ARTICLE
Ca bon dioxide fluxes inc ease om day o nigh
ac oss Eu opean s eams
Ka in A e meye 1,2,3✉, Joan Pe e Casas-Ruiz 4,5, Thomas Fuss6, Ada Pas o 4,5,34, Sophie Cau y-F aunié7,
Danny Shea h8,35, Anna C. Nydahl1, Albe o Do e o9,10, Ana Paula Po ela 11,12, B ian C. Doyle13,
Nikolay Simo 14, Ca he ine Gu mann Robe s8, Geo g H. Nied is 15, Xisca Timone 4,5, Vesela E imo a 16,
Lau a Ba al-F aga5, Tea Bašić8,36, Joachim Aude 17,37, Anne Deininge 18,38, Geo gina Buss 8,
S e ano Fenoglio 10,19, Nú ia Ca alán 4,5,39,40, El i a de Ey o 20, F ancesca Pilo o 18,41,
Jo di-René Mo 4,21, Juliana Mon ei o22, Da id Fle che 8, Ch is ian Noss23, Mi iam Colls4,5,
Magdalena Nagle 24, Liu Liu 23,25, Cla a Rome o González-Quijano26, Fe an Rome o4,5, Nina Pansch25,
José L. J. Ledesma 17,27,28, Josephine Pegg 8,29, Ma cus Klaus18,42, Anna F eixa 4,5,
Sonia He e o O ega25, Cla a Mendoza-Le a 7,23, Adam Bednařík30,43, Jé émy A. Fon ielle25,
Pe e J. Gilbe 31, Lyubomi A. Kende o 32, Ma in Rulík30 & Pascal Bodme 23,33,44
Globally, inland wa e s emi o e 2 Pg o ca bon pe yea as ca bon dioxide, o which he
majo i y o igina es om s eams and i e s. Despi e he global significance o flu ial ca bon
dioxide emissions, li le is known abou hei diel dynamics. He e we p esen a la ge-scale
assessmen o day- and nigh - ime ca bon dioxide fluxes a he wa e -ai in e ace ac oss 34
Eu opean s eams. We di ec ly measu ed fluxes ou imes be ween Oc obe 2016 and July
2017 using d i ing chambe s. Median fluxes a e 1.4 and 2.1 mmol m−2h−1a midday and
midnigh , espec i ely, wi h nigh fluxes exceeding hose du ing he day by 39%. We a i-
bu e diel ca bon dioxide flux a iabili y mainly o changes in he wa e pa ial p essu e o
ca bon dioxide. Howe e , no consis en d i e s could be iden ified ac oss si es. Ou findings
highligh widesp ead day-nigh changes in flu ial ca bon dioxide fluxes and sugges ha he
ime o day g ea ly influences measu ed ca bon dioxide fluxes ac oss Eu opean s eams.
h ps://doi.o g/10.1038/s43247-021-00192-w OPEN
A lis o au ho a filia ions appea s a he end o he pape .
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Inland wa e s a e impo an sou ces o a mosphe ic ca bon
dioxide (CO
2
) pa ially o se ing he e es ial ca bon sink1,2.
S eams and i e s he ein ep esen majo CO
2
emi e s3.
Flu ial CO
2
fluxes a e p ima ily con olled by he gas exchange
eloci y a he wa e -ai in e ace (k) and he g adien be ween he
wa e and a mosphe ic pa ial p essu es o CO
2
(pCO
2
)4. Bo h
pa ame e s a e highly a iable in space and ime5,6, causing
unce ain y in he magni ude o egional and global flu ial CO
2
emissions2.
The high spa io empo al a iabili y o kand wa e pCO
2
can be
a ibu ed o a complex in e play o unde lying con ols. While k
in s eams is mos ly d i en by wa e u bulence c ea ed by a -
ia ions in flow and s eam mo phology7, he wa e pCO
2
is
influenced by he deg ee o hyd ological connec i i y be ween he
s eam and he adjacen ipa ian soils8as well as by in-s eam
p ocesses (e.g., s eam me abolism). The supply o CO
2
om
ex e nal sou ces, such as soil wa e o g oundwa e , in o s eams,
a ies wi h each and season5,9. Fu he mo e, seasonal and diel
changes in s eam pCO
2
a e a ibu ed o s eam me abolism
d i en by empe a u e and sola adia ion10–13. Ecosys em
espi a ion, a sou ce o CO
2
in he s eam, akes place h oughou
he whole day, and g oss p ima y p oduc ion, a sink o CO
2
,
occu s only du ing dayligh . Tempe a u e and sola adia ion also
di ec ly influence wa e pCO
2
, he o me by changing he solu-
bili y o he gas and he la e due o pho omine aliza ion14.
Howe e , ques ions emain ega ding he magni ude and ela i e
d i e s o seasonal and diel fluc ua ions o CO
2
fluxes in s eams.
P esen ly, mos flu ial CO
2
emission alues a e de i ed om k
es ima es based on wa e eloci y and s eam channel slope and
on wa e pCO
2
alues indi ec ly calcula ed om alkalini y, pH,
and empe a u e3. This app oach ails o cap u e he high spa-
io empo al a iabili y obse ed o kand pCO
2
and he e o e can
p o ide imp ecise es ima es o CO
2
fluxes15,16. Di ec field
obse a ions p o ide he means o imp o e es ima es and
unde s anding o he d i e s behind spa io empo al a iabili y,
and hus he dynamics o CO
2
ou gassing om unning wa e s.
Howe e , besides mos ly local s udies ha indi ec ly in e CO
2
fluxes om pCO
2
and k11,12,17,18, no di ec measu emen s exis
ha compa e day- ime and nigh - ime CO
2
fluxes om s eams
on a la ge spa ial scale.
