Prospects and challenges of simulating river channel response to future climate change

1 River channel hydraulics

Fluvial processes, and the physical laws behind them, are expected to perform similarly in the future as at present. Thus, the models applied for present and past in-channel changes are assumed to be applicable for future predictions also. The spatial numerical solution techniques of the conservation of mass and momentum equations (Navier–Stokes) within hydro- and morphodynamic models enable the calculation of fluid motion, including unsteady flow, in geometrically complex river channels with spatially and temporally varying boundary conditions (Bates et al., 2005; Sambrook Smith et al., 2006; Wright, 2005). These simulation capabilities are required as future flows in river channels need to be modelled as unsteady due to the expected changes in hydrology. The simulations can be performed in one, two or three dimensions. The one-dimensional (1D) models simulate in the downstream direction only from one cross-section to the next with results averaged for each cross-section. As can be seen from Table 1, which collates the main characteristics of models used to simulate reach-scale future in-channel change, most future simulations are performed in the one dimension (Table 1). Two-dimensional (2D) models solve shallow water equations for water level and depth-averaged velocities in two spatial directions (Nelson et al., 2003; Pender and Néelz, 2007). These are mainly applicable for simulations of a few years (i.e. the near future) and at the event scale. As a consequence, only a couple of examples of future 2D hydrodynamic simulations exist (Lane et al., 2007; Lotsari et al., 2010; Veijalainen et al., 2010). In three-dimensional (3D) models, the vertical dimension, that is, secondary flows and turbulence, is also included (Nelson et al., 2003). These multi-dimensional models require more computing power because the equations are solved on mesh or grid form geometry. Therefore, the choice of the hydrodynamic model depends on the complexity of the processes to be analysed, the time span in question, the availability and quality of the field data and the computational limitations (Formann et al., 2007). To date, no 3D future hydrodynamic simulations have been performed.

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Table 1.

The main characteristics of future in-channel change simulation approaches.

Publication	Model type	Flood inundation	Erosional forces	Bed load	Suspended load	Vertical change	Lateral change	Future discharge scenarios	Land cover/sediment supply change	Base level change	Grain size change
Veijalainen et al. (2010)	2D hydrodynamic model	x						x
Lane et al. (2007)	Coupled 1D/2D hydrodynamic model	x				x (measured)		x
Lotsari et al. (2010)	2D hydrodynamic model		x					x
Lotsari et al. (2014)	1D hydrodynamic model		x					x		x
Kiat et al. (2008)	1D morphodynamic model			x		x	x				x
Verhaar et al. (2008)	1D morphodynamic model			x	x	x		x		x	x
Verhaar et al. (2010)	1D morphodynamic model			x	x	x		x		x	x
Verhaar et al. (2011)	1D morphodynamic model			x	x	x		x		x	x
Boyer et al. (2010)	1D morphodynamic model			x	x	x		x		x	x
Gomez et al. (2009)	1D morphodynamic model, and hydrological/suspended sediment model			x	x	x		x	x	x	x
Ziliani and Surian (2012)	cellular model			x	a	x	x		x		a

^aNot mentioned/analysed, even though the model is capable of performing this based on Van De Wiel et al. (2007).

Reduced complexity cellular models, first developed by Murray and Paola (1994) for braided river applications, can simulate centennial to millennial river evolution (Nicholas et al., 2006). However, they have not been widely applied for future simulations of natural river channels (Table 1). Channel and/or floodplain geometry is represented in grid cells from fine to broad scales. Equations such as Navier–Stokes are computationally too demanding for cellular models, so more efficient algorithms have been applied (Coulthard et al., 2007; Van De Wiel et al., 2007). Different reduced complexity model representations exist (Nicholas and Quine, 2007), but for example a flow-sweeping algorithm can be used to calculate a steady-state, uniform flow approximation to the flow field (Coulthard et al., 2012; Van De Wiel et al., 2007; Ziliani and Surian, 2012). In this type of approach, discharge is distributed to all neighbouring cells within the sweep width range according to differences in water elevation of the donor cell and bed elevations in the receiving cell (Van De Wiel et al., 2007). The Manning’s equation can be used to calculate flow depth and velocity from discharges. This is a similar concept to the implicit solution schemes employed in finite difference algorithms, that is, of hydrodynamic models (Van De Wiel et al., 2007). However, the sweeping algorithm does not conserve momentum nor distinguish between primary and secondary flows.

2 Sediment transport and vertical channel evolution

The inclusion of sediment transport and river bed topographical updates in models is important, since their absence may cause uncertainties in flow predictions (Hunt, 2002). The analysis and simulation of solely future suspended sediment transport, that is, not including bed load or channel bed elevation changes, have mostly been presented at a catchment scale and not within river channels (Asselman et al., 2003; Mukundan et al., 2013; Ward et al., 2009). These catchment-scale suspended sediment analyses have, therefore, not been included in the present review. Similarly, we have excluded the work of Goode et al. (2013) and Thodsen et al. (2008) despite them including suspended sediment transport in their reach-scale in-channel studies. This is because Thodsen et al. (2008) applied only a concept of time-series analysis of suspended sediment concentrations, that is, rating curves, as a modelling approach together with discharge scenarios, whilst Goode et al. (2013) applied only an empirical scour shear model together with discharge scenarios, so neither applied numerical in-channel simulation approaches.

Both suspended and bed load can be incorporated into morphodynamic models, which can therefore predict vertical river bed changes. These models include, in addition to the equations already included in the hydrodynamic models, the equations for the initiation of sediment particle motion, the conservation of sediment (e.g. the Exner equation), as well as a bed update scheme. The equations for particle motion have been developed for different grain sizes (e.g. Meyer-Peter and Müller, 1948; Van Rijn, 1984a, 1984b, 1984c) and the river bed is updated according to transport rates (Callaghan et al., 2006). These morphodynamic simulations can be performed in one, two and three dimensions (e.g. Copeland, 1990; Dargahi, 2004; Simon and Darby, 1997). Van De Wiel et al. (2011) noted that such morphodynamic models had not yet been applied for environmental change studies due to the extensive data requirements and the demands on computational power for long-term larger scale studies; however, Verhaar et al. (2008) had already applied these models for morphological climate change impact analysis. Since then, there has been an increasing number of studies using such modelling approaches (Boyer et al., 2010; Gomez et al., 2009; Verhaar et al., 2010, 2011). To date, however, only 1D morphodynamic models have been applied for future channel change predictions (Table 1: Boyer et al., 2010; Gomez et al., 2009; Kiat et al., 2008; Verhaar et al., 2008, 2010, 2011).

