ó á ó á Aproximación a la dinámica de Ecosistemas Marinos
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ó á ó á Aproximación a la dinámica de Ecosistemas Marinos
Aproximación ó a la dinámica á de Ecosistemas Marinos Coastal Zone Ecosystem Management Coastal zone management requires a good understanding of marine ecosystem dynamics y are constituted by y a large g number of components p Marine ecosystems showing complex interactions. Simplifying the marine ecosystem structure and its dynamics is helpful. Máster Internacional en Gestión de Zonas Costeras y Estuáricas A way for such simplification is through conceptual models. LIM-UPC Modelling interactions of ecosystem components allows getting an approach h to t ecosystem t d dynamics. i Nixon Bahamón An approach, but not a good understanding, on the ecosystem dynamics can be reached in a couple of teaching hours. bahamon@ceab.csic.es www.marinecometrics.com www marinecometrics com www.ceab.csic.es/~oceans Here we go! Centre d’Estudis Avançats de Blanes (CEAB(CEAB-CSIC) Barcelona, 15 de febrero de 2010 Ecosystem--based management Ecosystem 1-6: Dominio pelágico 1. Región nerítica; 2. Región oceánica; 3. Zona Epipelágica. Epipelágica. 4. Zona Batial (4a (4a.. Zona Mesopelágica; Mesopelágica; 4b 4b.. Zona Batipelágica); 5. Zona Abisopelágica o Abisal; 6. Zona Hadalopelágica o Hadal Hadal;; (t: termoclina permanente) Source: http://www.ebmtools.org 3 A-D: Dominio bentónico A. Plataforma continental; B. Talud continental (B1 (B1.. Talud continental superior; B2 B2.. Talud continental inferior); C. Llanura abisal; D. Fosa hadal. hadal. 4 Fuente: Wikipedia Clasificación de los ecosistemas marinos Según la distancia a la costa • Zona nerítica: desde la línea de la costa hasta el borde de la plataforma p continental. • Zona oceánica: fuera del límite de la plataforma continental. Según la profundidad • Zona fótica: zona iluminada. – Zona epipelágica: pp g hasta el límite de la p plataforma continental ((200 m de profundidad). Tiene lugar la producción primaria (fotosíntesis). • Zona afótica: zona oscura. – Zona mesopelágica: 200 - 1.000 m. Abundante zooplancton. Se encuentra la termoclina permanente. – Zona batipelágica: 1.000 - 3.000 m. – Zona abisopelágica o abisal: 3.000 - 6.000 m. – Zona hadopelágica o hadal: más de 6.000 m; fosas oceánicas Clasificación de los ecosistemas marinos Sistema bentónico (fondo marino) El fondo marino ((rocoso,, p pedregoso, g , arenoso,, fangoso) g ) está p poblado p por organismos bentónicos. . • La región fótica: – Zona supralitoral (no sumergida) – Zona mesolitoral (intermareal) – Zona sublitoral: (p (permanentemente sumergida g en la p plataforma)) • La – – – – región afótica: Zona circalitoral: ((externa de la p plataforma sin vegetación) g ) Zona batial: (talud continental entre 200-3.000 m.) Zona abisal: (fondo oceánico, llanuras oceánicas, entre 3.000-6.000 m.) Zona hadal: (Zonas de subducción o de fosasa oceánicas 6.000 - 10,000 m) 5 Gulf of Lions Catalan Sea MFSPP-VOS MFSPPCruises Black Sea Adriatic Sea Tyrrhenian Sea 6 Aegean Sea Alboran Sea Ionian Sea Levantine basin AQUA--MODIS Sea AQUA Sea--surface chlorophyll, chlorophyll, March 2009 (Source Source:: http://oceancolor.gsfc.nasa.gov) Gulf of Lions Catalan Sea Alboran Sea Adriatic Sea Black Sea Tyrrhenian Sea Aegean Sea Ionian Sea Levantine basin AQUA--MODIS Sea AQUA Sea--surface chlorophyll, chlorophyll, September 2009 (Source Source:: http://oceancolor.gsfc.nasa.gov) Source:: Source A. Cruzado, Chief Sci Sci.. Ocean. Ocean. Lab., Lab., CEABCEAB-CSIC. 7 Prep.. by L. Simic Prep 25/01/01, Blanes, Spain 8 What drives ocean circulation? Global surface