Geography Reference
In-Depth Information
Table 5.1. Dimensionless numbers for pore-water dominated hydrology at long time scales
Dimensionless
groups
Dimensionless number
Interpretation
Application
Climate
E
p
/P
Aridity index, R
Ratio of average demand for
moisture to average supply of
moisture
Approximate water balance
(e.g., using Budyko curve)
|
δ
p
−
R
δ
E
|
Seasonality index, S
Amplitude of the seasonal cycle of
precipitation minus potential
evaporation
Seasonal pattern of atmospheric
moisture surplus/deficit
Canopy and
soil
w
cm
/(P/N)
Canopy storage index,
W
c
Ratio of canopy storage to
characteristic rainfall event depth
Throughfall
k
τ
e
/(P/N)
Relative infiltration, K
Ratio of characteristic infiltration
rate to characteristic rainfall
event rate
Infiltration excess
w
rm
/P
τ
Rootzone storage index,
W
r
Ratio of soil water storage capacity
to annual rainfall
Seasonal filling of soil moisture
deficit
Saturated flow
DL/
(T
o
tan
βτ
)
Advection response
index, t
o
Ratio of travel time for advective
signal to duration of seasonal
forcing
Responsiveness of lateral
subsurface flow
T
o
tan
β
/LP
Relative transmissivity,
T
Ratio of maximum lateral outflow to
characteristic water input rate
Depth to water table
—
Slope of topographic
index distribution,
ω
Rate at which saturated area expands
Saturation excess runoff
Climate variables: mean annual precipitation, P; mean annual potential evaporation, E
p
; dimensionless amplitudes of precipitation
and potential evaporation,
δ
P
,
δ
E
; number of rain events per unit time, N; duration of annual cycle,
τ
; characteristic duration of
rainfall event,
τ
e
.
Canopy and soil variables: average interception storage, w
cm
; mean saturated hydraulic conductivity at surface, k; rootzone water holding
capacity, w
rm
.
Saturated flow variables: depth to bedrock (or aquifer thickness), D; length of hillslope (or other relevant flowpath), L; transmissivity, T
o
;
slope of topography (or head gradient), tan
β
.
After Woods (2003) and Wagener et al. (2007).
homogeneity tests for the index flood method. Dalrymple
(
1960
) proposed a test, described in several classic text-
books (e.g., Chow,
1964
), to assess flood homogeneity by
analysing the variability of the maximum annual flood peak
CV and/or skewness (CS) across multiple sites (see also,
among others, Lettenmaier et al.,
1987
; Stedinger and Lu,
1995
; Hosking and Wallis,
1997
). Viglione et al.(
2007b
)
compared the power of several homogeneity tests and Cas-
tellarin et al.(
2008
) showed how the cross-correlation
among sites can affect the performance of the tests.
In this topic, the term homogeneity is used in a still more
comprehensive way, to mean that a single model structure
can be used to describe variability across a group. For
example, a group of catchments could be considered homo-
geneous if a single regression model, parameterised with
different catchment characteristics, can capture the variabil-
ity of a hydrological signature of interest for the group. If
geostatistical methods are being applied, then the assump-
tion that a given spatial correlation structure is valid for a
given study area effectively enforces homogeneity within
that study area (a single model of the correlation structure
can describe the spatial variability). Where process-based
methods are used, a group of catchments are hydrologically
homogeneous (similar) if the same dominant processes
drive the behaviour of all the catchments (Wagener et al.,
2007
). For instance, the assumptions of the derived distri-
bution approach might hold across a homogeneous group,
or a given model structure of a rainfall
runoff model might
apply to all the catchments under consideration.
Chapter 10
will deal with regionalisation of model parameters
-
for this
approach to be valid the model structure must be fixed for
the whole region: that is, the region must be hydrologically
homogeneous in terms of model structure. Although this
comprehensive idea of hydrological homogeneity (similar-
ity) is not rigorously statistically defined, it is very useful in
practice and will appear throughout this topic.
When grouping catchments, there is a trade-off between
hydrological homogeneity and the size of the group.
Larger pooling groups improve the reliability of estimates
made for a target catchment, to the extent that the pooling
-
Search WWH ::
Custom Search