Comparison of hydrological model structures based on ...€¦ · ing and modelling of low ﬂow are...

Hydrol. Earth Syst. Sci., 15, 3447–3459, 2011www.hydrol-earth-syst-sci.net/15/3447/2011/doi:10.5194/hess-15-3447-2011© Author(s) 2011. CC Attribution 3.0 License.

Hydrology andEarth System

Sciences

Comparison of hydrological model structures based on recessionand low flow simulations

M. Staudinger1, K. Stahl2, J. Seibert1, M. P. Clark 3, and L. M. Tallaksen4

1Department of Geography, University of Zurich, Zurich, Switzerland2Institute of Hydrology Freiburg, Albert-Ludwigs University, Freiburg, Germany3University Cooperation for Atmospheric Research, Boulder, Colorado, USA4Department of Geosciences, University of Oslo, Oslo, Norway

Received: 8 July 2011 – Published in Hydrol. Earth Syst. Sci. Discuss.: 13 July 2011Revised: 27 October 2011 – Accepted: 1 November 2011 – Published: 17 November 2011

Abstract. Low flows are often poorly reproduced by com-monly used hydrological models, which are traditionally de-signed to meet peak flow situations. Hence, there is a need toimprove hydrological models for low flow prediction. Thisstudy assessed the impact of model structure on low flowsimulations and recession behaviour using the Frameworkfor Understanding Structural Errors (FUSE). FUSE identifiesthe set of subjective decisions made when building a hydro-logical model and provides multiple options for each mod-eling decision. Altogether 79 models were created and ap-plied to simulate stream flows in the snow dominated head-water catchment Narsjø in Norway (119 km2). All modelswere calibrated using an automatic optimisation method. Theresults showed that simulations of summer low flows werepoorer than simulations of winter low flows, reflecting theimportance of different hydrological processes. The modelstructure influencing winter low flow simulations is the lowerlayer architecture, whereas various model structures wereidentified to influence model performance during summer.

1 Motivation

Hydrological low flow periods and droughts affect watersupply for drinking water, irrigation, industrial needs, hy-dropower production and ecosystems. Their occurrence isalso of importance regarding environmental flow and wa-ter quality requirements, which are strongly connected to

Correspondence to:M. Staudinger([email protected])

critical low flows (Vogel and Fennessey, 1995). Low flowand droughts affect many sectors and occur in every countryalbeit in different perceived severity. There is a wide range ofconsequences related to low flow and drought and monitor-ing and modelling of low flow are crucial for their analysisand prediction. However, low flows are poorly reproducedby many hydrological models since these are traditionallydesigned to simulate the runoff response to rainfall.

A revision of model concepts regarding low flows requiresa clear understanding of the model’s structural deficits; inother words “when does it go wrong and which part of themodel is the origin?” (Reusser et al., 2009). A common ap-proach to investigate the impact of the differences in modelstructure is to perform model intercomparison experiments(e.g.Henderson-Sellers et al., 1993; Reed et al., 2004; Duanet al., 2006; Breuer et al., 2009andHollander et al., 2009).Such experiments have been helpful to explore model sim-ulation performance of lumped (Duan et al., 2006; Breueret al., 2009), semi-distributed (Duan et al., 2006; Hollanderet al., 2009) and distributed (Henderson-Sellers et al., 1993;Reed et al., 2004; Hollander et al., 2009) models in a consis-tent way using the same input data. The reasons for the dif-ferences, however, remain unclear since each model uses dif-ferent interacting parametrisations to simulate the hydrologi-cal processes (Clark et al., 2008). Perrin et al.(2001) studiedthe relation between the number of optimized parameters andmodel performance in a multi-model, multi-catchment ex-periment, and discussed the problem of over-parametrisationand parameter uncertainty.

Discrepancies between observed and simulated stream-flow can arise from errors in the input data rather than weak-nesses in model structure. This complicates the investigation

Published by Copernicus Publications on behalf of the European Geosciences Union.

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3448 M. Staudinger et al.: Comparison of hydrological model structures

of the impact of the differences in model structure.Clarket al. (2008) created a computational framework that en-ables a separate evaluation of each model component. TheFramework for Understanding Structural Errors (FUSE) dif-fers from others as it modularises individual flux equationsinstead of linking available submodels. FUSE identifiesthe set of subjective decisions while creating a hydrologi-cal model and offers multiple options for each model de-cision. This approach can thus help to get a better under-standing of the hydrological processes occurring.Clark et al.(2008) first introduced FUSE, as a diagnostic tool to eval-uate the performance of hydrological model structures us-ing the Nash-Sutcliffe efficiency for two climatically differ-ent catchments.Clark and Kavetski(2010) evaluated severalclasses of numerical time stepping schemes in order to findappropriate numerical methods used to solve the governingmodel equations of hydrological models. The experimentalsetup included beside different distinct time stepping algo-rithms, eight conceptual rainfall runoff models derived fromthe parent models. Another recent application of FUSE isdocumented in the two-part series ofMcMillan et al. (2011)andClark et al.(2011b). First, they used precipitation, soilmoisture and streamflow data to estimate the dominant hy-drological processes of a catchment. Then, plausible repre-sentations of these processes in conceptual models were for-mulated (McMillan et al., 2011). In the second part, theyevaluated FUSE models regarding their capability to simu-late those processes (Clark et al., 2011b).

