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Journal of Hydrology 388 (2010) 273–279
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Journal of Hydrology
journal homepage: www.elsevier .com/ locate / jhydrol
A comparison between pulse and constant rate additions as methods for theestimation of nutrient uptake efficiency in-streams
Marta Álvarez a,*, Lorenzo Proia b, Antonio Ruggiero c, Francesc Sabater a, Andrea Butturini a
a Departament d’Ecologia, Facultat de Biologia. Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spainb Institute of Aquatic Ecology, Department of Enviromental Sciences, University of Girona, Campus Montilivi, 17071 Girona, Spainc Dipartimento di Biologia, Università degli Studi di Roma ‘‘Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
a r t i c l e i n f o s u m m a r y
Article history:Received 18 August 2009Received in revised form 24 April 2010Accepted 3 May 2010
This manuscript was handled by L. Charlet,Editor-in-Chief, with the assistance ofBernhard Wehrli, Associate Editor
Keywords:Nutrient retentionPulse additionConstant rate additionPhosphateStreams
0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.05.006
* Corresponding author. Tel.: +34 934031190; fax:E-mail addresses: [email protected] (M. Álv
(L. Proia), [email protected] (A. Ruggiero),[email protected] (A. Butturini).
Nutrient retention efficiency, an indicator of stream function, has become a significant focus of researchin fluvial biogeochemistry. The most popular method used to measure nutrient retention efficiency isconstant rate addition (CRA), although studies using pulse addition (PA) as an alternative have been pub-lished. The similarities of the results produced by the two methods have not yet been explored. With theaim of clarifying this uncertainty, the present study assessed the similarities between the results of theCRA and PA experiments. Thirteen phosphate CRA–PA paired additions were performed in two differentMediterranean streams. We used ANOVA to compare the results of the uptake rate coefficients from theCRA (KtCRA) and the PA (KtPA) experiments. Results from CRA and PA were significantly different, with KtCRA
being higher than KtPA in most cases, however, the difference between KtCRA and KtPA decreased as specificwater residence time increased. When specific water residence time exceeded a specific threshold value,they became equal (KtCRA � KtPA). Results suggested that the differences in nutrient retention estimatesbetween the two methods may be a consequence of the difference in solute spreading along the streamreaches that shape the duration and magnitude of solute interaction across the surface water and stream-bed interface.
� 2010 Elsevier B.V. All rights reserved.
1. Introduction
Nutrient enrichment experiments are widely used to assess theability of stream ecosystems to retain solutes (Meyer and Likens,1979; Munn and Meyer, 1990; D’Angelo et al., 1991; Websteret al., 2000). This approach is based on increasing the backgroundconcentration of a nutrient in-stream water and monitoring itsdownstream temporal and spatial decay as result of biotic–abioticprocesses. Models that conceptualise solute hydrological transportand temporal dynamics vary in complexity. They range from all-inclusive three-dimensional models with complex hydrologicalinteractions, to simple one-dimensional box models that do notconsider the effects of dispersion and transient storage (Runkel,2007). Independent of hydrological complexity, both temporaland spatial solute decay can be described by the following first-order kinetic equations:
dCdt¼ �KtC ð1Þ
ll rights reserved.
+34 934111438.arez), [email protected]@ub.edu (F. Sabater),
or:
dCdx¼ �KsC ð2Þ
where C is the nutrient concentration, t and x are time and space,respectively, and Kt (T�1) and Ks (L�1) are the first order temporaland spatial uptake rates, respectively. In Eq. (2), the inverse of Ks
is the nutrient uptake length (Sw) in the nutrient spiraling theory(Newbold et al., 1981).
Technically, there are two ways of performing solute additionsand therefore of estimating nutrient retention: constant rate addi-tion (CRA) and pulse addition (PA). In CRA, solutes are released at aconstant flow until the downstream concentration reaches a con-stant value. This conceptual plateau condition indicates that theconcentration of the added nutrient is uniformly distributed alongthe entire study reach. In PA experiments, nutrients are released atonce and a pulse of added nutrients moves rapidly downstream(Gordon et al., 2004).
