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Ocean – shelf-sea interaction.
 
  
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'''Algal bloom dynamics'''
  
 
 
==Introduction==
 
  
Deep ocean basins have typical depths of 4000 m or more. However, continents are typically surrounded by continental “shelf” above which the depth of the sea is typically 0-200 m. At the edge of the shelf, there is a steep slope down to oceanic depths in most places. The extent of the shelf (sea) varies from zero around atolls and volcanic sea mounts (for example) to tens of kilometres typically but hundreds of kilometres off NW Europe, Argentina and around much of the Arctic Ocean (Figure 1).  
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Algal bloom is a short-lasting strong increase of an algal population. The concentration of [[algae]] multiplies a thousand or even a million fold and collapses shortly after. Algal blooms are a worldwide phenomenon that occurs when the water temperature is favorable and light and nutrients are sufficiently available. Due to [[eutrophication]] of the coastal waters, algal blooms have become more frequent. Global warming may also play a role. This article introduces some elementary notions that provide insight into the phenomenon of algal blooms. A simple model of algal bloom dynamics is presented in the appendix.
  
[[Image: GlobalShelf.jpg|thumb|400px|right|Figure 1: Global map showing continental shelf areas in cyan.  Public Domain, https://commons.wikimedia.org/w/index.php?curid=617528]]
 
  
Questions of global cycling entail the quantity, transformation and fate of materials carried between the shelf seas and ocean, and hence processes of ocean-shelf transport and exchange.  For example, transport from the open ocean across the shelf edge is estimated to bring most of the nitrogen and half of the phosphate used in global shelf-sea export production (Liu et al.<ref> Liu KK, Atkinson L, Quiñones RA, Talaue-McManus L, 2010. Biogeochemistry of Continental Margins in a Global Context.  Pp3-24 in Carbon and Nutrient Fluxes in Continental Margins: A Global Synthesis (eds Liu KK, Atkinson L, Quiñones RA, Talaue-McManus L), Springer. </ref>); these transports support the shelf seas’ enhanced primary production and thence 90% of the world’s commercial fish catch (Pauly et al.<ref> Pauly D, Christensen V, Guenette Set al. 2002. Towards sustainability in world fisheries. Nature 418(6898), 689-695.</ref>).  Hence many ocean-shelf sea interaction studies have taken place (Table 1 lists some), illustrating strong biogeochemical interests but necessary physics underpinning.
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==Introduction==
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[[Image:meris_cover.png |300px|thumb|right| Fig. 1. Envisat MERIS true colour image of a phytoplankton bloom in the Barents Sea]]
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Algae are aquatic organisms that grow through [[photosynthesis]]. Many thousands of different algae species are known (Andersen, 1992<ref>Andersen, R.A. 1992. Diversity of eukaryotic algae. Biodiversity and Conservation 1: 267-292</ref>). In this article we focus on micro-algae, collectively called '[[phytoplankton]]'. This includes also certain types of bacteria in marine waters (sometimes called 'bacterioplankton') that grow through photosynthesis and produce blooms, although not belonging to the algae family. The most common phytoplankton species in seawater are diatoms, flagellates and cyanobacteria. The smallest species (picophytoplankton, size < 2 micron, consisting mostly of cyanobacteria) have the highest nutrient-uptake efficiency and are therefore most abundant in nutrient-poor ocean waters, whereas the larger diatoms tend to dominate the phytoplanktonic biomass in nutrient-rich waters (Edwards et al., 2011<ref>Edwards, K. F., Klausmeier, C. A. and Litchman, E. 2011. Evidence for a three-way trade-off between nitrogen and phosphorus competitive abilities and cell size in phytoplankton. Ecology 92: 2085–2095</ref>; Burson et al., 2018<ref>Burson, A., Stomp, M., Greenwell, E., Grosse, J. and Huisman, J. 2018. Competition for nutrients and light: testing advances in resource competition with a natural phytoplankton community. Ecology 99: 1108–1118</ref>). Blooms of large phytoplankton species only occur when the temperature does not exceed a critical limit of about 15<sup>o</sup>C (Cloern, 2018<ref>Cloern, J.E. 2018. Why large cells dominate estuarine phytoplankton. Limnology and Oceanography 63: 392-409</ref>).  Algae blooms can extend over large areas, as illustrated in Fig. 1.
  
Physical processes control the large-scale movement and irreversible small-scale mixing of water and its constituents. At the shelf edge, steep bathymetry may inhibit ocean-shelf exchange: integration of the momentum equation through depth and around a depth contour shows that net cross-contour transport is entirely attributable to ageostrophy (Huthnance <ref name=H95> Huthnance JM, 1995. Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge. Progress in Oceanography 35(4), 353-431.</ref>, Appendix A). That is, transport across depth contours is enabled by (i) time scales of a day or less, or (ii) space scales of a few kilometres or less, or (iii) depth contours changing direction on similarly short space scales or (iv) enough friction to stop the flow in a day or so.
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All phytoplankton species grow by absorbing dissolved CO<sub>2</sub> under the influence of light and thereby emit oxygen. Marine phytoplankton contributes almost half to the total oxygen production on Earth (Behrenfeld et al., 1998<ref>Field, C. B., Behrenfeld, M. J., Randerson, J. T. and Falkowski, P. 1998. Primary production of the biosphere: integrating terrestrial and oceanic components. Science 281: 237–240</ref>). Phytoplankton species are called [[Autotrophic|'autotrophs']] or [[Primary production|'primary producers']], because they are able to feed and produce organic material from mineral substances. They are a food source for other marine organisms, [[zooplankton]] in the first place. They are therefore at the basis of the [[food web]] of marine life. For more details about the different plankton species, see the article [[Marine Plankton]].  
  
The combination of sloping topography and stratification gives rise to shelf-edge processes satisfying one or more of the criteria (i-iv).  These include coastal-trapped waves; instability, meanders and friction-induced Ekman transport associated with along-slope currents; eddies; upwelling, fronts and filaments: down-welling, cascading; tides, surges; internal tides and waves; surface waves; topography (capes and canyons).
 
  
In view of the complex set of processes, often complex topography and the small scales favouring cross-slope flow, our approach to better representation of ocean-shelf interaction is to develop models with fine resolution (of order 1 km).  These then need testing against detailed measurements in areas with contrasting conditions (hence varied processes).
 
  
The above processes occur with varying intensity according to context, but some (e.g. wind-induced upwelling or down-welling, tides) enable cross-slope transports of order 1 m2/s or more (per metre of shelf edge). This is small compared with transports of order 100s m2/s (per metre width) in strong ocean currents such as the Gulf Stream. However, the global length of shelf edge, O(5 x 105 km) (Robinson et al.<ref> Robinson AR, Brink KH, Ducklow HW, Jahnke RA, Rothschild BJ, 2005. Interdisciplinary multiscale coastal dynamical processes and interaction. The Sea 13 (Robinson AR, Brink KH, eds.), 3-35.</ref>), gives a global aggregate cross-slope transport probably exceeding the transport in any ocean current.
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==Conditions for growth: light, temperature and nutrients==
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Besides CO<sub>2</sub> and sunlight, phytoplankton needs certain nutrients for growth. These are primarily the minerals nitrogen N, phosphorus P and silicon Si (mainly in the form of dissolved salts, nitrate, phosphate and silicate, respectively, see [[Continental Nutrient Sources and Nutrient Transformation]]). Small amounts of iron Fe and certain vitamins are also required. Lack of any of these nutrients limits the growth of phytoplankton. The ratio in which these nutrients are needed has been determined in the past at 106 C: 16 N: 1 P, the so-called [[Redfield ratio]]. However, the ratio varies by species, allowing some species to grow better or less well than others under certain conditions. Growth further depends critically on light and temperature (Bissinger et al., 2008<ref> Bissinger, J. E., Montagnes, D. J. S., Sharples, J., and Atkinson, D. 2008. Predicting marine phytoplankton maximum growth rates from temperature: improving on the Eppley curve using quantile regression. Limnol. Oceanogr. 53: 487–493. doi: 10.4319/lo.2008.53.2.0487</ref>; Boyd et al., 2013<ref>Boyd, P.W., Rynearson, T.A,. Armstrong, E.A., Fu, F., Hayashi, K., et al., 2013. Marine Phytoplankton Temperature versus Growth Responses from Polar to Tropical Waters – Outcome of a Scientific Community-Wide Study. PLoS ONE 8(5): e63091. doi:10.1371/journal.pone.0063091</ref>). Here too, the optimum values are specific to each algal species.
  
In the following, typical estimates of exchanges are given in m2/s: volume per second across a 1 m sector of shelf edge. These are the same units as for dispersion coefficient <math>K</math>, a different quantity but related: <math>K dC/dx</math> or <math>K \Delta C / L_x</math> represents transport <math>|u'C'|</math>  due to unresolved fluctuations of current <math>u'</math> and constituent <math>C'</math>. Thus:
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[[Image:AlgaeBloomTerschelling.jpg|thumb|450px|right|Fig. 2. Multi-annual observation record of the alga ''Chaetoceros socialis'' (red spikes) at a measuring point in the North Sea 10 km north of the Dutch Wadden island of Terschelling. Simultaneous measurements of the local nitrate concentration (black) and surface salinity (blue). From Wagner-Cremer et al. (2018)<ref>Wagner-Cremer, F., Steur, F. van Wezel, R., Verweij, G. and Kouwets, F. 2018. Wat momentopnamen van fytoplankton ons kunnen vertellen over de geschiedenis van de kust. H2O-Online / 19 januari 2018</ref>.]]
  
<math>K \sim | u'| L_x/h</math> and exchange <math> |u'|h/2 \sim Kh/2L_x \qquad (1) , </math>
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Phytoplankton can grow under favorable conditions unrestrained as long as there is no restriction in the availability of the necessary nutrients. Population growth occurs through division of the parent cell, with the formation of two or more offspring. The cell division frequency for each species is different and depends on temperature and light; it can happen every few hours, but also every few days. Since this applies to each individual in the population, growth has an exponential character. Huge population growth is therefore possible in a short time.
  
with <math>h, \; L_x</math> the depth at the shelf edge and the shelf width, respectively.
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An example of the explosive short-lived nature of algal blooms is illustrated in Fig. 2, showing a multi-year observation record of the alga ''Chaetoceros socialis'' at a measuring station in the North Sea 10 km north of the Dutch Wadden island of Terschelling. The figure also shows observations of the nitrogen concentration (dissolved nitrate) and the salinity at the measuring point.
If as occasionally below we estimate <math>K</math>, then a (dimensionless) factor <math>h/2L_x</math> is applicable to estimate the associated exchange.
 