current system 10 Open University, Ocean Circulation, 2007 The Ocean Conveyor Belt What drives ocean circulation? Seawater flows along the horizontal plane and in the vertical: Typical speeds of the horizontal flow or currents: ~ 0.01-1.0 m/s yp vertical speeds p within the stratified ocean: ~ 0.001 m/s Typical 1. Wind driven circulation: The wind exerting a stress on the sea surface induces movement of that water. This is called Ekman Layer transport, which extends to the surface 50 to 200 meters. The wind driven circulation is characterized by large clock-wise and counter clock-wise flowing gyres, such as the subtropical and sub polar gyres. 2 Thermohaline circulation: Buoyancy (heat and freshwater) fluxes between 2. the ocean and atmosphere that alter the density of the surface water. The thermohaline circulation engages the full volume of the ocean into the climate system, by allowing all of the ocean water to 'meet' and interact directly the atmosphere (on a time scale of 100 100-1000 1000 years). Ocean circulation driven by density differences. (Density is controlled by ocean temperature and saltiness.) Cold, dense water in the Arctic merges with salty water from the Gulf Stream to create the sinking North Atlantic Deep Water (NADW) in the NorwegianGreenland Sea Sea. The NADW helps to drive global ocean circulation circulation. Illustration The M Factory © Smithsonian Institution. From: http://forces.si.edu/arctic/02_02_04.html 3. Geostrophic Currents: The ocean currents are for the most part geostrophic, meaning that the Coriolis Force balances the horizontal pressure gradients. gradients 4. Inertial Currents: Curve motion produced by the Coriolis force when wind ceases to blow. http://eesc.columbia.edu/courses/ees/climate/lectures/o_circ.html Sverdrup's p Theory y of the Oceanic Circulation • Answers to the questions can be found in a series of three remarkable papers published from 1947 to 1951. • In the first, first Harald Sverdrup (1947) showed that the circulation in the upper kilometer or so of the ocean is directly related to the curl of the wind stress. Ecuaciones de Momento En dinámica de fluidos, las ecuaciones de momento describen el movimiento de un fluido compresible no viscoso. viscoso q ≈ Euler eq.q sin Fr)) Ecuaciones de momento = Navier-Stokes eq. Gradiente de presión Fuerza de Coriolis (~7.3 x105 radianes s-1 • Henry Stommel (1948) showed that the circulation in oceanic gyres is asymmetric because the Coriolis force varies with latitude. • Finally, Walter Munk (1950) added eddy viscosity and pp layers y of the Pacific. calculated the circulation of the upper Together the three oceanographers laid the foundations for a modern theory of ocean circulation. latitud fricción http //ocean o ld tam ed / eso ces/ocng te tbook/chapte 11/chapte 11 01 htm http://oceanworld.tamu.edu/resources/ocng_textbook/chapter11/chapter11_01.htm Harald Sverdrup (1947). The Oceans: Their Physics, Chemistry and General Biology Circulación termohalina y transporte de partículas Molar redfield ratios Δ P: Δ N: Δ Si: Δ C = 1:16:15:106 (Brzezinski, Brzezinski, 1985). Open University, Mar.Biog.Cycles, 2005 16 Parámetro conservativo PO (Fosfato preformado) Utilización aparente de oxígeno (AOU) 17 Niveles troficos del ecosistema marino 18 Fishing grounds in a benthic environment Barcelona Th hrophic c level Iberian peninsula The Blanes Canyon Western Mediterranean Sea In the Blanes canyon A. antennatus dwells from 600 to 900 m depth, coinciding with the lower boundary of Levantine Intermediate Water (LIW) and the upper boundary of Western Mediterranean Deep Water (WMDW). The Blanes canyon y Fuente: Sarda et al. 2009. Prog. Oceanog. 