OR/14/011 Component summary

From MediaWiki
Revision as of 10:59, 22 April 2022 by Ajhil (talk | contribs) (→‎Debris flow component)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
Barkwith, A* and Coulthard, T J**. 2011. CLiDE version 1.0 user guide. British Geological Survey Open Report, OR/14/011.

* British Geological Survey, Environmental Science Centre, Keyworth, Nottingham, NG12 5GG, UK
** Department of Geography, Environment and Earth Science, University of Hull, Cottingham Road, Hull, HU6 7RX, UK

Introduction

This section introduces the major components of the CLiDE platform and their driving equations. Many of the components interact with each other, providing information about differing parameters at a range of time steps. The hydrological component (SLiM) employs a surface water partitioning module to divide water between the atmosphere, the surface and subsurface (Figure 1). The groundwater module dictates the flow of subsurface water and Lisflood the flow of surface water. These two components interact directly through the passing of baseflow to rivers and indirectly through the calculation of groundwater recharge by SLiM. Sediment transport is divided into fluvial and non-fluvial processes. The fluvial sediment transport processes are dictated by the hydrological component, in particular Lisflood, which provide the energy to move sediment of differing grain sizes. Non-fluvial sediment transport processes can also be affected by hydrology, for example high groundwater water levels can trigger debris flows within the SCIDDICA debris flow module.

Figure 1    Schematic overview of the main linkages between the CLiDE platform hydrological components. Dashed lines represent data required from the previous timestep and solid lines data from the current timestep.

Water partitioning component

The partitioning of rainfall between, evaporation, runoff and recharge to groundwater in the CLiDE platform is achieved using the soil water partitioning model SLiM (Wang et al., 2012[1]). SLiM implements a simple technique that represents potential groundwater recharge and runoff processes based on spatio-temporally distributed soil moisture conditions. Soil moisture is a function of; rainfall, actual evapotranspiration, soil moisture condition, topography, soil type, crop type and baseflow properties. This method represents soil water processes responding to variable soil water storage properties (see Rushton, 2003[2]) and vegetation growth stages (see Allen et al., 1998[3]).

Within SLiM, rainfall that isn’t evaporated, or doesn’t contribute directly to runoff, can be either intercepted by plants or reach the ground surface and infiltrate into the soil. The latter has the effect of increasing near surface soil storage and reducing the soil moisture deficit (SMD). Soil water can be extracted by plant roots for transpiration or drawn to the bare soil surface for evaporation. When soil moisture reaches field capacity and is unable to store further additions of water, water drains freely in the saturated soil. At field capacity if there are additional water inputs, lateral runoff (routed by Lisflood) occurs if a gradient exists towards adjacent locations. If the rainfall intensity is greater than the capacity of soil to maintain infiltration, water accumulates on the soil surface and becomes surface runoff. Water not accounted for in soil storage, evapotranspiration or uptake by vegetation is termed excess water (Ew). Excess water is divided between runoff (Ro) and recharge to groundwater (Re) based on a baseflow index parameter (BFI). The BFI may be derived through a calibration process or estimated from data by performing a baseflow separation on a river flow time-series. Surface runoff and recharge to groundwater are calculated using equations 2.1 and 2.2:


BFI is an average surface to subsurface water partitioning ratio reflecting the permeable nature of the catchment in addition to other catchment characteristics. In general greater runoff and reduced recharge is observed in areas with steeper slopes. Consequently equations 2.1 and 2.2 are modified to allow average (S overbar) and nodal (S) terrain gradient to be factored into the calculation of recharge and runoff:

Surface water routing component

Routing of surface runoff and channel flow is controlled by Lisflood (Van der Knijff et al., 2010[4]), a two-dimensional hydrodynamic flow model. Routing is based on the one dimensional Saint-Venant equations, as modified by Bates et al. (2010)[5], where the derived equation (2.6) takes into account; acceleration, water surface gradient and friction properties and has enhanced stability due to increased friction forcing water flow towards zero (Liang et al., 2006[6]):

If the flow depth (hf), as calculated using the surface partitioning component, is above a defined threshold and stability criteria are met, the flux between cells at the proceeding time-step (qt+dt) depends on the water surface gradient between the adjacent cells (S), Manning’s coefficient (n), the time-step length (dt) and the gravitational constant (g). For each time-step flow between neighbouring cells is computed and flow depths updated simultaneously at all points within the model domain. A full description of CAESAR-Lisflood is provided by Coulthard et al. (2013).