  
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The conditions for algal blooms vary with the seasons. This is not only due to temperature and light. In the winter, nutrient-rich organic material is stirred from the seabed. Therefore, nutrient concentrations are often highest in early spring (N hemisphere). With increasing light and temperature, the conditions for algal bloom become optimal; the largest algal blooms therefore occur in general during springtime. The strongest algal growth takes place in the upper water layer where light penetrates best, the so-called euphotic zone. Intensive mixing over the water column is less favorable because it moves part of the phytoplankton into deeper water layers, where growth is limited due to a lack of light. In the oceans, algal blooms are typically concentrated in a rather thin surface layer. Vertical mixing is counteracted by density stratification, whereby water with a higher temperature and/or lower salinity floats on top of colder/saltier seawater. Organic detritus, because of its specific density, tends to be collected at the interface zone (picnocline), where nutrients are released after mineralization of the detritus. This creates ideal conditions for the development of strong algal blooms, especially blooms of mixotrophic algae that feed both on nutrients and organic material (Berdalet et al., 2014<ref name=Ber>Berdalet, E.,McManus, M.A., Ross, O.N., Burchard, H., Chavez, F.P., Jaffe, J.S., Jenkinson, I.R., Kudela, R., Lips, I., Lips, U., Lucas, A., Rivas, D., Ruiz-delaTorre, M.C., Ryan, J., Sullivan, J.M.k and Yamazakim H. 2014. Understanding harmful algae in stratified systems: Review of progress and future directions. Deep-Sea Research II 101: 4–20</ref>; Sigman and Hain, 2012<ref>Sigman, D. M. and Hain, M. P. 2012. The Biological Productivity of the Ocean. Nature Education Knowledge 3: 21 https://www.nature.com/scitable/knowledge/library/the-biological-productivity-of-the-ocean-70631104/</ref>).
  
==Processes==
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The size of a plankton bloom is generally expressed in terms of organic carbon weight, <math>g \, C</math>. The value can be obtained by taking samples and measuring the ash-free dry biomass content (see [[In situ monitoring of eutrophication]], [[Sampling tools for the marine environment]]). However, it is most usual to estimate phytoplankton biomass by quantifying chlorophyll a, the photosynthetic pigment common to all types of algae. It can be determined by various optical techniques due to its [[fluorescence]] properties. Techniques are described in the articles [[Estimation of spatial distribution of phytoplankton in the North Sea]], [[Determining coastal water constituents from space]], [[Differentiation of major algal groups by optical absorption signatures]].
  
===Coastal-trapped waves===
 
  
These are the basic waves that travel along the continental shelf and slope. Scales are typically one to several days and tens to hundreds of kilometres according to the width of the continental shelf and slope. The lowest mode (0) ‘Kelvin’ waves, also coastally trapped, travel cyclonically around ocean basins but with typical scales of thousands of kilometres both alongshore and for offshore decrease of properties.
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==Other factors that condition algal blooms==
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===Inter-species competition===
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The conditions for optimal growth are not the same for different algal species present in a particular coastal area. The species that uses the available resources with the highest efficiency will experience the strongest growth. Therefore, the dynamics of algal blooms cannot be estimated from the average reproduction rate of the various algae species. A common assumption is that the composition of the algal population adapts rapidly, so that optimal use is made of the growth potential provided by the available resources: light, temperature and nutrients. For example, field observations by Philippart et al. (2000<ref name=Ph>Philippart, C.J.M., Cadée, G.C., van Raaphorst, W. and Riegman, R. 2000. Long-term phytoplankton-nutrient interactions in a shallow coastal sea: algal community structure, nutrient budgets and denitrification potential. Limnology and Oceanography 45: 131-144</ref>) in the Wadden Sea show that the composition of the algal population is adjusted to the ratio between different nutrients, in particular N and P. In a modelling approach based on this assumption, the composition of the algal population (numbers of constituent species) is determined by optimizing at each time step the utilization of the available resources (light and nutrients). The utilization of these resources during this time step yields the new available light and nutrients for which the composition of the algal population is optimized in the next time step. These models assume fast growth rates, such that the algal population is always tuned to optimum resource utilization at each time step. Numerical simulations by Los and Wijsman (2007<ref>Los, F.J. and Wijsman, J.M.W. 2007. Application of a validated primary production model (BLOOM) as a screening tool for marine, coastal and transitional waters. Journal of Marine Systems 64: 201-215</ref>) of algal blooms based on this assumption generally show fair similarity to field observations. Another factor influencing the competition between algal species for light and nutrients is the ability of certain algal species to migrate towards zones that offer the best growth conditions. In this way these algae can outcompete non-motile species, especially in low-turbulence environments (Klausmeier and Litchman, 2001<ref>Klausmeier, C.A. and Litchman, E. 2001. Algal games: The vertical distribution of phytoplankton in poorly mixed water columns. Limnol. Oceanogr. 46: 1998–2007</ref>).
  
[[Image: CTWandNodes.jpg|thumb|700px|center|Figure 2. Left panel: Sketch of form of elevation for mode 1 coastal-trapped wave. Right panel: Sketch of cross-slope structure of mode 3 coastal-trapped wave. The 3 lines sloping away from the sea floor denote zeros of pressure.]]
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===Predation===
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The size of algal populations is limited not only by shortage of nutrients, but also by mortality and predation. Algae are an essential food source for many organisms in the sea. The main phytoplankton grazers are zooplankton species, which come in different shapes and sizes. The smallest zooplankton (micro-zooplankton, mainly flagellates, ciliates and mixotrophic phytoplankton), while grazing on the smallest phytoplankton species, can adapt quickly to changes in the prey population and thus largely controls the size of picophytoplankton blooms. This is less the case for the larger zooplankton, that consists mainly of herbivore copepods in the oceans and of filter feeding benthos and [[benthic]] larvae in estuarine environments. Blooms of larger phytoplankton species (diatoms, dinoflagellates), that dominate in eutrophic and nitrogen-controlled conditions<ref name=Ph></ref>, are therefore less sensitive to grazer dynamics. The lesser grazing sensitivity can also be due to flight behavior (Harvey and Mende-Deuer, 2012<ref>Harvey, E.L. and Menden-Deuer, S. 2012. Predator-Induced Fleeing Behaviors in Phytoplankton: A New Mechanism for Harmful Algal Bloom Formation? PLoS ONE 7(9): e46438. https://doi.org/10.1371/journal.pone.0046438</ref>) or a lower nutrient content of larger phytoplankton (Branco et al., 2020<ref>Branco,P., Egas, M., Hall, S.R. and Huisman, J. 2020. Why Do Phytoplankton Evolve Large Size in Response to Grazing? The American Naturalist vol. 195 , no. 1</ref>). Digestion of phytoplankton by large zooplankton species leads to excretion of organic material in the form of fecal pellets. In the deep ocean, fecal pellets sink to the bottom; in this way CO<sub>2</sub> and nutrients are removed from the marine ecosystem. In shallow coastal waters, fecal pellets are mineralized on the bottom where the released nutrients are exploited by the [[benthic]] ecosystem. Organic bottom material that is stirred up by waves and currents provides nutrients to the [[pelagic]] phytoplankton. Organic matter and nutrients are stored in the soil where net sedimentation occurs, but otherwise the recycling of nutrients in coastal waters is stronger than in the ocean.
  
[[Image: CTWdir.jpg|thumb|300px|right|Figure 3: Sketch showing main sense of coastal-trapped wave propagation around ocean boundaries. Energy (but not phase) may travel in the reverse sense of the small arrows.]]
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===Mortality===
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Phytoplankton mortality is largely due to viral infections (Baudoux, 2007<ref>Baudoux, A-C. 2007. The role of viruses in marine phytoplankton mortality. Thesis Groningen University, 148 pp</ref>). In the (sub)tropical ocean, the contribution of viruses to the decay of algal blooms is similar or even superior to the impact of grazing, whereas grazing dominates at higher latitudes (Mojica et al., 2016<ref> Mojica, K.D.A., Huisman, J., Wilhelm, S.W. and Brussaard, C.P.D. 2016. Latitudinal variation in virus-induced mortality of phytoplankton across the North Atlantic Ocean. The ISME Journal 10: 500–513; doi:10.1038/ismej.2015.130</ref>). The mortality rate of phytoplankton exceeds in some cases the growth rate, but is generally lower. Most dead algae are too small to sink to the bottom. Part of the dead algae is broken down by bacteria in the euphotic zone, where the released nutrients fuel new blooms. Another part aggregates with other organic and inorganic particles until reaching a mass that makes the aggregates sink to the bottom. In the oceans, these sinking particles (called 'marine snow') are sequestered in deep water layers. In addition to gravitational sinking, downward transport of organic matter in the ocean also occurs in downwelling regions (see the article [[Shelf sea exchange with the ocean]]) and through episodic localized subduction currents (Llort et al., 2018<ref>Llort, J., Langlais, C., Matear, R., Moreau, S., Lenton, A. and Strutton, P. G. 2018. Evaluating Southern Ocean Carbon Eddy-Pump From Biogeochemical-Argo Floats. Journal of Geophysical Research Oceans 123: 971–984</ref>). The total ocean carbon sink due to these different processes is in the order of ¼ of the total global carbon emissions (De Vries et al., 2019<ref>DeVries, T., Le Querec, C., Andrew, O., Berthet, S., Hauck, J., Ilyina, T., Landschutzer, P., Lenton, A., Lima, A.D., Nowicki, M., Schwinger, J. and Seferian, R. 2019. Decadal trends in the ocean carbon sink. PNAS 116: 11646–11651</ref>).
  
Coastal-trapped waves have been widely observed, along coastlines of various orientations and all continents in both the Northern and Southern Hemispheres. Mode 1 with simple structure (usually one offshore zero of bottom pressure; figure 2 left panel) has been most often identified; its peak coastal elevation is relatively easily measured.  Higher modes (with more offshore zeros; figure 2 right panel) have been identified off Oregon, the Middle Atlantic Bight and New South Wales (Australia).
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==Consequences of algal blooms==
  
Coastal-trapped waves are not an independent cause of transports; their significance is in propagating shelf-wide day-to-day variations. Examples are
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===Increased fishery yields===
* oceanic tides with large coastal sea-level variations and (on broad shelves) large currents
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There is strong evidence that eutrophication of coastal waters has led to an increase in primary production and an increase in the food supply for higher [[Trophic level|trophic]] species. A strong increase in fishing yields in eutrophicated coastal waters can be attributed to this increased primary production (Nixon, 1988<ref>Nixon, S. W. 1988. Physical energy inputs and the comparative ecology of lake and marine ecosystems. Limnol. Oceanogr. 33: 1005–1025</ref>; Nixon and Buckley, 2002<ref>Nixon, S.W. and Buckley, B. A. 2002. “A strikingly rich zone” – Nutrient enrichment and secondary production in coastal marine ecosystems. Estuaries 25: 782–796</ref>).
* storm surges; strong currents and large changes of sea level induced by weather (atmospheric pressure and especially winds)
 
* wind-forced upwelling,
 
* along-slope currents and poleward undercurrents common on the eastern sides of oceans,
 
* responses to oceanic eddies and alongshore pressure gradients.
 
  
Thus transports induced in one location may appear later at another.  The sense of phase propagation is cyclonic around an ocean basin (anti-clockwise in the northern hemisphere; clockwise in the southern hemisphere; figure 3). However, short-wave energy may travel slowly in the opposite sense, especially if stratification is weak (Huthnance<ref name=H95></ref>).
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===Oxygen depletion===
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Algal blooms operate by photosynthesis and therefore produce a lot of oxygen. The reverse happens when the bloom decays; oxygen is extracted from the water when the organic material is mineralized (the work of bacteria). The oxygen demand of a collapsing algal bloom can be very high. Dissolved oxygen will be depleted if the water is not flushed or aerated fast enough, a situation called anoxia. This is a common phenomenon in lakes, but it can also occur in lagoons and estuaries. In cases where differences in temperature or salinity between upper and lower water layers stratify the water column, anoxia can easily arise in the lower water layer (see [[Estuarine turbidity maximum]]). This is on the one hand due to mineralization of sinking organic material, and on the other hand due to suppression of turbulent mixing with water of the more aerated and oxygen-rich top layer. Most organisms cannot live in anoxic water and die, and thus aggravate anoxia. Oxygen depletion is often an indirect result of eutrophication, that stimulates the formation of algal blooms in the upper water layer.
  
