Can whales mix the ocean?

Abstract

Ocean mixing influences global climate and enhances primary productivity
by transporting nutrient rich water into the euphotic zone. The
contribution of the swimming biosphere to diapycnal mixing in the ocean
has been hypothesised to occur on scales similar to that of tides or
winds, however, the extent to which this contributes to nutrient
transport and stimulates primary productivity has not been explored.
Here, we introduce a novel method to estimate the diapycnal diffusivity
that occurs as a result of a sperm whale swimming through a pycnocline.
Nutrient profiles from the Hawaiian Ocean are used to further estimate
the amount of nitrogen transported into the euphotic zone and the
primary productivity stimulated as a result. We estimate that the 80
sperm whales that travel through an area of 104
km2 surrounding Hawaii increase diapycnal diffusivity by
10-6 m2 s-1 which results in the flux
of 105 kg of nitrogen into the euphotic zone each year. This
nitrogen input subsequently stimulates 6 × 105 kg of
carbon per year. The nutrient input of swimming sperm whales is modest
compared to dominant modes of nutrient transport such as nitrogen
fixation but occurs more consistently and thus may provide the nutrients
necessary to enable phytoplankton growth and survival in the absence of
other seasonal and daily nutrient inputs.

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Biogeosciences Discuss., 9, 8387–8403, 2012
www.biogeosciences-discuss.net/9/8387/2012/
doi:10.5194/bgd-9-8387-2012
© Author(s) 2012. CC Attribution 3.0 License.
Biogeosciences
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This discussion paper is/has been under review for the journal Biogeosciences (BG).
Please refer to the corresponding final paper in BG if available.
Can whales mix the ocean?
T. J. Lavery1, B. Roudnew1, L. Seuront1, J. G. Mitchell1, and J. Middleton2
1Biological Sciences, Flinders University, GPO Box 2100, Adelaide, S.A., 5001, Australia
2Aquatic Sciences, South Australian Research and Development Institute (SARDI), 2 Hamra
Ave, West Beach S.A., 5042, Australia
Received: 7 May 2012 – Accepted: 22 May 2012 – Published: 12 July 2012
Correspondence to: T. Lavery (trish.lavery@flinders.edu.au)
Published by Copernicus Publications on behalf of the European Geosciences Union.
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Abstract
Ocean mixing influences global climate and enhances primary productivity by trans-
porting nutrient rich water into the euphotic zone. The contribution of the swimming
biosphere to diapycnal mixing in the ocean has been hypothesised to occur on scales
similar to that of tides or winds, however, the extent to which this contributes to nu-5
trient transport and stimulates primary productivity has not been explored. Here, we
introduce a novel method to estimate the diapycnal diffusivity that occurs as a result
of a sperm whale swimming through a pycnocline. Nutrient profiles from the Hawaiian
Ocean are used to further estimate the amount of nitrogen transported into the eu-
photic zone and the primary productivity stimulated as a result. We estimate that the10
80 sperm whales that travel through an area of 104km2surrounding Hawaii increase
diapycnal diffusivity by 10−6m2s−1which results in the flux of 105kg of nitrogen into
the euphotic zone each year. This nitrogen input subsequently stimulates 6 ×105kg of
carbon per year. The nutrient input of swimming sperm whales is modest compared to
dominant modes of nutrient transport such as nitrogen fixation but occurs more con-15
sistently and thus may provide the nutrients necessary to enable phytoplankton growth
and survival in the absence of other seasonal and daily nutrient inputs.
1 Introduction
Diapycnal mixing plays a key role in a wide range of oceanic processes. Mixing is
crucial for meridional overturning circulation which shapes our global climate by en-20
abling the poleward transport of energy in the form of heat (Munk and Wunsch, 1998).
Meridional overturning circulation determines the extent of contact between oceanic
deep water and the atmosphere and this in turn influences the flux of CO2between
the ocean and the atmosphere. Without diapycnal mixing to overcome ocean stratifi-
cation, the ocean would turn to a pool of stagnant water within a few thousand years25
(Munk and Wunsch, 1998). Climate models are thus very sensitive to the influence of
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diapycnal mixing yet this remains one of the least understood parameters in climate
models (Dalan et al., 2005). Climate change is expected to increase stratification, and
so depress diapycnal mixing, in the ocean (Sarmiento et al., 1998) and for this rea-
son it is increasingly important to understand the sources, magnitude and effects of
diapycnal mixing.5
Diapycnal mixing also exerts local effects on marine ecosystems. Diapycnal mixing
transports nutrients from the nutrient-rich deep ocean into the nutrient-limited euphotic
zone and thereby stimulates the phytoplankton blooms that form the basis of marine
food webs. Diapycnal mixing influences fisheries productivity because the large plank-
ton that are crucial for channelling nutrients into the pelagic food webs proliferate in10
episodic turbulent environments where high nutrient levels in the water allow a selec-
tive advantage for their large cell size (Kiorboe, 1993; Margalef, 1997). Large plankton
increase fisheries productivity by uncoupling the microbial loop and channelling nutri-
ents into pelagic food chains (Alcaraz, 1997; Kiorboe, 1993). The magnitude of fish
production is thus often related more to the frequency of diapycnal mixing, than to the15
overall primary productivity (Kiorboe, 1993).
