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Natural flow in managed catchments: A case study of a modelling approach
PII: S0043-1354(98)00268-1
Wat. Res. Vol. 33, No. 3, pp. 621±630, 1999 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00
NATURAL FLOW IN MANAGED CATCHMENTS: A CASE STUDY OF A MODELLING APPROACH M S. M. DUNN* and R. C. FERRIER*
Macaulay Land Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, U.K. (First received September 1997; accepted in revised form June 1998) AbstractÐIn the U.K., the water resources of many catchments are heavily managed and the existing constraints on their use must be built into future management. Recent developments in catchment modelling mean that the practical use of models, to analyse catchment behaviour and assist with the management process, is a feasible option. However, few models include appropriate water management components that will permit application to those areas for which they are most needed. This paper describes the integration of simple management controls into a spatially distributed hydrological model and illustrates how the model can be used to assist in catchment management, through a case study of the Carron catchment in Central Scotland. The model was successfully applied to predict ¯ow in both the upland region of the catchment, where there are several reservoirs and signi®cant transfers of water and the lowland region of the catchment, which is a predominantly urban area. A simple modi®cation to the water management procedures illustrates how the model may be used to help achieve naturalisation of the ¯ow regime, thus satisfying the requirements of the precautionary principle. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐnaturalisation, management, modelling, catchment
INTRODUCTION
It is now accepted that the resources of a river basin should be managed as a whole, to minimise the potential con¯icts between the dierent users and activities in the catchment. Until recently, in industrialised and heavily populated nations such as the U.K., the primary consideration in most catchments has been to meet the demands of the public and industry for water supply and power generation. The management of water resources has evolved gradually over the years and many of the developments cannot simply be reversed. Instead they must be integrated in the most appropriate manner to future plans for managing the catchment. The challenge for the water manager is to identify potential con¯icts and the ¯exibility within the system that will allow these con¯icts to be minimised. The objectives of new European Community Water Policy as described in a recent Commission Communication (European Commission, 1996) identify a need for greater integration between factors such as water quantity and quality and water use and environmental protection. One of the key approaches underlying the new policy, is that of the precautionary principle, which advises that policy should err on the side of caution where there are *Author to whom all correspondence should be addressed. [Tel.: +44-1224-318611; Fax: +44-1224-311556; E-mail: [email protected]]. 621
doubts or where insucient information is available. One implication of this with respect to water management is that there should be an objective to maintain ¯ow regimes as close to natural as is feasible. Some water supply companies use sophisticated linear programming resource allocation tools to analyse the water management system. WRAP (water resource allocation planning) developed for Yorkshire Water (Likeman et al., 1995) is one example of a model that can be used in a region where there are over 130 reservoirs as well as borehole and river abstractions. However, the primary function of this and similar models is to determine the optimum strategy for abstracting water to minimise cost, whilst meeting consumer demand requirements. The models take no account of the natural hydrological system. Equally, there is a plethora of models available for analysing natural catchment hydrology, e.g. TOPMODEL (Beven et al., 1984) ARNO (Todini, 1996) and SHETRAN (Parkin, 1995), but few that are capable of analysing highly managed systems. Fewer still are capable of accounting for water management in any spatially distributed form, that would permit the more subtle relationships between natural ¯ows and management to be identi®ed. The water quality model QUASAR (Whitehead et al., 1997) goes some way towards this by combining hydrological and chemical inputs and outputs to a catchment river system on a reach basis. However,
622
S. M. Dunn and R. C. Ferrier Table 1. DIY model parameters
Parameter
Function
Saturated hydraulic conductivity Soil porosity Fast response threshold storage Fast response distance
control rate of slow response runo de®ne relationship between soil storage and head soil moisture level at which fast runo response is initiated de®ne density of localised drainage network for fast ¯ow routing (related to macropores, arti®cial drainage or rill generation) set lower limit on sub-surface ¯ow de®ne the hydraulic gradient for hill-slope model de®ne the hill-slope routing distance for each cell
Minimum soil storage-slope Slope to stream Flow path distance to stream
the model does not attempt to model the inter-relationships between these inputs and outputs and cannot therefore be used directly to investigate the eects of management. Thus, the existing range of modelling tools are limited in their ability to integrate the needs of catchment management in terms of the available water resource with that of the ecosystem value of the natural catchment. This paper describes the integration of a GIS based spatially distributed model of natural hydrology with a water management component, and demonstrates its value through a case study of the River Carron catchment, in Central Scotland. The case study describes how the hydrological model was adapted to take account of management and demonstrates how the model can be used to investigate possible approaches for improving water management practice in the catchment with respect to naturalisation of the ¯ows. MODELLING APPROACH
The aim of the research was to develop an integrated model capable of: (a) Predicting time-series of ¯ow in a managed catchment. (b) Demonstrating how dierent management strategies aect stream ¯ows at dierent locations. The distributed model used to describe the natural hydrology was originally developed for the Ythan catchment in NE Scotland. The model (hereafter referred to as DIY) is presented in detail in Dunn et al. (1998). The philosophy of the DIY model is to allow relatively detailed, 50 50 m resolution, data to be used to characterise hydrological processes at a small scale, and then to scale up to the catchment resolution by combining the hydrological responses from areas that are similar at the smaller scale. This is achieved by applying a disaggregated hill-slope ¯ow model to each characteristic 50 50 m cell in the catchment and calculating the temporal contribution that each cell makes to stream ¯ow. There are two basic response modes, fast and slow, with the relative importance of each mode determined by the soil moisture storage. The DIY model is driven by daily inputs of rainfall and evapotranspiration and involves 7 parameters which are listed in Table 1, together with an outline of their function.
The topographic parameters are derived from a Geographic Information System using a digital elevation model (DEM) and digital rivers data. In conjunction with the ®ve physical properties, relating to the soil and drainage system, they control the response of the Hill-slope model. Each of the parameters can in theory vary spatially, but to limit the number of variations of parameter combinations, only the most signi®cant and identi®able spatial dierences are included. The Hill-slope model output is scaled up to predict ¯ow at dierent locations on the stream network by using the GIS to identify the combination of characteristic cells (as determined by the model parameters) that drain to each point on the stream network. The Carron catchment, to which the model is applied here, contrasts sharply with the Ythan catchment, on which it was developed, in terms of its topography, climate, soils and land use. As such, this application will provide a useful additional test of the capability of the model. The model of the natural hydrology has been integrated with a water management component at the sub-catchment scale; where the sub-catchment outlets are de®ned by the location of principle management activities and major stream junctions. The spatial complexity introduced by the presence of reservoirs and aqueducts prevents more detailed spatial representation of the managed system. The combined natural and managed model is applied by sequential simulation of each sub-catchment down the network of the full catchment, at each stage generating predictions of the in¯ow to the downstream sub-catchment and transfers to other subcatchments. The predictions of ¯ow for the Carron are validated by comparing them with daily stream ¯ow measurements at two locations in the catchment. THE CARRON CATCHMENT
The River Carron at Carron Iron Works (NGR 2880 6823) drains a natural area of 187 km2 in Central Scotland (Fig. 1). The source of the river is in the west of the catchment, which is bounded by hills rising to 570 m, whilst the south is drained from lower land by the Red Burn and Bonny Water. In addition to the natural area, water may be diverted into the catchment from a further
Natural ¯ow in managed catchments
623
Fig. 1. The Carron catchment.