The use of cellular models, especially in present or past braided river channel studies, has increased in recent years (Coulthard et al., 2007; Doeschl-Wilson and Ashmore, 2005; Doeschl et al., 2006; Hodge et al., 2007; Murray and Paola, 1994; Nicholas et al., 2006; Sambrook Smith et al., 2006). However, many of these are simulated with theoretical channel conditions or flume experiments, and without conventional sediment transport equations to determine erosion and deposition that alter the channel form (Coulthard et al., 2007). There has only been one in-channel cellular modelling study focused on future change (Ziliani and Surian, 2012), where the cellular model used is a modified version of a landscape evolution model and applies a suite of physically based rules to simulate the entrainment, transport and deposition of sediments (Van De Wiel et al., 2007). The model therefore has the capability to transport sediments as either bed load or suspended load, which can be selected by the user for each of the grain sizes (Van De Wiel et al., 2007; Ziliani and Surian, 2012). Bed load is distributed proportionally to the local bed slope, but suspended load is routed according to flow velocity (Van De Wiel et al., 2007) and the river bed is updated according to the transported sediment load. Thus, Ziliani and Surian (2012) applied a reach mode of this cellular model, where sediment and water enter the system from one or more points. By contrast, Coulthard et al. (2012) applied the same model as Ziliani and Surian (2012) for the River Swale (UK) but used the landscape evolution version of the model, that is, the catchment mode where catchment geomorphology and sediment yield output were simulated. Due to this model’s coarse resolution and catchment-scale configuration, the Coulthard et al. (2012) paper falls outside the scope of this review; however, the paper provides valuable insights into the potential for applying cellular models in the future simulation of river channel reaches that we discuss in later sections.

3 Sediment transport and lateral channel evolution

Even though most morphodynamic models are not normally able to simulate lateral channel changes, some of the 1D models are now capable of simulating both vertical and lateral erosion (Kiat et al., 2008; Raven et al., 2011). Despite their potential in future in-channel change simulations, to date these have only been applied once – for relative short-term (2006–2016) sediment transport predictions (Kiat et al., 2008). The model applied by Kiat et al. (2008) was described more thoroughly by Chang (2006). In the model, the change in channel width depends on the sediment rate, bank configuration and bank erodibility, where the slope of an erodible bank is limited by the angle of repose of the material. This type of model is also capable of simulating curvature-induced scour and deposition based on the flow curvature (Chang, 2006).

Bank erosion models, which predict only lateral changes without bed elevation changes, are also available. However, they do not predict the in-channel processes in such detail as hydro- or morphodynamic models (Midgley et al., 2012). These have yet to be applied for future simulation approaches. There are also so-called classification models in fluvial geomorphology, which use the relation between discharge and slope of the river for predicting the existence of either multi-thread or single-thread channel types (Anisimov et al., 2008). These have been applied in future channel change predictions, but are excluded from the present review, since they do not simulate the in-channel processes.

Lateral channel changes have also been incorporated into cellular models. In the reach mode simulation approach of Ziliani and Surian (2012), in addition to the river bed changes discussed earlier, lateral erosion and bank failure are represented as local cellular automaton rules (Van De Wiel et al., 2007). The lateral erosion algorithm is split into the determination of local channel curvature, calculation of lateral erosion and distribution of the eroded sediments across the channel. Bank erosion is calculated based on the bank erosion coefficient, the near-bank flow velocity and water depth in the wet cells neighbouring the edge cell. Deposition is determined along the inside bank from the model’s automaton rules and the lateral redistribution of the eroded sediments is simulated using a cross-stream gradient. The future sediment flux simulations of Coulthard et al. (2012), performed in the catchment mode of this same cellular model, included these lateral channel evolution capabilities but were not analysed at the in-channel scale.

4 Input data and external forcing conditions

The main established input parameters applied to reach-scale in-channel change simulation studies include the channel geometry (grid, mesh or cross-section form), the properties of the flowing fluid (density, viscosity), the flow characteristics (discharge, velocity, water level) and estimates of resistance and roughness or grain size (Chanson, 1999; Hunter et al., 2007; Van De Wiel et al., 2007; Verhaar et al., 2008). The more sophisticated, or multi-dimensional, the model is the more input as well as calibration and validation data is needed. Future simulations require calibration and validation based on present or past data. Channel geometry is needed for the initial conditions in all reviewed models; however, morphodynamic and cellular model simulations also require this information from the final time step of calibration and validation periods. The in-channel change simulations require sufficiently detailed geometry for each simulation approach or river channel in question. For example, the reach-scale cellular model of Ziliani and Surian (2012) was based on relatively detailed geometry (25 m × 25 m cells) for their wide braiding reach, whilst the coarser resolution (50 m × 50 m grid) of Coulthard et al.’s (2012) model precluded the in-channel simulation of the narrow River Swale. Most commonly, and in sub-critical flow conditions, discharge and sediment supply are defined as the upstream boundary condition and water level as the downstream boundary condition. In addition, all models applied in fluvial transport simulations require measured sediment properties and transport rates (Gomez et al., 2009; Lane et al., 2007; Van De Wiel et al., 2007; Ziliani and Surian, 2012).

Future climatic (and/or other environmental) changes are depicted in the different models mainly via external forcing conditions, which Van De Wiel et al. (2011) highlighted as one of the main uncertainties of past environmental change analysis. External forcing conditions are extremely important to take into account for all types of future numerical in-channel change simulation approaches. External forcing includes changes to temperature, precipitation, discharge, water level, vegetation or land cover. These can be used as input data or boundary conditions for future simulations. The various future river channel simulation approaches require, in particular, information on future discharge, which can be simulated with hydrological models by using climate change scenarios as their input data (e.g. Andréasson et al., 2004; Bergström et al., 2001; Dankers and Feyen, 2008). The climate change signal (including precipitation and temperature) of climate scenarios, which is based on different regional climate models (RCMs) or global climate models (GCMs) and emission scenarios, is transferred to hydrological models for derivation of future discharge and flood magnitude data (Seguí et al., 2010). The 1990–2100 emission estimates were generated in the IPCC Special Report on Emission Scenarios (SRES) (IPCC, 2000), but new estimates of representative concentration pathways have been released together with the Fifth Assessment Report (IPCC, 2013b). There is thus wide variability of scenarios available for different regions. It must also be kept in mind that in addition to climatic changes, human influences, such as land use change and channelization, can cause major changes to fluvial processes and morphodynamics (Arnauld-Fassetta, 2003; Benito et al., 2010; Thorndycraft and Benito, 2006; Trimble, 2003).

1 Future flooding and hydrodynamics

To date we are aware of 11 studies that have simulated reach-scale future in-channel changes using hydro-/morphodynamic or cellular models. Despite there being many studies of discharge changes resulting from future climatic warming (e.g. Dankers and Feyen, 2008; Lehner et al., 2006), there are only a few examples of the application of hydrodynamic models to simulate future flood inundation and flow characteristics (Lane et al., 2007; Veijalainen et al., 2010) or erosion-sedimentation potential (Lotsari et al., 2010, 2014). A range of spatial and seasonal variability in predictions of future changes in floods and hydrodynamics occurred between the different climate change scenarios applied. Veijalainen et al. (2010) predicted 100-year flood discharges to decrease in Finland on average by 8–22% in 2070–2099 compared to the reference period (1971–2000), but there was considerable variation between different hydro-climatic regions studied, including both increases and decreases in flows (Table 2). However, in-channel simulations indicated that the changes in the extent of the flood inundation areas do not reflect linearly the changes in discharges, for example a –12.1 to –90.1% change in inundation area was modelled for the Lapuanjoki study site compared to a 10.9–31.9% decrease in 100-year flood discharge. Even though the importance of channel topography on the flood inundation results was raised in discussion, Veijalainen et al. (2010) did not include sediment transport or channel changes. By contrast, Lane et al. (2007) simulated future flood inundation changes and estimated the effects of river bed sedimentation based on observations of the River Wharfe (UK). Lane et al. (2007) found that bed aggradation occurred, increasing the frequency of flood inundation. Their study was the first where the importance of channel changes on future flooding was noted: the peak inundation extent of a 1-in-0.5-year-event was estimated to increase 12.2% by the 2050s due to climate change and 38.2% when 2002–2004 sedimentation was combined with the climate scenario for the 2050s. Hence, in-channel sedimentation was shown to increase the future sensitivity of flood inundation (Lane et al., 2007) and indeed sedimentation may have as much impact as climate change on inundation areas and flood risk. Even short duration alterations to channel configuration may lead to significant inundation changes, demonstrating the importance of modelling in-channel morphodynamics.

