Predicting the geomorphological responses of gravel-bed rivers to flow and

sediment source perturbations at the watershed scale: An application in an

Alpine watershed

Hernán A. Alcayaga a*, Luca Mao b, Philippe Belleudyc

*Corresponding author

1. Introduction

Rivers have been modified by human activities for centuries, with a remarkable

acceleration since the industrial revolution. One of the most frequent issues in

river management is the prediction of the fluvial system behavior due to

anthropogenic actions. The assessment of these responses is always complex

because there is a large number of variables and processes to consider, and

also interactions and feedbacks between processes. In fact, during the last fifty

years, fluvial geomorphologists have developed qualitative and quantitative

models to predict the behavior of rivers. One of the most important drivers that

motivated these investigations was to understand the channel river responses to

natural and human induced disturbances (Wohl, 2014). There are many possible

types of human alterations on fluvial systems, including gravel mining, river

training, watershed transformation (land use, reforestation, change in runoff

properties), including hydropower development. Hydropower development

comprises the construction of dams, reservoirs and diversion, is considered one

of the most relevant and impactful causes of fluvial system alteration (Grant,

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2012). The changes produced by dams and diversions on fluvial processes –

mainly alteration of both sediment and water fluxes – can be dramatic (Petts &

Gurnell, 2013).

Despite the large amount of technical and scientific literature about the

alterations of human activities, in particular large dams, on river morphology

(e.g., Graf, 2006; Schmidt and Wilcock, 2008; Baker et al. 2011; Csiki and

Rhoads, 2010; Draut et al., 2011), this field of investigation is still of significant

interest for both engineers and scientists. Historically, the majority of these

investigations have considered the morphological consequences of single source

of disturbance at the scale of river reach. The response to multiple drivers and

stressors in a watershed is still a considerable challenge. In fact, there are only

limited studies about the drivers of alterations at watershed or regional scales

(e.g. Gao et al., 2015).

Engineers, geologists and geographers have developed tools to study, analyze

and predict the responses of river morphology to human disturbances. A

classification of these tools was presented by Grant (2012). Based upon Grant’s

work we reclassified it into the two following classes:

1. Observation and understanding the response system based on study cases

This class includes single case studies, empirical analysis and synthesis

of multiple cases with derivation of some sort of systemic analysis.

2. Predictive modeling: from detailed deterministic to conceptual models.

More detailed model outputs in turn require more detailed inputs for

construction and validation. In general these models are applied only for

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single reaches and the input data are seldom fully obtained. Numerical

deterministic models are capable of simulating erosion, transport and

sedimentation processes in 1, 2 or 3D, including the transient period

between the perturbation and the response of the system. However, while

deterministic models can provide accurate results, a substantial constraint

of this approach is the need for highly accurate data inputs that are not

generally available at the watershed scale, particularly, when the spatial

and temporal scales are larges (watershed and couple of decades) and if

more than one perturbation is considered. This kind of model can be

simplified in analytical/predictive models based on sediment transport

equations, but still requires considerable efforts of modeling and with lower

confidence and weak predictive value. Conceptual models assume that

the fluvial system is in morphological equilibrium after perturbation

(Buffington, 2012). These conceptual and analytical models can provide

valuable results in terms of morphological trends or trajectories, but do not

inform on the time involved in the responses.

For this paper we propose a predictive tool for geomorphological trajectories of

the gravel-bed rivers based on (i) conceptual models in which relations were

derived from the observation and understanding of study cases, using the

experiences from systemic analyses; (ii) that take into account the effect of

disturbances of an initial state of the river system and; (iii) can be applicable and

developed at the watershed scale with assessment of the connectivity from the

upstream part of the watershed to the downstream reaches of the river.

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According the objectives and layout for this paper are,

- To develop a simplified and versatile framework for conceptual modellings

for a wide range of perturbations; and

- To test model functionality on a the Isère watershed, which has had

hydropower equipment installed during the last 60 years

2. State of art and context

The following sections present a relevant background that guides the analysis

and interpretations of the geomorphological responses of gravel-bed rivers to

disturbances. Because of the large spatial variability of processes and forms at

the scale of a complex watershed, and due to the paucity of input data, a

conceptual-analytical model approach was chosen to predict the river

morphology response using the Isère Alpine watershed as a test case and the

complex hydropower systems present in the watershed as disturbance sources.

The literature reveals that, conceptually, the current understanding of fluvial

response to disturbances is generally based on: (i) a general dependence of

geomorphological dynamics on first order drivers such as hydrological flow

regime and sediment supply conditions (second order drivers are for example

large woody debris and animals); (ii) the ability of the system to adapt, in case of

alteration on hydrological flow regime and sediment supply; and (iii) the

propagation of these disturbances with the gradual attenuation of these effects

downstream, due to tributaries that supply water and sediment fluxes.

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2.1. Fluvial morphological responses: driver variables and responses variables

(action and reaction).

The morphological characteristics of a channel (such as cross section, slope,

sinuosity, sediment grain size and distribution) are the result of erosion, transport

and, sedimentation processes. According to Thorne (1997), river morphology can

be rationally explained if distinctions are made between the different variables

involved on these processes. Variables can be classified as driver variables and

responses (adjustment or fit) variables, which respond and adjust to the driver

variables. Thorne introduced a third category, called boundary conditions

corresponding to the internal characteristics of the river reach, such as riparian

vegetation and bank confinement, which can limit the lateral displacement of the

channel.

