ANALYSISOFTHEEFFECT OFSMALL-SCALETURBULENCE ONTHEPHYTOPLANKTONDYNAMICS INTHEOPENOCEAN ModelingandNumericalSimulation intheVerticalDimension Jesu´ sE.GabaldonCasasayas Universitat Politecnica` de Catalunya Departament de F´ısica Aplicada ANALYSISOFTHEEFFECT OFSMALL-SCALETURBULENCE ONTHEPHYTOPLANKTONDYNAMICS INTHEOPENOCEAN ModelingandNumericalSimulation intheVerticalDimension Jesu´ sE.GabaldonCasasayas Ph.D.Dissertation Directedby:Dr.Jose´ ManuelRedondo Universitat Politecnica` de Catalunya Departament de F´ısica Aplicada “Life began in the ocean, and most of the many forms of life that ever existed on Earth lived, or still live, in the ocean.1” “But the upcoming days are the wisest witness of Truth.2” 1 Grant (1933). 2 Pindar, V b.C. CONTENTS Aknowledgments 1 Part I Introduction 3 Part II Methodological Background 15 1. Physical Framework :::::::::::::::::::::::::::::: 17 1.1 TheConservationEquation......................... 17 1.1.1TheAdvectionTerm........................19 1.1.2TheDiffusionTerms........................19 1.1.3TheSedimentationTerm......................20 1.1.4 AnOverallTransportTerm..................... 20 1.2GoverningEquations............................20 1.3 FurtherBio-PhysicalConsiderations.................... 21 1.3.1 DiffusionTransport......................... 21 1.3.2 SedimentationTransport...................... 23 1.4 TurbulentDiffusionTransport&PhytoplanktonDynamics........ 23 2. Concepts in Turbulence :::::::::::::::::::::::::::: 25 2.1 “What’sTurbulence?”........................... 25 2.1.1 DefinitionandCharacteristics................... 25 2.1.2 MolecularViscosityandTurbulentDiffusivity........... 28 2.2Two-DimensionalPhenomena.......................29 2.3CharacteristicScalesofTurbulence.....................29 2.3.1LengthScales............................29 2.3.2TimeScales.............................30 3. Turbulent Diffusion & Mixing in the Ocean :::::::::::::::::: 33 3.1 VerticalTransportofMatter........................ 34 3.2ParameterizationofTurbulentDiffusion..................35 3.2.1 TheBalanceofTurbulentKineticEnergy............. 36 3.2.2TheDissipativeMethod......................39 3.2.3 ParameterizationofOsborn.................... 39 3.2.4 ParameterizationofGaspar,Gregori´ sandLefevre......... 41 XIV Contents 3.3ADirectEstimationoftheTKEDissipation................42 4. Small-scale Mass Transport :::::::::::::::::::::::::: 45 4.1 DICTransportwithinPhytoplanktonicDBLs............... 47 4.2 NutrientFluxes&AbundanceofOrganisms................ 51 5. Modeling Photosynthesis :::::::::::::::::::::::::::: 55 5.1 Photosynthesisvs.Irradiance........................ 55 5.1.1 TemperatureandPhotosynthesis.................. 57 5.2 Bio-opticalModelsofPhytoplanktonicCFixation............. 57 5.2.1 LightAbsorptionbythePhytoplankton.............. 58 5.2.2 TheQuantumYield,φ.......................60 5.2.3 TheMaximumQuantumYield,φm .................61 6. The Biological Model ::::::::::::::::::::::::::::: 63 6.1 PrecedingStudies.............................. 64 6.2ModelDescription.............................65 6.2.1StateVariables...........................66 6.2.2FluxesofMatter..........................68 6.3OverviewoftheDrivingEquations.....................72 Part III Solving 73 7. Solution of the Governing Equations :::::::::::::::::::::: 75 7.1DiscretizationSchemes...........................75 7.1.1TheAdvectionTerm........................76 7.1.2TheDiffusionTerm.........................77 7.1.3TheBiologicalTerm........................78 7.2 CouplingtheBiologicalandPhysicalTerms................ 79 7.2.1ConvergenceCriteria........................79 Part IV Results 81 8. Dynamics of the Biological System :::::::::::::::::::::: 83 8.1PhotosyntheticalParameters........................83 αB βB B 8.1.1 , andPmax ParameterValues.................83 8.2 InitialValues................................ 85 8.3 BoundaryConditionsandForcing..................... 86 8.3.1 DiffusionTransportofNutrients.................. 86 8.3.2Temperature............................86 8.3.3 IrradianceSeries.......................... 86 8.4Results....................................87 Contents XV 8.4.1 CarbonDynamics.......................... 87 8.4.2NutrientDynamics.........................89 8.4.3 TheNutritionalStatusofthePhytoplankton............90 8.4.4 Day&NightBalancedMatterFlows. AnOverallAnalysisoftheBiologicalModel........... 93 8.4.5 TemperatureRegulationofCarbonandNitrogenFlows...... 