HYDROLOGICAL PROCESSES Hydrol. Process. 24, 2300–2312 (2010) Published online 26 April 2010 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/hyp.7679 Storm flow and baseflow response to reduced acid deposition — using Bayesian compositional analysis in hydrograph separation with changing end members D. Tetzlaff, 1 * M. J. Brewer, 2 I. A. Malcolm 3 and C. Soulsby 1 1 Northern Rivers Institute, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UF, UK 2 Biomathematics and Statistics Scotland, The Macaulay Land-Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, Scotland, UK 3 Freshwater Laboratory, Marine Scotland, Faskally, Pitlochry, Perthshire PH16 5LB, UK Abstract: In this paper, we present the analysis of long-term (since 1989) hydrochemical data from two small (ca 1 km 2 ) catchments in Central Scotland. Both catchments have experienced marked reductions in acid deposition. Time-series analysis of stream water alkalinity, although systematically changing as a result of recovery from acidification, was used to conceptualize how the composition and contribution of different hydrological sources responded over the study period. Nonlinear curve fitting methods allowed the temporal changes in concentration–discharge relationships to be sufficiently well described to assess the impact of reduced acid deposition on storm flow and baseflow hydrochemistry. A Bayesian compositional analysis was applied to facilitate chemically based hydrograph separation. This allowed temporal variation over longer time periods in catchment- scale hydrological source contributions (specifically groundwater) to be estimated. Although these showed no systematic trend, they did differ between the two catchments, most likely as a result of small, but significant differences in the riparian soil cover. Understanding such changes to high and low flows over time is of paramount importance as such flow extremes have the most relevance to applied problems, particularly those related to environmental change. Copyright 2010 John Wiley & Sons, Ltd. KEY WORDS end-member mixing; hydrograph separation; emergence; hot-spots; flow concentration curves Received 11 September 2009; Accepted 26 February 2010 INTRODUCTION Paucity of long-term data often frustrates attempts to understand how the quantity and quality of stream flow respond to drivers of hydrological and biogeochemical change (Lovett et al., 2007). Long-term hydrochemical data allow solutes to be used as tracers that can infer how hydrological and biogeochemical processes interact at the catchment-scale to influence the chemical compo- sition of different sources of water (Soulsby et al., 2004). Such information can also be used in chemically based hydrograph separation to estimate their contribution to stream water under different flow conditions (e.g. Rob- son and Neal, 1990; Wade et al., 1999). Of particular interest are the sources that contribute to the extremes of hydrological response at high and low flows, as these are often most vulnerable to the effects of short- and long- term environmental change and usually have the greatest significance in relation to the applied problems, such as flood generation, diffuse water pollution and the main- tenance of low flows (e.g. Evans et al., 2008; Tetzlaff * Correspondence to: Dr D. Tetzlaff, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UF, Scotland, UK. E-mail: [email protected]and Soulsby, 2008; Birkel et al., 2009). Thus, by investi- gating tracers at the extremes of hydrological response, it can be possible to make inferences about the function and response of different conceptual source areas (Lischeid, 2008; Birkel et al., 2010). Catchments in the UK uplands are often acid-sensitive, with base-poor geology and a cool wet climate result- ing in relatively thin, leached soils (UKAWRG, 1989). These catchments have also been subjected to acid atmo- spheric deposition over the past 200 years. As a result, acidification of surface waters has been widely reported (Reynolds et al., 1999). In many areas, this has been exacerbated by commercial forestry in the 20th cen- tury which involved fast-growing conifers such as Sitka Spruce (Picea sitchensis ) which increased dry and occult acid deposition (Wade et al., 2001; Harriman et al., 2003). Controls on pollution emissions have reduced acid deposition in most upland areas and recovery of surface water chemistry has been observed (e.g. Evans et al., 2008). Catchment recovery, however, is variable even within restricted regions, largely as a result of differences in catchment characteristics or the influence of other drivers of environmental change (Harriman et al., 2001; Ormerod and Durance, 2009). For example, although SO 4 deposition has decreased, other mobile anions have been Copyright 2010 John Wiley & Sons, Ltd.
Transcript
HYDROLOGICAL PROCESSESHydrol. Process. 24, 2300–2312 (2010)Published online 26 April 2010 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/hyp.7679
Storm flow and baseflow response to reduced aciddeposition—using Bayesian compositional
analysis in hydrograph separationwith changing end members
D. Tetzlaff,1* M. J. Brewer,2 I. A. Malcolm3 and C. Soulsby1
1 Northern Rivers Institute, School of Geosciences, University of Aberdeen, Aberdeen AB24 3UF, UK2 Biomathematics and Statistics Scotland, The Macaulay Land-Use Research Institute, Craigiebuckler, Aberdeen AB15 8QH, Scotland, UK
In this paper, we present the analysis of long-term (since 1989) hydrochemical data from two small (ca 1 km2) catchmentsin Central Scotland. Both catchments have experienced marked reductions in acid deposition. Time-series analysis of streamwater alkalinity, although systematically changing as a result of recovery from acidification, was used to conceptualize howthe composition and contribution of different hydrological sources responded over the study period. Nonlinear curve fittingmethods allowed the temporal changes in concentration–discharge relationships to be sufficiently well described to assess theimpact of reduced acid deposition on storm flow and baseflow hydrochemistry. A Bayesian compositional analysis was appliedto facilitate chemically based hydrograph separation. This allowed temporal variation over longer time periods in catchment-scale hydrological source contributions (specifically groundwater) to be estimated. Although these showed no systematic trend,they did differ between the two catchments, most likely as a result of small, but significant differences in the riparian soilcover. Understanding such changes to high and low flows over time is of paramount importance as such flow extremes havethe most relevance to applied problems, particularly those related to environmental change. Copyright 2010 John Wiley &Sons, Ltd.
