Point Processes

Point processes occur at the grid cell level for every cell in the active domain. In general, point processes are updated first and the updated cell values are used to simulate integrated processes. Point processes in GSSHA are not iterative; they are calculated based on the most current boundary conditions available at the update time.

1.2.1 Precipitation Distribution

Precipitation is input into the model using point rain gauge or radar estimates. Precipitation events must be defined in the model input. A precipitation event is defined as a number of temporal points where the time and rainfall are prescribed for each rain gauge or radar pixel. As the time is specified at each point, the precipitation increments can be at uneven time intervals. An

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unlimited number of gauges and points can be used, and the number of gauges can change between events. Precipitation is distributed over the grid using either Thiessen polygons or by inverse distance squared interpolation. When the model is run in continuous mode, hourly temperatures are required input, and precipitation is assumed to be frozen when the air temperature is at or below 0ºC. Frozen precipitation is not available for infiltration, ET, or runoff, until such time as it melts, as described below. In lieu of gauge data, precipitation may be applied as uniform rain rate over the basin for a fixed period of time.

This feature is particularly useful as a tool to aid in initial model setup.

1.2.2 Rainfall Interception

Inception of precipitation by vegetation is simulated in GSSHA using a three-parameter model that includes an initial volume of retention upon the initiation of rainfall and then a variable rate of retention based on precipitation rate, as described by Ogden and Julien (2002). Often in practice, interception is not explicitly simulated; rather, the effects of interception are included in the overland flow retention depth.

1.2.3 Infiltration

Ponded water on overland flow plane cells will infiltrate into the soil as dictated by soil hydraulic properties and antecedent moisture conditions, which may be affected by previous rainfall, run on, ET, and the location of the water table. The unsaturated zone that controls infiltration may be simulated with a 1-D formulation of Richards’ equation (RE) (Richards, 1931), which simulates infiltration, ET, and soil moisture movement in an integrated fashion. Infiltration may also be simulated using traditional Hortonian Green and Ampt (GA) (Green and Ampt, 1911) approaches. RE is a general equation and can be applied in any type of watershed or conditions. The GA methods represent significant simplifications of infiltration, as compared to RE. Calculation of infiltration with the GA methods also decouples the processes that occur in the unsaturated zone.

GA does not provide detailed soil moisture profiles, and vertical movement of water from the groundwater table to the unsaturated zone cannot be simulated.

Because solution of the nonlinear RE is computationally expensive, the simpler methods based on the GA equation are preferred when runoff is Hortonian, i.e., occurs due to infiltration excess, where the rainfall/run-on of water is greater than the possible infiltration rate. For fine-textured soils the Green and Ampt with distribution (GAR) method has been shown to closely mimic the RE solution (Ogden and Saghafian, 1997), and when applied in basins identified as Hortonian, the GAR method has been shown to produce results comparable with the RE (Downer and Ogden, 2003). However, when Hortonian flow is not the predominant streamflow-producing mechanism, application of GA type models is ill advised and can result in erroneous results (Downer et al., 2002a). For cases where Hortonian flow is not the predominant process generating streamflow the RE should be used, and coupled with the saturated groundwater solution as appropriate.

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1.2.3.1 Richards’ Equation

Processes in the unsaturated zone primarily occur in the vertical direction (Refsgard and Storm, 1995) and GSSHA solves the one-dimensional (vertical direction) head-based form of RE:

0

where: C is the specific moisture capacity, ψ is the soil capillary head (cm), z is the vertical coordinate (downward positive) (cm), t is time (h), K(ψ) is the effective hydraulic conductivity (cm h^-1), and W is the source/sink term (cm h^-1).

The head-based formulation is often used in hydrologic models because it allows solution of RE in both saturated and unsaturated conditions (Haverkamp et al. 1977), and rainfall, ET, and groundwater recharge can be simulated without a change in variable. Mass balance problems associated with solution of the head-based formula are avoided by using flux updating (Kirkland et al., 1992).

Two different methods can be used to describe soil water retention curves:

the Brooks and Corey method (1964) as extended by Hutson and Cass (1987), and the method of Havercamp et al. (1977) as modified by Lappala et al. (1987).