The aim o his s udy was o assess he magni ude and d i e s
o s eam CO
2
flux a ia ions be ween day and nigh ac oss
Eu opean s eams. We hypo hesized ha CO
2
fluxes would di e
be ween day and nigh due o diel a ia ions in e es ial ino -
ganic ca bon inpu s, in si u me abolism, and empe a u e. As
highe empe a u es and sola adia ion may d i e di e ences in
pCO
2
, we expec ed a highe di e ence be ween day- ime and
nigh - ime fluxes wi h wa me empe a u es and a lowe la i-
udes. Hence, we measu ed day- ime and nigh - ime fluxes o
CO
2
a ou di e en pe iods h oughou one yea om
34 s eams (S ahle s eam o de s om 1 o 6) in 11 coun ies
ac oss Eu ope ollowing a s anda dized p ocedu e. CO
2
fluxes
we e measu ed s a ing a midday (11 a.m. G eenwich Mean
Time (GMT)) and midnigh (11 p.m. GMT) wi h d i ing flux
chambe s equipped wi h CO
2
senso s as desc ibed in Bas iken
e al.19. In he majo i y o he Eu opean s eams, we ound
inc eased CO
2
fluxes a he wa e –ai in e ace in he nigh
compa ed o he day wi h a median inc ease o 0.5 mmol m−2
h−1. Mos o he obse ed CO
2
flux a iabili y was explained by
changes in pCO
2
om day o nigh wi h mo e p onounced
changes a lowe la i udes.
Resul s and discussion
Magni ude o CO
2
flux a ia ion om day o nigh . Midday
CO
2
fluxes a he wa e –ai in e ace anged om −2.7 (up ake)
o 19.9 mmol m−2h−1(emission) (1.4 [0.5, 3.1]; median [in e -
qua ile ange (IQR)]; n=107) and midnigh fluxes anged om
−0.3 o 25.6 mmol m−2h−1(2.1 [0.9, 3.7]; n=107) (Fig. 1a;
Supplemen a y Table S3). Ou measu ed fluxes a e compa able o
o he s udies conduc ed in empe a e and bo eal s eams ha
used chambe s20,21 o empi ical models12,22,23, al hough hey
we e in he lowe ange o he numbe s modeled in a s udy in he
USA23 (Supplemen a y Fig. S2). The lowe numbe s migh be due
o he lack o ibu a y inflows, la ge woody deb is, and s ong
hyd aulic jumps in he selec ed s eam sec ions (Supplemen a y
Sampling manual).
To assess s eam CO
2
flux a ia ions be ween day and nigh ,
we compu ed he di e ence o nigh - ime minus day- ime fluxes
o each s eam and sampling pe iod, whe e posi i e numbe s
indica e an inc ease om day o nigh and ice e sa (Fig. 1b).
Di e ences in CO
2
fluxes amoun ed o 0.5 mmol m−2h−1[0.1,
1.4] (n=107) ac oss all si es and sampling pe iods, which is
equi alen o a ela i e inc ease o 39% [4%, 100%] (n=101; n
educed due o exclusion o ela i e compa isons o ze o flux a
day- ime) (Fig. 2). Al oge he , hese esul s poin owa ds a high
ele ance o nigh - ime CO
2
fluxes as epo ed ea lie o single
p e-alpine s eams12, s eam ne wo ks13,17 o i e s18, and in a
ecen compila ion o diel CO
2
da a om 66 s eams wo ldwide24.
A ough annual ex apola ion o fluxes om ou s udy si es
(Supplemen a y Me hods) shows ha he inclusion o nigh - ime
fluxes inc eases annual es ima es o si e-specific s eam CO
2
emissions by 16% [6%; 25%] (Supplemen a y Table S4). Hence,
ou measu emen s and he simplified ex apola ion o ou da a
emphasize he need o collec and in eg a e nigh - ime CO
2
flux
da a in o sampling p o ocols as well as egional upscaling e o s.
Looking in o he indi idual compa isons, we ound 83
inc eases in median CO
2
fluxes om day o nigh wi h se en
compa isons whe e he s eam e en swi ched om a sink o a
sou ce o CO
2
o he a mosphe e (Supplemen a y Table S3).
Howe e , we also ound ou compa isons whe e median CO
2
fluxes a day and nigh we e he same and 20 dec eases in he
nigh (Supplemen a y Table S3). These esul s and also o he
s udies13,25,26 sugges ha he di ec ion and s eng h o diel pCO
2
pa e n can be la gely a iable ac oss space and ime.
Diel CO
2
flux di e ences a y as a unc ion o la i ude and
wa e empe a u e. The diel di e ences in CO
2
fluxes we e sig-
nifican ly nega i ely ela ed o la i ude (Table 1A), wi h sub-
s an ial diel a ia ion mo e likely a lowe la i udes. Likewise, he
in e ac ion wi h la i ude and he wa e empe a u e was sig-
nifican (Table 1A), which migh be explained by highe em-
pe a u es a lowe la i udes du ing he sampling pe iods and
highe sola adia ion boos ing in-s eam p ima y p oduc ion27.
This da ase is de i ed om only 34 s eams dis ibu ed ac oss
di e en clima e zones in Eu ope. Howe e , o ou knowledge, i
is cu en ly he la ges s udy o i s kind, using flux chambe s o
measu e CO
2
fluxes, and compa e hose fluxes a day- ime and
nigh - ime on such a spa ial scale.
We ound no significan di e ences in he magni ude o diel
di e ences in CO
2
fluxes ela ed o wa e empe a u e (Table 1A)
using a linea mixed-e ec model (LME). Howe e , compa ing he
CO
2
fluxes a midday o midnigh a he di e en sampling pe iods,
we de ec ed significan diel changes in CO
2
fluxes in Oc obe ,
Janua y, and Ap il (Fig. 1a). Con a y o ou expec a ion ha highe
di e ences can be expec ed a highe empe a u es, we did
no de ec significan changes om day o nigh in July (Fig. 1a),
du ing which pe iod he lowes changes in absolu e numbe s we e
eco ded (0.3 mmol m−2h−1;Fig.1b). The highes di e ences o
CO
2
fluxes om day o nigh we e measu ed du ing Ap il
(1.1 mmol m−2h−1), ollowed by Janua y (0.5 mmol m−2h−1)
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and Oc obe (0.5 mmol m−2h−1). Lowe day-nigh changes in July
could be explained by inc eased ipa ian shading educing
pho osyn hesis28,29. Fo example, educed in-s eam pho osyn hesis
in summe compa ed o sp ing has been shown o a subalpine
s eam ne wo k29 o a empe a e o es ed headwa e s eam28.