Commonly, streamflow recession is modelled as the out-flow from a, or a set of, linear or non-linear reservoirs. Inperiods with no input, i.e. precipitation or snow melt, out-flow from the reservoirs control the streamflow and thus, themodel behaviour during low flow. Real hydrological pro-cesses can be more complex. Therefore, it is of interest tohave a closer look at the hydrograph recession, and care-fully evaluate model simulations of recession behaviour. Theshape of the observed recession curve reflects the gradual de-pletion of water stored in a catchment during periods with lit-tle or no precipitation. Initially, the recession curve is steepas quick flow components like overland flow and subsurfaceflow contribute to streamflow. The recession curve flattenswith time as e.g. delayed water from deeper subsurface stor-ages contributes, and may become nearly constant if sus-tained by outflow from the groundwater storage or from aglacier (Smakhtin, 2001). The recession curve describes inan integrated manner how different factors in a catchmentinfluence the generation of streamflow in dry weather peri-ods (Tallaksen, 1995). Hydrogeology, relief and climate havebeen found to be the most important catchment properties af-fecting the recession rate (Tallaksen, 1995). Catchments witha slow recession rate are typically groundwater dominated,while impermeable catchments with little storage show fasterrecession rates. Moreover, summer recessions are usuallyfaster than autumn or winter recessions (e.g.Federer, 1973;Tallaksen, 1995).

Several studies exist that link recession analysis with thestructure of hydrological models (e.g.Ambroise et al., 1996;Wittenberg, 1999; Clark et al., 2009; Harman et al., 2009).In this study the model structures are systematically analysedusing FUSE. The associated model performance is evaluatedwith respect to the ability to simulate low flows and reces-sion behaviour. This is done for one catchment only to allowa more detailed insight in the model structures. The mainobjective is to investigate the relative influence of a singlemodel structure on the model performance. As there are dis-tinct differences in the recession rates found for summer andwinter, one task is to study how model structure is connectedto the seasonal performance for low flow simulation. Thispaper aims to contribute to the improvement of hydrologicalmodels for low flow prediction.

2 Data and study area

The data are from the 119 km2 headwater catchment Narsjø,located in the South-East of Norway (Fig.1) with an alti-tude range between 737 and 1595 m a.s.l. (Engeland, 2002).Narsjø is a subcatchment of the Upper Glomma basin, whichis characterised by a continental climate with cold wintersand relatively warm summers (Engeland, 2002). The annualsnow melt flood dominates the hydrological regime. Themost pronounced low flow period occurs in winter, causedby precipitation being stored in snow and ice. A second lowflow period occurs in summer, caused by a lack of precipita-tion and losses due to evapotranspiration (Engeland, 2002).

The geology can be divided into two main areas: one areaconsists of schists and phyllites that occur in combinationwith fine grained till soil, the other area consists of igneousrocks (granite, gneiss and gabbro) usually in combinationwith coarser till (Engeland, 2002). This geological charac-teristic influences the properties of soil and vegetation. Thequaternary remains, consisting of several types of till and flu-vial deposits as well as bogs and lakes, form a wide, openmountain landscape with gentle slopes. The land cover isbarely influenced by humans (0.3 % agricultural land) and iscomposed of 23.7 % forest, 60.9 % open land, 12.0 % bogsand 3.0 % lakes (Engeland, 2002).

The streamflow data used are daily time series of observeddischarge measured at the outlet of the Narsjø catchment(provided by the Norwegian Water Resources and Energydirectorate, NVE). In addition, daily time series of precipi-tation interpolated from 12 surrounding meteorological sta-tions and potential evaporation (Beldring et al., 2003) wereavailable. The time series cover the period from 6 May 1981to 31 December 1995.

Hydrol. Earth Syst. Sci., 15, 3447–3459, 2011 www.hydrol-earth-syst-sci.net/15/3447/2011/

M. Staudinger et al.: Comparison of hydrological model structures 3449

Fig. 1. Location of the Narsjø catchment (modified afterBeldringet al., 2003).

3 Methods

3.1 Snow accumulation and melt

Narsjø is a snow dominated catchment, however, there wasno snow routine implemented in the version of FUSE usedfor this study. Hence, the input data was pre-processed witha snow accumulation and melt model. This corresponds toan implemented snow routine. Here, a simple degree daymethod was applied. The daily change in snow water equiva-lent1SWE [mm day−1] is equal to the difference in the dailysnow accumulationas [mm day−1] and the daily snow meltms [mm day−1] (Eq. 1).

