Multi-scale permeability estimation for a tropical catchment

Tags: John Wiley & Sons, permeability, HYDROLOGICAL PROCESSES, Chappell, estimates, Beven, depth, measurements, slope, John Wiley and Sons, river discharge, soil pipes, parameter values, Hillslope Hydrology, Process Studies, permeabilities, estimation, parameter sets, natural soil pipes, model parameter sets, Sabah Foundation, geometric mean, Forestry Upstream Division, scale, parameter uncertainty, log-normal distribution, N. Chappell, hillslope, steady-state response, propagation velocities, Lancaster University, data sets, catchment hydrology, catchment dynamics, statistical distribution, exponential function, soil permeability, catchment scale, Model inversion, TOPMODEL, Economic Planning Unit, Computer Models of Watershed Hydrology, Royal Society of London, UK Natural Environment Research Council, Cambridge University Press, Waidi Sinun, Danum Valley, Danum Valley Management Committee, Danum Valley Rainforest Research, Dr Waidi Sinun, Department of Malaysia, REFERENCES Ambroise, Malaysia, initial range, digital terrain model, model parameters, grid resolution, model parameter, Mark Sherlock, Sabah State Secretary, Ternan J. L., Hydrology and Water Management, J. Hydrol., Water Resour, saturated soil
Content: Hydrological Processes Hydrol. Process. 12, 1507±1523 (1998) Multi-scale permeability estimation for a tropical catchment Nick A. Chappell,1* Stewart W. Franks and Jonny Larenus2 1Centre for Research on Environmental Systems and Statistics, IENS, Lancaster University, Lancaster LA1 4YQ, UK 2Danum Valley Field Centre, Forestry Upstream Division, Sabah Foundation, 91112 Lahad Datu, Sabah, Malaysia
Abstract: Physically based and spatially distributed modelling of catchment hydrology involves the estimation of block or whole-hillslope permeabilities. Invariably these estimates are derived by calibration against rainfall±runo response. Rarely are these estimates rigorously compared with parameter measurements made at the small scale. This study uses a parametrically simple model, TOPMODEL, and an uncertainty framework to derive permeability at the catchment scale. The utility of expert knowledge of the internal catchment dynamics (i.e. extent of saturated area) in constraining parameter uncertainty is demonstrated. Model-derived estimates are then compared with core-based measurements of permeability appropriately up-scaled. The observed dierences between the permeability estimates derived by the two methods might be attributed to the role of intermediate scale features (natural soil pipes). An alternative method of determining block permeabilities at the intermediate or hillslope scale is described. This method uses pulse-wave tests and explicitly incorporates the resultant eects of phenomena such as soil piping and kinematic wave migration. The study aims to highlight issues associated with parameterizing or validating distributed models, rather than to provide a de®nitive solution. The fact that the permeability distribution within the Borneo study catchment is comparatively simple, assists the comparisons. The ®eld data were collected in terrain covered by equatorial rainforest. Combined ®eld measurement and modelling programmes are rare within such environments. # 1998 John Wiley & Sons, Ltd. KEY WORDS parameter uncertainty; permeability, soil piping; TOPMODEL; upscaling
INTRODUCTION Spatial patterns in the hydraulic properties of soil or weathered rock aect the direction and magnitude of subsurface Їow (e.g. Zaslavsky and Sinai, 1981; Chappell et al., 1990). These hydraulic properties include the moisture release characteristic, porosity and dispersivity, though it is the property of permeability that usually exerts the greatest control on the Їow vectors. Use of catchment-scale hydrological models that incorporate spatially distributed permeability estimates is an acknowledgement of these eects. Typically, application of these models involves the use of very limited numbers of small-scale permeability measurements as initial estimates of larger scale block parameters. The parameter set of these block or hillslope-scale parameters that best predicts the river discharge hydrograph is then identi®ed by automatic calibration (Beven, 1989; Anderson and Burt, 1990). Rigorous comparisons of ®eld-measured permeability and that derived by catchment-scale model inversion are rarely attempted. This is probably because of uncertainties caused by: (a) limited ®eld data, (b) the need to up-scale measurements or (c) non-uniqueness of model
* Correspondence to: Dr. N. Chappell, Institute of Environmental and natural sciences, Lancaster University, Lancaster, LA1 4YQ. Contract grant sponsors: Royal Society of London and UK NERC. Contract grant number: GR3/9439 (NERC).
CCC 0885±6087/98/091507±17$17Б50 # 1998 John Wiley & Sons, Ltd.