Driver variables for a river reach are considered from upstream watershed input

conditions: these are spatially distributed variables such as the climate and

geology, which determine the topography, soil, and the natural type of vegetation

cover. Another relevant control is human activities (e.g. land use, management

practices, hydraulics works). These variables define the first order of local

drivers, namely the sediment and water fluxes (Werritty, 1997; Church, 2002;

Grant et al., 2003; Buffington, 2012). However, some authors also give a relevant

importance to large wood and in-channel vegetation (e.g. Buffington et al., 2003

and 2012; Piégay and Gurnell, 1997; and in this ESPL special volume

Takebayashi, 2016 and; Bertoldi and Ruiz-Villanueva 2016), which are

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considered as second order drivers if compared with sediments and hydrological

flow regimes at the spatial scale of this investigation. It is for this reason that

hydrological flow regimens and sediment supply are considered as the more

important drivers variables in this study.

A response variable can change due to a disturbance on a driver variable,

absorbing or modifying the morphological characteristics of the fluvial system.

These responses depend on the magnitude, intensity and duration of the

disturbance, river typology (i.e. their sensitivity to changes according Schumm,

1991), and on the geomorphic activity of its tributaries. A first type of response

corresponds to an accommodation of the morphological characteristics of the

river (adaptation without changes) as a part of its inherent variability. A second

type of response corresponds to an abrupt change of the morphological

characteristics, known as fluvial metamorphosis (Piégay and Schumm, 2003).

According to Schumm (1973), to achieve a morphological transformation of this

kind, a river must first surpass a morphological threshold (see also Schumm,

1977; Champpell, 1983; Werritty, 1997; and Huggett, 2012). In this work, nine

response variables were selected to describe the reaction of the fluvial

morphology due to a perturbation on the driver variables, which are presented

later (in section 3.2 and Table 1, first column).

Boundary conditions (internal conditions of the reach) express the degree of

freedom of mobility. For the development of this model, the local singularities and

some limitations of the variability of adjustment variables were taken into

account. The lateral mobility of the riverbed can be restricted if the riverbed it is

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confined or semi-confined, for example if there are physical barriers such as

levees or by biological characteristic of the riverbank, in particular the role of the

riparian vegetation (e.g. Tal and Paola, 2007). Horizontal mobility is determined

by the storage of bed sediments, in terms of the quantity of sediments available

to be transported and depth of this layer to bedrock (rock outcrops fix the bed

level).

2.2. The equilibrium conditions and time scale of changes

Riverbeds are constantly adjusting and adapting in response to the sequences of

flood events associated with the regional climate and local meteorological

conditions.

In modeling and predicting channel changes, the concept of equilibrium condition

is often used (Buffington, 2012; Church and Ferguson, 2015). In this work, we

consider a river reach to be in equilibrium when there are no disturbances on

driver variables. This implies that the sediment supplies (from upstream reaches

and from hillslopes and banks within the same reach) are substantially

equivalent to the transport capacity over a time period of several years. This

assumption allows for geometric (bedforms, depth, width and local slope) and

grain size changes at a shorter time scale, but considers these variations

negligible over the long-term. The initial condition of the river morphology in this

work corresponds to the current state of the river before a disturbance to the

driver variables.

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A fluvial system reacts to a change of water and sediment regimes at a wide

range of spatial and temporal scales. According to Graf (1977) and Brandt

(2000b), channel morphology changes rapidly after a disturbance, followed by an

exponential decay in change. Williams and Wolman (1984) also showed that the

evolution of bed level in 12 rivers after dam construction was fast immediately

after construction, and gradually the effects decreased until stabilization.

Buffington (2012), based on the Knigton’s work (1984) presented responses

variables in alluvial rivers as function of the spatial and temporal scales ranging

in orders of magnitude. These changes can last from minutes (for local changes

in grain size and textural patches) to many decades or centuries (for stream

gradient and channel sinuosity). Taking into account these physical processes in

rivers, the order of the temporal scales considered is from many years to some

decades. These conceptual models, including the model presented in this work,

do not consider the temporal evolution, which is only possible to take in account

in numerical models.

Gregory (2006) and Gregory and Downs (2008) used the Schumm (1979) and

Graf (1977) approaches to describe the kinetics of river response after a

disturbance. If a system in equilibrium (initial equilibrium) is perturbed modifying a

driver variable, a transient period will start. The transient period is called the

response time, composed of a reaction time and relaxation time. During the

transient period the system evolves to achieve a new equilibrium state, marking

the end of this transient. According to many previous studies (Phillips, 1996;

Grant et al., 2003; Petts and Gurnell, 2005; Grant, 2012, Ziliani and Surian,

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2012), for an homogeneous river reach, the response to a disturbance can be

conceptualized as a trajectory (from an initial equilibrium state to a new

equilibrium state). Each response variable can have a different response time

and the response time of the whole river system can last from decades to

centuries or millennia.

2.3. From upstream to downstream: river reaches segmentation and connectivity

of hydro-sedimentary fluxes.

The river network of a watershed is naturally or artificially segmented into

different homogeneous reaches, taking into consideration their morphological

characteristics and the type of disturbance and its localization (e.g. changes in

sediment fluxes in a specific location). The morphological characteristics of the

reaches are based mainly on bed slope, lateral mobility (river bank conditions:

confined and whether), vertical mobility (a fixed bed level) and river confluences.

