Has land cover a significant impact on mean annual streamflow? An international assessment using 1508 catchments

Journal of Hydrology (2008) 357, 303– 316

available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/jhydrol

Has land cover a significant impact on mean annual streamflow? An international assessment using 1508 catchments Ludovic Oudin a b

a,*

´assian b, Julien Lerat b, Claude Michel , Vazken Andre

b,1

UPMC Univ Paris 06, UMR 7619 Sisyphe, Case 105, 4 Place Jussieu, 75252 Paris, Cedex 05, France Cemagref, Hydrosystems and Bioprocesses Research Unit, Parc de Tourvoie, BP 44, 92163 Antony Cedex, France

Received 17 April 2007; received in revised form 1 February 2008; accepted 13 May 2008

KEYWORDS Rainfall-runoff modeling; Land cover; Long-term water balance; Overparameterization; Sensitivity analysis; Budyko formula

Summary This paper investigates the link between vegetation types and long-term water balance in catchment areas. We focus on the most widely used water balance formulas – or models – that relate long-term annual streamflow to long-term annual rainfall and long-term potential evapotranspiration estimates. Our investigation seeks to assess whether long-term streamflow can be explained by land cover attributes. As all but one of these formulas do not use land cover information, we develop a methodology to introduce land cover information into the models’ formulations. Then, the modified formulas are compared to the original ones in terms of performance and a sensitivity analysis is performed, with a special focus on the parameters representing vegetation characteristics. In line with the global coverage of long-term water balance models, we base our work on as many basins as possible (1508) representing as large a hydroclimatic variety as possible. Results show that introducing additional degrees of freedom within the original formulas improves overall model efficiency, and that land cover information makes only a small but nonetheless significant contribution to this improvement. ª 2008 Elsevier B.V. All rights reserved.

Introduction Are we able to predict the effects of land-use changes on streamflow? * Corresponding author. Tel.: +33 144277026; fax: +33 144275125. E-mail address: [email protected] (L. Oudin). 1 Retired.

Predicting the hydrological impact of land-use changes is critical for water resource management. Over the past century, a large number of field experiments have been

0022-1694/$ - see front matter ª 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2008.05.021

304 conducted to quantify the impact of vegetation changes on catchment water balance. Although vegetation changes have been shown to have significant yield impacts (see Bosch and Hewlett, 1982; Andre ´assian, 2004 for a review), generalizing the results of small catchments experiments has proved very difficult. In his review, Hibbert (1967) concluded that the response of catchments to land-use changes was ‘‘highly variable and for the most part unpredictable.’’ More than 30 years later, Kokkonen and Jakeman (2001) state that ‘‘there are still no credible models to predict the effect on hydrological response of land-use change in gauged catchments.’’ Some authors consider that only truly physically based distributed models should be used for predicting the impact of land cover changes, as they require no calibration and take their credibility from the physical equations on which they are based. However, because of process scaling problems (Grayson et al., 1992), the existing physically based models are still unable to function completely without calibration, and therefore we believe that they need to be submitted to the same kind of sensitivity studies that empirical models require. The method proposed in this article is based on a downward, empirical approach (Klemes, 1983; Sivapalan et al., 2003). It consists in starting with simple hydrological models where, step by step, more complexity is introduced to account for vegetation types: we chose well-known mean annual water balance formulas as a starting point since they provide the simplest representation of the rainfall-runoff transformation, averaged over the long-term.

How should land cover information be integrated into water balance formulas? In this paper, we consider simple water balance formulas, applied at the multiannual time step. Some of these models were proposed 100 years ago but they are still widely used today, for instance to study the sensitivity of runoff to general climatic trends (Dooge et al., 1999; Arora, 2002) or to assess the impact of land-use changes (Zhang et al., 2001; Gallart and Llorens, 2004; Siriwardena et al., 2006). Water balance models aim at determining streamflow on the basis of rainfall and potential evapotranspiration; they are generally expressed as a dimensionless formulation:   ^ Q PE ¼f ð1Þ P P ^ is the computed long-term annual streamflow, P is where Q long-term annual rainfall and f is a function of the aridity index, i.e., the ratio of long-term annual potential evapotranspiration (PE) to rainfall (P). These models were developed empirically on different sets of catchments, thus, their formulations are likely influenced by both the specific climate conditions and the land cover characteristics of those catchments. However, these formulations do not take into account explicitly any vegetation characteristics, even if we know from paired catchment experiments (Hewlett, 1982; Calder, 1993; Hornbeck et al., 1993; Johnson, 1998; Cosandey et al., 2005) that evapotranspiration is favored on forested catchments, because of a higher interception of rainfall and a more comprehensive use of

