From rainfall to spring discharge: Coupling conduit flow,subsurface matrix flow and surface flow in karst systems using a discrete–continuum model

Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples.     

Comparing flow regime,channel hydraulics,and biological communities to infer flow–ecology relationships in the Mara River of Kenya and Tanzania

Abstract

Equatorial rivers of East Africa exhibit unusually complex seasonal and inter-annual flow regimes, and aquatic and adjacent terrestrial organisms have adapted to cope with this flow variability. This study examined the annual flow regime over the past 40 years for three gauging stations on the Mara River in Kenya and Tanzania, which is of international importance because it is the only perennial river traversing the Mara-Serengeti ecoregion. Select environmental flow components were quantified and converted to ecologically relevant hydraulic variables. Vegetation, macroinvertebrates, and fish were collected and identified at target study sites during low and high flows. The results were compared with available knowledge of the life histories and flow sensitivities of the riverine communities to infer flow–ecology relationships. Management implications are discussed, including the need to preserve a dynamic environmental flow regime to protect ecosystems in the region. The results for the Mara may serve as a useful model for river basins of the wider equatorial East Africa region.

Editor Z.W. Kundzewicz; Guest editor M. Acreman     

Newton–Krylov-multigrid solvers for large-scale,highly heterogeneous,variably saturated flow problems

In this paper, we present a class of solvers developed for the parallel solution of Richards' equation, a model used in variably saturated flow simulations. These solvers take advantage of the fast, robust convergence of globalized Newton methods as well as the parallel scalability of multigrid preconditioners. We compare two multigrid methods. The methods differ primarily in their handling of discontinuous and anisotropic permeability fields, with one method invoking a simple pointwise smoothing technique and the other a more expensive plane smoother. Computational results are presented to show the effectiveness of the entire nonlinear solution procedure, to demonstrate the effect of discontinuities and anisotropies, and to explore parallel efficiencies.     

Lava flow superposition: The reactivation of flow units in compound 'a'ā flows

Basaltic 'a'ā lava flows often demonstrate compound morphology, consisting of many juxtaposed and superposed flow units. Following observations made during the 2001 eruption of Mt. Etna, Sicily, we examine the processes that can result from the superposition of flow units when the underlying units are sufficiently young to have immature crusts and deformable cores. During this eruption, we observed that the emplacement of new surface flow units may reactivate older, underlying units by squeezing the still-hot flow core away from the site of loading. Here, we illustrate three different styles of reactivation that depend on the time elapsed between the emplacement of the two flow units, hence the rheological contrast between them. For relatively long time intervals (2 to 15 days), and consequently significant rheological contrasts, superposition can pressurise the underlying flow unit, leading to crustal rupture and the subsequent extrusion of a small volume of high yield strength lava. Following shorter intervals (1 to 2 days), the increased pressure caused by superposition can result in renewed, slow advance of the underlying immature flow unit front. On timescales of < 1 day, where there is little rheological contrast between the two units, the thin intervening crust can be disrupted during superposition, allowing mixing of the flow cores, large-scale reactivation of both units, and widespread channel drainage. This mechanism may explain the presence of drained channels in flows that are known to have been cooling-limited, contrary to the usual interpretation of drainage as an indicator of volume-limited behaviour. Because the remobilisation of previously stagnant lava can occur swiftly and unexpectedly, it may pose a significant hazard during the emplacement of compound flows. Constant monitoring of flow development to identify areas where superposition is occurring is therefore recommended, as this may allow potentially hazardous rapid drainage events to be forecast. Reactivation processes should also be borne in mind when reconstructing the emplacement of old lava flow fields, as failure to recognise their effects may result in the misinterpretation of features such as drained channels.     

