ENVIRONMETRICS, VOL. 6,465-472 (1995)

DYNAMIC RESPONSE CHARACTERISTICS OF THE PLYNLIMON CATCHMENTS AND PRELIMINARY

ANALYSIS OF RELATIONSHIPS TO PHYSICAL DESCRIPTORS

C. E. M. SEFTON, P. G. WHITEHEAD, A. EATHERALL AND I. G. LITTLEWOOD Insriture of Hydrology. Crowmarsh Gifford, Wullingford, OX10 8BB, UK

AND

A. J. JAKEMAN Cenlre.for Resource and En~ironmental Studies, Australian National University, Canberra, ACT 0200, Australia

1. INTRODUCTION

Assessment of the impacts of environmental change on hydrological systems at regional or national scale requires a modelling technique capable of spatial extrapolation. Few such techniques, providing a regional or national picture of hydrological impact, are currently available. The proposed regionalization methodology, outlined in Jakeman et al. (1992), is being applied to up to 100 gauged UK catchments of various size, geology, topography and climate using a rainfall-runoff model IHACRES (a program for Identification of unit Hydro- graph And Component flows from Rainfall, Evapotranspiration and Streamflow data). Dynamic response characteristics (DRCs), such as the proportion of slow flow, identified by the model are being related to physical catchment descriptors (PCDs) such as soil type, slope and area, obtained from a geographical information system (GIs). Extrapolation to ungauged catchments should then be possible and the resulting hydrological GIS of the UK would allow spatial analysis of the hydrological impact of environmental changes in climate and land use.

This paper presents a preliminary application of the methodology using the Plynlimon experimental catchments in central Wales for which good hydrological and physical descriptor records exist. Eight catchments are modelled: the headwaters of the Wye and Severn rivers and the three main subcatchments of each, the Gwy, Cyff and Iago and Hafren, Hore and Tanllwyth, respectively. Relationships between DRCs and PCDs are investigated and interpreted in the context of the wider project.

2. THE PLYNLIMON CATCHMENTS

2.1. Site description and data

Figure 1 shows a map of the study site which has a total area of 19.25 km2. The Plynlimon landscape is dominated by rolling hills dissected by steep valleys. It has an altitude range from 319m to 738mODN and the majority of land slopes are below 15". The geology of the main

CCC 1 180-4009/95/050465-08 0 N.E.R.C.

466 C. SEFTON ET AL.

0 Major flow gauging station

WYE CATCHMENT

Figure 1. The Plynlimon catchments

catchments is similar, comprising Palaeozoic grits, mudstones and shales. The predominant soil type is peaty with raw peat on the Plynlimon plateau of the upper catchments and free-draining earth in the lower Wye. The tributary streams, which flow largely over bedrock, are characterized by their steep gradients, heavy sediment loads and high flood/drought ratios. The catchments have a wet climate, receiving more than 2000 mm of rainfall a year, and geological evidence is that the catchments are watertight (Kirby et al. 1991). A full description of the physiography, vegetation and geology of the catchments is found in Kirby et al. (1991) and Newson (1976). Data for the modelling comprise time series of rainfall, streamflow and temperature. Daily, 12 hourly, 6 hourly and hourly time intervals were applied and 6 hourly chosen as a compromise between the short interval required to model a small, flashy catchment, and the problems of model identification associated with an excess of data.

2.2. Selection of PCDs

Selection of PCDs was based on likely significance, avoidance of highly correlated variables, accessibility of data for any UK catchment (Natural Environment Research Council 1975) and localized knowledge of Plynlimon. Four main groups of variables were expected to be significant in the national picture: size, topography, geology and drainage density (Natural Environment Research Council 1975). In the case of Plynlimon (Table I), by the above criteria and by inspection of results; catchment area was selected to represent size; channel slope, land slope and the skew of ln(a/ tan p) to describe topography; and stream frequency and ditching to describe the drainage. (The measure of ditching is required to complete representation of the drainage pattern of the Severn basins, in particular. The standard measurement of drainage ditching, to be used for the UK study, is too coarse to include drainage ditching.) Stream length and drainage density were omitted because of correlation with area and stream frequency, respectively. Soil type was selected in preference to geology since the catchments are geologically very similar (Kirby et al. 1991). A measure of land use, the 67 per cent forest cover of the Severn to 1 per cent

U

.c 2 5 7

Tab

le I.

Phy

sica

l cat

chm

ent d

escr

ipto

rs f

or th

e Pl

ynlim

on c

atch

men

ts

V

Mea

n la

nd

5 S1

085

Stre

am fr

eque

ncy

slop

e %

raw

pea

t Sk

ew

m

Are

a (k

m’)

(m/k

m)

(junc

/km

2)

(deg

rees

) %

fore

st

HO

ST 2

9 %

ditc

hing

ln

(a/ t

an 8

) 2 >

7

Seve

rn

8.70

63

.5

3.68

10

.2

67

32.4

29

1.

