3.2 THE PITMAN MODEL
3.2.1 Structure of the GW-Pitman Model
The modified version of the model used in this study is known as GW-PITMAN and the main difference from the original model is that it incorporates explicit groundwater fluxes. It also includes a number of storages such as rainfall interception and soil moisture and model accounts for the dominant hydrological processes such as infiltration, evapotranspiration, surface runoff, soil moisture runoff and groundwater recharge. These processes are presented as a conceptual model structure in Figure 3.2. The methods for simulating the individual processes and the associated parameters have been presented many times in the literature and are summarised in the following sub-sections. The model requires monthly precipitation and potential evapotranspiration as input data for each sub-basin.
46 Figure 3.2 Flow diagram representing the structure of the modified Pitman model
(Source: Hughes et al., 2006a) 3.2.2 Parameters and Conceptual Functions
In attempting to represent known hydrological processes, together with possible water uses, the Pitman model has a total of 40 parameters. Of these, 28 influence the natural catchment hydrological response, while others are related to water use and abstraction. The 28 parameters represent the surface, sub-surface, groundwater processes as well as flow routing (Table 3.1) and some (PI1, PI2, ZMIN) can be seasonally variable. Each sub-basin in the distribution system has its own parameter set.
47 Table 3.1 Parameters of the Pitman model.
Parameter Units Parameter Description
RDF - Rainfall distribution factor
AI - Impervious fraction of sub-basin
PI1, PI2 mm Interception storage for vegetation types (2)
AFOR % Percentage area with vegetation 2
FF - Ratio of potential evaporation rate for veg2 relative to veg1
PE mm/year Annual potential evapotranspiration
ZMIN mm/month Minimum sub-basin absorption rate ZAVE mm/month Average sub-basin absorption rate ZMAX mm/month Maximum sub-basin absorption rate
ST mm Maximum storage capacity
SL mm Minimum moisture storage below which no GW recharge occurs
POW - Power of moisture storage-runoff Equation
FT mm/month Runoff from moisture storage at full capacity
GPOW - Power of moisture storage in GW recharge Equation
GW mm/month Maximum groundwater recharge
RIP % Controls the riparian evaporation losses from GW storage
R - Evaporation-moisture storage relationship
TL month Lag of surface and soil moisture runoff
CL month Channels routing coefficient
D DENS km/km2 Drainage density
T m2/day Transmissivity
S - Storativity
GW Slope - Initial groundwater gradient
RWL m Groundwater rest water level
Rainfall distribution Factor (RDF)
The rainfall distribution function accounts for the distribution of total monthly rainfall over four model iterations. The function depends on both rainfall amount and the value of the RDF parameter. Lower values of this parameter indicate a more even monthly rainfall distribution.
The original model (Pitman, 1973) had a fixed value of 1.28.
Interception (PI1, PI2)
This function is used to represent the amount of rainfall intercepted by vegetation cover. The interception function is controlled by the interception parameters, PI, which are allowed to vary seasonally to cater for changes in vegetation cover throughout the year. Two different types of vegetation (PI1 and PI2) can be used to account for major vegetation differences and specifically to allow for managed forest plantations.
48 Surface runoff (AI, ZMIN, ZAVE, ZMAX, ST)
In the Pitman rainfall-runoff model, surface runoff is conceived as being generated in three ways: i) from an impermeable surface (AI), ii) when the rainfall amount is higher than the absorption capacity (ZMIN, ZAVE, ZMAX), and iii) when the maximum soil moisture storage (ST) is exceeded. The soil absorption capacity is controlled by a triangular distribution function defined by ZMIN, ZAVE and ZMAX.
Soil moisture storage and runoff (ST, FT, POW)
The depth of runoff from the soil moisture storage is determined by a non-linear relationship between runoff and relative storage. The power of this relationship is defined by POW, while FT represents the maximum runoff rate (mm month-1) at maximum soil moisture storage (ST).
Groundwater Recharge (ST, SL, GW, GPOW)
The groundwater recharge function uses a similar non-linear relationship as the soil moisture runoff function, with GW representing the maximum monthly recharge rate (mm month-1) at ST and GPOW the power of the relationship. Parameter SL is the soil moisture storage level (mm) at which recharge ceases.
Evaporation from the soil moisture storage (ST, PE, R)
The annual potential evaporation parameter (PE) is distributed into 12 monthly mean values (an additional model input). The actual evapotranspiration in any month is determined as a function of the current soil moisture storage level (relative to ST), the current monthly potential evapotranspiration value relative to the maximum monthly values and parameter R. R ranges from 0 to 1, where 0 implies higher evaporation that continues to low moisture storage levels.
When R is 1, evaporation ceases at progressively higher moisture levels as the monthly potential evapotranspiration decreases. Low values of R therefore imply shallow rooting depths and less effective evapotranspiration.
Groundwater storage and discharge (S, T, DDENS, GW Slope, RWL, RIP)
Hughes (2004) describes the relatively simple geometry approach used to determine groundwater storage and discharge to the river. Groundwater recharge inputs, drainage outputs to the river, drainage to downstream catchments and evapotranspiration losses from the riparian strip (RIP) are used to update the assumed gradient of groundwater within a sub- basin. When the gradient is positive drainage to the channel occurs and is calculated from the gradient, transmissivity (T) and channel length (derived from sub-basin area and drainage density). When negative gradients occur, riparian strip evapotranspiration and downstream
49 drainage are progressively reduced until groundwater storage reaches the level equivalent to the rest water level. Transmission losses from upstream channel flows can occur when the gradient is negative. More details can be obtained from Hughes (2004a) and Tanner (2014).