1 urbext1990

3.01

The ReFH rainfall-runoff model and the design event inputs have been calibrated so as to match, on average, flood frequency curves derived from pooled statistical analysis at 100 gauging stations. The model was calibrated up to return periods of 150 years, relatively long compared with the FEH rainfall-runoff model, which was only calibrated to the 10-year return period. The number of catchments used to calibrate the two methods is similar; however, calibration of the ReFH method used more data at each site, and included larger events. The ReFH method differs from the original FEH design event model in that it has been calibrated such that the T-year design rainfall

Table 13.4 Comparison of FEH rainfall-runoff and ReFH methods

ReFH

Losses calculation

Unit hydrograph shape Baseflow calculation Specification of return period

Seasonality

Constant percentage runoff

Triangle

Constant

Rainfall return period different from flow (winter event)

Winter/summer rainfall profiles

Varies through event, calculated by continuous accounting of soil moisture Kinked triangle Varies through event Calibrated such that design rainfall return period is the same as the required flow return period. Losses adjusted for return period Rainfall depth and initial soil moisture vary with season

Fig. 13.9 Design inputs and modelled hydrograph for a 1000-year return period event over the River Brett.

is used to generate the T-year design flow. The calculation of ReFH model parameters and design inputs also accounts for seasonality. Table 13.4 summarises the main differences between the original FEH and the ReFH design event methods.

Fig. 13.9 shows the design rainfall, net rainfall and runoff components estimated using the ReFH method for a 1000-year return period event on the River Brett, as described earlier. The change in effective percentage runoff during the event can be seen by comparison of the design rainfall and net rainfall hyetographs. The ReFH model was used in this study to obtain a hydrograph estimate for the long return period of 1000 years. For such a rare event, the pooled FEH statistical method, which used 500 station-years of record, is not considered adequate for confident estimation. The design event method is chosen instead so as to make use of information in rainfall

Volumetric Drop Size Distribution

Fig. 13.9 Design inputs and modelled hydrograph for a 1000-year return period event over the River Brett.

frequency estimates, which are regarded as more reliable for very rare events, because many rainfall records are significantly longer than flow records.

13.6 Low-flow estimation in the UK

A key element in water resources planning is to assess the low-flow resource available from water-courses. This provides information on whether there is a surplus or deficit of water available to meet current licensed abstractions. Scenarios are usually evaluated with reference to the flow rate that can be expected for a specified number of days in the year, i.e. the flow-duration curve. Hydrological analysis is therefore required to estimate mean flow and flow-duration curve statistics. In 1998 a survey found that there were 4400 requests for low-flow statistics made each year in the Environment Agency (Gustard et al., 2004).

The approach used in the UK for assessing low flow for abstraction management planning is to produce flow-duration curves for a range of situations including the natural, current and future demand scenarios. Flow-duration curves can be derived directly from the many continuous recording flow gauges in England and Wales. However, despite this dense gauging network, by international standards, over 95 per cent of river reaches in England and Wales are distant from a flow-measuring station. At these sites a model to regionalise the low-flow statistics is required.

There are many techniques that have been applied in different parts of the world for estimating statistics describing the low-flow regime at ungauged sites. In Europe, studies include Martin and Cunnane (1976) in Ireland, Lundquist and Krokli (1985) in Norway, and Gustard et al. (1989) in northern and western Europe. Tallaksen and van Lanen (2004) give an overview of the low-flow hydrology methods.

The 1980 Low Flow Studies Report (Institute of Hydrology, 1980) was the first major study of the relationships between low-flow regimes and physiographic and climatic catchment characteristics in the UK. Subsequently there have been many regional low-flow estimation procedures developed for application within the UK including Pirt and Douglas (1982), Gustard et al. (1987) and Young et al. (2000). The basis for the methods now used in the UK was presented in detail by Holmes et al. (2002a, b) and are incorporated into the LowFlows software (see Section 13.6.4).

13.6.1 Naturalised river flows

Natural river flow regimes are dependent on rainfall, temperature and evaporation. On a local scale, the flow regime is controlled by the physical properties of a catchment, including geology, land use and the presence of surface water bodies. River flow regimes are also affected directly and indirectly by human activities. A review of over 1600 gauging stations has identified that <20 per cent of gauged catchments within the UK can be regarded as being natural (Gustard et al., 1992). The impacts of these activities vary considerably and are dependent to a certain extent on the characteristics of the catchment.

