUCC,(4) the stochastic simulation, and(5) the statistical inference.
The main structure of the model (modules) employed inthis study is schematically depicted in Fig. 1.
2.1. Scenario definition
The standard scenario approach was adopted in this studyin order to make the subsequent modelling steps compati-ble with several General Circulation Model (GCM) simulationscarried out by the Intergovernmental Panel on Climate Change(IPCC) (Houghton et al., 2001). Thus, various “development sce-narios” were envisaged, each of them to be composed of both a“macroclimatic” and a “socioeconomic” scenario. The formerprovided the framework for the climatic conditions for a futureworld under given hypothesised emission scenarios whereasthe latter provided the framework for the driving forces behindthe land use/cover changes at the mesoscale. Consequently,the information contained therein is assumed exogenous forthe subsequent simulations. It is worth noting that scenar-
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 47
Fig. 1 – Main structure of the model.
ios are “neither predictions nor forecasts of future conditions.Rather they describe alternative plausible futures that con-form to sets of circumstances or constraints within which theyoccur” (Hammond, 1996).
Moreover, within a development scenario, a number ofprobable development paths or futures were explored bystochastic simulations in order to assess the uncertainty of thesystem under common starting conditions. In general, a devel-opment scenario should address the change in attitudes andfuture social values as well as the interpretation of a region’sexternal conditions, and provide assumptions (explicit or im-plicit) as to the mechanisms of causes and effects of changingpatterns (Samaniego, 2003).
2.2. Land use/cover-change model
In this study, the term land use is used in the sense of hu-man employment of the land, whereas the term land coveris used to denote the physical state of the land (Turner andMeyer, 1991). The former is related to the anthropogenicsystem whereas the latter is related to the natural system.The present state of land use in a given place is the out-come of competing potential uses – seldom complementaryto each other – under certain constraints imposed by ei-ther nature (i.e. vegetation – land cover, soils, topography –slopes, and climate) or human regulations (e.g. planning laws,property rights, market, and culture), or both (Turner et al.,1tt
rsT
sons such as economic cycles or population attitudes. They,in turn, may also influence the transition rates from one landcover/use type to another. Moreover, if land cover/use changesoccur independently at the microscale (i.e. at parcel level) withrelatively slow transition rates [say less than 5% per year,Robinson et al., 1998], then, no apparent effect on the hy-drological cycle of a mesoscale river basin can be detectedin the short term. Conversely, their long-term cumulative hy-drological consequences will be only perceived at mesoscale(Reimold, 1998); perhaps when it is too late to take counter-measures.
Because of these characteristics of this subsystem, a com-bination of the master equation and CA can be a feasi-ble alternative to model the land use/cover change pro-cess. These approaches require the following definitions andassumptions.
Let the pair (U(t),F) be a stochastic process resemblingthe land use/cover transformations to be endured by the sys-tem during the period t = 1, . . . , T. Here, U(t) = [Uij](t), (i, j) ∈ Zdenotes the land use/cover of a river basin ˝ at time pointt; T is the duration in years of the simulation period andZ = {(i, j) : 1 ≤ i ≤ N, 1 ≤ j ≤ N′} denotes a N × N′ integer latticecovering ˝. Furthermore, let us assume – for the sake of sim-plicity – that there exists a one to one relationship betweeneach land use and land cover class, so that each one canbe denoted by a single value q. Based on this definition, letS = {q : q = 0, 1 . . . , Q} be a finite state space denoting Q mutu-
993). (For more details on the interrelationships betweenhese two categories see Samaniego, 2003, and referencesherein.)
Since the onset of the Industrial Revolution, human actionsather than natural forces are the main source of change in thetates and flows of the biosphere (Turner and Meyer, 1991).hese driving forces also change over time due to many rea-
ally exclusive land use/cover classes, and one particular caseq = 0 for those cells within the lattice that are restricted or un-used, so that Uij(t) ∈ S, ∀(i, j), t. Finally, letF = {Fij}, (i, j) ∈ Z be aneighbourhood system where Fij ⊆ Z denotes the neighboursof cell (i, j).
Based on empirical evidence reported by Turner (1987),Brown et al. (2002) and the characteristics of the LUCC men-
48 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
tioned before, it can be assumed that the LUCC process isMarkovian. Put differently, the selection of the new stateUij(t + 1) for a given cell (i, j) depends only on the current stateUij(t) of this cell and those of its neighbourhood Fij (neigh-bourhood relationships were also used in the land use/coverchange model developed by Fritsch and reported in Niehoff etal., 2002) and not on prior states, thus it is assumed that thesystem, with respect to the LUCC process, has no memory.Formally, this can be written using conditional probabilitiesas follows:
P(
Uij(t + 1) = q′|Ulm(t) = q, ∀ (l, m) ∈ Z, ∀ t)
= P(
Uij(t + 1) = q′|Ulm(t) = q, ∀ (l, m) ∈ Fij
)(1)
At the micro level, the following master equation [seeWeidlich and Haag, 1983a,b, for technical details regardingits derivation from the Chapman–Kolmogorov equation] de-scribes the time evolution of the probability density of the landuse/cover state q′ (discrete) of a given cell (i, j), P(Uij(t) = q′) =P(q′, t)ij as:
∂
∂tP(q′, t)ij
=∑
q
[W(q′|q, t)ijP(q, t)ij − W(q|q′, t)ijP(q′, t)ij
], q, q′ > 0 (2)
where W(q′|q, t)ij is the transition probability per time unit (i.e.
information; �q′q, control parameters denoting both the polit-ical willingness and the society’s level of awareness with re-gard to environmental impacts and global sustainability. Theyact as dummy variables comprising all feedback effects thatchange in global climate and the hydrological basin’s charac-teristics may have upon the transition rates from one landuse/cover to another. The set of parameters will be scenariospecific and will be of key importance during the simula-tion. In general, they are values greater or equal to zero. Zeromeans that a transition is not possible and the greater thevalue, the greater the willingness to promote such transfor-mation; w(q′, q, t)ij, location and time specific factor indicat-ing the likelihood that a given cell will be transformed to an-other land use/cover type based on the neighbourhood con-ditions; zk(i, j), time independent driving force k, with (i, j) ∈ Z;�0(q′, q), scaling parameter for LUCC from q → q′; �0(q′, q), pa-rameter estimate for driving force k related with a LUCC fromq → q′.
The estimation of the transition probability (Eq. (5)) as-sumes that: (1) the driving forces will be constant or quasi-constant during the simulation time, and (2) that landscapechanges do not occur randomly in space but in patches orclusters. Both assumptions are reasonable and consistent withempirical studies (Brown et al., 2002). Consequently, w(q′, q, t)ijis estimated as:
w(q′, q, t)ij = 1Nc
|{(i, j) : Uij(t) = q′ ∧ (i, j) ∈ Fij}| (6)
probability transition rate) from state q to state q′, with q, q′ ∈ Sand q, q′ > 0. The first term of the right hand side of the Eq. (2)denotes the flux of the probability from all states q into stateq′, whereas the second term denotes the flux of the probabilityfrom state q′ into all states q.Additionally, the system should hold the normalisationcondition:∑
q
P(q, t)ij = 1, ∀(i, j) ∈ Z, t = 1, . . . , T (3)
which, in turn, implies that∑
q′∂∂t P(q′, t)ij ≡ 0.