Received 11 September 2009; Accepted 26 February 2010
INTRODUCTION
Paucity of long-term data often frustrates attempts tounderstand how the quantity and quality of stream flowrespond to drivers of hydrological and biogeochemicalchange (Lovett et al., 2007). Long-term hydrochemicaldata allow solutes to be used as tracers that can inferhow hydrological and biogeochemical processes interactat the catchment-scale to influence the chemical compo-sition of different sources of water (Soulsby et al., 2004).Such information can also be used in chemically basedhydrograph separation to estimate their contribution tostream water under different flow conditions (e.g. Rob-son and Neal, 1990; Wade et al., 1999). Of particularinterest are the sources that contribute to the extremes ofhydrological response at high and low flows, as these areoften most vulnerable to the effects of short- and long-term environmental change and usually have the greatestsignificance in relation to the applied problems, such asflood generation, diffuse water pollution and the main-tenance of low flows (e.g. Evans et al., 2008; Tetzlaff
* Correspondence to: Dr D. Tetzlaff, School of Geosciences, Universityof Aberdeen, Aberdeen AB24 3UF, Scotland, UK.E-mail: [email protected]
and Soulsby, 2008; Birkel et al., 2009). Thus, by investi-gating tracers at the extremes of hydrological response, itcan be possible to make inferences about the function andresponse of different conceptual source areas (Lischeid,2008; Birkel et al., 2010).
Catchments in the UK uplands are often acid-sensitive,with base-poor geology and a cool wet climate result-ing in relatively thin, leached soils (UKAWRG, 1989).These catchments have also been subjected to acid atmo-spheric deposition over the past 200 years. As a result,acidification of surface waters has been widely reported(Reynolds et al., 1999). In many areas, this has beenexacerbated by commercial forestry in the 20th cen-tury which involved fast-growing conifers such as SitkaSpruce (Picea sitchensis) which increased dry and occultacid deposition (Wade et al., 2001; Harriman et al.,2003). Controls on pollution emissions have reduced aciddeposition in most upland areas and recovery of surfacewater chemistry has been observed (e.g. Evans et al.,2008). Catchment recovery, however, is variable evenwithin restricted regions, largely as a result of differencesin catchment characteristics or the influence of otherdrivers of environmental change (Harriman et al., 2001;Ormerod and Durance, 2009). For example, although SO4
deposition has decreased, other mobile anions have been
Copyright 2010 John Wiley & Sons, Ltd.
STORM FLOW AND BASEFLOW RESPONSE TO REDUCED ACID DEPOSITION 2301
shown to offset the effects. Thus, elevated NO3 levelscan result from felling operations in commercial forests(Reynolds, 2004; Tetzlaff et al., 2007a). In addition, Cldeposition can vary inter-annually, resulting in acidify-ing stormy periods (Langan, 1989; Soulsby 1995a; Evanset al., 2001). Finally, soil recovery from acidificationappears to have enhanced decomposition leading to dis-solved organic carbon (DOC) increases, which may con-tribute to organic acid buffering (Monteith et al., 2007;Dawson et al., 2008, 2009).
These changing drivers operate against a backdrop ofcatchment heterogeneity and climatic variability, whichcan mediate the resulting impacts on stream chemistry athigh and low flows (Evans et al., 2008). For example,high flows generate acid episodes, which may increasein frequency as a result of climate change, and slowthe chemical recovery of some streams to reduced atmo-spheric deposition (Davies et al., 1992; Soulsby, 1995b;Evans et al., 2008). Acid episodes are generated byhydrological processes in the near-surface organic soilhorizons (e.g. overland flow and shallow subsurfacestorm flow) that rapidly route low alkalinity runoff tostreams (e.g. Robson et al., 1992; Soulsby and Reynolds,1993). However, the partitioning of runoff between suchnear-surface flow paths and the recharge of deeper,buffered groundwater sources has been shown to behighly variable, even in catchments that may appear to besuperficially similar (Soulsby et al., 2006; Tetzlaff et al.,2007b). Thus, recent work used conservative tracers toestimate mean transit times (MTT) of water in uplandcatchments and showed that these vary between a fewmonths to a few years, largely depending upon catchmentsoil cover (Hrachowitz et al., 2009). Such differencesin water routing and storage are likely to have a majorinfluence on the timing of the response of stream chem-istry to environmental change, and the degree to whichthese may be damped by internal catchment storage andmixing processes (Soulsby et al., 2009). For example,catchments with longer MTTs are usually dominated bydeeper subsurface processes and have higher groundwatercontributions, which can buffer acidity more effectively(Reynolds et al., 1986; Soulsby et al., 2007). In addition,the importance of hydrological and biogeochemical ‘hotspots’ has recently been recognized as a possible expla-nation for differences in catchment function (McClainet al., 2003). These are relatively restricted zones withincatchments where particular landscape features, such asriparian zones or floodplains, have a disproportionateinfluence on runoff generation and/or stream chemistry(e.g. Smart et al., 2001; McGlynn and McDonnell, 2003).Thus, the interaction of complex heterogeneous hillslopescale processes may underpin simple, emergent hydro-chemical behaviour at the larger catchment scale.