22 km2 of the River Endrick catchment, to the northwest. Data from the Land Cover of Scotland 1988 data set (MLURI, 1993) show the dominant land use in the catchment to be improved grassland, which covers much of the central and eastern areas. There is a large area of coniferous plantation in the west and urban land dominates the south and east. The urban area includes the new town of Cumbernauld as well as much of the Falkirk and Larbert area. There is a strong precipitation gradient across the catchment from a mean annual rainfall of 758 mm at Polmonthill, to the east, to 1665 mm at Waterhead, at a height of 360 m in the west. The population of the east of the catchment is around 100,000 and as a consequence, the water resources of the upper Carron Valley are heavily managed for public water supply. An area of 38 km2 of the natural catchment drains directly into Carron Valley reservoir and a further 25 km2 is controlled by the Earlsburn reservoirs and by diversions into aqueducts that link areas to reservoirs in the north. The urban area imposes additional constraints on the management of the water resources through the generation of both sewage euent and poor quality urban runo. The combination of high rainfall with poorly drained soils in the west suggests that the hydrology is likely to be dominated by movement of water close to the land surface. Recharge to groundwater sources will be limited by the low permeability of the overlying soils. The urban area will also generate a substantial amount of rapid runo from its impermeable surfaces. The eect of these character-
istics is to create a rapidly responding system, although the presence of the reservoirs will damp the runo from the upland areas during periods of re-®ll. CLIMATE
Given the high precipitation gradient across the Carron catchment, an understanding of the spatial variability of the rainfall is a prerequisite to successful hydrological modelling. Therefore, data from 18 raingauges, within and close to the catchment, were analysed to identify spatial relationships. To achieve a consistent set of data, the long term mean annual rainfall (LTMAR) at each site was estimated. Sites where a long record was available were used to estimate the ratio of the mean annual rainfall, calculated over dierent periods, to the LTMAR. In this way, the measurements from each gauge were converted to the same standard period of 1941±1970. Linear regression analysis between the elevation of each gauge and its easting, to re¯ect the dominance of westerly winds, gave the following relationship to estimate the long term mean annual rainfall (P in mm): P 1:96:H ÿ 14:3:E 1190 with R2 0:90
1
where H is elevation (m) and E is distance east of NGR easting 260000 (km). The regression analysis provides a method for estimating the annual rainfall in dierent parts of the catchment. However, the relationship must be treated with some caution for higher elevations, as the highest gauge used to derive the equations was
624
S. M. Dunn and R. C. Ferrier
at 360 m and the rainfall at this location is slightly overestimated. A similar analysis carried out by Johnson (1995) at Balquhidder, some 40 km further north, found a signi®cantly lower elevation factor of 0.78 as compared to the 1.96 derived here. Estimates of evapotranspiration in the catchment have been based on monthly MORECS potential evapotranspiration totals for the area, with an allowance for land use and soil moisture status. A ®xed percentage of the daily rainfall is assumed to be lost from interception evaporation, with the percentage determined by the land cover. Based on more detailed analysis from other upland areas of the U.K. (Dunn and Mackay, 1995) values of 25, 5
and 10% were assumed, respectively, for forested land, urban land and other land covers. The remaining evapotranspiration loss was estimated from the potential rate, with a soil moisture limitation derived from the antecedent input of net ``rainfall ÿ evapotranspiration''.
WATER MANAGEMENT
A simpli®ed representation of the water management system in the Carron catchment is illustrated at the sub-catchment scale, used by the model, in Fig. 2.
Fig. 2. Sub-catchment management model structure.
Natural ¯ow in managed catchments
The complex system of reservoirs and aqueducts has developed in an ad hoc manner over a long period. The original function of some of the reservoirs is unclear and ecient management of the resources is a complex issue. A study of the water resources of the Carron Valley above Longhill was undertaken for the Central Regional Council in 1983 (Central Regional Council Water and Drainage Department, 1983). The study was aimed at identifying cost eective methods for improving the eciency of use of the Carron Valley resources, to provide a cheaper source of water than that provided by the forced purchase of water from outside the region. Material from the 1983 study has been supplemented by additional information and data relating to the current operational procedures (Durward, East of Scotland Water Authority, personal communication). In particular, data have been made available, by the East of Scotland Water Authority, from a system of telemetry that was installed in 1992 to monitor and control the releases, abstractions and levels in Carron Valley reservoir. This data set provides important information for use in the development and testing of the water management component of the catchment model. Carron Valley reservoir is the largest water body in the catchment with a capacity of 21.4 Mm3. It is the main source of public water supply in the catchment, feeding two ®lter stations with typical abstraction rates of the order of 1.2 and 0.05 m3 sÿ1. Compensation ¯ow must be released from the reservoir to both the River Carron, at the east end, and to the River Endrick (out of the catchment), at the west end. The Earlsburn reservoirs in the north of the catchment regulate ¯ows and can be used both to assist in achieving the required minimum ¯ow in the River Carron and to control the transfer of water to Loch Coulter, via Buckieburn reservoir. Once ¯ow has passed the otake point on the Earl's Burn it can no longer be controlled, which means that in practice the majority of the ¯ow is diverted to Loch Coulter where it may still be used. Buckieburn reservoir acts as a transfer basin between the Earl's Burn and Loch Coulter and also receives diverted water from 2.8 km2 of the catchment to its north. The Buckie Burn receives compensation ¯ow from the reservoir and also any spill of excess water from Loch Coulter. In the lower part of the catchment there are three principle sewage treatment works at Bonnybridge, Dunnswood and Denny that typically discharge 0.11, 0.12 and 0.09 m3 sÿ1, respectively. The ¯ow routing in the urban areas is signi®cantly modi®ed by storm water sewers but it is assumed that, for modelling purposes, it can be represented as an analogous process to the natural regime, with altered values for parameters such as hydraulic conduc-
625
tivity and fast response distance. Industrial abstractions and releases are assumed to be self-balancing in terms of ¯ow volume.