1SWE = as − ms. (1)

The snow model separates the precipitationP [mm day−1]into rain and snow using a temperature threshold. Hence,there is only snow accumulationas in the catchment whenthe measured temperatureT [◦C] is below the threshold tem-peratureTacc (Eq.2).

as =

{0, T ≥ Tacc,

P , T < Tacc.(2)

In this study Tacc was set to 1.0◦C. The daily snowmelt ms was computed (Eq.3) with a melt factorMf of

3.0◦C−1 day−1 and a melt threshold temperatureTmelt of0◦C.

ms =

{Mf (T − Tmelt), T ≥ Tmelt and SWE> 0,

0, T < Tmelt and SWE= 0.(3)

The chosen melt factor was based onSeibert(1999) whofound melt factors in Sweden to vary between 1.5 and4◦C−1 day−1, where the first value is suited for open andthe latter for forested sites. The degree day method was ex-tended with a refreeze factorrf [−] which accounts for rainthat does not directly contribute to runoff due to the waterholding capacity of an existing snow cover (Eq.4).

P =

0, T ≥ Tacc,

P , T ≥ Tacc andP ≥ rf SWE,

(1 − rf) ms, T ≥ Tacc andP < rf SWE.

(4)

3.2 FUSE framework

The use of FUSE as a diagnostic tool to detect the impact ofmodel structure involved the following three steps: (1) pre-scription of the type of model (2) definition of the majormodel-building decisions and (3) preparation of multiple op-tions for each model building decision (Clark et al., 2008).In this study, the type of model was limited to lumped hy-drological, that were run at a daily time step (although themodels are not limited to a daily time step). Four con-ceptual parent models were selected to be recombined tonew FUSE-models: ARNO-VIC (Zhao, 1977), TOPMODEL(Beven and Kirkby, 1979), PRMS (Leavesley et al., 1983)and SACRAMENTO (Burnash, 1995). Simplified wiring di-agrams of the generating parent models are shown in Fig.2.The selection of the parent FUSE models was here limited tofour well known models, covering common principles usedin conceptual hydrological models.

All parent models consist of equally plausible structuresand the important processes could be broken down into fluxesoccurring in the upper layer and lower layer, evaporation,percolation, subsurface flow and surface runoff (model build-ing options).

Some processes were not explicitly modelled, includinginterception by the vegetation canopy as well as specific sur-face energy balance calculations. Routing was calculatedby a two parameter Gamma distribution (Press et al., 1992).Thus, all models represent the subsurface with a similar levelof detail and thus differences that emerged from differentplausible model structures were emphasised rather than dif-ferences due to the set of processes represented. The modeldecision options that were made separately for each of theFUSE models are described next (more details to the decisionoptions e.g. equations can be found inClark et al., 2011b). Asummary of those decisions that were permuted for this studycan be found in Table1 and the abbreviations from Table1will be referred to later in the text.

www.hydrol-earth-syst-sci.net/15/3447/2011/ Hydrol. Earth Syst. Sci., 15, 3447–3459, 2011


Fig. 2. Simplified wiring diagrams of the parent models (modified afterClark et al., 2008).

3.2.1 Upper layer

The water content of the upper soil layer was either definedas a single state variable or split into tension storage and freestorage, with an additional option to further subdivide thefree storage into below and above field capacity (Table1).

3.2.2 Lower layer

The lower soil layer was either defined by a single state vari-able with unlimited storage and no lower layer evapotranspi-ration, by a single state variable with fixed storage and nolower layer evapotranspiration or as a tension storage com-bined with two parallel tanks (Table1). All subsurface flowoptions (see below) are closely connected to the lower layer,this is why the choice of subsurface flow and lower-layeroption is realised as a single model decision within FUSE(Clark et al., 2008).

3.2.3 Evaporation

Evaporation was parameterised by the sequential evaporationscheme (Clark et al., 2008): first potential evaporative de-mand is supplied by evaporation from the upper layer andthen any residual demand by water from the lower layer.

3.2.4 Percolation

In FUSE there are three percolation options each havingtwo parameters (Table1). The architecture of the parentmodel VIC is equivalent to the gravity drainage term in theRichard’s equation (e.g.Boone and Wetzel, 1996), often re-sulting in a large exponent to limit drainage below field ca-pacity (water can percolate from the wilting point to satura-tion). The equation used in PRMS does not allow drainagebelow field capacity (water can percolate from the field ca-pacity to saturation). Non-linearities in the SACRAMENTOparametrisation are controlled by the moisture content in thelower layer, meaning percolation will be fastest when the



Table 1. FUSE model decision options.

Model structure Model option Abbreviation

Upper layer architectureU Upper layer divided into tension and free storage Utension1Free storage plus tension storage sub-divided into recharge and excessUtension2Upper layer defined by a single state variable Uonestate

Lower layer architecture Tension storage combined with two parallel tanks Ltens2plland subsurface flowL Storage of unlimited size combined with linear fraction rate Lunlimfrc

Storage of unlimited size combined with power recession LunlimpowStorage of fixed size with non-linear storage function Lfixedsiz

Surface runoffS ARNO/Xzang/VIC parametrisation Sarno/vicPRMS variant; fraction of upper tension storage SprmsTOPMODEL parametrisation Stmdl

PercolationP Water from field capacity to saturation available for percolation Pf2satWater from wilting point to saturation available for percolation Pw2satPercolation defined by moisture content in lower layer architecture Plower

lower layer is dry (Clark et al., 2008). All three options wereused as model decision options.