Howe e , compa ing he canopy co e o he s eams and he
di e ences in CO
2
fluxes om day o nigh (Supplemen a y
Fig. S3h) e ealed no clea pa e n. A p obable al e na e explana ion
is ha CO
2
p oduc ion ia pho omine aliza ion du ing he day
coun e ac ed a dec ease ia CO
2
fixa ion by pho osyn hesis30 and
diminished diel pCO
2
and ul ima ely CO
2
flux changes. This
highligh s he complex in e play be ween di e en ligh -dependen
p ocesses in s eams influencing pCO
2
on a diel scale.
The impo ance o yea - ound measu emen s is highligh ed by
he Janua y da a se con aining he second-highes diel CO
2
flux
changes. Eu opean ice- ee s eams may be pe cei ed “do man ”
du ing hese pe iods and ep esen a i e CO
2
flux es ima es a e
hus o en missing3. Ou Janua y da a showed a magni ude o flux
compa ed o he es o he yea ac oss he Eu opean s eams as
well as high diel a iabili y in CO
2
fluxes (Fig. 1). This may be
a ibu ed in pa o he la i udinal co e age o ou s udy as we
included s eams om he bo eal o he Medi e anean. Fo
example, he wa e empe a u es o he Spanish s eams we e s ill
ela i ely high in win e wi h a ound 2.8–9.5 °C du ing he day
whe eas Swedish s eams showed hese empe a u es in Oc obe
and Ap il. A s udy in he co e minous US looking in o s eam
pCO
2
a iabili y also epo s a ying s eng hs o diel pCO
2
a iabili y, dependen on he in es iga ed s eam and ime25.
Hence, diel pCO
2
and CO
2
flux a iabili y can be la ge in s eams
o he no he n hemisphe e, s essing he need o un a el he si e-
specific d i e s o and mechanisms behind hese diel changes.
Fig. 1 Day- o-nigh changes o CO
2
fluxes a he wa e –ai in e ace o he sampled Eu opean s eams. S eam CO
2
fluxes (in mmol CO
2
m−2h−1)a
day- ime (yellow) and nigh - ime (blue) (a) and he calcula ed changes om nigh minus day (ΔCO
2
flux) (b) o all da a and sepa a ely o each sampling
pe iod. In he sampling pe iods compa isons in (a), CO
2
fluxes o indi idual s eam si es a e indica ed by ed (day) and ligh blue (nigh ) do s. The
boxplo s isualize he median o all s eam si es (line), he fi s and hi d qua iles (hinges), he 1.5*in e -qua ile anges (whiske s), and he ou lie s
ou side he ange o 1.5*in e -qua ile anges (black do s). On op o (a) a e p alues e ie ed om pai ed compa isons o median CO
2
fluxes es ed by
Wilcoxon signed- ank es s and he sample size (n). Significan p alues wi h p< 0.05 a e in bold wi h an as e isk. The di e ences in he CO
2
fluxes (b)in
mmol CO
2
m−2h−1 om day o nigh a e o Oc obe : 0.5 [0.1, 1.2]; Janua y: 0.5 [0.3, 0.9]; Ap il: 1.1 [0.1, 2.3]; July: 0.3 [−0.2, 1.1] (median [IQR]).
Fig. 2 Rela i e changes in CO
2
fluxes om day o nigh o all da a
oge he and o each sampling pe iod. A posi i e alue indica es an
inc ease in CO
2
fluxes du ing he nigh and ice e sa (exp essed as a
%-change o he day ime alues). Ou lie s (>1.5*IQR) we e excluded o
illus a ion pu poses as he la ge ela i e a ia ion in hese fluxes was due o
mino absolu e a ia ion in fluxes close o ze o. The median ela i e changes
we e posi i e h oughou all sampling pe iods, anging om 32% [0.6%, 95%]
in Oc obe , 38% [16%, 50%] in Janua y, 60% [7%, 177%] in Ap il, o 24%
[−16%, 69%] in July (median [IQR]; n=26, 21, 28, and 26, espec i ely).
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Diel CO
2
flux a iabili y d i en by changes in wa e pCO
2
.To
unde s and he mechanisms behind he obse ed changes in CO
2
fluxes om day o nigh , we fi s selec ed he wo p ima y con-
ols o CO
2
fluxes a he wa e –ai in e ace, i.e., he gas exchange
eloci y and wa e pCO
2
and explo ed he influence o hese
pa ame e s on absolu e CO
2
flux changes using an LME. The diel
CO
2
flux a iabili y in Eu opean s eams could be mos ly
a ibu ed o changes in wa e pCO
2
(Table 1B), whe eas changes
in he gas exchange eloci y kappea ed less impo an . In ac , we
did no measu e significan a ia ions in k om day o nigh in
ou s eams (Fig. 3; Supplemen a y Fig. S4h). Al hough diel
a iabili ies o gas exchange eloci ies ha e been epo ed o CO
2
and o he gases31,32, he majo i y o he in es iga ed s eams in
his s udy did no show hose changes. The pCO
2
as a majo
d i e o diel CO
2
flux a iabili y was also iden ified by a global
compila ion o high- equency CO
2
measu emen s24. Conse-
quen ly, i no majo changes in physical d i e s o gas exchanges
occu ha s ongly a ec he u bulence, such as hea y ain
e en s, i is su ficien o ocus on pCO
2
o assessing diel flux
changes a he wa e –ai in e ace.