64

>

Haf

ren

3.61

59

.4

3.81

9.

0 48

56

.4

22

1.45

0

Hor

e 3.

08

70.5

4.

22

11.7

78

22

.6

25

1.60

;;j E

Tanl

lwyt

h 0.

89

109.

5 3.

37

8.6

100

6.3

12

1.14

m

r! G 7 3 E ? 5 Q i5

WY

e 10

.55

31.2

3.

19

10.6

1

4.8

6 1.

89

GWY

3.98

20

.3

4.52

11

.3

0 12

.7

3 1.

69

1.55

V

CY

ff 3.

13

21.6

3.

51

9.9

0 0.

0 7

Iago

1.

02

30.7

4.

90

10.1

3

0.25

5

1.54

S108

5: s

trea

m c

hann

el s

lope

mea

sure

d be

twee

n 10

per

cen

t and

85

per

cent

of

the

stre

am le

ngth

in m

/km

St

ream

freq

uenc

y: n

umbe

r of

stre

am ju

nctio

ns, a

s sh

own

on 1

: 25

000

map

, div

ided

by

catc

hmen

t are

a H

OST

cla

ss 2

9: r

aw p

eat f

rom

Hyd

rolo

gy o

f So

il Ty

pes

clas

sific

atio

n (B

oorm

an e

t al

. 199

5)

Yof

ores

t and

Yod

itchi

ng a

s at

198

4 In

(a/ t

an p

): a

topo

grap

hica

l ind

ex m

easu

ring

susc

eptib

ility

to s

atur

atio

n, w

here

a is

flow

acc

umul

atio

n an

d p

hills

lope

gra

dien

t (B

even

and

Kir

kby,

197

9)

0

z 2

468 C. SEFTON ET AL.

of the Wye, the remainder being grassland, completes the set of PCDs. The measures of forest, S1085 and ditching were drawn from previous Plynlimon studies ( k r b y et al. 1991), the other PCDs from GIS datasets of soil type (Boorman et al. 1995) and elevation (Morris and Flavin, 1990).

3. THE IHACRES MODEL

IHACRES is a lumped parameter rainfall-runoff model, first described in Jakeman et al. (1990), comprising two modules: a non-linear simple conceptual module which calculates rainfall excess from rainfall and temperature, and a linear model to convert rainfall excess to streamflow using a parametric unit hydrograph approach. Rainfall excess is that proportion of the rainfall that contributes to the volume of runoff. Streamflow separation is achieved by convoluting the rainfall excess with identified components of the unit hydrograph. Most commonly, two component flows are identified (Jakeman et al. 1991), quick and slow, and this is the configura- tion used in the Plynlimon study. The model has minimal data requirements, needing only time series of rainfall, streamflow and temperature, and is parametrically efficient, estimating a total of six parameters. A modified non-linear module, module 3 as described in Littlewood and Post (1 993), is used.

For a two component separation of the unit hydrograph, the linear module equations can be written

xz = -aqxi- 1 + P q U k

x i = -asxi- 1 + &Uk

Xk = x; + xi

(1)

(2)

(3) where U k is rainfall excess at time step k, x k is streamflow at time step k, a and p are model parameters (denoting unitgraph recession rate and peak, respectively), and s and q denote quick and slow components.

The dynamic response characteristics of the linear module are then derived as follows:

T, = -A/ In(-a,) T~ = -A/ ln(-as)

V, = Pq/[(l + aq)l

Iq = Pq

V, = PSA(1 + c-ys)l

4 = Ps where Vq + V, = 1 and A is the time series sampling interval.

T~ (7,) is the decay time constant of the quick (slow) flow hydrograph following a unit input of rainfall excess, Vq ( V,) the proportion, by volume, of water passing through the quick (slow) component and Iq ( I , ) the proportion that the quick (slow) component contributes to the peak of the total unit hydrograph.

4. RESULTS AND DISCUSSION

4.1. Selection of a calibration period

In order to minimize systematic or random variation of DRCs with time, modelling of the two main catchments to identify DRCs was preceded by selection of a subperiod, or subperiods, which best represented the catchments’ flow regimes. Ten subperiods were selected from a four year period of data, from 1980-83, covering a range of flow conditions, each subperiod starting and ending with low flow. For each subperiod, a model was calibrated and then validated on each

DYNAMIC RESPONSE CHARACTERISTICS OF PLYNLIMON CATCHMENTS 469

='O 1 I I

Severn Figure 2. Calibration model fits

of the other subperiods, and also on the whole four year period (data not shown) (Jakeman et al. 1993). Model fit (R2) and bias (as a percentage of streamflow variance and mean explained) were used as measures of model performance and hence two subperiods were selected (May 1980 to April 1981 and September 1982 to June 1983) as best representative of the catchments' flow regimes.