L. Oudin et al. the soil water-holding capacity (Milly, 1994). Therefore, we decided to revisit a number of well-known water balance formulas in order to study whether they can be made explicitly sensitive on catchment’s vegetation characteristics. The general expression for these revisited formulas becomes:   ^ Q PE ð2Þ ¼F ; LCi P P where LCi is the fractional coverage of the ith vegetation type over the catchment. Recently, several authors, adopting different approaches, have developed such models with apparent success (see e.g., Zhang et al., 2001; Lu et al., 2003). However, we wished to be extremely careful, since we consider that there are two unavoidable provisos to fulfill before using these models: • First, as they have been developed empirically on sometimes a low number of catchments, formulas must be tested exhaustively on different catchments. • Second, a sensitivity analysis is needed, particularly on the vegetation-related parameter(s). Indeed, the explicit introduction of fractional coverage of diverse land use into a formula is not alone proof of its predictive power for the impact of land-cover changes: the modified formulation must prove its credibility by showing that it is actually sensitive to the land cover characteristics. Thus, sensitivity analyses are required to ensure that newly introduced parameters are not mere fudge factors that increase the numerical flexibility of the formula without a proved link to the hydrological processes they are assumed to represent.

Scope of the paper This paper aims at testing and revisiting various classical water balance formulas, where the fractions of diverse vegetation types are introduced as additional variables. We do not address explicitly the problem of the effect of land-use change on streamflow, but look rather for empirical evidence that the type of vegetation cover can be discriminative from a water-balance point of view. Indeed, we consider static land cover information: the fractional coverage of several vegetation types over the catchments. However, the relatively large dataset used allow to draw quite general conclusions, which could be the basis for further research on the issue of the impact of land use changes on catchment behavior. The originality of this work lies in the large dataset (1508 worldwide basins; see section ‘Material’) and in the step-bystep approach used to introduce land cover as a new variable of the water balance models (see section ‘A systematic approach .... balance models’). The most important and surprising results, however, come from the sensitivity analysis of the revised formulas (see section ‘Results’).

Material Simple water balance models For a given region, the mean annual streamflow (Q) rates are governed primarily by the available energy (i.e., the

Has land cover a significant impact on mean annual streamflow? evaporative demand) and precipitation (P). If potential evaporation rates are fairly low, then the runoff-to-precipitation ratio is likely to be high, i.e., close to unity. Similarly, this ratio is expected to be low (near zero) where potential evapotranspiration is very high, resulting in high atmospheric losses. On the basis of these considerations, climatologists and hydrologists built simple water balance models, relating the runoff ratio (Q/P) to the aridity index (PE/P). In this paper, we used five of these classical water balance formulas, developed by Schreiber (1904), Ol’Dekop (1911), Turc (1954), Budyko (1974) and Zhang et al. (2001). All of these models are rather simple and have relatively similar functional forms (see Fig. 1). Studies that have attempted to compare these formulas generally report no significant differences in terms of efficiency in estimating mean annual streamflow (see e.g. Arora, 2002; Mouelhi, 2003; Mouelhi et al., 2006). Since those models are based on the water balance equation, they are all conservative and cannot be used on catchments with significant interbasin groundwater flows (see the discussion of the Turc formula by Le Moine et al., 2007). Moreover, those models were developed on relatively temperate climates, meaning that we should be cautious when using them on arid or semiarid conditions.

Dataset Since the water balance models used in this study were developed empirically, sometimes on small catchment sets, it was important to test these models extensively on a larger set of catchments. The formulas used here only require long-term values of mean annual Penman (1948) potential evapotranspiration (PE) and rainfall (P). Mean annual streamflow (Q) is only used to assess model performance. Note that the PE formulations embedded in these models were originally quite different (see the discussion by Choudhury, 1999) and were perhaps more appropriate to relatively humid climates. Thus, we should be cautious when transposing these relationships to other types of climate.