Empirical studies based on historical records (Bell, 1974;Berry et al., 1996; Brown et al., 2002) provided strong evi-dence that the transition probabilities not only depend onlocal land use/cover but also on socioeconomic factors, landuse policies, and morphological characteristics of the terrain.Hence, based on the random utility theory, and the probabil-ity normalisation condition, W(q′|q, t)ij can be determined asfollows:
W(q′|q, t)ij =
⎧⎨⎩
p(q′, q, t)ij, ∀q′ �= q
1 −∑
n
p(n, q, t)ij, ∀q′ = q, n �= q (4)
with
p(q′, q, t)ij = �q′q�q′qw(q′, q, t)ij
× exp(�0(q′, q) +∑
k�k(q′, q)zk(i, j))
1 +∑
nexp(�0(n, q) + ∑
k�k(n, q)zk(i, j))
(5)
where n, index in the range ∈ {1, . . . , Q}, and n �= q; k, indexin the range ∈ {1, . . . , K}; K: number of exogenous variables re-garded as driving forces behind a land use/cover change; �q′q,calibration and scaling parameters to be determined with past
where |{·}| represents the cardinality of the set composed ofall neighbours of the cell (i, j) having a land use/cover type q′
at the tth transition. Nc denotes the number of neighboursof a given cell and c an integer denoting the neighbourhoodconfiguration. In the present case, the Moore neighbourhoodwill be used, i.e. c = 2, which means that a typical cell thatdoes not belong to a corner and/or a side of the lattice haseight neighbours, thus Nc = 8. In the other two cases, Nc takesthe values of 3 and 5, respectively.
The neighbourhood of cell (i, j) has to fulfil the followingcondition (Geman and Geman, 1984):
Fij = {(l, m) ∈ Z : 0 < (l − i)2 + (m − j)2 ≤ c} (7)
2.3. Quantification of hydrological consequences ofLUCC
In general, there are two main approaches to quantify thehydrological consequences of land use/cover change in amesoscale catchment, namely to use either a conceptual hy-drological model [the “so-called” physically based modelsare in fact conceptual ones due to the implicit upscaling ofsome of the microscale physical laws employed therein, seeBloschl, 2001; Beven, 2001], or input–output empirical relation-ships. The former employs a mixture of process understand-ing and/or governing physical laws to describe the water cyclewhereas the latter rely entirely on ad hoc relationships whichrelates characteristics of interest based on data available. Bothapproaches have advantages and disadvantages. The main ad-vantage of using a conceptual model with respect to an input–output relationship is that the form of the functional relat-ing the state variables is not ad hoc but determined by phys-ical laws and/or basic principles that can be validated at the
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 49
microscale. Conceptual models, however, tend to be overpa-rameterised and are, in general, computationally expensive.Input–output relationships are, on the contrary, quite parsi-monious and robust. This characteristic makes them a goodchoice to analyse long-term trends, seasonality as well as todetermine system’s dominant processes. For this reason, theuse of input–output relationships were considered appropri-ate for this study, although there is no reason why the formercannot be used within the context of the model structure pre-sented here.
Consequently, in order to quantify the hydrological conse-quences of LUCC, several parametric models were calibratedin order to simulate the development of observed runoff char-acteristics for a given set of mesoscale catchments. Thesemodels can be seen as nonlinear cause–effect relationshipsthat relate a given runoff characteristic with a set of explana-tory variables such as (1) physiographical factors 〈G〉, (2) sharesof land cover types 〈U〉, and (3) climatic or meteorological fac-tors 〈M〉. Here, the operator 〈·〉 denotes a vector composed byeither the integral or a spatial statistic of a set of variablesdefined on the lattice Z. For the formal definition of the hy-drological subsystem the following definitions are required.
Let Ybh(t) be the h runoff characteristic observed in basin bat time point t, and fh(·) a nonlinear function relating a setof explanatory variables {xb1, . . . , xbE}(t) ≡ {〈G〉b, 〈U〉b, 〈M〉b}(t).Moreover, let ˇ a vector of parameters to be calibrated and val-idated based on historical records, and E the total number ofeg
wut
tisgniiapB
2
Si
M
Mgobui
lation, however, should be seen as possible paths to the futureand hence should not be interpreted alone but in a statisticalsense. Based on an ensemble of realisations, one can for ex-ample, estimate the probability with which a given event mayoccur, or the average trend of a given variable as well as itsconfidence intervals.
In order to find solutions for the system M, some funda-mental assumptions have to be made regarding the resam-pling techniques as well as the degree of interdependence andvariability of the variables:
(1) The morphological variables 〈G〉 are invariant for the pe-riod of the simulation.
(2) The land use/cover shares – i.e 〈U〉/A, where A is the area ofthe catchment – are obtained as realisations of the modeldescribed in Section 2.2. This submodel, however, doesnot have direct feedback links either from the hydrolog-ical models or from the climatic variables. Put differently,this model was built in such a way that the climate andland use/cover changes influence the hydrological charac-teristics of the basin, but the changes in the latter do notinduce changes in the former in the short term. The mainreason for this simplification is that a change in the watercycle and the land cover of a mesoscale catchment inducesa infinitesimal change in the macroclimate whereas theircumulative long-term effect (centuries), in space and time,is not insignificant (Cada and Hunsaker, 1990). This short-
xplanatory variables. Hence, the relationships can be writtenenerally as:
Ybh(t) = fh (〈G〉b(t), 〈U〉b(t), 〈M〉b(t), ˇ) + εb(t),
∀ b = 1, . . . , B ∧ t = 1, . . . , T (8)
here εb(t) is an error term with zero mean but otherwise ofndefined distribution, and B is the number of basins used forhe calibration and validation stages.
Each model fh(·) was calibrated and selected with a methodhat chose a parsimonious, robust nonlinear model by solv-ng a constrained multiobjective optimisation problem, whoseolution space is composed of all feasible combinations ofiven explanatory variables. By definition, a feasible combi-ation is composed only of statistically significative variables
n which each sub-category must have at least one variable,.e. 〈G〉b, 〈U〉b, 〈M〉b �= ∅. The significance of each variable wasssessed by a nonparametric test. For more details on this ap-roach please refer to Samaniego (2003) and Samaniego andardossy (2005).
.4. Stochastic simulation and statistical inference
ummarising, the formal representation of the system to benvestigated is:
= (Y, 〈G〉˝, 〈U〉˝, 〈M〉˝,F, z, ˇ, �, �, �) (9)
is a stochastic system whose main characteristic is thativen a starting condition it does not always lead to the sameutput. Hence, it does not display a deterministic regularity,ut the ensemble of possible outputs exhibits a statistical reg-larity. This property of the system will allow an understand-
ng of the functioning of the system. The results of the simu-
coming of the model was compensated by the introductionof scenario specific parameters denoted by �.