Received 3 June 1997 Accepted 18 September 1997
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parameter sets. In response, this study attempts to make such a comparison. For this comparison, a reasonably large data set of core-based permeabilities is used in a region where the spatial pattern is expected to be relatively simple. This improves the reliability of the conclusions. To improve the reliability further, the catchment-derived permeability estimates are based on the use of a parametrically simple, yet physically based model within an uncertainty framework. Several literature reviews (e.g. Beven and Germann, 1982; Jones, 1990) demonstrate that many hillslopes contain systems of preferential channels known as macropores or natural soil pipes. Some studies indicate that Їow within soil pipes can be a dominant pathway for the movement of storm rainfall to rivers, yet characterization is dicult given the complex nature of their networks. Small-scale measurements of the permeability of soil in between these discrete preferential paths may, therefore, be seen to underestimate the `block permeability' (Wen and GoВ mez-HernaВ ndez, 1996) of a larger, hillslope-sized unit of soil. The catchment used for our model inversion contains active pipe systems. Return Їows are observed to discharge from resurgences 0.01 and 0.5 m in diameter during some storm periods. As a consequence, it is expected that our model-derived permeabilities will be larger than those derived from core-scale measurements. Direct characterization of larger soil blocks as a single unit, perhaps the size of a whole hillslope, may be a way to include the eects of pipe systems (Jones, 1990; Chappell and Ternan, 1992; Bonell and Balek, 1993). Such measurement is dicult, though an attempt at this using a pulse-wave test is presented for our study area. The study area is within a region of tropical rainforest that has been subject to some disturbance by selective, commercial logging. The localized eects of such activities on the river regime, slope instability and sediment delivery can be studied with the aid of physically based and spatially distributed modelling (e.g. Wicks and Bathurst, 1996). Such modelling requires block permeabilities representative of terrain elements smaller than the catchment unit but larger than the core-scale measurements. This study aims to develop a greater understanding of permeability estimation at this intermediate, or hillslope, scale. Such work is particularly important within tropical areas, where the rate of land conversion can be high and where there are few soil hydraulic data or modelling studies (Bonell and Balek, 1993; Bruijnzeel, 1996).
RESEARCH SITE Multi-scale estimation of permeability was made within a 12 km2 region of haplic alisol soil close to the Danum Valley Field Centre (Pusat Luar Lembah Danum). The centre is located at 117848.75H E and 5801H N on the east coast of the Malaysian state of Sabah, Borneo. The Forestry Upstream Division of the Sabah Foundation maintain the centre, with additional support from the Royal Society of London. The climate at the Danum Valley Field Centre is equatorial with relatively little seasonality and an 11-year (1986±1996) mean rainfall of 2778 (+s320) mm. To the west and south-east of the ®eld centre the terrain is covered by primary rainforest. The forest type is lowland dipterocarp. The 4 km2 Sapat Kalisun catchment lies to the north-east of the centre and is comprised of forest, selectively logged during 1988 and 1989. Figure 1 shows the sampling areas for the three estimation methods. Core-scale measurements of permeability were taken over a 6 km2 region. The catchment-scale estimates used data for the 60-ha Baru catchment. The hillslope-scale pulse-wave tests were undertaken on a 60 m2 plot within the same catchment. The research area is underlain by the Kuamut geological formation, which is a melange comprised largely of mudstones and sandstones (Leong, 1974). Soil of the FAO haplic alisol (Alh) unit dominates on this geological association (N. Chappell, unpublished data). These unstable soils were formerly classi®ed (FAO±UNESCO, 1974) with the more stable soils of the current acrisol unit (FAO-UNESCO, 1990). Acrisol±alisol soils are the dominant soils in lowland south-east Asia (FAO±UNESCO, 1990). Stratigraphic logs from numerous soil pits and roadside exposures indicate that the solum (i.e. the A and B soil horizons) is typically 1.5 m deep and overlies 1.5 m of weathered rock (i.e. C horizon). The total depth of permeable media is, therefore, approximately 3 m. The same logs indicate that very little catenary change in soil type is apparent within the alisol soil of the research area. The presence of such patterns would complicate up-scaling of the core-based permeability measurements (Chappell and Ternan, 1992).
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Figure 1. The 12 km2 research area (near the Danum Valley Field Centre, Ulu Segama region of Sabah, Malaysian Borneo)
The catchment-scale estimation of permeability used rainfall and river discharge data monitored in the Baru catchment over a six-month period from 6 May to 8 November 1995. Rainfall was digitally recorded at Steyshen Enam in the centre of the catchment (Figure 1). Discharge was derived from threshold-datalogged stage measurements made at a rated control section. Hourly averaged Їows were derived from these data (Figure 2). The hillslope-scale tests were undertaken within a single plot that extended from the watershed divide to the second-order stream Р Sungai Baru Barat within the Baru catchment (Figure 1). Further experimental details will be described within the separate sections on the core-based, catchment-based and hillslope-based approaches of permeability estimation.