Modifications on the continuity of water and sediment fluxes are two important

disturbances on the more relevant fluvial geomorphic drivers (water and

sediment). The continuity of these fluxes can be affected if the magnitudes,

frequencies and timing are modified from an initial reference condition.

For the tested case (application of the model to the Isère river watershed) the

sources of disturbance taken into account were the hydropower structures. The

structures considered to partition a reach in the hydrographic network are, intake

water points, release water points, and large dams, considering that these kinds

of structures can affects the processes of sediments transport and hydrological

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flow regimes. Taking in account the timescale of the river response, structures

like barrage dams (diversion dam which large gates) capable to generate

flushing; allow the continuity of sediments transport (considered as a transparent

structure for the continuity of the sediment transport). The river confluences for

the more important streams in terms of sediments yield and water discharge are

also locations where the river network is segmented.

From upstream to downstream in the river network, hydrological and sedimentary

disturbances are transmitted and attenuated by the compensation of the water

and sediment supplies from tributary streams. In the case of the sediments

surplus or deficit, the effects can also be balanced by sediments delivered from

the bed and banks or sedimented in the bed and banks, translated as a channel

aggradation or degradation and narrowing or widening.

3. Description of the proposed conceptual model

This section describes how changes on the main drivers are computed. A

proposal is made relatively to initial equilibrium conditions in the present state of

the model. Proposed formulations are simplified and can be discussed, improved

and adapted to other cases and particular situations. Their use in the framework

of the conceptual model is presented at the end of the section.

3.1. The quantification of changes on driver variables:

a. - Changes on the hydrological flow regime

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In hydrological sciences and engineering projects, an hydrological flow regime is

characterized by the magnitude, frequency, timing, duration and variability of

discharges. Large and infrequent floods can completely change the morphology

of a system (Tamminga et al., 2015), but low and constant discharge can also

contribute to evolve the river morphology (Asahi et al., 2013). From a

morphological point of view, two characteristic discharges are the most important,

namely i) the critical discharge associated to the incipient sediment motion (e.g.

Recking, 2009 and 2013) and ii) the channel-forming discharge. The critical

discharge depends on the size of bed sediments (e.g. d50 or d84) and the local

channel slope and channel cross-section.

The channel-forming or dominant discharge (e.g. Wolman and Miller, 1960;

Leopold et al., 1964; Andrews, 1980) can be considered the discharge that (as in

steady state) produces the same morphological result as the combined effects of

the entire hydrological flow regime. Even if difficult to assess, channel-forming

discharge is often used for river restoration and natural channel design (Doyle et

al., 2007; Lave 2009), and it is usually considered as: a) being equal to the

bankfull discharge (Navratil et al., 2006), b) the effective discharge (calculated

according to the Wolman and Miller, 1960 procedure), and c) the discharge

associated with a certain return period (see also, FISRWG, 1998), which in most

cases roughly corresponds to a 2 year return period (Biedenharn et al., 2008).

In this paper describing the first version of the model, the channel-forming

discharge is identified as the discharge with a return period of two years. For

each reach, flow duration curves are used to determine the change in the

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number of the days that the channel-forming discharge was equal or was

exceeded during the period before and after the perturbation on the hydrological

flow.

The indicator used to subsequently assess the hydrological alteration

downstream in each river reach was calculated as (Alcayaga et al., 2012;

Alcayaga, 2013):

1pre

post

NQNQ

FQ(1)

where FQ is the Indicator of alteration for hydrological regime based in the

frequency change of the channel-forming discharge, and NQpre and NQpost:

Numbers of days or percentile of exceedance of the channel-forming discharge

before and after the alteration, respectively.

Evidently, this choice is a simple approach and other approaches can be adapted

to compute FQ, according on data availability and the specific characteristics of

the site. In every case, FQ is a proxy to quantify the alteration of the “energy”

available for morphological transformations of the channel. FQ=-1 means that in

the final state, the transport capacity is null; FQ=0 in the case of unchanged

conditions, and FQ positive means an increase of the energy and transport

capacity.

b.- Changes on sediment supply

Although bedload can represent a relatively small percentage of the total

sediment load (Collins and Dunne, 1990; Turowski et al., 2010), bedload

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determines the morphology and habitat of gravel-bed rivers (Kondolf, 1997). For

this reason only bedload volumes and sources are considered in this study.

Particularly, volumes of sediment available on internal sources (banks and

channel bed), external sources (hillslopes), and the degree of connectivity

between hillslopes and streams are considered. To evaluate the intensity of

sediment supplied to each reach we applied a simplified method, which only

takes in account the external supply from both the hillslope and from the

upstream reach, as a continuity function of the sediment transport.

As our objective was to build a simplified model to use at the watershed scale,

then in-channel processes relative to sediment supply (internal sources) were not

taken into account, due to the complexity of the temporal and spatial scales.

Following the same logic to assess the alteration on the hydrological flow regime,

the indicator we used was (Alcayaga et al., 2012; Alcayaga 2013):

1pre

post

SSSS

AS(2)

where AS is an indicator of alteration for sediments supply (bed load sediment),

based on the changes of the intensity of sediment supply from upstream reaches,

and lateral sediments supply in the reach under analysis, and SSpre and SSpost are

potential intensity of the sediments supply estimated with a simplified method,

before and after a disturbance in the continuity of the supply, respectively.