97 8.4.6 TemperatureandtheNutritionalStatus..............100 9. Mass Transport within Diffusive Boundary Layers ::::::::::::::: 101 9.1 TransportofCarbon.............................101 9.2 TransportofNitrogenandPhosphorus...................102 9.3 OverallMassTransportwithinPhytoplanktonicDBLs...........105 10. Dynamics of the Physical-Biological System ::::::::::::::::: 109 10.1EnvironmentalSetup............................110 10.1.1TheBiologicalStateVariables...................111 10.1.2ParameterField...........................111 10.2Forcing...................................111 10.2.1LightField.............................112 10.2.2VerticalTurbulentDiffusionTransport...............112 10.3Results....................................119 10.3.1CarbonFixation..........................119 10.3.2OperationalQuantumYield....................120 10.3.3StateVariables...........................123 10.3.4VerticalC:NFluxRatios......................125 Part V Final Discussion & Conclusions 127 Part VI Appendixes 133 Appendix 135 A. Dataset and Forcing Time Series :::::::::::::::::::::::: 137 A.1Temperature,SalinityandDensity.....................137 A.2Chlorophylla................................139 A.3Nitrate....................................139 A.4Irradiance..................................139 A.4.1CalibrationoftheUnderwaterLightField.............140 A.5TurbulentDiffusionCoefficients......................140 A.6Dataset(Plots)................................140 XVI Contents B. Parameter Values :::::::::::::::::::::::::::::::: 149 C. Vertical attenuation values of chlorophyll a :::::::::::::::::: 151 D. Deduction of General Quantum Yield Equations :::::::::::::::: 153 Part VII References 155 AKNOWLEDGMENTS Besides all the people I ever talked with about science, I am very glad to express my grat- itude to the people who directly, or indirectly, helped me in finding my niche in scientific research. I feel sincerely indebted to Dr. Antonio Cruzado, from the Centre d’Estudis Avanc¸ats de Blanes (CSIC), who gave me the first chance in entering the field of modelling of aquatic ecological processes. I shared with him more than two years of good humor and work. I want also to thank to Dr. Ramiro Varela, now at the Universidade de Vigo. Both they became my first teachers and partners in modelling and numerical simulation. As a matter of fact, this Ph.D. started in the CEAB’s atmosphere. In Blanes, I was also lucky to meet Dr. Tarzan Legovic,´ from the Rudjer Boskovic´ Institute (Zagreb, Croatia), and his wife Emine. I am indebted to their stimulating experi- ence, fine sense of humor and enthusiasm. In 1995 I moved to the Applied Physics Department, at the Universitat Politecnica` de Catalunya (UPC), where I initially found a suggesting atmosphere for developping my research work. There, I started my Ph.D. on the study of the influence of small-scale turbulence on phytoplankton dynamics. As a biologist, I want to thank the professors of the department not to make me feel like a stranger among them. I specially want to express my gratitude to Dr. Jordi Vila` Guerau de Arellano. I en- joyed luckily further than his friendship, but his real mastery and talent. He and Dr. Gerber van der Graaf, both contributed in building a creative environment in the Fluid Dynamics Reasearch Group. Their loss was painfully felt by the Group. I thank also Dr. Celia` Marrase´ and Dr. Marta Estrada, from the Institut de Ciencies` del Mar (CSIC), Barcelona, and Dr. Tim Granata, from the Centre d’Estudis Avanc¸ats de Blanes (CSIC)3, and Dr. Marta Alarcon, from the UPC. They provided me with data and, more than that, with their fruitful comments. Finally, my work was stimulated by the long stage (two years, almost) at the Lim- nologisches Institut from the Universitat¨ Konstanz, Germany. Its long-term biological and physical database of Lake Constance provided me with a deeper understanding of the biology of aquatic ecosystems. I also wish to thank Dr. Ursula Gaedke for giving me the oportunity of collabo- rating in the project Entwicklung eines dynamischen Simulationsmodells mit komplexer Nahrungsnetzstruktur fur¨ die Freiwasserzone mitteleuropaischer¨ Seen (Development of a dynamical simulation model with a complex food-web structure for the central-european 3 Now he is back to the Department of Civil and Environmental Engineering and Geodetic Science, at Ohio State University. lakes). I feel also indebted with Dr. Beatriz Vidondo for the “summer advice note”, and her fruitful conversations. I also keep very happy memories of a lot of friends who, somehow, positively influenced my work, among them: Dr. Thomas Gries, Dr. Tinus Wessels, Dr. Dietmar Straile, Angelika Siegfried, Markus Holzmann, Stefan Hoernchen, Karin Roggenbrodt, Kerstin Bitner, Christoph Wittkugel... In Catalonia, I do not forget mentioning Dr. Jordi Lopez,´ Ferran Paune,´ Cesar` Guitierrez´ and Oriol Mart´ı, for their long friendship and support. And, how could I (anybody) forget Maria Ozilea Bezerra Menezes; for the shared experiences at the Applied Physics department. Finally, this thesis was provided with data yielded by the next