4.2. Inter-catchment variation in DRCs and DRC/PCD relationships

Following selection of the subperiods, models were calibrated for each of the catchments for both of the subperiods. Calibration model fits of observed to modelled streamflow were satisfactory, both for the Wye (mean R2 0.81) and the Severn (0.85). Calibrations for the Wye and Severn for November 1982/February 1983, are given in Figure 2 (Severn R2 0-85, Wye 0.81) and an example of hydrograph separation, for the Hafren 1980/1981 is given in Figure 3.

The dynamic response characteristics identified by the linear module in IHACRES for each calibration are given in Table 11. Plots demonstrated that although there is often a significant difference in DRC values between the two calibration periods, particularly for the Wye, inter- catchment patterns are maintained (Figures 4 and 5). Thus, although differences between

zo.ol

Figure 3. Hydrograph separation for the Hafren catchment

470 C . SEFTON ET A L

1

1.9

1.8

1.7

- 1 ::: 1.4

1.1

1.2

1.1

I

Table 11. Dynamic response characteristics for the Plynlimon catchments

- - ~

: - - - -

1980/198 1 1982/ 1983

T~ (x6hrs) T~ (x6hrs) V, 4 T~ (x6hrs) T~ (x6hrs) V, 4 Severn Hafren Hore Tanllwyth

WYe G W Y CYff Iago

1.69 1.73 1.46 1.23

1.44 1.35 1.30 1.46

39.3 0.26 0.020 37.1 0.34 0.030 53.2 0.25 0.012

125.8 0.21 0.004

31.7 0.27 0.022 34.4 0.26 0.019 25.7 0.31 0.031 72.4 0.11 0,003

1.81 1.57 1.52 1.42

1.18 1.22 1.14 1.33

45.5 0.28 0.019 34.1 0.41 0.040 59.4 0.27 0.013

225.0 0.24 0.003

24.7 0.41 0.046 31.4 0.33 0.027 19.7 0.37 0.047 73.1 0.33 0.013

Figure 4. Relationship between catchment area and 7,

0.05 ,

0 10 a0 Y) 40 Yl M nosrc lv l~ lp~uus COW)

+Sevcrn(1980/81) +Wye(1980/81) +Severn(1982/83) -o-wYe(1982/83)

Figure 5 . Relationship between I, and raw peat coverage

DYNAMIC RESPONSE CHARACTERISTICS OF PLYNLIMON CATCHMENTS 47 1

catchment DRCs are small (mean T~ for 1980/1981 1.458, standard deviation 0.18) they are significant in that they are not due to model error but to inherent differences in catchment response as manifest in the time series data. Values of V, for, say, 1982/83 for the 8 catchments (mean 0.33, SD 0.064) are comparable to those of base flow index (1976-84) found in Kirby et al. (1991) (mean 0.32, SD 0.038). Plots of DRCs against PCDs must be interpreted with care, both because of the small number of catchments modelled so far and the unforseeable or unavoidable correlations found between some fundamental PCDs, namely forest cover, channel slope and ditching. However, it may be conjectured that the quick time constants of the Severn catchments, in particular, are influenced by catchment size (Figure 4) and that the speed of flow decay (10.9 hours for the main Severn catchment, relative to the Wye 7.1 hours), reflects the effects of a forest canopy; interception and drier soil conditions. Of most note with the slow time constants is the unexpectedly slow response of the two smallest catchments, the Iago and the Tanllwyth, which may be because a 6 hourly time step is too long to capture the response of these catchments. This may be especially anticipated in the case of the Tanllwyth, where the dense network of drainage ditches would encourage a flashy response but where the total forest cover suggests another possible cause of a slow response, supported by the correlation coefficient of 0.64 between forest cover and the slow time constant.

With respect to the measures of hydrograph separation, V, and I,, for the Plynlimon catchments, much of the variation can be explained by the HOST classifications. Figure 5 shows the relationship between Z, and HOST class 29, which represents the blanket peat on the Plynlimon plateau. The peat is underlain by drift deposits which fieldwork has shown to sustain low flows (Kirby et af. 1991). As the peat cover increases, so does the contribution of the slow component of streamflow, suggesting input from such a source. The relatively high Z, of the Wye and its Cyff subcatchment would then be explained by their partial coverage by free-draining brown earth which would produce a less flashy response than the peaty soil covering the bulk of the site. In addition to pedological effects, correlations of -0.92 (1980/1981) and -0.98 (1982/ 1983) between Z, and stream frequency for the Wye indicate that a dense network of streams will decrease the slow flow contribution to streamflow.