In constant rate additions, the plateau condition along the studyreach optimises the solute exchange between the water columnand the entire streambed reach. In contrast, in pulse additions aspatial and temporal gradient of nutrient concentration is gener-ated along the reach and only a segment of the experimentalstream reach is affected by the nutrient pulse at any one time. As
274 M. Álvarez et al. / Journal of Hydrology 388 (2010) 273–279
a result, the stream reach that can effectively contribute to theretention of nutrients is shorter than the experimental reach. Fur-thermore, due to hydrological dispersion the nutrient pulse is de-creased and dispersed as it moves downstream. As a result,during PA experiments, the upstream stretches are exposed to ahigh nutrient concentration peak over a short period, while down-stream zones receive a low nutrient peak over a long period.
Based on Eqs. (1) and (2), nutrient decay can be estimated in thetemporal and spatial domain. To estimate nutrient decay in thetemporal domain, the temporal nutrient breakthrough curve mustbe monitored at the downstream sampling point. This makes itpossible to calculate the mass of nutrients leaving the study reach,from which the temporal in-stream uptake rate (Kt) can then becalculated (Wilcock et al., 2002). In both constant rate and pulseaddition methods, the Kt can be estimated. Nevertheless, if thenutrient spatial decay (Ks) is required, the spatial nutrient break-through curve must be monitored along the entire experimentalstream reach. This process is extremely arduous during a pulseaddition and is only feasible in a constant rate addition experimentbecause of the uniform nutrient distribution along the experimen-tal reach during plateau conditions. In addition, with the Ks valueobtained after a constant rate addition experiment, all nutrient up-take metrics within the spiraling framework (i.e. uptake length,uptake rate, and uptake velocity) can be calculated. The constantrate addition method is therefore used much more widely by thescientific community than the pulse addition for calculating nutri-ent retention values; only the protocols of the constant rate addi-tion method are so far described in manuals such as Hauer andLamberti (2006).
However, the constant rate addition method has an importantmethodological constraint: the discharge must remain steadythroughout sampling to successfully obtain a plateau (StreamSolute Workshop, 1990). This limitation has forced researches toexecute their experiments in small streams and under basal dis-charge conditions (Doyle, 2005) and researches have only recentlystarted to study large rivers with the aid of pulse additions (Tanket al., 2008; Dodds et al., 2008). The pulse addition method is notconstrained in the same way (at priori), which means it could beapplied under higher and/or changing flow conditions. Further-more, it requires neither a peristaltic pump nor an energy source.Nevertheless, the value for the uptake rate value obtained withthe pulse addition method cannot be incorporated into thespiraling metric theory because it does not meet the criterion ofa uniform solute distribution along the stream reach. Furthermore,the entire study reach does not contribute to the solute retentionin unison. This reduces its potential application. Some studies havedisregarded this restriction and incorporated the Kt, obtainedthrough the pulse addition method, into the nutrient spiralingmetrics theory (Wilcock et al., 2002) based onto the followingequation:
vKt¼ Sw ð3Þ
where v is the water velocity (m/s).In a recent report, Payn et al. (2008) analysed differences be-
tween PA and CRA conservative solute breakthrough curves froma hydrological perspective (Payn et al., 2008; Gooseff et al.,2008). However, the extent to which estimations for nutrient up-take rate obtained with the pulse addition method differ from thatof the constant rate addition method have not yet been explored.This assessment is necessary to establish how the pulse additionmethod compares with the constant rate addition method in termsof performance and applicability, which will help to determinewhether pulse could replace constant rate addition in situationsin which the CRA method is unfeasible.
Therefore, the objective of this study was to explore, in a statis-tically comparable way, how closely temporal uptake rates (Kt)determined by pulse addition, approximate to those determinedby constant rate addition.