Where direct sampling of source waters is unavail-able or inadequate, flow concentration plots have beenused as a means of estimating conceptual catchment-scale source compositions of, for example, ‘soil water’and ‘groundwater’, on the basis of high flow and lowflow samples, respectively (e.g. Robson and Neal, 1990;
Wade et al., 1999; Foster et al., 2001). Despite the prag-matism of the approach, the question of the resultinghydrograph separations being tautological has been raisedas an obvious criticism (e.g. Lischeid, 2008). Neverthe-less, long-term time series of stream water chemistrydata are often the only means available for inferring howhydrological and biogeochemical processes are interact-ing in response to recovery from acidification or otherenvironmental change and warrant further investigation.Flow-concentration relationships are useful indicators ofthe interactions between catchment hydrological func-tion and biogeochemical processes (Godsey et al., 2010).Moreover, examining the changes in flow-concentrationrelationships over time can provide informative insightsinto how catchment hydrology and hydrochemistry mightbe affected by environmental change (Evans et al., 2008).Flow concentration plots of conservative tracers can alsobe useful for conceptualizing why different catchmentsmay respond differently to the same forcing factors(Ormerod and Durance, 2009) or for end-member mix-ing and chemically based hydrograph separations (Burns,2002).
End-member mixing usually involves using direct mea-surements of catchment sources, such as soil waters andgroundwater, along with stream samples to resolve theircomposition (e.g. Hooper et al., 1990; Christophersenet al., 1993). However, there are well-known difficul-ties associated with the frequency and longevity of directsource water sampling, and the spatial variation andtemporal dynamics of end members (see review in Lis-cheid, 2008). As a consequence, end-member mixinganalyses result often in uncertainties that are difficult toquantify (Genereux, 1998; Soulsby et al., 2003). Theseproblems are compounded when there is directional,systematic temporal change in the chemical parametersused to define end members caused by environmen-tal change, such as recovery from acidification (Tetzlaffet al., 2007a).
Recent developments in Bayesian statistics haveresulted in generic methods of compositional analysiswhich offer the potential for overcoming at least someof the difficulties associated with quantitative attribu-tion of stream water to different inferred sources (e.g.Billheimer, 2001). These tools have been applied toflow-concentration plots to constrain end-member mix-ing models and test hypotheses about catchment hydro-logical function (Brewer et al., 2005). In this context,here we examine 17 years of stream chemistry data fromtwo headwater catchments in the acid-sensitive Britishuplands at Loch Ard, in Central Scotland. The overall aimis to evaluate whether compositional analysis can be usedover longer time periods to facilitate chemically basedhydrograph separation when there has been a systematicchange in end-member composition. A particular focusis the assessment of how reduction in acid deposition hasaffected the chemistry of the main hydrological sourcesdominating baseflow and storm flow. The specific objec-tives are to (i) quantitatively assess temporal changes in
storm flow and baseflow alkalinity representing concep-tual end members in terms of hydrological sources of‘soil water’ and ‘groundwater’ in the two catchments; and(ii) apply Bayesian compositional analysis as a statisticaltool in hydrograph separation to assess how hydrolog-ical function might influence the way in which streamchemistry responds to reduced acid deposition.
STUDY AREA
Loch Ard is in the Central Highlands of Scotland, justnorth of the densely populated, industrialized centralbelt (Figure 1). This moderately sloping upland areahas been a focus for commercial forestry since the1950s, which involved large plantations of Sitka Spruce(Picea sitchensis). Two forested catchments at LochArd, B10 (0Ð9 km2) and B11 (1Ð4 km2), are sites oflong-term hydrological and hydrochemical monitoring(Figure 1 and Table I). The geology is dominated bylow permeability, slow-weathering metamorphic rocks
(Miller et al., 1990). The most common soils in bothcatchments are acidic, minerogenic gleys, though B11has significant coverage of humic/peaty gley soils andadditionally has a small area of deep peat soils (Histosols)in a flat riparian wetland (Figure 1b). The wetland islocated in the centre of the catchment which the streamflows through and which the mid-catchment hillslopesdrain into and has been shown to be a ‘hot spot’ havingan effect on stream chemistry (Tetzlaff et al., 2007a;Dawson et al., 2008). B10 is steeper and has extensivebedrock outcrops around the catchment interfluves.