In a second s ep, we es ed he influence o biogeochemical
pa ame e s ha a y on a diel scale on wa e pCO
2
day- o-nigh
di e ences (Table 1C). This LME iden ified a link be ween he
day- o-nigh changes in wa e pCO
2
and wa e dissol ed O
2
, wi h
pCO
2
gene ally inc easing and O
2
dec easing om day o nigh
(Supplemen a y Fig. S4b, c). This po en ially eflec s a diel cycle
o CO
2
con olled by aqua ic p ima y p oduc ion and espi a ion
(in-s eam me abolism). Hence, e en hough in si u me abolism
may play a mino ole in de e mining he baseline pCO
2
and flux
in smalle s eams (mos ly con olled by e es ial inpu s23), ou
esul s sugges ha me abolism can be an impo an d i e o he
diel fluc ua ions in CO
2
fluxes. Indeed, inc eased wa e pCO
2
du ing he nigh has been a ibu ed o a dec ease in CO
2
fixa ion
by p ima y p oduce s13,18,24, al hough a ecen s udy sugges s
ha he adjacen g oundwa e can also show measu able bu less
p onounced diel pCO
2
a ia ions33. P e ious esea ch sugges s
ha in si u mine aliza ion o CO
2
should play a la ge ole in CO
2
dynamics in la ge s eams because hey a e less influenced by
ex e nal CO
2
sou ces23. Ne e heless, we did no find any end in
CO
2
flux day- o-nigh di e ences wi h s eam wid h o discha ge
as a p oxy o size (Supplemen a y Fig. S3c, ) o wi h s eam
o de (Supplemen a y Fig. S5) al hough o he s udies sugges
change o e a size g adien 23,34. Fu he mo e, he LME es ing
hyd omo phological and ca chmen a iables on pCO
2
day- o-
nigh di e ences (Table 1D) did no e eal significan ela ion-
ships wi h ei he o hese d i e s. This could ei he be due o he
ac ha we missed he bes p oxy ha de e mines day- o-nigh
di e ences in pCO
2
in Eu opean s eams o ha he e a e no
common d i e s among he in es iga ed s eams. La ge diel
a iabili y o CO
2
pa e ns wi hin one Swedish s eam26 o
among US headwa e s eams25 ha e been desc ibed, which
complica es he iden ifica ion o gene al d i e s. Hence, u he
esea ch is needed o deciphe he diel a iabili y o he sou ces
and dynamics o pCO
2
in s eams and o unde s and he
en i onmen al, hyd omo phological, and ca chmen d i e s
be o e hei impo ance on a egional o global scale can be
assessed.
In-s eam me abolism wi h pho osyn he ic CO
2
fixa ion
diminishing pCO
2
du ing he day may explain he inc ease in
CO
2
fluxes om day o nigh , bu canno explain why in some
ins ances we measu ed a lowe CO
2
flux a nigh . Po en ial
explana ions o a lowe nigh flux migh include: (i) highe
a mosphe ic CO
2
concen a ions due o he absence o e es ial
CO
2
fixa ion du ing nigh and he e o e a lowe
wa e –a mosphe e pCO
2
g adien , (ii) pho omine aliza ion o
Table 1 Resul s o he linea mixed-e ec models (LME).
Response
a iable
Fixed e ec χ2(1) pSign
(A) Tes ing spa ial and empo al hypo heses
CO
2
flux
di e ence
om day
o nigh
La i ude 7.4207 0.006 −
Wa e
empe a u e (day)
0.0168 0.897
Wa e empe a u e
(day)*la i ude
4.9594 0.026 +
(B) Tes ing physical and biogeochemical d i e s o CO
2
flux changes
CO
2
flux
di e ence
om day
o nigh
ΔWa e pCO
2
4.9497 0.026 +
ΔGas ans e
eloci y k
0.5613 0.454
(C) Tes ing biogeochemical d i e s o pCO
2
changes
pCO
2
di e ence
om day
o nigh
ΔWa e O
2
concen a ion
7.9879 0.005 −
ΔpH 0.0345 0.853
ΔConduc i i y 0.0293 0.864
ΔT
w
−T
a
a(p oxy o
hea flux)
1.6720 0.196
ΔWa e empe a u e 0.8731 0.350
(D) Tes ing ca chmen and hyd omo phological d i e s o pCO
2
changes
pCO
2
di e ence
om day
o nigh
Day leng h 1.7244 0.189
S eam we ed wid h 0.3748 0.540
Discha ge 3.4458 0.063
% o es 0.0950 0.758
Ca chmen a ea 2.3656 0.124
aHea flux calcula ed as wa e empe a u e (T
w
) minus ai empe a u e (T
a
).
(A) Ma ginal R2=0.12, condi ional R2=0.18, sample size =107.
(B) Ma ginal R2=0.08, condi ional R2=0.10, sample size =77.
(C) Ma ginal R2=0.13, condi ional R2=0.33, sample size =78.
(D) Ma ginal R2=0.11, condi ional R2=0.13, sample size =68.
The e ec s o la i ude and wa e empe a u e du ing he day (A) and he e ec o day- o-nigh
di e ences o pCO
2
and he gas ans e eloci y (Δ=nigh minus day alues) (B) on he day-
o-nigh di e ence o CO
2
fluxes we e es ed. Fu he mo e, he e ec o day- o-nigh di e ences
o physical and biogeochemical pa ame e s (C) and he e ec o ca chmen and
hyd omo phological ela ed pa ame e s (D) on he day- o-nigh di e ences o pCO
2
we e
e alua ed. S eam ID was included as a andom e ec on he in e cep . Significances o fixed
e ec s we e assessed wi h likelihood a io es s wi h deg ees o eedom =1. The slope
di ec ion (sign) o he e ec is indica ed wi h –o +when significan . Significan p alues <
0.05 a e in bold.
Fig. 3 Diel changes in CO
2
fluxes (FCO
2
) and o he physical and chemical
pa ame e s o Oc obe /Janua y/Ap il and July, espec i ely. The
physical and chemical pa ame e s comp ise a mosphe ic CO
2
(Ai CO
2
),
he di e ences o CO
2
concen a ions in he wa e minus he ai (CO
2
g adien
), he wa e –ai gas ans e eloci y (k), he di e ences o
empe a u es in he wa e minus he ai (T
w
−T
a
), he wa e empe a u e
(WT), he oxygen concen a ion in he wa e (O
2
), pH in he wa e , he
pa ial p essu e o CO
2
in he wa e (pCO
2
), and conduc i i y (Cond). The
a ows indica e significan inc eases (↑) o significan dec eases (↓) om
day o nigh and he line indica es no significan change (―) es ed by a
Wilcoxon signed- ank es (see Supplemen a y Fig. S4 o mo e
in o ma ion). The di e ences be ween he sampling pe iods Oc obe /
Janua y/Ap il and July, espec i ely, de ec ed in his Eu opean s udy a e
highligh ed in ed.