305

Moreover, in order to test the potential to use vegetation cover data within these models, we also collected the fraction of diverse vegetation types for each catchment. Data from several datasets were assembled for this study, resulting in a preliminary set of 2739 catchments. In a first step, we identified and removed all catchments with significant anthropogenic effects affecting runoff (anthropogenic effects were assessed in terms of the presence of significant reservoirs in the catchment and the presence of significant interbasins water transfers). In a second step, we performed some initial analyses to examine whether it was possible to close the long-term water balance. As far as French catchments were concerned, we benefited of a previous study that estimated of interbasin groundwater flows across the topographic catchment boundaries due to karstic conditions and porous aquifers (Le Moine et al., 2007). For other countries, we simply removed those catchments that fall outside the appropriate range of application for water balance models, e.g. runoff yield greater than unity or P–Q greater than potential evapotranspiration. Those catchments were not further used in this paper. After this selection, 1508 catchments located in four countries (see Fig. 2) were retained for this study: • 397 French catchments, from the datasets used by Perrin et al. (2001), Oudin et al. (2005) and Le Moine et al. (2007); • 662 catchments from the United Kingdom, collected from the UK National River Flow Archive; • 423 catchments from the United States, which are part of the MOPEX dataset (Schaake et al., 2006); • 26 Swedish catchments from the NOPEX dataset (Halldin et al., 1999). Fig. 3 presents the (PE/P, Q/P) pairs for the 1508 basins. Fractional coverage of each vegetation type is estimated according the CORINE classification (CLC, 1993) for catchments in France, United Kingdom and Sweden, and the University of Maryland vegetation classification system for the

1 Schreiber [1904] Ol'Dekop [1911]

0.8

Turc [1954] Budyko [1974] Zhang et al. [2001] with w=1.0

Q/P

0.6

0.4

0.2

0 0

1

2

3

4

PE/P

Figure 1

Comparison of runoff ratio predicted by the Schreiber, Ol’dekop, Turc, Budyko and Zhang et al.’s functional forms.

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Figure 2

Location of the basins used in France, Sweden, the United States, Australia and Great Britain.

US catchments. In order to synthesize and homogenize these data, we retained five major vegetation types: forest, grassland, cropland, shrub and heath, and the other nonvegetated land cover. The test sample represents different hydrological systems with varied climatic conditions from semi-arid to temperate (see Table 1). However, two possible biases can be mentioned at this stage. First, the temperate climate is dominant due to the great numbers of catchments from France and the United Kingdom (Fig. 3 confirms the preponderance of the temperate climate in the test sample). Second, the fractional coverage of vegetation cover does not

present the same distribution for all countries, e.g. forested areas in UK catchments are rather low, compared to those of other countries (see Fig. 5). This is why we analyze in section ‘Resampling of the Catchment set to assess possible dataset bias’ whether the characteristics of our dataset had a significant impact on the results. A systematic approach to determining the relevance of land cover in water balance models In order to assess the relevance of land cover information in water balance models, we adopted a three-step methodology:

Has land cover a significant impact on mean annual streamflow?

307

1.0

Theoretical asymptotes Schreiber [1904] Ol'Dekop [1911] Studied basins

0.8

Q/P

0.6

0.4

0.2

0.0 0

1

2

3

4

PE/P

Figure 3

Table 1

Basins used and their (Q/P; PE/P) characteristics.

Ranges in size and hydroclimatic characteristics of the catchment sample

Country

Great Britain

United States

France

Sweden

Number of basins Basin area, km2 Range of mean annual rainfall, mm Range of mean annual Penman PE, mm Range of mean annual streamflow, mm

662 1–9948 555–2912 450–630 102–2692

423 67–10329 260–2686 580–1750 5–1961

397 5–9423 647–1985 524–845 104–1512

26 6–1293 660–952 509–545 194–461

1. Selection and testing of well-known water balance models that do not take into account land cover information in their original formulation (for all but one formula) but have proved their ability to represent the Q/P-to-PE/P relationship over a variety of catchments; 2. Modification of these models to make them use the additional land cover information, for which we followed a top-down approach similar to that presented by Zhang et al. (2001); 3. Assessment of the sensitivity of these water balance models to land cover information.

Modification of original water balance formulas The classical water balance models cited earlier do not explicitly use land cover characteristics (except the one developed by Zhang et al. (2001)). To introduce this additional information within these formulas, we followed a top–down (or downward) approach, starting from the simple representation of the catchment behavior given by the water balance models and then modifying the formulations to introduce the fractional coverage of land cover types, while attempting to keep the parsimony of the original formulation. To this aim, for each original water balance formula, the mean annual streamflow at the outlet of the catchment was computed as a weighted combination of the contributions from each vegetation type of the catchment:

