Extension of the WASA model: Water and sediment routing in the river network Working Report SESAM-Project, University of Potsdam, July 2005 Eva Nora Müller enmue@uni-potsdam.de 1 Introduction to model concept The existing river routine of the WASA model (Güntner 2002) of water flow was extended to include a spatially distributed, semi-process-based modelling approach for the modelling of water and sediment transport through the river network. The implemented modelling approach is similar to the routing routines from the SWAT model (Soil Water Assessment Tool, Neitsch et al. 2002) model and the SWIM model (Soil Water integrated Modelling, Krysanova and Wechsung 2000). The new river modelling approach gives an alternative to the original WASA water routing that was based on daily linear response functions (Bronstert et al. 1999). The new water routing provides two options based on the kinematic wave approximation: the Muskingum river routing method and the variable storage method. Flow rate, velocity and flow depth are calculated for each river stretch and each time step using the Manning s equation. A trapezoidal channel dimension is used to approximate the river cross-sections. If water level exceeds bankfull depth, the flow is simulated across a pre-defined floodplain. Sediment transport is modelled using the transport capacity concept. The maximum concentration of sediment that can be transported by the water is calculated as a function of peak flow velocity. If the actual sediment concentration exceeds the maximum concentration, deposition occurs; otherwise degradation of the riverbed is calculated as a function of a channel erodibility factor. A more detailed review on the calculation methods can be found in the Theoretical Documentation of the SWAT model, Chapters 23 and 24 by Neitsch et al. The model can be run with variable time steps. Transmission losses through riverbed infiltration and evaporation are accounted for. 2 Input parameters for routing routines The new routing routine enables a spatially distributed representation of river stretch characteristics. The flow calculations are carried out in routing order, i.e. the river stretches which are located most upstream are calculated first. The routing order is specified in routing.dat (see WASA documentation, Mueller and Güntner 2005). The key model input parameters for water and sediment routing are summarised in Table 1. The data are stored in an input file called river.dat that assigns each sub-basin with a specific map ID a corresponding river stretch.
In addition, the initial conditions of source reaches, equivalent to the beginning of the river, have to be specified. The format of the input file river.dat is given in Figure 1. The hourly or daily runoff, groundwater and erosion rates into the river network are supplied by the hillslope components of the WASA model. Table 1 Input parameters for river routing approach Water routing Sediment routing Length of river reach [km] Bankful depth of river reach [m] Bankful width of river reach [m] Slope of river reach [m/m] Manning s n of river reach [-] Saturated hydraulic conductivity the river bed [mm/h] Bank flow recession constant Muskingum coefficients msk_co1, msk_co2, msk_x Initial conditions for source reaches [m3/s] River erodibility factor of river reach [cm/hr/pa] River cover factor of river reach [-] Peak flow rate adjustment factor Coefficients for transport capacity equation Specification of river parameters Subasin-ID [-], width(m), depth(m), slope(m/m), length (km9, manning s n (-), Ksat (mm/h), erodibility (-) factor, cover factor (-), baseflow, msk_co1, msk_co2, msk_x, Q_spring(m3/s) 9 20 0.5 0.13 22.35 0.1 25 0.1 0 0 0 0 0.2 0.1 10 10 0.5 0.17 12.05 0.1 25 0.1 0 0 0 0 0.2 0.1 Figure 1 Format of routing input file river.dat 3 Subroutine structure: The existing Fortran routines of the SWAT model were used as a basis for the computational implementation of the new routing scheme into the WASA code. The main routing calculations as well as the initialisation and reading of the river input files are carried out in routing.f90. The following sub-routines were added to the WASA code for the calculation of sub-processes: muskingum.f90: contains the flow calculation using the Muskingum method 1. Calculation of water volume in reach 2. Calculation of cross-section area of current flow, flow depth, wetted perimeter and hydraulic radius 3. Calculation of flow in reach with Manning Equation 4. Calculation of Muskingum coefficients 5. Calculation of discharge out of the reach and water storage in reach at end of time step variable_stor_routing.f90: contains the flow calculation using the variable storage method 1. Calculation of water volume in reach 2