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o ganic ma e o CO
2
coun e ac ing he CO
2
fixa ion by p ima y
p oduce s du ing day- ime, and (iii) lowe u bulence due o a
dec ease in s eam discha ge in he nigh . We ound significan
inc eases in a mosphe ic CO
2
close o he in es iga ed s eams a
nigh . Howe e , his was usually accompanied by concomi an
inc eases in wa e pCO
2
and he e o e did no ansla e in o
smalle CO
2
g adien s be ween he wa e –ai in e ace (Fig. 3;
Supplemen a y Fig. S4b, e, i). P oduc ion o CO
2
due o
pho omine aliza ion o dissol ed o ganic ca bon (DOC) could
play a ole in diel CO
2
dynamics in s eams wi h high amoun s o
colo ed e es ial o ganic ma e 35. In he highly colo ed s eams,
diel CO
2
pa e ns can addi ionally be influenced by DOC shading
diminishing ben hic p ima y p oduc ion36. In Oc obe , we
measu ed DOC concen a ions in a subse o he in es iga ed
s eams o ano he s udy37 whe e an ag icul u al s eam in
Sweden and pea land-domina ed s eams in G ea B i ain had
high DOC concen a ions (>10 mg L−1) whe eas he median
DOC was much lowe wi h 2.6 mg L−137. Due o he limi ed da a,
we could no es he e ec o DOC on pCO
2
changes and we can
nei he confi m no exclude ha pho omine aliza ion migh play
a ole o diel pCO
2
and consequen ly CO
2
flux a iabili y in he
s udied s eams. We did find, none heless, ha he majo i y o he
s eams whe e CO
2
fluxes we e lowe du ing he nigh also had a
lowe gas ans e eloci y (k
600
), likely due o a sligh dec ease in
s eam discha ge and he e o e u bulence. Thus, while he e was
a gene al endency o inc eased pCO
2
om day o nigh (only 4
ou o 20 dec eases in CO
2
fluxes om day o nigh showed a
concomi an dec ease in wa e pCO
2
), indi idual s eams a single
ime poin s seemed o expe ience diel fluc ua ions in discha ge as
desc ibed elsewhe e38. This can simul aneously educe he gas
exchange eloci y o he s eam and he e o e cause lowe nigh -
ime CO
2
fluxes. In his s udy, we only measu ed s eam
discha ge du ing he day, and he e o e he impo ance o his
mechanism emains o be confi med.
Maximum CO
2
flux di e ences migh be e en highe —lim-
i a ions o he s udy design. Fo o ganiza ional easons, he
sampling scheme o his collabo a i e s udy was s anda dized o
fixed imes o measu emen s o he day and he nigh . All eams
ac oss Eu ope s a ed hei measu emen s a 11:00 (midday) and
23:00 GMT (midnigh ) du ing each sampling pe iod, which has
consequences o he magni ude o he obse ed diel a iabili y o
he CO
2
fluxes. The la ges diel di e ences in s eam pCO
2
ha e
gene ally been de ec ed a he end o he day compa ed o he end
o he nigh 12,18,39. In an ag icul u al Swedish s eam, diel max-
imum and minimum CO
2
concen a ions we e eached a 04:00
and 16:00 (GMT), espec i ely, du ing sp ing and ea ly summe
pe iods (la e Ap il o ea ly July) whe e diel dynamics we e mos
p onounced26. In hese scena ios, sampling midday and mid-
nigh , as conduc ed in his s udy, would be close o hose maxima
and minima as hey can be eached al eady ea lie du ing he day
(see Supplemen a y Fig. S6 in May). Howe e , he maxima and
minima o diel CO
2
dynamics in s eams can a y la gely (see
Supplemen a y Fig. S6 in Oc obe , Ap il, July). In ano he
example o Ge man s eams39, he imes o minima and maxima
di e be ween s eams and imes, and he fixed ime poin s
chosen in his s udy would miss he maximum di e ences ha
can be obse ed (see Supplemen a y Fig. S7 in Augus ). Hence,
ou es ima es could be conse a i e as we compa ed fixed ime
poin s a midday and midnigh . In gene al, CO
2
flux measu e-
men s in s eams a e highly sensi i e owa ds he ime o he day
because diel minimum and maximum o pCO
2
can a y la gely
om mon h o mon h bu also om day o day. As we ound ha
he diel a iabili y o pCO
2
was he majo d i e o diel CO
2
fluxes, we ecommend u u e s udies ha plan o measu e CO
2
fluxes di ec ly wi h he chambe me hod, o addi ionally moni o
he diel a iabili y o pCO
2
wi h logge s a a high empo al eso-
lu ion. This app oach will p o ide he oppo uni y o es ima e i
he measu emen s a e done du ing peak imes o no .
While ou esul s p o ide a fi s insigh in o he d i e s o day-
nigh di e ences in CO
2
fluxes, he high unce ain y in he
models as well as he some imes opposing pa e ns—inc eases
and dec eases om day o nigh in di e en s eams and
sampling pe iods—poin owa ds di e en d i e s a ying on a
empo al and spa ial scale. We ecommend ha u u e s udy
designs inco po a e high- equency CO
2
da a oge he wi h
biogeochemical a iables om he s eam (e.g., O
2
) and
he a mosphe e (e.g., CO
2
o empe a u e)40. Addi ionally, we
ecommend including adioac i e o s able ca bon iso ope
signa u es o ack po en ial sou ces o CO
2
and hei changes
in s eams41,42 o be e assess e es ial–aqua ic linkages.
Linking empo al pa e ns o flu ial CO
2
fluxes wi h hei d i e s
ac oss la ge spa ial scales is a pa h owa ds a mo e accu a e
unde s anding o hei ole in egional and global ca bon cycles.
Ou esul s demons a e ha , in many s eams ac oss Eu ope,
nigh - ime CO
2
fluxes exceed day- ime, esul ing in a po en ial
unde es ima ion o global CO
2
emissions om inland wa e s i
no conside ed. I is hus c i ical o accoun o he diel a iabili y
o flu ial CO
2
fluxes o accu a e daily and annual es ima es o
CO
2
emissions om inland wa e s.
Me hods
Sampling scheme. The p ojec included 16 eams dis ibu ed ac oss 11 Eu opean
coun ies. E e y eam sampled one o h ee s eams (Supplemen a y Table S1)
e e y 3 mon hs (Oc obe 2016/Janua y 2017/Ap il 2017/July 2017) wi hin a ime
ame o 2 weeks h oughou a whole yea . These sampling pe iods oughly co e
he seasons au umn/win e /sp ing/summe al hough, due o he la ge la i udinal
co e age o he sampling si es, he seasons and hei cha ac e is ics a y la gely. In
o al, 34 s eam si es (Supplemen a y Fig. S1) we e isi ed each sampling pe iod
du ing he specified 2 weeks’ ime ame excep o 11 s eams in Janua y ha we e
ozen du ing he sampling weeks (Supplemen a y Table S3).
