WATER RESOURCES RESEARCH, VOL. 39, NO. 7, 1177, doi:10.1029/2000WR000130, 2003

Changes in stream nitrate concentrations due to land management

practices, ecological succession, and climate: Developing a systems

approach to integrated catchment response

F.WonallDepartment of Geological Sciences, Science Laboratories, South Road, Durham, UK

--W. T. SwankCoweeta Hydro-logic Laboratory, Southern Research Station, USDA Forest Service, Otto, North Carolina, USA

T.P. Burt -Department of Geography, Science Laboratories, South Road, Durham, UK

Received 6 December 2000; revised 23 April 2002; accepted 14 May 2002; published 10 July 2003.

[i] This study uses time series analysis to examine long-term stream water nitrateconcentration records from a pair of forested catchments at the Coweeta HydrologicLaboratory, North Carolina, USA. Monthly average concentrations were available from1970 through 1997 for two forested catchments, one of which was clear-felled in 1977 andthe other maintained as a control. The time series were decomposed into their trend andannual cycle before modeling as an autoregressive (AR) process. AR models werecalculated for both an expanding and a shifting window so that prefelling could be directlycompared with the effects of tree clearance. In comparison with flow records for both of *the catchments, transfer function-noise models were calculated on a moving windowbasis, and the impulse functions were derived. Analysis shows that both catchmentsshow an annual memory effect but that the clear-felled catchment shows, in addition, a6-month memory effect The annual effect in the control catchment responds to droughtconditions while in the felled catchment, it reflects the change in vegetation. The6-month effect in the felled catchment responds to drought conditions independent ofboth the annual effect and of logging operations. The control catchment shows nosignificant impulse function with respect to flow, while for the felled catchment adistinct impulsivity develops over time subsequent to logging and coincident with the onsetof nitrogen saturation. By examining the nature of the nitrate export, rather than solely thelevels of export, a systems approach can be taken to understanding catchment behavior.Such an approach shows that the catchment is in metastable equilibrium with respect to itshydrological pathways and nitrogen reserves but in dynamic equilibrium with respect tolong-term temperature change. The onset of nitrogen saturation may represent irreversiblechanges in the catchment behavior, and impulsivity, with respect to streamflow, representsa new indicator of N-saturated conditions. INDEX TERMS: 1871 Hydrology: Surfece water.quality; 1803 Hydrology: Anthropogenic effects; KEYWORDS: nitrate, streamwater, forest hydrology, climate *change, ecological change

Citation: Worrall, R, W. T. Swank, and T. P. Burt, Changes in stream nitrate concentrations due to land management practices,ecological succession, and climate: Developing a systems approach to integrated catchment response, Water Resour. Res., 39(7), 1177,doi:10.1029/2000WR000130, 2003.

1. Introduction identification of N saturation, where N availability exceeds[2] Nitrate concentratiQns in surface and groundwaters ffl-situ> biological demands with consequent increases in N

continuetobeamatteTofconcernthroughoutthedeveloped ^P?4 »»J P088*16 detrimental consequences on waterworld [Burt et a/., 1993]. As a result of this concern, spatial W^™* "P*1* ̂ systems l*Jf * <*" ^9-Stoddardand temporal variations of nitrate concentrations in catch- 19941- * saturated conditions could be a result of increasedments have been analyzed in order to help understand atoosphenc deposition m Europe and Jie USA [^er^ a/.,nitrate export from river basins. The export of nitrogen 1997; EmmettetaL, 1995]. The link between atmosphericfrom forested catchments has been well studied with the deposition and N export has led to the extension of the

critical loads concept [Bull, 1991] to nitrogen loads and itsrole in acidification [Murdoch and Stoddard, 1992; Stod-

Copyright 2003 by me American Geophysical Union. dard, 1991] and eutrophication [Emmett and Reynolds,0043-1397/03/2000WR000130S09.00 1996]. Such saturation has been induced experimentally to

HWC 1-1

HWC 1-2 WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

understand response dynamics [Adams et aL, 1997; Rey-nolds et al., 1998].

[3] Interest in forest nutrient dynamics has been used toevaluate the long-term role of management [Knoepp andSwank, 1997]. Particular attention has focused on the effectsof tree harvesting [Reynolds et aL, 199S; Romanowicz et aL,1996; Neal et aL, 1998a, 1998b; Kamari et aL, 1998], thecomparison of harvesting techniques Mann et aL, 1988;Lundborg, 1997] and the management of riparian zoneswithin forests [Cirmo and McDonnell, 1997], Ecosystemchanges have been considered, including: climate changes

- [McNulty et aL, 1997], forest fire [Vose et aL, 1999], andinsect infestations [Swank et aL, 1981].

[4] The interest in nitrate cycling and nutrient response toexternal drivers means that many time series of data havebeen collected and examined. Several studies have exam-ined die trend in records. Arheimer et al. [1996], examiningforested catchments in Scandanavia, showed that althoughstrong correlations with flow were recorded, the strongesteffect on nitrate concentration was the relative length of thegrowing and dormant seasons. Also working in Scandina-vian catchments, Stdlnacke et al. [1999] showed thatincreases in the nitrate concentration trend were moreclosely related to reductions hi phosphorus concentrationsthan nitrogen saturation. Reynolds et aL [1992] showed thatalthough the trend in nitrate levels following a severedrought was unaffected, the amplitude of the annual cyclewas increased and took several years to recover to pre-drought levels. Creed et al. [1996] explained the annualnitrate export from a forested catchment hi terms of aflushing hypothesis [Hornberger et aL, 1994], and a similarexplanation was used by Edmonds and Blew [1997]. Swankand Vose [1997] compared nitrate export trends and sea-sonal variations for a range of experimental catchmentswithin a basin undergoing a range of management practices.They showed that saturation levels were related to intensityof management, with the highest saturation states correlat-ing with the most disturbed watersheds. However, littlework has been conducted on the nature of the export ratherthan the export itself Worrall and Hurt [1999], working hiagricultural catchments, showed that the trend and theseasonal cycle were not die only components of a nitratetime series that could be analyzed. Detailed time seriesanalysis can provide additional information on die nature ofexport and catchment response to external and internaldrivers (e.g., climate change and land use management)tiiat is not available by other approaches.