AS=-1 means that in the final stage, there is no sediment supply from the

upstream reach; AS=0 in the case of unchanged conditions, and AS=+1 means a

doubling of the sediment sources upstream of the reach under consideration.

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In the present state of our model, the intensity of sediment supply SS of a sub-

basin that drains to a river reach is the combination of hillslope capacity and of

outlet properties for transferring it downstream. Hillslope capacity of the sub-

basin is estimated using a semi-qualitative approach, considering the following

three variables: lithology (surface geology), land cover and relief (hillslope

gradients). All these variables represented in a Geographical Information System

(GIS), were classified according to their capacity to deliver sediments (see

Tables 2, 3 and 4). More details are given in section 4 of this paper. The result is

a new GIS layer representing an overlapping of the previously classified layers

(Table 5). This layer represents the potential supply of sediments from the

hillslopes and is called SS. This combination and classification assumes that all

three factors (geology, terrain gradient and land cover) have an equivalent

impact on the sediment supply. SS hillslope is computed from pre and post

values as the sum of individual pixel indexes within the sub-basin, considering

the path of the sediment in the watershed river network (upstream -

downstream). In the case of an obstruction in the sediment path such as a lake, a

reservoir, check dams, or a large dam at the outlet of the sub-basin, there is no

continuity of bedload downstream (Brune, 1953; Lewis et al., 2013; Kondolf et al.,

2014) and the above-computed hillslope capacity is modified in consequence.

3.2. Disturbance vector

The values of FQ and AS for each river reach form a vector named the

disturbance vector. The direction of these vectors is associated with a trend or

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trajectory of channel changes and its magnitude represents the intensity of the

perturbation.

a.-The direction of the disturbance vector and morphological trends

The indicators FQ and AS are represented as two principal axes forming a

Cartesian coordinate system (the explanations hereafter refer to Figure 1),

defining four directions associated with the angles (0°, 90°, 180° and 270°). The

FQ axis (positive or negative) is a representation of the incremental or

decremented of the river reach “energy”. In the same way the AS axe (positive or

negative) is a core of the increment or decrease in sediment supply from

upstream. Two secondary axes are also relevant and they define others four

directions (45°, 135°, 225° and 315°). For the direction 45°, the fluvial processes

increased in intensity (more sediment supply and an increment of the channel-

forming discharge frequency). For the direction 225°, the processes decreased in

intensity (less sediment supply and a reduction of the channel forming discharge

frequency). These two directions (45° and 225°) bisect the Cartesian plane, with

zones associated with two basic morphological responses of the channel:

sedimentation and erosion. The first zone –sedimentation- corresponds to an

increment of AS (increase of sediment supply) and a decrement of FQ

(diminution of the discharges frequency capable of doing morphologic work). The

second zone –erosion- occurs just the opposite, when AS decreased and FQ

increased. In the border of these two directions (45° and 225°) the morphological

response of the channel depends on other more complex and specific factors,

such as the geological channel history (Grant et al., 2003).

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All these eight directions (defined by the four axes) correspond to morphological

trends or trajectories of the expected changes in the channel (see Table 1) based

on an extensive review of the literature, empirical relations, case studies, and

conceptual models, which have been developed during the last sixty years. The

main references we used to associate the eight directions with to build this model

are: Lane (1955); Schumm (1969; 1977); Petts (1980); Williams and Wolman

(1984); Kellerhals and Church (1989); Brandt (2000a); Brandt (2000b); Huang

and Nanson (2002); Grant et al., (2003); Grant (2012); Petts and Gurnell (2005);

Schmidt and Wilcock (2008); and Dust and Wohl (2012). Modified from Alcayaga

et al. (2012) and Alcayaga (2013), Table 1 and Figure 1 show the nine

morphological variables (bed elevation, bed slope, width, depth, wetted area, d50,

terrace formation, and colonization of vegetation) their responses, associate with

the eight directions (as angles in degree).

b.- The magnitude and continuity of the disturbance vector

The disturbance vector for each river reach has an origin from an initial non-

perturbed condition (the origin of the Cartesian coordinate system) and an end

point given by each FQ and AS; this distance represents the magnitude of the

disturbance vector. The magnitude corresponds to the intensity of the

disturbance classified in three classes as low (< 0.15), medium (0.15 – 0.30) and

strong (> 0.30).

Additionally, there is continuity in the trends for each response variable, as

depicted in the graph of Figure 1. For example, the bed slope (S) increases in the

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graph from 90 until 180; afterwards, there is a zone in which an inflexion in the

trend occurs at 225; then S decreases from 270 until 0 and the next inflexion

zone occurs at 45. If the direction of the disturbance vector does not correspond

exactly to one of these eight principal directions (the 8 axes in the Figure 1), the

final response is determined using a weighted function of the distance between

the two closed axes with respect to the calculated disturbance vector. Regarding

the colonization of the vegetation, this response refers to the possibility of

encroachment of the vegetation into the active channel.

Figure 1. Graphical representation of the disturbance vector (shown in red) and

the main direction of the morphological response

The methodological approach proposed here could be applied to a wide range of

fluvial systems which suffer alterations in hydrology and sediment supply due to

natural or anthropic disturbances.