Precipitation is around 2000 mm per annum (rangingbetween 1490 and 2500 mm in the period of record) andaverage air temperatures range from 2Ð8 °C in January to13Ð7 °C in July. Snow is a minor component of the annualwater balance and the both streams have a very ‘flashy’hydrological regime (Figure 2). Storm runoff is sourcedfrom flows paths in the upper soil horizons (Dawsonet al., 2008) and mean residence times are short—ca5–7 months for both catchments (Tetzlaff et al., 2007a;
(a)
(b) (c)
Figure 1. (a) Slope; (b) soil cover in B10 and B11 (HOST refers to the UK Hydrology of Soil Type classes); (c) Areas and time periods of fellingoperations
Figure 2. Stream hydrographs for B10 and B11, exemplary shown for thefirst 4 years of the investigation period
Hrachowitz et al., 2009). Groundwater comprises slowseepage from quite small stores of water in deepersoil horizons, drift deposits and bedrock fractures whichare relatively unresponsive to short-term hydrologicaldynamics (Tetzlaff et al., 2007a).
Air pollution legislation has resulted in a markedreduction in acid deposition, mainly from the industri-alized Scottish central belt, and improvements in streamwater quality over the period of record have been reported(Harriman et al., 2001). In addition, forestry operationshave led to incremental felling of the two catchments(Figure 1c). A portion of B10s catchment was felled in1988, with much of the remainder being felled between2003 and 2005. The lower portion of B11 was felledbetween 1997 and 1999 with further sections felled in2003–2005 (Tetzlaff et al., 2007a). Generally, the areas
felled at any given time comprised <35% of the totalcatchment area.
METHODS
Sampling methods
Details of the sampling program and analytical meth-ods used at Loch Ard are presented in Tetzlaff et al.,2007a. Briefly, weekly precipitation and stream sampleshave been collected since 1981. However, flow data hasonly been available since 1989, and so only the period1989–2005 was used. Samples were analysed for a suiteof determinands, including pH, alkalinity, major cationsand anions and DOCAlkalinity was estimated from a2-end point titration to pH 4Ð5 and 4Ð2. Alkalinity iswidely used as a tracer that is assumed to be conser-vative on mixing and well suited to chemically basedhydrograph separation techniques in upland UK catch-ments (e.g. Robson and Neal, 1990; Neal et al., 1997;Wade et al., 1999). It closely approximates the chemi-cally conservative parameter of acid neutralising capacity(ANC), which differentiates acidic, soil-derived runoffcomponents and deeper, more buffered groundwater com-ponents and can be used to estimate their relative propor-tions on conservative mixing in streams (Drever, 1998).As organic acids in DOC can contribute to alkalinity andpH ¾4Ð0 and may not be fully neutralized in titration,empirical equations (e.g. Cantrell, et al. 1990; Hill andNeal, 1997) are sometimes used to adjust alkalinity valesfor ANC (using an assumed mole site density for DOC).However, at the Loch Ard sites DOC is poorly corre-lated with flow and pH (e.g. Dawson et al., 2008) andanalysis suggested that this adjustment introduced greateruncertainty into the ANC estimates and made little dif-ference to the resulting hydrograph separations (cf. Nealet al., 1997; Tetzlaff et al., 2007a). Hence, the alkalinitywas used here to approximate ANC and assumed to beconservative on mixing in the subsequent analysis.
Long-term water quality data are summarized byannual means and ranges (Table II). Previous work byTetzlaff et al. (2007a) has shown a systematic increasein stream alkalinity at both sites resulting from declininglevels of acid deposition (Figure 3). Given the utilityof alkalinity in hydrograph separation, particular focuscentred on examining these temporal changes in flow-concentration relationships. Because of the systematicchanges in alkalinity, the whole dataset showed littlerelationship with flow (Figure 4a and b), however, thestructure became clearer when annual relationships wereexamined (Figure 4c and d). The annual relationshipswere described using a statistical random effects modelwhich fitted year-specific, nonlinear (Weibull) curves.This allows pooling of information across years, makingmore efficient use of the data when compared to fitting17 entirely separate curves (Pinheiro and Bates, 2000).
STORM FLOW AND BASEFLOW RESPONSE TO REDUCED ACID DEPOSITION 2305
(a) (b)
(c) (d)
Figure 4. Flow-concentration plots for all years (a, b) and exemplary shown for 1992 (c) B10 and (d) B11
Experiments with different nonlinear models resulted inthe application of a four-parameter Weibull curve asan appropriate descriptor of the relationship betweenalkalinity and flow for each year. We used the ‘nlmepackage’ (Pinheiro et al., 2008) in R (R DevelopmentCore Team, 2008) for model fitting.
The form of the Weibull curve used related alkalinityK with flow rate R via
K D a � b ð exp(� exp�c� ð Rd)
where a corresponds to the asymptote as R ! 1, bis the ‘drop’ representing the difference between zeroand infinite flows, and c and d control the curvature,i.e. the shape of the alkalinity/flow relationship. Inhydrological terms, the parameter a can be interpretedas the mean alkalinity as infinite flow (i.e. very largeflows) is approached, and the combination a � b reflectsthe expected alkalinity as flows approach zero (i.e.very low flows). We allowed year-specific versions ofparameters a, b and c, but a common d across all years,as 17 years worth of data was insufficient to be ableto feasibly determine two variable curvature parameters.The year-specific parameters included a linear term withyear (i.e. we allowed a, b and c to vary linearly withyear) and a random effect term by year. In essence, themodel allows for detection of ‘straight-line’ trends inthe mean alkalinity value for the highest flows, in themean alkalinity difference between highest and lowestflows, and in the shape of the fitted curves across years.
