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Oceanicturbulenceand
phytoplanktondynamics
HidekatsuYamazakiandhisteam
TokyoUniversityofMarineScienceandTechnology
by
MicroorganismsinTurbulentFlows,Feb8-12,2016
PhytoplanktonProducHon(PrimaryProducHon)
Nutrients
Light
Requires
Diatom
Dinoflagellate
Issues
• CellismoHle
• Turbulenceandmixing
• LightadaptaHon• HowdotheydistribuHoninspace?
MicrostructureProfiler
TemperatureTurbulentShear
Temperaturegradient
Patchystructure
TherateofkineHcenergydissipaHon(ε)
Order10-8~10-7Wkg-1
Niskin
Fluorescence
Dep
th
ConvenHonalapproach
Howdotheyreallydistributeinspace?
ConvenHonalsamplingvs.microstructures
Deployment
CTDat0.1m/s(tethered)
TurboMAPat0.6m/s(freefall)
CTD/Seapoint
TurboMAP/LED
1maveragevaluesofCTD(red)andTurboMAP(blue)
IsthisresoluHonsufficient?SatoandYamazaki(2007)
ResoluHonislessthan2mm!
LaserChsensor
PatentNo.4904505RegistraHondate:January20,2012
TurboMAP-L
Twoshearprobes
FP07
CTD
3axisAccelerometer
LEDprobe
Laserprobe
FP07
P
Shearprobe
LED
Laser
C&T
Again,1maveragesagree!
―laser―SeaPoint―LED Niskin
Fluorescence[a.u.]
Dep
th[m
]
Mean
StandarddeviaHo
n
Comparison
ObservaHons
2005 2011 Ohtsuchibay�
LakeBiwa�
Setoinlet�
Sagamirivermouth�
Ararivermouth�
Tokyobay
Kuroshioextension�
SantaBarbarachannel
Alldata
Mean
SD
0 10 20 30
10
20
30
40
50
60
70
80
90
100C hlorophylllaser[µg/L ]
10 15 20
10
20
30
40
50
60
70
80
90
100
T [C o]-5 0 5
10
20
30
40
50
60
70
80
90
100
S hear1[s-1]0 10 20 30C hlorophyllL E D[µg/L ]
24 25 26σθ
33 34 35S alinity[psu]
-12 -10 -8 -6ε
0 10 20 30C hlorophyllL E D[µg/L ]
33 34 35S alinity[psu]
24 25 26σθ
-12 -10 -8 -6ε
0 10 20 30
10
20
30
40
50
60
70
80
90
100
Dep
th[m
]
C hlorophyllL aser[µg/L ]
10-1
100
101
10210
-5
10-4
10-3
10-2
10-1
100
101
cpm
power
powerspectrum
�
�
laserLE Dk-5/3
1m<
1m>
k-5/3
Spectra
White!
Fluorescencesignalpdf LED Laser
0 10 20 30
10
20
30
40
50
60
70
80
90
100
Dep
th[m
]
C hlorophyllL aser[µg/L ]
Laser and LED show different pdf.
fluorescence:lognormalpdf
KS test at5 Laser× LED
Sato&Yamazaki,2008
Laserfluorescence:Gumbelpdf
⎥⎦
⎤⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
⎟⎠
⎞⎜⎝
⎛ −−−
⎭⎬⎫
⎩⎨⎧
⎟⎠
⎞⎜⎝
⎛ −−=
θµ
θµ
θxx
xf expexpexp1
)(
KStest5Laser
PatchdistribuHon
0 10 20 30 40 50
23
23.05
23.1
23.15
23.2
C hlorophyllprofile
C hlorophyll[µg/l]
Dep
th[m
]
�
�
LaserLE DMean
Threshold 10μg/
0 10 20 30 40 50 60
22
22.5
23
23.5
24
24.5
25
25.5
26
26.5
27
C hlorophyllprofile
C hlorophyll[µg/l]
Dep
th[m
]
�
�
LaserLE DP eak
#ofPatch 169
λ mean 29.6mm
0 50 100 1500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance(k)[mm]
P(X≤k)c
df
C DF P eaktoP eakD istancelaser&P oisson
�
�
LaserC hlorophyllP oissonprocess
#ofpatch 169
λ mean 29.6mm
Threshold 5μg/
0 10 20 30 40 50 60
22
22.5
23
23.5
24
24.5
25
25.5
26
26.5
27
C hlorophyllprofile
C hlorophyll[µg/l]
Dep
th[m
]
�
�
LaserLE DP eak
#ofpatch 272
λ mean 18.4mm
PatchdistribuHonISNOTPoisson!