MANAGEMENT MODEL
There are four dierent forms of ¯ow management control that apply to the Carron sub-catchments, relating to the following cases: (1) Flow controlled by a reservoir at the outlet of the sub-catchment (applies to Carron Valley reservoir, CVR, and Earls Burn reservoir, EBR, subcatchments). (2) As for case (1), except that excess ¯ow above compensation may be transferred to an adjacent sub-catchment, rather than passed directly downstream (applies to Buckie Burn otake, BBO, subcatchment). (3) Flow controlled by an otake, with no storage, at the outlet of the sub-catchment (applies to Earls Burn otake, EBO, sub-catchment). (4) Flow controlled by a reservoir at the top of the sub-catchment, with spill into an adjacent subcatchment (applies to Auchenbowie Burn, AUB, sub-catchment). Although these management controls have been identi®ed speci®cally for the Carron catchment, they are generally applicable to other managed catchments and the modelling procedure could be readily transferred. The simpli®ed network structure illustrated in Fig. 2 de®nes each sub-catchment according to its principle management controls and identi®es the natural and arti®cial links between each sub-catchment. For each of the management cases described above, a dierent set of rules is applied as described below, using an explicit ®nite dierence sub-catchment storage balance. Case (1): Reservoir at sub-catchment outlet The net in¯ow to the reservoir for sub-catchment i is calculated at time-step t by: Ii,t Qiÿ1,t Ti,t ÿ Ci,t ÿ Ai,t Ri,t
2
where Ii,t is the natural sub-catchment runo at time t (L3Tÿ1); Qi ÿ 1,t is the out¯ow from the upstream sub-catchment i ÿ 1 at time t (L3Tÿ1); Ti,t is the net transfer into sub-catchment i at time t (L3Tÿ1); Ci,t is the reservoir compensation ¯ow at time t (L3Tÿ1); Ai,t is the abstraction from the reservoir at time t (L3Tÿ1) and Ri,t is the net addition to the reservoir storage at time t (L3Tÿ1). A cumulative balance of the reservoir storage is maintained to determine whether there is any spill from the reservoir. The reservoir excess is calculated from the storage at the previous time-step by: Xi,t Si,tÿ1 Ri,t
3
where, Xi,t is the reservoir excess at time t (L3Tÿ1)
626
S. M. Dunn and R. C. Ferrier
and Si,t is the reservoir storage balance, below spill height, at time t (L3Tÿ1). If there is a positive reservoir excess, spill occurs and the reservoir storage balance is reset to zero, otherwise the sub-catchment out¯ow consists only of the compensation ¯ow: For Xi,t > 0;
Qi,t Ci,t Xi,t
For Xi,t <0;
Qi,t Ci,t
and
and
Si,t 0 4
Si,t Xi,t
5
Case (2): Reservoir at outlet and transfer of excess Case (2) is identical to case (1) except that the out¯ow from the sub-catchment is limited to the compensation ¯ow and a fraction of the excess ¯ow. The remaining excess ¯ow is transferred to an adjacent sub-catchment that is not directly downstream. For Xi,t > 0;
Tj,t f Xi,t ;
Qi,t Ci,t 1 ÿ f Xi,t ; For Xi,t <0;
Tj,t 0;
Si,t 0
Qi,t Ci,t ;
6
Si,t Xi,t 7
where the symbols are as for case (1) and Tj,t is the transfer out of the sub-catchment into some neighbouring sub-catchment, j, at time t (L3Tÿ1) and f is the fraction of excess runo transferred out of the sub-catchment. Case (3): Otake at sub-catchment outlet Where there is an otake at the outlet, the subcatchment out¯ow is normally limited to satisfy the compensation ¯ow requirements of the stream. Additional runo may be arti®cially transferred by aqueduct or pipe to an adjacent sub-catchment. The equations controlling this management are: Ii,t Qiÿ1,t Ti,t ÿ Ci,t Xi,t
8
Qi,t ÿ Ci,t 1 ÿ f Xi,t
9
Tj,t f Xi,t
10
Case (4): Reservoir at top of sub-catchment For the ®nal case, the controlling equations are basically identical to case (2) except that the natural in¯ow to the sub-catchment does not contribute to the reservoir storage balance; this is controlled purely by upstream inputs, transfers and abstractions: Qiÿ1,t Ti,t ÿ Ci,t ÿ Ai,t Ri,t
11
When the reservoir is full, spill occurs back in the direction of the input transfers, such that the ®nal sub-catchment out¯ow consists only of the natural ¯ow contribution and the compensation ¯ow:
Qi,t Ci,t Ii,t
12
Xi,t Si,tÿ1 Ri,t
13
For Xi,t > 0;
Tj,t Xi,t
For Xi,t <0;
Tj,t 0 and
and Si,t 0 Si,t Xi,t
14 15
The management model is superimposed on the natural ¯ow model for each of the sub-catchments in turn and the total runo accumulated down the network. For the Earl's Burn and Buckie Burn otakes it is assumed that under the present management system, the maximum amount of water is transferred to Loch Coulter, i.e. the fraction, f, is assigned a value of 1. However, when Loch Coulter Reservoir is full, spill is transferred back into the Buckie Burn sub-catchment and f is set to zero. The sub-catchments not de®ned by any of the above management cases were treated as natural, except that inputs from sewage treatment works were added to the natural ¯ow predictions for the urban sub-catchments. MODEL SIMULATIONS
The model simulations were performed for 1995; the only year for which both meteorological and management data were available. The DIY model was applied using daily data; this being the best resolution available both for meteorological and water management data. The daily prediction may lead to some inaccuracy in terms of peak ¯ows, but is sucient for estimation of the total ¯uxes. An internal model time-step of 2 h is used to maintain numerical stability. The rainfall input was based on measurements from four gauges and converted to the appropriate spatial area of each sub-catchment by applying equation 1 to weight the values relative to the location of the raingauge. The two topographic parameters of the DIY model were derived from a 50 m digital elevation model (DEM) of the catchment using Arc/Info GRID functions, in the same manner as for the Ythan catchment (Dunn et al., 1998). Table 2 details some of the physical characteristics of each of the sub-catchments, averaged over the area. The remaining model parameters were calibrated for the upland sub-catchments by using data from Carron Valley reservoir. The predictions of natural ¯ow for the CVR sub-catchment were compared with a time-series of the dierence between the reservoir change in storage and the managed ¯uxes, estimated from the telemetry data. The accuracy of this balance is limited by the relationship between reservoir depth and storage. The calibrated parameter values generated a reasonable comparison with the reservoir balance for the period of re®ll (R2=0.56). The values re¯ect the dominance of the
Natural ¯ow in managed catchments
627
Table 2. Sub-catchment averaged physical characteristics Sub-catchment EBR EBO CVR LGH BBO AUB HWD RED BNY CTL
Area (km2)
Mean elevation (m)
Mean slope (m/m)
Mean distance to stream (m)
LTMAR (mm)
6.1 6.5 37.8 19.0 5.8 21.5 23.3 22.4 29.5 15.0
392 331 328 252 280 134 129 128 83 36
0.049 0.090 0.092 0.095 0.056 0.053 0.062 0.052 0.037 0.028
576 349 401 436 385 387 367 393 374 372
1806 1679 1740 1478 1536 1177 1159 1173 1033 869
fast response mode, with only a small base¯ow component. The physical parameters for the three urban subcatchments in the east were calibrated by comparing predictions from a simulation for 1994 for the CCY sub-catchment with measurements from the gauging station at Castlecary. The values from the upland parameterisation were found to give an equally good ®t to the urban sub-catchments. This indicates that the speed of runo from the relatively ¯at impermeable surfaces in the urban area is similar to that from the steeper upland slopes. Results from the 1995 simulations were compared with gauged ¯ows in the river at Headswood and Castlecary. The area draining to Headswood includes all of the upper Carron Valley and hence covers the principle area of water management. The sub-catchment above Castlecary includes the urban area around Cumbernauld. The bottom two urban sub-catchments, the Bonny Water and the Carron
down to its tidal limit, are not gauged for ¯ow and therefore cannot be validated. Headswood simulations Figure 3(a) shows a comparison between the predictions of ¯ow for the managed catchment with the measured ¯ow at Headswood. In general, there is an acceptable match between the predictions and observations, with an R2 value of 0.75 and a standard error of estimate of 3 m3 sÿ1. As indicated earlier, the R2 value is controlled largely by the accuracy of the peak ¯ow predictions, which are themselves strongly dependent on the rainfall input. The eect of the management on the ¯ow simulations is illustrated by Fig. 3(b). The main dierence between the two simulations is observed during the summer and autumn periods, when the reservoirs are re-®lling their storage. The improvement in prediction of ¯ow that can be attributed to the management model is displayed by the dierence in the R2 value, which drops to 0.65 when the
Fig. 3. 1995 ¯ow predictions at Headswood: (a) measured and predicted managed ¯ow, (b) predicted managed and predicted natural ¯ow.