(3) The climatic variables are drawn from their multivariatejoint distribution. The resampling procedure, however, hasto be done sequentially since the climatic variables aremutually dependent. This method is called a conditionalMonte Carlo simulation (Hammersley and Handscomb,1964). The procedure is as follows. Firstly, a variable – sayxe – assumed to be independent is drawn from their re-spective empirical distribution function (EDF) F(xe). For asubsequent variable – say xe′ – however, the distributionfrom which it is drawn has to be modified by the value ofthe primary variable. This modified distribution is calledthe conditional distribution, which can be formally writ-ten as:
FXe′ |Xe (xe′ |xe) = P(Xe′ ≤ xe′ |Xe = xe), ∀e′ �= e (10)
The simulations in the present study were carried out withthe following algorithm.
Algorithm 1. Stochastic simulation
(1) Define all scenario specific parameters, e.g. �.(2) For r = 1, . . . , R.
(a) For t = 1, . . . , T.(i) Resample without replacement of a cell (i, j) ∈ Z,
whose land use/cover is q.(ii) Solve the master equation for cell (i, j) [Eq. (2)].
(iii) Select at random a land use/cover category q′.(iv) With a probability P(q′, t)ij accept a transition from
q → q′.(v) Repeat steps (2a.i) to (2a.iv) ∀(i, j) ∈ Z.
(vi) Estimate land use/cover shares based on Ur˝(t).
50 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
(vii) Resample with replacement the independent vari-ables xe from their respective EDFs.
(viii) Resample with replacement the remaining cli-matic variables Mr
˝(t) from their respective condi-tional distribution functions [Eq. (10)].
(ix) Scale up all climatic variables according to the sce-nario conditions. Check additional constraints. Incase they are not fulfilled return to step (2a.viii).
(x) Estimate Y˝h(t) = fh(〈G〉˝(t), 〈U〉˝(t), 〈M〉˝(t), ˇ), ∀h.(b) Estimate the long-term means for each realisation
¯Yhr = �[Y˝hr(t)], ∀h, r; t = 1, . . . , T.(3) Estimate means and variances of each runoff characteris-
tic at each point in time t:
¯Yh(t) = �[Y˝hr(t)],
and
var(Yh(t)) = �[(Y˝hr(t) − ¯Yh(t))2], ∀t, h; r = 1, . . . , R.
(4) Estimate ¯Yh = �[Y˝hr(t)], ∀h, t = 1, . . . , T; r = 1, . . . , R.(5) For h = 1, . . . , H.
(a) Estimate from the simulated-EDF for the long-termmeans {Yh(r) : r = 1, . . . , R} the exceedance probabil-ities ˛h with respect to historical records as ˛h =1 − (r/(R + 1)), where r must satisfy the conditionYh(r−1) ≤ �[Y˝h] < Yh(r).
(b) Estimate 95% confidence intervals based on {Y : r =
Table 1 – Land use/cover categories and their averageproducer’s accuracy (PA) (i.e. error of omission) obtainedduring the classification of the LANDSAT scenes of 1975,1984, and 1993
q Land covercategory
PA Land use category
1 Forest 0.98 Deciduous, conifer, mixed forest2 Impervious
cover0.99 Built-up and commercial areas
Transportation and industrial areas3 Permeable
cover0.97 Recreation and agricultural areas
3. Application
3.1. The study area
The proposed simulation model was applied in the catch-ment located upstream of the gauging station Denkendorf-Sägewerk in the river Korsch, Germany (see Fig. 2). Its areais 126.3 km2 and because of its vicinity to Stuttgart it has en-dured a rapid land use/cover change in the past four decades –mainly from agricultural areas to settlement – reaching a grossdensity of about 720 in./km2 by the end of 2001 (Samaniego,2003).
3.2. Calibration and validation of the LUCC model
Considering the data availability for the study area, three (Q =3) mutually exclusive land use/cover classes were simulatedby the LUCC model described in Section 2.2. Furthermore, eachof these land use/cover categories should have a remarkablydifferent hydrological response. The categories adopted areshown in Table 1.
-Wur
h(r)
1, . . . , R}.
where R is the number of realisations (i.e. size of the en-semble for each development scenario); T an index denotingthe duration of the simulation period; H the number of runoffcharacteristics; �[·] the expectation of a given random variable;and Yh(r) denotes the r smallest value among a set of estimatedvalues of Yh (values are sorted in ascending order).
Fig. 2 – Location of the study area within the State of Badennetwork and main settlements in the region.
ttemberg, Germany, as well as the main transportation
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 51
Table 2 – Potential predictors of land use/cover change
k Variable Description Unit Source
1 z1(i, j) Distance to main highways [m] Digitised 1:50 000 topographic maps2 z2(i, j) Distance to towns and settlements
with metro or railway connection[m] Digitised 1:50 000 topographic maps
3 z3(i, j) Distance to streams [m] From DEM, 30 m × 30 m4 z4(i, j) Elevation [m] DEM, 30 m × 30 m5 z5(i, j) Slope [◦] From DEM, 30 m × 30 m6 z6(i, j) Aspect relative to south [◦] From DEM, 30 m × 30 m
The procedure to calibrate the LUCC model comprised thefollowing steps.
The first step was the definition of the potential predic-tors zk(i, j) conceived as proximate sources of a land use/coverchange. They denote the accessibility to main transportationaxes, jobs, amenities (located in towns and settlements) aswell as morphological variables, which were assumed to betime invariant during the simulation period. A summary ofthese variables is shown in Table 2. Each predictor was de-fined on a lattice whose size is 393 × 745 and where each cell(i, j) has a resolution of 30 m × 30 m.
The second step was the definition of five independentrandom samples, one for each possible land use/cover tran-sition q → q′. Each sample was fixed to 2000 observationsand included a binary indicator variable Iqq′ (i, j) and thecorresponding values of the exogenous variables zk(i, j) ,i.e. each sample is composed of the following information{Iqq′ (i, j), z1(i, j), . . . , z6(i, j) : (i, j) ∈ Z}. The binary indicator vari-able denotes the probability of occurrence of a land use/coverchange. If it has occurred it takes the value 1, if not it takesthe value 0, or formally:
Iq′q(i, j) ={
1, if Uij(t1) = q′ ∧ Uij(t0) = q ∧ q �= q′
0, if Uij(t1) = Uij(t0) = q(11)
where t0 and t1 represent the years 1975 and 1993, respec-tively (calibration years). Due to the relatively high classifica-t1wrsa
o
eralised linear model, which assumed that the observationsof the binary indicator Iq′q provided by a given sample wererealisations of a Bernoulli distribution. Consequently, the ex-pectation of Iq′q – which equals the probability – was estimatedas follows:
E[Iq′q] = P(q′, q) = e�(zk)
1 + e�(zk)(12)
where �(zk) is the linear predictor defined as:
�(zk) = �0(q′, q) +K∑
k=1
�k(q′, q)zk(i, j) (13)
Upon this basis, the best models were obtained by applyinga stepwise searching algorithm described in Samaniego (2003)in order to select the best model given K predictors. The coeffi-cients �k(q′, q) were fitted by the maximum likelihood method.The results for the most robust models are shown in Table 3.All variables were significant at the 5% level.