3.2.5 Subsurface flow

There are four subsurface flow options (Table1). Subsurfaceflow was modelled either by a single linear storage, by twoparallel connected linear reservoirs or by nonlinear storagefunctions like in ARNO/VIC or TOPMODEL (Clark et al.,2008). TOPMODEL requires a distribution of topographicindex values for each catchment (Beven and Kirkby, 1979).For the Narsjø catchment the distribution was derived usinga three-parameter Gamma distribution followingSivapalanet al.(1987).

3.2.6 Surface runoff

Surface runoff was generated using a saturation-excessmechanism, when it rains on saturated areas of the basin. Thesurface runoff is distributed according to the topographic in-dex distribution (defined inClark et al., 2008).

3.2.7 Bucket overflow

Additional fluxes of water may occur when one of the stor-ages reaches its capacity. In the upper layer, the bucket over-flow from the primary tension storage carries over precipi-tation that falls into the second tension storage. The bucketoverflow from a tension storage carries precipitation into afree storage and from the free storage it adds to surfacerunoff. In the lower soil layer, the bucket overflow fromtension storage forms additional percolation into free stor-age and from free storage again additional subsurface flow.Following Kavetski and Kuczera(2007), logistic functions

were used to smooth the thresholds associated with a fixedcapacity of model storages.

3.2.8 Routing

The time delay in runoff was modelled using a two-parameterGamma distribution (Press et al., 1992), with an adjustablemean of the Gamma distribution. The shape of the time delayhistogram, however, was fixed by setting the shape parameterto 3.0 to keep the number of adjustable parameters small.

3.3 Model calibration

All FUSE models were calibrated using the Shuffled Com-plex Evolution algorithm (SCE) which was parameterisedbased on the recommendations ofDuan et al.(1994). A max-imum of 10 000 trials was allowed before the optimisationwas terminated. Within five shuffling loops the value hadto change by 10 % or the optimisation was terminated. Thenumber of complexes in the initial population was set to 10.Each complex contained 2Nopt + 1 points, each sub-complexNopt + 1 points and 2Nopt + 1 evolution steps were allowedfor each complex before shuffling, whereNopt was the num-ber of parameters to be optimised in the calibration proce-dure, respectively. The algorithm was used to minimise themean absolute relative error (FMARE) (Eq.5). FMARE rangesbetween zero and infinity with the optimum at zero.

FMARE =1

n

n∑i=1

|Qobs(i) − Qsim(i)|

Qobs(i)(5)

The calibration was performed for 15 yr using a three yearsspin up period. As recommended byClark and Kavetski(2010) for conceptual hydrological models, the fixed stepimplicit Euler method was used as numerical time steppingscheme.



3.4 Low flow and recession analysis

The performance of the model was then evaluated using thelogarithmic Nash-Sutcliffe efficiency.FlogNSE was basedon log-transformed streamflow series from observationQobsand simulationQsim (Eq.6). This metric ranges between mi-nus infinity and one and a perfect model would result in 1.

FlogNSE = 1 −

n∑i=1

(ln (Qobs(i)) − ln (Qsim(i)))2

n∑i=1

(ln (Qobs(i)) − ln

(Qobs

))2(6)

As a good model should be able to produce reasonable re-sults for a range of objective functions the performance wasevaluated usingFlogNSE, whereas the models were calibratedusingFMARE. Calibration and validation by the two objec-tive functions is done on the entire series, but both objectivefunctions chosen emphasize the lower flow ranges of the hy-drograph.

Several studies use recession analysis to infer the exponentin a non-linear storage (Ambroise et al., 1996; Wittenberg,1999; Clark et al., 2009; Kirchner, 2009), or, more generally,provide guidance on the structure of a hydrological model(Clark et al., 2009; Harman et al., 2009). Recession anal-ysis is also useful as a diagnostic tool for model evaluation(McMillan et al., 2011; Clark et al., 2011b). In this studythe relationship between the negative change in streamflowover time−

dQdt

[mm day−2] and the corresponding stream-flow Q [mm] was analysed using the method ofBrutsaert andNieber(1977). For the evaluation of the model performanceof recessions both modelled and observed data were used.The method was modified by using flexible (instead of fixed)time steps scaled to the observed streamflow1Q betweentime steps as recommended byRupp and Selker(2006). Ourstudy was based on daily observations and similar toPalm-roth et al.(2010), the lower and upper limits of the time stepwere set to 1 and 5 days, respectively. The time step was thenfound by setting the maximum difference in1Q (threshold)between to time steps equal to 0.1 % of the mean observedstreamflow at that point. As both−dQ

dtandQ span several

orders of magnitude, their relation is plotted in log-log-space.The data points in the plots including all recessions of the hy-drograph and might thus be composed of both subsurface andoverland flow. Overland flow would mainly affect the upperrange of streamflow values. Hence, the upper range in theplots of −dQ

dtandQ should be treated with special care if

interpreted regarding storage release. In case of an exponen-tial recession (simple linear storage model) the relation canbe expressed as in Eq. (7), wherep is a constant. However,a power function results in Eq. (8), with the additional coef-ficientq.