628
S. M. Dunn and R. C. Ferrier Table 3. 1995 Sub-catchment contributions to runo at four locations, under both managed and natural conditions
Stream location
CVR
EBR
EBO
BBO
LGH
AUB
HWD
Total
Managed sub-catchment contributions (Mm3/yr) Carron U/S of Buckie B 20.5 1.7 Buckie B. outlet ÿ 5.8 Auchenbowie B. outlet ÿ 0.2 Carron at Headswood 20.5 7.5
2.1 6.9 0.3 9
ÿ 5.7 0.2 5.9
20.3 ÿ ÿ 20.3
ÿ ÿ 16.8 16.8
ÿ ÿ ÿ 20.5
44.6 18.4 17.5 101
Natural sub-catchment contributions (Mm3/yr) Carron U/S of Buckie B 50.4 Buckie B. outlet ÿ Auchenbowie B. outlet ÿ Carron at Headswood 50.4
9.9 ÿ ÿ 9.9
ÿ 6.5 ÿ 6.5
20.3 ÿ ÿ 20.3
ÿ ÿ 16.8 16.8
ÿ ÿ ÿ 17.6
88.9 6.5 16.8 130
8.3 ÿ ÿ 8.3
natural ¯ow is compared with the measured ¯ow. The contributions of each sub-catchment to the total ¯ow at four locations is summarised in Table 3, for both the managed and natural scenarios. These data indicate the signi®cance of each sub-catchment in terms of its contribution to the total ¯ow and highlight the locations of the major management activities. The majority of the error in the model simulations can be attributed to uncertainties in rainfall and evapotranspiration, particularly during March, when there is a clear discrepancy in both the managed and natural ¯ow predictions. An analysis of the error in the predictions indicates that there is little bias, with an even spread of under and over-estimates across the range of ¯ows and an average error of estimate of +0.05 m3 sÿ1. There is one outlier, with an error of ÿ28 m3/s, which occurs at the beginning of March and precedes a short period where ¯ows are underestimated. This corresponds to a period when snow was lying for several days in Central Scotland. Castlecary simulations Despite the predominance of urban land in the Castlecary sub-catchment, the river ¯ows can be successfully predicted using the DIY model (Fig. 4). The R2 value for the calibration year of 1994 was 0.77 and for 1995 was 0.75. The small peaks during the summer period are dicult to predict accurately, as there is a very ®ne balance between the rainfall, evapotranspiration and soil storage; if the evapotranspiration is slightly too high, or the soil
storage slightly too low, the fast ¯ow will not occur. MODEL APPLICATION TO INVESTIGATE ALTERNATIVE MANAGEMENT
The inclusion of a management component in the model of the Carron provides a simple tool for investigating how dierent management strategies would aect stream ¯ows. There are two ways in which the management may be modi®ed; the ®rst involving simple adjustments to abstraction levels and reservoir releases, and the second involving adjustments to the rules controlling the intra-basin transfers. The validation simulation was based on the assumption that ¯ows in the Carron catchment are controlled to maximise the potential for storing water; a strategy that will ensure maximum eciency for the water company. To this end, the fraction, f, de®ning the amount of water transferred to Loch Coulter from the Earl's Burn and Buckie Burn, was assigned a value of 1. The eect of this strategy is to over supply Loch Coulter, generating substantial spill from the reservoir. The predicted managed ¯ows in the Buckie Burn are considerably higher than the natural ¯ow would be [Fig. 5(a)]. At the same time, the ¯ows in the River Carron above the Buckie Burn in¯ow are kept to an absolute minimum [Fig. 5(b)]. An alternative management strategy, that would help to minimise disruption of the natural system, would be to limit the transfers of water from the
Fig. 4. 1995 ¯ow predictions at Castlecary.
Natural ¯ow in managed catchments
629
Fig. 5. 1995 predictions of natural and managed ¯ow: (a) at Buckie Burn outlet, (b) in R. Carron upstream of Buckie Burn.
Earl's Burn to those periods when the reservoirs are drawn down. The eect of this strategy on ¯ows can be modelled by introducing a feedback loop to the management model: For Sj,tÿ1 0;
fi,t 0
16
For Sj,tÿ1 <0;
fi,t 1
17
where j represents sub-catchment BBR for i of EBO. The outcome of applying this strategy is summarised in Table 4, in terms of the total predicted runo for the year, under the natural and managed systems, in the Buckie Burn (BBO) and in the River Carron above the Buckie Burn in¯ow (LGH U/S BBO). It is clear that the introduction of a simple feedback on the management controls has helped to revert the ¯ows in both streams towards their natural regime, without aecting the ability of the system to supply the same amount of water or maintain compensation ¯ows. Thus, the modi®ed management would have no detrimental eect for commercial water supply. In relative terms, the greatest disruption of the natural system would remain during periods of low ¯ow, but the high ¯ows, important in determining much of the phy-
siography of the stream, are returned to their natural level. This example involves a simple modi®cation to management strategy that is common sense when demonstrated by the model simulations. However, without the numerical analysis, the spatial changes in ¯ow caused by the water management would not be apparent and therefore such strategies may not be implemented as a matter of course. It is in these situations that modelling can be of great bene®t in integrated catchment management. DISCUSSION AND CONCLUSIONS
The case study of the Carron catchment has highlighted how signi®cantly the natural hydrology of an area may be modi®ed by water management. In the past, hydrological models have not been capable of dealing with such a managed system in any spatially disaggregated way, yet it is in catchments of this type that integrated catchment management is going to be particularly important, as they are the areas that are most likely to have been subject to change. The abstractions in the Carron reduce the total volume of runo from the upland area by 25% in 1995 and a further 10% of the total is unnecessarily re-routed. This has signi®cant eect on
Table 4. 1995 Total runo in the Carron upstream of the Buckie Burn and in the Buckie Burn under dierent management scenarios Sub-catchment
Natural runo (Mm3/y)r
Managed runo (Mm3/yr)
Modi®ed managed runo (Mm3/yr)
BBO LGH U/S BBO
6.5 88.9
18.4 44.6
4.1 59.0
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S. M. Dunn and R. C. Ferrier
the ¯ows which may in turn have implications for other uses and resources of the catchment. A water management component has been developed to describe the transfers and storage of water in the Carron and has been successfully linked to the DIY model at a sub-catchment scale. The combined model permits the in¯uences of the primary management controls to be examined at a resolution that is appropriate to understanding catchment processes. The management component comprises generalised rules that describe reservoir behaviour and water transfers and should be equally as applicable to other catchments as to the Carron, enabling the modelling procedure to be readily transferred. The simulations for both the upland and urban areas demonstrated that the combined model is capable of predicting daily time-series of ¯ow to an acceptable degree of accuracy, given the limitations on available data. The application to the Carron also supports the capacity of the DIY model to represent the hydrology of a catchment dominated by near surface processes, rather than the sub-surface processes for which the model was originally developed. Application of the management model to the Carron Valley sub-catchments demonstrated how the system could be used to assist with the development of management strategies. The challenge for the water managers in a catchment of this type is to ®nd the best compromise between management and the environment. In this particular example, a signi®cant improvement towards the naturalisation of ¯ows could be achieved by the implementation of a simple feedback check on the status of the reservoir storage. Without the spatial analysis of the ¯ows, the opportunity for this improvement is unlikely to have been identi®ed. AcknowledgementsÐThis research was funded by the Scottish Oce Agriculture, Environment and Fisheries
Department. Mr G. Durward at the East of Scotland Water Authority was particularly helpful in providing details of water management operational procedures and access to telemetry data. Stream ¯ow and climate data were kindly supplied by the Scottish Environmental Protection Agency. REFERENCES
Beven K. J., Kirkby M. J., Schoeld N. and Tagg A. (1984) Testing a physically-based ¯ood forecasting model (TOPMODEL) for three U.K. catchments. J. Hydrol. 69, 119±143. Central Regional Council Water and Drainage Department (1983) The Water Resources of the Carron Valley. Prepared by R. H. Cuthbertson and Partners, Edinburgh. Dunn S. M. and Mackay R. (1995) Spatial variation in evapotranspiration and the in¯uence of land use on catchment hydrology. J. Hydrol. 171, 49±73. Dunn S. M., McAlister E. and Ferrier R. C. (1998) Development and application of a distributed catchment scale hydrological model for the River Ythan, NE Scotland. Hydrol. Processes 12, 401±416. European Commission (1996) Commission Communication to the Council and the European Parliament on European Community Water Policy. COM(96) 59. Johnson R. C. (1995) Rainfall distribution in two catchments in Scotland. Proceedings of BHS 5th National Hydrology Symposium, Edinburgh, pp. 8.17±8.21. Likeman M. J., Field S. R., Stevens I. M. and Fleming S. E. (1995) Applications of resource allocation technology in Yorkshire Water. Proceedings of BHS 5th National Hydrology Symposium, Edinburgh, pp. 1.7±1.13. MLURI (1993) The Land Cover of Scotland 1988. Macaulay Land Use Research Institute, Aberdeen, Scotland. Parkin G. (1995) SHETRAN Water Flow Component. WRSRU/TR/9510/61.0. Water Resource Systems Research Unit, Department of Civil Engineering, University of Newcastle upon Tyne. Todini E. (1996) The ARNO rainfall-runo model. J. Hydrol. 175, 339±382. Whitehead P. G., Williams R. J. and Lewis D. R. (1997) Quality simulation along river systems (QUASAR): model theory and development. Sci. Tot. Env. J. 194± 195, 437±445.