In order to validate the land use/cover model, two landuse/cover maps were used: one from 1984 and another from1993. The former was used as the starting condition while thelatter was the goal to be reached by the proposed model. Then,using the parameters shown in Table 3 and correspondingscaling parameters, the model was run 100 times (i.e. R = 100)for this interval of 9 years. As a result, 100 realisations for theland use/cover state in 1993 were obtained and compared with
roba
33232
ion accuracy obtained for the land cover categories (see Table), it was assumed that this source of uncertainty (comparedith the others) will not have a significative influence on the
esults. More accurate imagery will certainly improve the re-ults of the LUCC model, unfortunately this information is notvailable for the study area.
The calibration of the parameters needed for (5) was carriedut independently for each transition probability using a gen-
Table 3 – Estimated model coefficients for each transition p
Transition �0(q′, q) �1(q′, q)
From q To q′
1 2 +5.966E−01 +7.030E−01 3 +5.561E+00 −9.179E−02 3 +3.027E+00 −1.018E−03 1 −3.168E+00 +4.267E−03 2 −3.678E+00 +1.227E−0
Transition probabilities were later annualised.
the mapped land cover map from 1993 using the error matrixapproach commonly employed in remote sensing. The errormatrix tallies all possible combinations of true (mapped) andsimulated land cover categories [for more details please referto Jensen (2005)]. On average, the realisations showed that themodel had an overall accuracy of 85%. (The overall accuracyis the ratio between the total number of cells with a perfectlysimulated land cover category and the total number of cells.)
bility using observations of 1975 and 1993
�2(q′, q) �4(q′, q) �5(q′, q)
−9.173E−02 −1.259E−03 −1.768E−03−8.639E−02 −5.745E−04 −7.529E−04−8.011E−02 −8.123E−05 +9.876E−04+1.798E−01 −2.508E−04 +5.638E−04+3.160E−02 −9.757E−04 −5.455E−04
52 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
3.3. Calibration of the hydrological models
In the present study 46 sub-catchments located in the Up-per Neckar catchment, Germany (see Fig. 2) were used tocalibrate the hydrological models described in Section 2.3.For all these basins, 41 possible explanatory variables and10 runoff characteristics were quantified with 1-year timesteps during the calibration period ranging from 1961 to1993. The explanatory variables were arranged in the fol-lowing way: 〈G〉 = {x1, . . . , x16}, 〈U〉 = {x17, . . . , x19}, and 〈M〉 ={x20, . . . , x41}.
Here, 〈G〉 denotes a vector composed of many relevantphysiographic variables and a hydrogeological one repre-sented by x16 (see Table 4). Land use/cover variables 〈U〉 arerepresented by the fractions of each land cover categories. Fi-nally, the meteorological variables 〈M〉, comprise a numberof characteristics related with precipitation, temperature, andcirculation patterns at each catchment. It is worth noting thatduring the calibration and searching of good models, manyvariables were eliminated because they were either correlatedwith other ones, or were not significant as it was initially as-sumed. The criteria for the selection of runoff characteristicswere derived from the water resources management point ofview, where the extremes and annual volumes play a very im-portant role for the design of physical infrastructure and landuse planning.
The composition and type of the best models obtained
Tabl
e4
–S
um
mar
yof
the
com
pos
itio
n,m
odel
typ
esas
wel
las
the
cali
brat
edp
aram
eter
sco
rres
pon
din
gto
the
the
best
hyd
rolo
gica
lmod
els
fou
nd
Ru
nof
fch
ar.
Mod
elty
pe
ˇ0
ˇE
∗Pa
ram
eter
i(ˇ
i)
13
45
78
910
1112
1314
1516
17
Y1
MLP
2−4
7.6
+0.2
2+0
.09
+0.2
1+0
.09
−0.1
2−0
.31
Y2
POT
+20.
3+0
.65
+0.1
3+0
.10
−1.8
2−0
.65
+0.0
1−0
.30
Y3
MLP
2−4
.6+1
.33
+0.1
1−0
.38
−0.0
1−0
.01
Y4
POT
+3.0
e4−0
.03
+1.1
9+0
.54
−0.3
1−3
.30
Y5
MLP
1+1
.9e2
+0.0
1+3
.73
+0.0
1−0
.08
−0.0
9+0
.42
Y6
POT
+1.4
2+0
.06
Y7
MLP
2+0
.89
+3.3
7+0
.11
Y8
POT
+0.0
2−0
.64
+0.5
6+0
.22
−0.0
1−0
.13
Y9
MLP
2+0
.10
+4.9
2−0
.82
−1.1
4−0
.29
+0.4
9−0
.01
Y10
MLP
2−0
.27
+14.
7−0
.08
−0.7
1−2
.13
+0.2
4+0
.07
Ru
nof
fch
ar.
Mod
elty
pe
Para
met
eri(
ˇi)
1819
2122
2526
2728
2930
3132
3338
4041
Y1
MLP
2+0
.86
+1.2
0Y
2PO
T−0
.02
+1.9
5−0
.23
Y3
MLP
2+0
.05
+0.8
5Y
4PO
T−0
.07
+2.0
9−0
.91
Y5
MLP
1+0
.42
−0.7
5+1
.80
Y6
POT
−0.1
2+0
.95
Y7
MLP
2+0
.11
−0.5
0+1
.14
Y8
POT
−0.1
7+ 0
.76
+0.0
6+0
.16
Y9
MLP
2+0
.01
+1.1
0+0
.45
Y10
MLP
2+0
.87
Th
eca
libr
atio
np
erio
dw
asin
allc
ases
from
1961
to19
93w
ith
year
lyti
me
step
s.