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Table 2.

Future in-channel change predictions.

Publication	Simulated river	Channel material	Model	Time span	Scenarios	Aims	Future forecasts
Veijalainen et al. (2010)	Finland: Ounasjoki 9 km, Lapuanjoki 3 km, Kokemäenjoki 13 km main reach + distributaries, Uskelanjoki 3 km	Ounasjoki (sand), Lapuanjoki, Kokemäenjoki and Uskelanjoki (sand/cohesive)	2D hydrodynamic model: TUFLOW	2010–2039, 2070–2099	20 scen. (different GCMs, RCMs and emission scen.)	An overall picture (67 sites) of the changes in floods The changes in flood inundation (4 sites) To evaluate the usefulness of continental-scale hydrological scenarios on a national scale	Great spatial and temporal variability in scenarios Seasonal changes: winter discharges increase, especially in southern Finland Flood inundation does not change linearly with the discharge changes Sea level influences greatly on inundation in coastal reaches
Lane et al. (2007)	UK: River Wharfe 6 km	Gravel	Coupled 1D/2D hydrodynamic model: HEC-RAS	2050, 2080	1 GCM, 1 emission scen.	Future climate change effects on river channel change and flood risk	River bed aggradation, increase in the frequency of flood inundation 16 months measured in-channel sedimentation cause circa half of the climate change-induced increase in inundation
Lotsari et al. (2010)	Finland/Norway: Lower Tana River 7 km	Sand	2D hydro-dynamic model: TUFLOW	2010–2099	2 GCMs, 1 RCM, 3 emission scen.	The future changes in floods and spatial variability of velocity, bed shear stress and stream power	Diminishing high discharges and erosional forces The theoretical thresholds for bed load transport will be still exceeded in the future
Lotsari et al. (2014)	Finland: Kokemäenjoki River c. 43 km	Silt and sand	1D hydrodynamic model: HEC-RAS	2070–2099	4 GCMs, 3 RCMs and 2 emission scen.	The combined impacts of future discharge and sea level changes on erosion and sedimentation potential	Increasing autumn and winter, but diminishing summer discharges: shear stresses and particle movement followed these changes Discharge changes have in total greater influence than sea level changes: mostly increasing exceeding of particle movement threshold The river reaches closest to the sea, where sea levels are forecast to increase, may experience increased sedimentation potential
Kiat et al. (2008)	Malaysia: Kulim River 9 km/130 km2	Sand and gravel (D50= 1–2.4 mm)	Morphodynamic model: FLUVIAL-12	1991–2016	No scenarios: historical and design hydrograph	The river stability for a long period due to changes made by nature or human activities	The channel will be stable in most locations in future, but slight degradation occurs Decrease in sediment size by 2016: finer sediments will be more prone to erosion Design flood hydrograph based on 2010 land use predicted degradation at most cross-sections after the peak
Verhaar et al. (2008)	Canada (St-Lawrence River): Batiscan 17 km, Richelieu 15 km, St-François 15 km, St-Maurice 14 km	Mixed (clay/silt to sand/gravel)	1D morphodynamic model: SEDROUT4-M	2010– 2099	3 GCMs, 2 emission scen., 2 base level scen.	To summarize modifications done to SEDROUT4, to verify these new features and to increase its utility for river responses to short-term climate change scenarios	Mean annual discharges remain similar, but floods change significantly under different scenarios: increasing extreme erosion events A continuous decrease in downstream water level and a general trend of lower bed levels, although transient aggradation may occur Sedimentation and erosion sequences modify the vertical grain size distribution greatly by 2100: coarser particles in the upper profile
Verhaar et al. (2010)	Canada (St-Lawrence River): Batiscan 17 km, Richelieu 15 km, St-François 15 km, St-Maurice 14 km	Mixed (clay/silt to sand/gravel)	1D morphodynamic model: SEDROUT4-M	2010–2099	3 GCMs, 2 emission scen., 3 base level scen.	Effects of climate-induced changes on the stability of, and sediment delivery from, relatively small tributaries of a very large river Annual scale approach	Variation in climate change impacts for each river and each GCM The magnitude of simulated change depends on the choice of GCM and the trend over time relates to the current state of the river Base level fall: degradation and increased sediment delivery in the rivers that are currently aggrading or in equilibrium The magnitude of base level fall is more important than its type for future development The effect of base level is more apparent towards 2099, whereas discharge change affects from the beginning of the simulation periods
Verhaar et al. (2011)	Canada (St-Lawrence River): Batiscan 17 km, Richelieu 15 km, St-François 15 km	Mixed (clay/silt to sand/gravel)	1D morphodynamic model: SEDROUT4-M	2010–2099	3 GCMs, 2 emission scen. (base level changes similar to Verhaar et al., 2010)	The climate-induced changes in the magnitude-frequency- duration relation for bed material load Event-scale approach	Larger flood events (particularly in winter) occur in all scenarios and the recurrence interval of 2-year floods becomes more frequent Increases in bed material transport rates, number of transport events and number of days in the year where sediment transport occurs More small-magnitude, short duration events for all tributaries and GCMs: they contribute more to the sediment volume Flood risk increases due to higher flood magnitude, but bed incision by more frequent extreme events partly compensates it
Boyer et al. (2010)	Canada (St-Lawrence River): St-François River 15 km, Richelieu River 15 km	Sand	1D morphodynamic model: SEDROUT4-M	2010–2099	3 GCMs, 2 emission scen., 3 base level scen.: the mean of all hydrological simulations	The effects of changes in base level and hydrological regimes on the sedimentary dynamics of tributary confluences The potential impacts on fluvial ecosystems	The greatest hydrological changes during winter (greater high discharge frequency) and spring (decreasing discharges and exceeding of transport threshold) Decreasing base levels: increase in sediment supply, extension of accumulation zones, modification of the extent of freshwater wetlands at the mouth of the tributaries with feedbacks on local flow and sediment distributions The combined effect of increasing high tributary discharge and low base levels: bed and bank erosion, in-channel migration, downstream migration of sediments The effects of changes in hydrological regime may be more significant than that of the expected base level changes
Gomez et al. (2009)	New Zealand: lower Waipaoa River c. 50 km	Gravel and sand	1D bed load/channel evolution model: TUGS; hydrological/suspended load model: HydroTrend	2030, 2080	15 climate conditions	The characteristics of sediment transport as a response to climate change To demonstrate the usage of existing models to forecast climate change impacts on fluvial sediment discharge	Climate change may reduce the mean flow by an average of 13% in the 2030s and 18% in the 2080s Depending on the climate change scenario, in the 2080s the suspended sediment discharge may either decline by 1 Mt/y or increase by 1.9 ± 1.1 Mt/y: adverse impacts have the potential to be offset or ameliorated by a modest (35%) increase in forest cover Possibly declining discharges and transport capacity in the 2030s and 2080s may result in overall decline of bed load transport rate by –28% within the river’s lower reaches
Ziliani and Surian (2012)	Italy: Tagliamento River 33 km	Gravel	Cellular model: CAESAR (reach mode)	2001–2081	4 sediment scen.	To improve understanding of the phases of adjustment and controlling factors in the river	The channel widening will continue in future, independently from sediment management strategies Channel width was larger in scenarios where bank protections were removed and smaller where upstream sediment input was reduced River is unstable and currently responds to past channel disturbances: changes in geometry and unit stream power Channel evolution is driven by sediment supply and flow regime

GCM: global climate model; RCM: regional climate model.