4. Application of the model to the Isère watershed

The application of our model has been exercise in order to assess it in a complex

watershed with numerous and important perturbation sources. The model was

tested on the Isère watershed upstream of the city of Grenoble (5700 km2). The

Isère mountain watershed is a sub-basin of the Rhône River (upper part of the

Rhone basin), located in southeastern France (Figure 2). Its main tributary is the

Arc River, and the second one is the Arly River. This watershed is a strongly

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anthropogenically-affected hydro-system (Nougier et al., 2015). Among other

sources of perturbations, the hydrological flow regime and the sediment supply

are altered by several hydropower systems (Vivian, 1994; Marnezy, 1999).

According to Peiry et al. (1999), the hydropower systems of the Isère watershed

(Figure 3) are among the oldest, densest, and likely most sophisticated in the

word. In the watershed there are three different types of hydropower plants:

impoundment (large dams), diversions (heavy transbasin diversions with

barrages) and pumped-storage. The applied model considers the effect of the

hydropower systems built during the 1950 and 1970, but with the following

limitations:

- The whole system is considered to be built at the same period, from an

initial steady state;

- Corresponding data are taken from official public sources, but they may

not be fully representative of the actual operating modes;

Other perturbations sources were not taken in account. Older ones include

climatic perturbation (Little Ice Age), the stabilization of mountain hillslopes

(forestation, engineering torrent control) (Provansal et al, 2014) and levees in the

downstream reaches. Recent perturbations are mainly intensive gravel mining

from the end of the Second Word War; these were completely stopped at the

beginning of 1980.

Figure 2. Location of the Isère watershed in the geographical French context.

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According to the criteria mentioned in section 2.3, river network segmentation

was built using its morphological characteristics (i.e. bed slope, confluences) and

the hydropower structure locations (i.e. water intakes, releases and large dams).

In total, 23 reaches (see figure 3) were identified. Codes were assigned to each

reach starting with the main stream from the headwater reach of Isère (code 100)

to the lower downstream reach (900); then the main affluent of the Isère (Arc

River) following the same logic (see Figure 3).

Figure 3. Location of the Isère watershed, sub-basin delineation, river reaches

with their codes and main hydropower canalizations and dams.

Overall, 16 discharge stations were used to calculate the FQ indicator. These

discharge time series were gathered from the Banque hydro data base

(www.hydro.eaufrance.fr). When the discharge stations were not located at the

beginning of the river reach, it was necessary to weight discharges using the

surface drainage area to estimate the discharge values associated with a return

period of two years.

The determination of AS was more complex, as it involved the use of information

from different sources, and a reclassification of this information according the

methodology explained above. For the Isère watershed, this classification,

organized by geology, relief and land cover, is described below (from Table 2 to

Table 4). The geological surface formations, and their mechanical characteristics,

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have a strong relationship to sediment supply. The qualitative classification

presented in Table 2 is based on information from the Bureau de Recherches

Géologiques et Minières de France (BRGM, 1980).

The topographic gradient of hillslopes is taken as the local gradient of the terrain.

The gradient is calculated using a Digital Elevation Model (DEM). The results (in

degrees) are then reclassified according to the groups shown in Table 3.

The land cover data used comes from the European CORINE project (2000). The

land cover for the Isère watershed was grouped and then classified into three

distinct classes according their potential for delivery of sediment (Table 4).

The combination of geology, gradient and land cover (codes from the Tables 2, 3

and 4) resulted in 15 class types for the potential intensity of sediment supply.

Then, for each sub-basin that corresponded to the drainage area of each river

reach, a single unique intensity value was obtained. Finally, these unique values

for reach sub-basin are added (as a continuum) from upstream to downstream

(as explained in section 3.1).

5. Results and discussion

FQ and AS were calculated for each reach of the river network. As an example,

we present the calculations FQ and AS for reach 300, which is influenced by the

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hydropower system in the upper basin (mainly by Tignes dam and Malgovert

power plant, and other smaller structures).

For reach 300, the channel-forming discharge (2-yr return period) is 102 (m3s-1),

and the flow duration curves for the conditions pre and post hydropower are

shown in Figure 4. For this reach, the flow regime is regulated by dams in the

upper part of the watershed, and by diversions (transbasin diversion). The effects

of these diversions are translated as a reduction of the channel-forming

discharge in terms of frequency. Then, the frequency of the channel-forming

discharge was reduced from the initial condition, resulting in a value for FQ of -

0.31.

Figure 4. Flow duration curves for the Isère river at Moûtiers downstream of the

Tignes large dam and Montrigon regulating reservoir. The curves correspond to

both periods before and after the initial operation of these dams during 1954.

The calculation of AS for the reach 300 implies consideration of the contributions

from upstream of the sub-basins associated with reaches 200 and 100. The first

calculation estimated the hillslope capacity of each pixel and sub-basin (SS)

through the overlapping of geology (table 2), terrain gradient (table 3) and land

cover (table 4), resulting in 45 possible values (see column 1 in Table 5). The

result of this combination is reclassified in 9 classes (see column 2 in Table 5),

assigning values from 1 (lower productivity) to 9 (higher productivity). The

hillslope capacity is presented in Figure 5 for individual pixels.

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Figure 5. Hillslope capacity reclassified for the sub-basins 100, 200 and 300

combining geology, terrain gradient and land cover.

The second calculation consisted in obtaining a single value of sediment supply

(SS) from the hillslopes of each sub-basin. The SS value for each sub-basin is

calculated by a weighted sum (value of pixel -1 to 9- multiplied by the number of

pixels with this respective value) and normalized by the total number of pixels in

each sub-basin. The SS values represent the potential of sediment delivery from

each sub-basin to its reach.