dQ

dt= −p Q (7)

dQ

dt= −p Qq (8)

The −dQdt

versusQ plots can become noisy. Therefore,points in a certain range ofQ were averaged to one valuerepresentative for this range (binned). Then, a polynomialfunction was fitted to the relationship between−

dQdt

andQ

(Eq.9) (Kirchner, 2009).

ln

(−dQ/dt

Q

)≈ a + b ln(Q) + c (ln(Q))2 (9)

The polynomial coefficients were fitted using a least squaresregression model. The significance of the regression modelwas tested with the Kolmogorov-Smirnov goodness-of-fittest (Massey Jr., 1951). The polynomial fitted to the observedrecessions is used as a benchmark model (seeSeibert, 2001)similar to the mean streamflow being used as a benchmarkmodel for the Nash-Sutcliffe efficiency (FNSE). Hence, pass-ing the Kolmogorov-Smirnov test, similar to aFNSE abovezero, is used as an objective decision for acceptable mod-els (similar or better than the benchmark). The choice of apolynomial followsKirchner (2009). It was used becauseof it offers both enough flexibility to adapt to the data andenough smoothness to allow moderate extrapolation beyondthe binned relationships. Scatter plots of the coefficientsb

andc in Eq. (9) were then used to compare observed and sim-ulated recession behaviour for the FUSE models that passedthe Kolmogorov-Smirnov goodness-of-fit test. The relation-ship between−dQ

dtandQ is in the following referred to as

the “recession relationship”.The recession behaviour was analysed for both the whole

year and the individual seasons. The seasonal recessionswere derived by splitting the recessions for the whole yearinto summer and winter recessions. Winter was defined asthe time from 15 October, when precipitation generally be-gins to fall as snow in the catchment, to 15 June, which isusually towards the end of the snowmelt period.

4 Results

4.1 Calibration

For 73 out of 79 FUSE models theFlogNSE was greater thanzero. In Fig.3 a scatter plot of the resulting values of theobjective functions for both calibration (FMARE) and evalua-tion (FlogNSE) is shown. The axes are ordered from high tolow model performance for both measures, which means thatthe points of best performance group in the lower left corner.It appears that theFlogNSE and theFMARE show a similarlygood model performance for theFlogNSE range from 1 to 0.8.However, for lowerFlogNSE the two objective functions dif-fer. While the models are considered poorer forFlogNSE,FMARE remains at the same level.



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FlogNSE

FM

AR

E

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

6.0e

−05

7.0e

−05

8.0e

−05

Fig. 3. FlogNSE versusFMARE for the 79 FUSE models after cali-bration with SCE (Shuffled Complex Evolution algorithm).

4.2 Model performance during low flows

All models with FlogNSE< 0 used the same combina-tion of lower layer/subsurface flow and percolation op-tions Lunlimpow and Plower (see Fig.4). The best models(FlogNSE> 0.8) used varying combinations. The majorityof the best models, however, used a lower layer/subsurfaceflow combination of eitherLtens2pll or Lfixedsiz. Many ofthe poor models used a combination ofLunlimfrc for lowerlayer/subsurface flow andPf2sat for percolation. The poor-est models in the group withFlogNSE> 0 primarily used thesame combination of lower layer/subsurface flow and perco-lation options as found for the poorest performing models(FlogNSE< 0). All possible upper layer and surface runoffoptions were found for the poorest performing models.

4.3 Recession behaviour

The observed flow values in the recession periods ranged be-tween 0.2 and 40 mm day−1 for Q and between 0.001 andabout 15 mm day−2 for −

dQdt

and in general showed a linear

recession relationship with higher−dQdt

for higherQ. Mostof the modelled recession relationships were similar in range,their shapes, however, differed: some appeared more con-vex, others more concave and a third group showed nearly alinear recession relationship. In comparison to the observedrange, some of the models produced an unrealistic scatter.For example, low flow values were modelled that were be-low the observed range (Fig.5f) and their associated reces-sion slopes were too steep (Fig.5e and f). The latter be-haviour was only found for models containing a combinationof the lower layer/subsurface flowLunlimpow and the perco-lation Plower. The model decision options for the example

0.5 0.6 0.7 0.8 0.9 1.0

Lfixedsiz/Pf2sat

Lfixedsiz/Plower

Lfixedsiz/Pw2sat

Ltens2pll/Pf2sat

Ltens2pll/Plower

Ltens2pll/Pw2sat

Lunlimfrc/Pf2sat

Lunlimfrc/Plower

Lunlimfrc/Pw2sat

Lunlimpow/Pf2sat

Lunlimpow/Plower

Lunlimpow/Pw2sat

Com

bina

tion

low

er la

yer/

perc

olat

ion

FlogNSE

Fig. 4. Boxplots of the performance of models using differentlower layer and percolation combinations. The box of models us-ing Lunlimpow andPlower includes model performances (FlogNSE)below zero.

models in Fig.5 are listed in Table2. The combinationsincluding theSprms surface runoff option (Fig.5b, d and f)show linear relationships, while the combinations includingStmdl (Fig. 5c and e) show convex or concave relationships.Figure5e includes the lower layer/subsurface flow and per-colation optionsLunlimpow andPlower and shows a large rangein −

dQdt

for the same flow values.The coefficientsb andc from Eq. (9) are shown in Fig.6.