[s] Analysis of time series by autoregressive modeling[e.g., Mann and Wold, 1943] has revealed that the export ofnitrate from a catchment shows a memory effect [Nadenand McDonald, 1989]. This memory effect is a form ofpersistence, with die previous condition of nitrate export indie catchment influencing present nitrate export Differingcatchments show a range of memory effects, which fornitrate time series' typically approximate to annual anddiennial effects, with differing scales of significance. Incatchments where multivariate records are kept, Le., a rangeof chemical and physical parameters are recorded, mencomparisons between these time series enables an under-standing of not only how nitrate export responds to changes,both internal and external to die catchment, but also how dieresponsiveness of the nitrate export changes. Long nitrate

C»t««UCritk

Figure 1. Location of die Coweeta laboratory withlocations of experimental and reference catchment used indiis study.

records can be linked to long-term internal ecosystemcontrols on nitrate export and also can be used to trackthese changes over time to understand how they respond toexternal factors, e.g., climate change. SuchMetailed recordsare available from die catchments of the Coweeta Hydro-logic Laboratory, North Carolina, USA. The number anddiversity of long-term catchment experiments being con-ducted at Coweeta provide a foundation for comparing bornmanaged and unmanaged catchments.

[6] The examination of long-term nitrate export recordsnot only aids understanding nitrate behavior but also allowsus to take a systems approach to catchment behavior. Thisapproach is embodied in die raison d'etre of die Coweetaexperiment that die quantity, timing, and quality of stream-flow provide an integrated measure of the success or failureof land management practices [Swank and Crossley, 1988].This study takes such an integrated approach to understand-ing how catchments respond to external and internal drivers.

2. Methodology2.1. Site Description

[7] The time series of nitrate concentrations analyzedhere originate from die Coweeta Hydrologic Laboratory,North Carolina, USA. Established in 1934, die Coweetawatersheds represent one of die longest continuous envi-ronmental studies presentiy available. The 2185 ha water-shed is divided into two adjacent basins (Figure 1). Theclimate of the region is classified as marine, humid temper-ate [Swift et al., 1988]. Mean annual precipitation variesfrom 1800 mm at low altitudes in die basin to 2500 mm atme highest altitudes, with March typically being the wettestmonth and snowfall making up less tiian 5% of dieprecipitation. Mean annual temperature is 12.6°C at diebase station, wim an average montiily low of 3.3°C hiJanuary and a high of 21.6°C in July. The geology of thebasin is dominated by metamorphic formations includingschists, gneisses and metasandstones [Hatcher, 1988]. Soilsfall into two orders: immature mceptisols and older, mature

WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT HWC 1 - 3

0.25 n

02.

i 0.15-

0.1 •

aos

1995

Figure 2. Nitrate concentrations in the Big Hurricane stream (die felled catchment) in comparison to thebest fit linear trend.

Ultisols. Steep faces at high elevations are covered by theumbric dystrochrepts of the Porter series, the remainingInceptisols are of the Chandler gravelly loam series. TheUltisols comprise typic hapludults and humic hapludults.lypic hapludults cover the largest area of the basin andconsist of the Coweeta-Evard gravelly loam and Faninsandy loam series. Mixed mesophytic forests characterizethe region and the four major forest types of the basin havebeen described by Day et at. [1988].

[s] This study focuses on the nitrate concentrationsobserved in a pair of catchments, 2 and 7; the nitrate time

series are shown in Figures 2 and 3, respectively. Catchment2 (Shope branch) is 12 ha in area with a maximum elevationof 1004 m. Catchment 7 (Big Hurricane) is 59 ha in size andreaches a maximum elevation of 1077 m. The two catch-ments are adjacent and have similar southerly aspects(Figure 1). Catchment 7 was commercially clear-felled,cable logged and allowed to regenerate in 1977 and ishence forward referred to as the felled catchment [Swank etal., 2001]. As part of logging operations, 3 contour road-ways were constructed traversing the catchment at 300mintervals. Catchment 2 is one of the control catchments

0.05-1

0.045

1971 1S75 1980 1985Water Year

1990 1995

Figure 3. Nitrate concentrations in the Shope branch (control catchment) in comparison to the best fitlinear trend.

HWC 1-4 WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

within the basin and has remained undisturbed since 1927, itis henceforward referred to as the control catchment Streamgauging on both these catchments commenced in 1934 andnitrate monitoring in 1972. Stream water is sampled weekly.Samples are immediately refrigerated and analyzed within7 days. Before July 1990 nitrate was analyzed by automatedcadmium reduction method and thereafter by ion chroma-tography. Quality control is maintained by analysis ofstandards from an independent laboratory. Weekly valuesare flow weighted to provide the monthly time series.analyzed here.

[9] Stream discharge is measured "continuously on eachwatershed using 90° V notch weirs. Equally, a range ofmeteorological conditions are monitored in the catchmentthat mean that results of time series analysis can becompared to detailed rainfall and temperature records.