Wat. Res. Vol. 33, No. 3, pp. 621±630, 1999 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00
NATURAL FLOW IN MANAGED CATCHMENTS: A CASE STUDY OF A MODELLING APPROACH M S. M. DUNN* and R. C. FERRIER*
Macaulay Land Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, U.K. (First received September 1997; accepted in revised form June 1998) AbstractÐIn the U.K., the water resources of many catchments are heavily managed and the existing constraints on their use must be built into future management. Recent developments in catchment modelling mean that the practical use of models, to analyse catchment behaviour and assist with the management process, is a feasible option. However, few models include appropriate water management components that will permit application to those areas for which they are most needed. This paper describes the integration of simple management controls into a spatially distributed hydrological model and illustrates how the model can be used to assist in catchment management, through a case study of the Carron catchment in Central Scotland. The model was successfully applied to predict ¯ow in both the upland region of the catchment, where there are several reservoirs and signi®cant transfers of water and the lowland region of the catchment, which is a predominantly urban area. A simple modi®cation to the water management procedures illustrates how the model may be used to help achieve naturalisation of the ¯ow regime, thus satisfying the requirements of the precautionary principle. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐnaturalisation, management, modelling, catchment
INTRODUCTION
It is now accepted that the resources of a river basin should be managed as a whole, to minimise the potential con¯icts between the dierent users and activities in the catchment. Until recently, in industrialised and heavily populated nations such as the U.K., the primary consideration in most catchments has been to meet the demands of the public and industry for water supply and power generation. The management of water resources has evolved gradually over the years and many of the developments cannot simply be reversed. Instead they must be integrated in the most appropriate manner to future plans for managing the catchment. The challenge for the water manager is to identify potential con¯icts and the ¯exibility within the system that will allow these con¯icts to be minimised. The objectives of new European Community Water Policy as described in a recent Commission Communication (European Commission, 1996) identify a need for greater integration between factors such as water quantity and quality and water use and environmental protection. One of the key approaches underlying the new policy, is that of the precautionary principle, which advises that policy should err on the side of caution where there are *Author to whom all correspondence should be addressed. [Tel.: +44-1224-318611; Fax: +44-1224-311556; E-mail: [email protected]]. 621
doubts or where insucient information is available. One implication of this with respect to water management is that there should be an objective to maintain ¯ow regimes as close to natural as is feasible. Some water supply companies use sophisticated linear programming resource allocation tools to analyse the water management system. WRAP (water resource allocation planning) developed for Yorkshire Water (Likeman et al., 1995) is one example of a model that can be used in a region where there are over 130 reservoirs as well as borehole and river abstractions. However, the primary function of this and similar models is to determine the optimum strategy for abstracting water to minimise cost, whilst meeting consumer demand requirements. The models take no account of the natural hydrological system. Equally, there is a plethora of models available for analysing natural catchment hydrology, e.g. TOPMODEL (Beven et al., 1984) ARNO (Todini, 1996) and SHETRAN (Parkin, 1995), but few that are capable of analysing highly managed systems. Fewer still are capable of accounting for water management in any spatially distributed form, that would permit the more subtle relationships between natural ¯ows and management to be identi®ed. The water quality model QUASAR (Whitehead et al., 1997) goes some way towards this by combining hydrological and chemical inputs and outputs to a catchment river system on a reach basis. However,
622
S. M. Dunn and R. C. Ferrier Table 1. DIY model parameters
Parameter
Function
Saturated hydraulic conductivity Soil porosity Fast response threshold storage Fast response distance
control rate of slow response runo de®ne relationship between soil storage and head soil moisture level at which fast runo response is initiated de®ne density of localised drainage network for fast ¯ow routing (related to macropores, arti®cial drainage or rill generation) set lower limit on sub-surface ¯ow de®ne the hydraulic gradient for hill-slope model de®ne the hill-slope routing distance for each cell
Minimum soil storage-slope Slope to stream Flow path distance to stream
the model does not attempt to model the inter-relationships between these inputs and outputs and cannot therefore be used directly to investigate the eects of management. Thus, the existing range of modelling tools are limited in their ability to integrate the needs of catchment management in terms of the available water resource with that of the ecosystem value of the natural catchment. This paper describes the integration of a GIS based spatially distributed model of natural hydrology with a water management component, and demonstrates its value through a case study of the River Carron catchment, in Central Scotland. The case study describes how the hydrological model was adapted to take account of management and demonstrates how the model can be used to investigate possible approaches for improving water management practice in the catchment with respect to naturalisation of the ¯ows. MODELLING APPROACH
The aim of the research was to develop an integrated model capable of: (a) Predicting time-series of ¯ow in a managed catchment. (b) Demonstrating how dierent management strategies aect stream ¯ows at dierent locations. The distributed model used to describe the natural hydrology was originally developed for the Ythan catchment in NE Scotland. The model (hereafter referred to as DIY) is presented in detail in Dunn et al. (1998). The philosophy of the DIY model is to allow relatively detailed, 50 50 m resolution, data to be used to characterise hydrological processes at a small scale, and then to scale up to the catchment resolution by combining the hydrological responses from areas that are similar at the smaller scale. This is achieved by applying a disaggregated hill-slope ¯ow model to each characteristic 50 50 m cell in the catchment and calculating the temporal contribution that each cell makes to stream ¯ow. There are two basic response modes, fast and slow, with the relative importance of each mode determined by the soil moisture storage. The DIY model is driven by daily inputs of rainfall and evapotranspiration and involves 7 parameters which are listed in Table 1, together with an outline of their function.
The topographic parameters are derived from a Geographic Information System using a digital elevation model (DEM) and digital rivers data. In conjunction with the ®ve physical properties, relating to the soil and drainage system, they control the response of the Hill-slope model. Each of the parameters can in theory vary spatially, but to limit the number of variations of parameter combinations, only the most signi®cant and identi®able spatial dierences are included. The Hill-slope model output is scaled up to predict ¯ow at dierent locations on the stream network by using the GIS to identify the combination of characteristic cells (as determined by the model parameters) that drain to each point on the stream network. The Carron catchment, to which the model is applied here, contrasts sharply with the Ythan catchment, on which it was developed, in terms of its topography, climate, soils and land use. As such, this application will provide a useful additional test of the capability of the model. The model of the natural hydrology has been integrated with a water management component at the sub-catchment scale; where the sub-catchment outlets are de®ned by the location of principle management activities and major stream junctions. The spatial complexity introduced by the presence of reservoirs and aqueducts prevents more detailed spatial representation of the managed system. The combined natural and managed model is applied by sequential simulation of each sub-catchment down the network of the full catchment, at each stage generating predictions of the in¯ow to the downstream sub-catchment and transfers to other subcatchments. The predictions of ¯ow for the Carron are validated by comparing them with daily stream ¯ow measurements at two locations in the catchment. THE CARRON CATCHMENT
The River Carron at Carron Iron Works (NGR 2880 6823) drains a natural area of 187 km2 in Central Scotland (Fig. 1). The source of the river is in the west of the catchment, which is bounded by hills rising to 570 m, whilst the south is drained from lower land by the Red Burn and Bonny Water. In addition to the natural area, water may be diverted into the catchment from a further
Natural ¯ow in managed catchments
623
Fig. 1. The Carron catchment.