2 Biomixing
The amount of energy needed to mix the ocean at observed levels is approximately
2.9 TW (Dewar et al., 2006). Winds and tides contribute approximately 1 TW each to
global mixing (Dewar et al., 2006). The difference between the contribution of winds20
and tides and the overall amount of energy required is thus approximately 1 TW. This
difference was long overlooked as the result of large geographical variations that are
averaged in global calculations, however, some researchers have recently suggested
that this energy budget imbalance may be a real effect, and that the action of swimming
marine organisms may exert enough energy to contribute significantly to ocean mixing25
(Dewar et al., 2006). If this hypothesis is correct then wind, tides and swimming marine
animals each contribute equally to global mixing.
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Biomixing is the term given to describe the action of organisms swimming through
the pycnocline and thereby mixing nutrient rich water into the euphotic zone. Initially
considered to be negligible (Munk, 1966), biomixing was revisited by Huntley and Zhou
(2004) who estimated kinetic energy production on the order of 10−5W kg−1for animals
ranging from krill to whales. Subsequent theoretical estimates suggest that the marine5
biosphere may contribute on the order of 1 TW to oceanic mixing (Dewar et al., 2006).
Direct measurements of turbulence behind a krill swarm have confirmed an increase
in turbulence on the order of 2–3 orders of magnitude compared to background levels
(Kunze et al., 2006).
Debate within the literature has since centred on whether kinetic energy imparted by10
the biosphere translates effectively into mixing. The mixing efficiency of the biosphere
was examined at buoyancy length scales of 3 to 10m and found to be low (Visser,
2007). The mechanical energy imparted to the ocean by small animals was found
to be dissipated almost immediately in the form of heat, and mixing efficiencies only
approached maximum levels in larger fish and marine mammals (Visser, 2007). It was15
argued that the relatively low abundance of these large animals was thought to make
their contribution to oceanic mixing negligible (Visser, 2007).
Darwinian mixing, the mixing that occurs when an object moves thorough a body of
water and entrains some of the fluid along with it, was examined recently and shown
to be effective in small organisms, which comprise the majority of the ocean biosphere20
(Katija and Dabiri, 2009). However, the passive particle that was used to illustrate Dar-
winian mixing by Katija and Dabiri (2009) was later criticized for significantly overes-
timating the mixing effect (Subramaian, 2010) because wakes associated with pas-
sive particles are substantially different to wakes behind an actively swimming particle
(Subramanian, 2010). Subramanian (2010) concluded that only large animals are able25
to significantly influence diapycnal mixing and that a methodology for estimating their
diapycnal diffusivity must go beyond examining them as a stationary particle and en-
compass the fact that they are actively swimming while moving through the pycnocline.
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Here we present a novel methodology for examining the diapycnal diffusivity that
occurs as an adult sperm whale ascends or descends through a pycnocline. To exam-
ine the regional influence of this diapycnal diffusivity, we use publicly available nutrient
profiles in the Hawaiian ocean (Karl et al., 2001) to estimate the flux of nitrogen that is
moved into the euphotic zone by the resident populations of sperm whales (Whitehead,5
2002). The Redfield ratio (Redfield, 1934) is used to estimate the primary productivity
that is stimulated as a result of the nitrogen input. In light of the knowledge that fish-
eries productivity is influenced more by the frequency of mixing than the overall primary
productivity (Kiorboe, 1993), we compare the frequency with which whales mix nutri-
ents into the photic zone against other dominant modes of nitrogen transport into the10
surface waters of Hawaii.