CO
2
fluxes we e measu ed once e e y sampling pe iod wi h d i ing flux
chambe s equipped wi h CO
2
senso s. This me hod has p o en o be a eliable and
leas biased di ec measu emen o CO
2
fluxes a he wa e –ai in e ace in
s eams19,43.CO
2
concen a ions in he chambe headspace we e logged e e y 30 s
o e a pe iod o 5–10 min du ing each un, and CO
2
fluxes we e calcula ed based
on he a e o change o e ime in pCO
2
in he chambe headspace. A each s eam,
we measu ed CO
2
fluxes wi h he flux chambe (fi e imes), pCO
2
in he
a mosphe e and wa e wi h he CO
2
senso s in he flux chambe (de ails desc ibed
in Supplemen a y Me hods), pH, empe a u e, conduc i i y, and oxygen in he
wa e wi h a mul ip obe (Supplemen a y Table S2). These measu emen s we e
s a ed a 11:00 and 23:00 (GMT) and las ed app oxima ely wo hou s and a e
e e ed o as midday and midnigh h oughou his a icle. S eam wid h, dep h,
canopy co e , and discha ge we e de e mined du ing he day (see Supplemen a y
Sampling manual o de ails). In addi ion, he ollowing in o ma ion was collec ed
o each s eam once du ing he s udy: s eam o de , clima e zone, ca chmen a ea
un il he endpoin o he in es iga ed s eam si e and he pe cen age o co e age o
di e en land use classes in his ca chmen a ea, and p edominan geology
(Supplemen a y Table S1).
Calcula ions o CO
2
fluxes and gas ans e eloci y. Flux a es we e ob ained
om he linea slopes o he pCO
2
in he chambe headspace o e ime and flux
was accep ed i he coe ficien o de e mina ion (R2) o he slope was a leas 0.6544.
An excep ion was made in cases whe e he slope was close o ze o and he pCO
2
in
he a mosphe e and wa e (measu ed a he same ime) we e a equilib ium. These
fluxes we e se o ze o. Final flux a es F(mmol CO
2
m−2h−1) we e calcula ed
acco ding o Eq. (1)45:
F¼S103PV
RTA 60 60;ð1Þ
whe e Sis he slope (ppm s−1), Pis he pCO
2
in he a mosphe e (a m), Vis he
olume (mL) o he d i ing chambe , Ris he gas cons an (82.0562 mL a m K−1
mol−1), Tis he chambe ai empe a u e (K), Ais he bo om a ea o he chambe
(m2), and he las e m is he con e sion om seconds o hou s. In his s udy, we
ollowed he sign con en ion whe eby posi i e alues indica e a CO
2
flux om he
s eam o he a mosphe e (sou ce) and nega i e alues indica e a flux om he
a mosphe e o he s eam (sink). The magni udes o a ia ions be ween day- ime
and nigh - ime measu emen s a e addi ionally s a ed as pe cen inc eases, which
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we e compu ed by di iding he di e ence be ween he alues a nigh minus day by
he alue a day and exp essing he esul as a pe cen change om day o nigh .
We used F(Eq.(1)) o calcula e he gas ans e eloci y (kin cm h−1)by
in e ing he equa ion o Fick’s law o gas di usion, acco ding o Eq. (2):
k¼F
kHðCO2wa e CO2ai Þ100;ð2Þ
whe e kH is Hen y’s cons an (in mol L−1a m−1) adjus ed o empe a u e46.
Fo compa ison o ans e eloci ies be ween si es and sampling pe iods and
wi h he li e a u e, k(Eq. ( 2)) was s anda dized o k
600
(Eq. (3)):
k600 ¼k600
Sc

0:5
ð3Þ
whe e kis he ans e eloci y a in si u empe a u e (T), Sc is he Schmid numbe
o in si u empe a u e T, he Schmid numbe o 20 °C in eshwa e is 600, and
ep esen ing a hyd odynamic ough wa e su ace ypical in s eams he exponen
o −0.5 was chosen47.
S a is ical analyses. All s a is ical analyses we e pe o med wi h median alues o
h ee o fi e floa ing chambe uns pe day and nigh , espec i ely, using he
s a is ical p og amming language R48 ( e sion 3.5.1). Samplings ha gene a ed less
han h ee alues o ei he day o nigh due o an R2o he slope <0.6544 we e
excluded om u he analysis educing he numbe om 136 o 107 day–nigh
compa isons. Fo ou s a is ical es s, he alpha le el was se o α=0.05. Significan
di e ences be ween day- ime and nigh - ime measu emen s o each sampling
pe iod ac oss all s eams we e es ed wi h Wilcoxon signed- ank es s49 whe e
median day- ime and nigh - ime alues o each s eam si e we e pai ed (Fig. 1a).
The same es s we e conduc ed o he o he biogeochemical a iables measu ed a
midday and midnigh (see Fig. 3; Supplemen a y Fig. S4).