Future discharge changes may also have varying impacts on erosional forces. In the high latitude Tana River (Northern Finland/Norway), erosional forces were forecast to mostly decrease, but without influencing the exceedance of sediment transport thresholds during snow-melt peak discharges (Lotsari et al., 2010). The range of changes due to different discharge scenarios was, however, great. In the case of the 1/250 year flood discharge, stream power changed +4.5 to –39.9% and bed shear stress by +2.6 to –26.5% for the period 2070–2099, when compared to 1971–2000. In the Kokemäenjoki River (south-western Finland), the simulated erosional forces differed greatly from the northern Tana River, since greater erosion was predicted in response to increasing discharges (Lotsari et al., 2014). In addition to the overall greater exceedance of critical thresholds and therefore the simulated erosion potential, seasonal changes also varied. In particular, during winter and autumn, increasing river channel erosion forces can be expected, particularly due to increased autumn and winter discharges, whilst other seasons may experience greater deposition (Lotsari et al., 2014). Blöschl and Zehe (2005) stated that the most obvious cause for limits to predictability is the non-linearity of hydrological systems, for example when processes switch between regimes, for example the thresholds of inception of sediment motion in streams. Lotsari et al. (2014) showed that this threshold may no longer be exceeded during some seasons due to diminishing future discharges. These thresholds are important to take into account in future riverine planning and predictions.

The inclusion of sea level scenarios in simulations of future erosional forces within coastal area rivers is also important, since scenarios with increasing sea level may cause greater deposition within river estuaries and thus change the exceedance of particle movement thresholds (Lotsari et al., 2014). The 30-year average boundary shear stresses of scenarios without a sea level change and the same scenarios with maximum and minimum sea level estimates varied between ±18 and ±20% for RCA3-Had-A1B and CNRM-B1 discharge scenarios, respectively. However, in the Kokemäenjoki River, Lotsari et al. (2014) found that changes in discharge were forecast to have in total a greater influence on erosional forces than the predicted sea level changes.

2 Future in-channel sediment transport and channel evolution

With regards to in-channel sediment transport and river channel evolution, most studies to date have been performed in the northern hemisphere and in sand or gravel bed rivers (e.g. Boyer et al., 2010; Verhaar et al., 2008, 2010, 2011). Most of the findings predict increasing fluvial transport and flood risk but also indicate seasonal changes (Table 2). The effect of changes to discharge and sediment supply are shown to be more important to channel evolution than sea or base level change. Also of relevance to the findings for future channel change was the role of present and past development of rivers. For example, past channel geometry and stream power changes were shown to influence channel widening and aggradation of river reaches (Ziliani and Surian, 2012).

The climate change scenarios that produce the highest predicted discharges may also result in the greatest change to the river bed (Boyer et al., 2010). In northern latitudes, winter discharge and erosional events have been mainly predicted to increase. For example, in Canada, four studies were carried out for the tributaries of the St. Lawrence River (Boyer et al., 2010; Verhaar et al., 2008, 2010, 2011). The seasonal effects were enhanced under all GCM scenarios because longer duration, and higher magnitude, winter events were predicted (Boyer et al., 2010; Verhaar et al., 2011). The impacts varied in different tributary study reaches, despite being spatially close to each other (Boyer et al., 2010; Verhaar et al., 2010). Both these studies used exactly the same GCMs and emission scenarios in all tributary watersheds, so were able to examine river response to other controlling factors, as Coulthard et al. (2005) did for their palaeohydrological study of the River Warfe (UK). In these Canadian rivers, the greatest hydrological and fluvial transport changes were simulated during the winter (with increasing frequency of high discharges) and spring seasons, characterized by decreasing discharge (Boyer et al., 2010). This is similar to some catchment-scale sediment transport analyses, which have forecast increased wintertime sediment transport in their study sites in the northern hemisphere (Coulthard et al., 2012; Thodsen et al., 2008). In particular, the extension of sediment accumulation zones was forecast by Boyer et al. (2010), whilst the projected increase in sediment supply was shown to modify the extent of freshwater wetlands at the mouth of the studied tributaries with feedback effects on local flow and sediment distributions. Larger flood events have also been forecast, which cause increases in effective and half-load discharges (i.e. the discharge above and below which half the long-term sediment load is transported), bed material transport rates, number of transport events, extreme erosion events and number of days in the year when sediment transport occurs (Boyer et al., 2010; Verhaar et al., 2008, 2011). According to Verhaar et al. (2011), the relative contribution to sediment volume of the large events (i.e. greater than half load discharge of 509, 1102 or 1225 m³/s, depending on the tributary) for CSIRO-Mk2 and HadCM3 scenarios varied between 77% and 88% of total sediment transport in all the tributaries, and for the ECHAM4 scenario between 68% and 72%. However, future bed load rate was predicted to have greater variation than discharge due to the non-linear character of sediment transport (Verhaar et al., 2011), a finding also noted at the catchment scale by Coulthard et al. (2012). In addition, an increased frequency of small-magnitude, short duration events, which have a greater contribution to sediment volume, are predicted (Verhaar et al., 2011). It was also demonstrated that, despite lower bed elevations, flood risk is likely to increase as a result of higher flood magnitude, even with falling base level. However, flood risk can also partly be compensated for by bed incision during more frequent extreme events (Verhaar et al., 2011).

Increasing average bed material and suspended sediment delivery have also been predicted for the St. Lawrence River (Table 1: Verhaar et al., 2010, 2011). Even without change to base level, increases in average bed material delivery are expected according to these studies, although the magnitude of simulated changes depended on the choice of GCM and the trend over time related to whether the river is currently aggrading, degrading or in equilibrium (Verhaar et al., 2010, 2011). Verhaar et al. (2010) showed that a fall in base level leads to degradation and increased sediment delivery in river channels that are currently either aggrading or in equilibrium, amplifying the effects of climate change on sediment delivery. Of particular interest is the finding that the magnitude of base level fall is more important for future channel development than its duration, that is, whether the fall was sudden or more prolonged. Thus, the work by Verhaar et al. (2010) was the first future in-channel change simulation where the present state of the river channel was acknowledged to be of relevance for its further future development. Also, Boyer et al. (2010) stated that the combined effect of both discharge and base level changes are important, as an increase of high discharges under low base water levels will result in bed erosion, in-channel migration, bank erosion and downstream migration of sediments in the river. In addition, Ziliani and Surian (2012) stated that in the future a river channel may still respond to past disturbances, which may have caused a change of channel geometry and unit stream power.

Few studies have simulated future bank erosion responses to climate change. In the Tagliamento River (Italy), it was shown that long-term future channel widening continues independently from sediment management strategies (Ziliani and Surian, 2012). Naturally, the channel width was greater with scenarios where bank protections were removed, but smaller if sediment input was reduced. However, overall the average channel width increased despite different management strategies from 760 m in 2009 to 960–1015 m in 2040 and to 1180–1230 m in 2080. They also found that channel evolution is driven by both sediment supply and flow regime.