The Havercamp method requires field or laboratory data to fit coefficients.

Brooks and Corey parameters may be fit, or estimated from literature values.

The upper boundary condition varies depending on the state of the top (zero) cell: specified flux if there is no surface ponding, or specified pressure (head) when there is surface ponding. The zero cell in the column is located above the ground surface, and a pressure is always specified for this cell. For a flux boundary condition, the pressure in the top cell is zero and the flux is added to cells via the source term, W. In the case of a head boundary condition, the pressure in the top cell is equal to the depth of ponded water, and water that enters the top cell is infiltration.

Infiltration at the land surface is controlled by K, which is dependent on the soil moisture. For a flux boundary condition the cell-centered value of the first cell (cell below the zero cell) is used. If ponding occurs, the cell-centered value may be used, or K at the soil surface may be assumed to be the saturation value (Ks), or an average of Ks and the cell-centered value. The use of these alternatives to the cell-centered method may allow the use of larger cell sizes in the unsaturated zone without seriously affecting calculated hydrologic fluxes (Downer and Ogden, 2003).

Three different lower boundary conditions can be specified. When the effect of the water table on processes in the upper soil column is negligible the lower boundary condition is a zero head gradient. The lower boundary can also represent a water table located a fixed distance from the soil surface, and the last cell is placed at the saturated groundwater table. The head at the top of the cell is zero, and the head at cell’s center is positive. In the third case, the groundwater table elevation is allowed to vary, and the size of the last non-boundary cell and the number of cells changes as the water table rises and falls. Complete details

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of implementation of RE in GSSHA can be found in Downer (2002) and Downer and Ogden (2004a,b).

1.2.3.2 Green and Ampt-Based Methods

There are three optional GA-based methods to calculate infiltration for Hortonian basins: (1) traditional GA infiltration, (2) multilayer GA, and (3) GAR. While the simple GA method has been shown to be useful for simulating infiltration in many soils, extension of the GA model to three soil layers allows several important common natural phenomena such as layered soils, non-uniform initial soil moistures, surface crust, lenses, and high water tables, to be treated with a similar, simple approach. The traditional GA and multilayer GA approaches are used for single-event rainfall when there are no significant periods of rainfall hiatus. The GAR approach is used when there are significant breaks in the rainfall, or for continuous simulations. The GAR method expands the capability of GA by redistributing soil moisture during periods of no- or low-intensity rainfall. This allows infiltration capacity to recover for the next burst of storm intensity, and makes the GAR method suitable for simulating multiple rainfall events in series. To accommodate the coupling of the unsaturated and saturated zones the implementation of GAR in GSSHA is slightly different than in CASC2D. In GSSHA GAR infiltration does not stop at the end of events; rather, infiltration ceases when the overland flow cells are dry.

Formulation and application of the GA model is well described in other sources (e.g., Maidment, 1993) as well as the GAR method (Ogden and Saghafian, 1997). The GA models as implemented in GSSHA are described in Ogden and Julien (2002). Formulation, solution, and application of the multi-layered GA model as applied in the GSSHA model are presented in the GSSHA User’s Manual (Downer and Ogden, 2004c).

1.2.4 Evapotranspiration

Senarath et al. (2000) demonstrated the need for computing initial soil moistures for predictions of episodic runoff. ET represents a major source of soil water loss. In GSSHA potential evapotranspiration (PET) may be computed using two different options: bare-ground evaporation from the land surface using the formulation suggested by Deardorff (1978), and ET from a vegetated land surface using the Penman-Monteith equation (Monteith, 1975).

Variants of these two representations are widely used in land-surface schemes of climate and distributed hydrologic models (e.g., Dickinson et al., 1986; Beven and Kirkby, 1979). The ET calculations used in GSSHA have been described elsewhere (Senarath et al., 2000; Ogden and Julien, 2002). In general, the Penman-Monteith method is most suitable for vegetated watersheds as it accounts for vegetation shading, wind resistance, and transpiration through leaves.