as a result of applying the method briefly described in Sec-tion 2.3, are shown in Table 4. The explanatory variables inthese models are significant at the 5% level. The size of thevarious samples used for the calibration ranged from 830 to1300 observations. It is worth mentioning that all these par-simonious models were able to capture quite well the year toyear variability and past trends during the calibration periodfrom 1961 to 1993 (using the whole data sets) as confirmedby the correlation coefficient r shown in Table 5 (Samaniego,2003; Samaniego and Bardossy, 2005). Moreover, a split sam-pling technique was employed in order to check how wellthese models perform under changing macroclimatic condi-tions. In order to do it so, the original samples were artifi-cially split into two disjoint subsets called: cold years and warmyears. A cold year was defined as that whose monthly meantemperature in January or July is lower than the median ofthe respective monthly mean temperatures during the pe-riod from 1961 to 1993. A warm year is, thus, the comple-ment. Subsequently, all models were calibrated on the coldyears and then applied to the warm years. The correlationcoefficient rs, shown in Table 5, indicates the goodness oftheir predictions. This test shows that, at the most, the ex-plained variance of the most affected model (Y9) was reducedby approximately 55%. Other models were barely or much lessaffected, though. Additionally, BIAS and root-mean-squarederror (RMSE) statistics for the whole and the split samples– shown in Table 5 – also indicate that these models didnot exhibit systematic bias and that the RMSE was even re-duced in some cases. It should be acknowledged, however,that such a drastic change is not likely to happen in the sim-ulation period of this study (i.e. from 1994 to 2025). There-fore, these models were regarded as quite satisfactory con-sidering their reduced complexity. The meaning of the pre-
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 53
Table 5 – Quality measures (BIAS, and RMSE and r)obtained for the best models for both the whole and thesplit samples (denoted by the subindex s), respectively
Runoffcharacteristic
BIAS BIASs RMSE RMSEs r rs
Y1 +0.0 +4.3 28.5 71.9 0.96 0.81Y2 −0.1 +0.8 38.9 44.6 0.88 0.78Y3 +0.0 −0.1 3.0 0.7 0.78 0.70Y4 +0.0 −0.0 7.1 3.9 0.82 0.67Y5 +0.0 +0.3 14.9 2.6 0.75 0.65Y6 −0.1 +1.3 3.3 3.7 0.94 0.94Y7 +0.0 −0.1 2.3 2.0 0.94 0.92Y8 +0.0 +0.0 1.5 0.2 0.77 0.63Y9 +0.2 −0.0 1.1 0.1 0.87 0.58Y10 +0.0 −2.5 13.3 20.9 0.86 0.69
The calibration period was in all cases from 1961 to 1993 with yearlytime steps.
dictors as well as the explained variables shown in Table 4are:
x1 area of a given catchment (km2)x3 mean slope of the catchment (◦)x4 trimmed mean slope F(15) − F(85) (◦)x5 trimmed mean slope F(30) − F(70) (◦)x7 mean slope in floodplains (◦)x8 drainage density (m−1)x9 shape factorx10 fraction of north-facing slopesx11 fraction of south-facing slopesx12 mean elevation of the catchment (m)x13 difference between maximum and minimum eleva-
tion within a catchment (m)x14 fraction of saturated areasx15 mean field capacity (mm)x16 fraction of karstic formationsx17 fraction of forest coverx18 fraction of impervious coverx19 fraction of permeable coverx21 cumulative winter precipitation (mm)x22 cumulative summer precipitation (mm)x25 mean summer precipitation (mm)x26 antecedent precipitation index (API) (mm)x27 maximum annual API (mm)x
x
x
x
x
x
x
x
x
Y
Y
Y
Y4 specific peak in summer (mm)Y5 specific volume of the annual peak (mm)Y6 total duration of high flows in winter (day)Y7 total duration of high flows in summer (day)Y8 frequency of high flows in winter (year−1)Y9 frequency of high flows in summer (year−1)Y10 total drought duration in summer (day)
The wet and dry periods (see variable x38, x40, and x41) weredefined according to a wetness index, which, in turn, was es-timated taking into account the time series of both daily pre-cipitation and the European atmospheric circulation patterns(CP) (Hess and Brezowsky, 1969). Other meteorological vari-ables such as daily temperature and precipitation were inter-polated with External Drift Kriging to a spatial resolution of300 m×300 m. More details about the formal definition and es-timation of these variables can be found in Samaniego (2003).
In this study, three convex and continuously differentiablefunctions were investigated. The first one is a potential model(shortened to POT) that considers all possible explanatory vari-ables as having nonlinear relationships with the explainedvariable. The second model type, thereafter called MLP1, re-gards the climatic variables as the only ones having a non-linear relationship with the explained variable while the restare considered linearly related with the explained variable.Lastly, the third model type (shortened to MLP2) regards theland cover variables as the only ones exhibiting linear relation-
28 maximum winter API (mm)
29 maximum summer API (mm)
30 mean temperature in January (K)
31 mean temperature in July (K)
32 maximum temperature in January (K)
33 maximum temperature in July (K)
38 total number of “dry periods” with decreasing API insummer (day)
40 total number of “wet periods” in summer (day)
41 total number of “wet periods” occurring, simultane-ously with an API greater than a given threshold inwinter (day)
1 total discharge in winter (mm)
2 total discharge in summer (mm)
3 specific peak in winter (mm)
ships with the output variable. These models can be writtenexplicitly as:
Ytbh = ˇ0
∏e
(xtbe)ˇe + εt
b (14)
Ytbh = ˇ0 +
∑e
e �= e′
ˇjxtbe + ˇe′ (xt
be′ )ˇe′ + εtb (15)
and
Ytbh = ˇ0 +
∑e∈U
ˇextbe + ˇE∗
∏e
e /∈ U
(xtbe)ˇe + εt
b (16)
where e′ ∈ M, E∗ = E + 1, and {ˇ0, . . . , ˇj, . . . , ˇE∗ } are coefficientsto be optimised so that an estimator based on the random er-ror εt
bis minimised. In the present case, the most robust mod-
els found for Y2, Y4, Y6, and Y8 were of the type POT; whereasfor Y5 and the rest were of the type MLP1 and MLP2, respec-tively (see Table 4).
3.4. Socioeconomic scenarios
In the present study, for the sake of simplicity, only two so-cioeconomic scenarios termed S1 and S2 were conceived forthe study area. They are based on the actual socioeconomicand political situation in Germany and have some commonfeatures to ease comparison. For instance, the population inthe region (i.e. the municipal district of Stuttgart and Esslingencounty) will slightly decline at about 0.1% per year whereas theGDP per capita of the state of Baden-Wurttemberg will grow at
54 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
an average rate of about 2.3% per year.2 However, these scenar-ios have characteristic conditions with regard to the drivingforces and the society attitudes that promote land use/coverchanges, namely:
Scenario S1. The keyword for this scenario is status quo.The storyline of this scenario describes a future state of thestudy area in which its development can be explained as anextrapolation of past trends up to the year 2025. It will allow,for instance, a further reduction in forest covered area, whichshrank approximately 16% in the period 1975–1993. Gener-ally, a land use/cover change from forest into either farm-land or settlements does not take place in the state of Baden-Wurttemberg. Under specific circumstances, however, thistransition may happen according to the “Baden-WurttembergForest Law”.3 The historical records depicted in Fig. 4 consti-tute a clear example of these exceptions.