Widespread inflation and drainage of a pāhoehoe flow field: the Nesjahraun, Tingvellir, Iceland

This study describes the emplacement of the Nesjahraun, a basaltic lava flow that entered the lake Tingvallavatn, SW Iceland. High-resolution remotely sensed data were combined with fieldwork to map the flow field. Onshore, the Nesjahraun exhibits a variety of textures related to the widespread inflation and collapse of a pāhoehoe flow field. Its emplacement is interpreted as follows: Initially, the eruption produced sheet pāhoehoe. In the central part of the flow field, the lava has a platy-ridged surface, which is similar to some other lava flows in Iceland and on Mars. Here, the texture is interpreted to have formed by unsteady inflation of the brittle crust of stationary sheet pāhoehoe, causing it to break into separate plates. The ridges of broken pāhoehoe slabs formed as the plates of crust moved vertically past each other in a process similar to the formation of shatter rings. Upstream, fresh lava overflowed repeatedly from channels and tubes, covering the surface with shelly pāhoehoe. Formation of a 250-m-wide open channel through the flow field allowed the inflated central part of the flow to drain rapidly. This phase produced ‘a‘ā lava, which eroded the channel walls, carrying broken pāhoehoe slabs, lava balls and detaching large (>200 m long) rafts of compound shelly pāhoehoe lava. Much of this channelized lava flowed into the lake, leaving a network of drained channels and tubes in the upstream part of the flow. As in other locations, the platy-ridged texture is associated with a low underlying slope and high eruption rate. Here, its formation was possibly enhanced by lateral confinement, hindered entry into the lake and an elevated vent location. We suggest that formation of this type of platy-ridged lava, where the plates are smooth and the ridges are slabs of broken pāhoehoe, can occur without significant horizontal transport, as the surface crust is broken into plates in situ. This reconstruction of the emplacement of the Nesjahraun also demonstrates that high-resolution aerial survey data are extremely useful in the mapping and measurement of lithofacies distributions in large flow fields, but that fieldwork is still necessary to obtain the detailed textural information necessary to interpret them.     

Numerical modeling of geothermal groundwater flow in karst aquifer system in eastern Weibei, Shaanxi Province, China

The quantitative assessment of geothermal water resources is important to the exploitation and utilization of geothermal resources. In the geothermal water systems the density of groundwater changes with the temperature, therefore the variations in hydraulic heads and temperatures are very complicated. A three-dimensional density-dependent model coupling the groundwater flow and heat transport is established and used to simulate the geothermal water flow in the karst aquifers in eastern Weibei, Shaanxi Province, China. The multilayered karst aquifer system in the study area is cut by some major faults which control the regional groundwater flow. In order to calibrate and simulate the effect of the major faults, each fault is discretized as a belt of elements with special hydrological parameters in the numerical model. The groundwater dating data are used to be integrated with the groundwater flow pattern and calibrate the model. Simulation results show that the calculated hydraulic heads and temperature fit with the observed data well.     

GIS-based risk analysis of debris flow： an application in Sichuan, southwest China

Debris flow is a serious geologic hazard in China. It is estimated that nationally debris flows cause up to 2 billion RMB （250 million US$） in damages and 300-600 deaths and injuries annually. To mitigate debris flow hazards, it is necessary to map, model, and identify zones of debris flow hazards and vulnerability as to inform the local people about the potential risk with a geographic information system. This research presents a regional scale case study modeling debris flow risk （hazard and vulnerability） in Sichuan Province, Southwestern China. In this area, 3,290 debris flows have been identified and the spatial-temporal distribution and activity characteristics of them have been documented. Based on the available meteorological data, a Digital Elevation Model with the rate of 1：250,000 and a regional geological map, the 24-hr rainfall threshold （y） for debris flow occurrence is closely related （significant at 99% confidence level） to the index （x） defined using a geology factor （rock hardness： a） and a topographical factor （channel gradient： d） where y = 21 ＋ 10200 / x, in which x = 2.7 × e^a ＋ 1000 × d. The discipline is constructive in developing the rainfall threshold for debris flow activity in remote mountainous areas that lack data. For a given watershed, a four-level debris flow hazard map is developed by comparing the rainfall threshold to the design rainfall intensities with 50-, 20-, and 5-year average recurrence intervals, respectively. The degree of debris flow vulnerability is determined by the watershed socio-economic conditions. A four-class debris flow risk map, at the final phase of the research, is generated by combining debris flow hazards and vulnerability. With the debris flow risk assessment, the Sichuan Province is classified into the slight, moderate, severe and very severe regions, which accounts for 36%, 19%, 20% and 25% of total area respectively.     