In morphodynamic simulation approaches performed on the Waipaoa River, New Zealand (Gomez et al., 2009), climate change may reduce the mean flow by an average of 13% by 2030 and 18% by 2080, but depending on the climate change scenario the suspended sediment discharge may either decline or increase by the 2080s. Gomez et al. (2009) stated that the adverse impacts of climate change on the suspended sediment load have the potential to be offset or ameliorated by a 35% increase in forest cover, which reduces the mean annual suspended load by 6% in the 2030s, but a 14% decline in the forested area results in a 3% increase in the mean annual suspended load by the 2030s. The declining discharge and transport capacity of the channel may cause overall decline in the bed load transport rate within the river’s lower reaches. Despite the decrease in predicted bed load by the 2080s, a range in sediment discharges (9.4 ± 20.1 kt per year) was predicted under different scenarios (Table 2). However, this predicted bed load for the 2080s is greater than for the 2030s because aggradation reduces the accommodation space and modifies the river’s long profile. Like the findings of Lane et al. (2007), Gomez et al. (2009) showed that river capacity will be reduced and increasing flood risk is expected due to rising channel bed elevation.

The only future channel change study performed in an equatorial region (the Kulim River in Malaysia) indicated limited cross-sectional change and slowing erosion during the 2006–2016 simulation period (Kiat et al., 2008). They also showed that by 2016 sediment delivery may be twice as much as in 2006 but less sediment delivery occurs at downstream parts of the study site, with sediment size decreasing in certain reaches by 2016. These grain size changes, particularly vertical changes and coarser particles occurring in the upper part of the profile, were also predicted in the St. Lawrence River tributaries (Verhaar et al., 2008).

1 Future discharges

The key factors, and cause of greatest uncertainty in future reach-scale in-channel simulation approaches, are the external forcing conditions and how future climatic, hydrological and land cover changes are taken into account. In the case of hydrological forecasts, many climate models and scenarios have been used in simulation studies (Veijalainen et al., 2010). The magnitude of simulated discharge and bed material delivery change depends on the choice of the GCM (Verhaar et al., 2010). More precisely, the GCM can be the key controlling factor in determining future morphological adjustments of rivers. One interesting finding is that the choice of emission scenarios is much less important than the different GCMs and, in particular, emission scenarios have less effect on sediment delivery than on bed elevation (Verhaar et al., 2010). Future reach-scale suspended sediment transport changes have also varied greatly due to the contrasting hydrological scenarios applied (Gomez et al., 2009). This is also similar to some catchment-scale future sediment flux studies performed using probabilistic approaches (e.g. Coulthard et al., 2012). According to Verhaar et al. (2011), future research should continue to use more than one GCM scenario, unless or until GCM refinement leads to a convergence of climate predictions. However, the application of a limited range of climate scenarios was most common for the studies of future in-channel change predictions summarized in Table 3. Thus, the effect of GCM selection has had an important impact on the results of published studies to date. According to Boyer et al. (2010), the application of the mean result from multiple hydrological scenarios reduces the impact associated with extreme discharge values that may be generated using only one simulation.

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Table 3.

The strengths and weaknesses of published simulations of future in-channel changes.

Publication	Positive notifications	Negative notifications
Veijalainen et al. (2010)	Both daily and 100-year flood discharge changes 20 different discharge scenarios (both RCMs and GCMs	No morphodynamic model
Lane et al. (2007)	Good input data: river geometry from 1980 and 2002–2004, LiDAR data applied, coarse sediment movement measurements	No morphodynamic model and only one GCM and emission scenario Cross-sectionally averaged
Lotsari et al. (2010)	Both daily and 100-year flood discharge changes Both RCMs and GCMs included	No morphodynamic model
Lotsari et al. (2014)	Both RCMs (including direct data) and GCMs Sea level change (i.e. base level) scenarios	No morphodynamic model Cross-sectionally averaged
Kiat et al. (2008)	Calibrated with 2004–2006 data, and past periods since 1991 Many transport formulas tested Capable for simulating lateral erosion, channel curvature and meandering	No discharge scenarios, only urbanization/human impacts Future changes were simulated based on past hydrographs Cross-sectionally averaged
Verhaar et al. (2008)	Graded sediments and size-selectiveness in entrainment, bed stratigraphy during aggradation, temporal grain size changes Vertical variation in the initial bed composition Tidal effects at downstream boundary Able to route water and sediment around islands	Cross-sectionally averaged Only 1–2 years of bathymetry for calibration Only one GCM and emission scenarios Dam regulation data lacked from two tributaries Bed load samples were taken close to the threshold for motion Morphological calibration and validation were difficult due to sparse field data
Verhaar et al. (2010)	Good input data: circa 150 bed sediment samples from each tributary Flow and sediment routing in channels with islands Bed level and bed grain-size distribution are updated after each time step	Only 1–2 years of bathymetry for calibration The simulation of one river was stopped in 2053: one side of the island sedimented Cross-sectional comparisons were difficult between simulation outputs and measurements
Verhaar et al. (2011)	Allows the long profile and bed composition (and through them the local transport rate) to vary over time Flow and sediment routing in channels with islands Several transport equations were tested	Only 1-year bathymetry for calibration Cross-sectionally averaged: the width-averaged calculations underestimated total load The channel width was constant through time Inter-annual variability of climate variables of the reference period replicated for 2010–2099 Sediment supply to the reach was unknown
Boyer et al. (2010)	Bed stratigraphy changes during aggradation and graded sediments: downstream or vertical sediment size changes The model was modified for sand-bed rivers, and to allow water level and discharge variations Flow and sediment routing in channels with islands	Cross-sectionally averaged Bed elevation and sediment composition were constant at the upstream cross-sections The bed elevation changes were generally underestimated The results were highly dependent upon the hydrological simulations The mean results obtained from six hydrological simulations were applied
Gomez et al. (2009)	Cross-sections, sediment transport, flow and bed material data since middle 20th century Sea level changes as downstream boundary condition Vegetation/land cover change included in future simulations A unique feature: capable of simulating mixed sediments Applied both 2002 and 2007 geometry as initial condition: their effects on future simulations	TUGS: does not simulate local topographic features, such as bars, and there are no lateral sediment inputs Cross-sectionally averaged Local variations in particle size, sand content and bed elevation were not well represented: small under- and over-prediction
Ziliani and Surian (2012)	Sediment supply scenarios: two increasing, one with no change and one decreasing Included almost 200 years past data for calibration, and model was validated with 2001–2009 data DEM from LiDAR data: model’s spatial resolution 25 m × 25 m Calibration of the model with lateral erosion rate and maximum erode limit	Future changes played a minor part compared to the past Constant conditions for flow regime: years 2000–2010 were replicated several times Input data may have caused uncertainties Stated that future (2009–2015) channel widening depends on flow regimes, but applied only sediment transport scenarios and not long-term flow scenarios

GCM: global climate model; RCM: regional climate model.