===Along-slope currents===
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===Harmful algae===  
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Numerous algae species produce toxic substances and are therefore called harmful algae. Many aquatic (and non-aquatic) organisms are poisoned when they ingest large amounts of these toxic algae. This can happen when a bloom of harmful algae develops. Marine aquaculture is particularly affected by toxic algal blooms. Harmful algal blooms (HABs) are a natural and frequent phenomenon, similar to non-harmful algal blooms. The chemicals produced by harmful algae (e.g. certain species of diatoms and dinoflagellates) are a defence mechanism against predators, either through toxin production or feeding deterrence, see  [[Chemical ecology#Chemical ecology and phytoplankton]] and [[Functional metabolites in phytoplankton]]. However, some doubts exist about the effectiveness of these defence mechanisms to reduce grazing pressure by zooplankton (Zigone and Wyatt, 2004<ref name=Z> Zingone, A., Wyatt, T. 2004. Harmful algal blooms: keys to the understanding of the phytoplankton ecology. In: Robinson, A.R., McCarthy, J. and Rothschild, B.J. (eds.) The Sea. Harvard University Press, Harvard, pp 867-926 </ref>). There is some evidence that the size and frequency of harmful algal blooms are increasing (Hallegraeff, 1993<ref>Hallegraeff, G. M. 1993. A review of harmful algal blooms and their apparent global increase. Phycologia 32: 79–99</ref>). Some theories relate the increase in toxic algal blooms to eutrophication, in particular in situations where the natural nutrient ratio is disturbed; other theories point to global warming. However, a clear explanation of the causes is still lacking (Anderson, 2012<ref>Anderson, D. 2012. HABs in a changing world: a perspective on harmful algal blooms, their impacts, and research and management in a dynamic era of climactic and environmental change. Harmful Algae 2012 (2012). 2014;2012: 3-17</ref>).
  
[[Image: GSwarmRings.jpg|thumb|300px|left|Figure 4: Sea-Surface Temperature showing two warm rings drawing colder shelf water across the shelf edge (black line) on their eastern flanks.]]
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==Regional distribution of algal blooms==
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Algal blooms require light and nutrient-rich water. Nutrient-rich surface waters occur naturally in the so-called upwelling zones, areas where deep ocean water rises up (see the articles [[Ocean circulation]] and [[Shelf sea exchange with the ocean]]). Major upwelling zones are located along the Atlantic coast of Africa and the Pacific coasts of California and south America, where ocean surface currents are bent off the coast by the effect of Earth's rotation. Net primary productivity NPP (gross production minus respiration) can exceed 1000 <math>g \, C m^{-2} y^{-1}</math>, which is much more than the ocean average of about 150 <math>g \, C m^{-2} y^{-1}</math>. However, the highest nutrient concentrations are not found in the oceans, but in coastal waters, especially in estuaries and lagoons (Howarth, 1988<ref> Howarth, R.W. 1988. Nutrient limitation of net primary production in marine ecosystems, Annual Rev. Ecol. Syst. 19: 89–110 </ref>), mainly due to release of nutrients by human activities (see e.g. [[Eutrophication in coastal environments]]). Most of the primary production occurs during seasonal or episodic algal blooms. However, the annual NPP in coastal systems is not exceptionally high; values range typically from 50 to 400 <math>g \, C m^{-2} y^{-1}</math>. Large spatial differences occur within estuaries as well as strong interannual fluctuations, but on average the NPP seldom exceeds 500 <math>g \, C m^{-2} y^{-1}</math> (Cloern et al., 2014<ref> Cloern, J.E., Foster, S.Q. and Kleckner, A.E. 2014. Phytoplankton primary production in the world's estuarine -coastal ecosystems. Biogeosciences 11: 2477–2501 </ref>). A major reason is the greater importance of light as a limiting factor for algal growth than nutrient deficiency, especially in deep (often dredged) estuaries. This is due to the turbidity of the water in estuaries and lagoons and along the adjacent coast (see the articles [[Estuarine turbidity maximum]] and [[Which resource limits coastal phytoplankton growth/ abundance: underwater light or nutrients?]]). A model study by Liu et al. (2018<ref>Liu, B., de Swart, H. E. and de Jonge, V. N. 2018. Phytoplankton bloom dynamics in turbid, well-mixed estuaries: a model study. Estuarine, Coastal and Shelf Science. 211: 137-151</ref>) shows that in well-mixed turbid estuaries, algal blooms are restricted to the zone downstream from the [[estuarine turbidity maximum]]. The role of river discharge on algal blooms in estuaries is ambiguous. High discharges supply nutrients, but they also flush algae out of the estuary. Observations by McSweeney et al. (2016<ref>McSweeney, J. M., Chant, R. J., Wilkin, J. L. and Sommerfield, C. K. 2016. Suspended sediment impacts on light-limited productivity in the Delaware estuary. Estuaries and Coasts 40: 977–993</ref>) in the Delaware show that high river discharges generate stratification with favorable light conditions for algal blooms in the surface layer. In estuaries with large intertidal flats, [[pelagic]] algae have to compete for nutrients with [[benthic]] algae (De Jonge and van Beusekom, 1992<ref>De Jonge, V. N. and van Beusekom, J. E. E., 1992. Contribution of resuspended microphytobenthos to total phytoplankton in the Ems estuary and its possible role for grazers. Netherlands Journal of Sea Research 30: 91–105</ref>). Comparing observations from many estuaries, it appears that the total annual decay of organic matter in most estuaries is larger than the gross primary production. This means that, unlike other marine systems, these estuaries are net producers of CO<sub>2</sub> (Caffrey, 2004<ref>Caffrey, J. M. 2004. Factors controlling net ecosystem metabolism in US estuaries. Estuaries 27: 90–101</ref>; Gattuso et al., 1998<ref>Gattuso, J.-P., Frankignoulle, M., and Wollast, R. 1998. Carbon and carbonate metabolism in coastal aquatic ecosystems. Annual Rev. Ecol. Syst. 29: 405–433</ref>).
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[[Image: LeeuwinU.jpg|thumb|700px|right|Figure 5: The poleward Leeuwin current off Western Australia shown by warm sea-surface temperature.  At https://en.wikipedia.org/wiki/Leeuwin_Current.]]
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==Appendix==
  
Western boundary currents such as the Agulhas, Brazil Current, Gulf Stream and Kuroshio can be strong, sufficient to form meanders and eddies in some locations (e.g. Gulf Stream Rings; figure 4). They may also extend to the bottom to give a frictional cross-slope Ekman transport.  Reviews of the contribution of Gulf Stream Warm-Core Rings to shelf/slope water exchange (Joyce <ref> Joyce TM, 1991. Review of U.S. contributions to warm-core rings. Reviews of Geophysics, S29, 610-616.</ref>; Huthnance <ref name=H95></ref>) suggest an average O(0.5 m2/s) north-east of the separation of the Gulf Stream from the shelf.  
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The occurrence of algal blooms, with rapid emergence and equally rapid disappearance, is a prominent feature of eutrophication. This appendix provides a qualitative explanation of algal bloom dynamics, following the paper by Huppert et al. (2002<ref name =HBS>Huppert, A., Blasius, B. and Stone, L. 2002. A Model of Phytoplankton Blooms. The American Naturalist 159: 156-171</ref>). The explanation is based on a simple model in which an algal bloom is related to the available amount of a certain nutrient. This nutrient is assumed to be essential for the growth of the algal population, but to be present in such a low concentration that it limits the growth of the population. Because the uptake of the nutrient by the algae decreases the nutrient concentration, the population growth and the nutrient concentration form together a self-regulating feedback system. The different processes that play a role are set out below. The model is meant to enable a better understanding of the algal bloom process; it is too simple for application to real field situations because many of the processes discussed previously are ignored.
  
Along-slope currents are common at eastern ocean margins. Equatorward surface currents are associated with upwelling in the north and south Pacific and AtlanticPoleward flows over the upper continental slope occur off western USA, western Australia (figure 5) and western Europe, for example, forced by alongshore gradients in adjacent ocean density. In upwelling areas such poleward flow may be an undercurrent not showing at the surface.
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We call <math>P(t)</math> the biomass, representing the size of the algal population at time <math>t</math> in a certain volume <math>V</math> of the sea, and <math>N(t)</math> the average nutrient concentration in this volume. The temporal variation of the algal biomass, <math>dP/dt</math> and the nutrient concentration, <math>dN/dt</math>, is regulated by the following factors:
 +
* Nutrient uptake <math>B</math>. The uptake depends on the algal biomass <math>P</math> and on the nutrient concentration <math>N</math>. If the nutrient concentration is low (limiting), linearity of the dependence in both <math>P</math> and <math>N</math> is a reasonable assumption, <math>B=\beta (t) \, P \, N</math>The uptake efficiency <math>\beta(t)</math> depends on other environmental conditions for algal growth, in particular temperature and light. Nutrient uptake increases the algal biomass by <math>B_P=\beta_P(t) \, P \, N</math> and decreases the nutrient concentration by <math>B_N=-\beta_N(t) \, P \, N</math>. The ratio <math>\rho=\beta_N(t)/\beta_P(t)</math> is constant. Saturation of the nutrient uptake (i.e. <math>B</math> independent of <math>N</math> when <math>N</math> is abundant) is ignored.
 +
* Biomass decay with nutrient restitution <math>G</math>. The algal biomass decreases by respiration, mortality and mineralization of algal detritus, <math>G_P = - \gamma (t) \, P</math>, while the nutrient concentration increases with restitution of nutrient by <math>G_N=\rho \gamma (t) \, P</math>. It is assumed that respiration and mineralization are quasi-instantaneous processes; their efficiency for nutrient restitution is expressed by the rate factor <math>\gamma(t)</math>.
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* Nutrient loss <math>S</math> related to the loss of algal biomass by predation, sinking to the bottom and export, and therefore assumed proportional to the algal biomass: <math>S=- \sigma (t) \, P</math>. Predation by zooplankton depends not only on the algal biomass but also on the biomass of zooplankton. The zooplankton population itself depends on the algal biomass and increases when the algal biomass is high. However, zooplankton dynamics is ignored in the model.
 +
* Nutrient loss <math>A=-\alpha (t) \, N</math>, as a result of biogeochemical processes that limit the availability of nutrients for uptake by algae.
 +
* Nutrient supply from external sources, <math>Q</math>. Major external nutrient supplies (partly in the form of organic material) are coming from rivers, atmospheric deposition and stirring up of organic bed material.
  