Theb coefficient describes the slope and thec coefficient thecurvature of the binned recession relationships. The obser-vation pair can be found at the edge of the group resultingfrom the simulations having a largeb coefficient and a smallc coefficient. Most pairs are located in the lower right quar-ter, i.e. in the area of positive slope and negative curvature. Asmaller group can be found for positiveb andc coefficientsand only few models resulted in negativeb andc coefficients.None was fitted with negative slope and positive curvature.The few models that resulted in negative slope and negativecurvature usedLunlimpow for lower layer and subsurface flow,Sprms for surface runoff andPlower for percolation.

The models that resulted in both coefficients being positivepredominantly usedUonestatefor the upper layer architecture,often combined withLunlimfrc for lower layer/subsurfaceflow. The only differing model decision option for the up-per layer architecture within this group wasUtension2. Allsurface runoff structure model options were found in thisgroup. However, theStmdl parametrisation was found only in



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0.02 0.10 0.50 2.00 10.001e−

101e

−04

1e+

02

Q [mm/day]

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mm

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²]

Example 1

b)

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mm

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c)

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0.02 0.10 0.50 2.00 10.001e−

101e

−04

1e+

02

Q [mm/day]

−dQ

/dt [

mm

/day

²]

Example 3

d)

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0.02 0.10 0.50 2.00 10.001e−

101e

−04

1e+

02

Q [mm/day]

−dQ

/dt [

mm

/day

²]

Example 4

e)

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Fig. 5. Plots of recession relationships(a) observed recessions in blue, and(b)–(f) five examples of simulated recessions in red. The modeldecision options for the examples can be found in Table2.

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Fig. 6. Relation betweenb and c coefficients of the polynomialfunction fitted to binned recession relationships.

the particular combination withUonestateandLunlimfrc for theupper and lower layer architecture, respectively. The steepestslopes (coefficientb) were found for models containing theoptionLtens2pll for lower layer/subsurface flow.

4.4 Seasonal analysis

FlogNSE values separated for summer and winter differedfrom each other and also from those derived for the wholeyear (Fig.7). Model performance was generally lower for

the summer season, withFlogNSE< 0.4 for all models. Eightmodels hadFlogNSE values below zero. They all used thesame lower layer, subsurface flow and percolation structurecombination as those model that performed poorest for thewhole year. The models showing the best performance ofsummer recessions used all combinations including the TOP-MODEL surface runoff structureStmdl (Fig. 8).

However, in combination withLunlimpow for subsurfaceflow and lower layer models usingStmdl performed poorer.The direct comparison of the performance for summer andwinter resulted in a higherFlogNSE value for winter for al-most all models. Two models showed the opposite. Bothconsist of a tension storage in the upper layer (eitherUtension1or Utension2) and had exactly the same lower layer, subsur-face flow/percolation structure (Lunlimfrc). All models wheresummer shows a better performance than winter use the per-colation structurePf2sat. All but one of the seven modelswith a FlogNSE less than zero in winter, used the percola-tion optionPlower in combination withLunlimpow for lowerlayer and subsurface flow. The same subsurface flow andlower layer option in combination with eitherPf2sator Pw2satimproved the model performance. Models usingPlower incombination withLfixedsiz had a highFlogNSE, and an evenhigherFlogNSE whenStmdl was the surface runoff modelingoption. TheLtens2pll combined with any model option forthe other structures always performed better than aFlogNSEof 0.9 in winter. Most combinations ofLunlimfrc with Pf2satwere found to range betweenFlogNSE0.2 and 0.7. Combined



Table 2. Model decision options for the examples in Fig.5.

Example Upper Lower Percolation SurfaceLayer Layer runoff

1 Utension2 Lunlimpow Pf2sat Sprms2 Utension2 Lunlimfrc Pf2sat Stmdl3 Utension2 Lfixedsiz Plower Sprms4 Utension2 Lunlimpow Plower Stmdl5 Utension2 Lunlimpow Plower Sprms

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Fig. 7. FlogNSE for summer and winter compared toFlogNSE forthe whole year; the 8 models withFlogNSE< 0 are not shown.

with the surface runoff optionStmdl it resulted inFlogNSEval-ues of about 0.9.