The SS values for each sub-basin relates to reaches 100, 200 and 300 are 5.4,

5.7 and 4.7, respectively. To obtain the SSpre and SSpost required adding the SS

sub-basin values from upstream to downstream, considering the continuity or

discontinuity (presence of natural or artificial blockage) of sediment fluxes, as

described in section 3.1.b. Figure 6 shows the AS calculation for the reach 300,

where SSpre is the sum of the SS contribution from the sub-basins 100, 200 and

300 (SSpre=15.8). SSpost was calculated using the same sum of SS values

considering the blockage effect in the sediments fluxes due to Tignes dam

(SSpost=10.4), and subsequently AS was calculated for reach 300 result -0.34.

Montrigon barrage dam is considered as “transparent” in terms of sediments

fluxes, because it has Tainter gates located in the base of the dam.

Figure 6. SS values for the sub-basins, SSpre and SSpost values for the reaches

100, 200 and 300, represented by red arrows.

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For the same reach (code 300), FQ and AS resulted to be -0.31 and -0.34,

respectively. Using these two values, the magnitude of the disturbance vector

was calculated as 0.46, with a direction of 227.4. This vector is located in an

area where the morphological processes decrease in intensity as both FQ and

AS are reduced proportionally, in accordance with Figure 3. In a case such as

this when the disturbance vector is near to 45 or 225, the trajectory of the

changes are difficult to predict, and according Grant et al. (2003) the response of

the channel depends on specific factors. Thus, for this reach, only the response

variables (defined in Table 1) W (width, decrease), DP (channel depth, decrease)

and WA (wetter area, decrease) are predictable by the model.

The results for all the reaches of the Isère watershed are shown in Figure 7 and

Table 6.

Figure 7. Results for disturbance vectors as a function of FQ and AS

Figure 7 shows that all the disturbance vectors are located in the lower

hemisphere, suggesting that all reaches affected by the hydropower systems

experience incision. It is possible to appreciate also that a group of vectors (for

reaches 610 to 650) have nearly the same direction. These reaches correspond

to the main tributary of the Isère River, which is the Arc River. The Arc River is

characterized by featuring a pump-storage hydropower, but primarily for water

diversion structures with water gates capable to flush (these flushing operations

are carried out at least once a year); therefore, the flow regime is modified

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without modifying the continuity of sediment supply (considering a period over

many years). Figure 7 also shows that a group of vectors have trends with a

direction around 270° (reaches 200, 500, 600, 531 and 540). These trends are

the result of, in one case, the presence of a few large dams (e.g. the reach 200),

and in another case, the product of both a deficit in sediment supply remaining

from upstream and the water release points that “compensate” the discharge

intake upstream.

The magnitude of the vectors is related to the intensity of the morphological

changes. The intensity of the changes is related to the time response and the

distances downstream of the morphological effects, in addition to other variables

(e.g. the activity of the affluent downstream, which attenuates the disturbance

effects). We characterized the magnitude of the vector using three intensity

classes (presented in section 3.2) namely: > 0.15 low; 0.15 – 0.30 medium and;

<0.30 strong.

The validation of conceptual models in fluvial geomorphology is limited, in

particular when applied to large spatial scales. While an evaluation of the results

was possible only for the elevation of the riverbed, the aim of this study was to

apply the model in the Isère watershed in order to test the model on a very

complex system, and not seek in detail all the possible sources of morphological

perturbations. We checked the model results against the Peiry et al.’s (1994) field

observations (see Figure 8) and with the evolution of longitudinal profiles,

available for some portions of the reaches (see Figures 9a and 9b). The data for

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the longitudinal profiles were gathered from the Service de Nivellement Général

de la France (1908) and SOGREAH (1994). Of the 15 reaches in this study that

have field observations, six agreed with the model predictions by Peiry et al.

(1994) (500, 531, 540, 600, 620 and 630). For three other reaches, the model

results did not agree (610, 640 and 650). The model predicts aggradation for

these three cases, but the field observation from the Peiry et al. (1994) shows a

local incision. In particular, reach 610 (a head water reach) is influenced by water

derivation from hydropower intakes, without changes in sediments supply due to

HPs. Thus, the morphological channel response expected due to the reduction of

river discharge and consequently the transport capacity was aggradation.

However, gravel mining took place in this reach (Fig. 8). This point source (gravel

mining) of the morphological disturbance to sediment availability to be

transported was likely greater than the discharge perturbation introduced by

water diversion. We recall that for the case test in the Isère watershed, gravel

mining was not considered. For the remaining 6 reaches (300, 400, 670, 700,

800 and 900) the model was unable to definitively predict the evolution in

riverbed elevation, as the disturbance vectors were too close to 225°. Overall,

for 6 of 9 reaches with viable prediction, were in agreement with Peiry et al.

(1994). Specifically, for the longitudinal profiles of reaches 300 and 500, we verify

that the model was capable to predict the changes in the bed elevation. In the

case of reach 300 (mentioned in the first part of the results section) the response

was unchanged, and for reach 500 the result was bed degradation (due to a

heavy water release, displayed in Figures 3 and 6 as Diversion to Isère).

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Figure 8. Trends and intensities predicted by the model for bed elevation,

observations from Piery et al., (1994), and location of gravel mining on the active

channel (Rhône-Méditerranée and Corse Basin Committee, RMC 1995).