2. Calculation of cross-section area of current flow, flow depth, wetted perimeter and hydraulic radius 3. Calculation of flow in reach with Manning Equation 4. Calculation of travel time and storage coefficient 5. Calculation of discharge out of the reach and water storage in reach at end of time step routing_coefficients.f90: contains the calculations for travel time and flow depth 1. Calculation of initial water storage for each river stretch 2. Calculation of channel dimensions 3. Calculation of flow and travel time at bankfull depth 1.2 bankfull depth and 0.1 bankfull depth route_sediments.f90: contains the calculation for sediment-transport routing 1. Calculation of water volume and sediment mass in reach 2. Calculation of peak flow and peak velocity 3. Calculation of maximum sediment carrying capacity concentration 4. Comparison with current concentration 5. Calculation of net deposition and degradation 6. Calculation of sediment mass out of the reach and sediment storage in reach at end of time step 4 Linkage and interface with WASA hillslope and reservoir modules The hillslope module of the WASA model provides the fluxes of water and sediments from toposequences, landscape units and sub-basins. Water fluxes in the riverflow(day, subasin) array contain surface flow generated in the lowlands, and exfiltrated groundwater and should be given in m 3 /s. The sediment fluxes in the erosion(day, subasin,size_class) array from hillslopes as calculated by the MUSLE and/or HIDROSED approach should be given in tons/time step for each particle size classes, where the number of classes (variable size_class) is defined in the do.dat. The river routing routine provides the input fluxes of water and sediment to the reservoir module. Currently, the river routine supplies information on water (m 3 /s) and sediment (tons) fluxes into the reservoir, and receives the corresponding information from the reservoir module after the reservoir. Information on pre-defined particle size classes are read in and are organised by the hillslope module. 5 Spatial merging of hillslope inlet points and river stretches In the original WASA version, each sub-basin was linked to a single river stretch. The computational implementation was straightforward as for each calculation step the runoff water of sub-basin i was transferred to the corresponding river stretch i. This approach is not desirable for the current development of the WASA model because of the following two reasons: a) due to the finer spatial discretisation of the hillslope units as derived from the LUMP approach (Francke 2005) it becomes possible that a single characteristical river stretch has more than one inlet point for water and sediment discharges, e.g. for two different landscape units at either site of the river stretch. 3
b) If the hillslope characteristics are relatively homogenous and are defined by only one landscape units, but the river exhibits spatial variations over very short distance, it becomes possible that one conceptual inlet point for water and sediment discharge has to be distributed over several, separate river stretches. The spatial merging of hillslope and river discharge points is strongly linked to the computational implementation of the flux calculation in the WASA code. Currently, the WASA code structure mirrors the simple, former relationship of the spatial discretisation of the hillslope and river routing. The parameter and calculation arrays for both hillslope and river transport processes have an allocatable size depending on the number of sub-basins in the model domain. Once each water and sediment discharge is calculated for each sub-basin, the river routing routine loops through the number of sub-basins and assigns each hillslope to the corresponding river stretch. For the two enhanced types of spatial merging, as stated above, the current WASA calculation structure requires modification. This can be either done in the WASA code itself, or in a pre-processing module. The later is here preferred, to keep in the WASA code structure as transparent as possible. The following steps of procedure are proposed to implement an enhanced spatial merging of