Geoscience Reference
In-Depth Information
6.2 The Probability Distributed Moisture (PDM) and Grid to Grid
(G2G) Models
In many ways, the PDM model is a simple extension of some of the lumped storage models developed
in the 1960s (and later) to the case of multiple storages representing a spatial distribution of different
storage capacities in a catchment. It is a logical extension, in that we would expect that a distribution of
storages might be a better representation of the variability in the catchment than simple lumped storage
elements. However, in the original form outlined by Moore and Clarke (1981), the model makes no
real attempt to relate the distribution of storages to any physical characteristics of the catchment. In
fact, one of their main reasons for introducing a distribution of storages was to make the calibration
problem easier since they found that they obtained smoother response surfaces for their new model
formulation in comparison with models based on ESMA-type storage elements lumped at the catchment
scale. A smoother response surface, in general, makes it easier for an automatic parameter optimisation
routine to find the best fitting set of parameter values (but see the discussion of parameter calibration
in Chapter 7).
The basic idea of the PDM model is illustrated in Figure 6.1. The multiple storage elements are
allowed to fill and drain during rainstorm and interstorm periods respectively. If any storage is full
then any additional rainfall is assumed to reach the channel quickly as storm runoff. A slow drainage
component is allowed to deplete the storages between storms, contributing to the recession discharge in
the channel and setting up the initial storages prior to the next storm. Evapotranspiration is also taken
from each store during the interstorm periods.
In any storm, clearly those stores with the smallest storage capacity are filled first and start to produce
rapid runoff first. Each storage capacity is assumed to represent a certain proportion of the catchment
so that, as the stores fill, the proportion of the area producing fast runoff can also be calculated. This
area expands during rainstorms and contracts between rainstorms so that, in essence, the distribution
P
Surface storage
q
Surface runoff
S
s
2
E
Q
S
1
Recharge
q
b
S
3
Baseflow
Distribution of S
1
storage capacities
Groundwater storage
p(S)
S
Figure 6.1
Structure of the Probability Distributed Moisture (PDM) model.