The random effect part allows for variation betweenyears over and above any straight-line trends. We appliedmodel selection to remove parameters, which did notappear to be contributing significantly to the model fit.
Essentially, the method of end-member identificationthen proceeds as follows: first, we use a statistical methodknown as kernel density estimation (Silverman, 1986)to obtain a smooth estimate of the flow distributionsfor each of the 17 years in the study. Next, we usethe fitted Weibull curve relating alkalinity and flow tomap the flow distribution onto the alkalinity scale viaa probability integral transformation (Stuart and Ord,1987, p. 21) which gives an estimate of the alkalinitydistribution for each year. Finally, we take the Q10 andQ90 points from the fitted flow distributions and mapthese onto the alkalinity scale simply by evaluating theWeibull curve at these points. The resulting tails ofthe alkalinity distributions are the estimated end-memberdistributions of high flow and low flow sources. In otherwords, we assume that these give the best availableestimates of lumped catchment-scale end members of‘soil water’ (i.e. low alkalinity sources of overland flowand shallow sub-surface storm flow which dominatehigh flows) and a deeper ‘groundwater’ source (whichdominates low flows). In these catchments, these seemreasonable assumptions due to the flashy flow regime(Figure 2) and lack of groundwater response to highflows, which results in soil water dominance (Figure 4cand d). Moreover, direct sampling of water draining soilsurface horizons in Loch Ard forest in the 1980s indicated
alkalinities of around �75 to �35 µeq l�1, which areconsistent with those of storm flow, implying limitedbias by groundwater influence at this time (Miller et al.,1990). Further detail on the statistical development andimplementation of this method can be found in Breweret al. (2010).
Applying this approach is an improvement on themethods used in previous work (e.g. Wade et al., 1999;Foster et al., 2001; Brewer et al., 2005). These havetaken direct samples of alkalinity values (for the high-est and lowest flows as per Q10/Q90, for example, orfrom occasional soil water or groundwater samples) asthe end members and/or estimated the distributions byfitting Normal distributions to these data. This previousapproach is subject to error due to: (a) the small samplesize; (b) variation in single extreme alkalinity values; and(c) end-member distributions, as they represent extremevalues, having a skewed rather than a symmetric, Normal,distribution, as would seem intuitively reasonable. Thus,this new method allowed the best possible interpola-tion of annual hydrochemical characteristics from weeklysamples; using relationships between flow and alkalinityto predict daily alkalinity values from daily flows. Fromthese daily estimates, it was possible for the annual distri-butions of alkalinity to be estimated and various averagesand percentiles could be derived. In turn, this facilitatedthe identification of chemical end members for each year,which could be used to give an integrated inference of‘soil water’ and ‘groundwater’ chemistry at different timesteps, in a way that accounted for the systematic changesin stream chemistry resulting from reduced acid deposi-tion over the entire investigation period.
Hydrograph separations
Hydrograph separations were carried out using compo-sitional analysis in three contrasting ways, which definedthe end-member composition differently.
Method A defined end-members, that is ‘soil water’and ‘groundwater’, via the modelled alkalinity/flow rela-tionship and kernel density estimation as described inSection on Hydrochemical Trends, Flow-ConcentrationCurves and End-member Definition, on a per-year basis;
Method B was that of Brewer et al. (2005), also notedin Section on Hydrochemical Trends, Flow-ConcentrationCurves and End-member Definition, which simply usedthe alkalinity values for extreme flows to estimateparameters of Normal distributions for the ‘soil water’and ‘groundwater’ end members, again on a per-yearbasis; and
Method C implemented the approach via modellingalkalinity versus flow, but with data combined for allyears to give only a single distribution for each endmember.
Having obtained estimated distributions for the endmembers by Method A, we could then use these toconduct hydrograph separations for each year separately,in the manner of Brewer et al. (2005), replacing theNormal distributions used for the sources in that paper
(and in Method B) with the alkalinity distributionsdetailed above. In Brewer et al. (2005), the compositionalanalysis included the direct modelling of flow, so thatthe estimated proportions of the two end members wasinfluenced by the observed flow at each time point. Here,the proportion estimates for 1 year have been obtainedusing only the discharge for that particular year. The end-member for that year, however, contains flow informationfrom all years via the Weibull random effect model, thusreducing the circularity in the methodology.