Previous tracer addition experiments (Payn et al., 2008; Gooseffet al., 2008) highlighted the differences in solute concentration dis-tribution and exposure times between the PA and CRA experi-ments. In particular, they emphasise how the solute charge andflow vary in-stream dead zones depending on the addition methodapplied. Although the authors focused on hydrological dead zones,their observations can be applied to the entire streambed compart-ment. They argue that during pulse addition, the amount of solutemass that interacts with the streambed varies greatly along thereach. Overall, they found that downstream bed substrate reachesinteract with a lower solute mass than upstream reaches. By cou-pling these considerations with the evidence that during pulseaddition experiments only a fraction of the entire stream reachcontributes to nutrient retention, we can conclude that the valuesfor uptake rate coefficients (Kt) obtained with the constant rateaddition method (KtCRA) would be higher than those obtained withthe pulse addition method (KtPA). Therefore, we hypothesise that:
KtCRA > KtPA ð4Þ
Hydrological conditions strongly influence the solute temporaland spatial distribution during a pulse addition (Hubbard et al.,1982). For instance, at high specific water residence times (SWRT)or low discharges, the temporal and longitudinal spreading of sol-utes during the pulse addition becomes more relevant. Under thesehydrological conditions, a large portion of the streambed contrib-utes to solute retention at any one time. So, although we releasethe solute by pulse addition, the conditions that are created inthe reached are similar to conditions in a constant rate additionand, therefore, it is expected the two methods might provide sim-ilar results. Subsequently, an assumption of our hypothesis is thatat high specific water residence times, the imbalance of Eq. (4)changes to KtCRA � KtPA (Eq. (5)).
To test our hypothesis we performed a series of phosphate pulseaddition and constant rate addition experiments under differentdischarge conditions in two small Mediterranean streams thatdrain siliceous (Fuirosos) and calcareous (Simbrivio) catchments.Previous studies, based on CRA experiments revealed that phos-phate removal in calcareous streams was higher than in siliceousstreams (Martí and Sabater, 1996). A comparison of calcareousand siliceous streams would therefore enable us to asses whetherthe divergences in Kt estimations resulting from the differentmethods prevail over the differences expected resulting from lith-ological causes.
2. Study sites
The experiments were carried out in the Fuirosos and Simbrivio,two typical Mediterranean streams, differing in geology and hydro-logical regime. The Fuirosos drains a 10.5 km2 granitic catchmentarea near Barcelona (NE Spain, 41�420N, 2�340W, 50–770 a.s.l.).Mean annual precipitation is 750 mm (Ninyerola et al., 2000),which occurs mainly during autumn and spring, with occasionalsummer storms. Base flow is characterised by a long dry periodfrom June to late September–October and discharge during wetperiods ranges from 7 L/s in spring to 20 L/s in winter (Bernalet al., 2005). Temperatures range from 3 �C in January to 24 �C inAugust.
In the Fuirosos stream the soluble reactive phosphorous con-centration range from less than 0.005 to 0.05 mg/L (Von Schilleret al., 2008) averaging 0.02 ± 0.002 SD mg/L, and water velocityranged from 0.016 to 0.14 m/s.
resp
ecti
vely
.Cb
isth
eba
ckgr
ound
conc
entr
atio
n;C p
(PA
)an
dC p
(CR
A)
are
the
ters
mg/
L)K
tPA
(10�
3s�
1)
C p(C
RA
)(m
g/L)
KtC
RA
(10�
3s�
1)
0.02
90.
110.
210.
190.
060.
530.
230.
040.
30.
220.
070.
140.
210.
100.
170.
440.
031.
30.
70.
060.