0 20 40 60 80 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance(k)[mm]
P(X≤k)c
df
C DF P eaktoP eakD istancelaser&P oisson
�
�
LaserC hlorophyllP oissonprocess
#ofpatch 272
Λ mean 18.4mm
42mm
33mm
Amini-camerasystem
Doubelletal.(2009)
DigitalSHllLogger
119mm22mm
LEDfluorescencesensor
DSL
TurboMAP-L
(DSLcamera)
Lightsource LED
Max.depth 190m(m)
Samplingrate 5(Hz)
Samplingvolume 32(μL)
ResoluBon 59(μm)
EffecBvepixels 1024*1280(pixels)
Bio-loggingScience,TheUniv.ofTokyo
2cm
2cm
2cm
CameraDataProcessing
1. 340×340pixelcropping(area:2×2cm2)2. BluechannelextracHon3. Adjustmentofnon-uniformilluminaHon
4. BinaryimageproducHon
Whitearea>5pixels(ESDca.>120μm)
-SuspendedparHcleextracHon-ParHclepropertydeterminaHon
EquivalentdiameterMajoraxislengthMinoraxislengthNo.ofparHclesetc.
Method
Med.PatchIntensityDepth∼10.4m
High.PatchIntensityDepth∼11.1m
LowPatchIntensityDepth∼11.6m
depth(m
)TurboMAP:LED
chl-a(µg/l)∼1cm
∼1cm
∼1cm
TurboMAP-Lprofile
ε ParHclesize
SecJon1:TurbulenceandaggregaJon
ObservaBonfields
Obs.field Region Year #ofimage
Kuroshio09 Openwater 2009 21772
Kuroshio13 Openwater 2013 4187
Oshima Openwater 2013 2289
Miyake Openwater 2012 13238
Tokyobay Coast 2008 4860
Joga Coast 2011 5944
Tokyobay Coast 2012 18455
Otsuchi Coast 2013 4187
Tateyama Coast 2014 2491
Biwa Lake 2010 8466
1 2
7
10
43
5,6,8,9
0 10 20 30
10
20
30
40
50
60
70
80
90
100C hlorophylllaser[µg/L ]
10 15 20
10
20
30
40
50
60
70
80
90
100
T [C o]-5 0 5
10
20
30
40
50
60
70
80
90
100
S hear1[s-1]0 10 20 30C hlorophyllL E D[µg/L ]
24 25 26σθ
33 34 35S alinity[psu]
-12 -10 -8 -6ε
0 10 20 30C hlorophyllL E D[µg/L ]
33 34 35S alinity[psu]
24 25 26σθ
-12 -10 -8 -6ε
0 10 20 30
10
20
30
40
50
60
70
80
90
100
Dep
th[m
]
C hlorophyllL aser[µg/L ]
Laserprobe
SecJon1:TurbulenceandaggregaJon
Results–BiologicalpropertyofparBcles
Threshold
Resolvedaggregates?(Doubelletal.,2009)
Integratetheredarea
Integratedlaserfluorescenceintensity
Holographiccamera(HOLO)
DiatomchainAfewaggregatesetc.
ThecontentsofDSLimagedparHclesbackedupbyHOLObutnotenoughtoverifytheconsistencybetweenHOLO&DSL
WhataretheparHclesinthepics?
AnotherinstrumentinOshima
No.ofparHcles[cellsL-1]
Dep
th[m
]
MSS-HOLO LISST-HOLO DSLcamera
PlymouthUniv.HP.
