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Utrecht University

Jack J. Middelburg

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marine biogeochemistry carbon cycle earth system science oceanography

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This book provides a primer on marine carbon biogeochemistry for earth system scientists. It offers a concise treatment of key concepts and focuses on marine biogeochemical processes impacting the cycling of particulate carbon, particularly organic carbon.

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SPRINGER BRIEFS IN EARTH SYSTEM SCIENCES Jack J. Middelburg Marine Carbon Biogeochemistry A Primer for Earth System Scientists SpringerBriefs in Earth System Sciences Series editors Gerrit Lohmann, Universität Bremen, Bremen, Germany Lawrence A. Mysak, Department of Atmospheric and Oceanic Scien...

SPRINGER BRIEFS IN EARTH SYSTEM SCIENCES Jack J. Middelburg Marine Carbon Biogeochemistry A Primer for Earth System Scientists SpringerBriefs in Earth System Sciences Series editors Gerrit Lohmann, Universität Bremen, Bremen, Germany Lawrence A. Mysak, Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, QC, Canada Justus Notholt, Institute of Environmental Physics, University of Bremen, Bremen, Germany Jorge Rabassa, Laboratorio de Geomorfología y Cuaternario, CADIC-CONICET, Ushuaia, Tierra del Fuego, Argentina Vikram Unnithan, Department of Earth and Space Sciences, Jacobs University Bremen, Bremen, Germany SpringerBriefs in Earth System Sciences present concise summaries of cutting-edge research and practical applications. The series focuses on interdisciplinary research linking the lithosphere, atmosphere, biosphere, cryosphere, and hydrosphere building the system earth. It publishes peer-reviewed monographs under the editorial supervision of an international advisory board with the aim to publish 8 to 12 weeks after acceptance. Featuring compact volumes of 50 to 125 pages (approx. 20,000–70,000 words), the series covers a range of content from professional to academic such as: A timely reports of state-of-the art analytical techniques bridges between new research results snapshots of hot and/or emerging topics literature reviews in-depth case studies Briefs are published as part of Springer’s eBook collection, with millions of users worldwide. In addition, Briefs are available for individual print and electronic purchase. Briefs are characterized by fast, global electronic dissemination, standard publishing contracts, easy-to-use manuscript preparation and formatting guidelines, and expedited production schedules. Both solicited and unsolicited manuscripts are considered for publication in this series. More information about this series at http://www.springer.com/series/10032 Jack J. Middelburg Marine Carbon Biogeochemistry A Primer for Earth System Scientists Jack J. Middelburg Department of Earth Sciences Utrecht University Utrecht, The Netherlands ISSN 2191-589X ISSN 2191-5903 (electronic) SpringerBriefs in Earth System Sciences ISBN 978-3-030-10821-2 ISBN 978-3-030-10822-9 (eBook) https://doi.org/10.1007/978-3-030-10822-9 Library of Congress Control Number: 2018965889 © The Editor(s) (if applicable) and The Author(s) 2019. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adap- tation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made. The images or other third party material in this book are included in the book’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the book’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publi- cation does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface Biogeochemistry, a branch of Earth System Sciences, focusses on the two-way interactions between organisms and their environment, including the cycling of energy and elements and the functioning of organisms and ecosystems. To this end, physical, chemical, biological and geological processes are studied using field observations, experiments, modelling and theory. The discipline of biogeochem- istry has grown to such an extent that sub-disciplines have emerged. Consequently, producing a single comprehensive textbook covering all aspects, e.g., terrestrial, freshwater and marine domains, biogeochemical cycles and budgets of the major biological relevant elements, reconstruction of biogeochemical cycles in the past, earth system modelling, microbiological, organic and inorganic geochemical methods, theory and models, has become unworkable. This book provides a concise treatment of the main concepts in ocean carbon cycling research. It focusses on marine biogeochemical processes impacting the cycling of particulate carbon, in particular organic carbon. Other biogeochemical processes impacting nitrogen, phosphorus, sulphur, etc., and the identity of the organisms involved are only covered where needed to understand carbon biogeo- chemistry. Moreover, chemical and biological processes relevant to carbon cycling are central, i.e. for physical processes, the reader might consult the excellent ocean