PERMEABILITY ESTIMATION FROM CORE-SCALE MEASUREMENT All core-scale measurements of permeability were undertaken with a ring permeameter (Chappell and Ternan, 1997). This method was chosen for two reasons. First, the technique is based on a direct transformation of the Darcy equation and hence is not subject to geometrical approximations in the solution. Secondly, the method was chosen because of the acknowledged reliability of the permeability estimates produced. For example, Sherlock et al. (1995) demonstrated that permeability patterns derived by this method matched the patterns of tracer migration within their tropical acrisol±alisol soil.
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Figure 2. Six month period of river discharge used for the Baru catchment rainfall±runo modelling. Discharge has units of В1076 m s71 and the time base is in hours
A total of 70 core-based permeability measurements were taken at 26 pro®les on seven slopes within the 6 km2 region (Figure 1). Cores were extracted from six depths of 0.075, 0.225, 0.45, 0.75, 1.05 and 1.96 (+0.05) m into the pro®les. All testing was undertaken on 0.10 m long, 0.30 m diameter, undisturbed samples excavated from the ground and with test water at a temperature of 30+ 3 oC. All soil samples tested were collected from pro®les classi®ed as haplic alisol. Most cores were inserted vertically into the ground, though some of the deeper samples were inserted horizontally into pit faces. Voids such as desiccation cracks or root holes were not seen to have any preferential orientation within the sampled cores, so anisotropy at the core scale was not expected.
Results The data set of core-based permeabilities collected over the region shows a strong positive skew in the statistical distribution. Logarithmic transformation of the data produces the most symmetrical Box-andWhisker plot of the transforms applied (Figure 3; Wrinker and Hays, 1975) indicating that the underlying distribution is log-normal. These observations are con®rmed with the results of Kolmogorov±Smirnov tests for normality (Wrinker and Hays, 1975) where only the logarithmic transform is statistically signi®cant (Table I). Most catchment-scale data sets of soil permeability conform to log-normal statistical distributions (see, for example, the recent studies of Sherlock et al., 1995; Chappell and Franks, 1996). Less skew can be observed in a few data sets (e.g. Elsenbeer et al., 1992; Chappell et al., 1996). The centroid of a log-normal distribution is given by the geometric mean. The statistical variability (i.e. coecient of variation using the geometric mean) in the whole data set is 514%. This is high compared with those values for other published permeability data sets, for example, 86±190% in the review of Warrick and Nielsen (1980) and 358% in Chappell and Franks (1996). The spatial (vertical) variability in the permeability is more constrained, following a simple monotonic decline with depth (Figure 4a and b). The exponential function ®tted to median permeability estimates for each depth follows:
K Smed 42eА2Б188DR2 0Б92
1
where KS(med) this function
is is
the core-scale, median indicated by the high
permeability (m s71) at measurement depth D (m). The accuracy of coecient of determination (R2 0.92) and by the function lying
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Figure 3. Box-and-Whisker plots (a) Without transformation (В1076
(mWrsi7n1k)l,e(rb)aanfdterH2apyst,ra1n9s7f5o)rmoaftitohne,
(sct)ataifstteicra3lpditsrtarinbsufotiromnatoifont,h(ed)caofrtee-rsc4apletrpaenrsmfoerambailtiitoynd, aatnad.
(e) after log10 transformation
Table I. The results of Kolmogorov±Smirnov tests for 70 permeability measurements within the 6 km2 sampling area, Danum Valley. A signi®- cance level of greater than 0.95 indicates a normal distribution
Data
R2ppawtransformed
34p
transformed transformed
log10 transformed 7 1/x transformed
K±S statistic 0.3111 0.1825 0.1308 0.1068 0.0604 0.3252
Signi®cance level 0.00 0.02 0.19 0.41 1.00 0.00
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Figure 4. Vertical distribution of core-scale permeability data, with layer-speci®c centroid values represented by (a) the median (d), and (b) the geometric mean (). Permeability has units of В1076 m s71 and sampling depth is in metres. The bars in (a) represent the interquartile range (Wrinkler and Hays, 1975)
wholly within the interquartile range (Figure 4a). This function ®ts almost as well to the geometric mean permeability for each depth (Figure 4b), i.e.
