Model Formulation: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:

1. stability issues in the overland flow scheme,
2. the smallest rainfall interval,
3. the groundwater time step, and
4. 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	Overland flow scheme Rainfall interval Groundwater time step
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	Must be equal to or less than overland flow routing time step during runoff Equal to groundwater time step when groundwater discharge only	Courant number less than 1/6
Saturated groundwater flow	10 min - 1 d	Equal to overland flow time step during runoff Must maintain channel stability during discharge to stream	Maximum number of cells added or subtracted from unsaturated zone

Table 2 – Recommended time-steps and stability criteria used in the GSSHA model

File:Figure 4.jpg

Figure 4 – Example of temporal convergence study with hydrograph shifting at 150 s time step, oscillations at 180 s, and oscillations leading to a crash at 210 s.

GSSHA User's Manual

2 Model Formulation

2.1     Processes Simulated

2.2     Time Steps and Process Updates

2.3     Inputs