Period Model Order
5.2.3 Rainfall-Flow Modelling and Evapotranspiration
The effects of evapotranspiration on the rainfall-flow system have so far been regarded as inconsequential at W yresdale and have been im plicitly accounted for within the
structure of the model by the nonlinear effective rainfall com ponent. The w ater
balance derivation clearly indicates, however, that evapotranspiration is significant along with groundw ater losses at W yresdale, suggesting that evapotranspiration may need to be explicitly accounted for within the model.
Research from the Cow eeta catchment, USA, by Young and Beven (1994) and Young
et al., (1997) dem onstrated that the residuals of the rainfall-flow model show high
correlation with the mean daily temperature series, which in turn may be used as an indicator of actual evapotranspiration. Consequently, an im proved m odel fit can be achieved by developing a m ulti-input-single-output (M ISO) form of the rainfall-flow m odel, where the mean daily temperature series is introduced as an input to an additional linear TF.
In a sim ilar m anner, the residuals o f the estim ated rainfall-flow m odel were exam ined and are presented in Figure 5.4a. The daily tem perature series, m easured at Lancaster U niversity H azelrigg w eather station (7 km from W yresdale), corresponding to the two year tim e period of m easured data are presented in Figure 5.4b. Visual inspection of both series indicates that no obvious correlation is evident between them , which has
been confirm ed from numerical correlation analysis. This indicates that further
developm ent of the W yresdale model to include a tem perature com ponent is not required; clearly in this temperate upland catchm ent the tem perature forcing on evapotranspiration is not sufficiently strong to exert a strong influence on the overall catchm ent dynamic. W hilst this prevents the m odel from being developed in this regard, the data have, in fact, been thoroughly and objectively analysed and the inform ation utilised to its practical limits to produce the best rainfall-flow model from the available but rather limited data.
SRIV Estimated Model Error 0.03 0.02 £ n 0 S - 0 .0 1 -0.02 -0.03 0 100 200 300 400 500 600
S caled and Inverted Tem perature
S - 0 . 5
-1 .5
0 100 200 300 400 500 600
Days
Figure 5.4
(a)SRIV
estim ated m odel residuals 15/05/1994 - 01/02/1996, (b) Daily tem perature (instantaneous m easurem ent at 0900h), m easured at the LancasterU niversity H azelrigg w eather station for the corresponding time period.
5 .3 S
u s p e n d e dS
e d im e n tL
o a dM
o d e l l i n gThe key com ponent underpinning the DBM m odelling study of reservoir sedim entation at W yresdale, is the identification of a model relating rainfall to stream SSL at the reservoir inflow. W hilst a great deal of research has been directed at m odelling the rainfall-flow process, research into m odelling fluvial suspended sedim ent transport is still in a stage of com parative infancy. This is in part due to the difficulties in obtaining rainfall, flow and SSL data of sufficient quality, but also due to the underlying com plexity of the many nonlinear processes that com bine to control
transport is dependent upon the action of catchm ent hillslope processes, such as rill and gully developm ent and mass movements (Selby, 1993). Further, the sediment transport capacity of a stream is strongly flow dependent, w hich in turn is an inherently nonlinear process. It follows, therefore, that a m odel m ust account for these nonlinearities to successfully characterise catchm ent sedim ent transport.
C urrent m ethods o f prediction fall into two main categories. Firstly, determ inistic
m odels such as CREAM S (Knisel, 1980) and ANSW ERS (Beasley et a l , 1980) that
aim to capture the physical com plexity of sedim ent supply and delivery processes. These determ inistic models are often over-param eterised and require substantial field data for calibration. Secondly, simple nonlinear regression m odels between flow and SSL are often unable to adequately reproduce the dynamic nature o f fluvial systems and are, therefore, really inappropriate for m odelling suspended sedim ent (W alling, 1977). The short-comings of both techniques can be addressed, to some extent, by using transfer functions which are both dynamic and parsim onious in nature. Sharma
et al., (1979), Sharm a and Dickinson, (1980), Lem ke (1990; 1991) and W ang et a l ,
(1991), for exam ple, successfully utilise linear transfer functions for modelling suspended sedim ent load where flow is used as the model input.
U sing data obtained from 5 catchments situated within the Loess Plateau of China,
W ang et a l , (1991) successfully adopted linear T F ’s to model suspended sedim ent
load. D ue to the particular physiographic characteristics of the Loess Plateau,
sedim ent yield in this region is strongly transport dependent. The m ajority of rainfall in this region, derived from high magnitude short duration storms occurring in the sum m er m onths, is converted directly into runoff, with little lost to groundwater. As a
result, the relationship between runoff and sedim ent yield is very strong and a linear
TF is sufficient to characterise the dynamic. Sharm a et al., (1979), Sharm a and
D ickinson (1980) and Lemke (1990; 1991) both identified a linear TF m odel between log transform ed runoff and log transform ed SSL time series. As a consequence of log transform ing the data, they found that the nonlinear relationship existing between the two series had been partially linearised, to the extent that a linear TF was satisfactory to explain the behaviour within their study catchments.
The W yresdale catchm ent is particularly flashy and the rainfall-flow and flow -SSL relationships are inherently nonlinear. A lthough a linear m odel is able to approxim ate the rainfall-SSL relationship during wet conditions, it is unable to fit the data well during periods o f low flow. Consequently, for the purposes o f reconstructing the catchm ents SSL series, a hindcasting model with a nonlinear structure is required.