In the northern hemisphere temperate zone ET is subject to strong seasonal variations due to changes in climatic conditions and the vegetative cover. The seasonal variability of climatic conditions is reflected in the model with the hourly hydrometeorological inputs (Senarath et al., 2000). In GSSHA vegetative

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cover is represented with simple land use/land cover indexes, such as forest, pasture, etc. Senarath et al. (2000) determined that the distributed, watershed-scale application of the Penman-Monteith equation is most sensitive to the value of canopy resistance, and is quite insensitive to the other model parameters.

Since leaf area and canopy resistance can vary by several hundred percent over the course of the year for crops, grasses, and deciduous forest in temperate regions (Monteith, 1975; Doorenbos and Pruitt, 1977; Federer and Lash, 1978), seasonal vegetative variability is incorporated into GSSHA by varying the canopy resistance. Mid-growing season values of canopy resistance are input.

For each month an amplification factor is used to represent the change in the canopy resistance related to plant growth and dieoff. Downer and Ogden (2003) describe both the details of the method and the resulting improvements in predictions of soil moisture and outlet discharge for periods outside the growing season at the Goodwin Creek Experimental Watershed (GCEW) in north Mississippi.

Regardless of the method used to calculate potential ET (PET), the actual ET (AET) is computed from the PET by adjusting the PET for the soil moisture in each cell. How this is done depends on the method used to simulate the soil column as described in the next section.

1.2.5 Soil Moisture Accounting

If a uniform soil column is simulated with GAR as the selected infiltration method, then the bulk soil moisture from the specified root depth is used to adjust the ET as described by Ogden and Julien (2002). Soil moisture accounting begins at the end of the rainfall event, when the outlet discharge falls below a user-specified amount. The bulk soil moisture is computed as the total amount of soil moisture in the specified root depth at the end of a rainfall event.

This soil moisture is reduced hourly by the AET to compute the initial soil moisture to be used at the beginning of the next rainfall event. Soil moisture is adjusted due to AET only. Even though some small amount of water may remain on the overland flow plane, flowing and infiltrating, this does not affect the soil moisture accounting calculations.

When RE is chosen to simulate the soil column any water ponded on the surface of a cell is used to satisfy all or part of PET. Any water ponded on the land surface is reduced by PET. Any remaining PET demand is then applied to the unsaturated zone down to the specified root depth. AET is removed from the cells in the root zone in proportion to the size of each vertical computational cell. Similar to the methods used by Ogden and Julien (2002) for GAR, AET is calculated from PET using the relationship when θwp ≤ θ ≤ 0.75 θs wilting point water content. AET equals PET when θ > 0.75 θs, is increasingly

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less than PET as the soil approaches θ_s, and becomes zero at the θ_wp. The AET for each cell is added to the source term, W, in the RE solution (Equation 6.1).

1.2.6 Snowmelt

Precipitation that occurs at air temperatures below 0°C is added to a snowpack in each cell. The water in the pack becomes available for infiltration and runoff as it melts. The simplest representation of the snowpack is used; each 80 calories of heat added to the snowpack results in the release of 1 cm³ of meltwater (Linsley et al., 1982; Gray and Prowse, 1993). Hourly values of hydrometeorological variables allow both seasonal and diurnal variations in climatic conditions to be included in the heat balance. The amount of heat, H (cal cm^-2 hr^-1), available is computed from the components of the energy balance. In GSSHA the following components are accounted for: net radiation, heat in precipitation, heat transferred by sublimation and evaporation, and sensible heat transfer due to turbulence.

Precipitation accounts for the greatest addition of heat to the simulated snowpack. For nonprecipitation periods the net radiation is typically the dominant source of energy for melting of the snowpack (Gray and Prowse, 1993). The net radiation is computed using Stefan-Boltzmann’s law, with the assumptions that incoming radiation can be computed from the ambient temperature, Ta (C), and outgoing radiation is computed assuming the snowpack is at 0°C (Bras, 1990). The reader is referred to Downer (2002) and Downer and Ogden (2004a, c) for more details.

1.3 Integrated Processes