2.2. Decomposition of Time Series[10] There are a number of possible approaches to the

analysis of nitrate time series [Esterby, 1997]. It is assumedin this paper mat the monthly nitrate time series can betreated as a series of separable elements: the trend, theseasonal variation, and the residual [Wbrrall andBurt, 1998,equation 1]. This is a common approach to analyzing timeseries mat views the time series as a deterministic (trend andseasonal components) and a stochastic component (theresidual or error term) [Gottmann, 1981; Harvey, 1981],This study focuses on the analysis of the residual, acomponent previously ignored in studies of nitrate exportThe time series is decomposed into its trend and seasonalvariation using a multiplicative model A multiplicativemodel is preferred over an additive model because of theobvious nonstationarity in the time series from the felledcatchment, i.e., the amplitude of the annual cycle appears toincrease with the increasing trend in nitrate time series(Figure 2). The multiplicative model allows the seasonalindices to increase in line with the trend in the data.

Y(t) = a x trend x seasonal variation + residual, (1)

where Y(t) is the nitrate concentration over time and a is amodel coefficient ,

[11] Four alternative strategies were used for analyzingthe trend in the data: linear trend, quadratic trend, exponen-tial curve and S curve. The trend in the data is fitted usingleast squares regression and the series is detrended bydividing the data by the trend component as suggested bythe multiplicative model given in equation 1. The seasonalvariation is removed by use of seasonal indices. A centeredmoving average of length equal to that of the annual cycle iscalculated. Indeed, in this particular case, because theannual cycle length is an even number (i.e., 12 months),the moving average is a two-step process in order tosynchronize the moving average correctly. Once the movingaverage is obtained, ft is divided into the detrended data toobtain what can be referred to as raw seasonals. Within eachseasonal period, the median value of the raw seasonals iscalculated. It is these medians that make up the seasonalindices. The mean of the medians is adjusted so that theirmean is one; these seasonal indices are in turn used toseasonally adjust the data by dividing the detrended data bythem. The seasonal indices approach is: more responsive tothe actual data; brings fewer assumptions to the data than

fitting simple harmonic functions derived from Fourieranalysis; and is readily available in standard statisticalanalysis packages, e.g., Minitab (Minitab version 13.20).

2.3. Derivation of AR Models $[12] The first approach taken to the analysis of the

residual was the Mann-Wald process [Mann and Wald,1943; Gottmann, 1981]: this method calculates me best fitautoregressive (AR) model of me residuals. The Mann-Wald process is used because the identification of signifi-cant AR models is physically interpretable in terms of theprocesses of nitrate hydrology. The order of the AR modelwas systematically varied using both a step-up and a step-down procedure so as to avoid local minima in the modelfit The fit of the model was checked using the Quenouillemethod [Quenouille, 1947]. AR(p) (where p is the order ofthe model) was initially calculated for both series in theirentirety for p < 18 in order to identify significant ARmodels that could be tracked to understand their variationover the period of sampling. Six month and annual memoryeffects have been previously identified in water quality timeseries from a range of settings including nitrate time series[Wbrrall and Burt, 1999] and dissolved organic carbon timeseries [Naden and McDonald, 1989], and so these effectswere particularly focused on.

[13] After identifying significant memory effects for thewhole sequence, the variation in these effects are tracked intwo ways. The first is to calculate the AR(p) (where p is theorder of the model found to be significant for the entireseries) for a subset of the concentration record. The subsetstarts at the beginning of the record and the model is thenrecalculated, but the subset is allowed to expand by anumber of months equal to the annual cycle, Le., expansionin 12 month steps: this process is iterated until the wholerecord is covered. Thus mis method represents the calcula-tion of the time series model for an expanding windowacross the record. The initial length of the subset used in thisstudy was set at 72 months. The longer this subset, thegreater the opportunity for discerning significant effects.However, it was felt important to study the prefellingperiod, and thus the length of the subset was constrainedby the length of record prior to the clear felling in 1977.

[14] The second method is to use a shifting window. Inthis case the subset of the record for which the AR(p)model is to be calculated is set at a fixed length. Themodel, at the chosen value of p, is calculated for this lengthof subset starting at the beginning of the record. The modelis recalculated for the same length of subset, but the subset isshifted by the length of the annual cycle and this process isiterated until the end of the record is reached. In this waythe time series is being calculated for a shifting, ascontrasted to an expanding, window. The length of theshifting window is again set to 72 months so as toencompass the whole period prior to clear-felling of thefelled catchment In both the shifting and expanding win-dow methods the year referred to is the year at the end ofthe period being examined, e.g., in the subsequent discus-sion 1977 refers to the result for the previous six years, theperiod 1971-1977.

[is] By calculating the AR models for expanding andshifting windows multiple comparisons are being made andsignificance tested. Making such comparisons increases thepossibility of familywise error rate and it would certainly be

WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT HWC 1 -5

larger than the nominal 5% probability value if the 95%significance level is chosen. To minimize the familywiseerror rate comparison is also made with the 99% signifi-cance level in the Quenouille test

[16] Results from both shifting and expanding windowscan be compared to meteorological conditions prevailing inthe catchment A range of measures of the rainfall andtemperature can be used to examine the effect of externalclimatic drivers on the catchment nitrate response in com-parison to clear-felling and the vegetational succession.resulting from the forest regrowth.

[17] There is an assumption of honfoscedasticity made inthis approach to AR modeling. This assumption is particu-larly important if the goal is to provide a predictive model ofnitrate export, where an allowance for conditional hetero-scedasticity (ARCH \Bollersley, 1986]) would probablygive better predicitve power. However, the goal of thisresearch is to use AR modeling to examine long-termcatchment memory effects in the context of internal andexternal driving variables: Thus an allowance for condition-al heteroscedasticity would obscure the results while con-clusions from our analyses are valid. Similarly, a nonlinearfilter (e.g., Kalman filter) may well provide further infor-mation in understanding nitrate concentrations; however,the calculation of the AR model by using a shifting windowmeans that changes during the course of the period ofobservation can be tracked. The use of both shifting andexpanding windows of time enables an estimate of the scaleand time constants of effects to be made.