Finally, the compositional part of the analysis proceedsas follows: the alkalinity values Kij for the streamsamples for sample i in year j are assumed to becomprised of a weighted combination of latent (i.e.unobserved) draws from the source distributions. Thesedraws are denoted by Yij;10 and Yij;90 for the low andhigh flow sources, respectively, and suppose that thesample of stream water we collect has been obtained bymixing together two samples from the estimated sourcedistributions. These source contributions were modelledusing the ‘soil water’ and ‘groundwater’ end-memberdistributions derived via one of the Methods A–C. Theweights (for the weighted combinations) in this contextare the source proportions pij;10 and pij;90, and forNormal errors εij we model the stream samples via
Kij D pij;10Yij;10 C pij;90Yij;90 C εij
The proportions pij;10 and pij;90 must sum to 1 for eachsample i in each year j, and so to model the compositionproportions pij, we use log-ratios qij D log �pij;10/pij;90�and again assume Normality, via
qij ¾ N ��q;ij, �2q�, 8i,j
for the mean �q;ij on the log-ratio scale, with variance�2
q, and where we include covariate information on flowsin the model via
�q;ij D �q C ω ð Lij
for overall mean �q, log flow Lij and linear term ω.As this is a Bayesian analysis, prior distributions mustbe defined for all the model parameters and an overallmeasure of uncertainties at each step in the process isintegrated in the final hydrograph separations. Furtherdetail on this can be found in Brewer et al. (2005, 2010).
RESULTS
Hydrochemical trends
Both streams are acidic with low ionic strength(Table II). Cl and Na are the dominant anion and cation,respectively, and alkalinity is low. Many chemical deter-minands have shown directional change in the streams atLoch Ard, though in some cases the responses are some-what different in B10 and B11 (Figure 3). In terms ofrecovery from surface water acidification, alkalinity andpH have increased in both streams, though the increase
STORM FLOW AND BASEFLOW RESPONSE TO REDUCED ACID DEPOSITION 2307
is notably more marked in B10. This general recov-ery largely reflects the decline in SO4 concentrationsresulting from reduced S deposition (Figure 3). However,other mobile anions have shown different behaviour.Cl exhibits seasonality, with higher winter concentra-tions reflecting increased Atlantic storminess affectingprecipitation inputs compared with summer (Hrachowitzet al., 2009). Several years (e.g. 1989, 1993, 2002 and2005) reflect distinctively high pulses where Cl levelsare elevated in both streams. Nitrate is generally low,apart from elevated concentration in B10 following initialfelling operations in 1988. This reflected former log-ging practices where residual branches and foliage wereallowed to decompose in situ. In later felling, these wereremoved from the site, and thus N leaching was smallin both streams. DOC concentrations have increased inboth streams, but particularly B11, since the mid-1990sand this may have increased the contributions of organicacids to stream water (Dawson et al., 2008).
Flow-concentration curves
Storm flows derived from the organic peaty horizonshave reduced alkalinity compared to baseflows whichare derived from subsoil horizons, glacial drift andbedrock fractures (Figure 4c and d). However, alkalinityconcentrations are low during base flows and highflows in both catchments indicating the shallow natureof groundwater and the lack of deeper well-bufferedsources. B11 generally has lower high flow alkalinities,though both streams exhibit a ‘threshold-like’ responseat higher flows when soil-derived water becomes thedominant source of stormflow. This is also reflected inthe storm hydrographs shown in Figure 2.
The modelling procedures using the Weibull curvefitting suggested two parameters, one for each catchment,are linearly related to year—this is shown by theresulting parameter estimates in Table III. For B10, theestimated average alkalinity difference between near zeroand near infinite flows was 40Ð5 µeq l�1, whereas for thehighest flows the figure was predicted as �46Ð2 µeq l�1
for 1988 and an additional 1Ð30 units per year thereafter.For B11, the equivalent figure for near infinite flow wasa fixed �50Ð4 µeq l�1 across all years, but the differencebetween flows approaching zero and highest flows wasestimated as 24Ð7 µeq l�1 for 1988 and with the gapgrowing wider (i.e. the curve stretching in the direction ofthe Y-axis in Figure 5) by 2Ð5 units per year for the periodthereafter mainly reflecting increases at lower flows.
When flow-concentration plots for individual years areshown (by progressive shading of the fitted curves foreach year) these relationships can be seen clearly, as canmore generally the changing nature of the alkalinity-flowrelationship through time (Figure 5). This is evident inboth catchments, though more marked in B10 throughthe more easily identifiable asymptote parameter. Partic-ularly, noticeable is the increasing high flow alkalinityover time which results in a systematic change in thefitted flow-concentration relationships.
Table III. Estimated parameters for the Weibull fits for bothcatchments
Ł The asymptote parameter a here is modelled as �46.21 C 1.30Ł(year–1988); ŁŁ The drop parameter b here is modelled as �24.65 to2Ð48Ł (year-1988).
Distributions of stream alkalinity and end-memberdefinition
From these fitted models, and using a statistical model-based version of the stream hydrograph, the distributionof stream alkalinity was estimated for each year for eachstream (Figure 6). These distributions show the effects ofchanging acid deposition for each year and are generallyfairly symmetric though more skewed in wetter and drieryears. The distributions for B10 are less spread aroundthe median than in B11, reflecting the effects of loweralkalinity high flows in B11.