Figure 9. Comparison of the longitudinal profiles from the years 1908 and 1988.

Figure 9a is reach 300 between Isère at Montrigon and confluence Isère - Doron

de Bozel, showing relative stability. Figure 9b is reach 500 between Isère at La

Bâthie and confluence Isère – Arly, showing aggradation experienced by the

longitudinal.

While the model satisfactorily compared with field observations, it is important to

consider that there are other sources of alteration that can disturb the control

variables in alpine mountain rivers, like the Isère River. These include land use

changes (massive reforestation of hillslopes and rural development), river

channelization (river channel rectification, meandering cutoff, and embankments)

and gravel mining. Climate patterns could have also affected the Isère river

morphology. According to Peiry et al. (1994), the climatic period known as the

Little Ice Age affected the morphology of the Isère River, notable until the 1980.

For these reasons, the morphological changes of the Isère River are not solely a

product of hydropower systems upstream. Thus, a validation of model prediction

is greatly restricted. Additionally, Comiti (2012) adds that a limited number of

study cases exist, which thereby hinders any attempt to infer the relative

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contribution of potential causes to adjustments in morphology of the channels in

alpine mountain rivers. One of these cases is presented by Provansal et al.

(2014) for the Lower Rhône.

5.1 Limitations and perspectives of the method

The need for developing a simplified conceptual model predicting channel

changes due to anthropogenic disturbances is justified by the paucity of field data

that hamper the change of using more sophisticated approaches at the scale of

an entire watershed. From this point of view, the Isère watershed was no

exception. In this sense, the aim of the model application was to test the

robustness of the method in an extremely complex watershed using simple data.

The particular difficulties in working at watershed scale with strong anthropogenic

disturbance, is that there are often more than one source of disturbance, which

act at different spatial and temporal scales. As a result, model predictions are

difficult to validate. Additionally, there are other assumptions and limitations

within the model that we must note. First, our modeling approach considers only

the initial and final states of the channel in dynamic equilibrium. Thus, the

duration of the transition period is not evaluated, as well as the overlapping

effects of non-simultaneous perturbations, but it is possible to do the model, if

there are data available. Second, the perturbations introduced during the

transition period at a specific time, or distributed over time (e.g. climate change)

may potentially stop, accelerate or shift the processes, and divert the original

trajectory of morphological changes (it can include the changes in the land cover

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dynamics). This also is valid for dynamic riverine vegetation, considered here as

static.

Despite the simplicity of this model, and inherent assumptions and associated

limitations of it’s application, it provides a useful tool to perform predictions of

morphological trends, when the spatial domain is large and when the

perturbations are spatially distributed. Thus, this research presents a first attempt

at obtaining a “big picture” view regarding the behavior of morphological fluvial

systems. The simplicity of the model makes it flexible for a wide range of different

applications and scenarios similar to that tested here (e.g. sand and gravel

extraction, sediment replenishment, etc.). Possible future improvements of this

model would allow the evaluation of both the indicators related to the alteration

for the hydrological regime (FQ) and the alteration of sediment supply (AS). This

model uses a channel-forming discharge to evaluate sediment transport capacity.

However, discharge and transport capacity have a non-linear relationship (e.g.

using the transport capacity equations). FQ can be replaced by the relative

change of non-dimensional shear stress (Shields number) similar to the

proposition by Schmidt and Wilcock (2008). However, it is only possible at the

watershed scale when the detailed data are available.

The simple method to evaluate sediment supply intensity can be improved by

considering the stock of sediments in the active channel (available for transport),

for example, through time series of aerial photography or time series of bed

slope. However, this invariably brings us to the same challenge related to data

availability.

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An important issue that is not addressed by this type of model is the transient

duration period (reaction time), and -as mentioned before- possible trajectory

changes due to other changes introduced during this period (for example,

deforestation, climate change, etc.). In both cases this type of model is limited,

and can only be accomplished through numerical modeling. Consequently, the

challenge is not only to establish the trajectory of change, but also to know how

long these changes have occurred.

5.2. Final remarks

In general terms, anthropogenic disturbance to the river network are evaluated

individually at the scale of reach, and not as a system. In this study, we

attempted to evaluate the trend of morphological changes of a gravel-bed river at

the scale of river network, due to disturbance to two main morphological drivers:

hydrological flow regime and sediment supply, which are spatially distributed in a

watershed. The outcome of this study was the creation of a tool in the form of a

simple model capable of predicting the most likely directions of morphological

changes.

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This model is a useful tool for river management, river planning and for

assessment of morphological channel trends at the watershed scale. It can

estimate morphological channels trajectories due to hydropower projects by

considering the cumulative and synergistic effects at larger scales than just the

river reach. Its application is especially relevant for developing countries, for

example, in Chilean Patagonia or in Sub-Saharan Africa. In remote zones (where

data are not available), there are hydropower projects that consist of more than

one hydropower plant, and which could influence a large part of the watershed.

In cases such as these, conceptual models similar to the we present could be

better suited than traditional physically-based numerical models for predicting

morphological channel changes in watersheds.

Acknowledgements

The authors thank the suggestions, comments and advices provided by the

reviewers and associate editors, and for the excellent support of the SI editors to

improve the quality of this paper.

This work was supported by the FONDECYT project n. 11140764, funded by the

Chilean National Agency for the Science and Technology (CONICYT).