3 Study area and species
We consider the population of 80 sperm whales (Physeter macrocephalus) that inhabit
the waters surrounding Hawaii (Whitehead, 2002). Whales cannot influence mixing in
areas where they are absent, thus we wish to estimate the area of water that the whales15
travel through and upon which they are able to influence mixing (termed the “whale
path”). We estimate this by multiplying the horizontal distance travelled by each sperm
whale by the width of its turbulent wake. Sperm whales travel at 1.54 m s−1(Miller et al.,
2004) and complete one dive cycle every 67 min, consisting of 50 min diving and 17min
socialising at the surface (Whitehead, 2003). Within the 67 min dive cycle, 25 min is20
spent travelling horizontally at the bottom of the dive (Whitehead, 2003). We thus esti-
mate that each sperm whale travels a horizontal distance of 2.3 ×103m per dive cycle
(25 min ×1.54 m s−1). The width of the turbulent plume is estimated to be 9 m (see cal-
culations in Sect. 2.1 below), thus we can estimate that each sperm whale has the
potential to influence mixing in a body of water of 2.1 ×104m2per dive (9 m ×2310 m).25
Given that dive cycles occur on average once every 67 min, the whale path equates to
1.6 ×108m2yr−1(2.1 ×104m2×21.5 dives per day ×356 days per year). The 80 sperm
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whales that inhabit the waters of Hawaii thus have the potential to influence mixing in
an area of 1.3 ×1010 m2(80 ×1.6 ×108m2). This area (the whale path) is thus the area
of water over which a sperm whale travels and we now estimate the extent to which
whales influence mixing and nitrogen transport within this area of water.
3.1 Diapycnal diffusivity5
The increase in diapycnal diffusivity (Ksw) along the whale path caused by whales as-
cending or descending through a nutricline can be estimated using Eq. (1)
Ksw =S×Td×N×V(m2s−1) (1)
where Sis the average ascent/descent speed of a diving sperm whale (m s−1), Td
is the proportion of time a whale spends diving, Nis the density of whales (m−2)10
along the whale path, and Vis the volume of the turbulent wake behind a swimming
sperm whale (m3). The average swimming speed (S) of a diving/ascending sperm
whale is 1.54 m s−1(Miller et al., 2004). To calculate the proportion of time spent
diving and ascending (Td), we consider that sperm whales spend 75 % of their lives
foraging and, when foraging, typically engage in 50 min dive cycles which include15
15 min spent ascending and descending (Whitehead, 2003). Tdis thus estimated by
0.75 ×(15 / 50) =0.23. The 80 sperm whales in Hawaii influence an area of water of
1.6 ×108m2yr−1(see Sect. 2 above) and thus whale density is 6 ×10−9m−2along the
whale path.
The lack of flow visualisation experiments on sperm whales make it challenging to20
accurately determine the volume of the turbulent wake (V) behind a swimming whale,
however, it can be approximated using Eq. (2)
V=(π×0.5W×0.5 F)×L(m3) (2)
where Wis the width of the turbulent wake (m), Fis the fluke spread (m) and Lis the
length of the turbulent plume behind a swimming whale (m). Flow visualisation experi-25
ments have shown that the width of the turbulent wake is at least twice the maximum
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excursion (peak to peak amplitude) of the tail flukes (Anderson et al., 1998; Taylor et al.,
2003; Bandyopadhyay and Donnelly, 1998). The maximum excursion of the tail flukes
can be determined by multiplying the body length by the Strouhal number (Rohr and
Fish, 2004). We assume a Strouhal number for sperm whales of 0.3 (Rohr and Fish,
2004) and a body length of 15 m (Gosho et al., 1984), giving a maximum excursion5
of 4.5 m and a wake width (W) of 9m. The spread of the flukes (F) is estimated at
1 / 5 of the body length (Nishiwaki, 1972), equating to approximately 3 m in adult sperm
whales. The length of the turbulent wake (L) behind a spheroid body is typically es-
timated at 10 times the body diameter (Chernykh, 2006). Bose et al. (1990) lists the
sperm whales maximum girth as 7.8 m, equating to a diameter of approximately 2.5 m.10
Thus, the volume of the turbulent plume behind a swimming sperm whale (V) is thus
estimated by V=π×(4.5 m ×1.5 m) ×25 =530 m3. These calculations can be used to
provide an estimate of the diapycnal diffusivity resulting from the biomixing of sperm
whales (Ksw).