2.4. Derivation of the Impulse Function[is] Transfer-function noise models (TFN) were calculat-

ed for bom catchments against the streamflow record. Thefirst stage of calculating the TFN model is to derive anautoregressive integrated moving average (ARIMA [Boxand Jenkins, 1970]) model of the input series, in this casethe flow record. The model is derived using the method ofShumway [1988]. Because the nitrate time series (the outputseries) has been decomposed rather man differenced, theinput series was treated similarly and so the model derivedwas in fact an ARMA model To identify the order of theARMA model the autocorrelation function (ACF) and thepartial autocorrelation function (PACF) of the residualsfrom the decomposition of the input series were examined.In a series already made stationary, the number of signifi-cant lags in the PACF is taken as an estimate of the order ofthe autoregressive component of the ARMA model Theorder of the moving average component was estimated in asimilar fashion from the ACF. The necessity of allowing forseasonal autoregressive or seasonal moving average behav-ior can also be identified from the PACF and ACF respec-tively. The fit of the estimated ARMA model for the inputseries was tested by systematically varying the order of theAR and MA components to test the sufficiency of the fit Inthis case, calculating the variance of the residuals afterfitting the particular ARMA model was used as a measureof the model fit Once the ARMA of the input series hasbeen calculated satisfactorily, mis ARMA is used to filterthe output series (the nitrate record). The cross-correlationfunction can then be calculated between the residuals of theinput and output series; the result is the impulse function.The impulse function represents a measure of how respon-sive the output is to the input above and beyond that which

Table 1. Residual Variance of the Time Series After Removal ofthe Components of the Time Series Model3

Component

TrendLinearQuadraticExponential curveS curve

SeasonalAdditiveMultiplicative

AutoregressiveDiennialAnnual

Control Catchment

90909199

4139

1515

Felled Catchment

47456047

3328 '

2121

*For the control catchment the diennial antoregressive component is aAR(6) and the annual effect is AR(12). For the felled catchment the diennialautoregressive Component is AR(7) and the annual effect is AR(13).

can be explained by the other components of the time series,i.e., the trend, seasonal cycle and the ARMA component Inthe case being studied here it represents how an unpredictedflow, Le., that not predicted by the other components in thetime series analysis, influences the nitrate concentration? Ifconcentration/discharge relationships were calculated thesewould reflect seasonal differences and the .memory effectshighlighted by AR modeling. It is once a range of othercomponents have been removed that the link betweendischarge and concentration can be properly explored interms of how an impulse in one reflects changes in the othertime series.

[19] This approach to the derivation of an impulse func-tion is valid when the input and output series are indepen-dent of each other and when causal feedback can bediscounted. The significance of the cross-correlations wastested using a t-test Because of the problem of multiplecomparisons increasing the familywise error rate the resultsare also tested against the 99% significance level As withthe AR modeling, the impulse function was calculated forboth expanding and shifting windows across the record as ameans of tracking the change in impulsrviry of the catch-ments in response to natural and external drivers. Thisapproach to understanding relation between variables cre-ates a reliable and unbiased measure of the relation andreduces problems of autocorrelation between the series[Gurnell et al, 1992].

3. Results3.1. Time Series Decomposition

[20] Fits of the alternative approaches to the fitting of thetrend, as assessed by the percentage of the original varianceexplained, showed mat me fit of both me linear and thequadratic trend performed better than either the exponentialcurve or an S curve for both the felled catchment and thecontrol catchments (Table 1). The fitting of the quadratictrend gave a 2% improvement in fit for the felled catchmentin comparison to the fit of me linear trend and less than0.5% improvement in fit for the control catchment, as aresult the simpler linear trend was retained (Table 1 andFigures 2 and 3). Long term trends hi the data have beendiscussed by Swank and Vose [1997] and the correlationbetween nitrogen export from the catchment and the nitro-

HWC 1-6 WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

3i

2.5

2

1.5

0.5-

1 1

•felled catchment - pre-felllngBfeted catchment- post-fellingDimiUul c4tulunent

6 7Month

10 12

Figure 4. Seasonal indices for the control catchment and the felled catchment prior to and after felling.

gen content of the soils and biomass have been discussed byKnoepp and Swank [1997] and Elliot et al. [2002], andthese will not be discussed further here.

[21] Seasonal decomposition by an additive modelimproves the fit of model by 49 and 14% for the controland felled catchments; respectively (Table 1). The use of amultiplicative model improves the fit of the model by 51and 19% over the fit of the linear model for the control andfelled catchments, respectively (Table 1). The seasonalindices from control catchment show a marked asymmetryin the annual response (Figure 4). The peak nitrate concen-tration occurs: in August ?with a mfniimim in the wintermonths. The cycle shows a sharp peak and a broad, flattrough. This pattern is very similar to mat for mat prefellingin the felled catchment (Figure 4). This contrasts with thepattern from the felled catchment postfelling where the peakof nitrate concentration has jshifted to April and the mini-mum to October (Figure |4)j. Moreover, the shape of theresponse has shifted, with a broad, flat, symmetric peakduring the periods of winter and spring and a sharp,symmetric trough during the! autumn months. The decom-position was performed for the whole series including bothprecutting and postcutting, though the result will be dom-inated by the postcutting period.

I •• r i i3.2. ARModeling ' , : , , .