biogeochemical dynamics textbooks of Sarmiento and Gruber (2006; Princeton University Press) and Williams and Follows (2011; Cambridge University Press). My text aims to provide graduate students in marine and earth sciences a conceptual understanding of ocean carbon biogeochemistry, so that they are better equipped to read palaeorecords, can improve carbon biogeochemical models and generate more accurate projections of the functioning of the future ocean. Because the book is targeted at students having a background in environmental and earth sciences, some basic biological concepts are explained. Some basic understanding of calculus is expected. Simple mathematical models are used to highlight the most important factors governing carbon cycling in the ocean. The material here is based on a selection of lectures in my Utrecht University master course on Microbes and Biogeochemical Cycles. This first draft of this book was written during a three-month sabbatical stay at Department of Geosciences, Princeton University (April–June 2018). I thank Bess Ward, chair of that department, for providing a desk and a stimulating environment. v vi Preface This sabbatical stay was supported by a travel grant from the Netherlands Earth System Science Centre. I thank Bernie Boudreau for carefully scrutinizing the initial draft, Mathilde Hagens and Karline Soetaert for feedback on Chap. 5 and Anna de Kluijver for remarks on Chap. 6. Ton Markus improved my draft figures. Finally, I thank my wife and publisher Petra van Steenbergen. Utrecht, The Netherlands Jack J. Middelburg Contents 1 Introduction........................................... 1 1.1 From Geochemistry and Microbial Ecology to Biogeochemistry................................... 3 1.2 Focus on Carbon Processing in the Sea.................... 4 1.3 A 101 Budget for Organic Carbon in the Ocean.............. 5 References............................................. 8 2 Primary Production: From Inorganic to Organic Carbon........ 9 2.1 Primary Producers................................... 10 2.2 The Basics (For Individuals and Populations)................ 11 2.2.1 Maximum Growth Rate (l)....................... 12 2.2.2 Temperature Effect on Primary Production............ 13 2.2.3 Light........................................ 16 2.2.4 Nutrient Limitation............................. 18 2.3 From Theory and Axenic Mono-Cultures to Mixed Communities in the Field.............................. 19 2.3.1 Does Diversity Matter or Not?..................... 19 2.3.2 Chl the Biomass Proxy.......................... 20 2.3.3 Light Distribution.............................. 20 2.4 Factors Governing Primary Production..................... 22 2.4.1 Depth Distribution of Primary Production............. 23 2.4.2 Depth-Integrated Production....................... 23 2.4.3 Critical Depths................................ 27 References............................................. 33 3 The Return from Organic to Inorganic Carbon................ 37 3.1 Carbon Consumption Pathway in the Euphotic Zone.......... 38 3.2 Factors Governing Export of Organic Matter................ 40 3.3 Particulate Organic Carbon Fluxes in Ocean Interior........... 42 References............................................. 54 4 Carbon Processing at the Seafloor.......................... 57 4.1 Organic Matter Supply to Sediments...................... 57 4.2 The Consumers..................................... 60 vii viii Contents 4.3 Organic Carbon Degradation in Sediments.................. 61 4.4 Consequences for Sediment Biogeochemistry................ 65 4.5 Factors Governing Organic Carbon Burial.................. 70 References............................................. 73 5 Biogeochemical Processes and Inorganic Carbon Dynamics....... 77 5.1 The Basics......................................... 77 5.2 The Thermodynamic Basis............................. 80 5.3 Analytical Parameters of the CO2 System.................. 82 5.4 Buffering.......................................... 85 5.5 Carbonate Mineral Equilibria............................ 89 5.6 Dissolved Inorganic Carbon Systematics................... 90 5.7 The Impact of Biogeochemical Processes................... 90 References............................................. 104 6 Organic Matter is more than CH2O......................... 107 6.1 Redfield Organic Matter............................... 107 6.2 Non-redfield Organic Matter............................ 109 6.3 Organic Matter is Food................................ 110 6.4 Compositional Changes During Organic Matter Degradation..... 112 References............................................. 