Generally, in summer observed recession slopes weresteeper and flows were higher as compared to winter reces-sions which were slower with less steep slopes. Sometimes,a distinct non-linearity in recession slope was found witha considerably steeper recession slope from flow values ofabout 0.001 mm day−2 upwards. The recession relationshipscould be modelled with the polynomial (passed Kolmogorov-Smirnov-test) for 29 models for the winter season, for 44 forthe whole year and for 28 models for the summer season.The polynomial described different recession relationshipsfor summer and winter. The winterb andc coefficients ofthe polynomials are similar to those of the whole year. Thestructures of the underlying FUSE models were similar to theones found for the whole year, but the lower layer and subsur-face flow parametrisation were dominated byLtens2pll2. Onlysome models usedLunlimfrc, which was the dominant optionfor lower layer/subsurface flow for the whole year.

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Fig. 8. Boxplots of model performance for summer and winterstreamflow simulations for the three surface runoff decision options.

In summer, more models had positivec coefficients and in-deed there were cases where both coefficients were negative(Fig. 9).

5 Discussion

5.1 Model structures

The basic assumption in this study was that different modelstructures are the reason for the differences in model per-formance. Only four models performed well regarding theFlogNSE for both the whole year and for summer and winter.All used a combination of the lower layer/subsurface flowLfixedsiz, upper layerUtension2and the percolationPf2sat, con-taining at least two of the three components. For all otherwell performing models a systematic influence of a specificstructural decision could not clearly be found. The modelsperformed either better in one of the seasons or for the wholeyear.

Structural decisions that cause poor performance couldbe tracked based on the performance criteriaFlogNSE andthe simulation of the recession relationships. Such a struc-tural decision is the lower layer/subsurface flowLunlimpow incombination with the percolationPlower. This combinationcaused poor low flow simulations for the whole year as wellas for the seasonal time series. Most of the binned versionsof this combination could not be estimated using the poly-nomial as they did not pass the Kolomogorov Smirnov test.However, those that did pass, distinguished themselves bysteep recession slopes.

The comparison of the slopes of summer and winter re-cessions reveals no seasonal differences for models with ex-actly this lower layer/subsurface flow and percolation com-bination. Clark et al. (2008) explain that here the lower



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Fig. 9. Coefficients of the polynomial fitted to seasonal−dQ/dt to Q relationships.

layer is defined as a single state variable with no evaporationfrom this depth. The lower layer corresponds to the subsur-face flow which is conceptualised by a power law originatingfrom the parent model TOPMODEL. The main differencebetween the subsurface flow parametrisation in TOPMODELand the other parent models is its dependency on the underly-ing distribution of the topographic index. The storage capac-ity in TOPMODEL also depends on the topographic indexdistribution and can hence be smaller or greater dependingon the topography. In this study the Gamma distribution wasused to define the distribution of the topographic index tokeep some flexibility for calibration. Generally, the Gammadistribution is considered to be an appropriate assumption forthe topographic index distribution of most catchments (Siva-palan et al., 1987). However, the models that used the TOP-MODEL options may not have represented the topographyin the Narsjø catchment well enough.

The percolation optionPlower is dependent on the lowerlayer decision. It thus strengthens the assumptions made withthe lower layer/subsurface flow decision. The percolation op-tion causes the fastest drainage when the lower layer is dry(Clark et al., 2008). Steep recession slopes were modelledwith the combination ofPlower andLunlimpow. The calibra-tion with this combination appears to have caused a smallwater holding capacity of the lower layer resulting recessionsthat are steeper than recessions in the observed data.

For the winter recessions of the models containing thiscombination for lower layer/subsurface flow another factshould be kept in mind: in winter a snow storage is included.The precipitation data was pre-processed with the same snowroutine for all FUSE models. Models input in winter is pre-cipitation plus snow melt. Towards the end of the winterseason (May/June) this process might fill the storages with

small amounts of melt water and produce a prolongation ofthe recessions. The recessions modelled with the combina-tion of lower layer/subsurface flow and percolation optionsLunlimpow andPlower are too fast and this results in unreal-istic shapes of the recession relationships. The percolationoption Plower hence seems inappropriate for a combinationwith the lower layer/subsurface flowLunlimpow as it results inrecessions that are too fast in summer and in streamflow thatare too low in winter. None of the model decision combina-tions has such a distinct influence on model performance asthe combination ofLunlimpow andPlower.

There are further combinations that systematically influ-ence the seasonal performance: models containing the com-bination ofLunlimfrc for lower layer andPf2sat for percolationperform poorly for winter low flows.Pf2sat seems to influ-ence the models ability to simulate low flows as it was usedby all poorest performing models for winter. This means thatthe assumption of a percolation based on the field capacityshould not be used to simulate winter recessions.

In summer, however, other model decisions cause a poorperformance: one example isStmdl that models poor sum-mer recessions.Stmdl differs from other structures by sur-face runoff based on the distribution of the topographic in-dex. Many model combinations in summer perform poorerwhen they contain theStmdl surface runoff. In summer, sur-face runoff plays a larger role for recessions than in winter.