22 km2 of the River Endrick catchment, to the northwest. Data from the Land Cover of Scotland 1988 data set (MLURI, 1993) show the dominant land use in the catchment to be improved grassland, which covers much of the central and eastern areas. There is a large area of coniferous plantation in the west and urban land dominates the south and east. The urban area includes the new town of Cumbernauld as well as much of the Falkirk and Larbert area. There is a strong precipitation gradient across the catchment from a mean annual rainfall of 758 mm at Polmonthill, to the east, to 1665 mm at Waterhead, at a height of 360 m in the west. The population of the east of the catchment is around 100,000 and as a consequence, the water resources of the upper Carron Valley are heavily managed for public water supply. An area of 38 km2 of the natural catchment drains directly into Carron Valley reservoir and a further 25 km2 is controlled by the Earlsburn reservoirs and by diversions into aqueducts that link areas to reservoirs in the north. The urban area imposes additional constraints on the management of the water resources through the generation of both sewage euent and poor quality urban runo. The combination of high rainfall with poorly drained soils in the west suggests that the hydrology is likely to be dominated by movement of water close to the land surface. Recharge to groundwater sources will be limited by the low permeability of the overlying soils. The urban area will also generate a substantial amount of rapid runo from its impermeable surfaces. The eect of these character-
istics is to create a rapidly responding system, although the presence of the reservoirs will damp the runo from the upland areas during periods of re-®ll. CLIMATE
Given the high precipitation gradient across the Carron catchment, an understanding of the spatial variability of the rainfall is a prerequisite to successful hydrological modelling. Therefore, data from 18 raingauges, within and close to the catchment, were analysed to identify spatial relationships. To achieve a consistent set of data, the long term mean annual rainfall (LTMAR) at each site was estimated. Sites where a long record was available were used to estimate the ratio of the mean annual rainfall, calculated over dierent periods, to the LTMAR. In this way, the measurements from each gauge were converted to the same standard period of 1941±1970. Linear regression analysis between the elevation of each gauge and its easting, to re¯ect the dominance of westerly winds, gave the following relationship to estimate the long term mean annual rainfall (P in mm): P 1:96:H ÿ 14:3:E 1190 with R2 0:90
1
where H is elevation (m) and E is distance east of NGR easting 260000 (km). The regression analysis provides a method for estimating the annual rainfall in dierent parts of the catchment. However, the relationship must be treated with some caution for higher elevations, as the highest gauge used to derive the equations was
624
S. M. Dunn and R. C. Ferrier
at 360 m and the rainfall at this location is slightly overestimated. A similar analysis carried out by Johnson (1995) at Balquhidder, some 40 km further north, found a signi®cantly lower elevation factor of 0.78 as compared to the 1.96 derived here. Estimates of evapotranspiration in the catchment have been based on monthly MORECS potential evapotranspiration totals for the area, with an allowance for land use and soil moisture status. A ®xed percentage of the daily rainfall is assumed to be lost from interception evaporation, with the percentage determined by the land cover. Based on more detailed analysis from other upland areas of the U.K. (Dunn and Mackay, 1995) values of 25, 5
and 10% were assumed, respectively, for forested land, urban land and other land covers. The remaining evapotranspiration loss was estimated from the potential rate, with a soil moisture limitation derived from the antecedent input of net ``rainfall ÿ evapotranspiration''.
WATER MANAGEMENT
A simpli®ed representation of the water management system in the Carron catchment is illustrated at the sub-catchment scale, used by the model, in Fig. 2.
Fig. 2. Sub-catchment management model structure.
Natural ¯ow in managed catchments
The complex system of reservoirs and aqueducts has developed in an ad hoc manner over a long period. The original function of some of the reservoirs is unclear and ecient management of the resources is a complex issue. A study of the water resources of the Carron Valley above Longhill was undertaken for the Central Regional Council in 1983 (Central Regional Council Water and Drainage Department, 1983). The study was aimed at identifying cost eective methods for improving the eciency of use of the Carron Valley resources, to provide a cheaper source of water than that provided by the forced purchase of water from outside the region. Material from the 1983 study has been supplemented by additional information and data relating to the current operational procedures (Durward, East of Scotland Water Authority, personal communication). In particular, data have been made available, by the East of Scotland Water Authority, from a system of telemetry that was installed in 1992 to monitor and control the releases, abstractions and levels in Carron Valley reservoir. This data set provides important information for use in the development and testing of the water management component of the catchment model. Carron Valley reservoir is the largest water body in the catchment with a capacity of 21.4 Mm3. It is the main source of public water supply in the catchment, feeding two ®lter stations with typical abstraction rates of the order of 1.2 and 0.05 m3 sÿ1. Compensation ¯ow must be released from the reservoir to both the River Carron, at the east end, and to the River Endrick (out of the catchment), at the west end. The Earlsburn reservoirs in the north of the catchment regulate ¯ows and can be used both to assist in achieving the required minimum ¯ow in the River Carron and to control the transfer of water to Loch Coulter, via Buckieburn reservoir. Once ¯ow has passed the otake point on the Earl's Burn it can no longer be controlled, which means that in practice the majority of the ¯ow is diverted to Loch Coulter where it may still be used. Buckieburn reservoir acts as a transfer basin between the Earl's Burn and Loch Coulter and also receives diverted water from 2.8 km2 of the catchment to its north. The Buckie Burn receives compensation ¯ow from the reservoir and also any spill of excess water from Loch Coulter. In the lower part of the catchment there are three principle sewage treatment works at Bonnybridge, Dunnswood and Denny that typically discharge 0.11, 0.12 and 0.09 m3 sÿ1, respectively. The ¯ow routing in the urban areas is signi®cantly modi®ed by storm water sewers but it is assumed that, for modelling purposes, it can be represented as an analogous process to the natural regime, with altered values for parameters such as hydraulic conduc-
625
tivity and fast response distance. Industrial abstractions and releases are assumed to be self-balancing in terms of ¯ow volume.