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Table 1 Directions of the most probable trends of river responses as a function of FQ and AS

Responses Variables Angles in degree0° 45° 90° 135° 180° 225° 270° 315°

Bed elevation E D ? A A A ? D DBed slope S Channel Width W Channel Depth DP Wetted area WA Width to depth radio* WDR ? ? ? ?Mean particle size d50 ? ? Terrace formation T Y ? N N N Y/N Y YColonization of vegetation V N Y/N Y Y Y ? N N

D: degradation; A: aggradation; : increased; : decreased; : increased or decreased; ?: Not referenced in the literature; Y: occurrence of phenomena; N: nonoccurrence of phenomena; Y/N: occurrence or nonoccurrence of phenomena *according to Schumm (1969) and Huang and Nanson (2002)

Table 2Identification code used for the assessment of sediments supply based on the classification of the geological map (BRGM, 1980).Geological zone class Characteristics Mechanic

resistance Code

Piedmont - Bündner schist

Oceanic meta-sediments (ancient ocean detrital clay metamorphosed) whose metamorphism is slight.

High 100

Pre-alps limestone

Sedimentary rocks (easily soluble in water)

Medium 200

External Massif crystalline

Plutonic magmatic rocks (e.g. granite/complex plutonic-volcanic of the Belledonne mountain range)

High 300

Sedimentary cover of the central massifs

Sedimentary rocks Medium 200

881

882

883

884

885886887

888889890891892893894

895896897

Alpine corridor “Sillon alpin”

Alluvial Platform Low 300

Intra-alpine zone Magmatic or metamorphic rocks (crystalline and metamorphic rocks)

High 100

Table 3Identification code used in the sediment supply assessment and classification of terrain gradient

Terrain gradient

(in degree)

Description of potential sediment supply delivery Code

1 – 15 Very low 01015 – 30 Low 02030 – 45 Medium 03045 – 60 High 04060 – 90 Very high 050

Table 4 Identification of code used for land cover factors in the assessment of sediment supply, based on the database of CORINE project Level III.

Land cover class Classification according to the potential input of sediments Code

Urban, and forest areas Low 001

Agricultural areas and areas with low density of vegetation Medium 002

Bare soil, bare rock and mining exploitation areas

High 003

898899900901902903

904905

906907908

909910

Table 5 Classification of hillslope capacity for the combination of geology, terrain gradient and land cover, using tables 2, 3 and 4.

Combination codes of overlapping layers(Geology, terrain gradient, land cover)

SS sub-basin values

Qualitative sediment delivery

111 1 Very low112, 121, 211 2113, 122, 131, 212, 221, 311 3 Low123, 132, 141, 213, 222, 231, 312, 321 4133, 142, 151, 223, 232, 241, 313, 322, 331 5 Medium143, 152, 233, 242, 251, 323, 332, 341 6153, 243, 252, 333, 342, 351 7 High253, 343, 352 8353 9 Very high

911912913

914

Table 6.Results for all the reaches of the Isère watershed

Reach FQ AS Magnitude Angle E S W D WA WDR d50 T V100 0.43 -0.07 0.44 350.4 D ↓ ↑ ↑ ↑ ↑ ↑ Y N200 0.05 -0.48 0.48 275.7 D ↓ ↑ ↑ ↑ ↑ ↑ Y N300 -0.31 -0.34 0.46 227.4 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?310 -0.22 0.00 0.22 180.0 A ↑ ↓ ↓ ↓ ↓ ↓ N Y400 -0.25 -0.23 0.34 223.1 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?500 0.05 -0.22 0.23 282.0 D ↓ ↑ ↑ ↑ ↑ ↑ Y N510 0.00 0.00 0.00 0.0 NC NC NC NC NC NC NC NC NC520 -0.17 0.00 0.17 180.0 A ↑ ↓ ↓ ↓ ↓ ↓ N Y530 0.00 0.00 0.00 0.0 NC NC NC NC NC NC NC NC NC531 -0.07 -0.37 0.37 259.4 D ↓ ↑ ↑ ↑ ↑ ↑ Y N540 0.02 -0.06 0.07 287.5 D ↓ ↑ ↑ ↑ ↑ ↑ Y N600 0.04 -0.16 0.16 283.0 D ↓ ↑ ↑ ↑ ↑ ↑ Y N610 -0.43 -0.04 0.43 184.7 A ↑ ↓ ↓ ↓ ↓ ↓ N Y620 -0.37 -0.07 0.38 190.4 A ↑ ↓ ↓ ↓ ↓ ↓ N Y630 -0.39 -0.05 0.39 187.5 A ↑ ↓ ↓ ↓ ↓ ↓ N Y640 -0.38 -0.04 0.39 186.5 A ↑ ↓ ↓ ↓ ↓ ↓ N Y650 -0.38 -0.04 0.39 186.0 A ↑ ↓ ↓ ↓ ↓ ↓ N Y660 -0.04 -0.06 0.07 239.5 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?670 0.00 0.00 0.00 0.0 NC NC NC NC NC NC NC NC NC700 -0.06 -0.09 0.11 236.8 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?710 0.00 -0.03 0.03 270.0 D ↓ ↑ ↑ ↑ ↑ ↑ Y N800 -0.12 -0.09 0.15 216.0 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?900 -0.09 -0.08 0.12 223.4 ? ↓↑ ↓ ↓ ↓ ? ? Y/N ?NC: No changes, these reaches correspond to headwaters not influences by hydropower system

915916

917