A new tree-ring date for the “floating island” lava flow,Mount St. Helens,Washington

Anomalously narrow and missing rings in trees 12 m from Mount St. Helens' floating island lava flow, and synchronous growth increases in trees farther from the flow margin, are evidence that this andesitic flow was extruded between late summer 1799 and spring 1800 a.d., within a few months after the eruption of Mount St. Helens' dacitic layer T tephra. For ease of reference, we assign here an 1800 a.d. date to this flow. The new date shows that the start of Mount St. Helens' Goat Rocks eruptive period (1800–1857 a.d.) resembled the recent (1980–1986) activity in both petrochemical trends and timing. In both cases, an initial explosive eruption of dacite was quickly succeeded by the eruption of more mafic lavas; dacite lavas then reappeared during an extended concluding phase of activity. This behavior is consistent with a recently proposed fluid-dynamic model of magma withdrawal from a compositionally zoned magma chamber.     

Pyroclastic flow deposits of the 1991 eruption of Volcán de Colima,Mexico

The April 16, 1991, eruption of Volcán de Colima represents a classical example of partial dome collapse with the generation of progressively longer-runout, Merapi-type pyroclastic flows that traveled up to 4 km along the El Cordoban gullies (East, Central and West). The flows filled the gullies with block-and-ash flow deposits up to 10 m thick, of which, after 7 years of erosion, only remnants remained in the El Cordoban West and East gullies. The El Cordoban Central gully, however, provided a well-preserved and incised longitudinal section of the 1991 deposits. The deposits were emplaced as proximal and distal facies, separated by a change in slope angle from >30° to <20°. The proximal facies consists of massive, clast-supported flow units (up to 1 m thick) with andesite blocks locally supported by a matrix of coarse ash and devoid of segregation structures or grading. The distal facies consists of a massive, matrix-supported deposit up to 8 m thick, which contains dispersed andesite blocks in a fine ash matrix. In the distal facies, a train of blocks marks flow-unit upper boundaries and, although sorting is poor, some grading is present. Thin, finely stratified, or dune-bedded layers of fine ash material are locally present above or below units of both facies. Sedimentologic parameters show that the size or fraction of large pyroclasts (larger than –1 ) decreases from proximal to distal facies, as the percentage of matrix (0 to 4 ) increases, especially immediately beyond the break in slope. We propose that the propagation of the Colima pyroclastic flows is critically dependent on local slope angle, the presence of erodible slope debris, and the decrease in grain size with distance from the vent. The progressive fining is probably caused by some combination of erosion, clast breakup and deposition of larger pyroclasts, and is itself influenced by the slope angle. In the proximal region, the flows moved as granular avalanches, in which interacting grains ground each other and erosion occurred to produce an overriding dilute ash cloud. The maximum runout distance of the avalanches was controlled by the angle of repose of the material, and the volume and grain size of source and eroded material. Because the slope angle is close to the repose angle for this debris, granular avalanches were not able to propagate far beyond the change in slope. If, however, an avalanche had enough mass in finer grain size fractions, at least part of the flow continued beyond the break in slope and across the volcano apron, propagating in a turbulent state and depositing surge layers, or in an otherwise settling-modified state and depositing block-and-ash flow layers.Editorial responsibility: T Druitt     

Distribution characteristics of terrestrial heat flow density in Jiyang depression of Shengli Oilfield, East China

Terrestrialheatflowdensityistheamountofheatperunitareatransferringfromtheearthinteriortosurface,whichisanexteriorcharacteristicofthethermalandgeodynamicprocessesoccurringindeepmantle[1].Heatflow,asthemostdirectmannerofthermalprocessindeepearthandembodyingabundantinformationofgeology,geophysicsandgeodynamics,isasyntheticallythermalindexandplaysaveryimportantroleinstudyingnotonlytheactivityofcrust,thermalstructureofcrustanduppermantle,aswellasrheologicalstructureoflithosphere,butalsotheevaluation…     

Channel overflows of the Pōhue Bay flow,Mauna Loa,Hawai'i: examples of the contrast between surface and interior lava