Groundwater component

Groundwater flow is simulated using a two dimensional lattice of square cells interacting according to the von Neumann type neighbourhood, in a technique similar to that utilised by Rothman (1988). Cells consist of distributed hydraulic conductivity (k) and specific yield (Sy), and a datum referenced aquifer head (h) that is modified through time. Aquifer head is updated at each time-step using Darcy’s law to calculate water flux (qgw) between cells i and j:

where transmissivity (T) can be approximated by multiplying hydraulic conductivity by aquifer depth. The term 2TiTj/Ti+Tj is introduced as a flux limiter to improve stability when large outliers in transmissivity are encountered. The total flux for a central cell (qgwt) is a combination of; fluxes to neighbouring cells and additional source and sink terms. Recharge from the surface hydrological component provides the source term and baseflow to the surface acts as a sink. Total fluxes are used to update aquifer heads at each point in the domain simultaneously at each time step (dt) using the discrete mass balance equation:

Two user defined lateral boundary condition types have been implemented into the CLIDE code, allowing a variety of hydrological situations to be represented. Specified (Dirichlet) boundary conditions fix aquifer head at the boundary to the initial condition and a no-flow (Neumann B) condition sets flux across the boundary to zero. The base of the aquifer is defined as impermeable; however, leakage from the base of the modelled aquifer is included in the flux algorithm as a secondary sink term. The surface boundary allows a flux of water to be returned to the surface component as baseflow where aquifer head is greater than terrain height.

To ensure model stability, the cell Reynolds number (Rn) is calculated at each node for each time-step and a flag raised if it exceeds unity. Reduction of the Reynolds number is possible by reducing the time-step or increasing the cell size. Roache (1976)[7] defines the Reynolds number as:

Baseflow return to rivers at regions where the groundwater head is at a greater elevation than the surface water (r) for a particular node. The volume of water returned to rivers (qbf) is dependent on the specific yield of the groundwater node and the thickness (RBb) and hydraulic conductivity (RBk) of the river bed using the equation derived by Haitjema (1995)[8]:

Sediment transport component

There are several sediment transport models that can be used to evaluate landscape evolution at the decadal to centennial timescales required for the CLiDE. Coulthard (2001)[9] reviews these, and an overview of the theory behind modelling landscape evolution is presented by Tucker and Hancock (2010)[10]. The ability of current models to employ distributed fluvial and erosional processes gives an advantage over previous approaches (see Kinnell, 2010[11]), as they are based on DEMs, include distributed soil depths, allow surface runoff and can automatically determine inter-cell slope gradient and transport of sediment. For this study CAESAR was selected to provide the sediment transport and Graphical User Interface (GUI) properties for the CLiDE platform as it has a modular, versatile design and has been validated in a range of environmental settings. The reduced complexity cellular automaton (CA) nature of CAESAR facilitates simulation of regional scale catchments, with a high resolution spatio-temporal discretisation, at a relatively low computational cost. A novel cell scanning algorithm removes the need to employ grid sorting techniques, further reducing computation cost, and allows lateral surface flow diversion and conversion to be simulated. Due to its adaptable nature, CAESAR has been used for many applications including: modelling the response of river systems to environment change (Van De Wiel et al., 2011[12]), urban drainage management (Coulthard and Frostick, 2010[9]), human impact on fluvial regimes and fluxes of sediment (Hoffmann et al., 2010[13]), influences of vegetation on river development (Tooth et al., 2008[14]), catchment response to environmental change (Coulthard et al., 2005[15]), and more recently determining catchment soil loss rates (Hancock et al., 2011[16]).