68
0.57
0.15
1.56
0.65
0.01
1.64
2.87
0.01
3.74
1.21
0.01
1.71
1.11
0.01
1.09
1.91
0.02
1.62
M. Álvarez et al. / Journal of Hydrology 388 (2010) 273–279 275
The Simbrivio stream is a tributary of the Aniene River (TiberRiver basin, Central Italy) and has a calcareous basin that spansan area of approximately 60 km2, with a mean altitude of1.170 m a.s.l. (Ventriglia, 1990). Mean annual rainfall in the Simbri-vio is approximately 1593 mm. Precipitation is lowest in July(52 mm), and highest in November (236 mm) (De Cicco, 2007). An-nual temperatures range from 3 �C in winter to 18–19 �C in sum-mer (July–August) and soluble reactive phosphorous backgroundconcentration ranged from 0 to 0.006 mg/L averaging0.0035 ± 0.0004 SD mg/L. During the study period, the mean andstandard deviation of water velocity for Simbrivio were0.36 ± 0.23 m/s.
Nutrient addition experiments were conducted in pool and rifflereaches with no lateral or vertical water inputs or outputs. The to-tal length of the reach where additions were carried out in the Fuir-osos was approximately 100–110 m (Table 1) and total dischargewas between 76.6 and 12 L/s. We shortened the length of the studyreach to 57 and 41 m in two cases when discharge was so low (4and 3.4 L/s) that the CRA method was unfeasible. In the Simbrivio,the discharge was higher (37.1–203.3 L/s) and maintained a studyreach length of 175 m throughout the study period.
Tabl
e1
Hyd
rolo
gica
land
biog
eoch
emic
alpa
ram
eter
ses
tim
ated
for
each
addi
tion
. v,D
and
SWRT
are
the
wat
erve
loci
ty,d
ispe
rsio
nan
dsp
ecifi
cw
ater
resi
denc
eti
me
peak
conc
entr
atio
nm
easu
red
atth
edo
wns
trea
msa
mpl
ing
site
duri
ngth
epu
lse
(PA
)an
dco
nsta
ntra
tead
diti
ons
(CRA
).
Stre
amD
ata
Hyd
rolo
gica
lpa
ram
eter
sB
ioge
och
emic
alpa
ram
e
Rea
chle
ngt
h(m
)D
isch
arge
(L/s
)v
(m/s
)D
(m2/s
)SW
RT
(s/m
)C b
(mg/
L)C
p(P
A)
(
Fuir
osos
29/0
1/06
108
25.2
0.08
0.18
12.5
0.01
0.08
02/0
3/06
108
21.4
0.08
0.14
12.5
0.03
0.08
19/0
5/06
413.
40.
016
0.03
564
.52
0.01
0.07
10/1
0/06
103
12.0
0.06
0.09
815
.63
0.04
0.08
14/1
1/06
574.
00.
018
0.08
255
.56
0.03
0.09
17/0
4/07
112
76.6
0.14
0.2
7.14
0.02
0.08
26/0
4/07
112
18.1
0.07
0.13
14.2
90.
030.
06
Sim
briv
io05
/04/
0617
510
2.0
0.34
0.85
2.06
0.00
30.
1424
/04/
0617
520
3.3
0.81
1.6
1.66
0.00
40.
0124
/05/
0617
512
2.6
0.39
0.8
2.63
0.00
30.
0220
/06/
0617
563
.80.
260.
83.
940.
005
0.02
18/1
0/06
175
37.1
0.18
0.8
5.83
0.00
30.
0129
/11/
0617
546
.30.
20.
84.
960.
002
0.02
3. Methods
Seven phosphate pulse vs. constant rate addition experimentswere carried out in Fuirosos and six in Simbrivio. In each case weperformed the pulse addition experiments first and the constantrate addition second, after the background conditions were re-stored (when the downstream water returned to background con-ductivity). Solutions used for PA and for CRA consisted ofNaH2PO4H2O for soluble reactive phosphorous (SRP), NH4Cl tomaintain basal P:N ratio, and NaCl as conservative tracer, all dis-solved in river water.