A number of overflows from a large lava channel and tube system on the southwest rift zone of Mauna Loa were studied. Initial overflows were very low viscosity gas-rich phoehoe evidenced by flow-unit aspect ratios and vesicle sizes and contents. Calculated volumetric flow-rates in the channel range between 80 and 890 m³/s, and those of the overflows between 35 and 110 m³/s. After traveling tens to hundreds of meters the tops of these sheet-like overflows were disrupted into a surface composed of clinker and phoehoe fragments. After these 'a' overflows came to rest, lava from the interiors was able to break out on to the surface as phoehoe. The surface structure of a lava flow records the interaction between the differential shear rate (usually correlated with the volumetric flow-rate) and viscosity-induced resistance to flow. However, the interior of a flow, being better insulated, may react differently or record a later set of emplacement conditions. Clefts of toothpaste lava occurring within fields of clinker on proximal-type 'a' flows also record different shear rates during different times of flow emplacement. The interplay between viscosity and shear rate determines the final morphological lava type, and although no specific portion of lava ever makes a transition from 'a' back to phoehoe, parts of a flow can appear to do so.     

Quantifying flow–ecology relationships with functional linear models

Abstract

Hydrologic metrics have been used widely to quantify flow-ecology relationships; however, there are several challenges associated with their use, including the selection from a large number of available metrics and the limitation that metrics are a synthetic measure of a multi-dimensional flow regime. Using two case studies of fish species density and community composition, we illustrate the use of functional linear models to provide new insights into flow–ecology relationships and predict the expected impact of environmental flow scenarios, without relying on hydrologic metrics. The models identified statistically significant relationships to river flow over the 12 months prior to sampling (r² range 36–67%) and an environmental flow scenario that may enhance native species’ densities while controlling a non-native species. Hydrologic metrics continue to play an important role in ecohydrology and environmental flow management; however, functional linear models provide an approach that overcomes some of the limitations associated with their use.

Editor Z.W. Kundzewicz; Guest editor M. Acreman

Citation Stewart-Koster, B., Olden, J.D., and Gido, K.B., 2014. Quantifying flow–ecology relationships with functional linear models. Hydrological Sciences Journal, 59 (3–4), 629–644.     

Zircon U–Pb strain chronometry reveals deep impact-triggered flow

Large (> 100 km) meteorite impact cratering events play important roles in surface and biosphere evolution, however, their potential for widespread ductile modification of the lithosphere has been difficult to assess, due partly to our inability to isotopically age-correlate deep mineral fabrics with surface records. We have integrated benchmark U–Pb zircon dating methods (ID-TIMS, SHRIMP) with new microstructural techniques (EBSD, µXRD) to demonstrate that crystal–plastic deformation can cause rapid out-diffusion of radiogenic Pb and accompanying trace element alteration in crystalline zircon. We have used this phenomenon to directly date fabric in Archean zircons and xenoliths of the lower crust of South Africa at 2023 ± 15 million years, coeval with the 2020 ± 3 million year old Vredefort cratering event at surface, with extent ≥ 20,000 km². Our findings indicate that regional exogenic fabrics, similar to high-temperature tectonic fabrics, exist in ancient crust. Moreover, our results establish that crystal-plastic deformation in the lithosphere can now be directly dated and linked to planetary evolution by zircon U–Pb strain chronometry.     

Evidence of groundwater flow on Antizana ice-covered volcano,Ecuador / Mise en évidence d'écoulements souterrains sur le volcan englacé Antizana,Equateur

Abstract

Hydrological and glaciological data were gathered in the watershed (1.37 km²) of the Antizana Glacier 15 (0.7 km²) in the periods 1997–2002 and 1995–2005, respectively. In addition, tracer experiments were carried out to analyse the flow through permeable morainic deposits located between the glacier snout and the runoff gauging station. Over 11 years, the mean specific net balance of the glacier was negative (–627 mm w.e.), despite the occurrence of positive values in the La Niña years (1999–2000). From the glacier net mass balance between 1997 and 2002, it was found that the mean flow originating from ice melt was significantly higher than the mean discharge measured at the hydrological station. Analyses of tracer experiments and of the different components of the hydrological balance suggest groundwater flow that originates below the glacier accounts for the remaining water. This result is important for regional analyses of available water resources and for the relationship between hydro-cryospheric processes and volcanic activity.     