The remainder of this section describes the major features of CAESAR that have been retained by the CLiDE platform. CAESAR incorporates a scanning algorithm based upon the Moore neighbourhood of cells, similar to that used by Murray and Paola (1994[17], 1997[18]), to monitor the properties of surrounding cells. As with the hydrological model, space is discretised into a two-dimensional lattice of square cells; however, to increase stability and reduce computational cost, time-steps are not uniform and reduce as the anticipated amount of sediment flux increases. Tracking simulated time (t) allows inputs from coupled modules and some internal functions to be calculated on a regular time-step, reducing computational stress. Initial surface elevation is input from a grid referenced DEM that is modified as time progresses.

A modified version of TOPMODEL (Bevan and Kirkby, 1979[19]), a physically based, watershed model that simulates surface fluxes of water was initially used by CAESAR to derive the partitioning and routing of surface water. The algorithms that deal with the surface routing were subsequently replaced with Lisflood, improving the representation of channel flow and flooding events. The remaining TOPMODEL water partitioning algorithms were not desirable for the CLiDE platform. They do not provide the distributed soil moisture or recharge properties required to simulate the variety of environmental systems represented by current or potential future CLiDE modules (for example; landslides, dynamic vegetation, or groundwater). For this reason TOPMODEL was replaced in the platform by the bespoke coupled surface-subsurface hydrological model. The coupled component supplies surface water depths and flow properties needed by the CAESAR component to calculate sediment transport.

After flow depths have been updated, fluvial erosion and deposition are calculated, where fluvial sediment transport is determined using either the Wilcock and Crowe method, to calculate mixed-size particle movement (Wilcock and Crowe, 2003[20]), or the Einstein-Brown method to calculate particle movement of a single grainsize (Einstein, 1950[21]).

The Wilcock and Crowe formulation (equation 2.12) uses the fractional volume of a particular sediment size (Fi), shear velocity (u*), ratio of sediment to water density (s), gravity (g), and the function Wi (equation 2.13); which allows the total transport to be calculated (equation 2.14) from the fractional grain shear stress (τ) and a reference sheer stress ri):

The Wilcock and Crowe method can transport sediment within a catchment as both a suspended load and a bedload (Equation 2.15). Both depend on the volume of sediment transported per time-step, where the sediment transported from a central cell to a neighbouring cell (k) is calculated by equating the coefficient X to either; slope, for bedload transport, or velocity for suspended load transport. The calculation of suspended load transport is simplified, as it assumes an equal distribution of sediment throughout the water column. Sediment deposition also differs between the two transport types, with bedload sediment deposited (and subsequently re-entrained) at every time-step and suspended sediment deposition based on fall velocities.

Under a quasi-uniform sediment grain size regime the less computationally expensive Einstein method for transport may be employed. The formulation uses the relative density of submerged sediment (ps-p), grain size (D), flow depth and the water surface gradient to evaluate the forces (ψ) moving and restraining a particle (equation 2.16). A bedload transport rate can be calculated from these forces and used to approximate the flux of sediment (qsed) between cells (equation 2.17). The amount of sediment that can be transported is calculated and moved from the erodible layer.

Non-fluvial sediment transport occurs through instantaneous debris flow and a slower creep process. Debris flow is computed using a either two-dimensional sand pile algorithm (Metha and Barker, 1994), based on a critical slope angle, or a more complex model based on the SCIDDICA shallow landslide model (D’ambrosio et al., 2003; Di Gregorio et al., 1999). Both techniques use an iterative process, contained within a single time-step, to move material down slope to lower cells until the model is no longer out of equilibrium. Soil creep (Cr) is calculated using a gradient in elevation between cells on a monthly basis through the diffusion equation:

where S is difference in terrain elevation between cells.

Vegetation component

Vegetation cover in the model is implemented by specifying areas where vegetation covers the surface layer, which has the effect of binding sediment and reducing erodability (see Murray and Paola, 2003). A simple alluvial vegetation growth model is included, allowing linear growth of vegetation over time if it is not submerged. When vegetation has grown beyond a specified limit it restricts fluvial erosion to a percentage of that for uncovered sediment (default value is 10%). If flow shear stress exceeds a threshold the vegetation can be removed — thus exposing the sediment below to unhindered erosion. If vegetation becomes covered by sediment it can re-grow through the sediment layer, thus re-stabilising it.