For water management purposes, it is essential to differentiate between the natural and artificial components of stream-flow data. Fig. 13.10, for example, shows gauged and naturalised discharges for the River Thames at Kingston. Flow naturalisation is the process of adjusting an observed flow hydrograph to remove the effects of artificial influences. Artificial influences include surface and

Jan 2003 Mar 2003 May 2003 Jul 2003 Sep 2003 Nov 2003 Jan 2004

Fig. 13.10 Gauged and naturalised flow data for 2003 form the River Thames at Kingston, London, UK.

Jan 2003 Mar 2003 May 2003 Jul 2003 Sep 2003 Nov 2003 Jan 2004

Fig. 13.10 Gauged and naturalised flow data for 2003 form the River Thames at Kingston, London, UK.

groundwater abstractions, discharges from sewage treatment plants and industrial sources, impounding reservoirs, canal transfers and inter-basin transfer schemes. The difficulties in obtaining reliable data on these influences and the need for assumptions means that naturalisation is notoriously difficult to carry out and may be associated with errors up to something on the order of 40 per cent. Despite the uncertainty, separation of the components enables assessment of the natural reliable yield of the catchment, based upon the climatically driven variability of the natural stream flow. The impacts of actual and planned water resource management scenarios can then be compared with the natural flow regime to assess yield and environmental impact.

13.6.2 Estimation of low-flow statistics in the UK

Constraints on exploitation of water resources are concentrated around the low flows, and so estimation of the natural flow regime in water resources is often synonymous with assessing the low-flow statistics. Four methods for estimating low flows are commonly applied in the UK. These are:

(1) calculation of low-flow statistics from continuous gauged flow data series;

(2) direct measurement of flows by an occasional programme of flow measurement using current meters or temporary gauges;

(3) estimation of time series of river flow using rainfall-runoff models;

(4) estimation of flow statistics by using generalised models which relate low flows to the physical and climatic characteristics of the catchment.

Where continuous flow data are available for the catchment of interest, method 1 is the most accurate and preferred technique. However, flow estimates are often required for ungauged catchments and therefore method 4 is commonly used.

Table 13.5 Methodology for estimating natural and artificially influenced low-flow statistics for an ungauged location, as used in the UK in the 'LowFlows' system

Step

1 Estimation of key natural low-flow statistics for the ungauged catchment

2 Identification of all upstream artificial influences

3 Quantification of all individual upstream artificial influences

4 Simulation of the reduction in stream flow associated with abstractions from groundwater sources

5 Construction of a monthly artificial influence profile for upstream abstractions. Construction of release duration profiles for each upstream impounding reservoir

6 Combination of the estimated natural monthly low-flow statistics with the artificial influence profiles

7 Aggregation of monthly artificially influenced low-flow statistics

8 Estimation of natural and artificially influenced low-flow statistics for discrete river stretches

Data, model or output

Mean flow, monthly mean flow, monthly flow-duration curves and mean monthly minima

Abstractions from surface and groundwater sources, discharges to surface water, impacts of impounding reservoirs

Actual values of monthly abstraction rates, discharge returns and reservoir compensation flows (represented as release profiles)

Analytical model based on source and aquifer properties

Represents the net impact of all upstream abstractions and discharges (excluding those above any impounding reservoirs) within the catchment

Generates estimated artificially influenced monthly low-flow statistics

Generates annual artificially influenced flow statistics, mean flow and flow-duration curves

Generates residual flow diagrams

The impact of artificial influences is most severe during periods of low flows when absolute volumes of water transfers represent a significantly higher proportion of the natural flow regime. Natural low-flow statistics and artificial influence data are therefore analysed on a monthly basis and allows the seasonal variations to be taken into account. The overall methodology for estimating both natural and artificially influenced low-flow statistics in ungauged catchments is summarised within eight steps listed in Table 13.5.

¡3.6.3 Models for estimation of natural low-flow statistics

For regionalised analysis of flow duration statistics, it is usual to express the individual catchment daily flows as a percentage of the long-term mean flow for the catchment to remove the majority of the influence of hydrological scale. Low-flow estimation methods in the UK use the HOST hydrological response classification (Boorman et al., 1995) of soils as an indication of the hydrogeological and soil characteristics within a catchment, alongside data about average annual runoff. The procedure for estimating the annual flow-duration curve and mean flow from catchment characteristics is shown in Fig. 13.11.