To minimize the effect of nutrient enrichment on nutrient up-take estimations (Mulholland et al., 2002) the nutrient mass ofthe added solution was adjusted for each addition to keep nutri-ent addition as low as possible and, most important for our in-ter-method comparison, to generate similar nutrient increase atthe bottom sampling site, during the PA and CRA additions. Toaccomplish with these requirements, in each case, the streamdischarge was measured, by a pulse chloride addition (Gordonet al., 2004), before the nutrient additions. On the other hand,being impossible to estimate instantly in the field the back-ground SRP concentrations, we assumed, in all cases, a SRP basalconcentration of 0.02 mg/L in Fuirosos (Von Schiller et al., 2008)and 0.0035 mg/L in Simbrivio (unpublished from authors) (Table1).
In each pulse addition, the release solution was added to thestream in a single pulse at the top mid-channel of the reach whereturbulence would ensure adequate mixing with the stream water.In the constant rate addition method, the added solution was re-leased at the same place as in the pulse, but at a constant flow rate(Webster and Valett, 2006), using a battery-fed peristaltic pump.For each addition, conductivity changes caused by the tracer (Cl)were measured and recorded at the bottom of the reach with aconductimeter (WTW 340i) coupled to a data logger (CampbellCR10X). Water samples were collected at the bottom of the reachover the nutrient-pulse passage at different time intervals accord-ing to the curve slope, resulting in a total of 25–30 samples (aver-age). These samples, together with the water background samplestaken before the start of each nutrient release, were filtered in situthrough pre-ashed fibreglass filters (Whatman GF/F) and trans-ported to the laboratory. Samples were kept at 4 �C and analysedwithin 24 h for SRP, following the molybdenum-blue colorimetricmethod (Murphy and Riley, 1962).
Fig. 1. Solute spread index (SSI) for each pulse addition in the Fuirosos (closetriangles) and the Simbrivio (open squares).
276 M. Álvarez et al. / Journal of Hydrology 388 (2010) 273–279
The water velocity and hydrological dispersion estimationswere based on data from the preliminary chloride pulse addition.Average water velocity (v, m/s) was calculated by dividing thereach length by the time elapsed between solution release andthe conductivity centroid arrival at the downstream samplingpoint. The inverse of the velocity is the specific water residencetime (SWRT, s/m). Hydrological dispersion (D, m2/s) was calculatedby fitting the classical advection–dispersion model (De Smedtet al., 2005) to the observed conductivity temporal breakthroughcurve. Once v and D had been estimated, we calculated the spatialspreading along the study reach of the added solute observed dur-ing the pulse addition. To achieve this, we solved the advection–dispersion equation with respect to the space domain when thesolute pulse had arrived at the downstream sampling point (ts).By doing this, we obtained the spatial solute breakthrough curve,which allowed us to calculate the percentage of the stream reachin contact with the added solute at ts. We defined this relative lon-gitude at ts as the solute spreading index (SSI). In constant rateaddition, the entire reach study was in contact with the addedsolution at a time equal to ts, meaning that SSI was 100% by default.
For nutrient additions, we estimated the temporal uptake ratecoefficient (Kt) for both pulse (KtPA) and constant rate addition(KtCRA) using a mass balance between the phosphorous mass leav-ing the bottom of the reach (Md) and the mass of the initial nutrientreleased into the stream (Mi) (Wilcock et al., 2002):
lnðMi=MdÞtp
¼ KtCRA or KtPA ð5Þ
where tp is the mean water travel time in the experimental streamreaches. In PA, tp is the time taken for the concentration centroid toarrive at the downstream end of the reach (Hubbard et al., 1982). InCRA, tp is the time required for the nutrient concentration to reachhalf-plateau concentration. Md is estimated by integrating the nutri-ent temporal breakthrough curve at the downstream samplingpoint, multiplied by the stream discharge.
