1. LOICZ Biogeochemical Budgeting Procedures and Examples V Dupra and SV Smith Department of Oceanography University of Hawaii Honolulu, Hawaii 96822 vdupra@soest.hawaii.edu svsmith@soest.hawaii.edu

2. INTRODUCTION

3. Material budget System  outputs  inputs Net Sources or 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.

4. 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.

5. 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.

6. PROCEDURES AND EXAMPLES

7.  Locate system of interest Philippine Coastlines Resolution (1:250,000) http://crusty.er.usgs.gov//coast/

8.  Define boundary of the budget Subic Bay, Philippines Map from Microsoft Encarta Map from Microsoft Encarta

9. 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).

10. SIMPLE SINGLE BOX (well-mixed system)

11.  Calculate water balance dV syst /dt = V Q +V P +V E +V G +V O +V R V R = -(V Q +V P +V E +V G +V O ) at steady state:

12. Water balance illustration V P = 1,160V E = 680 V syst = 6 x 10 9 m 3 A syst = 324 x 10 6 m 2 V Q = 870 V G = 10 V R = -1,360 V R = -(V Q +V P +V E +V G +V O ) V R = -(870+1,160-680+10+0) V R = -1,360 x 10 6 m 3 yr -1 V O = 0 (assumed) Fluxes in 10 6 m 3 yr -1

13. V X = (-V R S R - V G S G )/(S Ocn – S Syst )  Calculate salt balance Eliminate terms that are equal to or near 0.

14. Salt balance to calculate V X and  V syst = 6 x 10 9 m 3 S syst = 27.0 psu S Q = 0 psu V Q S Q = 0 V R = -1,360 V R S R = -41,480 V X = (-V R S R -V G S G )/(S Ocn – S Syst ) S Ocn = 34.0 psu S R = (S Ocn + S Syst )/2 S R = 30.5 psu V X (S Ocn - S Syst ) = -V R S R -V G S G = 41,420 V X = (41,480 - 60 )/(34.0 – 27.0) V X = 5,917 x 10 6 m 3 yr -1   = V Syst /(V X + |V R |)   = 6,000/(5,917 + 1,360)   = 0.8 yr  300 days V X = 5,917  = 300 days S G = 6.0 psu V G S G = 60 Fluxes in 10 6 psu-m 3 yr -1

15.  Calculate non-conservative nutrient fluxes d(VY)/dt = V Q Y Q + V G Y G +V O Y O +V P Y P + V E Y E + V R Y R + V X (Y ocn - Y syst ) +  Y

16. System,Y Syst (  Y) River discharge (V Q Y Q ) Residual flux (V R Y R ); Y R = (Y Syst +Y Ocn )/2 Mixing flux (V X Y X ); Y X = (Y Ocn -Y Syst ) Ocean, Y Ocn Other sources (V O Y O ) d(VY)/dt = V Q Y Q + V G Y G + V O Y O +V P Y P + V E Y E + V R Y R + V X (Y ocn - Y syst ) +  Y 0 = V Q Y Q + V G Y G + V O Y O + V R Y R + V X (Y ocn - Y syst ) +  Y  Y = -V Q Y Q - V G Y G - V O Y O - V R Y R - V X (Y ocn - Y syst ) Schematic for a single-box estuary Eliminate terms that are equal to or near 0. Groundwater (V G Y G )

17. DIP balance illustration  Y = - V R Y R - V X (Y ocn - Y syst ) – V Q Y Q – V G Y G - V O Y O  DIP = - V R DIP R - V X (DIP ocn - DIP syst ) – V Q DIP Q - V G DIP G - V O DIP O  DIP = 544 - 2,367 – 261 –1 - 30 = -2,115 x 10 3 mole yr -1 DIP syst = 0.2  M DIP Q = 0.3 V Q DIP Q = 261 V R DIP R = -544 DIP Ocn = 0.6  M DIP R = 0.4  M V X (DIP Ocn - DIP Syst ) = 2,367  DIP = -2,115 DIP G = 0.1 V G DIP G = 1 V O DIP O = 30 (other sources, e.g., waste, aquaculture)  DIN = +15,780 x 10 3 mole yr -1 (calculated the same as  DIP) Fluxes in 10 3 mole yr -1

18. STOCHIOMETIC CALCULATIONS

19. Stoichiometric linkage of the non- conservative (  Y’s) 106CO 2 + 16H + + 16NO 3 - + H 3 PO 4 + 122H 2 O (CH 2 O) 106 (NH 3 ) 16 H 3 PO 4 + 138O 2 Redfield Equation (p-r) or net ecosystem metabolism, NEM = -  DIPx106(C:P) (nfix-denit) =  DIN obs -  DIN exp =  DIN obs -  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.