Wi h a fi s linea mixed-e ec model (LME) we es ed he la i udinal and wa e
empe a u e e ec on CO
2
flux di e ences om day o nigh . A second LME was
buil o e alua e he wo majo d i e s o CO
2
flux di e ences om day o nigh :
pCO
2
and gas exchange eloci y (k). A hi d LME was subsequen ly used o
de e mine he biochemical ac o s po en ially influencing he di e ences o he
nigh - ime minus day- ime pCO
2
, which was iden ified as he only significan
d i e in he second LME. Finally, a ou h LME was buil o e alua e he e ec o
ca chmen and hyd omo phological pa ame e s on he day- o-nigh di e ences o
pCO
2
. Fo hese es s, we used he “lme ” unc ion o he R-package “lme4”50 wi h
maximum-likelihood es ima ion. Fixed e ec s o he LME wi h biogeochemical
pa ame e s o pCO
2
di e ences om day o nigh included absolu e di e ences
om day o nigh o oxygen concen a ion in he wa e , pH, conduc i i y,
empe a u e g adien o a mosphe e and wa e , and wa e empe a u e. Fixed
e ec s o he LME wi h ca chmen and hyd omo phological pa ame e s included
day leng h (i.e., sun hou s om sun ise o sunse ), s eam we ed wid h, discha ge,
% o es o he ca chmen , and ca chmen a ea. These a iables a e mos ly emo ely
a ailable o s eams. Fo he LMEs we included s eam ID as a andom e ec
allowing di e en in e cep s o each s eam o accoun o pseudo eplica ion (one
da a poin pe sampling pe iod pe s eam) and z-scaled all fixed e ec s wi h he
“scale” unc ion be o e unning he models. S a is ical significances o fixed e ec s
we e assessed wi h likelihood a io es s using he unc ion “d op1”51. The
espec i e LMEs we e ollowed by a model alida ion, checking he esiduals o
no mal dis ibu ion and homogenei y o a iances52. A sepa a ion o he da ase o
check i d i e s be ween inc eases om day o nigh and dec eases om day o
nigh di e did no e eal accep able models in e ms o model alida ion (i.e.,
esiduals we e no no mally dis ibu ed). Al hough ou da ase p o ided a la ge
spa ial co e age on day–nigh di e ences in CO
2
fluxes in Eu opean s eams, i did
no ha e he s a is ical powe o es o significan d i e s sepa a ely o inc eases
and dec eases.
Da a a ailabili y
The da a ha suppo he findings o his s udy a e openly a ailable in figsha e a h ps://
doi.o g/10.6084/m9.figsha e.12717188.
Code a ailabili y
This manusc ip includes no code.
Recei ed: 13 No embe 2020; Accep ed: 21 May 2021;
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Acknowledgemen s
We hank he ini ia o s o he fi s Collabo a i e Eu opean F eshwa e Science P ojec o
Young Resea che s, he Eu opean Fede a ion o F eshwa e Sciences (EFFS) boa d, he
Eu opean F esh and Young Resea che s (EFYR) and he ep esen a i es o he F esh
Blood o F esh Wa e (FBFW) mee ings. We also hank he se en na ional eshwa e
socie ies financing his p ojec , namely he Ibe ian Associa ion o Limnology (AIL; Spain
and Po ugal), Deu sche Gesellscha ü Limnologie e.V. (DGL; Ge many), Swiss Socie y
o Hyd ology and Limnology (SGHL; Swi ze land), I alian Associa ion o Oceanog aphy
and Limnology (I aly), F eshwa e Biological Associa ion (FBA; Uni ed Kingdom),
F ench Limnological Associa ion (AFL; F ance), Aus ian Limnological Socie y (SIL-
Aus ia), as well as he Leibniz-Ins i u e o F eshwa e Ecology and Inland Fishe ies o
addi ional unds. Addi ional unding was awa ded o J.P.C.-R. by a Juan de la Cie a
pos doc o al g an om he Spanish Go e nmen (FJC2018-037791-I), o A.P.P. by a Ph.
D. g an om he Fundação pa a a Ciência e Tecnologia (SFRH/BD/115030/2016), o
B.C.D. by he Ma ine Ins i u e’s Cullen Ph.D. ellowship (G an No. CF/15/05), o N.C.
by he Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og am unde he
Ma ie Sklodowska-Cu ie g an ag eemen (No. 839709), o J.M. by FCT (Po uguese
Science Founda ion) h ough a Ph.D. g an (SFRH/BD/131924/2017), o J.P. by he DSI/
NRF Resea ch Chai in Inland Fishe ies and F eshwa e Ecology, o A.F. by he Juan de la
Cie a pos doc o al g an om he Spanish Go e nmen (FJCI-2017–33171), and o
C.M.-L. by he F ench Na ional Agency o Wa e and Aqua ic En i onmen s (ONEMA,
Ac ion 13, “Colma age, échanges nappe- i iè e e p ocessus biogéochimiques”). We
acknowledge Luigi Naselli-Flo es and An onio Camacho o hei encou agemen and
suppo du ing he p ojec . We also hank Da id Bas iken, Ing id Sundg en, and Thanh
Duc Nguyen o he in oduc ion o he logge and chambe cons uc ion and ad ice o
measu emen s o CO
2
fluxes wi h he chambe , Vincen Fugè e o his help in se ing up
he linea mixed-e ec models, and Vik o Rosenbe g o c ea ing he map. Fu he mo e,
we a e e y hank ul o Ra ael Ma cé and Paul del Gio gio o hei hough ul commen s
on he manusc ip and we hank h ee anonymous e iewe s o cons uc i e inpu s ha
imp o ed he manusc ip . Open access unding p o ided by Uni e si y o Vienna.
Au ho con ibu ions
K.A. and P.B. concei ed he s udy design, coo dina ed he p ojec and con ibu ed
equally o his wo k; all au ho s collec ed and analyzed he field da a and K.A. and P.B.
ga he ed and pe o med he quali y check o all da a; K.A., P.B., and J.P.C.-R. co-w o e
he pape wi h he help o M.K., G.H.N., and N.C. All au ho s (K.A., J.P.C.-R., T.F., A.P.,
S.C.-F., D.S., A.C.N., Al.D., A.P.P., B.C.D., N.S., C.G.R., G.H.N., X.T., V.E., L.B.-F., T.B.,
J.A., An.D., G.B., S.F., N.C., E.d.E., F.P., J.-R.M., J.M., D.F., C.N., M.C., M.N., L.L., C.R.
G.-Q., F.R., N.P., J.L.J.L., J.P., M.K., A.F., S.H.O., C.M.-L., A.B., J.A.F., P.J.G., L.A.K.,
M.R., P.B.) commen ed on he manusc ip .
Compe ing in e es s
The au ho s decla e no compe ing in e es s.
Addi ional in o ma ion
Supplemen a y in o ma ion The online e sion con ains supplemen a y ma e ial
a ailable a h ps://doi.o g/10.1038/s43247-021-00192-w.
Co espondence and eques s o ma e ials should be add essed o K.A.
Pee e iew in o ma ion Communica ions Ea h & En i onmen hanks he anonymous
e iewe s o hei con ibu ion o he pee e iew o his wo k. P ima y Handling
Edi o s: Joshua Dean and Joe Aslin.