Generally, model performance for low flows is easier toanalyse for winter than for summer. In summer, there areseveral fast responding storages that contribute to the stream-flow. The longer the recessions last, the less important be-come quickly draining storages that are prone to evaporationwhile slowly draining storages gain more influence. In ad-dition, there can be a considerable influence by transpirating



vegetation (Federer, 1973). In winter, the only storages thatare important are lower layer storages and snow. Since onlyone snow storage option was modelled, only the lower layerstorages matter. The results point out that the most impor-tant features for winter recession are directly connected tothe lower storages. Hence, it is rather surprising to find a dis-tinct modeling decision that causes a similar performance forboth winter and summer recessions (Lunlimpow plusPlower).

In this study the choice of model structures was con-strained to the structures of only four parent models. To keepthe analysis manageable, in addition some processes wereexplicitly exempt, similar to the approach used in the origi-nal FUSE model (Clark et al., 2008). This includes climateinput and hence required the preprocessing of the input datawas with a snow accumulation and melt model instead of in-cluding several structural decisions of a snow model. Snow isin fact important in the Narsjø catchment, and testing struc-tures describing the processes connected to snow might beworthwhile. This study, however, focused on the impact ofmodel structures used to represent groundwater storage andrelease behaviour. Future applications should consider test-ing more structures describing processes of snow melt andaccumulation, but also interception and evapotranspiration,all of which were described with a single structural deci-sion in this study. Further, the storage structural decisionsincluded in this study are not the only options. Combina-tions of linear and non-linear reservoirs in series or parallelas tested in other studies could be appropriate for the Narsjøcatchment as well (e.g.Wang, 2011). Generally, it should beconsidered that an exclusion of alternative process represen-tations using multiple hypothesis methods as FUSE can leadto the realization and evaluation of a model being biased bythe modelers view (Clark et al., 2011a).

5.2 Data quality

During the analysis some data issues common to winterstreamflow measurements emerged. When ice forms in theriver and at the gauging station, backwater effects may re-sult due to ice blocking the channel. This will affect thevalidity of the rating curve or stop measuring devices allto-gether requiring data gaps to be filled later (see e.g.Mooreet al., 2002). A few mostly horizontal stripes can be seen inthe Narsjø data when plotting flow on a log scale (Fig.5).However, here no gaps were filled (NVE, personal commu-nication, 2010).Rupp and Selker(2006) also mention thatmeasurement accuracy and changing rating curves in gen-eral may be the source of stripe-like patterns as in Fig.5a.The difficulties of measuring low flows, particularly in win-ter, are well known and difficult to avoid. More detailed dis-cussions can be found, for example, inTallaksen and vanLanen(2004).

In general, validation of models with observed data of poorquality may lead to the rejection of models that might infact be appropriate. A way to avoid the evaluation of model

performance by standard metrics, such as the mean squarederror, is to use diagnostic signatures (Yilmaz et al., 2008;Gupta et al., 2008). To include additional data on individ-ual processes within a catchment may be necessary to iden-tify scientifically defensible modeling strategies. Examplesof application of diagnostic signatures in recession analysiscan be found in e.g.McMillan et al. (2011) andClark et al.(2011b).

6 Conclusions

In this study the impact of model structure on low flow sim-ulations and recession behaviour has been assessed using theFramework for Understanding Structural Errors (FUSE). Us-ing specific model structure combinations of different con-ceptual models resulted in different model performances forsummer and winter low flows. Overall, individual struc-tural decisions never appeared to be an exclusive reason,but rather the combinations of specific structural decisionsaffected model performance. Evaluating withFlogNSE asobjective function, led to only a small number of modelsthat performed well. While most well performing modelsdid not allow for the detection of a systematic influence ofa model structure combination on the model performance,poor performance was more clearly linked to specific modelstructures.

A specific structural combination for lower layer, subsur-face flow and percolation was found that performed poorlyin both seasons. The lower layer and subsurface flow struc-tures influenced the winter low flow simulation, particularly.One main finding of this study was that there is a differencein model performance for summer and winter low flow andrecession. In fact, all the structural decision combinationsthat were salient in this study were season specific – besideone combination that led to the poorest performance, inde-pendent on the time period.

An important task would be to test this further for addi-tional catchments with a seasonal flow regime (with snow inwinter). In order to elucidate to which extent the influenceof the considered model on low flow simulations are catch-ment specific or can be generalized, it should be replicatedin other catchments. Those catchments should ideally be lo-cated in different topographical, geological and climatologi-cal regions.

The method itself, i.e. a systematic analysis of the struc-tures of hydrological models within the FUSE framework,using objective functions targeting at low flow and reces-sion behaviour, seems promising. For low flow modellingit seems appropriate to use multiple objective functions andnot to rely too much on a single function that is based on acomparison between simulated and observed data. Then, us-ing FUSE allows to look at the model structures separatelyand to investigate the influence of the model structure on themodel performance during low flow.



Acknowledgements.The authors thank the German AcademicExchange Service (DAAD) for their financial support and theNorwegian Water Resources and Energy Directorate (NVE) forproviding the data on which this study is based.

Edited by: N. Basu

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