117 Symbols B Biomass of phytoplankton or buffer value (Chap. 5) D Diffusion coefficient (area time−1); with Ds: diffusion of solutes in sediments, Db: particle mixing in sediments E Radiant energy (mol quanta area−1 time−1) EA Activation energy (J mol−1) F Flux of material (mol/gr area−1 time−1) G Quantity of organic carbon (mol/gr C per gr sediment, area or volume) k First-order rate/decay constant (time−1) kPAR Light extinction coefficient (length−1) K Half-saturation constant in Monod-type equation; KE: light saturation parameter; Kµ: growth (nutrient) half-saturation constant Kx Equilibrium constants (x = w, H, 1, 2) that depend on temperature, pressure and solution composition Kz Eddy-diffusion (mixing) coefficient in water column (area time−1) P Production (mol/gr volume−1 time−1) Q10 Increase in rate for 10 °C increase in T Q Cellular quota in Droop equation r First-order rate constant for phytoplankton (time−1) R0 Zero-order production or consumption term (mol/gr volume−1 time−1) t Time T Temperature (°C or K) w Particle settling in water column or sediment accumulation rate (length time−1) x Depth in sediment (length) z Depth in water column (length) zeu Euphotic zone depth (length) zc Compensation depth (length) where phytoplankton growth and respiration are equal zcr Critical depth (length) where phytoplankton production balances losses b Buffer value in terms of proton concentration btr Solute transfer coefficient at seafloor ix x Symbols / Porosity in sediment µ Maximum growth rate (time−1) h Maximum nutrient uptake q Dry density of particle (gr volume−1) w Carbon dioxide generated per unit carbonate precipitated Introduction 1 The name biogeochemistry implies that it is a discipline integrating data, knowl- edge, concepts and theory from biology, geosciences and chemistry. Biogeo- chemists extensively use approaches from a wide range of disciplines, including physical, chemical and biological oceanography, limnology, atmospheric sciences, ecology and microbiology, civil and environmental engineering, soil science and geochemistry. This diversity in scientific backgrounds stimulates cross-fertilization and research creativity, which are needed to elucidate the reciprocal relationships between living organisms and their environment at multiple scales during times of global change. Biogeochemistry aims to provide a holistic picture of natural ecosystem functioning. The challenge is to identify the right level of detail needed to understand the dynamics of elemental cycles and the functioning of biological communities. This implies that single-cell organism level studies and molecular orbital calculations of chemical reactions require upscaling to the appropriate temporal and spatial scale (often involving first-principle physics based models) to understand how natural ecosystems deal with perturbations and how life has shaped our planet. Although biogeochemistry developed as a full discipline in the mid-1980s with the launch of the international geosphere-biosphere program (IGBP, 1987) and the journals Biogeochemistry (1984) and Global Biogeochemical Cycles (1987), its roots can be traced back to early scientists documenting how living organisms transformed chemical substances, such as oxygen production during photosynthesis (Priestly, 1733–1804), phosphorus in organisms’ tissues (Lavoisier, 1743–1789) and nitrogen fixation by bacteria (Beijerinck, 1851–1931). Naturalist and avant-la-lettre multidisciplinary scientists, such as Alexander von Humboldt (1769– 1859). Charles Darwin (1808–1882) and Alfred Lotka (1880–1949), pioneered what we would recognize as biogeosciences in the 21st century. Darwins’ studies of atmospheric deposition, bioturbation and formation and sustenance of coral reefs are still key areas in modern biogeochemistry. The tight relationship between living organisms and their environment figured prominently in Lotka’s book “Elements of Physical Biology” (1925): “It is not so much the organism or the species that © The Author(s) 2019 1 J. J. Middelburg, Marine Carbon Biogeochemistry, SpringerBriefs in Earth System Sciences, https://doi.org/10.1007/978-3-030-10822-9_1 2 1 Introduction evolves, but the entire system, species and environment. The two are inseparable.” This concept that organisms shape the environment and govern elemental cycles on Earth underlies the biosphere concept of Vladimir Vernadsky (1863–1945), a geochemist and mineralogist, often considered the founder of biogeochemistry. G. Evelyn Hutchinson (1903–1991) was instrumental in establishing biogeo- chemical, whole-system approaches to study lakes. Alfred Redfield (1890–1983) discovered that nitrogen to phosphorus ratios of phytoplankton in seawater are constant and similar to dissolved ratios, implying co-evolution of the environment and organisms living in it. His seminal 1958 article started as follows “It is a recognized principle of ecology that the interaction of organisms and environment are reciprocal. The environment not only determines the conditions under which life exists, but the organisms influence the conditions prevailing in their environ- ment” (Redfield 1958). The latter was articulated in the Gaia hypothesis of Love- lock (1972): The Earth became and is maintained habitable because of multiple feedback mechanisms involving organisms. For instance, biologically mediated weathering of rocks removes carbon dioxide from the