Method
MSS-HOLO LISST-HOLO DSL
ImageresoluBon[µm] 11.5 25 120
Samplevolume[mm3] 451 780 8000
Fieldview[mm×mm] 5.2×3.5 7.0×5.3 20×20
Cameradepth[mm] 25 29 20
Samplingspeed[Hz] 5 1 5
MSSHOLO LISSTHOLO DSL
Commercialproduct
Method
Deploymentcontrolledbywinch Freefallmode
MSSHOLO LISSTHOLO DSL
2.ComparaHvestudies–HOLOandDSL
Results–parBcleabundance
Aggregateabundance(#/m3)
MSS-HOLO LISST-HOLO DSL
21.8 108.3 145.8
≈1.5×LISST-HOLO≈7×MSS-HOLO
DSL
MSSHOLO LISSTHOLO DSL
HigherresoluBons LowerresoluBon
DSLresultsexplained…
AggregaBon DisaggregaBon
Slope≈-2 Slope≈-4
Kolmogorovscale
―laser―SeaPoint―LED Niskin
Fluorescence[a.u.]
Dep
th[m
]
Mean
StandarddiviaHo
n
Comparison
Whatwegoaboutthisreality?
Conventional NP ecosystem model State variables
N: Nutrients P: Phytoplankton
Transfer functions Phytoplanktonresponsetolight
Phytoplanktonnutrientuptake
Lossrateduetodeath
Model equations
46
47
Choice of transfer functions f (I ) =C
g(N ) = NK + N
i(P) = D
Model equations
N + P = Constant�
Inreality,observedvariablesarehighlyintermihentNNNPPP
ʹ+=
ʹ+=
0
0
48
NPclosuremodel
With,
'""
of mean and fluctuating component of P and N variables using closure approach, which is widely used in study of ocean dynamics.
Closure model
Putting (7) and (8) into equations (4-5) and applying the Reynolds averaging method in space (details are described in the Appendix A) we get the following set of equations for temporal variation of , , , and" (
(9)
(10)
(11)
(12)
(13)
In the formulation of these equations it is assumed that N and P variables follow joint lognormal probability distribution functions, which forces the third and all higher odd order fluctuating terms to vanish. We also ignored the fourth and higher order terms in this analysis to achieve simple closure. Here, the first two equations give the time evolution of mean terms, the next two equations give the time evolution of variance terms, and the last equation represents the evolution of the covariance term.
It is worth noting that whiles the sum of remains constant, in this case and both are temporally conserved quantities. Therefore, defining and the above 5 equations can be reduced to 3 equations as follows:
(14)
(15)
0P 0N >!< 2P >!< 2N >!!< PN
030
20
200
000
)()(PD
NKNPK
NKPNK
NKPNC
dtdP
!""#
$%%&
'
+
>(<!
+
>((<+
+=
030
20
200
000
)()(PD
NKNPK
NKPNK
NKPNC
dtdN
+!!"
#$$%
&
+
>'<(
+
>''<+
+(=
>!<"##$
%&&'
(
+
>!!<+
+
>!<=
>!< 22
0
0
0
20
2
2)(
2 PDNKPNPK
NKPNC
dtPd
>!!<+""#
$%%&
'
+
>!<+
+
>!!<(=
>!< PNDNKNPK
NKPNNC
dtNd 2
)(2 2
0
20
0
02
)(
)()()(
2
20
20
0
20
>!!<">!<+
##$
%&&'
(
+
>!!<">!<+
+
>!<">!!<=
>!!<
PNPD
NKPNNPK
NKPPNNC
dtPNd
PN + 00 PN +
>!!<+>!<+>!< PNPN 222
APN =+ 00 BPNPN =>!!<+>!<+>!< 222
030
20
20
22
0
000
)}({)}({2)(
)()( PD
PAKNPK
PAKPNBK
PAKPPAC
dtdP
!""#
$%%&
'
!+
>(<!