This scenario assumes that the steady growth of incomeper capita combined with an excellent provision of road trans-portation network and stable taxation for fossil fuels will keepthe relationship between car-ownership and the demand forresidential floor space tightly correlated (r2 = 0.88 from 1974to 1997) as can be seen in Fig. 3. These indicators will con-tinue to grow at 2.6 and 1.5% per year, respectively. In additionto that, the rent for housing in Stuttgart and its surroundingswill soar due to the region’s high level of centrality. The impli-cation of these assumptions is that although the populationsettled in the region is quasi constant, the demand for larger
Fig. 3 – Increase rates of population, car ownership,employment, and share of settlement areas expressed inpercentage. The base year for all indicators is 1974(Statistical Office of Baden-Wurttemberg).
and the political decision-making bodies, in particular, willfinally become aware that a rapid urban sprawl representsa threat to the environment, which, in turn, may contributeto increased flooding and drought hazards in the region.Consequently, tougher land use by-laws and higher propertytax regulations will be adopted. As a result, the demandfor floor space per capita will be reduced significantly. Sec-ondly, the “Eco Tax” (tax on fuel that makes commuting
up to 2025 with 1-year time steps.
apartments and detached houses with large gardens located invillages and settlements with good road accessibility will growrapidly. As a result, new housing areas will appear everywherein the outskirts of Stuttgart and surrounding towns, accompa-nied by large shopping malls with huge parking places whilefloor space downtown will be swiftly taken by branches of theservice sector (Samaniego, 2003).
At the basin level, let 〈U〉(t) be a Q-dimension vector de-noting the area of each land use/cover category for the riverbasin ˝. As a consequence of the scenario S1 the evolution ofthese variables (see Fig. 4) was estimated based on a Markovchain whose annual transition matrix was adjusted to fitthe observations (1975, 1984, and 1993). The matrix obtainedwas:
〈U〉(t + 1) = 〈UT〉(t)
⎛⎝ 0.984 0.016 0
0 0.986 0.0140.002 0.018 0.980
⎞⎠ (17)
Based on this fast urban sprawl scenario, the LUCC modelwas scaled up so that the land use/cover categories forest, im-pervious, and permeable cover will reach in average 1280, 5950,and 5390 ha, respectively, by the end of 2025. Restricted areaswere preserved.
Scenario S2. The keyword for this scenario is local sustain-ability. The storyline of this scenario differs from the previousone in several topics. Firstly, the public opinion, in general,
2 Based on an external forecast carried out in 2002 by the Sta-tistical Office of Baden-Wurttemberg, http://www.statistik.baden-wuerttemberg.de/.
3 See §9 LWaldG, http://www.wald-online-bw.de/pdf/gesetze/LWaldG.pdf.
Fig. 4 – Land use/cover simulations based on Scenario S1and S2 conditions (upper and lower panel, respectively).The observation points were derived from the LANDSATscenes for 1975, 1984, and 1993. The simulation period is
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 55
more expensive) will be strengthened. Tax exceptions willbe introduced for smaller and pollution-free cars, whereashigher taxes will be imposed on vehicles with standard com-bustion engines. These regulations, along with a sufficientfrequency and capacity offered by almost pollution-free masstransportation systems, will slowdown the growth rate ofthe car-ownership ratio. As a result, the demand for spacerequired for new roads and parking places will be reduceddramatically. Because of the new legislation, the growth rateof impervious areas, as can be seen in Fig. 4, will slowdownfrom 1.3% per year of the “status quo” scenario to 0.4% peryear in scenario S2. The scenario denotes a consolidation ofthe urban fabric of the study area. Thirdly, the decrease offorest observed in the period 1975–1993 has been taken by thepublic opinion as a loss of German “identity”. Therefore, landuse/cover compensation rules stated in the EnvironmentalImpact Assessment (EIA) by-laws will be strengthened, andwherever possible reforestation projects will be initiated.At the end of the simulation period (i.e. 2025) the landuse/cover categories forest, impervious, and permeable coverwill have an average of 2160, 4390, and 6075 ha, respectively(Samaniego, 2003).
3.5. Macroclimatic scenarios
Currently, there is plenty of empirical evidence (Karl and Tren-berth, 1999; Houghton et al., 2001; Zwiers, 2002; Stocker, 2004)tvmtlcHtwaeuttoiglS
iTfasc
aebwle
increase of income per capita are pursued all over the world.The promotion of clean and resource-efficient technologieswill be very limited, and the main source of energy will stillbe fossil fuels. Global inequality will grow. Under these con-ditions, it is hypothesised that the atmospheric CO2 concen-tration will reach about 525 ppmv by the year 2050. GCM sim-ulations using CGCM1 (Boer et al., 2000) and HadCM2 (Johns,1996) under this emission scenario suggest that 30-year meanclimate changes at regional levels will be very likely to happenin the future. For Germany in particular, the most expected cli-matic disruptions in the future are summarised next. Precipi-tation will increase in winter due to an intensified hydrologi-cal cycle but will decrease in summer because of an increasedevapotranspiration. Furthermore, the intensity and frequencyof extreme precipitation events in summer will likely increase,mainly because of changes in atmospheric moisture, thunder-storm activity, and large-scale storm activity (Hennessy et al.,1997; McGuffie et al., 1999). In other words, the return periodof extreme events will be shortened. Consequently, magnitudeand frequency of high flows will most likely increase. It is alsovery likely that low-flow periods or droughts will increase dueto greater evaporation (Gregory et al., 1997). Mean tempera-ture will very likely increase in both seasons. The frequencyof minimum and maximum temperatures will also change,with fewer cold and frost days in winter, and much dryer andhotter days in summer (Houghton et al., 2001). In other words,weather patterns in this future world will become more in-
hat the Earth’s surface mean temperature has endured aery rapid increase during the last 100 years that “counters aillennial-scale cooling trend, which is consistent with long-
erm astronomical forcing” (Mann et al., 1999). Based on pa-eoclimatic data and instrumental records, the IPCC has con-luded that the average surface temperature in the Northernemisphere has increased by (0.6 ± 0.2) K during the 20th cen-
ury (Houghton et al., 2001). Since climate is changing, theeather and its meteorological variables used in this study
t mesoscale will certainly change in the future. However, tostimate how big these changes would be in a given placesing the results of a GCM is rather complicated because ofhe deep uncertainty involved in future estimates. The uncer-ainty of the system does not come only from the complexityf the system itself but also from future actions of human be-
ngs, especially with regard to both the amount of emissions ofreenhouse gases into the atmosphere and the magnitude ofand use/cover changes at the macroscale (Samaniego, 2003;tocker, 2004).
In the present study, macroclimatic scenarios were usedn order to deal with the uncertainty of climate in the future.hey provide the framework for the climatic conditions for a
uture world under given hypothesised macrosocioeconomicnd emission scenarios. In order to simplify the analysis, thistudy only conceives two extreme macroclimatic scenariosalled scenario C1 and C2, respectively.
Scenario C1. The keyword for this scenario is pessimistic,nd describes the worst-case situation. The storyline for thismission scenario corresponds to the“A2” scenario describedy McCarthy (2001). It envisages a heterogeneous future worldith a continuously growing population. Emphasis is given to
ocal, short-term solutions instead of long-term, globally ori-nted, and sustainable ones. Free market, consumerism, and
tense and erratic.Scenario C2. The keyword for this scenario is optimistic.