 +
We focus on the period in which the algal population experiences rapid growth and rapid decline. This period is assumed so short that the factors <math>\alpha, \beta, \gamma, \sigma</math> can be considered approximately constant. Collecting the expressions of the factors influencing the temporal variation of algal population, <math>dP/dt</math> and the nutrient concentration, <math>dN/dt</math>, we arrive at the equations:
  
 +
<math>dP/dt = B_P+G_P+S_P = (\beta \, N - \gamma - \sigma ) \, P , \qquad (A1)</math>
  
 +
<math>dN/dt = B_N +G_N + A + Q = \rho (\gamma - \beta \, N) \, P - \alpha \, N  + Q . \qquad (A2)</math>
  
 +
These coupled nonlinear equations are known as the Lotka-Volterra equations. The solution is not straightforward. It depends not only on the coefficients appearing in the equations but also on the initial conditions <math>P=P_0, \, N=N_0</math> at time <math>t=0</math>. Different types of long-term behavior of <math>P</math> and <math>N</math> may result: convergence to a static equilibrium state, to a cyclic state or to a state of chaotic fluctuations around certain attractors. We will not consider the long-term behavior, especially because the assumption of constant coefficients does not hold. For a qualitative understanding of the short-term behavior we will first consider the equilibrium solution of the Eqs. (A1) and (A2) corresponding to <math>dP/dt=0</math> and <math>dN/dt</math>. The equilibrium solution is given by the curves
  
 +
<math>N_{eq}=\large\frac{\gamma + \sigma}{\beta}\normalsize, \quad P_{eq}=\large\frac{Q -\alpha N}{\rho (\beta N - \gamma)}\normalsize. \qquad (A3)</math>
  
 +
These curves are drawn in Fig. 3. The curves cut the <math>P,N</math> phase plane in 4 phase sectors:
 +
* Green phase: <math>P</math> and <math>N</math> both increase;
 +
* Yellow phase: <math>P</math> increases, <math>N</math> decreases;
 +
* Red phase: <math>P</math> and <math>N</math> both decrease;
 +
* Blue phase: <math>P</math> decreases and <math>N</math> increases.
  
  
 +
{| border="0"
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|-
 +
| valign="top"|
 +
[[File:AlgaeBloomPhasePlane.jpg|thumb|520px|left|Fig. 3. Solution of the Lotka-Volterra equations (A1, A2), showing the coupled evolution of <math>P(t)</math> and<math>N(t)</math> in the <math>N-P</math> phase plane (solid line). The model parameters are set as follows: <math>\alpha=0, \, \beta=0.1/N_0/day, \, \rho=10^{-3},  \, \gamma=0, \, \sigma=0.1/day, \, Q=7.5 \, 10^{-3} N_0/day, </math> <math>N_0=0.1 g/m^3, P_0=6.10^{-5} g/m^3</math>. From Huppert et al. (2002)<ref name =HBS></ref>.]]
 +
| valign="top"|
 +
[[File:AlgaeBloomModel.jpg|thumb|left|400px|Fig. 4. Temporal evolution of the algal population <math>P(t)</math> (solid line) and the nutrient concentration <math>N(t)</math> (dashed line) according to the equations (A1, A2) with the same parameters as for Fig. 3. ]]
 +
|}
  
Upwelling is a consequence of wind-forced off-shelf surface Ekman transport <math>\tau_w / \rho f .</math>  (Here <math>\tau_w</math> is wind stress, <math>\rho</math> is sea density and <math>f</math> is Coriolis parameter.)  The associated along-shelf flow may become strong enough to go unstable and develop meanders and filaments (figure 6); these enhance cross-shelf transport beyond <math>\tau_w / \rho f .</math> In any case, flow at the bottom results in a bottom stress <math>\tau_b</math> and corresponding Ekman transport <math>\tau_b / \rho f .</math> which is off-shelf under poleward flow and on-shelf under equatorward flow. 
 
  
[[Image: UpwellCa.jpg|thumb|500px|left|Figure 6: Upwelling of California with meanders and filaments shown by cooler sea-surface temperature. At http://oceansjsu.com/105d/exped_climate/10.html]]
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Now consider the evolution graph in Fig. 3, which is obtained by numerical integration of the Eqs. (A1) and (A2) <ref name =HBS></ref>. The bloom starts in the green phase sector, where initially the algal biomass <math> P </math> is very small. The environmental conditions (temperature, light) have just become favorable for nutrient uptake, i.e. the uptake efficiency factor <math>\beta </math> has increased significantly. Shortly before (not shown in the figure), <math>\beta </math> was much smaller and <math>N_ {eq} </math> much larger, so that the algal population was still in the blue phase (i.e. decreasing in size). Due to the increased uptake efficiency, the biomass <math>P</math> is now increasing, but the increase is slow because the rate of increase is proportional to <math>P</math> (cf. A1). Nutrient uptake is still quite low and the nutrient concentration is still increasing due to the supply <math>Q</math>. However, with increasing population size <math>P</math> the nutrient uptake also increases and at some moment the nutrient concentration <math>N</math> changes from increasing to decreasing. The <math>P-N</math> system enters the yellow phase, where <math>P</math> will grow rapidly, because the rate of change <math>(\beta \, N - \gamma - \sigma ) \, P </math> (Eq. A1) is large and initially still increasing in spite of the decrease of <math>N</math> (Eq. A2). The algal bloom essentially takes place at the end of the green phase and the beginning of the yellow phase. The nutrient concentration decreases in the yellow phase and finally becomes so small that further growth of the algal biomass is no longer possible. At that time the algal biomass has reached its maximum and the <math>P-N</math> system enters the red phase, where the algal biomass decreases. The nutrient concentration continues its rapid decrease (cf. A2) because the uptake of nutrients by the algal population is still high. However, the algal population also declines at a fast rate because <math>(\beta \, N - \gamma - \sigma) \, P </math> (cf. A1) is large and negative. The collapse of the algal population mainly takes place in the red sector.  The decrease of the nutrient concentration ends when the uptake of nutrients has become very small, because of the small size of the algal population. The <math>P-N</math> system then enters the blue phase where <math>P</math> decreases further, while <math>N</math> increases, but both at a slow rate. The algal bloom as a function of time, corresponding to the trajectory in the <math>P-N</math> phase plane, is shown in Fig. 4.  It illustrates the dramatic increase and collapse of the algal biomass (5 orders of magnitude) in a short time. The peak of the bloom coincides with the strongest decrease of the nutrient concentration. The same coincidence is visible in the observation record of the plankton bloom and nutrient concentration in Fig. 2. It also appears, both in the model and the data, that the variation of the nutrient concentration is much less pronounced than the variation in the algal biomass.
  
[[Image: DownW.jpg|thumb|380px|right|Figure 7: Fluxes (Sv) above 150m (blue) and below 150m depth (red).  All fluxes are across the 200m contour shown; positive is onto the shelf except next to Norway (positive to north). From Huthnance et al.<ref name=H09> Huthnance JM, Holt JT, Wakelin SL, 2009. Deep ocean exchange with west-European shelf seas. Ocean Science 5, 621-634, doi:10.5194/os-5-621-2009.</ref>]]
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The nonlinearity of the algal bloom equations has implications that may appear surprising at first sight. One may notice, for instance, that complete nutrient depletion is not a necessary condition for the crash of the algal population. The point is that below a certain level, which is not necessarily very small, the nutrient concentration is insufficient to sustain a very large algal population.  
  
 +
The maximum algal population size that can be reached during the bloom is not linearly related to the initial nutrient concentration <math>N_0</math> and the initial population size <math>P_0</math>. Depending on the values of <math>N_0, P_0</math>, it can happen that an increase of either <math>N_0</math> or <math>P_0</math> leads to a smaller bloom size, instead of a larger size<ref name=HBS></ref>. According to the model, the nutrient concentration that is reached when the population enters the yellow phase determines to a large degree the maximum population size that can be reached during the yellow phase. This feature is not visible in the observations presented in Fig. 2. In fact, other factors such as sunlight and temperature also play a role. In the case of Fig. 2, it appears that the largest blooms are correlated with low salinity values. This points to a change in the type of water masses present at the measuring site. Stratification effects (suppression of vertical mixing) may also play a role in triggering plankton blooms (Berdalet et al., 2014<ref name=Ber></ref>).
  
Given a typical drag coefficient 0.00125 for wind stress over the sea (Kara et al. <ref> Kara, AB, Wallcraft AJ, Metzger EJ, Hurlburt HE, Fairall CW, 2007.  Wind stress drag coefficient over the global ocean.  Journal of Climate 20, 5856-5864.  DOI: http://dx.doi.org/10.1175/2007JCLI1825.1</ref>) and 0.0025 for currents above the sea bed (e.g. Green and McCave <ref name=GM> Green MO, McCave IN, 1995. Seabed drag coefficient under tidal currents in the eastern Irish Sea.  Journal of Geophysical Research 100 (C8), 16057–16069.  DOI: 10.1029/95JC01381</ref>), these Ekman transports are about 1 m2/s for a typical wind of 8 m/s or near-bed current 0.2 m/s.  For example, modelled 1960-2004 mean down-welling circulation for the north-west European shelf from Brittany to the Norwegian Trench was about 1.2 Sv (Huthnance et al. <ref name=H09> Huthnance JM, Holt JT, Wakelin SL, 2009. Deep ocean exchange with west-European shelf seas. Ocean Science 5, 621-634, doi:10.5194/os-5-621-2009.</ref>; figure 7) as a result of winds driving surface waters onto the shelf and bottom frictional Ekman transport off the shelf (1 Sv=1 km3/s).  The latter is associated with prevailing poleward flow of order 2 Sv along the continental slope (typically in 200 to 1000 m depth) around Ireland and Scotland.
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When all the factors influencing the algal bloom dynamics remain constant in time, the bloom model predicts that the system will tend to the equilibrium state <math>N_{eq}, P_{eq}</math> (eq. A3), which is stable if the nutrient loss rate <math>\alpha</math> is sufficiently small. In practice, however, the temporal variation of the factors influencing the bloom dynamics prevents the establishment of an equilibrium state. When time dependency of the factors in the model equations (A1, A2) is taken into account, the multi-annual behavior of model simulations can exhibit unpredictable chaotic fluctuations (Huppert et al., 2005<ref> Huppert, A., Blasius, B., Olinky, R. and Stone, L. 2005. A Model for Seasonal Phytoplankton Blooms. Journal of Theoretical Biology 236: 276–290</ref>). In case of a seasonally fluctuating uptake efficiency <math>\beta(t)</math>, the model produces chaotic behavior if the nutrient influx <math>Q</math> is low and the mortality rate <math>\sigma</math> is large.  
  
===Cascading===
 
  
[[Image: Cascade.jpg|thumb|500px|right|Figure 8: Cascade off Foxe Basin, based on data from Campbell <ref>Campbell NJ, 1964.  The origin of cold high salinity water in Foxe Basin.  Journal of Fisheries Research Board of Canada 21, 45–55.</ref>: salinity (solid lines) and temperature (shaded areas) in August–September 1955.  From Ivanov et al.<ref> Ivanov VV, Shapiro GI, Huthnance JM, Aleynik DL, Golovin PN, 2004.  Cascades of dense water around the world ocean.  Progress in Oceanography 60, 47-98.</ref>.]]  
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==Related articles==
 +
:[[Marine Plankton]]
 +
:[[Green Ocean modelling]]
 +
:[[Shelf sea exchange with the ocean]]
 +
:[[Continental Nutrient Sources and Nutrient Transformation]]
 +
:[[Which resource limits coastal phytoplankton growth/ abundance: underwater light or nutrients?]]
 +
:[[Possible consequences of eutrophication]]
 +
:[[Eutrophication in coastal environments]]
 +
:[[Threats to the coastal zone]]
 +
:[[Estuarine turbidity maximum]]
 +
:[[Differentiation of major algal groups by optical absorption signatures]]
 +
:[[Remote sensing of zooplankton]]
 +
:[[Estimation of spatial distribution of phytoplankton in the North Sea]]
 +
:[[Light fields and optics in coastal waters]]
 +
:[[The Continuous Plankton Recorder (CPR)]]
 +
:[[Diversity and classification of marine benthic algae]]
 +
:[[Functional metabolites in phytoplankton]]
  
Dense water formed by winter cooling of shallow shelf seas may cascade down the slope under gravity (figure 8), eventually leaving the sloping bottom at its density level. [The excess density may be enhanced if sea ice forms, adding salt to the unfrozen water.  Increased density resulting from salination through evaporation can also occur in hot dry conditions.]  Typical values of cascading fluxes are estimated as 0.5-1.6 m2/s (Shapiro et al. <ref> Shapiro GI, Huthnance JM, Ivanov VV, 2003.  Dense water cascading off the continental shelf.  Journal of Geophysical Research 108(C12), 3390. doi:10.1029/2002JC001488.</ref>), significant when and where they occur but highly intermittent.
 