Uncertainties also relate to the calculation of flood recurrence intervals, which, in the reviewed papers, were most commonly calculated by applying only one method (cf. Lotsari et al., 2010), for example Gumbel (Veijalainen et al., 2010) or Pearson III approaches (Verhaar et al., 2011). Recurrence intervals can be misleading because they are determined from the peak magnitude of flow and they do not take into account the magnitude and duration of out-of-bank flow (Lane et al., 2007). Lane et al. (2007) pointed out that sediment aggradation will not affect discharge return periods but will alter the frequency of inundation events. This is important to take into account in future in-channel studies. The reliability of the determination of recurrence intervals is also limited because future simulations are based on a 30-year reference period, such as 1971–2000, that is repeated in the future (Verhaar et al., 2011). In the case of future discharge simulations with hydrological models, and thus also in the within-channel hydro- and morphodynamic simulations applying these discharges, uncertainties also relate to the fact that the hydrological model is employed in conditions that have not occurred during the calibration period (Lotsari et al., 2010; Seibert, 2003).

The method to transfer the climate change signal to the hydrological model for future discharge scenarios may also be a source of uncertainty. For example, Verhaar et al. (2008, 2010, 2011) and Lotsari et al. (2010, 2014) applied the delta change method in their analyses of potential channel and sediment transport changes. In the delta change method the monthly temperature changes are added to those observed and precipitation changes are multiplied by the observed precipitation values of the control period, but the potential changes in rainfall variability and intensification of extreme precipitations are ignored. This issue can, however, be partly addressed by applying the temperature-dependent change method, which changes the lower winter and spring temperatures more than the higher temperatures (Lotsari et al., 2010). However, this was not taken into account by Verhaar et al. (2008, 2010, 2011). Other types of transfer methods are available for application in future in-channel change predictions, such as the bias-corrected direct RCM data (Lotsari et al., 2014). However, in some of these RCM data simulations, and thus also future in-channel change predictions, it is assumed that future climate variability remains the same as presently (Lotsari et al., 2014). The latest enhancements in future discharge predictions are one of the major prerequisites for future simulations of within-channel changes. Due to the uncertainty in the projected climate changes scenarios and variability caused by the stochastic nature of the simulated rainfall, probabilistic approaches with multiple repeated simulations for each scenario have been encouraged for future simulation approaches (Coulthard et al., 2012). So far, none of the reach-scale in-channel future simulation studies have included this kind of approach, but the evidence from catchment-scale studies suggest this has potential for reach-scale future simulations.

2 Future base level changes

Only a few of the future simulations reviewed have taken base level changes, including sea or river water level changes, into account (Table 2). Verhaar et al. (2008, 2010, 2011) applied both gradual and step changes at a certain point in time, in addition to no-change future conditions. In coastal rivers, sea level is used as the downstream boundary condition of the models. Lotsari et al. (2014) and Veijalainen et al. (2010) had taken the possible relative sea level changes (including isostatic land uplift) into account in their hydrodynamic simulation of future erosional force changes. These reach-scale in-channel studies, where both discharge and base level change effects are combined, are still rare in the literature. Both Verhaar et al. (2010) and Lotsari et al. (2014) showed for rivers with very low energy slopes that backwater effects of downstream base level on hydraulics and bed shear stress can persist far upstream. Therefore, in river reaches close to the sea, or tributary rivers where the downstream boundary is defined by changes in the main river, these possible base level changes should not be ignored when simulating future river channel changes. However, interestingly, Gomez et al. (2009) did not find difference in the channel change trends whether the sea level changes were included or not.

3 Future land cover and sediment supply changes

Although land use effects have been recognized as an important driver of change in the studies of past river environments (e.g. Notebaert et al., 2011), the simulation of future land use change has proved difficult and many of the future in-channel change simulation approaches have ignored this external forcing condition. Only Gomez et al. (2009) have taken into account the land cover changes when simulating future in-channel processes, whilst Ziliani and Surian (2012) considered the changes occurring in the upstream watershed on sediment supply (bed load). Gomez et al. (2009) also simulated the effects of potential human-induced changes in land use on the suspended sediment discharge by superimposing a change in the vegetation cover on the climate change scenarios. Feedback systems between hydro-climatic conditions, land cover and morphodynamics were shown to increase the uncertainties (Gomez et al., 2009) and should be included in future simulation approaches. However, in contrast to this view, Ziliani and Surian (2012) showed that changes in sediment supply in the catchment area had no, or minor, effects on the channel of the Tagliamento River.

1 Temporal and spatial representation/resolution

Simulated time spans for modelling future river response tend to be shorter and over smaller spatial extent, with prediction usually performed in river lengths of 3–50 km (Table 2), than in palaeohydrological modelling studies (e.g. Coulthard et al., 2005) or contemporary process studies such as Saleh et al. (2013). This is because future centennial-scale in-channel simulations are computationally demanding; therefore, only 1D morphodynamic models have been applied at centennial timescales to date and there is a need for multi-dimensional models capable of these long-term simulations. However, at the present time it is the 1D models that are the most capable of simulating large river reaches and longer time spans. The results presented in the reviewed morphodynamic approaches have therefore been cross-sectionally averaged. This has implications as, for example, width-averaged 1D calculations may underestimate the total sediment load, because local bed load is a non-linear function of the local flow strength and because the excess flow strength over the threshold of motion varies spatially (Verhaar et al., 2011). The future bed load rate of Verhaar et al. (2011) had higher variation than discharge due to this non-linear character of sediment transport. However, Gomez et al. (2009) showed that local variability, which a 1D model cannot completely replicate, did not appear to have a substantial effect on future in-channel changes. This finding supports the application of 1D models in further future in-channel change simulations, particularly since they may be modified to support the needs of future in-channel change simulations. For example, Verhaar et al. (2008) were able to modify a 1D morphodynamic model, which was originally developed for gravel bed rivers, so that it allowed for simulation of a wider range of grain sizes, variable discharge, downstream water level fluctuations and flow and sediment routing in channels with islands.

However, there are also examples of failed 1D morphodynamic simulations of future changes due to the spatial channel representation of the model and its sediment flow. In one tributary of the St. Lawrence River where the morphology of the channel was characterized by islands, simulation by Verhaar et al. (2010) failed because one of the bifurcations experienced unrealistic sedimentation. Therefore, the need for 2D models, which are capable of dealing with islands and bifurcations, was acknowledged by Verhaar et al. (2010). An alternative approach may be the use of cellular models, as their spatial representation can be comparable to that of 2D models. For example, the cellular model of Ziliani and Surian (2012) was performed in a wide braiding river reach with a 25 m × 25 m spatial resolution. The advantage of this cellular model, compared to the 1D hydro- and morphodynamic models, is that it uses a grid form and so it is possible to simulate spatial variations at a particular cross-section, including for large river systems. Even though the study reach lengths of the 1D model studies were similar to the future reach-scale cellular model approach (i.e. >30 km), the spatial representation is better than for the cross-sectionally averaged 1D models.

Hydro- and morphodynamic models have been applied at event, annual and centennial scales. The appropriate simulated time span depends on the spatial representation. Despite the advantages in spatial representation of 2D models over 1D models, their computational times are still, at present, very long for continuous centennial-scale simulations and only event-scale in-channel change simulations have been performed with them (Table 1). Thus, 2D models should be developed so that they can run long-term, unsteady simulations of bed material transport and incorporate the impacts of bank erosion on channel evolution (Verhaar et al., 2011). Since future simulations have been modelled for shorter time periods than, for example, historical or palaeo-studies, the millennial-scale simulation problems, as noted by Van De Wiel et al. (2011), have not arisen in future simulation studies. The usual time period for future in-channel change analysis is one of 30 years, most commonly for the time periods 2010–2039, 2040–2069 and 2070–2099 (e.g. Verhaar et al., 2008, 2011). Some of the in-channel change simulations are done only with the extreme flow events of the different discharge scenarios (Lotsari et al., 2010; Verhaar et al., 2011), thus the simulated hydrographs have been of short duration. However, 1D models have successfully been used to simulate continuous daily discharge series until 2100 (Lotsari et al., 2014).