Hydrograph separations
This identification of high flow and low flow endmembers facilitated temporal differentiation of flows intocatchment-scale hydrological source contributions of ‘soilwater’ and ‘groundwater’ in a way that specificallyaccounted for temporal changes in end-member com-position. In the analysis by Method A, end memberswere drawn from a more realistic skewed distribution.All three methods in turn allowed the application oftwo-component mixing models that were embedded ina Bayesian uncertainty analysis.
Separations for B10 for each weekly sample for 1994are shown in Figure 7 comparing Method A with thepreviously used Method B, as fitted time series ofestimated groundwater proportions. Credible intervals(the Bayesian alternative to confidence intervals forillustration of uncertainty) are notably narrower for theproportions estimated via Method A compared withthe Method B. This reflects the fact that the sourcedistributions of the two end members defined by MethodB are strongly influenced by natural variability andpotential bias inherent in small sample numbers (3–5) inthe top 10% of flows and the resulting uncertainty. Thenew Method A partially resolves this problem by usingthe modelled alkalinity/flow relationship to gain a betterestimate of the likely extremes of alkalinity by removing
Figure 5. Year-specific, nonlinear Weibull curves showing temporal changes in flow-alkalinity relationships, (a) B10 and (b) B11. Connected symbolsfrom left to right show changes from 1989 to 2005; if the near infinite flow asymptotes of the curves are increasing over time, there should be an
upward trend visible in the triangles
Figure 6. The estimated distributions of alkalinity values for three (example) years for (a) B10 and (b) B11 with corresponding end-membershighlighted for high flow (soil water) and low flow (groundwater). The distribution of flow was modelled using a non-parametric density estimate(a kernel density estimate) on a year-by-year basis, which was then transformed via the fitted Weibull curve onto the alkalinity scale. The Q10 andQ90 points were calculated for these flow distributions and the fitted Weibull curve was used to map these points onto the alkalinity scale to give the
end-member inner limits as shown
the need to consider just a small handful of observationsfor each end member.
The applied hydrograph separation estimated ground-water contributions to stream flow for each year (Figure8). The variability in Method C is apparent due to the lim-itations of using non-temporally varying end members.The separations for each year derived with Method A aretabulated in Table IV, which shows that ‘groundwatercontributions’ from B10 were higher but more variablethan in B11. Moreover, Method A also shows that thecompositional analysis successfully removes the influ-ence of systematic changes in end-member compositionto provide relatively consistent hydrograph separations.There is a relationship between the annual runoff totals
and the groundwater contributions for B10 (r2 D 0Ð47),whereas the groundwater contribution in B11 is relativelyconstant. There was no evidence that the method was ableto detect any changes resulting from any of the forestfelling in the catchments.
DISCUSSION
We used long-term data sets of stream hydrochemistryas indicators of the response of two small catchmentsto reduced acid deposition. This showed that the twosites, like others in the UK uplands (e.g. Ormerod andDurance, 2009), are recovering—albeit differently—to
STORM FLOW AND BASEFLOW RESPONSE TO REDUCED ACID DEPOSITION 2309
Figure 7. Comparison of estimated groundwater proportions for Methods (A) and (B), plotted against time; B10 and 11, exemplary shown for 1994.The dashed lines represent 95% credible intervals
Figure 8. Tracer-based hydrograph separation by year applying the threeMethods A, B and C (Method A defined ‘soil water’ and ‘groundwa-ter0027 end-members via the modelled alkalinity/flow relationship andkernel density estimation on a per-year basis; Method B used the alka-linity values for extreme flows to estimate parameters of Normal distri-butions for the end members, again on a per-year basis; and Method Cimplemented the approach via modelling alkalinity versus flow, but withdata combined for all years to give only a single distribution for each
end member)
the effects of acidification, by exhibiting increases inpH and alkalinity. Often catchment monitoring meansthat such records of long-term catchment-scale responseare our best means for inferring changing processes,as detailed, mechanistic studies of small-scale processesare much scarcer and typically of a short (ca 1 year)duration. Yet, inferring processes from catchment-scaleresponses is inherently difficult, as averaging or can-celling of effects, or emergent behaviour at larger scalescan at best hinder interpretation, or worse result in inter-pretation that is wrong (Taugbol and Neal, 1992; Lis-cheid, 2008).
Table IV. Summary of groundwater contributions (using MethodA)
The Bayesian compositional analysis was undertakento try to use catchment-scale stream water chemistry toinfer changes and/or differences in hydrological func-tion and is aimed at utilizing statistical approaches (e.g.combining ideas from Brewer, 2000 and Brewer et al.,2005) that maximize the use that can be made ofsuch long-term data sets. Although alkalinity has provenutility as a tracer in hydrograph separations, recoveryfrom acidification dictate that there has been tempo-ral changes in concentrations at high and low flows.Fitting Weibull curves to the annual flow-concentrationplots for alkalinity helped capture this dynamic changeand to model how it was most likely affecting thecomposition of the dominant sources of high andlow flows for individual years. This demonstrated aclear difference in the ways the two catchments wereresponding: B10 exhibited increases in alkalinity athigh flows and low flows, whilst only low flows atB11 exhibited a substantial change over the entire time
period of 17 years. High flows in B11 increased onlymarginally.