hillslope and river transport processes in a pre-processing module: Derive the river network and define characteristic river stretches as a function of geology, slope and hydraulic parameters. The corresponding parameters for each stretch are stored in river.dat; each stretch is assigned a unique ID. Change the spatial representation of the river in the GIS software from polyline to raster. Load the river raster with the characteristics river stretches into the GRASS GIS (check projections) Derive spatially referenced landscape units in raster format for the hillslopes with the LUMP approach in the GRASS GIS Develop an algorithm that performs the spatial merging in GRASS GIS: (1) combine adjacent areas belonging to the same LU until a specified maximum size is reached (corresponds to the maximum size of a subbasin in the parametrisation). The resulting area is a sub-basin which is given a unique id. (2) find the inlet points of the derived sub-basins along the river and their relative position in the respective river stretch (3) redefine the river stretches by subdividing the initial stretches at the computed inlet points (4) Prepare three river module input files: (1) the original river.dat as defined above (2) a new file river_spatial.dat: this file contains the river IDs for all stretches and a length fraction to georeference the location of the inlet points, as derived through spatial merging. The file does not contain all parameter information for each new river stretch, but rather the 4
IDs for pre-defined characteristic river stretches as given in river.dat. (3) a modified file routing.dat: this file contains the routing (in stream flow order) for all new river stretches (e.g. before spatial merging: stretch 1 gives water to stretch 2; after spatial merging: stretch 1 is split into three new stretches with certain lengths and new IDs: 10, 11, and 12; the flow is now routing from 1011122 Advantages of the spatial merging: - water and sediment sources from the hillslope can be located closer to their true origin - river routing within the sub-basins becomes possible hillslope-river interaction and river transport are modelled more realistically Applicability of the spatial merging: - feasible, if the data situation allows for reasonable fine discretisation of LU and/or river stretches Implementation of the method as a general tool of spatial discretisation 6 Problems Spatial merging of river stretches and hillslopes Sediment transport capacity formulae are currently very simple; Initial conditions for river storage, river flow etc. Differentiation between bedload and suspended load, between different particle-size classes, uniform and non-uniform sediment mixtures Riverbed changes over time 5
7 Application of the river routing scheme to the Esera Watershed The river routing scheme was applied to the modelling of water transport through the Esera Watershed (Huesca, NE Spain) up to the Barasona Reservoir. Figure 2 displays a map of the Esera Watershed with the corresponding river network and catchment boundaries. Figure 2 Esera Watershed with river network The total catchment area above the Barasona Reservoir is approximately 1511 km 2. For the modelling exercise, the model domain is delimited upstream of Esera en Eriste (Villanova), which reduces the model domain to a size of ca. 1387 km 2. Initial conditions for river discharge data are available for the station at Eriste (Station No. 145). Simulation studies are carried out in the first instance for the year 2001. Annual rainfall of 2001 varies between 529 mm in the southern parts, to 592 mm in the central and up to 878 mm in the mountainous parts of the catchment. Testing data for water discharge are available 6
for two discharge stations at Esera en Graus (Station No. 13, temporal resolution: one day) and Isabena en Capella (Station 47, temporal resolution: 15 minutes). Model input parameters on river profile slope were derived from a 45-m resolution digital elevation model. The widths and depths of individual cross-sections were roughly approximated through analysis of 5-m resolution aerial photography. Values for Manning s n were derived from the work of Verdu (2003). The saturated hydraulic conductivity values were derived from the SWAT user manual. All river input parameters urgently require verification through a field survey of representative river stretches. The preliminary parameterisation data are summarised in Table 2, with the