  
===Tides===
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==External sources==
 +
:[https://en.wikipedia.org/wiki/Phytoplankton Phytoplankton]
 +
:[https://en.wikipedia.org/wiki/Algae Algae]
 +
:[https://en.wikipedia.org/wiki/Marine_primary_production Marine primary production]
  
Tides are a consequence of gravitational forces on the solid earth and especially on the ocean.  The forcing is global in scale and mainly acts on wide ocean basins.  However, the largest tidal elevations are seen at coasts bounding broad shelf seas, where tidal currents are strongest and much of the global tidal energy dissipation occurs.  Thus tides are an example of full ocean – shelf sea interaction, with further amplification on broad shelves.
 
  
Consider a uniform shelf of width <math>W</math> and semi-diurnal tidal range <math>R</math>.  A volume <math>WR</math> per unit length has to be supplied in 6.2 hours to fill the “tidal prism” between low and high tide.  If sinusoidal in time, the required tidal current across the shelf edge in depth <math>h</math> reaches <math>\pi WR/T</math> (<math>T</math> is the semidiurnal tidal period).  For example, the Celtic Sea (continental shelf) south-west of the UK is up to 400 km wide with large tidal range, e.g. 4 m at Newlyn.  <math>\pi WR/T</math> with <math>h</math> = 150 m gives about 0.75 m/s.  Thus in places the peak ebb and flood currents exceed 0.5 m/s; the corresponding exchanges are as much as 80 m2/s.
 
  
However, semi-diurnal tidal exchanges are reversed every 6.2 h; this is too soon for much to happen in the water, reducing their effect.  Long-term exchange is associated with tides through shear dispersion, coefficient about <math>10^3|U^2|</math> or 500 m2/s (Prandle<ref> Prandle D, 1984.  A modelling study of the mixing of 137Cs in the seas of the European continental shelf.  Philosophical Transactions of the Royal Society of London A, 310, 407–436.</ref>).  From (1) we estimate the associated exchange as 0.1 m2/s or more (<math>h= 150 \; m, \; L_x \le 400 \; km</math>).
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==References==
 
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<references/>
===Surges===
 
 
 
This refers to flows driven by weather systems so that spatial scales typically correspond to the width of shelf and time-scales are several hours to a day or two.  Shallow shelf seas are relatively easily accelerated.  Hence mode 1 coastal-trapped waves tend to be generated on account of their matching scales (Huthnance <ref name=H95></ref>).  Thus longer-period wind forcing tends to be associated with along-slope flow; higher frequencies break the geostrophic constraint to allow cross-slope flow, especially near a mode-1 frequency maximum for which the wave tends to have anti-cyclonically polarised flow near the shelf edge.  Otherwise surges tend to be over the shelf, not in deeper water, with maximum elevation at the coast.
 
 
 
===Internal tides and waves===
 
 
 
[[Image: InternalW.jpg|thumb|400px|right|Figure 9: Thermistor chain cross-section of temperature (<math>^{\circ}C</math>) through internal wave packet over continental slope depth 400 m.  Data from RV Colonel Templer from 0100 to 0200 UTC on the 19th August 1995, Hebrides shelf edge west of Scotland near 56.5°N, 9.1°W.]]
 
 
 
Internal tides are formed when shelf-edge topography causes vertical displacements in cross-slope tidal flow.  If they were entirely linear, then no net transport would result during a tidal cycle.  However (i) layer thickness may correlate with oscillatory velocity (Spingys et al. <ref> Spingys C, Williams RG, Green JAM, Hopkins JE, Sharples J, 2016??  Tidal bolus transport and heat supply onto continental shelves.  ??submitted?? </ref>) and (ii) strong cross-slope tidal currents generate large-amplitude internal tides.
 
 
 
(i) Let the velocity <math>u</math> in a layer between two isopycnals be separated into time-mean and time-varying components, such that <math>u = \hat u + u'</math>, and likewise the thickness of the pycnocline <math>h = \hat h + h'</math>.  The time average transport, <math><hu></math>, is then composed of a time-mean and a time-varying (‘eddy’) transport:
 
 
 
<math><hu> = \hat h \hat u + <h'u'></math>.
 
 
 
[For a single layer or a surface wave, the ‘eddy’ transport is equivalent to the Stokes Drift.  However, for multiple layers no such equivalence has been found.]  For a sinusoidal layer with small relative wave amplitude <math>a/h</math>,  we have <math><h'u'> = c a^2/2\hat h</math> where <math>c</math> is the phase speed.  Such ‘eddy’ transport is liable to be offset by opposing mean flow <math>\hat u</math> in the same layer or elsewhere.
 
 
 
(ii) If vertical displacements are a substantial fraction of water depth, then the motion is non-linear, the waves steepen and form one or more solitons (figure 9) which carry water “bodily” as part of the wave form (e.g. Vlasenko et al. <ref> Vlasenko V, Stashchuk N, Inall ME, Hopkins JE, 2014.  Tidal energy conversion in a global hot spot: On the 3‐D dynamics of baroclinic tides at the Celtic Sea shelf break.  Journal of Geophysical Research: Oceans 119 (6), 3249-3265.</ref> for the Celtic Sea; Lien et al. <ref> Lien R-C, Tang TY, Chang MH, D’Asaro EA, 2005.  Energy of nonlinear internal waves in the South China Sea.  Geophysical Research Letters 32 (5).  DOI: 10.1029/2004GL022012</ref> for the South China Sea).  Then the transport can be estimated from the soliton amplitude, length and speed; up to 1m2/s in extreme cases such as the Celtic Sea, NW Australia and Georges Bank (Huthnance<ref name=H95></ref>, reviewing several authors’ work).
 
 
 
Internal waves occur at all frequencies <math>\sigma</math> from the Coriolis frequency <math>f</math> to the buoyancy frequency <math>N</math>, and all wave directions. They occur throughout the ocean from wind and tidal forcing; their oceanic spectrum is empirically near-universal except close to sources (Garrett and Munk<ref>Garret CJR and Munk WH (1979) Internal Waves in the Ocean. Ann. Rev. Fluid Mech. 11, 339-369</ref>); the energy density corresponds to an estimated shelf-ward energy fIux of the order of 1 kW/m (Huthnance<ref name=H81> Huthnance JM, 1981.  Waves and currents near the continental shelf edge. Progress in Oceanography 10, 193-226.</ref>).  Their strong vertical and horizontal currents, and breaking in places, cause turbulent mixing affecting many ocean processes.  If the sea-floor slope closely matches the waves’ characteristic slope <math>[(\sigma^2-f^2)/(N^2-\sigma^2)]^{1/2}</math> then the currents may be amplified several times within a bottom boundary layer.
 
 
 
The shelf edge provides an effective source of internal waves: at internal tidal frequencies as above with higher-frequency contributions if non-linearities are significant; as standing lee waves in longer-period flow along a rough continental slope (Thorpe <ref> Thorpe SA, 1992.  The generation of internal waves by flow over the rough topography of a continental slope.  Proceedings of the Royal Society of London, A439, 115-130.</ref>) and analogously around a seamount (Chapman and Haidvogel<ref> Chapman DC, Haidvogel DB, 1993.  Generation of internal Iee waves trapped over a tall isolated seamount.  Geophysical and Astrophysical Fluid Dynamics 69, 33-54.</ref>).  Moreover, internal wave motion along characteristics is reflected off the sloping bottom, with a change of wavelength.  Internal wave energy may also transmit to the shelf; but reflection is strong if the bottom slope exceeds the characteristic slope for the wave (Hall et al. <ref> Hall RA, Huthnance JM, Williams RG, 2013.  Internal wave reflection on shelf slopes with depth-varying stratification.  Journal of Physical Oceanography 43, 248-258.</ref>).  The most energetic known internal waves are generated in Luzon Strait (NE South China Sea) and cause turbulence exceeding 10,000 times background ocean turbulence (Alford et al. <ref> Alford MH, Peacock T, MacKinnon JA, Nash JD, Buijsman MC, Centurioni LR, Chao S-Y, Chang M-H, Farmer DM, Fringer OB, Fu K-H, Gallacher PC, Graber HC, Helfrich KR, Jachec SM, Jackson CR, Klymak JM, Ko DS, Jan S, Johnston TMS, Legg S, Lee I-H, Lien R-C, Mercier MJ, Moum JN, Musgrave R, Park J-H, Pickering AI, Pinkel R, Rainville L, Ramp SR, Rudnick DL, Sarkar S, Scotti A, Simmons HL, St Laurent LC, Venayagamoorthy SK, Wang Y-H, Wang J, Yang YJ, Paluszkiewicz T, Tang T-Y, 2015.  The formation and fate of internal waves in the South China Sea.  Nature 521, 65-69.</ref>)
 
 
 
===Surface waves===
 
  
These may contribute to circulation and exchange via non-linear rectification of their currents.  Estimated surface wave currents (Kenyon 1969) are <math>0.015 w - 0.035 w</math> under wind speed <math>w</math>, decaying with depth on a scale <math>w/3</math> in mks units. The Stokes Drift (Lagrangian - Eulerian) transport <math> < \int u dt . \vec \nabla \vec u > \sim 0.01 \; w^2</math> is thus comparable with the Ekman transport <math>\tau/ \rho f </math> in mks units. Typically, the waves and Stokes Drift have an on-shelf component owing to the greater scope for generation provided by the off-shelf area of ocean.  This transport is concentrated near the surface; it represents a difference (tracked water movement - average velocity at one point) rather than absolute circulation and is likely to be offset by opposing flow elsewhere in the water column.
 
  
Shelf edge topography only affects the longest waves.  For example, with the criterion (wavenumber × depth) < 2, only waves of period > 14 s “feel” the bottom at 100 m depth.
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[[Category:Coastal and marine ecosystems]]   
 
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[[Category:Eutrophication]]
 
 
==Impacts==
 
 
 
These include surface elevations and waves, especially at the coast.  Circulation of water, and energy going into turbulence and mixing, all affect  water properties and contents.
 
 
 
===Surface elevations and waves===
 
 
 
Theory and modelling suggest that sea-level variability on the longest spatial scales transmits from ocean to shelf-sea and coast (e.g. Huthnance <ref name=H87>Huthnance JM, 1987.  Along-shelf evolution and sea levels across the continental slope. Continental Shelf Research 7, 957-974.</ref><ref name=H04>Huthnance JM, 2004.  Ocean‐to‐shelf signal transmission: A parameter study.  Journal of Geophysical Research: Oceans 109, C12029, 11pp.  doi:10.1029/2004JC002358.)</ref>).  Tides are a notable example.  However, satellite altimetry shows a minimum of sea-level variance at the shelf edge, compared with the shelf sea and open ocean (Hughes and Meredith <ref> Hughes CW, Meredith MP, 2006.  Coherent sea-level fluctuations along the global continental slope. Philosophical Transactions of the Royal Society of London, A, 364 (1841). 885-901. 10.1098/rsta.2006.1744</ref>), yet coherence along the continental slope.  This suggests that shelf seas and open oceans have separate causes of sea-level variations (e.g. weather and eddies respectively) but some inhibition to transmission across the continental slope.  Weather over the shelf tends to generate coastal-trapped wave mode 1, which typically has a node near the shelf edge, and perhaps typical eddy scales are too short.  This is the subject of continuing research.
 