82: 227-238 Coll et al., 2008 Ecosistema pelágico Seasonal changes g in upper pp water layers y EUPHOTIC ZONE EUPHOTIC ZONE MIXED-LAYER Phy -N NO -N N Zoo -N NH4 -N NO -N 200 m NO3-N winter Summer phytoplankton chlorophyll in the 24.5° North Atlantic WOCE section 01 .02 02 .03 03 .05 05 .11 .22 .33 .55 1 MIXED-LAYER Phy -N N NO -N N Zoo -N NH4 -N NO -N Ph -N Phy N NO -N N Zoo -N NH4 -N NO -N Phy -N NO -N N Zoo -N NH4 -N NO -N NO3-N NO3 -N NO3 -N spring summer autumn Surface chlorophyll a and trophic levels of the oceans 2 Eutrophic Mesotrophic SeaWiFS Station 101 90 83 75 67 50 59 42 35 27 20 12 -50 Chl a (mg m-3) 1 Oligotrophic -100 Depth (m) D -150 -200 -250 -300 -350 -400 -450 -75° Chlorophyll a (mg / m3) -70° -65° -60° -55° -50° -45° Longitude Bahamon et al., 2003 -40° -35° -30° -25° -20° A.Morel (1996) S Nixon S. (1995) Surface Clorophyll a Oligotrophic 0.05 mg Chl a m-3 M t hi 0.5 Mesotrophic 0 5 mg Chl a m-33 Eutrophic >1 mg Chl a m-3 Depth-integrated PP <0.5 g C m-2 d-1 0 5 -1.5 0.5 1 5 g C m-22 d-11 1.5 - 2.5 g C m-2 d-1 Observation, Analysis and Modeling of Marine Systems Daily data reception & Publication on the web Temperature Humidity Irradiance Wind speed & direction Pressure Temperature GPS Data processing Chlorophyll •Mixed layer models (Evans - Parslow, 1985; Fasham et al., 1990) Solar panels Data processing & assimilation in numerical i l models Lab analysis Phone card Data logger Batteries Field sampling on board R/V & VOS T, S IM1 25 m Mooring Site Blanes Station 3D Coupled Physical Biogeochemical M d l Model Current-meter IM2 50 m •Vertically V i ll resolved l d models: d l z-dependent: z-level systems (~1 to 5 m layer thickness) with ith turbulent t b l t diffusion diff i parameterisations t i ti (Varela (V l ett al., l 1994; Oguz et al., 1996; Levy et al., 1998; Bahamon and Cruzado, 2003, etc…) CEAB-CSIC 1 DV Coupled Physical Biogeochemical Model Vertical resolution of models Antenna Bi--directional communication Bi Temperature Salinity PAR Dissolved Oxygen Turbidity Chlorophyll sigma-dependent: vertical coordinates are layers following terrain; of common use in ocean circulation models (e. g. Mellor and Yamada Yamada, 1974; Zavatarelli et al al., 2000, 2000 Ahumada & Cruzado, 2007, etc...) Isopycnal-dependent: Isopycnal dependent: vertical coordinates are isopycnals Operational Oceanography, CEAB-CSIC Grids used in 3D models Some model references: Y. Tony Song & Yi Chao. 1999; Blumberg & Mellor. 1987; 27 Schopf, PS. 1995, etc. Figures from Open University, Ocean Circulation, 2007 z vs. sigma coordinate models z vs. sigma coordinate models Simulation of the vertical temperature in an area of the Algerian Sea Depth (m) D -50 -100 -150 -200 -250 Model results 300 30 360 330 120 90 60 Time ((days) y ) Bahamon, 2002 The nitrogen cycling in a pelagic ecosystem Heat,wind wind stress, H2O,H N22,0, O2 N , CO Heat, stress, 2 ,2 O2 , CO2 Atmosphere ATMOSPHERE Los modelos biogeoquímicos representan un conjunto de interacciones entre procesos biológicos, geológicos y químicos Ocean OCEAN Small p phytoplankton y p Un modelo acoplado representa la interacción de elementos bióticos y abióticos con diferentes aproximaciones (relaciones funcionales) Modelo físico + bio-geo-químico bio geo químico o biológico o ecológico o = Modelo acoplado Small zooplankton p Grazing Grazing Later ral bounddary LATER RAL BOUND DARIES El acoplamiento de los procesos biogeoquímicos y ecológicos a los procesos hidrodinámicos (medioambientales) dan como resultado un modelo acoplado Large phytoplankton Uptake Mortality Exudation DIN Mortality + Fecal pellets Excretion NO2 Nitrification