sub-basin ID numbers as depicted in Figure 2. Table 2 Preliminary parameterisation of river model for the Esera Watershed Specification of river parameters Subasin-ID [-], width(m), depth(m), slope(m/m), length (km9, manning s n (-), Ksat (mm/h), erodibility factor (-), cover factor (-), baseflow, msk_co1, msk_co2, msk_x, Q_spring(m3/s) 9 20 1 0.03 22.35 0.1 25 0.1 0 0 0 0 0.2 0.1 10 10 1 0.06 12.05 0.1 25 0.1 0 0 0 0 0.2 0.1 11 20 1 0.03 7.69 0.1 25 0.1 0 0 0 0 0.2 0 12 10 1 0.06 8.45 0.1 25 0.1 0 0 0 0 0.2 0.1 13 30 1 0.03 4.29 0.1 25 0.1 0 0 0 0 0.2 0 14 15 1 0.06 14.84 0.1 25 0.1 0 0 0 0 0.2 0.1 15 40 1 0.01 30 0.1 25 0.1 0 0 0 0 0.2 0 16 10 1 0.04 29.04 0.1 25 0.1 0 0 0 0 0.2 0.1 17 10 1 0.04 12.2 0.1 25 0.1 0 0 0 0 0.2 0.1 18 20 1 0.02 15.3 0.1 25 0.1 0 0 0 0 0.2 0 19 15 1 0.04 12.64 0.1 25 0.1 0 0 0 0 0.2 0.1 20 20 1 0.01 17.76 0.1 25 0.1 0 0 0 0 0.2 0 21 50 1 0.01 3.47 0.1 25 0.1 0 0 0 0 0.2 0 22 10 1 0.03 12.16 0.1 25 0.1 0 0 0 0 0.2 0.1 23 75 1 0.01 0.01 0.1 25 0.1 0 0 0 0 0.2 0 As no data on runoff and groundwater discharge are available yet from the WASA hillslope modelling, a very simple approach based on a constant runoff coefficient of 50 % of the daily rainfall and a constant areal groundwater discharge of 0.01 m 3 /(s*km 2 ) into the river is used to generate time series for water input for the first modelling exercises. Figure 3 shows simulations of discharge at the outlet of sub-basin 5 (as defined in Figure 1), close to the discharge measurement station Graus (Station 13 in Figure 1). Time step of calculation does have a significant influence on modelling results: a daily time step underestimates the peak discharge in comparison to the hourly time step due to the numerical stability criterion of the Muskingum routing method. Time steps up to 12 hours give sufficient results. Figure 4 compares the simulated discharge (as derived from a time step of one hour) with the observed discharge at the Graus Station for the year 2001. The simulated time series follows the general pattern of peak and low flow of the observed one, however, the results should be greatly improved when proper runoff and groundwater discharge data from the WASA model are available as input to the river model. 7
Discharge at Grauss (Esera River) with daily and hourly time step Discharge [m3/sec] 300 250 200 150 100 50 0 0 100 200 300 Time [days] dt = 1 hour dt = 24 hours Discharge at Grauss (Esera River) with variable time steps Discharge [m3/sec] 100 80 60 40 20 0 0 48 96 144 192 240 288 336 384 432 480 Time [hours] dt = 1 hour dt = 12 hours dt = 4 hours dt = 24 hours Figure 3 Simulated discharge at Graus (Station 13 in Figure 2) for the Esera River with various time steps Observed versus simulated discharge at Graus (Esera River) for year 2001 300 Discharge [m3/sec] 250 200 150 100 50 0 0 100 200 300 Time [days ] Observed discharge Simulated discharge Figure 4 Comparison of simulated and observed discharge at Graus (Station 13 in Figure 2) for the Esera River for year 2001 8
References Bronstert, A., A. Güntner, A. Jaeger et al. Großräumige hydrologische Parameterisierung und Modellierung als Teil der integrierten Modellierung. In Modellierung des Wasser- und Stofftransports in großen Einzugsgebieten. Edited by N. Fohrer and P. Döll. Kassel: Kassel University Press, 1999. Francke, T. (2005) Consistency tests of the Landscape Unit Mapping Program (LUMP) for WASA. Working Report, SESAM-Project, Version 0.2 Güntner, A. Large-scale hydrological modelling in the semi-arid North-East of Brazil. PIK- Report No. 77. 2002. Potsdam Institute for Climate Research, Germany (http://www.pikpotsdam.de/pik_web/publications/pik_reports/reports/reports/pr.77/pr77.pdf) Krysanova,V., F. Wechsung (2000) SWIM (Soil and Water Integrated Model) User Manual, Version: SWIM-8. Internet resource (accessed on 02.05.05): http://www.pikpotsdam.de/~valen/swim_manual/swim-chapter1.pdf Mueller, E.N. and A. Güntner (2005) WASA Model Documentation, Working Report SESAM-Project, Universität Potsdam / Geoforschungszentrum Potsdam Neitsch, S.L., J.G. Arnold, J.R. Kiniry, J.R. Williams, K.W. King (2002a): Soil and Water Assessment Tool. Theoretical Documentation, Version 2000. Published by Texas Water Resources Institute, TWRI Report TR-191 Verdu, J. M. (2003) Analysis and modelling of the hydrological and fluvial response of a large mountainous Mediterranean catchment (Isabena River, Pre-Pyrenees), Unpublished PhD thesis, University of Lleida 9