atmosphere and generates bicarbonate and cations that eventually arrive in the ocean, where calcifiers produce the minerals calcite and aragonite and release carbon dioxide back to the atmosphere. The above one-paragraph summary of the history of biogeochemistry does not mean that it was a linear or smooth process. While the early pioneers (before the second world war) were not hindered much by disciplinary boundaries between physics, biology, chemistry and earth sciences, the exponential growth of scientific knowledge and the consequent specialization and success of reductionism to advance science, had led to an under appreciation of holistic approaches crossing disciplinary boundaries during the period 1945–1990. Addressing holistic research questions may require development of new concepts and methods, but often involves application and combination of well-established theory or methods from multiple disciplines. The latter implies finding the optimal balance between biology, chemistry and physics to advance our understanding of biogeochemical processes. For instance, all biogeochemical models have to trade-off spatial resolution in the physical domain with the number of chemical elements/compounds and the diversity of organisms to be included. Ignoring spatial dimensions and hetero- geneity through the use of box models may seem highly simplistic to a physical oceanographer, but may be sufficient to obtain first-order understanding of ele- mental cycling. Similarly, organic carbon flows can be investigated via study of the organisms involved, the composition of the organic matter or by quantifying the rates of transformation, without considering the identity of the organisms involved. Each disciplinary approach has its strengths and weaknesses, and they are unfor- tunately not always internally consistent. However, this confrontation of different disciplinary concepts has advanced our understanding (Middelburg 2018). In the next section, we will discuss why many geochemists embraced biogeochemistry. 1.1 From Geochemistry and Microbial Ecology to Biogeochemistry 3 1.1 From Geochemistry and Microbial Ecology to Biogeochemistry Geochemistry is a branch of earth sciences that applies chemical tools and theory to study earth materials (minerals, rocks, sediments and water) to advance under- standing of the Earth and its components. While early studies focused on the distribution of elements and minerals using tools from analytical chemistry, the next step involved the use of chemical thermodynamics to explain and predict the occurrence and assemblages of minerals in sediments and rocks. The thermody- namic approach was and is very powerful in high-temperature systems (igneous rocks, volcanism, metamorphism, hydrothermal vents), but it was less successful in predicting geochemical processes at the earth surface. Geochemists studying earth surface processes soon realized that predictions based on thermodynamics, i.e. the Gibbs free energy change of a reaction, provided a necessary condition whether a certain reaction could take place, but not a sufficient constraint whether it would take place because of kinetics and biology. Realizing the limitations of the thermodynamic approach, the field of geo- chemical kinetics developed from the 1980s onwards (Lasaga 1998). Much pro- gress was made studying mineral precipitation and dissolution kinetics as a function of solution composition (e.g. pH) and environmental conditions (e.g., temperature). These laboratory studies were done under well constrained conditions and in the absence of living organisms. However, application of these experimentally deter- mined kinetic parameters to natural systems revealed that chemical kinetics often could not explain the differences between predictions based on chemical thermo- dynamics and kinetics, and observations in natural systems. These unfortunate discrepancies were attributed to the black box ‘biology’ or ‘bugs’. Before the molecular biology revolution, microbial ecology was severely method limited. Samples from the field were investigated using microscopy and total counts of bacteria were reported. Microbiologists were isolating a biased subset of microbes from their environment and studying their metabolic capabilities in the laboratory. To investigate whether these microbial processes occur in nature, microbial ecologists developed isotope and micro-sensor techniques to quantify rates of metabolism in natural environments (e.g., oxygen production or con- sumption, carbon fixation, sulfate reduction). These microbial transformation rates were of interest to geochemists because they represented the actual reaction rates, rather than the ones predicted from geochemical kinetics. Microbial ecologists and geochemists started to collaborate systematically and a new discipline emerged in which cross-fertilization of concepts, approaches and methods stimulated not only research questions at the interface but also in the respective disciplines. Stable isotope and organic geochemical biomarker