Hydrologic indicators of hydraulic conditions that drive flow–biota relationships

Abstract

This article tests the association between streamflow alteration and the alteration of ecologically significant hydraulic environments. There has been a recent shift in environmental flow assessments to develop rapid desktop-based approaches that are applicable in a regional context. Streamflow statistics (e.g. minimum monthly flow) are often chosen to predict the impact of streamflow alteration on aquatic ecosystems. The assumption that the flow–biota relationship will be obscured by the effect of how streamflow interacts with channel morphology is often acknowledged, but not quantified. In this study, streamflow statistics are derived for 19 reaches in four river systems in Victoria, Australia. Hydraulic metrics were used to quantify ecologically significant surface flow conditions (Froude number) and the area of bench inundation, shallow and deep water. Multivariate analysis was used to investigate the correlation between streamflow statistics altered with regulation and the hydraulic metrics. It was found that streamflow statistics have a weak correlation to surface flow condition and the area of shallow water under natural streamflow conditions. The results show that hydrologic statistics have limited utility in quantifying changes in hydraulic environments. A similar magnitude of flow alteration can produce diverse hydraulic results. The confounding influence of channel morphology prevents streamflow statistics being an adequate surrogate for the assessment of hydraulic alteration. Modelling flow–biota relationships in a regional context is limited by the inadequacy of streamflow statistics to model ecologically significant hydraulic function. Improving knowledge of ecohydraulically significant hydrologic statistics will improve the effectiveness of environmental flow planning to sustain instream habitat conditions. A probabilistic approach is required to enable a risk-based approach to desktop generalization of flow–biota relations.

Editor Z.W. Kundzewicz; Guest editor M. Acreman

Citation Turner, M. and Stewardson, M., 2014. Hydrologic indicators of hydraulic conditions that drive flow–biota relationships. Hydrological Sciences Journal, 59 (3–4), 659–672.     

Conditional simulations of water–oil flow in heterogeneous porous media

This study is an extension of the stochastic analysis of transient two-phase flow in randomly heterogeneous porous media (Chen et al. in Water Resour Res 42:W03425, 2006), by incorporating direct measurements of the random soil properties. The log-transformed intrinsic permeability, soil pore size distribution parameter, and van Genuchten fitting parameter are treated as stochastic variables that are normally distributed with a separable exponential covariance model. These three random variables conditioned on given measurements are decomposed via Karhunen–Loève decomposition. Combined with the conditional eigenvalues and eigenfunctions of random variables, we conduct a series of numerical simulations using stochastic transient water–oil flow model (Chen et al. in Water Resour Res 42:W03425, 2006) based on the KLME approach to investigate how the number and location of measurement points, different random soil properties, as well as the correlation length of the random soil properties, affect the stochastic behavior of water and oil flow in heterogeneous porous media.     

Effects of non-submerged boulder on flow characteristics – A field investigation

The effect of fully submerged boulders on the flow structure in channels has been studied by some researchers. However, many natural streams have bed material with boulders that are not fully submerged under water. In many natural streams, boulders cover between 1% and 10% of the area of the stream reach. The effect of non-submerged boulders on the velocity profile and flow characteristics is very important for assessing riverbed deformation. The objectives of this paper are to find the pattern of velocity distribution around a non-submerged boulder and to compare it with the classical studies on flow resistance and Reynolds stress distribution in open channels. Also, by considering the variation in the Reynolds stress distribution at different locations around a non-submerged boulder, the effect of a non-submerged boulder on the estimation of shear velocity and resistance to flow has been investigated. Results indicates that inside the scour hole caused by a non-submerged boulder in a river velocity distributions are irregular. However, velocity distributions are regular outside the scour hole. The presence of the boulder causes a considerable deviation of the Reynolds shear stress from the classic distribution, showing a non-specific distribution with negative values. The classical methods for calculating shear velocity are not suitable because these methods do not give detailed velocity and Reynolds stress distributions in natural rivers with a lot of boulders. Thus, the effect of a non-submerged boulder on the estimation of the resistance to flow by considering the variations in velocity and Reynolds stress distributions at different locations around a non-submerged boulder is important and needs to be studied in a natural river instead of just in laboratory flumes. The negative values in Reynolds stress distribution around a boulder indicate that the classical methods are unable to predict resistance to flow, and also show strong turbulence inside the scour hole where the complex flow conditions present ambiguous Reynolds stress distributions. In the current study, to obtain a reasonable estimation of parameters in natural rivers, the classical method has been modified by considering velocity and Reynolds stress distributions through the boundary layer method.     