^ ¼ Q

X

^i LCi  Q

ð3Þ

i

^ i is the mean annual streamflow (in mm/yr) comwhere Q puted for the part of the catchment covered by the ith land ^ i was computed using modified formulacover type. Each Q tions of the original models. As land cover was classified according to five classes, models’ formulation was modified by adding five free parameters (h1–h5), each one with a possibly different value to account for specific contribution of each land cover type. These values need to be determined empirically (by calibration) over the catchment set. Table 2 presents the revised model formulations. Note that many variants were tested, but we only present here the modifications that yielded the best model performance. Generally speaking, the optimal solution consists in introducing the land cover-specific parameter as a multiplier of the aridity index (PE/P), while keeping the same theoretical limits. Thus, when the value of the parameter increases, the computed runoff yield is decreased; the value of h equal to unity corresponding to the original water balance model formula. Since only five parameters needed calibration, there was no optimization problems and the algorithm used followed a steepest descent method to move step by step in the parameter space toward the optimum parameter set (Edijatno et al., 1999). The objective function used to optimize the parameter values is the root mean square error (RMSE) computed on the runoff yield:

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Figure 4

Scheme of the methodology used to assess the relevance of land cover data in water balance models.

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2ffi u n u1 X Q ^ Q k k RMSEðQ =PÞ ¼ t  n k¼1 Pk Pk

ð4Þ

where Qk is the observed long-term annual streamflow of basin k, Pk is the observed long-term annual precipitation ^ k is the computed long-term annual over basin k, Q streamflow of basin k and n is the total number of catchments.

Assessing the sensitivity of the modified water balance formulas to land cover In a typical downward approach, the additional model complexity induced by accounting explicitly for land cover information shall be justified if and only if the three following conditions are fulfilled: (i) the performance of the model is improved, (ii) the sensitivity of the water balance models to the fractional coverage of vegetation type can be demonstrated; (iii) the interpretation of the parameter values is sensible. To this aim, we compared the performance of three types of models, with the notations indicated in Table 3. We assigned suffixes to the model names, as follows: • Models with suffix ‘O’ (SCHO, OLDO, TURO, BUDO, ZHAO) are the original water balance models, with no additional vegetation parameters except the Zhang et al., (2001) formula, which already includes vegetation information (the fractional coverage of forest) in its original formulation; • Models with suffix ‘LC’ (SCHLC, OLDLC, TURLC, BUDLC, ZHALC) are the modified water balance models that take into account the fraction of each vegetation type, with

five additional parameters Hereafter, these land cover accounting formulations are denoted ‘‘LC accounting models’’; • Models with suffix ‘NLC’ (SCHNLC, OLDNLC, TURNLC, BUDNLC, ZHANLC) are similar to the models with suffix ‘LC’, but a single parameter value is assigned for all vegetation types. These models can be considered as lumped versions of the vegetation-dependent models; they were only introduced to be compared with the previous ones, in order to study the sensitivity to the additional parameters used in the vegetation-dependent models. Hereafter, these non land cover accounting formulations are denoted ‘‘NLC accounting models’’. Fig. 4 summarizes the overall methodology and Table 3 presents the formulas tested in this article.

Assessing the water balance models’ efficiency Since the modified models need calibration of some parameters, their performance must be tested in verification mode. Therefore, here we adapted the recommendations made by Klemesˇ (1986): we split the catchment set into two subsets. The model parameters were then calibrated on each subset and tested over the other subset. To ensure that the two subsets had similar variability, the four countries that composed the catchment set were similarly represented in the two subsets (see Fig. 5). We used two criteria to assess the goodness of fit of the water balance models: the root mean square error on runoff yield (see Eq. (3)) and the root mean square error computed on runoff.

w ¼ 2:0 for forested areas w ¼ 0:5 for non-forested areas P

P

1 ¼ 1þPEþwð PE 2 with Þ

b Q P Zhang et al.(2001)a

o0:5   1 1  exp  PE tanh½ðPE P P Þ  P

Budyko (1974)

n  PE

¼1 b Q P

Turc (1954)

1 2 0:5 ½1þðPE PÞ 

¼1 b Q P

Ol’Dekop (1911)

PE 1 ¼ 1  PE P tanh½ð P Þ 

b Q P

Schreiber (1904)

a The original model proposed by Zhang et al.(2001) already used forest cover data. Therefore, the sole modification brought to its formulation consists in recalibrating parameter h for forested and non-forested areas.