[22] For the control catchment, analysis of the wholeseries showedilhat a significant annual effect exists, but no6-month effect could be discerned (data not shown). The12-month effect was positive, Is., it acts to increase nitrateconcentrations in the present month. The 12-month effectwas; shown by both expanding and shifting window anal-yses. The magnitude of the: memory effect is taken as themagnitude of the pth coefficient in the AR(p) model (a,,),the significance of the effect is then judged relative to themagnitude of the pth coefficient that shows a 95% proba-bility of being significantly different from zero as calculatedby the Quenouille method (a^/). Therefore values are quoted

as the ratio Op/ap, where 3p is the pth coefficient of theAR(p) model and a^, the coefficient 1that has a 95%probability of not being zero for that model: a value ofOp/ap/ > 1 indicates a significant result at the 95% level Inthe case of the control catchment the magnitude of thetwelfth coefficient of the best fit model is compared to themagnitude of the twelfth coefficient mat would be signif-icantly different from zero (at the 95% level) for mat lengthof series. The fit of an autoregressive model improves thefit of me time series model by 24% over the fit of themultiplicative model for the control catchment (Table 1).The residual after removal of the annual effect illustratesmat after model development only 15% of the originalvariance remains unexplained (Figure 5) and residuals arenormally distributed (Figure 6).

[23] Assessing the time series for the control catchmentusing an expanding window (Figure 7) shows two peaks inthe memory separated by a significant disappearance of thememory with a decline in the memory toward me end of therecord. The transition back to a significant memory corre-sponds to the onset of the severest drought in the catchmentduring the period of the record. However, the lowest pointof the drought corresponds to the peak in the memory in1987. As this is an expanding window perspective, an effectmust be large, short-lived and dominate the calculatedmemory in the following years. This suggests that thedrought is marked by an initial decrease in memory andmen a rapid return. This might well be expected if thepossible response to a change in state is considered. If thechange is sufficiently large, men that year will have norelation to the previous and hence memory effects declinerapidly. Burt et ol [1988] and Reynolds et al [1992] showthat the effect of drought in different environments (agri-cultural and moorland) is to cause increased nitrate runoff inthe year after a severe drought This effect could not beaccounted for hi the trend or seasonal variation of the seriesso will remain into the residual and be part of the ARanalysis. Hence a large positive response recurs in years

WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT HWC 1-7

0.05

0.03

0.02

101

-0.011971 1975 1980 1985

WMwyor1990 1995

Figure 5. The original data for the control catchment in comparison to the residual time series afterremoval of the Unear trend, seasonal indices, and AR(12).

subsequent to the onset of drought This mechanism impliesthat response to drought may-be nonlinear. There are dryand wet years throughout the period of the record, but onlyme driest years cause a distinct response. The decrease inmemory in 1994 (month 276) must also be a large singleyear effect

[24] The shifting window analysis for the control catch-ment (Figure 8) shows more detail of the response to thedrought with the peak in memory occurring near the startof the drought with a decreasing memory effect in theyears preceding the drought when annual rainfall is in-creasing.

[25] For the felled catchment, analysis of the whole seriesshows both a significant diennial and annual effect How-ever, these effects manifest themselves as a 7-month effectand a 13-month effect Also, in this catchment the annual(13-month effect) has a significant negative effect, andconversely the diennial effect is positive. This is the reverseof mat observed in the control catchment The fit of anautoregressive model improves the fit of the time seriesmodel by 7% over the fit of the multiplicative model for thefelled catchment (Table 1). The residual after removal of theannual effect illustrates that after model development only21% of the original variance remains unexplained (Figure 9).

60

50

' 30

20

I

Figure 6. The distribution of residuals from the control catchment after the removal of the Unear trend,seasonal indices, and AR(12).

HWC 1 - 8 WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

1971I

Figure 7. The scale and significance of the annual memory effect for the control catchment, calculatedfor increasing time periods (expanding wmdow) as ap/ap, over the period of observation for the controlcatchment, where p = 12, and a^ is Quenouille test statistic at the 95% level, with the 99% levelillustrated. The year refers to the year at the end of the calculation period.

1

Both the annual and diennial effects were investigated asexpanding and shifting windows. !

[26] The diennial month effect, followed with an [expand-ing window (Figure 10) shows that the memory is significantthroughout the period of the record. Following clear-fellingin the 72nd month of the record, a sustained nsje in the

: magnitude of the diennial memory effect is obseved until1992 after which a decline is observed:at the eid of therecord. In comparison to the prevailing climatic conditions,

: this trend shows no relation with the annual precipil a'tion, butrather a good visual correlation with die annual j averagetemperature. Analyses using average temperature'for eitherthe growing or the dormant season do not improve thiscomparison. The clear-felling of the felled catchment coin-

cides with lowest average temperature over the period of thestudy and precedes a 15 year rising trend in temperature. Theexpanding window technique is relatively Conservative andevents that affect only one year of the record will be severelydamped out by the other years being considered. This meansthat only long-term effects will have a significant and lastingaffect on the catchment memory as viewed in an expandingwindow. Since the window expands,! the effect on thememoir would diminish if the year-on-year effect wereconstant The magnitude of the memory; in this case dimin-ishes, land the peak of the effect (1992) lags behind themaximum in the annual average temperature (1991), Thisimplies a linear affect of average temperature on catchmentnitrate1 memory.