3.2 Nitrogen transport15
In this section we use nitrogen profiles measured in the Hawaiian ocean (Karl et al.,
2001) to estimate the nitrogen transported into the photic zone (Nf) as a result of the
diapycnal diffusivity resulting from sperm whale biomixing (Ksw). Nitrogen flux across
the nutricline resulting from biomixing by sperm whales (Nf) can be estimated by Eq. (3)
20
Nf=Ksw ×G(kgnitrogen year−1) (3)
where Gis the nitrogen gradient (kg N m−3m−1) over the pycnocline. We consider the
nutricline at Station ALOHA (22◦450N 158◦W) and average publicly available data col-
lected during six Hawaiian Ocean Time-Series research cruises throughout 2008 (Karl
et al., 2001). We are interested here in nitrogen transport into the euphotic zone and25
so consider the change in nitrogen levels across the 0.1% light level, which occurs at
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approximately 125 m depth (Buesseler et al., 2008). Sperm whales pass through this
depth as they descend 300 m to 800 m on foraging dives (Whitehead, 2003). We ex-
amine recorded nitrogen concentrations measured immediately above the 125m depth
(measurements were taken at depths ranging from 60 m to 121 m) and immediately be-
low the 125 m depth (ranging from 125 m to 161 m) (Karl et al., 2001). After calculating5
the change over the 0.1 % light level for each of the six cruises (Table 1), we then aver-
aged these to obtain a gradient of 0.015 µmol nitrogenkg−1m−1which is equivalent to
a gradient of G=2.2 ×10−7kg nitrogen m−3m−1.
3.3 Carbon fixation
The nitrogen flux into the euphotic zone can be used to estimate the amount of primary10
productivity that would be stimulated as a result of biomixing by sperm whales. The
Redfield ratio is used to conservatively (Sambrotto et al., 1993) estimate the amount
of carbon fixed in response to the nitrogen mixed into the euphotic zone by swimming
sperm whales. The Redfield ratio describes the stoichiometric ratio of carbon to nitro-
gen in phytoplankton cells as being 106 : 16 (Redfield, 1934).15
4 Results and discussion
4.1 Sperm whale mixing, nitrogen transport and primary production
The diapycnal diffusivity caused by each sperm whale moving through the base of the
euphotic zone is Ksw =10−6m2s−1. The flux of nitrogen transported into the euphotic
zone as a result of this diapycnal diffusivity is Nf=1.3 ×103kg of nitrogen per year20
per sperm whale which would in turn stimulate 7 ×103kg of primary production (car-
bon) per year. The overall contribution of 80 sperm whales to the nitrogen budget of
the Hawaiian euphotic zone along the whale path is 105kg nitrogen yr−1which would
stimulate production of 6 ×105kg carbon yr−1.
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The nitrogen flux resulting from sperm whales swimming through the pycnocline is
modest compared to the dominant modes of nitrogen flux into the Hawaiian photic
zone (Fig. 1). Within the 1010 m2whale path, sperm whales mix 105kg nitrogen yr−1
into the photic zone. In contrast, diatom (Rhizosolenia) mats migrate between surface
waters and the nitrate pools of the deep ocean and transport 3 ×106kg nitrogen yr−1
5
into the euphotic zone as they do so (Villareal et al., 1993). Nitrogen fixation along the
whale path results in an increase of 8 ×106kg nitrogen available to the euphotic zone
per year. Event mixing is the largest contributor of nitrogen along the whale path and
results in transport of 2 ×107kg nitrogen transported into the euphotic zone per year.
4.2 Ecosystem effects of nitrogen transport by sperm whales10
While the overall amount of nitrogen transported by sperm whales is moderate, sperm
whales spend 75 % of their time engaged in foraging (Whitehead, 2003) and spend only
7 % of each day sleeping (Miller et al., 2008) so their nutrient contribution to the photic
zone occurs throughout the day and night on an approximately hourly basis per whale.
This is in contrast to the other dominant modes of nitrogen transport which occur only15
during daylight hours for nitrogen fixation and nitrogen transport by Rhizosolenia mats,
or on average once per month for event mixing. Thus while nitrogen inputs from sperm
whales occur continuously, the nitrogen inputs from nitrogen fixation and migrating
diatom mats are absent for approximately 50% of the time, while nutrient inputs from
event mixing are absent for 95 % of the time (Fig. 2).20
Spatiotemporal consistency of nutrient supply to the photic zone can be as impor-
tant in determining the productivity of high trophic level fish stocks as the overall mag-
nitude of primary production (Kioboe, 1993). Phytoplankton have little ability to store
nutrients (McCarthy and Goldman, 1979) and so the consistent, albeit low, levels of
nutrient inputs that occur as a result of sperm whale-induced diapycnal mixing may25
allow phytoplankton to survive periods when other sources of nutrients are absent.
When background levels of nutrients are undetectable, phytoplankton are particularly
proficient in exploiting spikes of nutrients (McCarthy and Goldman, 1979) by increasing
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their nitrogen affinity to quickly utilise a nutrient pulse at rates greater than the steady
growth rate (Raimbault and Gentihomme, 1990). The low levels of nitrogen introduced
by swimming sperm whales are thus likely to be assimilated quickly and efficiently into
phytoplankton cells where they can contribute to ecosystem productivity.