The catchments are similar in geology, topography and climate, which prohibits quantitative methods of analysis of DRC/PCD relationships without reference to the wider picture involving many, more varied catchments. This is demonstrated in Figure 6, where the relationship between V, and the skew of ln(a/ tanp) is investigated for a range of catchments (Whitehead and Hornberger, personal communication). The Plynlimon catchments fall in a limited area and do not, alone, demonstrate the correlation revealed by a wider range of catchments. When many more catchments have been modelled, use of quantitative analysis techniques such as principal

C

Q *5 2 Llyn Brianne (CIS)

3 Coweeta 36 6.00 4Coweeta34

MoMchy[e

2.00 4.00 skew of In (altanp) distribution

* 5 2 LL Brianne IC16) - -. ,.- - ~ . . I I I 3 Coweeta 36

skew of In (altanp) distribution MoMchy[e 6.00 4Coweeta34 2.00 4.00

6 KiMon oPlynlimon Catchments

Figure 6 . Relationship between V, and topography

472 C. SEFTON ET A L

components, regression and the Karhunen-Loeve transformation (Whitehead and Young, 1979; Kittler and Young, 1973), will be valid.

5. CONCLUSIONS

For each of the eight Plynlimon catchments, IHACRES was calibrated for two separate periods. Inter-catchment relationships between physical catchment descriptors and dynamic response characteristics of the linear module for 1980/ 198 1 were generally substantiated by the 1982/ 1983 calibrations. Qualitative analysis of the relationships was complicated by correlation of some PCDs, but area, topography, soil type and land use were found to explain much of the variation in DRCs. Quantitative analysis techniques such as principal components analysis, which would address the problems of correlation, are, however, not meaningful with so few data points, particularly as they represent very similar catchments. Such methods will be used when many, more varied catchments have been modelled and relationships found may be extrapolated to allow determination of the hydrology of ungauged catchments, given a set of PCDs.

REFERENCES

Beven, K. J, and Kirkby, M. J. (1979). ‘A physically based variable contributing area model of basin hydrology’, Hydrological Sciences Bulletin 24( l), 43-69.

Boorman, D. B., Hollis, J. M. and Lilly, A. (1995). ‘Hydrology of Soil Types; a hydrologically based classification of the soils of the U K . Institute of Hydrology Report No. 126, Wallingford, Oxfordshire.

Jakeman, A. J.. Chen, T. H., Post, D. A,, Hornberger, G. M., Littlewood, I . G. and Whitehead, P. G. (1993). ‘Assessing uncertainties in hydrological response to climate at large scale’, Macroscale Modelling of the Hydrosphere. Proceedings of the Yokohama Symposium, IAHS Publication No 214, W. B. Wilkinson (ed)

Jakeman, A. J., Hornberger, G. M., Littlewood, I. G., Whitehead, P. G., Harvey, J. W. and Bencala, K. E. (1992). ‘A systematic approach to modelling the dynamic linkage of climate, physical catchment descriptors and hydrological response components’, Mathematics and Computers in Simulation, 33,

Jakeman, A. J., Littlewood, I . G. and Symons, H. D. (1991). ‘Features and applications of IHACRES’, in Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, R. Vichne- vetsky and J. Miller (eds) Dublin, Ireland. Vol. 4, pp. 1963-1967.

Jakeman, A. J., Littlewood, I. G. and Whitehead, P. G. (1990). ‘Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments’. Journal of Hydrology, 117, 275-300.

Kirby, C., Newson, M. D. and Gilman, K. (eds) (1991). ‘Plynlimon research: the first two decades’, IH Report No. 109. Wallingford, Oxfordshire.

Kittler, J. and Young, P. C. (1973). ‘A new approach to feature selection based on the Karhunen-Loeve expansion’, Partern Recognition. 5, 335-352.

Littlewood, I . G. and Post, D. A. (1993) ‘Preliminary assessment of rainfall excess (loss) models for time series analysis of daily rainfall-runoff dynamics’, Proc. of International Congress on Modelling and Simulation, M. J. McAleer and A. J. Jakeman (eds). University of Western Australia.

Morris, D. G. and Flavin, R. W. (1990). ‘A digital terrain model for hydrology,’ in Proc. 4th Infernational symposium on spatial data handling (Zurich). International Geographical Union, Columbus, Ohio, USA, pp. 250-262.

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Natural Environment Research Council (1 975). Flood Studies Report, Vol. I. Hydrological Studies. Newson, M. D. (1976). ‘The physiography, deposits and vegetation of the Plynlimon catchments’, IH

Whitehead, P. G. and Young, P. C. (1979). ‘Water quality in river systems: Monte Carlo Analysis’, Water Report No. 30.

Resources Research, 15, No. 2. pp. 451-459.