LOICZ Biogeochemical Budgeting Procedures and Examples

V Dupra and SV SmithDepartment of OceanographyUniversity of HawaiiHonolulu, Hawaii 96822vdupra@soest.hawaii.edusvsmith@soest.hawaii.edu

INTRODUCTIONINTRODUCTION

Material budget

System

outputs inputs

Net Sourcesor Sinks

[sources – sinks] = outputs - inputs

LOICZ budgeting assumes that materials are conserved. The difference ([sources – sinks]) of imported (inputs) and exported (outputs) materials may be explained by the processes within the system.

Note: Details of the LOICZ biogeochemical budgeting are discussed at http://www.nioz.nl/loicz and in Gordon et al., 1996.

Three parts of the LOICZ budget approach

1) Estimate conservative material fluxes (i.e. water and salt);

2) Calculate non-conservative nutrient fluxes; and

3) Infer apparent net system biogeochemical performance from non-conservative nutrient fluxes.

Outline of the procedure

I. Define the physical boundaries of the system of interest;

II. Calculate water and salt balance;

III. Estimate nutrient balance; and

IV. Derive the apparent net biogeochemical processes.

PROCEDURES AND EXAMPLES

Locate system of interest

Philippine CoastlinesResolution (1:250,000) http://crusty.er.usgs.gov//coast/

PhilippinesSouth China Sea

Luzon

Subic Bay

0 400 Kilometers

N

Define boundary of the budget

Subic Bay, PhilippinesSubic Bay, Philippines Map from Microsoft EncartaMap from Microsoft Encarta

Variables required

• System area and volume;• River runoff, precipitation, evaporation;• Salinity gradient;• Nutrient loads;• Dissolved inorganic phosphorus (DIP); • Dissolved inorganic nitrogen (DIN);• DOP, DON (if available); and• DIC (if available).

SIMPLE SINGLE BOX(well-mixed system)

Calculate water balance

dVsyst/dt = VQ+VP+VE+VG+VO+VR

VR = -(VQ+VP+VE+VG+VO)

at steady state:

Water balance illustration

VP = 1,160VE = 680

Vsyst = 6 x 109 m3

Asyst = 324 x 106 m2

VQ = 870

VG = 10

VR = -1,360

VR = -(VQ+VP+VE+VG+VO)

VR = -(870+1,160-680+10+0)

VR = -1,360 x 106 m3 yr-1

VO = 0 (assumed)

Fluxes in 10Fluxes in 1066 m m33 yr yr-1-1

VX = (-VRSR - VGSG )/(SOcn – SSyst)

Calculate salt balance

Eliminate terms that are equal to or near 0.Eliminate terms that are equal to or near 0.

Salt balance to calculate VX and

Vsyst = 6 x 109 m3

Ssyst = 27.0 psu

SQ = 0 psuVQSQ = 0

VR = -1,360VRSR = -41,480

VX = (-VRSR -VGSG)/(SOcn – SSyst)

SOcn = 34.0 psu SR = (SOcn+ SSyst)/2 SR = 30.5 psu

VX(SOcn- SSyst) = -VRSR -VGSG = 41,420

VX = (41,480 - 60 )/(34.0 – 27.0)

VX = 5,917 x 106 m3 yr-1

= VSyst/(VX + |VR|)

= 6,000/(5,917 + 1,360)

= 0.8 yr 300 days

VX = 5,917

= 300 daysSG = 6.0 psuVGSG = 60

Fluxes in 10Fluxes in 1066 psu-m psu-m33 yr yr-1-1

Calculate non-conservative nutrient fluxes

d(VY)/dt = VQYQ + VGYG +VOYO +VPYP + VEYE + VRYR + VX(Yocn - Ysyst) + Y

System,YSyst

(Y)

River discharge(VQYQ)

Residual flux(VRYR); YR = (YSyst+YOcn)/2

Mixing flux(VXYX); YX = (YOcn-YSyst)

Ocean, YOcn

Other sources (VOYO)

d(VY)/dt = VQYQ + VGYG + VOYO +VPYP + VEYE + VRYR + VX(Yocn - Ysyst) + Y

0 = VQYQ + VGYG + VOYO + VRYR + VX(Yocn - Ysyst) + Y

Y = -VQYQ - VGYG - VOYO - VRYR - VX(Yocn - Ysyst)

Schematic for a single-box estuary

Eliminate terms that are equal to or near 0.