Morphological complexities and hazards during the emplacement of channel-fed `a`ā lava flow fields: A study of the 2001 lower flow field on Etna

Long-lived basaltic eruptions often produce structurally complex, compound `a`ā flow fields. Here we reconstruct the development of a compound flow field emplaced during the 2001 eruption of Mt. Etna (Italy). Following an initial phase of cooling-limited advance, the reactivation of stationary flows by superposition of new units caused significant channel drainage. Later, blockages in the channel and effusion rate variations resulted in breaching events that produced two new major flow branches. We also examined small-scale, late-stage ‘squeeze-up’ extrusions that were widespread in the flow field. We classified these as ‘flows’, ‘tumuli’ or ‘spines’ on the basis of their morphology, which depended on the rheology, extrusion rate and cooling history of the lava. Squeeze-up flows were produced when the lava was fluid enough to drain away from the source bocca, but fragmented to produce blade-like features that differed markedly from `a`ā clinker. As activity waned, increased cooling and degassing led to lava arriving at boccas with a higher yield strength. In many cases this was unable to flow after extrusion, and laterally extensive, near-vertical sheets of lava developed. These are considered to be exogenous forms of tumuli. In the highest yield strength cases, near-solid lava was extruded from the flow core as a result of ramping, forming spines. The morphology and location of the squeeze-ups provides insight into the flow rheology at the time of their formation. Because they represent the final stages of activity of the flow, they may also help to refine estimates of the most advanced rheological states in which lava can be considered to flow. Our observations suggest that real-time monitoring of compound flow field evolution may allow complex processes such as channel breaching and bocca formation to be forecast. In addition, documenting the occurrence and morphology of squeeze-ups may allow us to determine whether there is any risk of a stalled flow front being reactivated. This will therefore enhance our ability to track and assess hazard posed by lava flow emplacement.     

Does quantifying antecedent flow conditions improve stream phosphorus export estimation?

A reliable and economical method for the estimation of nutrient export (e.g. phosphorus) in stream flow from catchments is necessary to quantify the impact of land use or land use change upon aquatic systems. The transport of phosphorus (P) from soil to water is known to impact negatively on water quality. A key observation from studies is that most P export occurs during high stream flow. However, it is not yet clear how flood-antecedent conditions affect the P export during flood events. In this study, the P loss from soil to water as represented by soluble reactive phosphorus (SRP) in stream waters from three different catchments, varying in land use, scale and location in Ireland was monitored over 1 year. This study examined the role of antecedent stream flow conditions on SRP export and identifies a catchment-specific relationship between SRP flood event load (EL) and a flow ratio (FR). The FR is defined as the ratio of the flood event volume (EV) to the pre-event volume (PEV). The latter is the cumulative flow volume for a number of days preceding the event. This PEV period was found to be longer (average 81 days) in the grassland catchments which were known to be saturated with soil P than in the forested catchments (average 21 days) with minimal soil P. This FR ratio is a measure of the antecedent hydrological state (wet or dry) of the catchment. For SRP for each catchment, a specific relationship between SRP EL and FR was identified. The annual SRP export was estimated, using this ratio and compared with the concentration/discharge (C/Q) method. The new flow ratio method was used with data from 12 flood events during the year to estimate an annual export of SRP. For the two grassland catchments in the study, using the FR method, we estimated an SRP export of 1.77 and 0.41 kg ha⁻¹ yr⁻¹. Using the C/Q method, for the same sites, our estimate of SRP export was 1.70 and 0.50 kg ha⁻¹ yr⁻¹ respectively. The C/Q method used SRP concentrations covering 40% of the year while the FR method used only 12 flood events covering less than 2% of the year. This new method which takes account of the antecedent flow state of the river is an alternative to and may be more promising than the traditional C/Q method, particularly when short duration or flood sampling of water quality is carried out.