 
 
[[Image: SeaLevel.jpg|thumb|500px|right|Figure 10: Map of rates of change in sea surface height (geocentric sea level) for the period 1993–2012 from satellite altimetry.  Colour interval is 2 mm/year, zero is pale blue/white boundary.  From Church et al. <ref name=C> Church JA, Clark PU, Cazenave A, Gregory JM, Jevrejeva S, Levermann A, Merrifield MA, Milne GA, Nerem RS, Nunn PD, Payne AJ, Pfeffer WT, Stammer D, Unnikrishnan AS, 2013: Sea Level Change. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.</ref>.]]
 
 
 
Sea level is rising globally and typical rates at the coast are similar to those in the open ocean now inferred from satellite altimetry.  However, local sea level change can differ from the global average (figure 10).  In the western tropical Pacific, sea level rise rates were up to 10 mm/yr averaged over 1993 to 2012 compared with a global mean of about 3 mm/yr.  In contrast, sea level fell during this period in most of the east Pacific from Alaska to Peru.  Varying winds, variability such as El Niño, oceanic thermal expansion and melted ice can alter ocean currents and associated sea level differences (Church et al. <ref name=C></ref>).  Ice re-distribution as water affects the earth’s gravitational field and hence “level”.  These factors are all large-scale and are expected to transmit from ocean basins across the shelf to the coast.  [Other factors are local or associated with land movement: water extraction, sediment compaction, tectonics, storms, earthquakes, landslides, uplift after the last ice age.]   
 
 
 
The largest (and usually longest) surface waves are generated over a large “fetch” (extent of open ocean giving uninterrupted wind forcing).  Hence they tend to come from deep ocean to shelf sea where they may have most impact: long waves steepen in shallower water; soft coasts and mobile sediments are vulnerable to stresses from wave motion.
 
 
 
===Flushing / water renewal===
 
 
 
These concepts are best applied to semi-enclosed seas with coasts bounding well-defined inflows and outflows.  [In open sea areas, flushing and residence times can be arbitrarily shortened merely by decreasing the area in question.]  However, these concepts help to assess the effectiveness of ocean-shelf transports.  Thus around <math>42^{circ}N</math>  off north-west Spain, average exchange across the 200m depth contour was estimated as 3.1 m2/s (Huthnance et al. <ref> Huthnance JM, Van Aken HM, White M, Barton ED, Le Cann B, Coelho EF, Fanjul EA, Miller P, Vitorino J, 2002.  Ocean margin exchange - water flux estimates.  Journal of Marine Systems 32 (1-3), 107-137.</ref>), a large value and sufficient to replace the shelf–sea cross-section 3.32 km2 in only  about 12 days.  Estimates Irish Sea outflow are similarly 2 to 3 m2/s [i.e. mostly 0.7 – 1.1 × 105 m3/s through the North Channel width 35 km (Knight and Howarth, 1999)].  However, this is only the volume of the Irish Sea in about one year (resupplied mostly by water originally from the Atlantic).  Similarly inflows to the North Sea are 1.5-2Sv mostly from the North (e.g. Otto et al. <ref> Otto L, Zimmerman JTF, Furnes G, Mork M, Saetre R, Becker G, 1990.  Review of the physical oceanography of the North Sea.  Netherlands Journal of Sea Research 26 (2), 161-238.</ref>), corresponding to 2 to 3 m2/s on average across Scotland – Shetland – Norway. However, the North Sea is large and this inflow only amounts to the North Sea volume in about one year.  Indeed, within the North Sea, the northern area tends to be flushed in a shorter time whereas in the centre the through-flow is much slower.
 
 
 
===Turbulence and Mixing===
 
 
 
[[Image: SSCpump.jpg|thumb|400px|right|Figure 11: Sketch of south-north section through the North Sea. The shallow south is vertically mixed.  In the north, respiration is mainly below the summer thermocline (dotted line) and subject to exchange with the North Atlantic.  From Thomas et al.<ref> Thomas H, Bozec Y, Elkalay K, de Baar HJW, 2004. Enhanced open ocean storage of CO2 from shelf sea pumping.  Science 304, 1005-1008.</ref>).]]
 
 
 
As elsewhere, important processes for generating turbulence and consequent mixing near the continental shelf edge are: wind forcing and surface waves for surface mixing, internal tides and waves for mixing in the interior, tidal currents and internal waves near the bottom (e.g. Huthnance <ref name=H95></ref>).  The intensity varies greatly according to context.  At the Celtic Sea shelf edge, internal waves are very variable (e.g. Green at al. <ref> Green JAM, Simpson JH, Legg S, Palmer MR, 2008.  Internal waves, baroclinic energy fluxes and mixing at the European shelf edge.  Continental Shelf Research 28, 937-950.</ref> but large, especially at (irregular) times near spring tides, and are associated with pycnocline mixing and density reduction near the bottom (Palmer et al. <ref> Palmer MR, Stephenson GR, Inall ME, Balfour C, Düsterhus A, Green JAM, 2015.  Turbulence and mixing by internal waves in the Celtic Sea determined from ocean glider microstructure measurements. Journal of Marine Systems 144, 57-69.</ref>).  An upward flux of nitrate with a spring-neap cycle further demonstrates internal tidal forcing, associated with the passage of internal solitons around spring tides (Sharples et al. <ref name=S07> Sharples J, Tweddle JF, Green JAM, Palmer MR, Kim Y-N, Hickman AE, Holligan PM, Moore CM, Rippeth TP, Simpson JH, Krivtsov  V, 2007.  Spring-neap modulation of internal tide mixing and vertical nitrate fluxes at a shelf edge in summer.  Limnology and Oceanography 52 (5), 1735-1747.</ref>).
 
 
 
'''Biogeochemistry'''
 
Many studies have discussed enhanced primary production on continental shelves in upwelling regions.  These are typically at sub-tropical eastern ocean margins; winds with an equatorward component (at least seasonally) drive surface Ekman transport offshore.  These surface waters are replaced by nutrient-rich waters from below, fuelling phytoplankton growth.  Prevailing winds give the north-west European continental shelf overall down-welling circulation.  Nevertheless, studies suggest a net supply of nitrate from the ocean to the North Sea (e.g. Pätsch and Kühn <ref> Pätsch J, Kühn W, 2008.  Nitrogen and carbon cycling in the North Sea and exchange with the North Atlantic—A model study. Part I. Nitrogen budget and fluxes.  Continental Shelf Research 28 (6), 767-787.</ref>) and to the west of Scotland (Proctor et al. <ref name=P03> Proctor R, Chen F, Tett PB, 2003.  Carbon and nitrogen fluxes across the Hebridean shelf break, estimated by a 2D coupled physical-microbiological model.    Science of the Total Environment 314, 787-800.</ref>).  Moreover, sinking of ensuing plankton leads to an off-shelf near-bottom carbon flux west of Scotland (Proctor et al. <ref name=P03></ref>) as suggested more widely from Ireland to the Norwegian Trench on the basis of the down-welling circulation (Holt et al. <ref> Holt J, Wakelin S, Huthnance J, 2009.  Down-welling circulation of the northwest European continental shelf: A driving mechanism for the continental shelf carbon pump.  Geophysical Research Letters 36, L14602.</ref>; Wakelin et al. <ref> Wakelin SL, Holt JT, Blackford JC, Allen JI, Butenschön M, Artioli Y, 2012.  Modeling the carbon fluxes of the northwest European continental shelf: Validation and budgets. Journal of Geophysical Research Oceans 117 (C5), C05020.  DOI: 10.1029/2011JC007402.</ref>).
 
 
 
Seasonally stratified shelf seas may act as sinks of atmospheric CO2 (the shelf-sea carbon “pump”).  Primary production takes up atmospheric CO2; sinking, sub-thermocline respiration of organic matter and off-shelf transport in a bottom layer follow before winter mixing gives re-exposure to the atmosphere (figure 11).  Nitrate and carbon cycles over Goban Spur, as constructed in OMEX (Wollast and Chou <ref> Wollast R, Chou L, 2001.  The carbon cycle at the ocean margin in the northern Gulf of Biscay.  Deep-Sea Research II, 48 (14-15), 3265-3293.</ref>), also involve import of nitrate to the shelf from the deeper ocean and export of carbon from the shelf break to deeper on the continental slope.  Distinctive mixing by internal tides and solitons at the Celtic Sea shelf edge, with the resulting upward nitrate flux, fuels a sub-surface chlorophyll maximum demonstrating consequent growth of phytoplankton.  Compared with the adjacent Celtic (shelf) Sea and northeast Atlantic Ocean, shelf-edge vertical mixing of nitrate is enhanced and correspondingly the largest phytoplankton cells are found in surface waters there (Sharples et al. <ref name=S07></ref><ref name=S09> Sharples J, Moore CM, Hickman AE, Holligan PM, Tweddle JF, Palmer MR, Simpson JH, 2009.  Internal tidal mixing as a control on continental margin ecosystems.  Geophys. Res. Lett., 36, L23603, doi:10.1029/2009GL040683.</ref>).  The shelf-edge internal tide (globally ubiquitous) is suggested to support shelf-edge fisheries by providing large-celled phytoplankton for first-feeding fish larvae without any need to coincide with a spring bloom; moreover large-cell  phytoplankton favour particulate organic carbon export and sequestration in deep water and sediments (Sharples et al. <ref name=S09></ref>).
 
 
 
 
 
 
 
[[Image: JHtable.jpg|thumb|1000px|center|Table1: Some ocean – shelf sea interaction studies.]]
 
 
 
 
 
==References==
 
 
 
<references/>
 

Revision as of 22:01, 2 August 2020

Algal bloom dynamics


Algal bloom is a short-lasting strong increase of an algal population. The concentration of algae multiplies a thousand or even a million fold and collapses shortly after. Algal blooms are a worldwide phenomenon that occurs when the water temperature is favorable and light and nutrients are sufficiently available. Due to eutrophication of the coastal waters, algal blooms have become more frequent. Global warming may also play a role. This article introduces some elementary notions that provide insight into the phenomenon of algal blooms. A simple model of algal bloom dynamics is presented in the appendix.


Introduction

Fig. 1. Envisat MERIS true colour image of a phytoplankton bloom in the Barents Sea

Algae are aquatic organisms that grow through photosynthesis. Many thousands of different algae species are known (Andersen, 1992[1]). In this article we focus on micro-algae, collectively called 'phytoplankton'. This includes also certain types of bacteria in marine waters (sometimes called 'bacterioplankton') that grow through photosynthesis and produce blooms, although not belonging to the algae family. The most common phytoplankton species in seawater are diatoms, flagellates and cyanobacteria. The smallest species (picophytoplankton, size < 2 micron, consisting mostly of cyanobacteria) have the highest nutrient-uptake efficiency and are therefore most abundant in nutrient-poor ocean waters, whereas the larger diatoms tend to dominate the phytoplanktonic biomass in nutrient-rich waters (Edwards et al., 2011[2]; Burson et al., 2018[3]). Blooms of large phytoplankton species only occur when the temperature does not exceed a critical limit of about 15oC (Cloern, 2018[4]). Algae blooms can extend over large areas, as illustrated in Fig. 1.