KSgeo 52eА2Б2907DR2 0Б88
2
where KS(geo) is the core-scale, geometric mean permeability (m s71) at measurement depth D (m). Using Equation (2), the geometric mean of core-scale measurements along this vertical distribution is 1.65 В 1076 m s71. The vertical permeability distribution is the result of the typical development of an acrisol±alisol within the humid tropics. The argillation process has resulted in reducing permeability down through the A and B horizons. Permeability reduces further from the B to C (weathered rock) to R (solid rock) horizon as a result of the un-interrupted in situ chemical weathering of the bedrock (Fitzpatrick, 1971). Permeability may not decline monotonically with depth where soils are developed on deposits such as head, glacio-lacustrine drift or river terrace alluvium (Chappell and Ternan, 1992). Under such conditions, estimating the lateral block permeability can be dicult. In the case of the alisol pro®le at Danum, however, the monotonic permeability distribution makes the averaging process comparatively simple.
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Figure 5. Lateral block permeability and transmissivity distributions derived by up-scaling core-based measurements using an harmonic
mean
and
an
arithmetic
mean.
(a)
The lateral block permeability per saturated part of the pro®le (b) the lateral transmissivity (T) in units of В1076 m2 s71
(KSC)
in
units
of
В1076
m
s71,
and
Lateral block permeabilities are equal to an arithmetic to harmonic average of core-scale values (Cardwell and Parsons, 1945). The variation relates to the geometry of the Їow pathways. It is often dicult to de®ne a priori the up-scaling method more precisely (Wen and GoВ mez-HernaВ ndez, 1996). Both averaging methods are, therefore, used to demonstrate uncertainty in the up-scaling. Calculated estimates of the lateral block permeability per saturated part of the pro®le (KSC) are presented in Figure 5a. These estimates can be multiplied by the saturated depth to give the lateral transmissivity distribution (Figure 5b). For example, the lateral transmissivity when the ground is fully saturated (T0) would be 23.6 В 1076 m2s71 (Figure 5b). These data can be compared with results of the model inversion undertaken using catchment-scale data.
PERMEABILITY ESTIMATION FROM CATCHMENT-SCALE INVERSION Catchment-scale model inversion provides a means by which lateral block permeabilties may be derived through the assessment of likely model parameterizations that reproduce a given river discharge record. However, consideration of calibration uncertainty issues is required. As discussed by Beven (1989), many physically based models are over-parameterized in the sense that their parametric requirements are greater than can be derived through traditional model calibration techniques. Several studies have demonstrated that non-unique, near-optimal, model parameter sets (as de®ned by some objective function) may be met in many dierent areas of the parameter space (e.g. Freer et al., 1996; Franks
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et al., 1998). If model calibration is performed with the measured discharge record alone, many parameter sets may be found that reproduce this calibration variable equally well. This phenomenon indicates that parameter interactions are important in determining the behaviour of the model. If information is collected pertaining to the internal behaviour of a catchment, then these additional data may be used to reject model parameterizations that reproduce the discharge but are not physically acceptable. Internal variables that have been used to constrain uncertainty include borehole records (Lamb, 1996) and the extent of surface saturation (Franks et al., 1997). In particular, the utility of surface saturation extent estimates was recently demonstrated in a study by Franks et al. (1998). ERS-1 synthetic airborne radar (SAR) data were employed to map the extent of surface saturation. These data were then used to constrain uncertainties in their catchment model (TOPMODEL). It was shown that the consequent reduction in terms of the feasible range of saturated transmissivity was great, even though the uncertainty in the estimates of saturated area was large. Given the utility of saturation extent estimates in constraining the feasible parameter space, a similar criterion is employed in this study. TOPMODEL is also the model chosen for this study at Danum. The model was selected because it describes the dominant hydrological processes in physically based terms, yet requires few model parameters (Beven et al., 1995). The model is based on the premise that distributed hydrological responses are related to the topography, and thus employs a topographic index of hydrological similarity (z), i.e.


z ln
a T0 tan b
3
where a is the upslope contributing area to a given point (m2), T0 is the lateral transmissivity, when the soil and weathered rock pro®le is saturated to the ground surface (m2 s71), and tan b is the local slope angle at
that point (Ambroise et al., 1996). TOPmodel simulations produce time-series both of the river discharge (Q, in m s71) and of the catchment-average saturation de®cit (S", in m) where
S"

А
m A

Sz ln RdA
4
and m is the discharge recession parameter (m), A is the catchment area (m2) and R is the rainfall input (m). This can be related to a catchment-average, water-table head using
H

D
А
S" Zeff
5
where H is the water-table head above the solid rock (m), D is the depth to the solid rock (m) and Ze is the eective porosity. Within this study, an estimate of the eective porosity was derived from the dierence between the total porosity and the moisture content at А1.5 kPa capillary potential (after Luxmoore, 1981; Watson and Luxmoore, 1986). Within TOPMODEL the lateral transmissivity of the saturated part of the pro®le, T (m2 s71) is typically assumed to follow an exponential decline with water table depth, following
T T 0eАS" am
6
The lateral block permeability over the saturated part of the pro®le (KSM, m s71) is then
K SM

T H
7
This KSM parameter can be compared with the parameter KSC that is upscaled from the core-based measurements.