Problems Ungauged Basins
Fig. 13.11 Estimation of naturalised low-flow statistics for ungauged catchment.

The methods are based around using a digital terrain model to generate a catchment boundary for any location on a watercourse. Using this boundary, the physical catchment characteristics are extracted from digital grids.

A region-of-influence (ROI) regionalisation approach is used as described by Holmes etal. (2002a). The ROI approach develops an estimate of a flow statistic at an ungauged 'target' catchment from observed values of that flow statistic made at a set of gauged catchments, which are considered to be hydrologically similar to the target. This set is considered a 'region' within the space defined by the parameters used to assess similarity (note that this is not necessarily geographical space). In application to a catchment, the methods can be summarised as the following steps:

(1) catchment similarity is assessed by calculating a weighted Euclidean distance, in HOST parameter space, between the target catchment and the catchments within a similar climatic pool;

(2) a 'region' is formed around the target catchment by ranking all of the catchments in the data pool by their weighted Euclidean distance in HOST space and selecting the five catchments that are closest to the target catchment;

(3) a standardised annual flow duration curve is estimated for the ungauged site by taking a weighted combination of the standardised flow duration curves for the gauged catchments within the region.

In step 1, the Euclidean between the target catchment, indexed by t, and the ith catchment from the climatically similar data pool is calculated as

where Wm is the weight applied to the mth of M catchment characteristics and Xmi is the standardised value of that catchment characteristic for catchment i. The catchment characteristics used are the fractional extents of the HOST classes within a catchment, which will vary between zero and unity. Differing weights are applied for each HOST class to reflect the fact that relatively small proportions of certain HOST classes strongly influence the variability of the flows within a catchment.

The process for estimating the standardised annual flow-duration curve for the target site from those within the region involves weighting each of the donor catchment flow-duration curves by the inverse absolute distance, in weighted HOST space, of the catchment from the target catchment. Thus, greater weight was given to catchments that are more similar in HOST characteristics to the target catchment.

The standardised flow-duration curve has to be re-scaled by multiplication with an estimate of the mean flow to compute the required flow-duration statistics for resource assessment. An estimate of the long-term natural mean flow is obtained by re-scaling an estimated value of annual runoff by catchment area. For the UK low-flows procedures, an annual average runoff grid was derived from the output of a daily time-step, regionalised soil moisture accounting model based on the Penman drying curve and calibrated against stream flow data (Holmes et al., 2002b).

Long-term natural mean monthly flows are calculated using a ROI approach where similarity is measured with respect to both HOST classes and average annual rainfall. Long-term natural average flow-duration curves for specific calendar months are generated in an identical manner to the long-term average flow-duration curves. These standardised curves are re-scaled by the long-term natural mean monthly flows.

13.6.4 Software tools

The UK-standard methods described above are implemented in the LowFlows software4 (Young et al., 2003; Holmes et al., 2005), which is widely used by the Environment Agency in the development of Catchment Abstraction Management Strategies (CAMS; see Chapter 17) in England and Wales, and by SEPA in the implementation of the Controlled Activity Regulations in Scotland.

13.6.5 Estimation of artificially influenced flow statistics

Versions of the LowFlows software used operationally include a geo-referenced database of influence features, such as surface and groundwater abstractions, impounding reservoirs and discharges. The information held for these features may be very complex; e.g. a licence to abstract may relate to tens of distinct sites, which in turn may be licensed for abstraction relating to multiple purposes. The licensed quantities for the whole licence, its constituent sites and individual purposes may also be highly interdependent.

Abstraction and discharge points are quantified in terms of a typical monthly volume for each calendar month within the year; this is termed a monthly profile. In the case of abstraction licences and discharge consents, the monthly volumes relate to water that is either abstracted or discharged. The software will use actual recorded data, if loaded, to represent the monthly profile for a site, or if no actual data are available, the software will estimate a profile based on authorised volumes and patterns observed in historical data.

For abstractions from groundwater, an estimate of the impact of the monthly abstraction profile on the nearest river reach is derived. This is derived using an algorithm based upon the Jenkins superposition method (Jenkins, 1970), applied to the Theis analytical solution for predicting the impact of a groundwater abstraction from an unconfined aquifer. This algorithm requires the user to define values for aquifer transmissivity and storativity. The distance of the abstraction site from the nearest stream is calculated automatically using the grid reference of the site in conjunction with a stored digital river network.