P

P

1 ¼ 1þPEþhð PE 2 Þ P

b Q

PE PE 1 0:5 ¼ 1  fPE P ½1  expðh P Þ tanh½ð P Þ g P

b Q

1 2 0:5 ½1þðhPE PÞ 

¼1 P

b Q

PE 1 ¼ 1  h PE P tanh½ðh P Þ  P

b Q

Non Land cover accounting models (suffix ‘NLC’) bi Q PE P ¼ expðh P Þ

Land cover accounting model (suffix ‘LC’) ( bi Q PE P ¼ expðhi P Þ P b b ( Q ¼ i LCi  Q i b Qi PE PE 1 P ¼ 1  hi P tanh½ðhi P Þ  P b b Q ¼ i LCi  Q i 8 < Qb i 1 P ¼ 1  ½1þðhi PEÞ2 0:5 P P :b bi Q ¼ i LCi  Q ( b i Qb Q PE PE PE 1 0:5 P ¼ P ¼ 1  f P ½1  expðhi P Þtanh½ð P Þ g P b b Q ¼ i LCi  Q i 8 < Qb i 1 P ¼ 1þPEþhi ðPEÞ2 P P :b P bi Q ¼ i LCi  Q Original models (suffix ‘O’) b Q PE P ¼ expð P Þ Name

^ i represents the runoff from catchment area vegetated with the ith vegetation type and LCi is the Table 2 Modifications brought to the original water balance models. Q fractional coverage of the ith vegetation type.

Has land cover a significant impact on mean annual streamflow?

309

Results To assess whether our introduction of land cover information into water balance models is warranted by observations, we analyzed both the performance of the modified water balance models and the sensitivity of these water balance models to land cover information. This section is structured as follows: • First, we compare the performance of the original water balance models (SCHO, OLDO, TURO, BUDO, ZHAO) to the performance of the LC accounting models (SCHLC, OLDLC, TURLC, BUDLC, ZHALC), which can benefit from the additional flexibility offered by the five calibrated parameters (h1–h5); • Second, we compare the performance of the LC accounting models (SCHLC, OLDLC, TURLC, BUDLC, ZHALC) with simpler non LC accounting modified models (SCHNLC, OLDNLC, TURNLC, BUDNLC, ZHANLC). This comparison provides a means to assess the actual sensitivity of the modified water balance models to land cover data, and to make the difference between the impact of the additional information brought by land-cover types and the impact of the additional numerical flexibility brought by more parameters; • Third, an analysis on parameter values is performed in order to investigate the consistency of the proposed reparameterizations; • Last, we discuss possible biases that might affect the validity of our conclusions because of the specificity of our catchment set.

Performance of the water balance models Table 4 summarizes the performance obtained by the tested water balance models and Fig. 6 shows the computed streamflows versus the observed streamflows for the original Budyko model (BUDO), as an example of the original models’ results. The performance is summarized by the RMSE computed on runoff yield and the RMSE computed on runoff over the entire catchment set. As for the modified water balance models, we present in Table 4 the efficiencies obtained in calibration mode and in validation mode to give an idea of the robustness of these models. Note that for original models, no calibration was performed and therefore the RMSE computed are in validation mode. The first major result is that all five original models performed relatively well and similarly, with RMSE(Q/P) ranging from 0.059 to 0.083 and RMSE(Q) ranging from 65 mm/ yr to 88 mm/yr (see Table 4). This is not surprising since the different functional forms were quite similar (see Fig. 1). Two of the five original models (TURO, BUDO) were slightly more efficient than the others. The second major result is that original models were systematically improved when introducing land cover information along with the h parameter values, the differences between the RMSE(Q) values ranging from 12 mm/yr to 40 mm/yr. Note also that the improvement brought by the new formulations appears to be model-specific and for the best original models (TURO, BUDO), it was relatively

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LC

modest. Thus, one of the achievements of the reformulations is to even out the performance of all the water balance models. Last, the RMSE computed in calibration are quite similar to those computed in validation, showing that the calibration is robust, i.e., that the transferability of the model is good. This is reassuring and confirms that the dataset is broad enough to draw stable and significant conclusions.

LC

Sensitivity of the water balance models to land cover data

Table 3 Notations and characteristics of tested water balance models Notation

Original model reference

Number of calibrated parameters

Input data needed

SCHO SCHNLC SCHLC OLDO OLDNLC OLDLC TURO TURNLC TURLC BUDO BUDNLC BUDLC ZHAO ZHANLC ZHALC

Schreiber (1904) Schreiber (1904) Schreiber (1904) Ol’Dekop (1911) Ol’Dekop (1911) Ol’Dekop (1911) Turc (1954) Turc (1954) Turc (1954) Budyko (1974) Budyko (1974) Budyko (1974) Zhang et al.(2001) Zhang et al.(2001) Zhang et al.(2001)

0 1 5 0 1 5 0 1 5 0 1 5 0 1 5

P, P, P, P, P, P, P, P, P, P, P, P, P, P, P,

PE PE PE, PE PE PE, PE PE PE, PE PE PE, PE, PE PE,

LC

LC LC LC

‘O’ means that the original model is used, ‘LC’ means that a modified version of the model was calibrated with separation of the catchment into five land cover areas and ‘NLC’ means that only one parameter is calibrated.