Sperm whales likely mix nutrients directly into the deep chlorophyll maximum and5
the high numerical density of phytoplankton cells in the deep chlorophyll maximum
may mean that nutrients are quickly taken up by phytoplankton and that subsequently
there is rapid stimulation of primary production. The deep chlorophyll maximum is lo-
cated immediately above the pycnocline in the Hawaiian ocean (Huisman et al., 2006).
Mixing by whales is likely to be effective at supplying the deep chlorophyll maximum10
with nutrients directly, in contrast to nitrogen fixation which occurs higher in the water
column, and event mixing which likely disrupts the deep chlorophyll maximum. Whales
thus deliver nutrients to an area rich in phytoplankton cells which can quickly exploit
the nutrient pulse (McCarthy and Goldman, 1979).
The reduction of sperm whale populations as a result of historical exploitation may15
have reduced the amount of new nitrogen entering the euphotic zone of the Hawaiian
Ocean by reducing whale-induced diapycnal mixing. Worldwide, sperm whale popula-
tions have been reduced to approximately 32 % of their historical abundances by com-
mercial whaling (Whitehead, 2002). Assuming this is true for the Hawaiian area, histor-
ical sperm whale populations in Hawaii would have once numbered approximately 250.20
The larger sperm whale populations of the past would have increased diapycnal diffu-
sivity and stimulated the flux of 3 ×105kg nitrogen yr−1into the euphotic zone. Thus,
the Hawaiian ocean has essentially lost 2 ×105kg of new nitrogen per year as a result
of commercial whaling and this has likely decreased primary production in the region
by 106kg carbon per year.25
Here we have examined the influence of biomixing by a low density population of
sperm whales in Hawaii and find that the resulting nitrogen flux is modest compared to
the dominant modes of nitrogen flux in the area. However, the methodology introduced
here can be easily adapted to determine the contribution of other marine mammals to
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diapycnal mixing. Densities of whales in areas such as foraging grounds can be four
orders of magnitude greater than sperm whale densities considered here (Nowacek
et al., 2011) and this would dramatically increase the amount of diapycnal mixing and
the resultant flux of nutrients into the euphotic zone. Sperm whales mix nutrients into
the deep chlorophyll maximum throughout the day and night and the consistency of5
this nutrient input may increase the importance of these nutrients to primary producers
above that indicated by examining the magnitude of nitrogen inputs alone. This find-
ing adds to a growing body of knowledge regarding the top-down influence of marine
mammals on the nutrient budgets of marine and coastal ecosystems. Whales influence
the flux of nutrients in the marine ecosystem by excretion and defecation of nutrients10
(Smetacek, 2008; Nicol et al., 2010; Roman and McCarthy, 2010; Lavery et al., 2010,
2012a and b), the sinking of their carcass after death (Smith, 1985) and likely via tilling
of the ocean floor during foraging (Hans Nelson and Johnson, 1987). Here we added
biomixing to these mechanisms and show that it is a source of low magnitude but high
frequency nitrogen flux to the euphotic zone of the Hawaiian ocean.15
Acknowledgements. This publication utilises nutrient profiles obtained from Hawaiian Ocean
Time-series observations supported by the US National Science Foundation under Grant OCE-
0926766. The authors thank Victor Smetacek and Mark Doubell for helpful discussions. Tr-
ish Lavery was supported during this research by an Australian Postgraduate Award Scholar-
ship.20
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Table 1. Data obtained from the Hawaiian Ocean Time-Series and used to estimate the nitro-
gen gradient over the 0.1% light level which represents the base of the euphotic zone in the
Hawaiian ocean.
Identification Depth Nitrogen Gradient
number (m) concentration µmol N kg−1m−1
µmol N kg−1m−1
HOT 199 70 0.16 0.02
125 1.26
HOT 200 60 0.08 0.11
126 0.78
HOT 202 102 0.11 0.011
135 0.47
HOT 203 121 0.19 0.007
161 0.46
HOT 204 112 0.06 0.0141
149 0.58
HOT 205 122 0.45 0.029
154 1.37
Average gradient 0.015
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Fig. 1. The flux of nitrogen into an area of 104km2in the Hawaiian ocean as a result of diapycnal
mixing by sperm whales, migration of diatom mats, nitrogen fixation and event mixing.
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Fig. 2. A comparison of the magnitude and frequency of nitrogen inputs into the photic zone of
the Hawaiian ocean as a result of diapycnal mixing by sperm whales, migration of diatom mats,
nitrogen fixation and event mixing.
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