All phytoplankton species grow by absorbing dissolved CO2 under the influence of light and thereby emit oxygen. Marine phytoplankton contributes almost half to the total oxygen production on Earth (Behrenfeld et al., 1998[5]). Phytoplankton species are called 'autotrophs' or 'primary producers', because they are able to feed and produce organic material from mineral substances. They are a food source for other marine organisms, zooplankton in the first place. They are therefore at the basis of the food web of marine life. For more details about the different plankton species, see the article Marine Plankton.


Conditions for growth: light, temperature and nutrients

Besides CO2 and sunlight, phytoplankton needs certain nutrients for growth. These are primarily the minerals nitrogen N, phosphorus P and silicon Si (mainly in the form of dissolved salts, nitrate, phosphate and silicate, respectively, see Continental Nutrient Sources and Nutrient Transformation). Small amounts of iron Fe and certain vitamins are also required. Lack of any of these nutrients limits the growth of phytoplankton. The ratio in which these nutrients are needed has been determined in the past at 106 C: 16 N: 1 P, the so-called Redfield ratio. However, the ratio varies by species, allowing some species to grow better or less well than others under certain conditions. Growth further depends critically on light and temperature (Bissinger et al., 2008[6]; Boyd et al., 2013[7]). Here too, the optimum values are specific to each algal species.

Fig. 2. Multi-annual observation record of the alga Chaetoceros socialis (red spikes) at a measuring point in the North Sea 10 km north of the Dutch Wadden island of Terschelling. Simultaneous measurements of the local nitrate concentration (black) and surface salinity (blue). From Wagner-Cremer et al. (2018)[8].

Phytoplankton can grow under favorable conditions unrestrained as long as there is no restriction in the availability of the necessary nutrients. Population growth occurs through division of the parent cell, with the formation of two or more offspring. The cell division frequency for each species is different and depends on temperature and light; it can happen every few hours, but also every few days. Since this applies to each individual in the population, growth has an exponential character. Huge population growth is therefore possible in a short time.

An example of the explosive short-lived nature of algal blooms is illustrated in Fig. 2, showing a multi-year observation record of the alga Chaetoceros socialis at a measuring station in the North Sea 10 km north of the Dutch Wadden island of Terschelling. The figure also shows observations of the nitrogen concentration (dissolved nitrate) and the salinity at the measuring point.

The conditions for algal blooms vary with the seasons. This is not only due to temperature and light. In the winter, nutrient-rich organic material is stirred from the seabed. Therefore, nutrient concentrations are often highest in early spring (N hemisphere). With increasing light and temperature, the conditions for algal bloom become optimal; the largest algal blooms therefore occur in general during springtime. The strongest algal growth takes place in the upper water layer where light penetrates best, the so-called euphotic zone. Intensive mixing over the water column is less favorable because it moves part of the phytoplankton into deeper water layers, where growth is limited due to a lack of light. In the oceans, algal blooms are typically concentrated in a rather thin surface layer. Vertical mixing is counteracted by density stratification, whereby water with a higher temperature and/or lower salinity floats on top of colder/saltier seawater. Organic detritus, because of its specific density, tends to be collected at the interface zone (picnocline), where nutrients are released after mineralization of the detritus. This creates ideal conditions for the development of strong algal blooms, especially blooms of mixotrophic algae that feed both on nutrients and organic material (Berdalet et al., 2014[9]; Sigman and Hain, 2012[10]).

The size of a plankton bloom is generally expressed in terms of organic carbon weight, [math]g \, C[/math]. The value can be obtained by taking samples and measuring the ash-free dry biomass content (see In situ monitoring of eutrophication, Sampling tools for the marine environment). However, it is most usual to estimate phytoplankton biomass by quantifying chlorophyll a, the photosynthetic pigment common to all types of algae. It can be determined by various optical techniques due to its fluorescence properties. Techniques are described in the articles Estimation of spatial distribution of phytoplankton in the North Sea, Determining coastal water constituents from space, Differentiation of major algal groups by optical absorption signatures.


Other factors that condition algal blooms

Inter-species competition

The conditions for optimal growth are not the same for different algal species present in a particular coastal area. The species that uses the available resources with the highest efficiency will experience the strongest growth. Therefore, the dynamics of algal blooms cannot be estimated from the average reproduction rate of the various algae species. A common assumption is that the composition of the algal population adapts rapidly, so that optimal use is made of the growth potential provided by the available resources: light, temperature and nutrients. For example, field observations by Philippart et al. (2000[11]) in the Wadden Sea show that the composition of the algal population is adjusted to the ratio between different nutrients, in particular N and P. In a modelling approach based on this assumption, the composition of the algal population (numbers of constituent species) is determined by optimizing at each time step the utilization of the available resources (light and nutrients). The utilization of these resources during this time step yields the new available light and nutrients for which the composition of the algal population is optimized in the next time step. These models assume fast growth rates, such that the algal population is always tuned to optimum resource utilization at each time step. Numerical simulations by Los and Wijsman (2007[12]) of algal blooms based on this assumption generally show fair similarity to field observations. Another factor influencing the competition between algal species for light and nutrients is the ability of certain algal species to migrate towards zones that offer the best growth conditions. In this way these algae can outcompete non-motile species, especially in low-turbulence environments (Klausmeier and Litchman, 2001[13]).

Predation

The size of algal populations is limited not only by shortage of nutrients, but also by mortality and predation. Algae are an essential food source for many organisms in the sea. The main phytoplankton grazers are zooplankton species, which come in different shapes and sizes. The smallest zooplankton (micro-zooplankton, mainly flagellates, ciliates and mixotrophic phytoplankton), while grazing on the smallest phytoplankton species, can adapt quickly to changes in the prey population and thus largely controls the size of picophytoplankton blooms. This is less the case for the larger zooplankton, that consists mainly of herbivore copepods in the oceans and of filter feeding benthos and benthic larvae in estuarine environments. Blooms of larger phytoplankton species (diatoms, dinoflagellates), that dominate in eutrophic and nitrogen-controlled conditions[11], are therefore less sensitive to grazer dynamics. The lesser grazing sensitivity can also be due to flight behavior (Harvey and Mende-Deuer, 2012[14]) or a lower nutrient content of larger phytoplankton (Branco et al., 2020[15]). Digestion of phytoplankton by large zooplankton species leads to excretion of organic material in the form of fecal pellets. In the deep ocean, fecal pellets sink to the bottom; in this way CO2 and nutrients are removed from the marine ecosystem. In shallow coastal waters, fecal pellets are mineralized on the bottom where the released nutrients are exploited by the benthic ecosystem. Organic bottom material that is stirred up by waves and currents provides nutrients to the pelagic phytoplankton. Organic matter and nutrients are stored in the soil where net sedimentation occurs, but otherwise the recycling of nutrients in coastal waters is stronger than in the ocean.

Mortality

Phytoplankton mortality is largely due to viral infections (Baudoux, 2007[16]). In the (sub)tropical ocean, the contribution of viruses to the decay of algal blooms is similar or even superior to the impact of grazing, whereas grazing dominates at higher latitudes (Mojica et al., 2016[17]). The mortality rate of phytoplankton exceeds in some cases the growth rate, but is generally lower. Most dead algae are too small to sink to the bottom. Part of the dead algae is broken down by bacteria in the euphotic zone, where the released nutrients fuel new blooms. Another part aggregates with other organic and inorganic particles until reaching a mass that makes the aggregates sink to the bottom. In the oceans, these sinking particles (called 'marine snow') are sequestered in deep water layers. In addition to gravitational sinking, downward transport of organic matter in the ocean also occurs in downwelling regions (see the article Shelf sea exchange with the ocean) and through episodic localized subduction currents (Llort et al., 2018[18]). The total ocean carbon sink due to these different processes is in the order of ¼ of the total global carbon emissions (De Vries et al., 2019[19]).

Consequences of algal blooms

Increased fishery yields

There is strong evidence that eutrophication of coastal waters has led to an increase in primary production and an increase in the food supply for higher trophic species. A strong increase in fishing yields in eutrophicated coastal waters can be attributed to this increased primary production (Nixon, 1988[20]; Nixon and Buckley, 2002[21]).

Oxygen depletion

Algal blooms operate by photosynthesis and therefore produce a lot of oxygen. The reverse happens when the bloom decays; oxygen is extracted from the water when the organic material is mineralized (the work of bacteria). The oxygen demand of a collapsing algal bloom can be very high. Dissolved oxygen will be depleted if the water is not flushed or aerated fast enough, a situation called anoxia. This is a common phenomenon in lakes, but it can also occur in lagoons and estuaries. In cases where differences in temperature or salinity between upper and lower water layers stratify the water column, anoxia can easily arise in the lower water layer (see Estuarine turbidity maximum). This is on the one hand due to mineralization of sinking organic material, and on the other hand due to suppression of turbulent mixing with water of the more aerated and oxygen-rich top layer. Most organisms cannot live in anoxic water and die, and thus aggravate anoxia. Oxygen depletion is often an indirect result of eutrophication, that stimulates the formation of algal blooms in the upper water layer.

Harmful algae

Numerous algae species produce toxic substances and are therefore called harmful algae. Many aquatic (and non-aquatic) organisms are poisoned when they ingest large amounts of these toxic algae. This can happen when a bloom of harmful algae develops. Marine aquaculture is particularly affected by toxic algal blooms. Harmful algal blooms (HABs) are a natural and frequent phenomenon, similar to non-harmful algal blooms. The chemicals produced by harmful algae (e.g. certain species of diatoms and dinoflagellates) are a defence mechanism against predators, either through toxin production or feeding deterrence, see Chemical ecology#Chemical ecology and phytoplankton and Functional metabolites in phytoplankton. However, some doubts exist about the effectiveness of these defence mechanisms to reduce grazing pressure by zooplankton (Zigone and Wyatt, 2004[22]). There is some evidence that the size and frequency of harmful algal blooms are increasing (Hallegraeff, 1993[23]). Some theories relate the increase in toxic algal blooms to eutrophication, in particular in situations where the natural nutrient ratio is disturbed; other theories point to global warming. However, a clear explanation of the causes is still lacking (Anderson, 2012[24]).

Regional distribution of algal blooms

Algal blooms require light and nutrient-rich water. Nutrient-rich surface waters occur naturally in the so-called upwelling zones, areas where deep ocean water rises up (see the articles Ocean circulation and Shelf sea exchange with the ocean). Major upwelling zones are located along the Atlantic coast of Africa and the Pacific coasts of California and south America, where ocean surface currents are bent off the coast by the effect of Earth's rotation. Net primary productivity NPP (gross production minus respiration) can exceed 1000 [math]g \, C m^{-2} y^{-1}[/math], which is much more than the ocean average of about 150 [math]g \, C m^{-2} y^{-1}[/math]. However, the highest nutrient concentrations are not found in the oceans, but in coastal waters, especially in estuaries and lagoons (Howarth, 1988[25]), mainly due to release of nutrients by human activities (see e.g. Eutrophication in coastal environments). Most of the primary production occurs during seasonal or episodic algal blooms. However, the annual NPP in coastal systems is not exceptionally high; values range typically from 50 to 400 [math]g \, C m^{-2} y^{-1}[/math]. Large spatial differences occur within estuaries as well as strong interannual fluctuations, but on average the NPP seldom exceeds 500 [math]g \, C m^{-2} y^{-1}[/math] (Cloern et al., 2014[26]). A major reason is the greater importance of light as a limiting factor for algal growth than nutrient deficiency, especially in deep (often dredged) estuaries. This is due to the turbidity of the water in estuaries and lagoons and along the adjacent coast (see the articles Estuarine turbidity maximum and Which resource limits coastal phytoplankton growth/ abundance: underwater light or nutrients?). A model study by Liu et al. (2018[27]) shows that in well-mixed turbid estuaries, algal blooms are restricted to the zone downstream from the estuarine turbidity maximum. The role of river discharge on algal blooms in estuaries is ambiguous. High discharges supply nutrients, but they also flush algae out of the estuary. Observations by McSweeney et al. (2016[28]) in the Delaware show that high river discharges generate stratification with favorable light conditions for algal blooms in the surface layer. In estuaries with large intertidal flats, pelagic algae have to compete for nutrients with benthic algae (De Jonge and van Beusekom, 1992[29]). Comparing observations from many estuaries, it appears that the total annual decay of organic matter in most estuaries is larger than the gross primary production. This means that, unlike other marine systems, these estuaries are net producers of CO2 (Caffrey, 2004[30]; Gattuso et al., 1998[31]).