techniques and detailed knowledge on mineral phases have enriched geomicrobiology, while knowledge on microbes and their capabilities and activities has advanced the understanding of elemental cycling. This integration of microbial ecology and geochemistry has evolved well regarding tools (e.g., the use of compound-specific isotope analysis and nanoSIMS 4 1 Introduction in microbial ecology for identity-activity measurements), but less so in terms of concepts and theoretical development. Moreover, there is more to biology than microbiology. Animals and plants have a major impact on biogeochemical cycles, not only via their metabolic activities (primary production, nutrient uptake, respi- ration), but also via their direct impact on microbes (grazing, predation) and their indirect impact via the environment (ecosystem engineering: e.g., bioturbation, soil formation). This additional macrobiological component of biogeochemistry is increasingly being recognized (Middelburg 2018). 1.2 Focus on Carbon Processing in the Sea This book focuses on biogeochemical processes relevant to carbon and aims to provide the reader (graduate students and researchers) with insight into the func- tioning of marine ecosystems. A carbon centric approach has been adopted, but other elements are included where relevant or needed; the biogeochemical cycles of nitrogen, phosphorus, iron and sulfur are not discussed in detail. Furthermore, the organisms involved in carbon cycling are not discussed in detail for two reasons. First, this book focuses on concepts and the exact identity of the organisms involved or the systems (open ocean, coastal, lake) is then less relevant. Secondly, our knowledge of the link between organism identity and activity in natural environments is limited. For instance, primary production rates are often quantified and phyto- plankton community composition is characterized as well, but their relationship is poorly known. The extent of particle mixing by animals in sediments can be quan- tified and the benthic community composition can be described, but the contribution of individual species to particle mixing cannot be estimated in a simple manner. The following chapters will respectively deal with production (Chap. 2) and consumption (Chap. 3) of organic carbon in the water column, the processing of organic carbon at the seafloor (Chap. 4), the impact of biogeochemical processes on inorganic carbon dynamics (Chap. 5), and the composition of organic matter (Chap. 6). The carbon cycle is covered using concepts, approaches and theories from different subdisciplines within ecology (phycologists, microbial ecologists and benthic ecologists) and geochemistry (inorganic and organics) and crosses the divides between pelagic and benthic systems, and coastal and open ocean. The book aims to provide the reader with enhanced insight via the use of very simple, generic mathematical models, such as the one presented in Box 1.1. Because of our focus on concepts, in particular the biological processes involved, there will be little attention to biogeochemical budgets and the role of large-scale physical processes in the ocean (Sarmiento and Gruber 2006; Williams and Follows 2011). Accurate carbon budgets are essential for a first-order understanding of biogeochemical cycles, but it is important to understand the mechanisms involved before adequate projections can be made for the functioning of System Earth and its ecosystems in times of change. To set the stage for a detailed presentation of biogeochemical processes, we first introduce a simple organic carbon budget for the ocean. 1.3 A 101 Budget for Organic Carbon in the Ocean 5 1.3 A 101 Budget for Organic Carbon in the Ocean Establishing carbon budgets in the ocean, in particular during the Anthropocene, is a far from trivial task, involving assimilation of synoptic remote sensing and sparse and scarce field observations with deep insight and numerical modelling of the transport and reaction processes in the ocean. The important processes and thus flows of carbon in the ocean are related to primary production, export of organic carbon from the surface layer to ocean interior, deposition of organic carbon at the seafloor and organic carbon burial in sediments. Accepting 25% uncertainty, these numbers are well constrained at 50 Pg C y−1 (1 Pg or 1 Gt is 1015 gr) for net primary production, 10 Pg C y−1 for export production, 2 Pg C y−1 for carbon deposition at the seafloor and 0.2 Pg C y−1 for organic carbon burial (Fig. 1.1). Although no detailed, closed complete carbon budgets will be presented, estimates for individual processes, including gross primary production, chemoautotrophy and coastal processes, are presented in the following chapters. However, the 50-10-2-0.2 rule for carbon produced, transferred to the ocean interior, deposited at Fig. 1.1 Simplified budget of carbon flows in the ocean. Each year net phytoplankton production is about 50 Pg C (1 Pg = 1 Gt = 1015 g), 10 Pg is exported to the ocean interior, the other 40 Pg