The storyline of this emission scenario corresponds to sce-nario “B1” described by McCarthy (2001). It describes a con-vergent future world with a global population stabilising inmid-century. “Global Sustainability” is the motto of all gov-ernments on Earth, which implement global solutions for eco-nomic and environmental issues. Most of the energy demandwill be covered by renewable energy sources. Promotion ofclean and resource efficient technologies will be a key ele-ment of the decision-making process. As a result, CO2 emis-sions as well as other greenhouse gasses will decrease after2050, and the atmospheric CO2 concentration will reach about550 ppmv only by the year 2100. The GCM mentioned above fedwith these conditions predict that the climatic changes in Ger-many will be much less severe than those in scenario “C1”; infact, the difference between these scenarios in growth rate perdecade for both mean precipitation and temperature is in re-lation of 3:1 approximately. The mean temperature increase,for instance, by the year 2020 will remain under the 95% con-fidence interval of the natural variability (McCarthy, 2001), butthe change of mean precipitation in winter will certainly ex-ceed the natural variability of the last century – about 0.1% perdecade (New et al., 2000).
3.6. Assembling the development scenarios
In the present study, the development scenarios were assem-bled by combining one socioeconomic scenario (S1, S2) withone macroclimatic scenario (C1, C2) at a time. As a result,four development scenarios were obtained, which were calledC1S1, C1S2, C2S1, and C2S2, respectively. The specific condi-tions for each of them are shown in Table 6.
56 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
Table 6 – Growth rates and changes in the occurrence probability for each development scenarios
Variable Development scenario
Description Symbol Class/season/cat. C1S1 C2S1 C1S2 C2S2
[%/yr]Land cover x17 Forest −0.9 −0.9 +0.7 +0.7
x18 Imper. cover +1.3 +1.3 +0.4 +0.4x19 Perme. cover −0.8 −0.8 −0.5 −0.5
[%/decade]Mean precipitationa {x : F(x) < 0.9} x24 Winter +4.1 +1.6 +4.1 +1.6
x25 Summer −2.7 −1.0 −2.7 −1.0Probability P(X ≤ x)
Low precipitationa {x : F(x) ≤ 0.1} x24 Winter �b � � �
x25 Summer 0 � 0 �
Prob. and magnitude [%/decade ]High precipitationa {x : F(x) ≥ 0.9} x24 Winter � � � �
x25 Summer +4.0 � +4.0 �
[%/decade]Mean temperaturea {x : F(x) < 0.9} x30 Winter +2.1 +0.8 +2.1 +0.8
x31 Summer +2.9 +1.1 +2.9 +1.1Probabilityc P(X ≤ x)
Low temperaturea {x : F(x) ≤ 0.1} x30 Winter 0 � 0 �
x31 Summer 0 � 0 �
Prob. and magnitude [%/decade ]High temperaturea {x : F(x) ≥ 0.9} x30 Winter � � � �
x31 Summer +10.0 � +10.0 �
[%/decade ]Annual precipitationd x21 Winter +3.9 +1.6 +3.9 +1.6
x22 Summer −2.7 −1.0 −2.7 −1.0[%/decade ]
Maximum APId x27 Annual +1.4 +0.5 +1.4 +0.5x28 Winter +3.9 +1.5 +3.9 +1.5x29 Summer 0.0 0.0 0.0 0.0
[%/decade]Maximum temperature x32 Winter +2.0 +0.7 +2.0 +0.7
x33 Summer +1.6 +0.6 +1.6 +0.6[%/decade ]
ATI at annual peak discharged x21 Annual −0.2 −0.1 −0.2 −0.1[%/decade ]
Duration of a given category of Circulation Patternsd x41 Winter/Wet +6.9 +2.7 +6.9 +2.7x40 Summer/Wet −8.9 −3.5 −8.9 −3.5x29 Summer/Dry +9.0 +3.3 +9.0 +3.3
a Based on GCM simulations under a given emission scenario.b Denotes that there will be no significant change in magnitude or that the probability of occurrence will remain equal to that of the reference
period 1961–1993.c Based on the PDF of the variable during the reference period.d Based on potential relationships between a given variable and x24, x25, x30, and x31.
4. Results and discussion
The behaviour of the system, roughly represented by themodel M, was assessed by 2500 realisations under each setof development scenario conditions. In all these simulations,1994 was used as the reference year. The simulation periodwas set from 1994 to 2025 with yearly time steps. As a sum-mary of these simulations, the average growth rate in percentper decade for each simulated variable as well as the prob-ability that the long-term mean of a given variable will beexceeded were estimated, which are shown in Table 7. Thelong-term means were estimated with the information avail-able for the period ranging from 1961 to 1993. In the presentcase, the exceedance probability can be interpreted as fol-
lows: if the probability is greater than, say, 0.95, this meansthat it is very likely that the past mean of a given variablewill be surpassed in the future; or put differently, that theexpectation of such a variable will increase over time. Onthe contrary, a value less than 0.05 will mean that the pastmean of a variable will be hardly reached, thus, a decreasingtendency of the expectation of such a variable is very likelyforeseeable.
Based on the results of the simulations shown in Table 7and Fig. 5 it can be clearly seen that the hydrological systemof the studied catchment will endure the greatest disruptionsunder the C1S1 scenario conditions, and conversely, the leastones under scenario C2S2. The other two scenarios, i.e. C1S2and C2S1, are in-between the previous two. For a more de-tailed hydrological interpretation of the results please refer
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 57
Table 7 – Average percent change per decade and probability of exceeding the long-term means for each simulatedvariable
Variable [%/decade ] Exceedance probability
Symbol Mean C1S1 C2S1 C1S2 C2S2 C1S1 C2S1 C1S2 C2S2
Y1 181.2 mm +6.9 +5.4 +3.7 +2.4 1.000 1.000 1.000 1.000Y2 153.4 mm −2.6 −6.8 +0.4 −4.1 0.332 0.020 0.238 0.020Y3 7.1 mm +8.8 +5.4 +5.4 +2.5 0.218 0.037 0.052 0.002Y4 9.1 mm −3.7 −1.6 +0.1 −0.6 0.335 0.335 0.231 0.229Y5 25.8 mm +9.9 +3.2 +8.0 +2.2 1.000 0.992 1.000 0.973Y6 10.0 day +5.6 +6.2 +2.3 +2.7 0.732 0.775 0.580 0.649Y7 8.1 day −1.9 −4.5 +1.8 −1.1 1.000 0.995 0.998 0.984Y8 4.3 year−1 +7.1 +3.5 +4.4 +1.3 0.920 0.712 0.786 0.460Y9 4.9 year−1 −2.8 −2.6 −1.2 −1.8 0.265 0.219 0.071 0.060Y10 21.2 day +8.4 +8.0 +3.7 +3.8 0.437 0.423 0.703 0.716
1994 was used as the reference year.
to Samaniego (2003). Summarising, the following hydrologicaleffects can be foreseen.