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Parameter T0 m Td SRMAX
Table II. Parameter ranges for the Monte Carlo sampling
Minimum 1.87 В 1076 0 0 0
Maximum 45 7.0 В 1073 5.4 В 104 0.6
Units m2 s71 m s m71 m
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Model implementation within an uncertainty framework A number of recent studies (e.g. Bruneau et al., 1995; Wolock and McCabe, 1995) have shown how calibration-derived parameters (in particular T0) are partly dependent on the grid resolution employed in the derivation of the topographic index. The T0 parameter can compensate for a lack of resolution in the digital terrain model (DTM). Saulnier et al. (1997) have, however, demonstrated that the sensitivity of T0 to the grid resolution may be reduced, if the permanent channel is removed from the derivation of the topographic index. Therefore, in this study, a ®ne resolution DTM (i.e. 10 m) was employed and the permanent channel was removed from the calculation of the topographic index distribution. The initial ranges in block parameters of T0 , m, Td and SRMAX (Table II) were set wider than the largest ranges used within previous TOPMODEL simulations (cf. the review of Beven et al., 1995). For example, the initial range in the critical T0 parameter covered almost eight orders of magnitude (Table II). Model inversion is achieved within an uncertainty framework, thus explicitly recognizing and incorporating the problem of non-uniqueness of model simulations arising from dierent model parameter sets. A Monte Carlo sampling strategy was adopted for the selection of contending model parameter sets. Ten thousand parameter sets were selected with random parameter values taken from uniform distributions for each parameter. The acceptability of each model parameter set for discharge prediction alone was then determined through the model eciency measure of Nash and Sutclie (1970). Incorporation of expert knowledge Observations of the internal behaviour of the Baru catchment over several years provide a basis for further constraining the range of possible parameter sets. Visual observations of ground conditions during extreme storm events, combined with the results of runo plot data (e.g. Sinun et al., 1992), indicate that overland Їow is very limited within the Baru catchment. The spatial extent of saturated soil and the associated overland Їow (during storms) is largely con®ned to the narrow permanent and ephemeral channels. From these observations the minimum and maximum saturated area (excluding the permanent channel) for the Baru catchment is given as 2 and 10%, respectively (this range is set wider than that expected to take account of uncertainties in the estimation). TOPMODEL simulates the spatial extent of surface saturation by combining the predictions of saturation de®cit (S") with the topographic index distribution. Model parameter sets that produced saturated areas outside this 2-10% range were, therefore, rejected as non-behavioural. The predicted saturation de®cits were also used to derive the lateral block permeabilities [Equations (5)±(7)] using a priori-de®ned estimates of pro®le depth and eective porosity. Pro®le depth (D) was set to the regional average of 3 m. Moisture release characteristics have been determined for 17 cores collected from the subsoil in the west of the 12 km2 research region (M. Sherlock, personal communication). The average eective porosity (Ze) from these data was 0.025 m3 m73. Results Figure 6 shows scattergrams for the four model parameters T0 , m, Td and SRMAX plotted against the model eciency when calibrated on discharge alone. From these plots it can be seen that reasonable ®ts may be achieved in many areas of the parameter space. This indicates that robust identi®cation of individual parameter values cannot be achieved after model inversion conditioned on discharge alone.
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Figure 6. Scattergrams of model eciency against (a) m (metres), (b) T0 (ln[m2 s71]), (c) Td (В1075s m71), and (d) SRMAX (metres) parameters after comparison with TOPMODEL discharge predictions alone
Figure 7 shows the scattergrams of the same four parameters after application of the saturated area
rejection criterion. It can be seen that conditioning the model parameter sets according to the predicted
extent of the saturated ground markedly aects those parameter sets that are deemed acceptable.
Figures 6c, 6d and 7c, 7d indicate that the Monte Carlo simulations are insensitive to the two model para-
meters of the unsaturated zone time delay (Td) and the maximum root zone storage (SRMAX). In contrast,
the response surface for the exponential recession parameter (m) displays a marked optimal peak, corresponding to a value of approximately 3.5 В 1073 m (Figures 6a and 7a). This value is comparable to the m value of 2.6 В 1073 m derived independently using MRCtool of Lamb (1996). This gives some con®dence
that the range in m may be very much constrained.