NO 3 DON NH 4 PO N Sinking Excretion Predation Large zooplankton Excretion Uptake Laterall boundary ry Modelos biogeoquímicos g q Mortality Bacteria Mineralisation DEEPER WATERS Fasham et al., 1990 Comparison between surface Chl Chl--a from a 3D model and satellite observations in NW Mediterranean Sea Cambio instantáneo de una población: Modelo biológico Nt+1 = Nt - (d+e) + (b+i) La población de una especie en un momento determinado (Nt+1) (i.e. una microalga seleccionada como posible indicadora ambiental) está determinada por: el número actual de individuos (Nt) menos el número de individuos que mueren (d) o emigran (e), más los individuos que nacen (b) e inmigran (i) Bernardello et al. 2007 Cambio instantáneo de una población: Modelo biológico y físico (acoplado) Fases para la implementación de un modelo ecológico • Calibración ( ) ∂PHY ∂ ⎡ ∂PHY ⎤ ∂PHY K + = − w+w ⎢ ⎥ s ∂z ∂t ∂z ⎣ z ∂z ⎦ ( + PHY U NO3 +U NO2 +U NH4 )− PHY EXU − G La variación temporal de un grupo funcional (PHY, fitoplancton) dependerá de componente difusivo (…K ( Kz…) menos las pérdidas por advección vertical y hundimiento de las células (…w+ws…) más factores biológicos: consumo de nitrógeno g menos pérdidas de nitrógeno y consumo por parte del zooplancton – ¿E ¿Es adecuada d d lla parametrización t i ió d dell modelo? d l ? – ¿El modelo reacciona como se espera? • Verificación V ifi ió – ¿El modelo es estable a largo plazo? – ¿ Conserva la masa? • Validación – ¿Los datos observados se corresponden con los estimados? – Análisis A áli i cualitativo lit ti y cuantitativo tit ti d de lla simulación i l ió en relación l ió con las observaciones. • Sensibilidad – Sensibilidad a las formulaciones, parámetros, constantes, submodelos, variables de estado. – Análisis estadístico de las simulaciones en relación a la sensibilidad de parámetros, etc. Example: 1DV model of the oligotrophic pelagic environment Model description Irradiance, lenght of daylight Surface = 0 m Mixed layer A physical/ecological model is proposed to assess the time dependent vertical variability of plankton and nutrients in oligotrophic pelagic ecosystems: western Mediterranean and subtropical NE Atlantic Euphotic layer • Blanes is 1DV , z-dependent • Simulates vertical fluxes in the upper 300 m of the water column N-stock • Vertical V ti l resolution l ti = 3m 3 δz=3 Turbulent Mi i Mixing (Kz ,Wz ) • Variable non-uniform non uniform vertical turbulent diffusion (Osborn, 1980) Bottom = 300 m N-Input N-Output • Depth-uniform (0.05 m/d) upward vertical velocity Physical components A vertical ti l tturbulent b l t diff diffusion i model d l σθ(kg m-3) 28.0 0m 100 m K (m2 s-1) N (s-1) 10-33 29.0 -2 2 10 1 10 -3 10 Typical summer stratification Mixed layer Pycnocline N 2(Z) = − 200 m Water Stability (BruntVaisala) K(z) = g ∂ρ • ρw ∂ Z ε(z) 0.25 N 2 Physical p components Application pp c o oof thee vertical turbulent diffusion model to a subtropical North Atlantic section (above 500 m depth) (Z) 300 m Density anomaly 10-8 ε 10-7 (m 2 s -3 ) TKE Turbulent diffusion Osborn, 1980 Bahamón et al., 2003 Physical components : Time evolution of daylight and PAR Time evolution of irradiance • The Th B Brock k (1981) equations ti allow ll th the llength th off d daylight li ht (L1) to be computed according to latitude ⎛ ⎡ ⎧ t + L1 − 12 ⎫⎤ ⎞ PAR(0, t) = PAR(0)⎜⎜1 + cos ⎢2π⎨ ⎬⎥ ⎟⎟ L1 ⎭⎦ ⎠ ⎣ ⎩ ⎝ 500 PAR (W Watts m -2) N ⎞ ⎛ PAR(0) = P0 + P1 sin ⎜ 2π ⎟ ⎝ 365 ⎠ PAR (Watts m-22) 18 Daylightt (Hours) • Time variation of PAR in surface: D li h (h Daylight (hours)) 15 12 9 400 300 200 100 6 0 2000 4000 6000 Time (Hours) 8000 0 2000 4000 6000 Time (Hours) Subtropical NE Atlantic Catalan Sea