1.6

0.8

1.2

0.8

0.4

0.6

0.4

0.2

0.0 U Fr ni te an d Ki ce ng U do ni te m C dS at t ch ate s m en ts Su et bs e Su t 1 bs et 2

100

100

100

90

90

90

80

80

50 40 30 20

70 60 50 40 30 20

Grassland coverage (%)

60

Cropland coverage (%)

70

Fr ni te an d Ki ce ng U do ni te m C dS at ch tate s m en ts Su et bs e Su t 1 bs et 2

U

0.0

U ni t e Fr a d nc K e U ing ni te dom C dS at ch tat m es en t Su set bs e Su t 1 bs et 2

80 70 60 50 40 30 20

10

10

0

0

0

U ni te

Fr an d Ki ce ng U do ni te m C dS at t ch ate s m en ts Su et bs e Su t 1 bs et 2

10

U Fr ni te an d Ki ce ng U do ni te m C dS at t ch ate s m en ts Su et bs e Su t 1 bs et 2

Forest coverage (%)

10

1.0

Runoff yield (Q/P) [-]

100

Aridity index (PE/P) [-]

1000

2.0

U Fr ni te an d Ki ce ng U do ni te m C dS at ch tate s m en ts Su et bs e Su t 1 bs et 2

Catchment area (km²)

10000

As seen in section 4.1, the models modified to account for land cover classes (LC accounting models) perform better than original models. The problem is that we are not sure that this is actually caused by introducing land cover information: it could also result from the reparameterization of the original models. Thus, in this section, we assess the sensitivity of the modified water balance models to land cover information by comparing the performance of LC accounting models (SCHLC, OLDLC, TURLC, BUDLC, ZHALC), for which five parameters were calibrated (h1–h5) and simpler non LC accounting modified models (SCHNLC, OLDNLC, TURNLC, BUDNLC, ZHANLC), for which only one parameter was calibrated: h.

Figure 5 Distributions of catchment characteristics over the entire database and the two subsets. The boxes are delimited by the percentiles 0.25 and 0.75, the median is marked with a thick line and the whiskers are delimited by the percentiles 0.10 and 0.90.

Has land cover a significant impact on mean annual streamflow? Table 4

Performance of original models and modified LC accounting models

Model name

Original models

Schreiber Ol’Dekop Turc Budyko Zhang

Modified LC accounting models Calibration

Validation

Calibration

Validation

RMSE(Q/P) (–)

RMSE(Q) (mm/yr)

RMSE(Q/P) (–)

RMSE(Q/P) (–)

RMSE(Q) (mm/yr)

RMSE(Q) (mm/yr)

0.0822 0.0805 0.0603 0.0591 0.0832

78.7 88.4 68.4 64.8 78.6

0.0526 0.0495 0.0510 0.0513 0.0547

0.0530 0.0498 0.0513 0.0519 0.0552

55.6 48.7 51.9 52.7 59.3

55.7 48.9 52.1 52.9 59.4

3000

1:1

2500 Computed Streamflow (mm/yr)

2000

1500

1000

500

0 0

500

1000

1500

2000

2500

3000

Observed Streamflow (mm/yr)

Figure 6 Computed streamflows (in validation) versus observed streamflows with the original Budyko water balance model (BUDO).

Fig. 7 plots the performance of all the water balance models used in this study, and particularly the differences between the three possible options: original models, LC

accounting models and modified non LC accounting models. It is interesting to note that although the LC accounting models yield efficiencies systematically higher than that of modified non LC accounting models, calibrating only one parameter allows to reach a level of performance close to the one of the 5-parameter models. This shows that the land cover information add limited (but significant) contribution to the improvement of the original models. Except for the Turc-Pike and Budyko formulas, a large part of the overall improvement resulted from a sheer numerical effect: allowing more flexibility. In order to determine which of the land cover classes is the most informative, as well as in an attempt to reduce the number of calibrated parameters in the LC accounting models, we tested some intermediary formulations of the models between the full 5-parameter version of the revisited Budyko formulation (BUDLC) and the original version (BUDO). This was done by merging progressively the land cover classes, and testing a total of 28 alternative formulations, with degrees of freedom (i.e. calibrated parameters) ranging from 0 to 4. Fig. 9 shows the performance of those alternative formulations with respect to the number of calibrated parameters. It appears that a less parameterized version (with only three free parameters) allows to reach satisfactory level of efficiency, compared to the 5-parameter version, even if the 5-parameter version does always offer the best performance. Table 5 summarizes those performances and indicates for each formulation, the land