Figure 6b shows the scattergram for the catchment average, lateral transmissivity when the pro®le is
saturated achieving
thoigthheegrociuenndciesus r(fia.ec.et(hTo0s)eaggraeiantsetrththeamno0d.5e)l
eciency. From this occur across a large
plot it range
can be seen that model ®ts of the parameter space. In
contrast, Figure 7b shows that by incorporating the saturation extent criterion, the range of values producing the best ®ts (above an eciency of 0.5) is markedly constrained to the range 0.189±4.910 m2 s71.
Within this study, the transmissivity has been conditioned by the rainfall±runo behaviour of the catch-
ment, given the imposed physical constraints. Whilst the range of possible transmissivity remains large, high
and low values of transmissivity capable of reproducing the measured discharges, but not the expected
surface saturation, have been rejected. This approach contrasts with most applications of physically based
catchment models, which de®ne a priori parameter ranges with site-speci®c, core-scale estimates. Sets of
optimal parameter values are then de®ned within these ranges using discharge predictions. The minimum and maximum T0 (0.189 and 4.910 m2 s71) values and the peak m value (3.5 В 1073 m) are used to calculate the distribution of lateral block permeability per the saturated part of the pro®le (KSM).
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Figure 7. Scattergrams of model eciency against (a) m (metres), (b) T0 (ln[m2 s71]), (c) Td (В1075 s m71), and (d) SRMAX (metres) parameters after comparison with discharge predictions that produce between 2 and 10% saturated area
This parameter is comparable with the core-derived (KSC) and hillslope-derived (next section) parameters.
Catchment-derived KSM catchment-average water
data are plotted in Figure 8 as solid lines. These data are shown for the range of table heads predicted for the simulation period (i.e. 1.08±2.30 m for the minimum
(T00.,02a5ndm30.m8573t)ois1g.8a8inmed
for by
the maximum T0). Some corroboration of the observing the predicted water table (Figure 9). A
eective porosity level predicted to
estimate be at the
base of the solum (Figure 9) is not inconsistent with borehole and tensiometer observations made across the
12 km2 Danum region (N. Chappell unpublished data). An Ze estimate of, for example 0.10 m3 m73 (a factor
of four larger water table to
than the estimate used), would have within 0.5 m of the ground surface.
reduced the estimates of KSM , but raised the predicted Such groundwater conditions are inconsistent with the
borehole and tensiometer observations.
Those catchment-scale models that are physically-based have been developed to allow three dimensional
patterns in subcatchment-scale processes to be predicted. Within the Danum research area, down-pro®le
patterns in permeability are observed (Figure 4). At other experimental sites downslope (catenary) patterns
in permeability are also observed (Chappell and Ternan, 1992). In such circumstances, it becomes dicult to
up-scale core-based measurements, for subsequent comparison with rainfall±runo±derived permeability
estimates (Chappell and Ternan, 1992; Wen and GoВ mez-HernaВ ndez, 1996). An alternative to up-scaling
block permeabilities from core-scale estimates would be to derive them directly. In the case of the hillslope,
such estimates would aim to incorporate the resultant eect of down-pro®le and downslope permeability.
Furthermore, the complex variably saturated nature of a slope (including the eects of soil pipes or macro-
pores, kinematic and pressure waves) could be included. The hillslope is also the terrain scale that contains
the `average' water path-line along which rainfall is translated to river-Їow. Hillslopes may, therefore, be
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Figure
8. Lateral block permeability derived from the model measurements (РР, KSC). Lateral block permeability
hiansveurnsiitosnof(±В±10±7, 6KmSMs)А1anadndthwaattedretraivbelde
by up-scaling core-based head is in metres
Figure 9. Average water table heads (in metres) predicted with an eective porosity of 0.025 m3 m73 and (a) the maximum T0 , and (b) the minimum T0 .
seen to be the elementary unit that characterize the internal behaviour of catchments (Germann, 1990; Jones, 1990; O'Loughlin, 1990; Chappell and Ternan, 1992).