20. Stoichiometric calculations (p-r)= -  DIPx106(C:P) = -(-2,115) x 106 = +224,190 x 10 3 mole yr -1 = +2 mmol m -2 day -1 (nfix-denit) =  DIN obs -  DIN exp =  DIN obs -  DIPx16(N:P) = 15,780 – (-2,115 x 16) = +49,620 x 10 3 mole yr -1 = +0.4 mmol m -2 day -1 Note:Derived net processes are apparent net performance of the system. Other non-biological processes may be responsible for the some of the uptake or release of the  Y’s.

21. TWO-LAYER BOX (STRATIFIED SYSTEM)

22. Stratified system (two-layer box model)

23. Two-layer water and salt budget model Upper Layer S Syst-s Lower Layer S Syst-d V Q (Runoff) V Q S Q V Z (Volume Mixing) V Z (S Syst-d -S Syst-s ) V Deep’ (Entrainment) V Deep’ S Syst-d V Surf (Surface Flow) V Surf S Syst-s V Deep (Deep Water Flow) V Deep S Ocn-d S Ocn-d V Q +V P + V E + V Surf + V Deep' = 0 V Q S Q + V Surf S Syst-s + V Deep‘ S Syst-d + V Z (S Syst-d - S Syst-s ) = 0 VEVE VPVP

24. Two-layer budget equations V Q + V Surf + V Deep = 0 V Deep = V R' (S Syst-s )/(S Syst-s -S Ocn-d ) V R’ = -V Q -V P -V E V Z = V Deep (S Ocn-d -S Syst-d )/(S Syst-d -S Syst-s )  = V Syst /(|V Surf |) Note: Visit LOICZ website for detailed derivation of the above equations.

25. Water and salt budget for stratified system (illustration) Water flux in 10 6 m 3 day -1 and salt flux in 10 6 psu-m 3 day -1. Lower Layer V Syst-d = 55.0x10 9 m 3 S Syst-d = 31.2 psu  = 466 days S Q = 0.1 psu V Q = 10 V Q S Q = 1 V Z = 37 V Z (S Syst-d -S Syst-s ) = 122 V Deep’ = 81 V Deep’ S Syst-d = 2,527 V Surf = 95 V Surf S Syst-s = 2,650 V Deep = 81 V Deep S Ocn-d = 2,649 S Ocn-d = 32.7 psu V E = 0V P = 4 Aysen Sound Upper Layer V syst-s = 11.8x10 9 m 3 S Syst-s = 27.9 psu  = 89 days  Syst = 703 days

26. Two-layer nutrient budget model Upper Layer Y Syst-s  Y Syst-s Lower Layer Y syst-d  Y Syst-d River discharge (V Q Y Q ) Mixing flux (V Z (Y Syst-d -Y syst-s )) Entrainment flux( V Deep’ Y Syst-d ) Upper layer residual flux (V Surf Y Syst-s ) Lower layer residual flux (V Deep Y Ocn-d ) Ocean lower Layer, Y ocn-d  Y Syst = (  Y Syst-s +  Y Syst- d )

27. DIP balance for stratified system (illustration) Fluxes in 10 3 mole day -1. Lower Layer DIP Syst-d = 1.7  M  DIP = +32 DIP Q = 0.1  M V Q = 10 V Q DIP Q = 1 V Z = 37 V Z (DIP Syst-d -DIP Syst-s )=7 V Deep’ = 81 V Deep’ DIP Syst-d = 138 V Surf = 95 V Surf DIP Syst-s = 143 V Deep = 81 V Deep DIP Ocn-d = 113 DIP Ocn-d = 1.4  M Aysen Sound Upper Layer DIP Syst-s = 1.5  M  DIP = -3  DIP Syst = +29

28. COMPLEX SYSTEMS IN SERIES

29. Pelorus Sound, New Zealand Red dashed lines show segmentation of the system. N UpperPelorus LowerPelorus TawhitinuiReach HavelockArm KenepuruArm

30. Schematic of systems in series Segmentation for Pelorus Sound Budget.

31. Water balance for stratified systems in series Complex system like Pelorus Sound can be budgeted as a combination of single-layer and two-layer segments.

32. TEMPORAL AND SPATIAL VARIATION

33. 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, 0 Y = 1, 5, 50, 100 Systems should be segmented spatially or temporally if there is significant spatial and temporal variation. The algebraic reason is that in general the product of averages does not equal the average of the products. Visit the web site <http://data.ecology.su.se/MNODE/ Methods/spattemp.htm> for a more detailed explanation of this point.

34. Temporal patterns of the variables The 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

35. End