!+
>(<!>(<!+
!+
!=
>!<"##$
%&&'
(
"+
>!<">!<"+
"+
>!<"=
>!< 22
0
220
0
20
2
2)}({2
)()(
)(2 PD
PAKPNBPK
PAKPPAC
dtPd
0D—ClosureequaBons
N0 +P0 = A< !N 2 > + < !P 2 > +2 < !N !P > = B
β =BA2
49
Equations with dimensionless variables and parameters
)""
(16)
The above equations lie in five dimensional parameter spaces. By appropriately rescaling the equations with A and B, this dependency is reduced to three dimensionless parameters. The scaling factors and dimensionless parameters are given in Table 1, and the scaled equations can be written as follows:
(17)
(18)
(19)
With and .
The values of the scaled variables n0 and p0, corresponding to the variables N0 and P0 respectively lie between 0 and 1. Similarly, the values of x, y lies between 0 and 1 if the term z, which is associated with the covariance of the fluctuating components-, is positive. For negative covariance, the values of x, y can exceed 1. Now we define the normalized sum of variance and covariance as followed:
(20)
where, B is the variance of sum of and , and therefore, " value actually reflects the overall strength of the fluctuating components and modifies the model dynamics. Other dimensionless variables and parameters of the model equations (17-19) are described in table1. Similarly, the non-closure equation (6) can be reduced to the following form:
(21)
It is to be noted that for " = 0, equation (17) of the closure model reduces to equation (21), which corresponds to the non-closure model.
Table 1. Definition of different quantities used in the model and their dimensions.
Quantity Definition Dimension Scaling factor Dimensionless quantity
A Sum of Nitrate (approximately total nutrient)
µg N l-1 - -
)(
)}({)}({2)()(
2
22
20
20
0
220
2
>!<">!<"+
##$
%&&'
(
"+
>!<+
"+
>!<">!<"""=
>!<
PNBD
PAKNPK
PAKPNBPAC
dtNd
030
02
00
000
)}1({)}1({2)1(
)1()1(
ppkypk
pkyxk
pkpp
ddp
!""
#$
$+$
$+
$$+
$+
$=
xpkyxpk
pkxp
ddx
!"
2)}1({)1(
)1()1(
2 20
0
0
0 ##+
##+
#+
#=
)1()}1({
2)}1({)1()1(
20
0
0
0 yxpkypk
pkyxp
ddy
!!+!+
!!+
!!!!= "
#
100 =+ pn 12 =++ zyx
>!!< PN
222222 //)(/)2( ABAPNAPNPN =>!+!<=>!!<+>!<+>!<="
N ! P!
ppkpp
ddp
!"
##+
#=
)1()1(
)""
(16)
The above equations lie in five dimensional parameter spaces. By appropriately rescaling the equations with A and B, this dependency is reduced to three dimensionless parameters. The scaling factors and dimensionless parameters are given in Table 1, and the scaled equations can be written as follows:
(17)
(18)
(19)
With and .
The values of the scaled variables n0 and p0, corresponding to the variables N0 and P0 respectively lie between 0 and 1. Similarly, the values of x, y lies between 0 and 1 if the term z, which is associated with the covariance of the fluctuating components-, is positive. For negative covariance, the values of x, y can exceed 1. Now we define the normalized sum of variance and covariance as followed:
(20)
where, B is the variance of sum of and , and therefore, " value actually reflects the overall strength of the fluctuating components and modifies the model dynamics. Other dimensionless variables and parameters of the model equations (17-19) are described in table1. Similarly, the non-closure equation (6) can be reduced to the following form:
(21)
It is to be noted that for " = 0, equation (17) of the closure model reduces to equation (21), which corresponds to the non-closure model.
Table 1. Definition of different quantities used in the model and their dimensions.
Quantity Definition Dimension Scaling factor Dimensionless quantity
A Sum of Nitrate (approximately total nutrient)
µg N l-1 - -
)(
)}({)}({2)()(
2
22
20
20
0
220
2
>!<">!<"+
##$
%&&'
(
"+
>!<+
"+
>!<">!<"""=
>!<
PNBD
PAKNPK
PAKPNBPAC
dtNd
030
02
00
000
)}1({)}1({2)1(
)1()1(
ppkypk
pkyxk
pkpp
ddp
!""
#$
$+$
$+
$$+
$+
$=
xpkyxpk
pkxp
ddx
!"