PERMEABILITY ESTIMATION FROM HILLSLOPE EXPERIMENTS The permeability of a soil and/or weathered rock is the rate of water Їow through a unit area of saturated media under a unit gradient. If the propagation rate of a water pulse through a hillslope is monitored and then corrected for the gradient (and other eects), then a very approximate estimate of the lateral block
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permeability can be obtained. A water pulse moving through several metres of soil may follow structures such as natural soil pipes. Where soil pipes are observed, lateral block permeability estimates based on hillslope-scale tests, may be more representative than those from averaged or up-scaled core-scale tests. There are two key problems with core-scale measurements. First, cores that largely comprise a soil pipe are not likely to be acceptable for permeameter tests. Secondly, the segmentation of a small pipe system into a series of discrete cores does not allow characterization of the pore continuity. Permeability is very sensitive to pore continuity (cf. Beven and Germann, 1982). In slopes where pipe Їow dominates the subsurface response to rainstorms, then whole-hillslope tests, however approximate, may give better estimates of model grid-scale permeability when required for validation or parameterization of physically-based catchment modelling. The distance between the stream and half way to the local catchment divide can be assumed to be the approximate average travel distance of rainwater migrating through the subsurface system (for shallow groundwater catchments). By applying a steady-state pulse of water to the slope at this mid-point and tracing the pulse to the stream, we can obtain a distribution of propagation velocities (V) for travel to any downslope location. If we assume that the hydraulic gradient between the mid-slope and monitoring location can be approximated by the sine of the slope angle (i.e. the dierence in gravitational potential over the slope distance), then lateral block permeability estimates can be derived from the propagation velocities. Given the approximations within the method and the need for parametric simplicity, we will estimate only two propagation velocities to each sampling point. The ®rst velocity, VS (m s71), is the ratio of, (a) the time from water injection to a steady-state response at a sampling location, and (b) the length of the path-line. The second velocity, VC (m s71), is the ratio of, (a) the centroid time between injection and steady-state response, and (b) the length of the path-line. These values are pore water velocities, so multiplication by the eective porosity (Ze) is required to calculate the block permeabilities, which are velocities per unit area. During our pulse-wave tests, water was applied over a 1 m width normal to the slope. The width of the resultant plume was observed to expand with distance from the injection point. The propagation of the water needs to be corrected for this dispersion by calculation of a dispersion factor, t, which is the across-slope width of plume at the monitoring point normalized by the width at the injection site. The complete calculation of the estimate of the lateral block permeability derived from, for example, VS , is therefore
K SVS

V SZeff tsin b
8
where KSVS is the lateral block permeability between the mid-slope and downslope monitoring point, as derived from Vs (m s71). The aim is to present a tractable solution rather than one that includes all terms (see O'Loughlin, 1990). The experimental hillslope installed within the Baru catchment was approximately 13 m in length from mid-slope to the stream channel. Twelve tensiometers were installed along a central transect (Figure 10). These tensiometers were ®tted with ceramic tips with a very fast response (Soil Moisture Equipment Corporation 655X01-B.5M2). The tensiometer network was supplemented with a grid of piezometers, although these are used only for de®nition of t within this study. Further de®nition of t was obtained by measuring the width of the return Їow zone developed along the stream bank during the tests. Several pulse-wave tests were undertaken on this slope, although the results of only one test (T1KO) are presented. During experiment T1KO a petrol water pump was used to spray-irrigate an area 1 m by 0.5 m at a rate of 100±200 mm hr71. This irrigation rate did not generate in®ltration excess or saturation excess overland Їow outside the sprayed area. Irrigation was continued until all tensiometers had clearly reached steady state; for experiment T1KO the supply was stopped after 6 hours.
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Figure 10. The distribution of tensiometer ceramics (symbol d) and piezometers (symbol :) along the central transect in the hillslope plot TR1 (Baru catchment)
Figure 11. Tensiometer response at the near-stream array (РР) and next array upslope (± ± ±) during experiment T1K0 (see Figure 10). Tensiometer readings are in В101 kPa
Results The response of the tensiometers at the two most downslope arrays during experiment T1KO is illustrated in Figure 11. Block permeabilities were calculated from the response propagation to each tensiometer during this experiment (Figure 12). The block permeabilities derived from responses close to the source appear highly uncertain. In contrast the responses at 5 to 12 m from the source give block permeability values that are similar for each pro®le and downslope location. Furthermore, the dierence between the values derived from the VS and VC is also relatively small, the geometric mean permeability from VS is 8.9 В 1076 m s71
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Figure 12. Lateral block permeabilities (KSVS and KSVC) derived from the hillslope pulse-wave tests (В1076 m s71). Average travel (path-line) distance is in metres.
and 14.8 В 1076 m s71 from VC . This indicates that the identi®cation of a representative propagation velocity is relatively robust.