3000

1971

Figure 8. The scale and significance of the annual memory effect for the control catchment, calculatedfor overlapping time periods (shifting window) as ap/ap, over the period of observation for the controlcatchment, where p = 12, and ap, is Quenouille test statistic at the 95% level, with the 99% levelillustrated. The year refers to me year at the end of the calculation period. '•

ICATCHMENT HWC

0.25

[27]

0.15

0.05

Figure 9. Theremoval of the

For the shifting

when95% 1tration in the present month experiences a dampening effect h sect infest ition [Swank

effect a randant ni rogen fixingdue to the nitrate concentrat ons a year previous.not 01musttbe sigiificant ;it the 99% level The switch in the ennualmemoeffect

WORRALL ET AL.: CHAN'

data for thetrend, seasonal i

lied catehmenlices. and AR(]13)

-0.05-

•0.11971

analysis, a clear tiuYefentia-tion between thle memory effects can be observed (TFigu re 11).The annual m;mory (13 nonth) is significant before theclear-cutting and returns 10 pears later. The annual m anory

gnificant (significance is still judgedel) is negative: mis means that the nitratte <

v ith eitherai equallycmnotberoust be

the residual ti ne series after

)r tempers ture. However, thenafter 1987, but again this change

a- b ack locus'

decreases it also stvitches its sign, although caretaken in interpreting effects that cannot be shown to 1

between 1976 and' clear-cutting a cfa nge that cannot be

101971

977 can be associate

The

associated

1975 1980

Figur 10. The scale and significancefor inc -easing time periods (expandingcatehrc ent, where p j= 7, and ap, is Queno^ulleThe ye ar refers to die year at the end o

with the

.Appalachian forests, with fixationkg N hs.-'a-1 (in the felled

nigrowth [Boring aniSvank, 19b ack locust ;hanges me i ature ofc eates an ac ditional sour •£ of nitroi

thddienniel/indiw) as

statistthe

I Appro dmateljvdth ecological

(Robitaa pseudo-at

is

ten years

ivers and so this swi ch; in the nitroj en

forest succession thetb:) dies back due

et al, 20J01]. Black locust islegume ip regenerated souther

estimated to averajgearly in th

|. Thus the die-backi nitrogen reserves an

i in the soil and fro

1985 1995

emory effc ct for Hi; fell sd catchment, calculated.v over me period df observation for the controlover me:atthe95°/period.

periodlevel, tath ihe 99% level illustrated.

HWC 1-ie WORRAli ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

Figure 11. The scale and signifi dienniel and annual memory effects for the felledcatchment, calculated for overlapping itime periods (shifting window). The pm coefficient, 3p over theperiod of observation for the felled catchment, where p = 7 and 13, in comparison to jfhe 95% and 99%

time 5eriod of 72 months. The year refers to the year at thece levels, the length ofsignificanend of th; calculation period.

the dei ;ompositior of woody material The contrast withclear-felling is thai whereas clear-felling causes ihe memoryeffect tjo disappear, the! die-back of black locus: causes thememory effect to : leturn.

[28] If it is assumed that a certain amount of memory canbe ascribed to an;' given annual cycle, Le., that one yearshows a more significant memory for previous concentra-tion thi u does ano her, it is possible in a qualitative sense jtoinvert i hese patterns to understand Ihe nature of the signalthat caused them, because this was i calculated on a 6-yearmoving; window basis, an effect in a single year would ha|ean app irent effect! over! a 6 year period, llf the response toclear-ft lling was limited to a single; rear then a step changein the moving wiidpw response would! be observed andwould last for app oximately six years. The effect observedhere lasts for at least ten yeaVs implying a response of atleast fb « years duration; If the respoi ise lalsted for more thanone ye tr but had a diminishing effe rt then this i would alsohave a diminishing effect on the shrJ ting 'window response,but an) diminishing response would have a tnintinmn timeconstart of six years. In this case the reversion of meannual memory takes at most 3 years (1984-1987). Thisimplies that there is a distinct reverse effect to that of theclear-felling that can be ascribed to mccessional changes.

[29] The diennial memory i allows a quite distinct pattern(Figure! 11). There is no switciing olf of the memory effectupon the clear-felting of the catchment The magnitude doesdecline gently, but changes- dramatically after 1982. Com-parison with Ihe annual precipitation shows that the mini-mum riemory response corresponds with the driest yearduring the study. Both catcimentsj show a response todrough, but the response manifests itself differently be-tween the two catchments.

3.3. Impulse Function[30] The order of the ARMA moc els for the flow in the i

control:catchment were ARMA (102), for the felled catch-

ment they are ARMA (504). The PACF and AGF for theresiduals of fitting ARMA (504) to the detrended anddeseasoned series for the felled catchment shoU that theseries show no significant lags ait the 95% level and so theARMA models can be viewed as a good fit leading onlywhite noise as a residual (Figure 12). The impulse functionis plotted as the ratio of the cross-correlation coefficienta Iculated against the correlation coefficient mat would besi jnificantly different from zero 'at the 95% level for serieso; 'that length, e.g., a value >1 represents a significant result(tie 99% significance level is also illustrated; Figure 13).No significant cross-correlations could be fourd in theimpulse functions derived for the control catchnnnit Con-si iering the entire recor i for the felled catchment, signifi-es nt cross-correlations ire observed at zero lag, Le., thecitchment responds impulsively to changes in steam dis-ci arge. Following the impulse function as a shif ing win-dow shows there is no s gnificant impulse functio: i prior todear-felling (Figure 13). There is no significant effect unti1980, a lag of 3 years behind the clear-felling when thecross-correlation at zero lag becomes significant Le., thecatchment develops impulsivity. This impulsivity, Le., sig-nificant cross-correlation at zero lag, is the domina it featureoi the impulse function across the record. The overallps ttern is one of increasing impulsivity over the period ofth; record. Considering pat a shifting window pe rspectivetends to average out changes in the catchment, it i s easy tosee large changes in the impulsivity of the catchmentHowever, the impulsiveness of the! catchment jbecomesstable toward the end of1 the study period.

t. Discussion[31] The differences between the catchments are marked.