Similarities between KtPA and KtCRA results were tested using atwo-way repeated-measures ANOVA. Method and stream typewere fixed factors and SWRT was included as a co-variable to elim-inate the hydrological effect in uptake differences. Results wereconsidered significant at p < 0.05. Statistical analyses were donewith SPSS (version 15.0, SPSS Inc., Chicago, Illinois).
Fig. 2. First-order uptake coefficient obtained by pulse (KtPA) and constant rateadditions (KtCRA) in the Fuirosos (A) and the Simbrivio (B) streams.
4. Results
Stream discharges were, on average, four times higher in theSimbrivio (95 ± 62.02 SD L/s) than in the Fuirosos (22.95 ± 25.08SD L/s) (Table 1). In the Fuirosos, the minimum and maximum dis-charges at which experiments were conducted were 3.4 and 76.6 L/s, respectively. Thus, we covered a highly representative range ofthe Fuirosos hydrology (Butturini et al., 2008).
Water velocities were, on average, one order of magnitudegreater in the Simbrivio (0.36 ± 0.23 SD m/s) than in the Fuirosos(0.07 ± 0.04 SD m/s). As a result, specific water residence time ismuch higher in the Fuirosos (7.14–64.52 s/m) than in the Simbrivio(1.66–5.83 s/m) (Table 1). The SWRT strongly influence the solutespreading in pulse addition. In the Fuirosos, a clear positive rela-tionship between the SSI and SWRT was observed (r = 0.96,p < 0.01, df = 5). At low SWRT, a maximum of 28% of the entirestream reach contributed to solute retention. This percentage in-creased to 60% at high SWRT values. An identical relationshipwas observed in the Simbrivio (r = 0.98, p < 0.01, df = 4) (Fig. 1),at which the SSI ranged from 32% to 46%.
An analysis of the estimations for overall phosphorous uptake inthe Simbrivio revealed the uptake rate values to be one order ofmagnitude greater than in the Fuirosos (Table 1). The inter-site dif-
ferences are significant when KtPA and KtCRA are analysed sepa-rately: mean KtPA was 1.4 � 10�3 ± 0.87 � 10�3 SD s�1 in theSimbrivio, and 0.29 � 10�3 ± 0.22 � 10�3 SD s�1 in the Fuirosos(t = �3.01, p < 0.05, df = 5.5); mean KtCRA was 1.9 � 10�3 ± 0.93 �10�3 SD s�1 in the Simbrivio, and 0.48 � 10�3 ± 0.41 � 10�3 SDs�1 in the Fuirosos (t = �3.6, p < 0.05, df = 11). Fig. 2 shows the re-sults for KtPA and KtCRA from each method and for both streams. Val-ues are ordered according to an increasing discharge range. No
Fig. 3. Relationship between KtCRA and KtPA. Close triangles are data from Fuirosos,open squares are from Simbrivio. Solid line shows the 1:1 relationship.
Fig. 4. Relationship between |DKt| values and SWRT (panel A) or SSI (panel B) forboth the Fuirosos (triangles) and the Simbrivio (squares). Trend lines are includedonly for a better visual perception.
M. Álvarez et al. / Journal of Hydrology 388 (2010) 273–279 277
relationship between variables (Q vs. KtPA, or Q vs. KtCRA) wasobserved.
By comparing the methods and the streams together, we ob-served that KtPA were positively and significantly correlated withKtCRA (r = 0.89, d.f. = 11, p < 0.001). Furthermore, in the constantrate addition method, the values for uptake rate were higher thanin the pulse addition method in eight experiments (�60% of cases).For the remaining experiments, the results from the two methodsfor the uptake rate coefficient are more alike; there was only oneinstance when KtPA clearly exceeds KtCRA (Fig. 3).