2)}1({)1(
)1()1(
2 20
0
0
0 ##+
##+
#+
#=
)1()}1({
2)}1({)1()1(
20
0
0
0 yxpkypk
pkyxp
ddy
!!+!+
!!+
!!!!= "
#
100 =+ pn 12 =++ zyx
>!!< PN
222222 //)(/)2( ABAPNAPNPN =>!+!<=>!!<+>!<+>!<="
N ! P!
ppkpp
ddp
!"
##+
#=
)1()1(
No. of variables: 3 No. of parameters: 3
6 steady state solutions
We need the following conditions: 1) The solution is not at the boundary. 2) The solution has to be stable.
50
Only one such solution exists!
(k=0.6,ε=0.4)
PlotofBmevariaBonof‘phytoplankton’forboththemodelsatdifferentβ values(in0-D)
ThereexistsacriBcalvalueofβ(sayβ*)abovewhichpandp0aredifferent!
51
52
Same location at different seasons
Mean and SD of phytoplankton at different depths from model simulation
53
#,""
justifiable as we see the similar behaviour in small-scale observation of phytoplankton data as depicted in Figure 8.
In real observations we see the coefficient of variation to vary from less than one to greater than one (Figure 8). Here, in Figure 10, the diagonal line characterizes the points where the mean and standard deviation are equal, indicating that the coefficient of variation is equal to one along this line. From our model results we also see the coefficient of variation to vary on both sides of the diagonal line depending on the value of the parameter ". From this figure we are also observing that as " increases the coefficient of variation increases. If the total nutrient of the system- A is conserved then the change of " implies the change of fluctuating components of the system. Because " = B/A2, and B represents the variance of overall fluctuating components. Therefore, from our analysis we can say that as the variance of the overall fluctuating components of the system increases, the coefficient of variation increases. Figure 10. Plot of mean versus standard deviation (SD) of phytoplankton at different depths (each point corresponds to a particular depth) for 8 different " values. Both axes are normalized by the value of A (=2 µg N l-1). Here the depth profile is obtained by changing the parameter value C, which decreases as depth increases and other two parameters K and D are kept constant at 1.2 µg N l-1 and 0.135 day-1.
We have also observed that the parameter " is more sensitive to the coefficient of variation when the total nutrient (A) of the system is high. These mathematical observations imply that in a particular area of ocean with high total nutrient, spatial variation will be low for low " value and therefore, the coefficient of variation will be low. This may be the reason for low coefficient of variation at the mouth of the Ara River (figure 8 c). With the change of season
N0 +P0 = A< !N 2 > + < !P 2 > +2 < !N !P > = B β =
BA2
hemostimportantparameter:
GOTMandNPclosure
Mean and SD of phytoplankton at different depths from model simulation
#,""
justifiable as we see the similar behaviour in small-scale observation of phytoplankton data as depicted in Figure 8.
In real observations we see the coefficient of variation to vary from less than one to greater than one (Figure 8). Here, in Figure 10, the diagonal line characterizes the points where the mean and standard deviation are equal, indicating that the coefficient of variation is equal to one along this line. From our model results we also see the coefficient of variation to vary on both sides of the diagonal line depending on the value of the parameter ". From this figure we are also observing that as " increases the coefficient of variation increases. If the total nutrient of the system- A is conserved then the change of " implies the change of fluctuating components of the system. Because " = B/A2, and B represents the variance of overall fluctuating components. Therefore, from our analysis we can say that as the variance of the overall fluctuating components of the system increases, the coefficient of variation increases. Figure 10. Plot of mean versus standard deviation (SD) of phytoplankton at different depths (each point corresponds to a particular depth) for 8 different " values. Both axes are normalized by the value of A (=2 µg N l-1). Here the depth profile is obtained by changing the parameter value C, which decreases as depth increases and other two parameters K and D are kept constant at 1.2 µg N l-1 and 0.135 day-1.