The method for adjusting natural flows for the impact of impounding reservoirs is equivalent to replacing natural river flows and artificial influences upstream of the dam site by 12 monthly reservoir release duration curves, which combine mean monthly compensation flows, reservoir spill and augmentation releases, or freshets if appropriate.

Based on the natural and artificially influenced estimation methods, the LowFlows system can be used to estimate the flow-duration curve for current or future abstractions scenarios.

Fig. 13.12 illustrates an example where one such scenario is compared with the (estimated) naturalised and artificially influenced flow regime, showing large differences in resource availability at low flows. This figure also illustrates the typical complexity

0 digitised boundaries 0 thumb-pins

□ gridl 000 0 abstraction:

□ gridOl 0 discharges 0 rivers 0 impoundme 0 spot gaugings 0 live site 0 saved boundaries

Overlays I Baselaners I

Outlet at SS847359

Scenario series at annual resolution [ungauged]

(* Flow from probability O Probability from flow Probability: | 9j | %

Fig. 13.12 Flow duration curves for natural and influenced flow regimes obtained from LowFlows.

Reprinted from Environmental Modelling & Software, Volume 20 Issue 2, M. G. R. Holmes, A. R. Young, T. H. Goodwin and R. Grew, A catchment-based water resource decision-support tool for the United Kingdom, Pages 197-202, Copyright (2005), with permission from Elsevier.

r of artificial influence features within a catchment where water resources are being exploited.

13.7 Some final comments on methods of regionalisation

The FEH and LowFlows methods are, as noted in the introduction to this chapter, a response to the requirement in practical applications of estimating the nature of the hydrological response for a catchment anywhere in the UK, with and without a local flow gauge. They depend, in estimating the response of ungauged basins, very heavily on statistical methods of regionalisation of the discharge frequency characteristics against catchment descriptor variables. Other countries have addressed the regionalisation problem using related statistical methods (e.g. Jennings et al., 1994; Pilgrim 1999; Turnipseed and Ries, 2007). It is known that such methods will produce rather uncertain estimates, but the methods are often used deterministically as current 'best estimates'.

It has been necessary to resort to these statistical relationships because our representations of hydrological processes, as embodied in the hydrological models of Chapter 12 are not yet good enough to be easily applied to ungauged catchments purely on the basis of knowledge of soil, geology and land management information. An international programme, the prediction of ungauged basins (PUB)1 initiative of the International Association of Hydrological Sciences, is currently under way to try to improve this situation and find ways of reducing the uncertainty in flood estimation more generally.

In the UK there have also been attempts to develop alternative methods for design flow estimation in ungauged based on continuous simulation, where gauged or simulated rainfall data are applied as inputs to a rainfall-runoff model such as PDM or TOPMODEL (see Chapter 12) to generate a long synthetic river flow series, which can be analysed using statistical techniques such as the flow-duration curve, FEH methods or plotting position formulae (Chapter 11). For a review of the development and application of the continuous simulation approach for flood estimation, see Lamb (2005). The approach is particularly useful for including temporal changes in climate input data, model parameters or artificial influences (e.g. abstractions or flood control structures). Regionalisation of the PDM and TATE models for flood frequency estimation in the UK has been described by Calver et al. (2005), whilst uncertainty about regionalised estimates was studied by Lamb and Kay (2004). Low flows have been modelled using a version of the PDM parameterised for the UK by Young (2002). The regionalisation of conceptual rainfall-runoff models in general has been discussed by Wagener et al. (2004) in the UK, Parajka et al. (2007) in Austria and Zhang et al. (2008) in the USA.

Notes

1 See http://pub.iwmi.org/UI/Content/Default.aspx?PGID=0

2 http://www.ceh.ac.uk/feh2/FEHintro.html

3 http://www.environment-agency.gov.uk/hiflows-uk

4 http://www.hydrosolutions.co.uk/lowflows.html

References

Acreman, M. C. and Horrocks, R. J. (1990) Flood frequency analysis for the 1988 Truro floods. Journal of the Institution Water and Environmental Management 4, 62-69.

Archer, D. R., Leesch, F. and Harwood, K. (2007) Assessment of severity of the extreme River Tyne flood in January 2005 using gauged and historical information. Hydrological Sciences Journal 52, 1-12.

Bayliss, A. C. and Reed, D. W. (2001) The Use of Historical Data in Flood Frequency Estimation. Report to Ministry of Agriculture, Fisheries and Food, Centre for Ecology and Hydrology, Wallingford.