Debris flow component

Shallow landsliding and debris flows are important mechanisms by which sediment is redistributed and delivered to the stream network. Most LEMs to date have relied on process-based rules to approximate the influence of landslides over long timescales (Dietrich et al., 2003; Korup et al., 2010). The CLiDE platform simulates shallow landslides and resulting debris flows using the SCIDDICA model (D’ambrosio et al., 2003; Di Gregorio et al., 1999). The model incorporates the changes in energy and water content associated with the flow and the resulting redistribution of debris and is triggered by evolving DEM and hydrological conditions.

The condition for debris flow initiation within SCIDDICA is based on infinite slope stability analysis (Selby, 1993) and computes the balance of driving and resisting forces operating on the hillslope. Infinite slope stability is a widely adopted approach for linking landslide hazard prediction to hydrological models. The model assumes that the length of the slope is several times the soil thickness and that lateral forces are negligible, an assumption that is unlikely to hold in topographic hollows where shallow landslides are commonly triggered (Reneau and Dietrich, 1987). The driving (shear) stress (Sd) acting to move soil down a slope is given by the thickness of soil '(hs)', the density of soil (ρs), and the angle of the slope (θ) they are acting on:

where g is acceleration due to gravity. On a stable hillslope, Sd is exceeded by frictional resisting strength Sr (shear strength), which is the product of the stress acting normal to a potential failure plane (σn) and a friction coefficient which is the tangent of the internal friction angle ϕ. The internal friction angle combines the plane friction resulting from when two grains are trying to slide past each other, and friction generated by grain interlocking within the mass (Carson and Kirkby, 1972). Shear strength is given by the Coulomb equation:

where C is the effective cohesion within the soil, ρw is water density and hw is the elevation of groundwater heads above the potential failure plane. Equating the condition for hillslope failure Sd>Sr and simplifying results in the trigger condition for landslide initiation (e.g. Pack et al., 2001; Rosso et al., 2006):

where C* is a dimensionless cohesion parameter defined as:

The hydrologic influence on slope stability is accounted for in the second bracketed term in equation 2.21. The pore pressure (u) acting on a potential failure plane is a product of Phw and ρw. By taking the ratio of SMD, produced by the SLiM water partitioning module (Section 2.2), to the total available pore space (mc), the soil will be dry when ratio is 1:1 or when Phw divided by SOb is zero in equation 2.21. Alternatively the soil will be saturated when; SMD is zero and SMD divided by mc equals zero or when Phw equals SOb. Thus we can replace Phw/SOb with (mc-SMD)/mc in equation 2.23:

The failure angle decreases with increasing moisture content due to loss of shear strength. Potential angle of failure can be lower than 20° for soils with lower internal friction angles which could result in the prediction of widespread slope failure if cohesion is not taken into consideration. Currently the landslide trigger condition within SCIDDICA assumes that the soil is permanently saturated so that for a prescribed internal friction angle, the failure angle would be given by the right hand edge of Figure 2. Equations 2.21 and 2.23 describe the link between stability and the hydrological conditions modelled within the CLiDE platform.

Figure 2    Variation in the failure angle for a shallow landslide as a function of soil moisture and the internal friction angle follow infinite slope stability analysis (see equation 2.23). Cohesion was assumed negligible (C* set to zero). Increased soil moisture causes a reduction in the angle up to which hillslopes might be stable.

Climate change component

Future changes in climate are likely to modify local and global temperatures and change rainfall patterns. This will lead to a modification in the distribution of river flow, soil water content and groundwater levels. Prediction of changes to future distributed precipitation and potential evapotranspiration is common place in global circulation models (GCMs) and downscaled regional climate models (RCMs), such as those encompassed by the UKCP09 dataset. Using these datasets we can simulate the effect of predicted future climate on surface hydrology, groundwater and the partitioning of water amongst the various stores.

The water partitioning model in the CLiDE platform uses a time series of distributed precipitation and potential evapotranspiration to drive surface and subsurface flow. The influence of climate change may be introduced by perturbing the input rainfall and potential evapotranspiration data on a monthly basis (see Section 3.13).