The existence of an annual pojsitive memory effect, asob'served for the control catchment, [has previously beenascribed to an increase in winter-summer rainfalls [Worrall

"

WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT HWC 1-11

Z5

i III Ll11 16 21 31 36 41 48 51 SB 61

Figure 12. The calculated t statistic of the ACF and PACF in comparison to the critical value of the tstatistic at the 95% level

and Burt, 1999]. This cannot be the case here over a such along period of time, but the scale of me effect is dependenton rainfall and especially the onset of drought conditions.An especially warm summer may stimulate nitrification andthis would have the twin effects of increasing nitrate exportabove that expected as part of the overall or seasonal trendswithin the catchment, and perhaps stimulate primary pro-duction within mat watershed. The increased primary pro-duction could carry over to the next summer as an increased•pool of mineralizable organic matter if primary productionwere in the from of leaf, rather man wood production. Thebalance between export and utilization of available nitrogen

would be critically dependent upon the balance of thehydrology and the nitrifiers. In a wet summer the balancewould favor export of nitrate, but in a dry summer it wouldfavor utilization and storage. The scale of any memoryeffect observed over the period of observation would thenrepresent the nature of the juxtaposition and transitionbetween wet and dry years.

[32] A similar approach can be used to explain thenegative annual memory effect observed for the felledcatchment If relative increases in nitrification activity wereexported from the catchment, rather than utilized within theecosystem, then that increase in mineralization would have

Z5-,

'•"&

1995Water year

Figure 13. The zero-lag cross-correlation coefficient of the impulse function derived from the felledcatchment, calculated for overlapping time periods (shifting windows), in comparison to the 95% and99% significance levels with the length of the overkpping time period of 72 months. The year refers tothe year at the end of the calculation period.

HWC 1-12 WORRALL ET AL.: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT

the effect of diminishing the pool of available nitrogen. Arelative decrease in the pool of available nitrogen wouldthen restrict productivity with the consequent effect for thesize of available nitrogen for subsequent years. This shift inthe balance of controls could result from either a differentset of hydrological pathways operating in the felled catch-ment as opposed to the control catchment or a difference incomposition of the soil microbial population - the former ismore likely. It is important to note that the negative annualeffect occurred prior to the clear-felling and returned later inthe sequence; then the difference in balance between factorscontrolling nitrate between the catchment must be due, inthis case, to innate differences between the catchments. Apositive annual memory effect tends to cause an increase inthe amplitude of the annual cycle and a negative effect tendsto cause a decrease in amplitude.

[33] The occurrence of a positive diennial memory effectin the felled catchment has me effect of diminishing theamplitude of the annual cycle and, as such, has the sameeffect as the negative annual memory effect observed in thiscatchment The fact that both memory effects would havethe same consequence might suggest, they are caused bysimilar mechanisms. However, as shown above, these twomemory effects do not correlate with each other over theperiod of the record. The increased export of nitrate duringperiods of high nitrate production would also mean in-creased transfer into longer residence time storage, e.g.,shallow groundwater. Transfer to storage would enhanceexport at a later data. Decrease in rainfall would lead todecrease in the amount of recharge to the regolith (on theorder of a few meters depth) and hence a diminishedmemory effect at mis scale. Evidence for such lag effectshas been previously described in the water yield studies atCoweeta [Douglass and Swank, 1972]. Changes in theecosystem resulting from clear-felling and/or natural suc-cession would have little or no effect on these pathways.

[34] The change in the nature and scale of the annualmemory effect can now be explained. The change in theannual response represents change in the balance betweenthe hydrological pathways and the reservoirs of availablenitrogen. After the catchment is clear-felled, the balance isentirely disrupted and the catchment switches, the annualeffect mimicking the diennial effect This suggests thatduring this period the entire catchment response, bom thediennial and annual effects, are under hydrological pathway.limitation. So the release of new reserves of nitrogen thatoccur as the catchment is clear-felled means that the systemin no longer supply-limited but appears to become transportlimited. Detailed studies of the N-cycle in the control andfelled catchment provide insight into biological responses toclear-felling. Soil organic matter and nitrogen pools in-creased 20-70% immediately following cutting and log-ging [Waide et al., 1988]. Increases of 20-250% in mineralnitrogen pools were also'- observed. These increases inavailable mineral nitrogen were attributed to moderateincreases in measured mineralization and substantialincreases in nitrification rates, reductions in soil heterotro-phic activity and plant nitrogen uptake, and increases inboth symbiotic and free-living N-fixation [Waide et al,1988]. However, hydrological pathway limitation is linkedto ecological succession, specifically the die-back of themajor nitrogen fixing species black locust (Robinia pseu-

doacacia), which alters the nature of the nitrogen reservoirsand returns the catchment to something more akin to itsinitial state. Clear-felling causes the release of nitrogenreserves and results in the disappearance of the negativememory effect, whereas the die-back of black locust givesthe reverse effect It may be initially thought that predationof black locust would create an additional source of nitro-gen. However, as one component of the ecosystem diesback another rises to take its place, so as one source iscreated, i.e., the black locust, the change in successioncreates another possible sink. Thus it may be the balanceof nitrogen supply across this successional transition ratherthan just the creation of a new source that causes theobserved change in the annual memory effect An additionalcomponent by this stage in the forest regrowth is nitrogenfrom the decomposition of the woody residues after loggingand incorporation in the soil.