The two-way repeated-measures ANOVA revealed the differ-ences in uptake rate coefficient between the methods as significant(F1,1 = 7.41, p < 0.05). The absolute differences between KtCRA andKtPA (|DKt|) obtained in each experiment appeared to be influencedby the hydrological conditions. In both streams, an increase in spe-cific water residence time resulted in a linear decrease of the |DKt|value until it approached zero (Fig. 4A). From this regression rela-tion between SWRT and |DKt|, we can calculate the SWRT value atwhich |DKt| becomes zero. It can be considered as a SWRT thresh-old point from which pulse and constant rate additions yield iden-tical Kt values. In the Fuirosos, the SWRT threshold is located atapproximately �15 s/m. When SWRT is above this threshold,KtCRA � KtPA; otherwise KtCRA > KtPA and the differences becomeincreasingly large as SWRT decreases (r = �0.96, p < 0.01, df = 3).In the Simbrivio, a similar pattern was observed (r = �0.99,p < 0.01, df = 4) with a SWRT threshold value located at �7 s/m(Fig. 4A).
5. Discussion
The results of the current study clearly indicate that the methodused to add the solute to the stream water influences estimationsof the uptake rate. Uptake values were generally higher in the con-stant rate addition experiments than in the pulse addition method;this applies to both streams. The stream channel removed theadded nutrients more efficiently when the nutrient concentrationreached a spatial and temporal plateau than it did under change-able concentrations. Therefore the empirical results corroboratedour hypothesis that KtCRA > KtPA. This then indicates that the differ-ences between estimations for KtCRA and KtPA may be due to differ-ences between the two addition methods, with regard to solutespatial distribution in the stream reaches and the interaction per-iod between the solute and the streambed (Gooseff et al., 2008).Unlike in the pulse addition method, the entire study reach in
the constant rate addition method is exposed to the same soluteconcentration during the plateau. In PA, solute is released intothe stream, just at the top mid-channel of the reach. Thus, it re-mains initially confined to the thalweg and moves and dispersesrapidly downstream according to the flow (Dodds et al., 2008). Inaddition to longitudinal dispersion, released solute is affected bythe two other dispersion components too. Vertical dispersion isnormally completed first, but lateral dispersion depends on thewidth of the stream and variations in velocity (Hubbard et al.,1982). Hence, when solute arrives (at time ts) at the downstreamsampling point, a portion of the reach might not have interactedwith the added nutrient. In fact, during the PA experiments inthe Fuirosos and the Simbrivio, the percentage of the total stream-bed reach that effectively interacted with the nutrient pulse attime ts (the SSI values) ranged from 28% to 60%.
Some research states that prolonged interaction between thesolute and the streambed surface may enhance nutrient retentionefficiency (Valett et al., 1996). Consequently, higher uptake ratesmay be expected under certain hydrological conditions thatstrengthen solute interactions between the water column andthe streambed. As water residence time increases (high SWRT),dispersion takes over from advection and the surface area in con-tact with the solute increases (high SSI values).
Under this perspective, our results show that the extent of thedifferences in uptake rate coefficients between pulse and constantrate additions (|DKt|) is inversely related to the water residence
278 M. Álvarez et al. / Journal of Hydrology 388 (2010) 273–279
time. For instance, in the Fuirosos when SWRT > 15 s/m (SSI > 40%),the difference in the uptake rate coefficients between methods wasnegligible (|DKt| � 0) (Fig. 4A).
It is important to note that solute transport and dispersion in-streams is regulated by local geomorphological characteristicsand specific hydrological conditions (Morrice et al., 1997). It istherefore reasonable to expect the specific water residence timethreshold at which |DKt| � 0 to differ depending on the stream.In fact, in the present study, the SWRT threshold in the Simbriviois approximately half that estimated in the Fuirosos.
By analysing the differences in |DKt| from the spatial solutespreading perspective, it can be seen that the two SWRT thresholdshave similar SSI values. Results show that |DKt| approaches zerowhen SSI is �40% in the Fuirosos and �45% in the Simbrivio(Fig. 4B). Therefore, the two different SWRT thresholds convergedto two rather similar SSI values. These results again highlight therelevance of solute spreading in enhancing nutrient retention effi-ciency in-streams.