The total discharge in winter, Y1, will increase at about 6.9%per decade in the worst-case scenario C1S1, which represents
a very rapid increase in urban sprawl (roughly 1.3% per year)accompanied by a continuous increase of mean air surfacetemperature caused by global warming. The total discharge insummer, Y2, will in general decrease because of higher tem-
Fga
ig. 5 – Deviations in percent of the mean of the simulated variaiven scenario conditions. The deviation of the mean value andnd a bar, respectively.
bles with respect to the respective historical mean underits 95% confidence interval are represented here with a dot
58 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
peratures and corresponding increasing evapotranspiration.Scenario C2S1, nevertheless, may endure increments as to thereference period. The 95% confidence intervals shown in Fig. 5indicate that the average total discharge in winter up to 2025would be 17–44% bigger that that of the base period (1961–1990)for scenario C1S1. In the most favourable scenario (C2S2) thesefigures will be as low as 7 and 34%, respectively.
Specific peaks in winter, Y3, will tend to increase in allscenarios. However, the largest deviation from the historicalmean corresponds to the development scenario C1S1. Landuse/cover change plays a very important role in this runoff in-dicator. The difference in percent between the socioeconomicscenarios S1 and S2 is about 3% per decade regardless of themacroclimatic settings. Specific peaks in summer, Y4, will tendto decrease in all scenarios with the exception of scenarioC2S1. In the latter, summers will not be much hotter as dur-ing the reference period but an increase of impervious coverwill reduce the concentration time of surface runoff, which,in turn, will tend to increase peak flows at the rate of 0.1% perdecade.
The specific volume of the annual peak event, Y5, is therunoff characteristics that is mostly affected by land coverchanges simulated in the study area. The difference betweenthe growth rates of this variable under socioeconomic scenar-ios S1 (i.e. urban sprawl) and S2 (i.e. densification) may rangefrom 5.8 to 6.7% per decade, depending on whether the futuremacroclimate conditions will be either moderate or exacer-
Fig. 6 – Relationship between the area of impervious coverand total winter discharge Y1 under C1S1 scenarioconditions. In both cases the historical records range from1961 to 1993 whereas the simulated values range from1994 to 2025. The dashed line depicts the trend of thevariable in both periods. During the simulation period andunder C1S1 scenario conditions this variable exhibited apositive trend of 6.9% per decade, see Table 7.
tion 1), but also highlights the need to carry out stochastic sim-ulations to understand the behaviour of environmental sys-tems. In this case, for instance, it is not possible to say whichpath the system would follow in the future, but it is possibleto say that if this river basin will endure land use/cover transi-tions in the coming future at rates comparable to what it hasalready had during the past decades, then, it is very likely thatthe expectation of the winter discharge will be greater thanits historical one (i.e. 1961–1993). This figure also depicts thatthe dispersion of the simulations is quite big, nevertheless, itshows that the expectation of them (see dashed line) exhibit aclear upward trend whose slope is significatively greater thanthe historical one. To complement this example, the evolutionover time of the impervious surfaces under the status quo (S1)scenario conditions is also shown in Fig. 7. In this figure, it isworth noting how the LUCC model exhibits an intrinsic un-certainty which tends to grow over time, however, simulatedvalues of variable x18 – denoted here by dots – follow the ten-dency forecasted by the Eq. (17).
bated, respectively (i.e. climate conditions of scenario C2 orC1 correspondingly). This implies that if scenario C1S1 wouldbecome true, the future volume of the annual peak flow couldbe between 15 and 43% greater than during the reference pe-riod with a 95% level of confidence. In other words, more in-tensive floods can certainly be expected downstream of thestudy area.
Total duration of high flows in winter, Y6, will be higher onaverage in the densification scenario (S2) than in the urbansprawl scenario (S1) assuming constant climatic conditions.Otherwise stated, discharges that occur less than 5% of thetime will persist during longer periods. Total duration of highflows in summer, Y7, will tend to decline in general mainly be-cause mean temperature in summer will increase. The growthrate in the densification scenario is even smaller because for-est regrowth occurs under this scenario, which implies higherrates of evapotranspiration and, hence, lower surface runoff.The exception is the scenario C2S1 (i.e. moderate climate andurban sprawl) where this variable will tend to grow at just 0.1%per decade.
Frequency of high flows will grow in winter, Y8, and con-versely, it will decline in summer, Y9. Moreover, the urbansprawl scenario (S1) will exhibit the larger growth rates underthe same climatic conditions. Finally, the total drought dura-tion in summer, Y10, will tend to increase faster in climaticscenario C1 than in C2. Land use/cover changes will have animpact on this variable but to a lesser degree as compared withthose originated by a macroclimatic change.
As an example of the behaviour of the simulated variables,the relationship between the imperviously covered areas andtotal winter discharge Y1 under C1S1 scenario conditions isshown in Fig. 6. This figure not only corroborates what wasstated about the intrinsic uncertainty of the system (see Sec-
Fig. 7 – Evolution of impervious cover in the study areabased on socioeconomic scenario S1. The forecasted trendand the observations were depicted as a reference.
e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61 59
Fig. 8 – Time series of land cover in the study area from 1960 to 1993. Additionally, two random realisations of the landuse/cover for the year 2025 under S1 and S2 scenario conditions.
Finally, the effects of the two socioeconomic scenarios canbe visualised along with a time series of land cover maps inFig. 8. As expected, the vicinity of existing towns and thoseplaces with high accessibility exhibit the highest probabilityfor a land use/cover change during the simulation period.
5. Conclusions
Considering the basic objective proposed at the beginning ofthis paper, it is possible to draw the following conclusions:
(1) Coupling parsimonious hydrological models of severalrunoff characteristics at the mesoscale with a simplestochastic land use/cover change model has proved to befeasible and enlightening. The approach followed here notonly allows one to relate a number of variables otherwiseexogenous to the system but also to produce results thathighlight the uncertainty of each component of the sys-tem as well as to take into account some of their synergyeffects.
(2) The use of holistic models and stochastic simulationsto deal with the deep uncertainty that characterizes theenvironmental systems and to detect possible structural
changes in the system should be a priority in future re-search. The advantage of this approach is that it allows oneto explore a wide range of plausible paths to the future thatmight occur under a given scenario. This approach doesnot eliminate the underlining uncertainty, but helps tofind ways to deal with it. By doing so, robust developmentstrategies aimed at boosting economic growth and raisingthe living standards of its inhabitants in the region with-out risking its long-term sustainability can be searchedfor. Additionally, it will contribute to improving our un-derstanding of nature (e.g. hidden relationships, scaleissues).
(3) The performance of the models should still be improved,e.g. by including missing feedback mechanisms and dy-namic driving forces in the LUCC model, by including newsources of data (e.g. from remote sensing), or by testingnew modelling techniques.
Acknowledgement
The authors appreciated the helpful comments from twoanonymous reviewers.
60 e c o l o g i c a l m o d e l l i n g 196 (2006) 45–61
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