We have also observed that the parameter " is more sensitive to the coefficient of variation when the total nutrient (A) of the system is high. These mathematical observations imply that in a particular area of ocean with high total nutrient, spatial variation will be low for low " value and therefore, the coefficient of variation will be low. This may be the reason for low coefficient of variation at the mouth of the Ara River (figure 8 c). With the change of season
At beta=0.1�
At beta=0.5�
At beta=1.0�
Same season at different locations
SimpleNPZModel
Z
NP
65
f (I ) = vmax
g(N ) = NK + N
i(P) =Mh(z) = R Pj(z) =G
ModelequaBons
dNdT
= −vmaxN
K + NP +M P +γ R PZ +G Z
dPdT
= vmaxN
K + NP −M P − R PZ
dZdT
= (1−γ ) R PZ −G Z
N +P + Z = A
Inreality,observedvariablesarehighlyintermihent
P = P0 (s, t)+ !P (s, t)N = N0 (s, t)+ !N (s, t)Z = Z0 (s, t)+ !Z (s, t)
66
Variable=Mean+FluctuaBngpart
WithassumpHon < P(s)>= P0 (s)
< N(s)>= N0 (s)< Z(s)>= Z0 (s)
< !P (s)>=< !N (s)>=< !Z (s)>= 0
ClosureEquaHons
67
dN0
dT= −vmax[
N0
K + N0
P0 −KP0
(K + N0 )3 < "N 2 > +
K(K + N0 )
2 < "N "P >]
+M P0 +γR [P0Z0+ < "P "Z >]+G Z0dP0dT
= vmax[N0
K + N0
P0 −KP0
(K + N0 )3 < "N 2 > +
K(K + N0 )
2 < "N "P >]
−M P0 − R [P0Z0+ < "P "Z >]dZ0dT
= (1−γ ) R [P0Z0+ < "P "Z >]−G Z0
P0 + Z0 + N0 = constant
Variance
68
12d < !N 2 >
dT= −vmax[
KP0(K + N0 )
2 < !N 2 > +N0
K + N0
< !N !P >]+M < !N !P >
+γR [Z0 < !N !P > +P0 < !N !Z >]+G < !N !Z >
12d < !P 2 >dT
= vmax[KP0
(K + N0 )2 < !N !P > +
N0
K + N0
< !P 2 >]
−M < !P 2 > −R [Z0 < !P 2 > +P0 < !P !Z >]12d < !Z 2 >dT
= (1−γ )R [Z0 < !P !Z > +P0 < !Z 2 >]−G < !Z 2 >
Co-variance
69
< !P 2 > + < !Z 2 > + < !N 2 > +2(< !N !P > + < !P !Z > + < !N !Z >) = constant
d < !N !P >dT
= vmax[KP0
(K + N0 )2 (< !N 2 > − < !N !P >)+ N0
K + N0
(< !N !P > − < !P 2 >)]
−M (< !N !P > − < !P 2 >)+G < !P !Z >
+ R [Z0 (γ < !P 2 > − < !N !P >)+P0 (γ < !P !Z > − < !N !Z >)]d < !P !Z >
dT= vmax[
KP0(K + N0 )
2 < !N !Z > +N0
K + N0
< !P !Z >]−M < !P !Z > −G < !P !Z >
+ R [Z0 ((1−γ )< !P 2 > − < !P !Z >)+P0 ((1−γ )< !P !Z > − < !Z 2 >)]d < !N !Z >
dT= −vmax[
KP0(K + N0 )
2 < !N !Z > +N0
k + N0
< !P !Z >]+M < !P !Z > +G(< !Z 2 > − < !N !Z >)
+ R [Z0 ((1−γ )< !N !P > +γ < !P !Z >)+P0 ((1−γ )< !N !Z > +γ < !Z 2 >)]
2 4 50
3
6
Non−closure model
Parameter r
Parameter k
Stability Region
0
2
4
6
k
r
k
r
0 1 2 3 4 50
2
4
6
k
r 0 1 2 3 4 5 k
r
Stability regionwhen β =1.0
Stabilityregionwhen β =2.5
Stability regionwhen β =3.0
Stability regionwhen β =2.0
0 2 4 6 8 100.5
1
1.5
2
2.5
3
3.5
4
Variability β
CV
CV for Phytoplankton
m=0.1
m=0.2
m=0.3
m=0.4
m=0.5
m=0.55
m=0.6
m=0.7
74
dNdt
= −vmaxN
k + NP +mP +γr P
kp +PZ + gZ
dPdt
= vmaxN
k + NP −mP − r P
kp +PZ
dZdt
= (1−γ )r Pkp +P
Z − gZ
