Template:GUM2
2 - Model Formulation
GSSHA is a physically-based, distributed-parameter, structured grid, hydrologic model that simulates the hydrologic response of a watershed subject to given hydrometeorological inputs. The watershed is divided into cells that comprise a uniform finite difference grid. Processes that occur before, during, and after a rainfall event are calculated for each grid cell and then the reponses from individual grid cells are integrated to produce the watershed response. Major components of the model include precipitation distribution, snowfall accumulation and melting, precipitation interception, infiltration, evapo-transpiration, surface water retention, surface runoff routing, channel flow routing, unsaturated zone modeling, saturated groundwater flow, overland sediment erosion, transport and deposition, channel routing of sediments, and constituent fate and transport on the overland and in channels.
During an event, rainfall is spatially and temporally distributed over the watershed. Rainfall may be intercepted by vegetation before reaching the land surface. Once an initial interception demand is reached, a fraction of the precipitation will reach the land surface. Upon reaching the land surface, precipitation may infiltrate due to gravity and capillary forces. Water remaining on the land surface may runoff as two dimensional (2-D) overland flow, after a specfied retention depth representing micro-topography has been reached. This water may eventually enter a stream and be routed to the watershed outlet as one dimensional (1-D) channelized flow. Between precipitation events, soil moisture accounting, evapo-transpiration (ET), and 2-D lateral groundwater flow may be occuring. When precipitation falls in the form of snowfall, the water equivalent volume remains on the land surface and is released as water according to an energy budget calculation.
On the overland flow plane sediment is detached due to rainfall impact and shear stresses due to overland flow. Sediments are routed overland along with the 2-D overland flow. Erosion and deposition continuously occurs on the overland plane as sediments are transported. Sediments may eventually be routed to the stream network where fines (silt and clay) are routed according the advection dispersion equation. Coarse materials are treated as bed load, which is computed according to Yang's method (ref).
Constituents may be assumed to within the soil column or on the land surface. In either case, constituent uptake occurs when water is ponded on the soil surface. Constituents move along in the 2-D overland flow, with reactions occuring as water moves across the watershed. Constituents may ultimately be deposisted into the stream network where they are transported according to the reactive advection dispersion equation.
2.1 Processes Simulated
GSSHA is a process-based model. Hydrologic processes that can be simulated and the methods used to approximate the processes with the GSSHA model are listed in Table 1. With the exception of channel routing, all processes and approximations in the original CASC2D model are also contained in the GSSHA model. The Preissmann channel routing routine (Cunge et al., 1980) was excluded because of known stability problems with the scheme when simulating trans-critical flows (Mesehle and Holly, 1997). Also, the upwind explicit channel routing method was replaced with a similar up-gradient explicit method.
| Process | Approximation |
|---|---|
| Precipitation distribution |
|
| Snowfall accumulation and melting |
|
| Precipitation interception |
|
| Overland water retention |
|
| Infiltration |
|
| Overland flow routing |
|
| Channel routing |
|
| Reservoir simulation |
|
| Evapo-transpiration |
|
| Soil moisture in the Vadose zone |
|
| Lateral groundwater flow |
|
| Stream/groundwater interaction |
|
| Exfiltration |
|
| Overland Erosion |
|
| Overland Sediment Deposition |
|
| Overland Sediment Routing |
|
| Channel Routing of Fine Sediments |
|
| Channel Routing of Sand |
|
| Reservoir Sources of Sediment |
|
| Reservoir Routing for Fines |
|
| Reservoir Routing for Sands |
|
| Reservoir Fines Deposition |
|
| Overland Constituent Loading |
|
| Overland Constituent Uptake |
|
| Overland Constituent Transport |
|
| Overland Reactions |
|
| Channel Constituent Loading |
|
| Channel Constituent Transport |
|
| Channel Reactions |
|
| Reservoir Constituent Loading |
|
| Reservoir Constituent Transport |
|
| Reservoir Reactions |
|
Table 1 – Processes and approximation techniques in the GSSHA model
GA – Green and Ampt (1911), GAR – Green and Ampt with Redistribution (Ogden and Saghafian, 1997), RE – Richards’ equation (1931), ADE – Alternating Direction Explicit (Downer et al., 2000), ADEPC – Alternating Direction Explicit, Predictor-Corrector (Downer et al, 2000).
2.2 Time Steps and Process Updates
In GSSHA the user specifies the overall model time step, in seconds, that the model uses to loop through the processes, check update times, and update processes. To avoid missing updates of processes, such as rainfall, that may be specified at 1 minute intervals, the overall model time step should be integer divisible into 60 seconds or an integer multiple of 60 s (i.e. 5,10,15,20,30,60,120,180,300). Time steps such as 7,9,13,16,21,45,90,270 should not be used, as they may result in unexpected internal model behavior. The model time step also must not be greater than the finest resolution of inputs, such as rainfall. Typical time steps for GSSHA range from 10 to 300 seconds. Smaller time steps may be required for particularly difficult problems.
The computational time step is an important parameter affecting the performance of GSSHA. In addition to setting the pace of the model, the overall model time step is used to set or initialize the temporal discretizations of many model processes. While many processes, such as channel routing, saturated and unsaturated groundwater flow, have internal model stability checks, some methods of overland flow routing do not. If the time step is too large the program may crash or produce inaccurate results. Very small time steps result in inordinately long simulation times. The best way to determine the most efficient time step is through a temporal convergence study, where the time step is varied and the model behavior is observed. This allows the user to determine the maximum time step that can be used with acceptable accuracy. As the time step is increased, the outlet hydrograph will begin to shift in position in relation to simulations with smaller time steps. As the time step is further increased, the discharge at the outlet will oscillate; further increases in the computational time-step will result in program crashes. Results of a temporal convergence study, featuring hydrograph shifting, oscillations, and model crash, are shown in Figure 4.