Cellular models now show great promise for future simulations because, by using simplifications of flow equations, coupled with sediment transport, they can rapidly simulate geomorphic processes over medium timescales (Coulthard et al., 2012; Ziliani and Surian, 2012) and detailed spatial resolutions (Van De Wiel et al., 2007; Ziliani and Surian, 2012), as demonstrated from a palaeohydrological perspective by Coulthard et al. (2005). Whilst cellular models have the capability to model centennial and millennial-scale simulations, to date the availability of future discharge scenarios is limited to the next 100 years. However, it is questionable whether such long time spans are desirable given typical river management timescales (Downs and Gregory, 2004) and it is the near-future (decadal) in-channel changes that have been shown to be of particular importance to simulate (Kiat et al., 2008; Lane et al., 2007).

2 Calibration and validation of the models for future simulations

A key challenge for future simulation research regards calibration and validation of the models used, as this has been performed based on the adjustment of model parameters against present or past observed data, such as water level and bathymetry (Lane et al., 2007). Lane et al. (2007) stated that models calibrated based on historical topography, discharge and water level data are likely to underestimate future water levels, and hence inundation and flood risk, if aggradation has occurred since the applied past event observational data. In such aggradational reaches, the calibrated friction value would therefore be too low for future channel conditions. This is clearly a problem for hydrodynamic simulations of future river channels, since all reviewed studies have applied present river geometry and channel materials to calculate roughness estimates.

The most effective means to test the accuracy of transport rate predictions of reach-scale morphodynamic or cellular models is against resurveys of river geometry (Verhaar et al., 2008; Ziliani and Surian, 2012). This necessitates a short calibration period as data on sediment accumulation or erosion needs to be gathered during the study (Verhaar et al., 2010). Clearly the application of short (e.g. one year) calibration periods for future century-scale channel simulations is problematic. Longer observation periods or historical data would be needed, such as has been applied in the studies of Kiat et al. (2008) and Ziliani and Surian (2012). Gomez et al. (2009) compared simulated channel change data with historical empirical observations (1948–2002) of aggradation in the river and the documented (1996) downstream variation in the size and composition of the subsurface bed material, which Verhaar et al. (2008) also stated to be important to include in calibrations and validations. Despite the fact that simulated changes in bed elevation were, throughout the study reach of the Waipaoa River, in broad agreement and consistent with the observed trends of bed changes, the calibration results were not perfect and differences in simulated and measured bed elevations occurred (Gomez et al., 2009). If the calibration results have uncertainties, these will inevitably cause uncertainties for future simulations.

One aspect that has emerged from this review is that cross-sectionally averaged results have been difficult to compare against observational data. Matching of detailed topographical measurements to cross-sectionally averaged 1D model results for modelled time intervals is demanding and sometimes not possible with sufficient reliability (Verhaar et al., 2010). However, problems do not only relate to the cross-sectional comparison of simulated and measured geometry but also to flow velocity and sediment transport data. It has been a challenge for researchers to perform extensive and reliable bed load sampling for model calibration. In particular, for many studies the calibration and validation have been difficult to do due to sparse and erroneous Helley–Smith bed load sampling (e.g. Verhaar et al., 2008). Blöschl and Zehe (2005) stated that bed load predictability is poor if the system is close to a threshold but improves as the system moves away from a particular threshold and towards stability. For example, Verhaar et al. (2008) measured bed load transport close to the flow conditions of initiation of particle motion and errors to the calibration bed loads occurred. The relationship between measured sediment transport and discharge was found to be highly variable also in the study site of Verhaar et al. (2011), where a morphodynamic simulation was performed.

Even though many of the future in-channel simulations demonstrated good correspondence with hydraulic parameters, in some studies the 1D simulations could not handle local within cross-section variations of flow velocity and thus sediment transport. Therefore, for in-channel change simulations the accuracy of the models depends partly on the quality and quantity of the input data (Kiat et al., 2008) with unreliable or sparse field data hampering model calibration and validation.

3 Representation of river channel material and transport equations

The representation of river channel material and transport equations arose as a key issue in this review and, in particular, the choice of transport equation has been crucial for morphodynamic models. There are many empirically developed equations, which are applicable in different types of rivers consisting of different grain size. So far, it has not been possible to develop a universal equation. This is problematic, since for future scenarios, sediment size and spatial sorting might also change and questions arise as to whether or not the presently applicable equations may be valid for future river channel sedimentary conditions. The empirical sediment transport formulae should, therefore, be applied with caution for long-term, including future channel change, simulations (Verhaar et al., 2008). Since the accuracy of sediment transport formulae has been questioned (e.g. Barry et al., 2004; Van Rijn, 1984a) and sediment transport models may not be as universal as thought (Papanicolaou et al., 2008), researchers have been encouraged to employ different models with a range of transport algorithms. The study by Kiat et al. (2008) was one of the few in this review that tested many transport algorithms before deciding on the best one according to the test simulations. However, the future in-channel change simulations showed that trends and differences between future scenarios can be identified, even if the applied sediment transport formula is systematically over- or under-predicting actual transport rates (Verhaar et al., 2008). On the other hand, Verhaar et al. (2011) stated that it is hard to assess the uncertainty in bed load transport predictions resulting from entrainment threshold and transport equations. Best practice, therefore, for simulations of future scenarios, is to use transport equations capable of simulating a wide range of sediment particle sizes.

A further challenge, with regard to sediment transport in future simulations, is the spatial and temporal change to bed sediment grain size and the active layer. The horizontal and vertical bed material composition and variation were often neglected in sediment transport and morphodynamic models at the beginning of the 21st century (van Ledden, 2002). Even in present day studies the input grain size, and whether only the D₅₀ or additional grain sizes are included, has been shown to influence simulation results (Lotsari et al., 2014). Some of the reviewed future simulation approaches only used a few sediment samples as the reference for roughness or for application in the actual transport equations. For example, since Gomez et al. (2009) did not have detailed knowledge of grain size variation, they used a constant particle size distribution to characterize long-term sediment supply. Verhaar et al. (2008) applied the same roughness spatially throughout the river reach but they did not have data to verify the roughness conditions for high flows, suggesting further issues for simulating extreme events.