The hydrograph separations carried out for the twostreams revealed greater and more variable groundwatercontributions to flow in B10, with an average estimatedcontribution to annual streamflow of 46Ð7% comparedwith 32Ð2% in B11. Although these values, especially forB10, may seem large for upland catchments, it shouldbe stressed that the groundwater is of low alkalinityand mainly reflects drainage from soil parent materialin drifts and fractures in crystalline bedrock, ratherthan deeper significant aquifers (Robins, 1990). As aresult, the chemical differences between the major runoffsources are relatively small and the resulting hydrographseparations have a high degree of uncertainty. Thus, thecredible intervals shown in Table IV indicate that theaverage contribution of these groundwater sources toannual runoff may be as low as 35% in B10 and 20%in B11.
Given the similarities of the two catchments andtheir stream flow regimes, the difference is somewhatsurprising. However, it can be hypothesized that thesedifferences are consistent with subtle differences in thetopography and soil cover of the two catchments. Thesedifferences seem to influence hydrological routing in thecatchment soils that produce a responsive flow regime,but with distinct differences in sources and associatedhydrochemistries. The B11 catchment is distinguishedby more complex hydropedology; the coverage of humicgley soils and peats have thicker, more acidic organicsoil horizons, which are likely to generate runoff oflower alkalinity than the dominant minerogenic gleys ofB10. In addition, the steeper nature of B10 results in agreater number of geological outcrops on the catchmentinterfluves, which probably facilitate deeper rechargethrough fractures. Perhaps most importantly, the topologyof the peat soils in B11 appears to act as a hydrochemical‘hot spot’ in the central part of the catchment wherethe stream actually distributes through a wetland at highflows. This has the potential to ‘re-acidify’ and resetchemistry drainage from upstream, especially at higherflows, and upslope. These factors would be consistentwith the more limited recovery of storm flow alkalinityin B11, as well as the lower groundwater contributionsinferred by the catchment-scale hydrograph separations.
The compositional analysis carried out here is not pre-sented as a panacea. For example, it does not overcomesome of the criticisms associated with hydrograph sepa-ration techniques, not least in that it is tautological indefining ‘soil’ and ‘groundwater’ end members. Nev-ertheless, the proposed Method A does go some waytowards reducing the tautology as it uses data from allyears to obtain end-member distributions for just 1 year.Significantly, the nature of these two catchments appearsparticularly well suited to the approach. This is due tothe ‘threshold-like’ behaviour of the flow-concentrationplots for individual years which indicate, consistent withthe soil characteristics and hydrogeology of Loch Ard,that groundwater contributions are low and relatively
stable during storm episodes. Thus, the approach is amethod that can maximize use of available informationin long-term date in a learning framework to concep-tualize catchment-scale response and provide a basis forinter-catchment comparison. In this case, this has impliedsome subtle, yet significant, differences, in the internalhillslope hydrology of small catchments that have allowhypotheses to be developed, which can be tested in rela-tion to smaller-scale process studies. Moreover, thesecan be focused on the parts of catchments that are mostlikely most significant for controlling the catchment-scalehydrological and biogeochemical response. That said, nomajor change in groundwater contributions to stream-flow as a result from forest operations appeared to bedetectable with the method. This may reflect the rela-tively small areas of each catchment impacted by felling,or the fact that any hydrological changes were subtle (e.g.reduced time to peak, or magnitude of peak flow) andneed to be identified using higher resolution (i.e. 15-mindata).
Emergent behaviour of hydrological and biogeochem-ical processes at the catchment scale often results in rel-atively simple and predictable functional characteristics(such as those demonstrated here between alkalinity andflow, subject to uncertainty modelled appropriately herevia Bayesian methodology). However, these are under-pinned by complex, heterogeneous processes at smallerhillslope scales (Sivapalan, 2003; Tetzlaff et al., 2008).Furthermore, even in experimental catchments (typicallyas here ca 1 km2), it is usually unknown how small-scaleprocesses, say at the soil profile or hillslope scale, areaffected by long- and short-term perturbations in tempo-rally variable forcing factors such as climatic variability,land use change and long-term, directional environmen-tal change (Holden, 2005). Even less is known abouthow such small-scale change in heterogeneous landscapesaggregate—often in nonlinear ways where ‘hot spots’may be important—to account for changes at the largercatchment scale, though this is the scale that is usu-ally monitored and observed (McDonnell et al., 2007).These limitations in our understanding, dictate that thereis clearly a need for a suite of approaches and develop-ment of new tools—such as those presented here—thatprovide better insights into how hydrological and biogeo-chemical processes at a range of scales are affected byenvironmental change.
ACKNOWLEDGEMENTS
Ron Harriman and numerous other staff of the FRSFreshwater Laboratory are thanked for initiating andcontinuing the Loch Ard study. This work has beenundertaken with the support of the Leverhulme Trust andthe Carnegie Trust for the Universities of Scotland. MarkBrewer was funded by the Scottish Government Ruraland Environment Research and Analysis Directorate.
STORM FLOW AND BASEFLOW RESPONSE TO REDUCED ACID DEPOSITION 2311
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