MANAGEMENT MODEL
There are four dierent forms of ¯ow management control that apply to the Carron sub-catchments, relating to the following cases: (1) Flow controlled by a reservoir at the outlet of the sub-catchment (applies to Carron Valley reservoir, CVR, and Earls Burn reservoir, EBR, subcatchments). (2) As for case (1), except that excess ¯ow above compensation may be transferred to an adjacent sub-catchment, rather than passed directly downstream (applies to Buckie Burn otake, BBO, subcatchment). (3) Flow controlled by an otake, with no storage, at the outlet of the sub-catchment (applies to Earls Burn otake, EBO, sub-catchment). (4) Flow controlled by a reservoir at the top of the sub-catchment, with spill into an adjacent subcatchment (applies to Auchenbowie Burn, AUB, sub-catchment). Although these management controls have been identi®ed speci®cally for the Carron catchment, they are generally applicable to other managed catchments and the modelling procedure could be readily transferred. The simpli®ed network structure illustrated in Fig. 2 de®nes each sub-catchment according to its principle management controls and identi®es the natural and arti®cial links between each sub-catchment. For each of the management cases described above, a dierent set of rules is applied as described below, using an explicit ®nite dierence sub-catchment storage balance. Case (1): Reservoir at sub-catchment outlet The net in¯ow to the reservoir for sub-catchment i is calculated at time-step t by: Ii,t Qiÿ1,t Ti,t ÿ Ci,t ÿ Ai,t Ri,t
2
where Ii,t is the natural sub-catchment runo at time t (L3Tÿ1); Qi ÿ 1,t is the out¯ow from the upstream sub-catchment i ÿ 1 at time t (L3Tÿ1); Ti,t is the net transfer into sub-catchment i at time t (L3Tÿ1); Ci,t is the reservoir compensation ¯ow at time t (L3Tÿ1); Ai,t is the abstraction from the reservoir at time t (L3Tÿ1) and Ri,t is the net addition to the reservoir storage at time t (L3Tÿ1). A cumulative balance of the reservoir storage is maintained to determine whether there is any spill from the reservoir. The reservoir excess is calculated from the storage at the previous time-step by: Xi,t Si,tÿ1 Ri,t
3
where, Xi,t is the reservoir excess at time t (L3Tÿ1)
626
S. M. Dunn and R. C. Ferrier
and Si,t is the reservoir storage balance, below spill height, at time t (L3Tÿ1). If there is a positive reservoir excess, spill occurs and the reservoir storage balance is reset to zero, otherwise the sub-catchment out¯ow consists only of the compensation ¯ow: For Xi,t > 0;
Qi,t Ci,t Xi,t
For Xi,t <0;
Qi,t Ci,t
and
and
Si,t 0 4
Si,t Xi,t
5
Case (2): Reservoir at outlet and transfer of excess Case (2) is identical to case (1) except that the out¯ow from the sub-catchment is limited to the compensation ¯ow and a fraction of the excess ¯ow. The remaining excess ¯ow is transferred to an adjacent sub-catchment that is not directly downstream. For Xi,t > 0;
Tj,t f Xi,t ;
Qi,t Ci,t 1 ÿ f Xi,t ; For Xi,t <0;
Tj,t 0;
Si,t 0
Qi,t Ci,t ;
6
Si,t Xi,t 7
where the symbols are as for case (1) and Tj,t is the transfer out of the sub-catchment into some neighbouring sub-catchment, j, at time t (L3Tÿ1) and f is the fraction of excess runo transferred out of the sub-catchment. Case (3): Otake at sub-catchment outlet Where there is an otake at the outlet, the subcatchment out¯ow is normally limited to satisfy the compensation ¯ow requirements of the stream. Additional runo may be arti®cially transferred by aqueduct or pipe to an adjacent sub-catchment. The equations controlling this management are: Ii,t Qiÿ1,t Ti,t ÿ Ci,t Xi,t
8
Qi,t ÿ Ci,t 1 ÿ f Xi,t
9
Tj,t f Xi,t
10
Case (4): Reservoir at top of sub-catchment For the ®nal case, the controlling equations are basically identical to case (2) except that the natural in¯ow to the sub-catchment does not contribute to the reservoir storage balance; this is controlled purely by upstream inputs, transfers and abstractions: Qiÿ1,t Ti,t ÿ Ci,t ÿ Ai,t Ri,t
11
When the reservoir is full, spill occurs back in the direction of the input transfers, such that the ®nal sub-catchment out¯ow consists only of the natural ¯ow contribution and the compensation ¯ow:
Qi,t Ci,t Ii,t
12
Xi,t Si,tÿ1 Ri,t
13
For Xi,t > 0;
Tj,t Xi,t
For Xi,t <0;
Tj,t 0 and
and Si,t 0 Si,t Xi,t
14 15
The management model is superimposed on the natural ¯ow model for each of the sub-catchments in turn and the total runo accumulated down the network. For the Earl's Burn and Buckie Burn otakes it is assumed that under the present management system, the maximum amount of water is transferred to Loch Coulter, i.e. the fraction, f, is assigned a value of 1. However, when Loch Coulter Reservoir is full, spill is transferred back into the Buckie Burn sub-catchment and f is set to zero. The sub-catchments not de®ned by any of the above management cases were treated as natural, except that inputs from sewage treatment works were added to the natural ¯ow predictions for the urban sub-catchments. MODEL SIMULATIONS
The model simulations were performed for 1995; the only year for which both meteorological and management data were available. The DIY model was applied using daily data; this being the best resolution available both for meteorological and water management data. The daily prediction may lead to some inaccuracy in terms of peak ¯ows, but is sucient for estimation of the total ¯uxes. An internal model time-step of 2 h is used to maintain numerical stability. The rainfall input was based on measurements from four gauges and converted to the appropriate spatial area of each sub-catchment by applying equation 1 to weight the values relative to the location of the raingauge. The two topographic parameters of the DIY model were derived from a 50 m digital elevation model (DEM) of the catchment using Arc/Info GRID functions, in the same manner as for the Ythan catchment (Dunn et al., 1998). Table 2 details some of the physical characteristics of each of the sub-catchments, averaged over the area. The remaining model parameters were calibrated for the upland sub-catchments by using data from Carron Valley reservoir. The predictions of natural ¯ow for the CVR sub-catchment were compared with a time-series of the dierence between the reservoir change in storage and the managed ¯uxes, estimated from the telemetry data. The accuracy of this balance is limited by the relationship between reservoir depth and storage. The calibrated parameter values generated a reasonable comparison with the reservoir balance for the period of re®ll (R2=0.56). The values re¯ect the dominance of the
Natural ¯ow in managed catchments
627
Table 2. Sub-catchment averaged physical characteristics Sub-catchment EBR EBO CVR LGH BBO AUB HWD RED BNY CTL
Area (km2)
Mean elevation (m)
Mean slope (m/m)
Mean distance to stream (m)
LTMAR (mm)
6.1 6.5 37.8 19.0 5.8 21.5 23.3 22.4 29.5 15.0
392 331 328 252 280 134 129 128 83 36
0.049 0.090 0.092 0.095 0.056 0.053 0.062 0.052 0.037 0.028
576 349 401 436 385 387 367 393 374 372
1806 1679 1740 1478 1536 1177 1159 1173 1033 869
fast response mode, with only a small base¯ow component. The physical parameters for the three urban subcatchments in the east were calibrated by comparing predictions from a simulation for 1994 for the CCY sub-catchment with measurements from the gauging station at Castlecary. The values from the upland parameterisation were found to give an equally good ®t to the urban sub-catchments. This indicates that the speed of runo from the relatively ¯at impermeable surfaces in the urban area is similar to that from the steeper upland slopes. Results from the 1995 simulations were compared with gauged ¯ows in the river at Headswood and Castlecary. The area draining to Headswood includes all of the upper Carron Valley and hence covers the principle area of water management. The sub-catchment above Castlecary includes the urban area around Cumbernauld. The bottom two urban sub-catchments, the Bonny Water and the Carron
down to its tidal limit, are not gauged for ¯ow and therefore cannot be validated. Headswood simulations Figure 3(a) shows a comparison between the predictions of ¯ow for the managed catchment with the measured ¯ow at Headswood. In general, there is an acceptable match between the predictions and observations, with an R2 value of 0.75 and a standard error of estimate of 3 m3 sÿ1. As indicated earlier, the R2 value is controlled largely by the accuracy of the peak ¯ow predictions, which are themselves strongly dependent on the rainfall input. The eect of the management on the ¯ow simulations is illustrated by Fig. 3(b). The main dierence between the two simulations is observed during the summer and autumn periods, when the reservoirs are re-®lling their storage. The improvement in prediction of ¯ow that can be attributed to the management model is displayed by the dierence in the R2 value, which drops to 0.65 when the
Fig. 3. 1995 ¯ow predictions at Headswood: (a) measured and predicted managed ¯ow, (b) predicted managed and predicted natural ¯ow.
