SECCION 4“ De los defensores públicos.

In contrast to the Lancaster D BM model, the IHACRES model (see e.g. Jakem an and H om berger 1993) utilises a conceptually form ulated nonlinear m odule, which exploits a catchm ent wetness index derived from past rainfall and w here appropriate, tem perature data, to obtain effective rainfall. The IHACRES model is a slightly m odified version of the rainfall-flow model first developed by Young and W hitehead from studies modelling the Bedford-Ouse River (Young, 1974; W hitehead and Young,

1975; W hitehead et a l , 1979; and Young 1984). Young and W hitehead introduced a

conceptual ‘rain filter’ to derive effective rainfall which incorporates the effects of soil m oisture and temperature dependent evapotranspiration, encapsulating the theory that rainfall, falling on a wet catchment, will generate a larger flow than if the catchm ent is dry. The ‘rain filter’ first adjusts rainfall r ( k) to account for evapotranspiration losses

using a tem perature dependent factor. The adjusted rainfall series r * ( k) is then

m ultiplied by a running catchment wetness index s ( k) , which itself, is derived from

past rainfall (and temperature) data. Although data from a num ber of catchments have been successfully m odelled utilising this ‘rain filter’ (see e.g. Jakem an et al., 1990a;

1993), it does, however, have a conceptual weakness: in the absence of rainfall, the ‘rain-filter’ does not directly allow for any evapotranspiration losses from the

catchm ent. This shortcoming has led to the derivation of a num ber of more

conceptually acceptable rain-filters. The basic IHACRES nonlinear loss module

calculates effective rainfall ue( k) by multiplying the catchm ent wetness index s ( k ) by

the m easured rainfall r ( k) as defined by equations (4.11-4.14),

s( k) = c r { k) + (1 - 1 / Tw) s (k - 1) ( 4 .1 2 )

The catchm ent wetness index (i.e. soil m oisture content) s ( k) is obtained at each time

step k (k = 1 ,2 ,...,TV) from an exponentially decaying w eight o f rainfall r ( k) at

previous tim e instants. The decreasing influence of past rainfall episodes on s ( k) can

be clearly shown in the full expansion of equation (4.12), where the term ( 1 - T W-1) N gets sm aller with time,

s (k) = c \ r( k) + ( \ - T ~ 1) r ( k - \ ) + ( l - T ~ ' ) 1r { k - 2 ) + — \ - ( I - T ~ ' ) Nr ( k - W)] (4.13)

Param eter Tw is a time constant representing the decay rate o f the catchm ent wetness

(or soil m oisture) in the absence of rainfall. The soil properties o f the catchm ent are

controlled by this parameter; the low er the value of Tw the faster the catchment

responds to the processes of wetting and drying and vice versa. Furtherm ore, in clim ates where evapotranspiration rates significantly influence the catchm ent wetness

dynam ics, the coefficient Tw, can be assumed to vary as a function of temperature

Tw(t(k)) is, therefore, inversely related to the decline rate o f the catchm ent wetness at

20° C , m odulated by param eter / . The values of param eters Tw and / are obtained

through objective optimisation, but the value of param eter c is selected such that the

total volum e of effective rainfall is equal to the total volum e o f discharge over the calibration period. For short time series, where changes in tem perature are not of

m .

sufficient m agnitude to cause any significant evapotranspiration effects, this extra term

Tw (t ( k)) can be held constant.

A dditional conceptualised versions of this nonlinear loss m odule have been designed to include additional com plexities, for example, to account for interception of incident precipitation by tree cover (Jakeman et a l 1994; Chen et a l , 1995). H owever, the

m odule described by equations (4.11-4.14) is adequate for the purposes of the present study.

4 .3

M

C

In the research to date, the efficiency of the effective rainfall m easure ue( k) in both

the Lancaster D BM and the IHACRES models has only been evaluated in relation to the perform ance of the models as a whole. In this section, this aspect of the model is evaluated m ore directly by com paring the surrogate soil m oisture measures with the actual antecedent dynamics measured at the Swiss catchment.

4.3.1 The Data

The data used in this research has been collected from the narrow Erienbach catchm ent situated in the Swiss pre-Alps by the Soil Physics Group at ETH, Zurich, as part of the on going NITREX project studying the effects o f nitrogen addition to small catchm ents (W right et a l , 1995). Erienbach is situated at 1200m a.s.l with a total area

of 0.7km 2 of which approximately 40% is forested and 60% is w etland and has an average total yearly precipitation of 2300mm.

T w o data series (D ata Series 1 and 2 ) have been collected from a muck humus soil plot

with an approximate area o f 15m2, representing one o f two soil types which characterise the catchment. The input and state variables measured at the plot scale are, rainfall r { k) ; flow y { k ) \ percentage soil w ater content p w c ( k ) \ and ground

w ater table depth g w { k ) . Where p w c ( k) and gw {k) w ere derived from

measurements made by sixteen soil moisture probes (TDR) and three piezometers respectively. A photograph o f the soil moisture probes in situ is shown in Figure 4.1.

The sampling interval for each state was 10 minutes although average hourly readings have been used in the analyses reported in this chapter.

Figure 4.2 shows the input and state variables from D ata Series 1. The im mediate response to rainfall inputs can be observed in both soil w ater m easurem ents p w c ( k)

and gw (& ). Sim ilar responses are observed in D ata Series 2 as shown in Figure 4.3.

Rainfall

3 3

0 100 200 300

Soil Moisture Content 055r 0.45* 0.4 200 0 100 300 Hourly Samples Runoff 3 3 0 100 200 300

Groundwater Table Depth

3 15 300 100 Hourly Samples 200 Samples

Figure 4.2.

1.

Rainfall Runoff 20 15 10 5 0 100 200 300 400 500 0 8 6 2 0 100 200 300 400 500 0

Soil Moisture Content Groundwater Table Depth 0.5 0.45 0.4 # 0.35 0.3 0.25 0.2 100 200 300 400 500 Hourly Samples 40 35 30 25 20 15 10 5 100 200 300 400 500 0 Hourly Samples

There is, however, some doubt over the quality of the soil m oisture content data in

D ata Series 2. The timing and the dynamics of this tim e series do not appear

consistent with rainfall, flow and depth to groundw ater table data. Episodes of rainfall result in a decrease in soil moisture content which clearly, m akes no physical sense.

Consultation with H. Feyen (pers. com.) from the Soil Physics Group, ETH,

highlighted that the soil m oisture content m onitoring equipm ent had m alfunctioned during this tim e period. Consequently, this percentage soil m oisture content time series (Data Series 2) was disregarded for use within the m odelling study. The next two sections utilise the Erienbach catchment data to identify and estim ate both the

Lancaster D BM and IHACRES nonlinear rainfall-flow models. The identified

surrogate soil m oisture series is then com pared to the percentage soil m oisture content

p w c ( k ) and depth to groundw ater table gw(Jc) variables.