0.09

100

0.08

90 80 RMSE (Q) [mm/yr]

0.07 0.06 RMSE (Q/P)

311

0.05 0.04 0.03

70 60 50 40 30

Original water balance models

0.02 0.01

Original water balance models

Modified non-LCA models

20

Modified non-LCA models

Modified LCA models

10

Modified LCA models

0

0 Schreiber

Ol'Dekop

Turc

Budyko

Water balance models

Figure 7

Zhang et al.

Schreiber

Ol'Dekop

Turc

Budyko

Zhang et al.

Water balance models

Performance in validation mode of the three types of water balance models (LCA: land cover accounting).

312 Table 5 types

L. Oudin et al. Sensitivity of the modified Budyko model: Model performance when merging some fractional coverage of vegetation-

No. of parameters

Vegetation types explicitly represented

Merged Vegetation types

RMSE (Q/P)

RMSE (Q)

5

–

0.0519

52.9

Forest, cropland Forest, grassland Forest, heath

0.0524 0.0539 0.0544

54.0 56.4 57.2

4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 2 2

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cover types that are explicitly taken into account. It was for us extremely surprising to find that forest appears to be the less relevant vegetation-type: if we split the catchment between the forested part and non-forested part, the performance of the model will be similar to the one-parameter version. Two interpretations are possible: either forest is after all not such a ‘‘large’’ water consumer or its impact is damped by the fact that rainfall input over forested regions (which are often located at higher elevations) is likely to be systematically underestimated. This underestimation of rainfall input would then hide part of a possibly larger impact of forest cover on the water balance.

Model parameter interpretation Fig. 8 presents the values of the calibrated parameters of the LC accounting models (i.e., h1–h5) and the parameter of the modified non LC accounting models (i.e., h). When interpreting those values, we should keep in mind that there is a natural correlation between climate and vegetationtype so that the calibrated parameters also reflect an

adjustment of the formulation to the climatic characteristics of the catchment set. Concerning modified ‘‘vegetation accounting’’ models, the value of the parameter associated with croplands was always greater than the others, meaning that the models tends to reduce runoff yield from the arable part of the catchment. Then, in decreasing order of their parameter value come Forest, Grasslands and Shrubland/heath. Those results are consistent with our a priori expectations since croplands, when irrigated, are likely to favor evapotranspiration, whereas evapotranspiration from shrubland and heath is likely to be controlled by stomatal resistance. However, the fact that the value of the parameter associated to forest is less than the one associated to croplands is definitely surprising: we would have expected from all the small forested catchment experiments to see forest with the highest parameter value. Another reassuring result is that the parameter (h) of the ‘‘non-vegetation accounting’’ models was always within the range of the parameters hi which is consistent with our a priori expectations. In interpreting the role of this parameter,

Has land cover a significant impact on mean annual streamflow?

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teristics. Besides, data (and particularly land cover data) were collected from diverse sources and the unavoidable arbitrary choices made during the classification might bias the results. To effectively test the influence of data on water balance model efficiency, a smaller set of very different catchments could be preferred. In this section, we repeat the previous approach, but on different subsets of catchments, in order to assess the robustness of our conclusions.

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one could argue that it allows the models to adapt their original formulations to the larger climatic diversity of our catchment set, which is generally much larger than the datasets over which these empirical formulas were developed originally.