Groundwater (VGYG)

DIP balance illustration

Y = - VRYR - VX(Yocn - Ysyst) – VQYQ – VGYG - VOYO

DIP = - VRDIPR - VX(DIPocn - DIPsyst) – VQDIPQ - VGDIPG - VODIPO

DIP = 544 - 2,367 – 261 –1 - 30 = -2,115 x 103 mole yr-1

DIPsyst = 0.2 M

DIPQ = 0.3VQDIPQ = 261

VRDIPR = -544

DIPOcn = 0.6 MDIPR = 0.4 M

VX(DIPOcn- DIPSyst) = 2,367

DIP = -2,115 DIPG = 0.1VGDIPG = 1

VODIPO = 30(other sources,e.g., waste, aquaculture)

DIN = +15,780 x 103 mole yr-1 (calculated the same as DIP)

Fluxes in 10Fluxes in 1033 mole yr mole yr-1-1

STOCHIOMETIC CALCULATIONS

Stoichiometric linkage of the non-conservative (Y’s)

106CO2 + 16H+ + 16NO3- + H3PO4 + 122H2O

(CH2O)106(NH3)16H3PO4 + 138O2

Redfield Equation(p-r) or net ecosystem metabolism, NEM = -DIPx106(C:P)

(nfix-denit) = DINobs - DINexp

= DINobs - DIPx16(N:P)

Where: (C:P) ratio is 106:1 and (N:P) ratio is 16:1 (Redfield ratio)

Note: Redfield C:N:P is a good approximation where local C:N:P is absent.

Stoichiometric calculations

(p-r)= -DIPx106(C:P)

= -(-2,115) x 106

= +224,190 x 103 mole yr-1

= +2 mmol m-2 day-1

(nfix-denit) = DINobs - DINexp

= DINobs - DIPx16(N:P)

= 15,780 – (-2,115 x 16)

= +49,620 x 103 mole yr-1

= +0.4 mmol m-2 day-1

Note:Note: Derived net processes are apparent net performance Derived net processes are apparent net performance of the system. Other non-biological processes may be responsible of the system. Other non-biological processes may be responsible for the some of the uptake or release of the for the some of the uptake or release of the Y’s. Y’s.

TWO-LAYER BOX(STRATIFIED SYSTEM)

Stratified system (two-layer box model)

Two-layer water and salt budget model

Upper LayerSSyst-s

Lower LayerSSyst-d

VQ (Runoff)

VQSQ

VZ (Volume Mixing)

VZ(SSyst-d-SSyst-s)VDeep’ (Entrainment)

VDeep’SSyst-d

VSurf (Surface Flow)

VSurfSSyst-s

VDeep (Deep Water Flow)

VDeepSOcn-d

SOcn-d

VQ +VP + VE + VSurf + VDeep' = 0

VQSQ + VSurfSSyst-s + VDeep‘SSyst-d + VZ(SSyst-d - SSyst-s) = 0

VE VP

Two-layer budget equations

VQ + VSurf + VDeep = 0

VDeep = VR'(SSyst-s)/(SSyst-s-SOcn-d )

VR’ = -VQ -VP -VE

VZ = VDeep(SOcn-d -SSyst-d)/(SSyst-d-SSyst-s)

= VSyst/(|VSurf|)

Note: Visit LOICZ website <http://data.ecology.su.se/MNODE/Methods/TWOLAYER.HTM> for detailed derivation of the above equations.

Water and salt budget for stratified system (illustration)

Water flux in 106 m3 day-1

and salt flux in106 psu-m3 day-1.