Black, A. R. and Law, F. (2004) Development and utilisation of a national web-based chronology of hydrological events. Hydrological Sciences Journal 49, 237-246.

Boorman, D. B., Hollis, J. M. and Lilly, A. (1995) Hydrology of Soil Types: a Hydrologi-cally Based Classification of the Soils of the United Kingdom. Institute of Hydrology, Report No. 126, Wallingford.

Calver, A., Crooks, S., Jones, D., Kay, A., Kjeldsen, T. and Reynard, N. (2005) National River Catchment Flood Frequency Method using Continuous Simulation Modelling. R&D Technical Report FD2106/TR, Department for Environment, Food and Rural Affaris, London.

Gustard, A., Bullock, A. and Dixon, J. M. (1992) Low Flow Estimation in the United Kingdom, Institute of Hydrology, Report No. 108, Wallingford.

Gustard, A., Marshall, D. C. W. and Sutcliffe, M. F. (1987) Low Flow Estimation in Scotland. Institute of Hydrology, Report No. 101, Wallingford.

Gustard, A., Roald, L., Demuth, S., Lumadjeng, H. and Gross, R. (1989) Flow Regimes from Experimental and Network Data (FREND) [in 2 vols]. Institute of Hydrology, Wallingford.

Gustard, A., Young, A. R., Rees, H. G. and Holmes, M. G. R. (2004) Operational hydrology. In: Tallaksen, L. M. and van Lanen, H. A. J. (eds) Hydrological Drought. Developments in Water Science, Vol. 48. Elsevier, Amsterdam, pp. 455-485.

Holmes, M. G. R., Young, A. R., Gustard, A. and Grew, R. A. (2002a) A new approach to estimating mean flow in the UK. Hydrology and Earth System Sciences 6, 709-720.

Holmes, M. G. R., Young, A. R., Gustard, A. and Grew, R. A. (2002b) A region of influence approach to predicting flow duration curves within ungauged catchments. Hydrology and Earth System Sciences 6, 721-731.

Holmes, M. G. R., Young, A. R., Goodwin, T. H. and Grew, R. (2005) A catchment-based water resource decision-support tool for the United Kingdom. Environmental Modelling and Software 20, 197-202.

Hosking, J. R. M. and Wallis, J. R. (1997) Regional Frequency Analysis: an Approach Based on L-Moments. Cambridge University Press, Cambridge.

Institution of Civil Engineers (1996) Floods and Reservoir Safety, 3rd edn. Thomas Telford, London.

Institute of Hydrology (IoH) (1980) Low Flow Studies. IoH, Wallingford.

Institute of Hydrology (1999) Flood Estimation Handbook. IoH, Wallingford.

Interagency Advisory Committee on Water Data (1982) Guidelines for Determining Flood Flow Frequency. Bulletin 17-B of the Hydrology Subcommittee: US. Geological Survey, Office of Water Data Coordination, Reston, VA, 183 pp. [Available from National Technical Information Service, Springfield, VA 22161 as report no. PB 86157278 or see http://www.fema.gov/mit/tsd/dl_flow.htm]

Jenkins, C. T. (1970) Computation of rate and volume of stream depletion by wells. In: Techniques of Water Resources Investigations of the USGS. Book 4. Hydrologist Analysis and Interpretation. US Government Printing Officer, Washington, DC.

Jennings, M. E., Thomas, W. O. Jr. and Riggs, H. C. (1994) Nationwide Summary of U.S. Geological Survey Regional Regression Equations for Estimating Magnitude and Frequency of Floods for Ungaged Sites. US Geological Survey Water-Resources Investigations Report 94-4002, 196 pp.

Kjeldsen, T. R. (2007) The Revitalised FSR/FEH Rainfall-Runoff Method. Flood Estimation Handbook Supplementary Report No. 1. Centre for Ecology and Hydrology (CEH), Wallingford. Also available at: www.ceh.ac.uk/FEH2/FEHReFH.html

Kjeldsen, T. R. and Jones, D. A. (2006) Prediction uncertainty in a median-based index flood method using L moments. Water Resources Research 42, W07414, doi:10.1029/ 2005WR004069.

Kjeldsen, T. R., Jones, D. A. and Bayliss, A. C. (2008) Improving the FEH Statistical Procedures for Flood Frequency Estimation. Environment Agency/Defra Science Report SC050050.