Resampling of the catchment set to assess possible dataset bias As seen in section 2, a large part of the catchment set is composed of UK, US and French catchments, with a temperate climate and limited forest cover in the UK. Therefore, it might be argued that the conclusions of our comparison depend on the variability of catchment charac-

Impact of the dataset’s climate and catchment characteristics In order to determine whether land cover information would be particularly relevant for some kinds of environment, we clustered some catchments regarding to their aridity index and their surface area. Ten groups were made, each composed of around 150 catchments, and the previous tests were performed again on these smaller samples. As in section ‘Sensitivity of the ..... cover data’, we compared the performance of original models, LC accounting models and non-LC accounting modified models. Fig. 10 plots the performance of the three possible options for two water balance models (Ol’Dekop and Budyko). As far as the aridity index is concerned, the non LC accounting modified models perform significantly better than the original models for wet climate conditions, meaning that the additional parameter h plays its role to adapt the formulations on those catchments. However, there is no specific improvement when introducing additional land cover information for arid or wet catchments. Then, concerning the catchment area, the improvement from the original models to the non LC accounting modified models is still important but less pronounced. However, it seems that the water balance models are significantly improved when introducing land cover data for small catchments. Impact of the geographic origin of catchment data In order to determine whether the results were homogeneous through the dataset, the previous tests were

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Has land cover a significant impact on mean annual streamflow? performed again on three national catchment sets (France, United Kingdom and United States). Fig. 11 shows the performance of the water balance models obtained in validation on the sub-sets of catchments. When comparing the RMSE(Q) obtained by the non LC accounting modified models and the LC accounting modified models, it appears that the improvement brought by land cover information is not homogeneous through the dataset: UK and French catchments benefit from this additional information but US catchments are not improved. This could be due to the method used to assess land cover types over European countries (Corine Land Cover Inventory). To conclude on this section, we showed some unavoidable limitations of the methodology used here to take into account land cover information into water balance models. Vegetation information seems to improve significantly the performance of water balance models on small (area < 10 km2) and relatively wet catchments. More research is needed to identify the reasons why on some catchments, land cover information has a greater link with catchment water balance. However, our results tend to confirm previous findings showing that in different basins, with specific climatological and pedological contexts, land cover do not have the same impact (see the review by Andre ´assian, 2004). In order to actually observe a water balance impact of land cover at the catchment scale, there are pedological and physiological conditions (Trimble et al., 1963; Cosandey, 1995; Vertessy et al., 2001), and also climate conditions, which complement the preceding ones: even where the soil is deep enough, a difference in water consumption will only become apparent if the climate has periods of hydrological surplus, allowing soil water reserves to be replenished.

Conclusion The issue of the hydrological impact of land cover often leads to passionate debate in the scientific community. Many techniques have been proposed to tackle this issue, and all have specific drawbacks. Here, we did not address explicitly the problem of the effect of land-use change on streamflow, but restricted our investigations to searching for empirical evidence that the type of vegetation cover can be discriminative from a water-balance point of view. To address this issue as objectively as possible, we chose a downward approach allowing hypothesis testing. Since this approach was empirical, it was important to examine it over a large catchment set. Therefore, we tested five classical water balance formulas over a worldwide set of 1508 catchments. This dataset is particularly interesting because of its size and its hydroclimatic diversity. Results show that: • The classical water balance formulas can be adapted to explicitly take information concerning land cover into account. The assimilation of land cover information into these formulas requires introducing additional parameters that need to be defined empirically by calibration over a large catchment set. • Calibration of parameters does improve the efficiency of all the water balance formulas (not only in calibration but in validation); sensitivity analysis showed that this

315 improvement is caused mainly by numerical reasons (adapting the formulations to this catchment set) and only partly by the information content of land cover classes. • Surprisingly, the less informative land cover type identified here is forest. To that extent, our work comes in contradiction with previous investigations (e.g. the work by Zhang et al., 2001).

Naturally, we do recognize that a more diverse catchment dataset would be welcome to confirm our findings, although the dataset used in this paper is already quite large. We believe that one of the main teachings of our work is that when developing (or using) any model aiming at assessing the hydrological impact of land cover, we need to (i) estimate the transferability of the model to other catchments and (ii) assess the sensitivity of the model to vegetation characteristics. As a natural perspective of this work, we would like to test the proposed model formulations on catchments within a non-stationarity context, i.e. with vegetation changing in time. We could also question the relevance of other candidates to explain mean annual streamflow such as mean depth to bedrock, mean slope, average basin soil porosity, etc., following a similar methodology.

Acknowledgments The authors thank the two anonymous reviewers for their constructive suggestions, which helped to improve the text. The authors thank Dr. Qingyun Duan and Dr. John Schaake for providing US data of the MOPEX database. Data for UK catchments were obtained through the National River Flow Archive (http://www.nerc-wallingford.ac.uk/ih/nrfa). The Swedish data used were obtained from the SINOP (System for Information in NOPEX) data base. Streamflow data on French catchments were provided by the HYDRO database of the French Ministry for the Environment. The authors are also grateful to Laurent Franchisteguy and Bruno Rambaldelli of Me ´te ´o France for the French climatic data.

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