References

  1. Wang, L, Barkwith, A, Jackson, C, and Ellis, M. 2012. SLiM : an improved soil moisture balance method to simulate runoff and potential groundwater recharge processes using spatio-temporal weather and catchment characteristics. 12th UK CARE Annual General Meeting, UK Chinese Association of Resources and Environment, Bristol, UK, 8 Sept 2012.
  2. Rushton, K R. 2003. Groundwater hydrology: conceptual and computational models. John Wiley and Sons Ltd, West Sussex, England.
  3. Allen, R, Pereira, L A, Raes, D, and Smith, M. 1998. Crop evapotranspiration: guidelines for computing crop water requirements. FAO, Irrigation and Drainage Paper No.56. FAO, Rome, Italy.
  4. Van der Knijff, J M, Younis, J, and De Roo, A P J. 2010. LISFLOOD: a GIS-based distributed model for river basin scale water balance and flood simulation. Int. J. Geogr. Inf. Sci., 24, 189–212.
  5. Bates, P D, Horritt, M S, and Fewtrell, T J. 2010. A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. J. Hydrol., 387, 33–45.
  6. Liang, D, Falconer, R A, and Lin, B. 2006. Improved numerical modelling of estuarine flows. Proceedings of the Institution of Civil Engineers, Maritime Engineering, 159 (1), 25–35
  7. Roache, P J. 1976. Computational Fluid Dynamics. Albuquerque, NM: Hermosa. Rev. 1976.
  8. Haitjema, H M. 1995. Analytic Element Modeling of Groundwater Flow, Academic Press, 394pp.
  9. 9.0 9.1 Coulthard, T J, and Frostick, L E. 2010. The Hull floods of 2007: implications for the governance and management of urban drainage systems. J. Flood Risk Manage., 3(3), 1–9.
  10. Tucker, G E, and Hancock, G R. 2010. Modelling landscape evolution. Earth Surf. Proc. Land., 35(1), 28–50.
  11. Kinnell, P I A. 2010. Event soil loss, runoff and the Universal Soil Loss Equation family of models: A review. J. Hydrol., 385(1–4), 384–397.
  12. Van de Wiel, M J, Coulthard, T J, Macklin, M G, and Lewin, J. 2011. Modelling the response of river systems to environmental change: Progress, problems and prospects for palaeo-environmental reconstructions. Earth Sci. Rev., 104(1–3), 167–185.
  13. Hoffmann, T, Thorndycraft, V R, Brown, A G, Coulthard, T J, Damnati, B, Kale, V S, Middelkoop, H, Notebaert, B, and Walling, D. 2010. Human impact on fluvial regimes and sediment flux during the Holocene: Review and future research agenda. Global Planet. Change, 72(3), 87–98.
  14. Tooth, S, Jansen, J D, Nanson, G, Coulthard, T J, and Pietsch, T. 2008. Riparian vegetation and the late Holocene development of an anabranching river: Magela Creek, northern Australia. GSA Bull., 120(7–8), 1021–1035.
  15. Coulthard, T J, Lewin, J, and Macklin, M G. 2005. Modelling differential and complex catchment response to environmental change. Geomorphology, 69(1–4), 224–241.
  16. Hancock, G R, Coulthard, T J, Martinez, C, and Kalma, J D. 2011. An evaluation of landscape evolution models to simulate decadal and centennial scale soil erosion in grassland catchments. J. Hydrol., 308, 171–183.
  17. Murray, A B, and Paola, C. 1994. A cellular model of braided rivers. Nature, 371, 54–57.
  18. Murray, A B, and Paola, C, 1997. Properties of a cellular braided-stream model. Earth Surf. Proc. Land., 22, 1001–1025.
  19. Bevan, K J, and Kirkby, M J. 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24((1), 43–69.
  20. Wilcock, P, and Crowe, J. 2003. Surface-based transport modelling for mixed-size sediment. J. Hydraul. Eng., 129(2), 120–128.
  21. Einstein, H A. 1950. The bed-load function for sediment transportation in open channel flows. Technical Bulletin 1026, USDA, Soil Conservation Science, 1–77.