Our results reveal that irrespective of the addition method, esti-mated Kt values for the Simbrivio were significantly higher thanthose estimated in the Fuirosos. Hence, we conclude from the re-sults of both methods, as expected, that the calcareous stream ismuch more efficient at retaining phosphate than the siliceousstream. Therefore, the fact that in most of cases KtCRA > KtPA doesnot mask the inter-site differences that probably reflect both nutri-ent limitation (Newbold, 1992) and abiotic uptake processes(Meyer, 1979 and Mulholland et al., 1985). Nevertheless, the factthat KtCRA > KtPA impedes the use of KtPA to estimate the uptakelength (Sw) or other nutrient retention parameters within the spi-raling metric theory. The KtPA can only be considered a relativelyaccurate surrogate of KtCRA, if the specific water residence time isequal to or smaller than the SWRT threshold value. Therefore, ifresearchers plan a set of pulse additions and successively convertthe KtPA values into the well-known Sw parameter to integrate theirresults within the well established literature data, it is necessary toperform a preliminary parallel experiment to compare PA and CRA,under different hydrological conditions. This calibration experi-ment could make it possible to quantify the magnitude of the dif-ferences between KtCRA and KtPA and verify how this differencevaries with respect to hydrological conditions. Therefore, the esti-mated Sw values obtained by Wilcock and colleagues (2002) in astudy based upon pulse addition experiments without a prelimin-ary calibration experiment should be considered with a degree ofcaution.
Our results may indicate that the constant rate addition methodoverestimates the ability of streambed to retain nutrients becausethe plateau conditions optimise the solute interaction across thewater column-streambed interface. Nevertheless, a plateau is anatypical situation in real systems in which, under natural condi-tions, the solute concentration continuously oscillates. This factmay be a crucial consideration when abrupt nutrient pulse inputsoccur as consequence of, for instance, water-treatment plants, acci-dental spills, or solute leaching during storm events. This is illus-trated by Meals et al. (1999) in their assessment of systemresponses to the dominant type of nutrient pollution in surfacewaters of the USA, in which they find that it occurs at discretepulse events.
5.1. Conclusions and implications
Our study illustrated the potential for the future application ofthe pulse addition method. Firstly, the magnitude of the differ-ences between KtCRA and KtPA must be established. This subse-quently helps identify the limitations of the pulse compared tothe constant rate addition method. With this information, PA couldthen be used in those hydrological conditions in which the CRA
method is unfeasible. As commented previously, nutrient retentionestimations are usually performed in small streams under basaldischarge conditions (Ensign and Doyle, 2006). Nevertheless dis-charge dynamic conditions (storms and drying phases) are far frombeing an unusual situation in unregulated streams. Therefore, if anexhaustive understanding of biogeochemical stream functioning isrequired, it will be necessary to quantify the nutrient retentionefficiency under oscillating discharge conditions. Under these dy-namic hydrological conditions, the pulse addition method mayconstitute a valuable tool to fill this gap in our knowledge.
Acknowledgements
We would like to thank Dolores Ruiz and Eusebi Vázquez fortheir help with field work in Fuirosos, and Francesc Oliva for hisassistance with statistical analysis. Thanks to Filippo Fabbri, Stef-ano Lecci, Federica Lacasella and Federica Capoccia for their helpwith field work in Simbrivio and Gianmaria Carchini for his finan-cial support. Our manuscript benefited from comments and sug-gestions by Steven Thomas. Lorenzo Proia was granted byProvincia di Roma and has now fellowship by EC (KebioeffectsMRTN-CT-2006-035695). Marta Álvarez was granted a fellowshipfrom the Research Staff Training Programme (Department of Edu-cation and Research of the Spanish Government). This research wasfounded by MEC Project (CGL2007-60144).
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