Lower LayerVSyst-d = 55.0x109 m3

SSyst-d = 31.2 psu = 466 days

SQ = 0.1 psuVQ = 10VQSQ = 1

VZ = 37VZ(SSyst-d-SSyst-s) = 122

VDeep’ = 81VDeep’SSyst-d = 2,527

VSurf = 95VSurfSSyst-s= 2,650

VDeep = 81VDeepSOcn-d = 2,649

SOcn-d = 32.7 psu

VE= 0 VP = 4

Aysen SoundUpper Layer

Vsyst-s = 11.8x109 m3

SSyst-s= 27.9 psu = 89 days

Syst = 703 days

Two-layer nutrient budget model

Upper LayerYSyst-s

YSyst-s

Lower LayerYsyst-d

YSyst-d

River discharge(VQYQ)

Mixing flux(VZ(YSyst-d-Ysyst-s))

Entrainment flux(VDeep’YSyst-d)

Upper layer residual flux(VSurfYSyst-s)

Lower layer residual flux(VDeepYOcn-d)

Ocean lower Layer, Yocn-d

YSyst = (YSyst-s+YSyst-d)

DIP balance for stratified system(illustration)

Fluxes in103 mole day-1.

Lower LayerDIPSyst-d = 1.7 M

DIP = +32

DIPQ = 0.1MVQ = 10VQDIPQ = 1

VZ = 37VZ(DIPSyst-d-DIPSyst-s)=7

VDeep’ = 81VDeep’DIPSyst-d = 138

VSurf = 95VSurfDIPSyst-s= 143

VDeep = 81VDeepDIPOcn-d = 113

DIPOcn-d = 1.4 M

Aysen SoundUpper Layer

DIPSyst-s= 1.5 MDIP = -3

DIPSyst = +29

COMPLEX SYSTEMS IN SERIES

Pelorus Sound, New Zealand

Red dashed lines show segmentation of the system.

NN

UpperUpperPelorusPelorus

LowerLower

PelorusPelorus TawhitinuiTawhitinuiReachReach

HavelockHavelockArmArm

KenepuruKenepuruArmArm

Schematic of systems in series

Segmentation for Pelorus Sound Budget.

Ocean

N

Lower Pelorus

Upper Pelorus

Havelock Arm

KenepuruArm

TawhitinuiReach

Beatrix, Clove Craig Bays

Water balance for stratified systems in series

Complex system likePelorus Sound can be budgeted as a combinationof single-layer and two-layer segments.

Pelorus Sound Steady-State Water Budget

0.2 0.7

0.6 1.4 0.8

0.7

266

2.4 2.1

2.6

76

116

1.4

3.4

2.4 10.5 3.6

480

15.1

12.9

590

470

19.3 19.3

893

20.0

19.3 48.0

47.3 31.5 47.3

944

2230

562.8 108.1

187.6

192.0

770 400

TEMPORAL AND SPATIALVARIATION

Implication of temporal and spatial variation

Products of the averages

= 5.5(39)

= 215

Averages of the products

= (15 + 30 + 50 +0)/4

= 24

X = 15, 6, 1, 0Y = 1, 5, 50, 100

Systems should be segmented spatially or temporally if there is Systems should be segmented spatially or temporally if there is significant spatial and temporal variation. The algebraic reasonsignificant spatial and temporal variation. The algebraic reasonis that in general the product of averages does not equal the average is that in general the product of averages does not equal the average of the products. Visit the web site <of the products. Visit the web site <http://data.ecology.su.se/MNODE/http://data.ecology.su.se/MNODE/Methods/spattemp.htmMethods/spattemp.htm> for a more detailed explanation of this point.> for a more detailed explanation of this point.

Temporal patterns of the variablesThe average of the nutrient flux does not equal to the product of the annual average flow and concentration. The budget based on the annual average data is simply not as accurate as the budget on the average fluxes.

Temporal gradients of variables will give clue to seasonal division of the data

End