HollingtypeIIZ-grazingrateinConvenBonalNPZmodel
dpdt=
(1− p− z)(k +1− p− z)
p− m p− r p(kp + p)
z
dz0dt
= (1−γ ) r p(kp + p)
z− g z
ConvenBonalNPZmodel:HollingtypeIIgrazingrate
75
dp0dt
=(1− p0 − z0 )(k +1− p0 − z0 )
p0 +k
(k +1− p0 − z0 )2β u− kp0
(k +1− p0 − z0 )3β x
− m p0 − r(p0
(kp + p0 )z0 +
kp(kp + p0 )
2β v−
kpz0(kp + p0 )
3β y)
dz0dt
= (1−γ ) r( p0(kp + p0 )
z0 +kp
(kp + p0 )2β v−
kpz0(kp + p0 )
3β y)− g z0
dxdt= 2(− (1− p0 − z0 )
(k +1− p0 − z0 )u− k p0(k +1− p0 − z0 )
2x + g2(1− x − y− z− 2u− 2v)
+ mu+ γ r[kp z0
(kp + p0 )2u+ p0(kp + p0 )
12(1− x − y− z− 2u− 2v)])
dydt= 2( (1− p0 − z0 )
(k +1− p0 − z0 )y+ k p0(k +1− p0 − z0 )
2u− m y− r(
kp z0(kp + p0 )
2y+ p0(kp + p0 )
v))
dzdt= 2((1−γ ) r (
kpz0(kp + p0 )
2v+ p0(kp + p0 )
z)− g z)
dudt=
(1− p0 − z0 )(k +1− p0 − z0 )
(u− y)+ kp0(k +1− p0 − z0 )
2(x −u)+ m (y−u)+ g v
+ r[kp z0
(kp + p0 )2(γ y−u)+ p0
(kp + p0 )(γ v− 1
2(1− x − y− z− 2u− 2v))]
dvdt=
(1− p0 − z0 )(k +1− p0 − z0 )
v+ kp0(k +1− p0 − z0 )
2
12(1− x − y− z− 2u− 2v)
− (m+ g)v+ r[kp z0
(kp + p0 )2{(1−γ ) y− v)}+ p0
(kp + p0 ){(1−γ )v− z}]
DimensionlessNPZClosuremodel:HollingtypeIIgrazingrate
MeanEqns
VarianceEqns
CovarianceEqns
r = 0.5,m = 0.3,k = 0.5,g = 0.15,kp =1.0,γ = 0.3
CoefficientofVariaBonofphytoplankton(CV)
CVwithvaryingbetavalueoveraparameter
77
NPZLinear
0 1 2 3 4 50
2
4
6k
Conventional NPZ
r 0 1 2 3 4 5
k
NPZ Closure (β = 1.0)
r
0 1 2 3 4 50
2
4
6
k
NPZ Closure (β = 2.0)
r 0 1 2 3 4 5 k
r
NPZ Closure (β = 3.0)
a b
c d
78
0 1 2 3 4 5012345
k
Conventional NPZ
r 0 1 2 3 4 50
1
2
3
4
5
k
Closure (β=1.0)
r
0 1 2 3 4 5012345
k
Closure (β=2.0)
r 0 1 2 3 4 5012345
k
r
Closure (β=3.0)
NPZHollingtypeII
79
0 1 2 3 4 50
1
2
3
k
Conventional NPZ
r0 1 2 3 4 50
1
2
3
k
Closure (β = 0.5)
r
0 1 2 3 4 50
1
2
3
k
Closure (β = 1.0)
r0 1 2 3 4 50
1
2
3 k
r
Closure (β = 2.0)
a b
c d
NPZHollingtypeIII
Joint Environmental Data Integration System: JEDI System
JEDISystemHOMEPAGEhyp://www2.kaiyodai.ac.jp/~hide/JEDI/index.html
Oshima Coastal Environmental data Acquisition Network System (OCEANS)
Moving Platform MEMO-pen�
Openwebsite:hyp://www2.kaiyodai.ac.jp/~hide/JEDI
ConHnuousPlanktonImagingandClassificaHonSystem(CPICS)
Method� Get image
Resolution� 2,750 x 2,200 pixels Field of view� 11.0 x 15.0 x 2.0 mm Frame rate� 6 frames per second (Image volume: 7.12 L h-1) Particle size: Larger than ca. 50 µm
CPICS take particle images living or non-living and save it as ROI (Region Of Interest) image automatically. We sorted 50,578 images into 39 categories including 29 plankton categories. These 29 planktonic categories were pooled per day. And we calculated the Bray-Curtis dissimilarity index from 40 days data and did the cluster analysis. We calculated Shannon-Wiener’s diversity index.