The appropriate time step strongly depends on watershed and rainfall characteristics. In general, shorter time steps must be used for:
- higher intensity storms,
- finer horizontal grid resolution (grid spacing),
- steeper watershed slopes,
- larger watershed areas, and
- smoother surfaces.
Shorter time steps must be used when backwater effects are generated in flat areas in the digital elevation model (DEM). If the time step is too long for any particular simulation the surface water depth in very flat areas may develop a checkerboard pattern due to oscillations in the water surface level. This eventually results in a crash. If this occurs the time step should be decreased and the simulation repeated.
At the time of this publication, only the time step for the saturated groundwater flow is specified in addition to the overall time step. The ET time step is fixed at 1 hr, the usual interval of hydrometeorological data available. To maintain stability the time step may be reduced internally for the explicit channel routing code, the unsaturated zone RE solver, the groundwater solver, and the explicit and ADE solutions for overland flow. Internal time step limitations in the model are described under the appropriate process sections. Rainfall updates are specified in the rainfall gage file and the interval between updates can vary as needed. Thus the overall time step is limited by:
- stability issues in the overland flow scheme,
- the smallest rainfall interval,
- the groundwater time step, and
- the need to be integer divisible into the groundwater time step and the smallest rainfall interval.
Timesteps for sediment and constituent fate and transport are based on the underlying hydrologic proecesses and do not have to be specified.
Guidance for time steps is shown in Table 2.
| PROCESS | TYPICAL TIME STEP |
DEPENDENCE | STABILITY CRITERIA |
|---|---|---|---|
| Overall model | 1s- 5 min |
|
|
| ET | 1 hr | Available hydrometeorological data | |
| Rainfall | 1 min - 1 d | Available rainfall data | |
| Interception | 1 min - 1 d | Rainfall interval | |
| GA Infiltration | 1s - 5 min | Same as overland flow scheme | |
| GA with Redistribution |
1s - 5 min | Same as overland flow scheme | |
| RE Infiltration | 1s - 1 hr | Dependent on change in water content (d/dt) | 0.0025<d/dt<0.025 Set by user |
| Overland flow routing | 1s - 5 min | Stability of overland flow scheme | |
| Explicit channel routing | 1s - 1 hr |
|
Courant number less than 1/6 |
| Saturated groundwater flow | 10 min - 1 d |
|
Maximum number of cells added or subtracted from unsaturated zone |
Table 2 – Recommended time-steps and stability criteria used in the GSSHA model
2.3 Inputs
GSSHA is a distributed-parameter, process-based model that requires the user to select the processes to be simulated and then provide the model with the data necessary to drive the selected options. Three types of input data are used. An ASCII text project file is used to provide the basic project information, select processes to be simulated, assign simulation parameters, and locate data files, tables and maps. Spatially distributed parameters can be assigned with maps of ASCII gridded data with a parameter value in each grid cell, with index maps and tables of parameter values that relate to the index maps, or with uniform values in every cell. Typically the data required to assign parameter values in every cell is not available. Standard practice in the application of GSSHA has been to develop index maps based on available data sources of land use, soil type, and vegetation. Typically these maps are combined to create a master land use/soil type/vegetation index map that can be used to assign all parameter values.
Parameters for each index map are then assigned using tables that reference the values in the index maps. A detailed description of using the index maps and Mapping Tables to build a GSSHA model is provided in Section 11. If available, the detailed maps containing parameter values in each cell, as described in Ogden (2000), may be input in lieu of the index maps and table.
Since distributed parameters may be assigned with a single uniform value in the project file, a table value linked to an index map, or with an ASCII map with a parameter value for every grid cell the model has been developed to prioritize parameter specification. While internally assigning parameter values the GSSHA model looks for the most detailed information first, GRASS ASCII maps, the second most detailed information second, table values linked to index maps, and finally a single uniform value from the project file. Once data from one of these sources is located, the search ends and the parameter values are assigned inside the GSSHA model. While this rule is generally applicable it is prudent not to specify multiple sources of the same parameter value in the project file. This avoids possible confusion and improper assignment of parameter values.
The Watershed Modeling System (WMS) interface, developed at the Environmental Modeling Research Laboratory (EMRL) at Brigham Young University, is recommended for developing input files and viewing output from the GSSHA model. The WMS produces GSSHA specific files from general Geographic Information System (GIS) data. WMS does not replace the functions of a GIS, though it can accept information in a variety of GIS formats. GSSHA relies on the GRASS ASCII data file format for storing spatially distributed data. The GRASS GIS is very helpful in the preparation of GSSHA data sets. Users of ARC/INFO and ARCVIEW can export data to GSSHA through the WMS interface. For more information about WMS, DoD and EPA personnel should contact:
- XMS Model Support
- Hydrologic Systems Branch
- Coastal and Hydraulics Laboratory
- Engineer Research Development Center
- 3909 Halls Ferry Road
- Vicksburg, MS, 39180
- (601) 634-4286
- http://chl.wes.army.mil/software
Other users seeking information about WMS, should contact:
- Aquaveo
- 3210 N Canyon Road
- Provo, Utah 84604
- 801-691-5530
- http://www.aquaveo.com/technical-support
- email: support@aquaveo.com