The widely applied approach of using a single fixed grain size in sediment transport equations may not represent the various size fractions within sediment mixtures (Wu et al., 2004). A feature of the morphodynamic model applied by Gomez et al. (2009) was that it was capable of simulating fine sediment dynamics in gravel deposits and, hence, the dynamics of bed load transport in channels in which the bed material contains a high proportion of sand. Similarly, Verhaar et al. (2008, 2010, 2011) applied a model capable of simulating mixed sediments. A positive approach of some models was inclusion of temporal grain size evolution, and therefore changes in channel roughness (Gomez et al., 2010; Kiat et al., 2008; Verhaar et al., 2008). Furthermore, grain size sorting has also been included in some of the reviewed in-channel model approaches (Verhaar et al., 2011). Even though both Verhaar et al. (2008, 2010, 2011) and Gomez et al. (2009) had models where active layer or surface layer thicknesses were possible to define, a constant thickness was applied throughout the simulations. Layer thickness influences the grain size distribution of the transport layer and is therefore important for modelling initiation of particle movement. Gomez et al. (2009) noted one particular strength of their simulation results was that the model successfully simulated the pattern of downstream fining and reproduced the downstream trends in the sand content of the subsurface bed material, as well as bed elevation, over prescribed periods of time. A positive quality of the model of Verhaar et al. (2008, 2010, 2011) was that artificial mixing between the sub-layers was avoided during alternating sedimentation and erosion. In addition, they noted that a stratigraphic record can be built during a long-term simulation, which was found as an advantage over some other 1D morphological models.

In cellular modelling approaches, several bed load or suspended load sediment fractions are possible to define depending on the grain sizes (Coulthard et al., 2012; Van De Wiel et al., 2007; Ziliani and Surian, 2012). Even though their model is capable of dealing with suspended load, Ziliani and Surian (2012) applied only bed load in their reach-scale analyses. Whilst the description of the model was somewhat limited in Ziliani and Surian (2012), it seems that sediment transport was driven by a mixed-size formula (sand, gravel and silt), which calculates transport rates for each sediment fraction, as referred to by Van De Wiel et al. (2007). There were many prospects for this model with regards to grain size representation, in line with those of the hydro- and morphodynamic models described above. The model applied by Ziliani and Surian (2012) allows for sediment heterogeneity and keeps track of several user-defined grain size fractions (Van De Wiel et al., 2007). Selective erosion, transport and deposition of these different fractions results in spatially (horizontal and vertical) variable sediment distributions. The capabilities of this model in updating horizontal and vertical grain size properties, according to future discharge and sediment transport forecasts, has also been demonstrated in the catchment mode approach by Coulthard et al. (2012). Thus, the characteristics of cellular models for representing grain size and sediment transport are good in comparison to the hydro- and morphodynamic models discussed.

4 Lateral erosion

Whilst morphodynamic and cellular models are capable of simulating lateral bank erosion, this process representation has only been applied for simulating both vertical and lateral erosion in the morphodynamic model of Kiat et al. (2008) and the cellular model of Ziliani and Surian (2012). Most of the reviewed papers that applied a morphodynamic model with vertical bed change simulations did not therefore include lateral channel changes (Table 2; e.g. Gomez et al., 2009; Verhaar et al. 2008, 2010, 2011). Some of the studies were performed in river reaches where lateral bank erosion and river migration occurs, but the applied 1D morphodynamic model was not able to take that into account. The inclusion of only either channel bed or bank evolution in the model is problematic, since these changes can influence each other over both the short and long term. Even though Lane et al. (2007) did not actually simulate future lateral changes with their hydrodynamic model, they stated that where river management restricts lateral movement of the channel and transfer of sediment into floodplain storage, the channel bed responds by aggradation. Also in the study by Verhaar et al. (2010), the channel width was considered constant through time and therefore no lateral changes in the channel were simulated. This caused the divergence in bed material flux to be accommodated entirely by a change in bed elevation. In reality, annual differences in both vertical and lateral channel changes occur depending on the water level fluctuations, therefore causing great uncertainties in future in-channel change predictions. In the case of degrading river channels bank erosion may increase in the future (Verhaar et al., 2010), therefore inclusion of both vertical and lateral changes in the models is important. The morphodynamic model of Gomez et al. (2009) did not simulate local topographic features, such as bars, or take into account lateral sediment inputs that cause pronounced local variations in the bed material along the river.

As previously mentioned, only Kiat et al. (2008) and Ziliani and Surian (2012) included lateral changes in their simulations. The morphodynamic model of Kiat et al. (2008) included the width adjustment component, which simulates inter-related changes in the channel bed profile, width variation and changes in bed topography induced by the curvature effect. Therefore, a good feature of this model is that in addition to lateral bank erosion, the changes in channel curvature and meandering can also be modelled. Thus, the model applied by Kiat et al. (2008) was the most sophisticated of the morphodynamic models reviewed; however, the complexity of this increased sophistication meant that it could only simulate a short future change period and with no consideration of climate change impacts on flow conditions.

The advantage of the cellular model of Ziliani and Surian (2012) was that a lateral erosion algorithm was implemented (Van De Wiel et al., 2007) and so their model was capable of simulating both meandering and braided channels, although note that the Ziliani and Surian (2012) study focused on a braided reach. These kinds of reach-scale future cellular model approaches have not been used before (Van De Wiel et al., 2007) but whilst there are prospects for applying such cellular modelling approaches, the fact that the flow-sweeping algorithm applied in the Ziliani and Surian model did not preserve momentum, and no primary and secondary flows were possible to distinguish, may influence the lateral erosion results (Van De Wiel et al., 2007).

5 Chain of multiple simulations

Most of the reviewed future natural river in-channel change analyses employed a chain of multiple different simulations, with the consequence that uncertainties accumulate with each simulation step, as is also evident in catchment-scale models of sediment flux (e.g. Coulthard et al., 2012; Mukundan et al., 2013; Thodsen et al., 2008). This is different to present or near past channel change studies, where input data relies on actual measurements and so no climate or hydrological models are needed to predict the input discharge data. Furthermore, the hydrodynamics need to be calibrated before simulating morphodynamics. In other words, each step of the modelling therefore needs its own input data and model calibrations.

All the studies listed in Table 1, except Kiat et al. (2008) and Ziliani and Surian (2012), applied discharge scenarios that were simulated based on climate change forcing that produced a wide range of predicted discharge changes. For example, in tributaries of the St. Lawrence River (Boyer et al., 2010) the spring discharge peaks varied 200–300 m³/s between applied discharge scenarios. Lotsari et al. (2010) showed –52.4 to –10.7% changes in the case of 1/2a floods and –39.6 to +3.5% changes in 1/250 year floods by 2070–2099 when compared to 1971–2000. Boyer et al. (2010) found that their morphological simulation results were highly dependent upon these hydrological simulations so applying a range of discharges, in addition to water level scenarios, to model input data causes greater variability in the hydro- and morphodynamic output data due to non-linearity. Using Boyer et al. (2010) again as an example, an increase in mean annual volume of sediments ranged from 236% to 530% for the Richelieu River and from 28% to 182% for the St. Francois River for the simulated time horizons of 2010–2039, 2040–2069 and 2070–2099. The sediment volume ranges were thus greater than for their simulated discharges, as also demonstrated by some catchment-scale approaches (Coulthard et al., 2012). Veijalainen et al. (2010) and Verhaar et al. (2010, 2011) also demonstrated the importance of hydrological simulation results on the findings of their hydro- and morphodynamic simulations at the reach scale, for example, the selection of the applied discharge scenarios influenced hydro- and morphodynamic simulation results. Veijalainen et al. (2010) applied many climate scenarios for hydrological simulations, but only selected a few examples in flood inundation simulations. Therefore, in addition to the uncertainties related to the hydrological simulation and model calibrations of both hydrological models and hydro- and morphodynamic models, the selections made by the researchers narrows or broadens the range of output results. Similarly, in catchment-scale studies, Coulthard et al. (2012) has noted this uncertainty caused by the cascade of simulations, particularly due to the non-linear nature of the climatic, hydrological and geomorphic systems.