[35] Assessing the timescales of the effects suggests thatboth the clear-felling and the change due to succession arefast transitions. From the argument in the previous section,the transition following clear-felling results in a state that isstable for at least five years and the effect of clear-fellingdoes not diminish over this period. Equally, once there is areturn to a negative memory effect that too is relativelystable. The implication being mat the annual response isbistable over this period and flips between differing states.Clear-felling of a catchment is a massive intervention and soit is perhaps not surprising mat it causes the nature of thecatchment response to change, and to change radically. It isnevertheless surprising that this effect does not diminish asthe forest ecosystem reestablishes over a period of approx-imately 12 years after the catchment is clear-felled. Rever-sion of the memory effect is only caused by the die-back ofthe major nitrogen fixing species in the catchment (Le.,black locust). This suggests that the change in memory isrobust, that the difference between hydrological and nitro-gen reservoir limitation is significant, and that the memoryof the system will not readily return to a predisturbed state.

[36] The nonlinearity represented by the transition be-tween states in the annual response for the felled catchmentcan be contrasted with the diennial effect which shows alinear response to changes in temperature but a nonlinearresponse to changes in rainfall. As observed in the controlcatchment the memory effect does not correlate withchanges in annual rainfall, it only responds once the annual^rainfall has decreased dramatically. This could be inter-preted as a threshold-type response in catchment behaviorand a threshold of rainfall could then be estimated. Equally,the control could be due to changes in the timing of rainfallthrough the year rather than in its absolute amount; it is notpossible to discern which is true in this case. The linearity ofthe response to changes in temperature may be due to thedifferent timescales between changes in average tempera-ture and changes in rainfall. Long-term changes with thesame wavelength as the length of the period of observation,may elicit a more linear response as the catchment has timeto adjust

[37] Prior to clear-felling both catchments 2 and 7,showed no significant impulsivity. The felled catchmentdevelops an impulsive response over the period of obser-vation, but not directly in response to clear-felling. Thecatchment moves from one stable state, as illustrated by the

WORRALL ET AJL: CHANGES IN STREAM NITRATE OF FORESTED CATCHMENT HWC 1-13

control catchment, to a different one as seen after 1989(Figure 13). Over the same period, me levels of nitrateexport mom the catchment have increased by an order ofmagnitude, an increase ascribed to the onset of N-saturation[Swank and Vose, 1997]. In a catchment where saturationmeans that surplus nitrogen is available then it is notsurprising that the nitrogen export becomes impulsive withrespect to the flow. The onset of stable impulsivity could betaken as indicative of catchment N-saturation. The presenceof significant, stable impulsivity after in 1989 suggests thatpeaks in nitrate would occur coincident with individualstorm events, while prior to this* time, the impulsivitysuggests that decreases hi nitrate concentration could occurduring storm events.

[ss] Taking a systems approach to understanding catch-ment behavior [Charley and Kennedy, 1971], it is possibleto interpret the transition between two states of the annualresponse as a condition of metastable equilibrium existingbetween the hydrological flow paths and the nitrogenreserves. This may also be true for the catchment responseto rainfall, where the memory effect shows nonlinear,threshold-type behavior. The drought conditions experi-enced during the period of observation are short-lived onthe timescale of the whole record and switches to a droughtresponse can be readily reversed because the rainfall returnsin subsequent years. Alternatively, the catchment responseis in dynamic equilibrium with respect to temperaturechanges. However, the nature of change in the catchmentresponse with respect to climatic drivers, metastable vs.dynamic, may correlate more with the typical wavelengthsof those drivers, Le., long-term drivers give a dynamicresponse while short-term drivers give a metastable re-sponse. With respect to ecological succession, the catch-ment shows a metastable equilibrium with one particularaspect of the succession. Such successional changes areeffectively irreversible and represent a thermodynamic tra-jectory hi the catchment response. Changes in this trajectorycan be interrupted only by energetic interventions such asclear-felling. The development of impulsivity within thefelled catchment with the onset of N-saturation would alsoappear to represent a mennodynamic trajectory however, N-saturation conditions at mis stage in the catchment's re-growth are driven by the nitrogen surplus generated by thefelling operations and in the postfelling changes. Thissupply of nitrogen would be expected to become exhaustedas the forest matures and as net primary production remainshigh, nitrate export would be expected to return to levelssimilar to that in the control catchment

5. Conclusions[39] This study shows that time series analysis represents

a useful technique in understanding the integrated responseof catchments to internal and external driving forces. Usingautoregressive (AR) modeling it is possible to show theexistence of significant memory effects. Both catchmentsshow an annual memory effect, but in one catchment thishas a positive effect whereas it is a negative effect in theother. In addition, the clear-felled catchment shows adiennial memory effect These memory effects represent abalance between control by hydrological pathways andcontrol by nitrogen reservoirs, which occur even betweenneighboring catchments.

[40] The annual memory effect in the control catchmentresponds to drought conditions while in the felled catchmentit reflects the change in vegetation. The diennial montheffect in the felled catchment responds to drought condi-tions independent of the annual effect and of loggingoperations. Deriving an impulse function for nitrate exportwith respect to streamflow shows that a significant impulsefunction develops subsequent to logging. Such a develop-ment correlates with the onset of N-saturation within thefelled catchment and can be taken as indicative of itApplying a systems approach shows that the catchment isin metastable equilibrium with respect to its flow paths andnitrogen reserves as influenced by ecological successionand management practice. Similarly, the catchment shows anonlinear response to changes hi rainfall, but is in dynamicequilibrium with temperature changes, reflecting the wave-length of climatic variations over the period of observation.Ecological succession following clear-cutting represents athermodynamic trajectory, which can only be reset bymassive management intervention such as further clear-felling.

USDA[41] Acknowledgments. This research was supported in part by

)A Forest Service, Southern Research Station, Coweeta HydrologicLaboratory, USA and in part by Hatfield College, Durham University,Durham, UK through a visiting fellowship to W.T. Sjwank.

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