is respired in the euphotic zone. Organic carbon degradation continues while particles settle through the ocean interior and only 2 Pg eventually arrives at the seafloor, the other 8 Pg is respired in the dark ocean. In sediments, the time scale available for degradation increases order of magnitude with the result that 90% of the organic carbon delivered is degraded and only 0.2 Pg C yr−1 is eventually buried and transferred from the biosphere to the geosphere 6 1 Introduction the seafloor and preserved in sediments, respectively, can easily be remembered and should be kept in mind when reading the details of carbon processing in the remaining of this book. Box 1.1: A simple mathematical model for reaction and transport In multiple chapters, we will make use of a very simple mathematical model in which the change in C (concentration, biomass) is due to the balance between diffusion (eddy Kz, molecular D), advection (sediment accretion particle/phytoplankton settling, w) and net effects of reactions (production and consumption). The basic equation is: @C @2C @C ¼D 2 w  kC þ R0 @t @x @x where @@Ct is the change in concentration (mol m−3) with time (t, s), D @@ xC2 is 2 the spatial change in transport due to diffusion with diffusion coefficient D (m2 s−1), w @@Cx is the spatial change in transport due to water flow or particle settling with velocity w (m s−1), positive downwards, kC is the con- sumption of substance C via a first order reaction with reactivity constant k (s−1) and R0 is a zero-order production term (that is, the substance C has no impact on the magnitude of this rate). This equation is based on spatially uniform mixing and settling rates and reactivity (i.e. D, w and k are constant). Moreover, we consider only steady-state conditions, i.e. there is no dependence   on time. This simplifies @C the math: the partial differential equation @ x becomes an ordinary differ-   ential equation dC dx : d2 C dC D w  kC þ R0 ¼ 0 dx2 dx If we first consider the situation without zero-order production or consump- tion (i.e. Ro = 0), the general solution is: C ¼ Aeax + Bebx pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w w2 þ 4kD w þ w2 þ 4kD where a ¼ and b ¼ 2D 2D and A and B are integration constant depending on the boundary conditions. The number of integration constants sets the number of boundary conditions required. We will use models for the semi-infinite domain: i.e., if x ! / then the gradient in C disappears ðdC dx ¼ 0Þ. Since all terms in b are positive, the 1.3 A 101 Budget for Organic Carbon in the Ocean 7 second term becomes infinite and the integration constant B must thus be zero for this boundary condition. For the upper boundary condition, we will explore two types: a fixed concentration and a fixed flux condition. If we know C = C0 at depth x = 0, then A is C0 and the solution is: C ¼ C0 eax : Sometimes we know the external flux (F) of C, then we have to balance the flux at the interface at x = 0, e.g.:  dC F ¼ D  þ wCjx¼0 dx x¼0 Next, we take the derivative of the remaining first-term of the general solution (Aeax ), to arrive at: F ¼ DaAea0 þ wAea0 Since e0 ¼ 1; A ¼ DaFþ w and the solution is: F C ¼ eax : Da þ w In some systems, transport is dominated by diffusion (e.g. molecular diffusion of oxygen in pore water, eddy diffusion of solutes and particles in water) and the advection term (w) can be ignored. The basic solutions given above qffiffiffiffi remain but now a ¼  D k and the pre-exponential term for the constant flux upper boundary becomes  Da F. In other systems transport is dominated by the advection term (e.g. settling particles in the water column) and then a ¼  w k and the flux upper boundary condition becomes w F. The above solutions are valid in the case that only first-order reaction occurs. The presence of zero-order reactions results in different solutions and these will be presented in the text where relevant. Similarly, the solutions presented are only valid if D, w and k are uniform with depth. In Chap. 3 we present an advection-first order degradation model in which we vary w and k with depth. Although user-friendly packages and accessible textbooks are available for numerical solving these and more complex equations (Boudreau 1997; Soetaert and Herman 2009), we restrict ourselves to analytical solutions because the relations among D, w and k in the various applications reveal important insights in the various process and governing factors, and the reader can implement the analytical solutions for further study. 