628
S. M. Dunn and R. C. Ferrier Table 3. 1995 Sub-catchment contributions to runo at four locations, under both managed and natural conditions
Stream location
CVR
EBR
EBO
BBO
LGH
AUB
HWD
Total
Managed sub-catchment contributions (Mm3/yr) Carron U/S of Buckie B 20.5 1.7 Buckie B. outlet ÿ 5.8 Auchenbowie B. outlet ÿ 0.2 Carron at Headswood 20.5 7.5
2.1 6.9 0.3 9
ÿ 5.7 0.2 5.9
20.3 ÿ ÿ 20.3
ÿ ÿ 16.8 16.8
ÿ ÿ ÿ 20.5
44.6 18.4 17.5 101
Natural sub-catchment contributions (Mm3/yr) Carron U/S of Buckie B 50.4 Buckie B. outlet ÿ Auchenbowie B. outlet ÿ Carron at Headswood 50.4
9.9 ÿ ÿ 9.9
ÿ 6.5 ÿ 6.5
20.3 ÿ ÿ 20.3
ÿ ÿ 16.8 16.8
ÿ ÿ ÿ 17.6
88.9 6.5 16.8 130
8.3 ÿ ÿ 8.3
natural ¯ow is compared with the measured ¯ow. The contributions of each sub-catchment to the total ¯ow at four locations is summarised in Table 3, for both the managed and natural scenarios. These data indicate the signi®cance of each sub-catchment in terms of its contribution to the total ¯ow and highlight the locations of the major management activities. The majority of the error in the model simulations can be attributed to uncertainties in rainfall and evapotranspiration, particularly during March, when there is a clear discrepancy in both the managed and natural ¯ow predictions. An analysis of the error in the predictions indicates that there is little bias, with an even spread of under and over-estimates across the range of ¯ows and an average error of estimate of +0.05 m3 sÿ1. There is one outlier, with an error of ÿ28 m3/s, which occurs at the beginning of March and precedes a short period where ¯ows are underestimated. This corresponds to a period when snow was lying for several days in Central Scotland. Castlecary simulations Despite the predominance of urban land in the Castlecary sub-catchment, the river ¯ows can be successfully predicted using the DIY model (Fig. 4). The R2 value for the calibration year of 1994 was 0.77 and for 1995 was 0.75. The small peaks during the summer period are dicult to predict accurately, as there is a very ®ne balance between the rainfall, evapotranspiration and soil storage; if the evapotranspiration is slightly too high, or the soil
storage slightly too low, the fast ¯ow will not occur. MODEL APPLICATION TO INVESTIGATE ALTERNATIVE MANAGEMENT
The inclusion of a management component in the model of the Carron provides a simple tool for investigating how dierent management strategies would aect stream ¯ows. There are two ways in which the management may be modi®ed; the ®rst involving simple adjustments to abstraction levels and reservoir releases, and the second involving adjustments to the rules controlling the intra-basin transfers. The validation simulation was based on the assumption that ¯ows in the Carron catchment are controlled to maximise the potential for storing water; a strategy that will ensure maximum eciency for the water company. To this end, the fraction, f, de®ning the amount of water transferred to Loch Coulter from the Earl's Burn and Buckie Burn, was assigned a value of 1. The eect of this strategy is to over supply Loch Coulter, generating substantial spill from the reservoir. The predicted managed ¯ows in the Buckie Burn are considerably higher than the natural ¯ow would be [Fig. 5(a)]. At the same time, the ¯ows in the River Carron above the Buckie Burn in¯ow are kept to an absolute minimum [Fig. 5(b)]. An alternative management strategy, that would help to minimise disruption of the natural system, would be to limit the transfers of water from the
Fig. 4. 1995 ¯ow predictions at Castlecary.
Natural ¯ow in managed catchments
629
Fig. 5. 1995 predictions of natural and managed ¯ow: (a) at Buckie Burn outlet, (b) in R. Carron upstream of Buckie Burn.
Earl's Burn to those periods when the reservoirs are drawn down. The eect of this strategy on ¯ows can be modelled by introducing a feedback loop to the management model: For Sj,tÿ1 0;
fi,t 0
16
For Sj,tÿ1 <0;
fi,t 1
17
where j represents sub-catchment BBR for i of EBO. The outcome of applying this strategy is summarised in Table 4, in terms of the total predicted runo for the year, under the natural and managed systems, in the Buckie Burn (BBO) and in the River Carron above the Buckie Burn in¯ow (LGH U/S BBO). It is clear that the introduction of a simple feedback on the management controls has helped to revert the ¯ows in both streams towards their natural regime, without aecting the ability of the system to supply the same amount of water or maintain compensation ¯ows. Thus, the modi®ed management would have no detrimental eect for commercial water supply. In relative terms, the greatest disruption of the natural system would remain during periods of low ¯ow, but the high ¯ows, important in determining much of the phy-
siography of the stream, are returned to their natural level. This example involves a simple modi®cation to management strategy that is common sense when demonstrated by the model simulations. However, without the numerical analysis, the spatial changes in ¯ow caused by the water management would not be apparent and therefore such strategies may not be implemented as a matter of course. It is in these situations that modelling can be of great bene®t in integrated catchment management. DISCUSSION AND CONCLUSIONS
The case study of the Carron catchment has highlighted how signi®cantly the natural hydrology of an area may be modi®ed by water management. In the past, hydrological models have not been capable of dealing with such a managed system in any spatially disaggregated way, yet it is in catchments of this type that integrated catchment management is going to be particularly important, as they are the areas that are most likely to have been subject to change. The abstractions in the Carron reduce the total volume of runo from the upland area by 25% in 1995 and a further 10% of the total is unnecessarily re-routed. This has signi®cant eect on
Table 4. 1995 Total runo in the Carron upstream of the Buckie Burn and in the Buckie Burn under dierent management scenarios Sub-catchment
Natural runo (Mm3/y)r
Managed runo (Mm3/yr)
Modi®ed managed runo (Mm3/yr)
BBO LGH U/S BBO
6.5 88.9
18.4 44.6
4.1 59.0
630
S. M. Dunn and R. C. Ferrier
the ¯ows which may in turn have implications for other uses and resources of the catchment. A water management component has been developed to describe the transfers and storage of water in the Carron and has been successfully linked to the DIY model at a sub-catchment scale. The combined model permits the in¯uences of the primary management controls to be examined at a resolution that is appropriate to understanding catchment processes. The management component comprises generalised rules that describe reservoir behaviour and water transfers and should be equally as applicable to other catchments as to the Carron, enabling the modelling procedure to be readily transferred. The simulations for both the upland and urban areas demonstrated that the combined model is capable of predicting daily time-series of ¯ow to an acceptable degree of accuracy, given the limitations on available data. The application to the Carron also supports the capacity of the DIY model to represent the hydrology of a catchment dominated by near surface processes, rather than the sub-surface processes for which the model was originally developed. Application of the management model to the Carron Valley sub-catchments demonstrated how the system could be used to assist with the development of management strategies. The challenge for the water managers in a catchment of this type is to ®nd the best compromise between management and the environment. In this particular example, a signi®cant improvement towards the naturalisation of ¯ows could be achieved by the implementation of a simple feedback check on the status of the reservoir storage. Without the spatial analysis of the ¯ows, the opportunity for this improvement is unlikely to have been identi®ed. AcknowledgementsÐThis research was funded by the Scottish Oce Agriculture, Environment and Fisheries
Department. Mr G. Durward at the East of Scotland Water Authority was particularly helpful in providing details of water management operational procedures and access to telemetry data. Stream ¯ow and climate data were kindly supplied by the Scottish Environmental Protection Agency. REFERENCES
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