Appendix

The occurrence of algal blooms, with rapid emergence and equally rapid disappearance, is a prominent feature of eutrophication. This appendix provides a qualitative explanation of algal bloom dynamics, following the paper by Huppert et al. (2002[32]). The explanation is based on a simple model in which an algal bloom is related to the available amount of a certain nutrient. This nutrient is assumed to be essential for the growth of the algal population, but to be present in such a low concentration that it limits the growth of the population. Because the uptake of the nutrient by the algae decreases the nutrient concentration, the population growth and the nutrient concentration form together a self-regulating feedback system. The different processes that play a role are set out below. The model is meant to enable a better understanding of the algal bloom process; it is too simple for application to real field situations because many of the processes discussed previously are ignored.

We call [math]P(t)[/math] the biomass, representing the size of the algal population at time [math]t[/math] in a certain volume [math]V[/math] of the sea, and [math]N(t)[/math] the average nutrient concentration in this volume. The temporal variation of the algal biomass, [math]dP/dt[/math] and the nutrient concentration, [math]dN/dt[/math], is regulated by the following factors:

  • Nutrient uptake [math]B[/math]. The uptake depends on the algal biomass [math]P[/math] and on the nutrient concentration [math]N[/math]. If the nutrient concentration is low (limiting), linearity of the dependence in both [math]P[/math] and [math]N[/math] is a reasonable assumption, [math]B=\beta (t) \, P \, N[/math]. The uptake efficiency [math]\beta(t)[/math] depends on other environmental conditions for algal growth, in particular temperature and light. Nutrient uptake increases the algal biomass by [math]B_P=\beta_P(t) \, P \, N[/math] and decreases the nutrient concentration by [math]B_N=-\beta_N(t) \, P \, N[/math]. The ratio [math]\rho=\beta_N(t)/\beta_P(t)[/math] is constant. Saturation of the nutrient uptake (i.e. [math]B[/math] independent of [math]N[/math] when [math]N[/math] is abundant) is ignored.
  • Biomass decay with nutrient restitution [math]G[/math]. The algal biomass decreases by respiration, mortality and mineralization of algal detritus, [math]G_P = - \gamma (t) \, P[/math], while the nutrient concentration increases with restitution of nutrient by [math]G_N=\rho \gamma (t) \, P[/math]. It is assumed that respiration and mineralization are quasi-instantaneous processes; their efficiency for nutrient restitution is expressed by the rate factor [math]\gamma(t)[/math].
  • Nutrient loss [math]S[/math] related to the loss of algal biomass by predation, sinking to the bottom and export, and therefore assumed proportional to the algal biomass: [math]S=- \sigma (t) \, P[/math]. Predation by zooplankton depends not only on the algal biomass but also on the biomass of zooplankton. The zooplankton population itself depends on the algal biomass and increases when the algal biomass is high. However, zooplankton dynamics is ignored in the model.
  • Nutrient loss [math]A=-\alpha (t) \, N[/math], as a result of biogeochemical processes that limit the availability of nutrients for uptake by algae.
  • Nutrient supply from external sources, [math]Q[/math]. Major external nutrient supplies (partly in the form of organic material) are coming from rivers, atmospheric deposition and stirring up of organic bed material.

We focus on the period in which the algal population experiences rapid growth and rapid decline. This period is assumed so short that the factors [math]\alpha, \beta, \gamma, \sigma[/math] can be considered approximately constant. Collecting the expressions of the factors influencing the temporal variation of algal population, [math]dP/dt[/math] and the nutrient concentration, [math]dN/dt[/math], we arrive at the equations:

[math]dP/dt = B_P+G_P+S_P = (\beta \, N - \gamma - \sigma ) \, P , \qquad (A1)[/math]

[math]dN/dt = B_N +G_N + A + Q = \rho (\gamma - \beta \, N) \, P - \alpha \, N + Q . \qquad (A2)[/math]

These coupled nonlinear equations are known as the Lotka-Volterra equations. The solution is not straightforward. It depends not only on the coefficients appearing in the equations but also on the initial conditions [math]P=P_0, \, N=N_0[/math] at time [math]t=0[/math]. Different types of long-term behavior of [math]P[/math] and [math]N[/math] may result: convergence to a static equilibrium state, to a cyclic state or to a state of chaotic fluctuations around certain attractors. We will not consider the long-term behavior, especially because the assumption of constant coefficients does not hold. For a qualitative understanding of the short-term behavior we will first consider the equilibrium solution of the Eqs. (A1) and (A2) corresponding to [math]dP/dt=0[/math] and [math]dN/dt[/math]. The equilibrium solution is given by the curves

[math]N_{eq}=\large\frac{\gamma + \sigma}{\beta}\normalsize, \quad P_{eq}=\large\frac{Q -\alpha N}{\rho (\beta N - \gamma)}\normalsize. \qquad (A3)[/math]

These curves are drawn in Fig. 3. The curves cut the [math]P,N[/math] phase plane in 4 phase sectors:

  • Green phase: [math]P[/math] and [math]N[/math] both increase;
  • Yellow phase: [math]P[/math] increases, [math]N[/math] decreases;
  • Red phase: [math]P[/math] and [math]N[/math] both decrease;
  • Blue phase: [math]P[/math] decreases and [math]N[/math] increases.


Fig. 3. Solution of the Lotka-Volterra equations (A1, A2), showing the coupled evolution of [math]P(t)[/math] and[math]N(t)[/math] in the [math]N-P[/math] phase plane (solid line). The model parameters are set as follows: [math]\alpha=0, \, \beta=0.1/N_0/day, \, \rho=10^{-3}, \, \gamma=0, \, \sigma=0.1/day, \, Q=7.5 \, 10^{-3} N_0/day, [/math] [math]N_0=0.1 g/m^3, P_0=6.10^{-5} g/m^3[/math]. From Huppert et al. (2002)[32].
Fig. 4. Temporal evolution of the algal population [math]P(t)[/math] (solid line) and the nutrient concentration [math]N(t)[/math] (dashed line) according to the equations (A1, A2) with the same parameters as for Fig. 3.


Now consider the evolution graph in Fig. 3, which is obtained by numerical integration of the Eqs. (A1) and (A2) [32]. The bloom starts in the green phase sector, where initially the algal biomass [math] P [/math] is very small. The environmental conditions (temperature, light) have just become favorable for nutrient uptake, i.e. the uptake efficiency factor [math]\beta [/math] has increased significantly. Shortly before (not shown in the figure), [math]\beta [/math] was much smaller and [math]N_ {eq} [/math] much larger, so that the algal population was still in the blue phase (i.e. decreasing in size). Due to the increased uptake efficiency, the biomass [math]P[/math] is now increasing, but the increase is slow because the rate of increase is proportional to [math]P[/math] (cf. A1). Nutrient uptake is still quite low and the nutrient concentration is still increasing due to the supply [math]Q[/math]. However, with increasing population size [math]P[/math] the nutrient uptake also increases and at some moment the nutrient concentration [math]N[/math] changes from increasing to decreasing. The [math]P-N[/math] system enters the yellow phase, where [math]P[/math] will grow rapidly, because the rate of change [math](\beta \, N - \gamma - \sigma ) \, P [/math] (Eq. A1) is large and initially still increasing in spite of the decrease of [math]N[/math] (Eq. A2). The algal bloom essentially takes place at the end of the green phase and the beginning of the yellow phase. The nutrient concentration decreases in the yellow phase and finally becomes so small that further growth of the algal biomass is no longer possible. At that time the algal biomass has reached its maximum and the [math]P-N[/math] system enters the red phase, where the algal biomass decreases. The nutrient concentration continues its rapid decrease (cf. A2) because the uptake of nutrients by the algal population is still high. However, the algal population also declines at a fast rate because [math](\beta \, N - \gamma - \sigma) \, P [/math] (cf. A1) is large and negative. The collapse of the algal population mainly takes place in the red sector. The decrease of the nutrient concentration ends when the uptake of nutrients has become very small, because of the small size of the algal population. The [math]P-N[/math] system then enters the blue phase where [math]P[/math] decreases further, while [math]N[/math] increases, but both at a slow rate. The algal bloom as a function of time, corresponding to the trajectory in the [math]P-N[/math] phase plane, is shown in Fig. 4. It illustrates the dramatic increase and collapse of the algal biomass (5 orders of magnitude) in a short time. The peak of the bloom coincides with the strongest decrease of the nutrient concentration. The same coincidence is visible in the observation record of the plankton bloom and nutrient concentration in Fig. 2. It also appears, both in the model and the data, that the variation of the nutrient concentration is much less pronounced than the variation in the algal biomass.

The nonlinearity of the algal bloom equations has implications that may appear surprising at first sight. One may notice, for instance, that complete nutrient depletion is not a necessary condition for the crash of the algal population. The point is that below a certain level, which is not necessarily very small, the nutrient concentration is insufficient to sustain a very large algal population.

The maximum algal population size that can be reached during the bloom is not linearly related to the initial nutrient concentration [math]N_0[/math] and the initial population size [math]P_0[/math]. Depending on the values of [math]N_0, P_0[/math], it can happen that an increase of either [math]N_0[/math] or [math]P_0[/math] leads to a smaller bloom size, instead of a larger size[32]. According to the model, the nutrient concentration that is reached when the population enters the yellow phase determines to a large degree the maximum population size that can be reached during the yellow phase. This feature is not visible in the observations presented in Fig. 2. In fact, other factors such as sunlight and temperature also play a role. In the case of Fig. 2, it appears that the largest blooms are correlated with low salinity values. This points to a change in the type of water masses present at the measuring site. Stratification effects (suppression of vertical mixing) may also play a role in triggering plankton blooms (Berdalet et al., 2014[9]).

When all the factors influencing the algal bloom dynamics remain constant in time, the bloom model predicts that the system will tend to the equilibrium state [math]N_{eq}, P_{eq}[/math] (eq. A3), which is stable if the nutrient loss rate [math]\alpha[/math] is sufficiently small. In practice, however, the temporal variation of the factors influencing the bloom dynamics prevents the establishment of an equilibrium state. When time dependency of the factors in the model equations (A1, A2) is taken into account, the multi-annual behavior of model simulations can exhibit unpredictable chaotic fluctuations (Huppert et al., 2005[33]). In case of a seasonally fluctuating uptake efficiency [math]\beta(t)[/math], the model produces chaotic behavior if the nutrient influx [math]Q[/math] is low and the mortality rate [math]\sigma[/math] is large.


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