COMPARISON OF CORE-, HILLSLOPE- AND CATCHMENT-SCALE ESTIMATES
Figure 8 shows the permeability estimates derived from core-based measurement and catchment-scale
inversion (data are plotted over the predicted water table range). The mean water table head during the
simulation period (approximated by a mean of the two traces in Figure 9) is 1.24 m. The lateral block
permeability at this The range from the
mean head is between 0.527 В 1076 and 13.7 В 1076 m s71 up-scaled core data (KSC) of 0.158 В 1076±0.311 В 1076 m
from the modelling (KSM). s71 is clearly less than the
model-derived range. Additionally, TOPMODEL assumes an exponential decline of lateral block permea-
bility with depth, as is observed with the arithmetically up-scaled KSC distribution. The slope of these two sets of lateral block permeability functions are, however, signi®cantly dierent (Figure 8). This may indicate
that there is a greater non-linearity in the catchment response than can be obtained from the core-scale
measurements. These observations could be explained by the presence of active soil pipes within the catch-
ment soils. These pipes would probably have their greatest eect on subsurface Їow in very wet catchment
conditions. Under such conditions the threshold for pipeЇow initiation (Gilman and Newson, 1980) might
be exceeded at many slope locations. Indeed, during storms where rainfall exceeded 50±100 mm d71, natural soil pipes (0.05±0.50 m diameter) in the Baru catchment have been observed to return water to the ground
surface. Soil piping may be a feature of such acrisol±alisol soils. Extensive piping has been noted in acrisol±
alisol soils in Sarawak, Malaysia (Baillie, 1975), Singapore (Sherlock et al., 1995) and the Amazon basin,
Peru (Elsenbeer and Lack, 1996). Such a conclusion is, however, tentative given the dearth of data on piping
within tropical soils (Jones, 1990).
The estimates of lateral block 8.9 В 1076 m s71 and KSVC of
permeability derived from the hillslope 14.8 В 1076 m s71) are consistent with
pulse-wave experiment (KSVS of those derived from the model
inversion (Figure 8). Furthermore, the hillslope-derived estimates are considerably larger than any of the up-
scaled core-based values (Figure 8). This supports the idea that the water plume applied to the experimental
hillslope migrates under the inЇuence of the soil pipes. Moreover, this may indicate that hillslope pulse-wave
experiments may be a better method of either parameterizing or validating catchment-scale models.
Under conditions of relatively high water table head (i.e. the peak of large storms) the model-derived KSM does, however, exceed the results from the hillslope experiment (i.e. KSVS and KSVC). This may indicate that there are other parts of the catchment that respond much faster than the experimental hillslope. There are
two possible explanations for this. First, some other slopes contain larger and hence more eective soil pipes
in comparison to the study slope. Secondly, some other parts of the catchment are, on average, wetter than
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HYDROLOGICAL PROCESSES, VOL. 12, 1507±1523 (1998)
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the experimental slope. At wetter locations the combined kinematic/pressure wave that results from a storm event may propagate more eciently through the slope. Clearly, hillslope-scale experiments need to be undertaken at other locations in the Baru catchment (and at a range of antecedent conditions). A distribution of KSVS or KSVC could be more realistically compared with the core- or catchment-derived permeability estimates.
CONCLUSIONS A region with a relatively simple vertical distribution of soil and weathered rock permeability has been identi®ed. The value of using uncertain expert knowledge of catchment internal behaviour in constraining model parameter uncertainty has been demonstrated. These two observations allow some reliability to be placed on comparisons between the model- and core-derived block permeability estimates. The comparison may indicate that there is a greater non-linearity in the catchment response than can be obtained from the core-scale measurements. This could be explained by the presence of active soil pipes within the catchment soils. approximate solutions to hillslope pulse-wave tests support the idea that soil pipes could have a signi®cant role in the generation of river response. If these hillslope-scale tests were to be conducted at dierent catchment locations and antecedent moisture conditions, they might prove useful in the parameterization of spatially distributed models of catchment hydrology. The utility of hillslope- or core-derived block permeability estimates in the parameterization of catchment models is dependent on a robust estimation of the eective porosity [see Equations (5) and (8)]. A theoretically, rather than an empirically, de®ned eective porosity (as presented here) would clearly improve con®dence in, and possibly the reliability of, this critical parameter.
ACKNOWLEDGEMENTS The authors are indebted to Kawi Bidin, Jamal Mohd. Hanapi, Jamal Abd. Majid and Mark Sherlock for their exemplary ®eld data collection, observations and comments. The considerable support of Dr Waidi Sinun and others of the Forestry Upstream Division, Sabah Foundation (Yayasan Sabah) is gratefully acknowledged. The Danum Valley Management Committee, the Economic Planning Unit of the Prime Minister's Department of Malaysia, the Sabah State Secretary and the Sabah Chief Minister's Department are thanked for their permission to conduct research in the Danum Valley area of Sabah, Malaysia. This work has been undertaken as part of the Danum Valley Rainforest Research and training programme under project 111 with the close collaboration of Dr Waidi Sinun and Kawi Bidin (Forestry Upstream Division). The study is also a core element of a hydrology programme that forms part of the south-east Asia rainforest research programme of the Royal Society of London (reference A/175). Financial support for this work has been provided by the Royal Society of London and UK Natural Environment Research Council (grant GR3/9439).
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