Kjeldsen, T. R., Lamb, R. and Blazkova, S. (2010) Uncertainty in flood frequency analysis. In: Beven, K. and Hall, J. (eds) Applied Uncertainty Analysis for Flood Risk Management Book. Imperial College Press, London, 500 pp.

Lamb, R. (2005) Rainfall-runoff modelling for flood frequency estimation. In: Anderson, M. G. and McDonnell, J. J. (eds) Encyclopedia of Hydrological Sciences, Vol. 3, Chapter 125 Wiley, Chichester.

Lamb, R. and Kay, A. L. (2004) Confidence intervals for a spatially generalized, continuous simulation flood frequency model for Great Britain. Water Resources Research 40, W07501, doi:10.1029/2003WR002428.

Lundquist, D. and Krokli, B. (1985) Low Flow Analysis. Norwegian Water Resources and Energy Administration, Oslo.

Marsh, T. J. (2002) Capitalising on river flow data to meet changing national needs - a UK perspective. Flow Measurement and Instrumentation 13, 291-298.

Martin, J. V. and Cunnane, C. (1976) Analysis and Prediction of Low-flow and Drought Volumes for Selected Irish Rivers. The Institution of Engineers of Ireland, Dublin.

Natural Environment Research Council (NERC) (1975) Flood Studies Report. NERC, London.

Parajka, J., Bloschl, G. and Merz, R. (2007) Regional calibration of catchment models: potential for ungauged catchments. Water Resources Research 43, W06406, doi:10.1029/ 2006WR005271.

Pilgrim, D. H. (ed.) (1999) Australian Rainfall and Runoff - a Guide to Flood Estimation. Institution of Engineers, Australia, Engineers Australia, 426 pp.

Pirt, J. and Douglas, R. (1982) A study of low flows using data from the Severn and Trent catchments. Journal of the Institution of Water Engineers and Scientists 36, 299-309.

Rosbjerg, D. and Madsen, H. (1995) Uncertainty measures of regional flood frequency estimators. Journal of Hydrology 167, 209-224.

Sivapalan, M., Wagener, T., Uhlenbrook, S., Zehe, E., Lakshmi, V., Liang, X., Tachikawara, Y. and Kumar, P. (eds) (2006) Predictions in Ungauged Basins (PUB): Promises and progress. IAHS Redbook Publ. no. 303, 520pp. ISBN 1-901502-48-1

Stedinger, J. R. and Cohn, T. A. (1986) Flood frequency analysis with historical and paleoflood information. Water Resources Research 22, 785-793.

Tallaksen, L. M. and van Lanen, H.A.J. (eds) (2004) Hydrological Drought, Vol. 48: Processes and Estimation Methods for Streamflow and Groundwater. Elsevier Science, Amsterdam, 579 pp.

Turnipseed, D. P. and Ries, K. G. III (2007) The National Streamflow Statistics Program: Estimating High and Low Streamflow Statistics for Ungaged Sites. US Geological Survey Fact Sheet XXX-07, 4 pp.

Wagener, T., Wheater, H. S. and Gupta, H. V. (2004) Rainfall-Runoff Modelling in Gauged and Ungauged Catchments. Imperial College Press, London, 306 pp.

Webster, P. and Ashfaq, A. (2003) Comparison of UK flood event characteristics with design guidelines. Water and Maritime Engineering 156, 33-40.

Young, A. R. (2002) River flow simulation within ungauged catchments using a daily rainfallrunoff model. In: Littlewood, I. (ed.) British Hydrological Society Occasional Paper No. 13: Continuous River Flow Simulation: Methods, Applications and Uncertainties, 80 pp.

Young, A. R., Gustard, A., Bullock, A., Sekulin, A. E. and Croker, K. M. (2000) A river network based hydrological model for predicting natural and influenced flow statistics at ungauged sites, LOIS Special Volume. Science of the Total Environment 251/252, 293-304.

Young, A. R., Grew, R. and Holmes, M. G. R. (2003) Low Flows 2000: a national water resources assessment and decision support tool. Water Science and Technology 48, 119-126.

Zhang, Z., Wagener, T., Reed, P. and Bhushan, R. (2008) Reducing uncertainty in predictions in ungauged basins by combining hydrologic indices regionalization and multiobjective optimization. Water Resources Research 44, W00B04, doi:10.1029/2008WR006833.

0 0

Post a comment