Rep in s and pe mission in o ma ion is a ailable a h p://www.na u e.com/ ep in s
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Open Access This a icle is licensed unde a C ea i e Commons
A ibu ion 4.0 In e na ional License, which pe mi s use, sha ing,
adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e
app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e
Commons license, and indica e i changes we e made. The images o o he hi d pa y
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1
Limnology/Depa men o Ecology and Gene ics, Uppsala Uni e si y, Uppsala, Sweden.
2
Wasse Clus e Lunz –Biologische S a ion, Lunz am See,
Aus ia.
3
Depa men o Func ional and E olu iona y Ecology, Uni e si y o Vienna, Vienna, Aus ia.
4
Ca alan Ins i u e o Wa e Resea ch
(ICRA), Gi ona, Spain.
5
Uni e si y o Gi ona (UdG), Gi ona, Spain.
6
Flu ial Ecosys em Ecology, Depa men o Ecology, Uni e si y o Innsb uck,
Innsb uck, Aus ia.
7
INRAE, UR Ri e ly, Cen e de Lyon-Villeu banne, Villeu banne, Cedex, F ance.
8
Depa men o Li e and En i onmen al
Sciences, Bou nemou h Uni e si y, Poole, UK.
9
Depa men o Sciences and Technological Inno a ion, Uni e si y o Piemon e O ien ale,
Alessand ia, I aly.
10
ALPSTREAM –Alpine S eam Resea ch Cen e , Os ana, I aly.
11
Resea ch Cen e in Biodi e si y and Gene ic Resou ces
(CIBIO-InBIO), Uni e si y o Po o, Vila do Conde, Po ugal.
12
Facul y o Sciences, Uni e si y o Po o, Po o, Po ugal.
13
Cen e o F eshwa e and
En i onmen al S udies, Dundalk Ins i u e o Technology, Dundalk, Co Lou h, I eland.
14
Na ional Museum o Na u al His o y, Bulga ian Academy o
Sciences, Sofia, Bulga ia.
15
Ri e and Conse a ion Resea ch, Depa men o Ecology, Uni e si y o Innsb uck, Innsb uck, Aus ia.
16
Depa men o
Aqua ic Ecosys ems, Ins i u e o Biodi e si y and Ecosys em Resea ch, Bulga ian Academy o Sciences, Sofia, Bulga ia.
17
Depa men o Aqua ic
Sciences and Assessmen , Swedish Uni e si y o Ag icul u al Sciences, Uppsala, Sweden.
18
Depa men o Ecology and En i onmen al Science,
Umeå Uni e si y, Umeå, Sweden.
19
Depa men o Li e Sciences and Sys ems Biology, Uni e si y o Tu in, Tu in, I aly.
20
Ma ine Ins i u e, Fu nace,
Newpo , Co Mayo, I eland.
21
Depa men o E olu iona y Biology, Ecology and En i onmen al Sciences, Facul y o Biology, Uni e si y o
Ba celona (UB), Ba celona, Spain.
22
Cen e o Ecology, E olu ion and En i onmen al Changes (cE3c), Faculdade de Ciências, Uni e sidade de
Lisboa, Lisboa, Po ugal.
23
Ins i u e o En i onmen al Sciences, Uni e si y o Koblenz-Landau, Landau, Ge many.
24
Ins i u e o Mic obiology,
Uni e si y o Innsb uck, Innsb uck, Aus ia.
25
Expe imen al Limnology, Leibniz-Ins i u e o F eshwa e Ecology and Inland Fishe ies (IGB), S echlin,
Ge many.
26
Ecohyd ology, Leibniz-Ins i u e o F eshwa e Ecology and Inland Fishe ies (IGB), Be lin, Ge many.
27
Cen e o Ad anced S udies o
Blanes, Spanish Na ional Resea ch Council, Blanes, Spain.
28
Ins i u e o Geog aphy and Geoecology, Ka ls uhe Ins i u e o Technology, Ka ls uhe,
Ge many.
29
Sou h A ican Ins i u e o Aqua ic Biodi e si y, Makhanda, Sou h A ica.
30
Depa men o Ecology and En i onmen al Sciences,
Palacký Uni e si y Olomouc, Olomouc, Czech Republic.
31
En i onmen al Resea ch Ins i u e, Uni e si y o Highlands and Islands (UHI), Thu so,
Sco land, UK.
32
Depa men o Gene al and Applied Hyd obiology, Sofia Uni e si y “S . Klimen Oh idski”,Sofia, Bulga ia.
33
Chemical Analy ics
and Biogeochemis y, Leibniz-Ins i u e o F eshwa e Ecology and Inland Fishe ies, Be lin, Ge many.
34
P esen add ess: Depa men o Biology,
Aa hus Uni e si y, Aa hus C, Denma k.
35
P esen add ess: Ins i u e o Global Heal h, Facul y o Medicine, Uni e si y o Gene a, Campus Bio ech,
Gene a, Swi ze land.
36
P esen add ess: Cen e o En i onmen , Fishe ies and Aquacul u e Science (Ce as), Lowes o , Su olk, UK.
37
P esen
add ess: Depa men o Bioscience, Aa hus Uni e si y, Silkebo g, Denma k.
38
P esen add ess: No wegian Ins i u e o Wa e Resea ch, Oslo,
No way.
39
P esen add ess: Labo a oi e des Sciences du Clima e de l’En i onnemen (LSCE), CEA, CNRS, UVSQ, Gi -Su -Y e e, F ance.
40
P esen add ess: Uni ed S a es Geological Su ey, Boulde , CO, USA.
41
P esen add ess: En i onmen al A chaeology Lab, Depa men o
His o ical, Philosophical and Religious s udies, Umeå Uni e si y, Umeå, Sweden.
42
P esen add ess: Depa men o Fo es Ecology and
Managemen , Swedish Uni e si y o Ag icul u al Sciences, Umeå, Sweden.
43
P esen add ess: Global Change Resea ch Ins i u e o he Czech
Academy o Sciences, B no, Czech Republic.
44
P esen add ess: G oupe de Reche che In e uni e si ai e en Limnologie, Dépa emen des Sciences
Biologiques, Uni e si é du Québec à Mon éal, Mon éal, Canada. ✉email: [email p o ec ed]
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