The depth variation of PAR - ⎛⎜⎜ kw +kc ∗ ⎡⎢⎣ PHY(i) ⎤⎥⎦∗ D ⎞⎟⎟ z⎠ PAR(i, ( t)) = PAR(i ( - 1,t)) exp ⎝ 100 % Deptth Light extinction in sea water Blanes Canyon head - NW Mediterranean, 2002 Water extinction 1.0 % + Phytoplankton selfshading 0.1% 8000 The biological g model fuelling g VOS 2 The upward diffusive flux of nitrogen (μmol m-2 s-1) results from the diffusivity (Kz) multiplied by the nitrate gradient: 3 5 4 6 9 8 7 10 -50 Depth -100 -150 Validation of temperature ((°C) C) simulations in the -200 ⎡ ∂N ⎤ N flux = K z ⎢ ∂z ⎥⎦ ⎣ ∂z -250 Field data 306 333 343 13 30 73 41 103 119 Algerian Sea The new production deduced from the Redfield ratio: 16 mol of nitrate = 106 mol of carbon Depth (m) -50 -100 -150 -200 -250 Model results 300 330 360 30 60 120 90 Time (days) Biological components and interactions VOS 2 3 5 4 6 9 8 7 10 A simplified nitrogen cycling conceptual model -50 Depth (m) -100 -150 NH4+ - N -200 -250 Validation of temperature (°C) simulations in the 306 13 30 73 41 103 119 Phytoplankton - N Sinking -100 Depth (m) F l pellets, Fecal ll t deaths Uptake p -50 C l Sea Catalan S Zooplankton p -N Grazing Uptake Field data 333 343 Excretion NO2- - N -150 Exudation NO3- - N -200 -250 300 Model results 330 360 30 Time (days) 60 90 120 Upward transport Best fitting parameters and coefficients The evolution equation q of N-phytoplankton p y p (PHY) ( ) ¿Which p parameters are best? Symbol Value KNO3 KNO2 KNH4 ψ γ VPHY μ ∈ Ω λ Kg Imax 0.9 0.8 0.7 1.5 0.025 3.0 01 0.1 80 20 30 1.68 1.2 Definition Units Half saturation constant for nitrate uptake Half saturation constant for nitrite uptake Half saturation constant for ammonium uptake p Ammonium inhibition parameter for nitrate and nitrite uptake Phytoplankton exudation fraction of nitrite Phytoplankton maximum growth rate Zooplankton mortalit mortality rate Ammonium fraction of zooplankton excretion Faecal pellets fraction of zooplankton excretion (detrital) Zooplankton oop a to assimilation ass at o eefficiency c e cy Zooplankton half saturation for ingestion Zooplankton maximum ingestion rate mmol N m-3 mmol N m-3 mmol N m-3 mmol N m-3 % d-1 d-11 % % % mmol N m-3 d-1 ∂PHY ∂ = ∂t ∂z ( ) ∂PHY ⎤ ∂PHY ⎡ ⎢⎣ K z ∂z ⎥⎦ − w + w s ∂z + ( + PHY U NO3 +U NO2 +U NH4 )− PHY EXU − G NH4+ - N Excretion Zooplankton - N Grazing Uptake Phytoplankton - N Fecal pellets, deaths Uptake Sinking NO2- - N Sensitivity analysis would give an insight on the effect of changing parameters on model simulations Some model interactions The phytoplankton uptake of nutrients (UNO3) is as follows: Uptake of nitrate: U NO3 = VPHY NO3 e Ψ (NH4) K NO3 + NO3 Uptake of nitrite U NO2 = V PHY NO2 eΨ(NH4) K NO2 + NO2 Uptake of ammonia NH4 U NH4 = VPHY K NO4 + NH4 Exudation NO3- - N Upward transport BLANES (model) run-time display Seasonal validation of N-phytoplankton (mmol m-3) in the Catalan Sea Simulations of N-phytoplankton p y p ((mmol m-3) 1.0 0.9 0.8 -100 0 0.6 0.5 -50 0.4 -200 0.3 Catalan Sea -300 0 0 0.7 60 120 180 240 Depth (m m) Depth ((m) 0 0.2 0 2 0.1 300 Depth (m) 0.5 -150 -200 -250 0.4 -100 -100 -300 winter 0.3 spring autumn summer -350 350 0.3 -200 Subtropical North Atlantic -300 0 0.0 120 180 240 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 Lines indicate model results. results Points indicate field observations 0.1 60 0.5 0.2 300 The evolution equations of nutrients: NH4+ - N Excretion i Zooplankton - N Grazing Uptake Fecal pellets, deaths Phytoplankton - N Uptake Sinking -- NO2 N Exudation N - Nitrate: ∂NO3 ∂ ⎡ ∂NO3 ⎤ ∂NO3 = ⎢K z w − − U NO3 ∗ PHY ∂t ∂z ⎣ ∂z ⎥⎦ ∂z N - Nitrite: ∂NO2 ∂ ⎡ ∂NO2 ⎤ ∂NO2 −w + PHYEXU − U NO2 ∗ PHY = ⎢K z ⎥ ∂z ∂t ∂z ⎣ ∂z ⎦ N - Ammonia: 55 ∂NH4 ∂ ⎡ ∂NH4 ⎤ ∂NH4 −w = ⎢K z + ∈ −U NH4 ∗ PHY ⎥ ∂t ∂z ∂z ⎣ ∂z ⎦ NO3- -N Upward transport Simulations of N-nitrate ((mmol m-3) 0 Seasonal validation of N-nitrate (mmol m-3) in the Catalan Sea 8 0 6 -50 5 4 3 -200 2 Catalan Sea -300 0 0 60 120 180 240 1 Depth (m) Depth (m) 7 -100 -100 -150 -200 300 4.0 .0 -250 250 Depth h (m) 3.5 3.0 -100 2.5 -300 summer spring winter autumn -350 2 0 2.0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 1.5 -200 1.0 Subtropical North Atlantic -300 300 0 60 120 180 240 0.5 Lines indicate model results and points indicate field observations 300 Simulations of N-nitrite ((mmol m-3) 0 Seasonal validation of N-nitrite (mmol m-3) in the Catalan Sea 0.7 0 0.5 0.4 0.3 -200 0.2 C t l Sea Catalan S -300 0 0 -50 60 120 180 240 0 1 0.1 300 0.45 Depth (m m) Depth (m m) 0.6 -100 -100 -150 -200 Deepth (m) 0 40 0.40 0.35 -100 -250 0.30 0.25 -300 winter 0.20 -200 0.15 0.10 -300 0 Subtropical North Atlantic 60 120 180 240 300 spring p g summer autumn -350 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.05 0.00 Lines indicate model results and points indicate field observations Algunas ventajas de la modelación numérica Model products p Estimates of vertical nitrogen g fluxes upwardthe p euphotic p zone Depth Advective fluxes Diffusive fluxes m -22 -11 µmol m d -22 -11 µmol m d • Validar hipótesis sobre elementos que forzan el ((eco)) sistema • Simular flujos realistas de cuencas oceánicas y topografía del fondo. Se pueden simular ( (predecir) d i ) ffuturos t escenarios i a nivel i l llocal, l regional, global. • Interpolar información dispersa de barcos barcos, boyas, boyas satélites Total fluxes -2 2 -1 1 µmol m d -2 2 -1 1 mol m y Catalan Sea 120 - 130 190 - 200 290 -300 144 298 380 1632 140 5 1776 438 385 0.64 0.16 0.14 582 197 5 606 317 192 0.22 0 11 0.11 0.07 Subtropical NE Atlantic 150 - 160 190 - 200 290 - 300 24 120 187 Algunas desventajas de la simulación numérica • La simulación ó no es fiel reflejo de la realidad. • Muchas posibles fuentes de error: condiciones i i i l iniciales, códigos ódi ffuente t (b (bugs), ) cálculo ál l d de lla difusión turbulenta, supuestos…etc. – Las ecuaciones algebraicas, esenciales en los códigos de los programas, son ecuaciones discretas o aproximaciones algebraicas l b i de d llas ecuaciones i dif diferenciales i l (grid ( id approx.). ) Referencias onon-line • Numerical Modelling g Theory y http://www.physics.uq.edu.au/xmds/documentation/html/node65.html • Introduction to physical oceanography. Robert Steward. Free web-based text book (and pdf) in physical oceanography and a chapter in numerical modelling http://www-ocean.tamu.edu/education/oceanworldold/resources/ocng_textbook/contents.html • Reference hidrodynamic model: Princeton Ocean Model (POM) http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom/ prácticos deben ser más simples p q que el sistema – Los modelos p real • List of coastal models http://www.scisoftware.com/environmental_software/referral.php http://woodshole.er.usgs.gov/operations/modeling/ecomsi.html http://www.ebmtools.org/ • …. ¿Dónde publicar o conseguir información sobre dinámica y modelado marino? • • • • • • • • • • • • • • • • • • • Ecological modelling Continental Shelf Research Deep Sea Research Dynamics of Atmospheres & Oceans Encyclopedia of Ocean Sciences Geophysical Research Letters Journal of Atmospheric & Oceanic Technology Journal of Geophysical Research Journal of Marine Research Journal of Marine Systems Journal of Physical Oceanography Ocean Dynamics Ocean Modeling Oceanography Physics Today Progress in Oceanography Nature, Science, Tellus PLoS (Public Library of Science) …