1.6 m�
CPICS�
LED� CAMERA�
CPICS�
1. Trichodesmium spp.
4. Chaetoceros spp.
5. Eucampia spp.
6. Rhizosolenia robusta�7. Rhizosolenia spp.8. Other Diatoms
9. Calanoida
10. Cyclopoida11. Harpacticoida
2. Ceratium spp.
3. Noctiluca scintillans�
15. Copepoda Nauplius
18. Cumacea19. Isopoda
13. Poecilostomatoida14. Unidentified Copepoda
23. Other Crustacean
20. Ostracoda
Phytoplankton Zooplankton
27. Hydrozoa
28. Larvacea
29. Polychaeta
30.Benthic Algae31. Polyp
32. Fish33. Air bubble34. Unkown
37. Barnacle exuviae
38. Other crustacean exuviae
35. Marine snow
36. Fecal pellet
39. Mineral grain24. Aulosphaera ��trigonopa�
Benthic species
Others
Particles
12. Monstrilloida
16. Decapoda
17. Amphipoda
26. Chaetognatha
25. Other Radiolaria
21. Mysida
22. Cypris Larva
1 2 3 4 5 7Term 6
Fig. 5. Significant wave height (m) and seven terms set in the present study.
0 1 2 3 4 5 6 7
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
Sign
ifica
nt w
ave
heig
ht (m
)
30
T1418 T1419Low pressure
Phytoplankton 4,148, 9%
Zooplankton 5,254, 12%
Benthic Species 237, 0%
Fish 3,075, 7% Particle
31,385, 69%
Air bubble 249, 1%
Unkown 1,423, 3%
Marine snow, 20,538, 66% Fecal pellet,
1,875, 6%
Barnacle exuviae, 136, 0%
Other crustacean
exuviae, 1,041, 3%
Mineral grain, 7,795,
25%
Composition of ParticleTrichodesmiu
m spp., 119, 3%
Ceratium spp., 60, 1%
Noctiluca scintillans, 239, 6% Chaetoceros
spp., 366, 9%
Eucampia spp., 1,035,
25%
Rhizosolenia robusta, 257, 6%
Rhizosolenia spp., 293, 7%
Other Diatoms,
1,779, 43%
Composition of Phytoplankton
Composition of all categories
Fig. 2. Composition of ROI images obtained with CPICS in the present study.�
0
100
200
300
400
500
600
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
Cou
nts p
er h
our
Fig. 6. Temporal change in the number of obtained ROI images per hour for phytoplankton (a), zooplankton (b) and particles (c).�
c
b
a
30
T1418 T1419 Phytoplankton
Zooplankton
Particle
Low pressure
0
2
4
6
8
10
12
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
0
100
200
300
400
500
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
0
2
4
6
8
10
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
0
100
200
300
400
500
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
0
10
20
30
40
50
60
21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Sep Oct
3635
30 30
Cou
nts p
er h
our 37 38
39
T1418 T1419 T1418 T1419
30 30
30
Marine snow
Other crustacean exuviae
Barnacle exuviae
Fecal pellet
Mineral grain
Fig. 9. Temporal change in the number of obtained ROI images per hour for each non-living particle.�
Low pressure Low pressure