8 1 Introduction References Boudreau BP (1997) Diagenetic models and their implementation. In: Modelling transport and reactions in aquatic sediments. Springer, p 414 Lasaga AC (1998) Kinetic theory in the Earth Sciences. Princeton University Press, p 811 Lotka AJ (1925) Principles of physical biology. Wiliams & Wilkins, Baltimore, p 460 Lovelock JE (1972) Gaia as seen through the atmosphere. Atmos Environ 6:579–580 Middelburg JJ (2018) Reviews and syntheses: to the bottom of carbon processing at the seafloor. Biogeosciences 5:413–427 Redfield AC (1958) The biological control of chemical factors in the environment. Am Sci 46:205–221 Sarmiento J, Gruber N (2006) Ocean biogeochemical dynamics. Princeton University Press, 526 pp Soetaert K, Herman, PMJ (2009) A practical guide to ecological modelling. Springer, 372 pp Williams RG, Follows MJ (2011) Ocean dynamics and the carbon cycle. Cambridge University Press, p 404 Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made. The images or other third party material in this chapter are included in the chapter’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Primary Production: From Inorganic to Organic Carbon 2 Primary production involves the formation of organic matter from inorganic carbon and nutrients. This requires external energy to provide the four electrons needed to reduce the carbon valence from four plus in inorganic carbon to near zero valence in organic matter. This energy can come from light or the oxidation of reduced compounds, and we use the terms photoautotrophy and chemo(litho)autotrophy, respectively. Total terrestrial and oceanic net primary production are each *50–55 Pg yr−1 (1 Pg = 1 Gt = 1015 g; Field et al. 1998). Within the ocean, carbon fixation by oceanic phytoplankton (*47 Pg yr−1) dominates over that by coastal phyto- plankton (*6.5 Pg yr−1; Dunne et al. 2007), benthic algae (*0.32 Pg yr−1; Gattuso et al. 2006), marine macrophytes (*1 Pg yr−1; Smith 1981) and chemo(litho) autotrophs (*0.4 and *0.37 Pg yr−1 in the water column and sediments, respectively; Middelburg 2011). Much of the chemolithoautrophy is based on energy from organic matter recycling. Since, photosynthesis by far dominates inorganic to organic carbon transfers, we will restrict this chapter to light driven primary production. Gross primary production refers to total carbon fixation/oxygen production, while net production refers to growth of primary producers and is lessened by respiration of the primary producer. Net primary production is available for growth and metabolic costs of heterotrophs, and it is the process most relevant for bio- geochemists and chemical oceanographers. For the time being, we present primary production as the formation of carbohydrates (CH2O) and ignore any complexities related to the formation of proteins, membranes and other cellular components (Chap. 6), because these require additional elements (nutrients). The overall pho- tosynthetic reaction is: CO2 + H2 O + light ! CH2 O + O2 © The Author(s) 2019 9 J. J. Middelburg, Marine Carbon Biogeochemistry, SpringerBriefs in Earth System Sciences, https://doi.org/10.1007/978-3-030-10822-9_2 10 2 Primary Production: From Inorganic to Organic Carbon It starts with the absorption of light energy by photosystem II (PSII): PSII 2H2 O þ light ! 4H þ þ 4e + O2 This reaction yields energy to generate adenosine triphosphate (ATP). The oxygen produced originates from the water and can be considered a waste product of photosynthesis. The protons and electrons generated subsequently react with nicotinamide adenine dinucleotide phosphate (NADP+) at photosystem I (PSI): PSI NADP þ þ H þ þ 2e ! NADPH: The energies of NADPH and ATP are then used to fix and reduce CO2 to form carbohydrate. RuBisCO CO2 þ 4H þ þ 4e ! CH2 O þ H2 O This reaction is normally mediated by the enzyme ribulose bis-phosphate car- boxylase (RuBisCO). Primary production is at the base of all life on earth; it is thus important to quantify it and to understand the governing factors. We will first present, at a very basic level, the primary producers. This will be followed by the introduction of the master equation of primary production, based on laboratory studies, and then a discussion of its application to natural systems. 2.1 Primary Producers Primary producers in the ocean vary from lm-sized phytoplankton to m-sized mangrove trees. Phytoplankton refers to photoautotrophs in the water that are transported with the currents (although they may be slowly settling). Biological oceanographers usually divide plankton (all organisms in the water that go with the current) into size classes (Table 2.1). Most phytoplankton are in the pico, nano and microplankton range (0.2–200 lm). The prefixes pico and nano have little to do with their usual meaning in physics and chemistry. Their small size gives them a high-surface-area-to-volume ratio which is highly favourable for taking up nutrients from a dilute solution. Within these phytoplankton size classes there is high diversity in terms of species composition and ecological functioning. Both small cyanobacteria (Synechococcus and Procholoroccus) and very small eukaryotes (e.g., Chlorophytes) contribute to the picoplankton. Microflagellates from various phytoplankton groups (Chlorophytes, Cryptophytes, Diatoms, Haptophytes) dom- inate the nanoplankton and differ in many aspects (cell wall, nutrient stoichiometry, 2.1 Primary Producers 11 Table 2.1 Plankton size classes in the ocean Size lass Name (example)

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