Inverse Modeling of the Microbial Loop J. Steele & A. Beet Woods Hole Oceanographic Institution.

Slides:

Advertisements

Similar presentations

Linear Programming. Introduction: Linear Programming deals with the optimization (max. or min.) of a function of variables, known as ‘objective function’,

Advertisements

The Marine Biology of Spongebob Squarepants

Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.

A Seasonal Nitrate Climatology For Georges Bank James J. Bisagni University of Massachusetts Dartmouth Physics Department & School for Marine Science and.

Energy Flow & Nutrient Cycle Big bugs have little bugs upon their backs to bite ‘em Little bugs have lesser ones an so ad infinitum.

Energy Flow & Nutrient Cycle

Taking a Square Root to Solve an Equation. Solve: In order to solve for x, you have to UNDO the squared first (i.e. square root) What are the number(s)

Grazing and Trophic Transfer Sam Rankin BOT 437 May 21, 2009.

Marine Plant Life and Ocean Life Zones

CE 311 K - Introduction to Computer Methods Daene C. McKinney

Using Cross Products Lesson 6-4. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross.

Non-Linear Simultaneous Equations

2.2 Solving Two-Step Equations I can solve two-step equations in one variable.

© 2007 by S - Squared, Inc. All Rights Reserved.

Solving Equations by Extracting Roots

3.5 – Solving Systems of Equations in Three Variables.

1 ECOLOGY of the ANTARCTIC SEA ICE ZONE EASIZ. 2 EASIZ Final Symposium Korcula, Croatia 27 September 2004 Hugh Ducklow & Robert Daniels College of William.

Marine Ecology of the Arctic Connectivity, change, and resilience Arny Blanchard Institute of Marine Science University of Alaska Fairbanks Oceanography.

OMSAP Public Meeting September 1999 Ecological Interactions in Massachusetts Bay A guide to how the MWRA Harbor and Outfall Monitoring Program evaluates.

Introduction to Linear Programming BSAD 141 Dave Novak.

Copyright © 2011 Pearson, Inc. 7.5 Systems of Inequalities in Two Variables.

MARINE BIOMES MODIFIED BY: MS. SHANNON. BIOMES A biome is a major, geographically extensive ecosystem, structurally characterized by its dominant life.

Week 11 Similar figures, Solutions, Solve, Square root, Sum, Term.

Production of Fish and Benthos on Georges Bank Estimates of benthic biomass and production Preliminary estimates of energy flow Dynamic fish population.

Open Ocean: Shallow Photic Zone Deepest: 100m, but light very low, blue spectrum Good photic zone ~50-60m Stable T, salinity Surface currents predictable:

Introduction to Quadratic Equations & Solving by Finding Square Roots Chapter 5.3.

Factor. 1)x² + 8x )y² – 4y – 21. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

Solving Quadratic Equations Quadratic Equations: Think of other examples?

Do Now 1) Factor. 3a2 – 26a + 35.

Lesson 1-8 Solving Addition and Subtraction Equations.

Solving One-Step Equations © 2007 by S - Squared, Inc. All Rights Reserved.

Pelagic C:N:P Stoichiometry in a Eutrophied Lake: Response to a

10-1 An Introduction to Systems A _______ is a set of sentences joined by the word ____ or by a ________________. Together these sentences describe a ______.

Aquatic Ecology Course Zoo 374

OMSAP Public Meeting September 1999 Benthic Nutrient Cycling in Boston Harbor and Massachusetts Bay Anne Giblin, Charles Hopkinson & Jane Tucker The Ecosystems.

The Substitution Method Objectives: To solve a system of equations by substituting for a variable.

Warm-Up 1) Determine whether (-1,7) is a solution of the system. 4 minutes 3x – y = -10 2) Solve for x where 5x + 3(2x – 1) = 5. -x + y = 8.

Solve Equations With Variables on Both Sides. Steps to Solve Equations with Variables on Both Sides  1) Do distributive property  2) Combine like terms.

2-4 Solving Equations with Variables on Both Sides.

Solving equations with variable on both sides Part 1.

Salinity Salinity is the total amount of solid material dissolved in water. Because the proportion of dissolved substances in seawater is such a small.

Equations Quadratic in form factorable equations

The Inverse of a Square Matrix

Inverse of a Square Matrix

Warm Up Check the solution to these problems; are they correct? If not, correct them. 3 – x = -17; x = -20 x/5 = 6; x = 30.

Solving Quadratic Equations by the Complete the Square Method

Notes Over 9.6 An Equation with One Solution

Flounder Histopathology and Chemistry

Solving Equations by Factoring and Problem Solving

Simple linear equation

Lakes & Large Impoundments Chapter 22

Simplify Expressions 34 A number divided by 3 is 7. n ÷ 3 = 7.

6-3 Solving Systems Using Elimination

7.5 Solving Radical Equations

2 Understanding Variables and Solving Equations.

Solving Percent Problem with Equations (7.2) Proportions (7.3)

INFM 718A / LBSC 705 Information For Decision Making

Inverse Matrices and Systems

Solving 1-Step Integer Equations

Solving Multi-Step Equations (2-3 and 2-4)

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Equations Quadratic in form factorable equations

The Marine Biology of Spongebob Squarepants

4 minutes Warm-Up 1) Determine whether (-1,7) is a solution of the system. 3x – y = -10 -x + y = 8 2) Solve for x where 5x + 3(2x – 1) = 5.

The Discovery of Ocean Life

11-5 Solving Rational Equations

Using Cross Products Chapter 3.

Presentation transcript:

Inverse Modeling of the Microbial Loop J. Steele & A. Beet Woods Hole Oceanographic Institution

Benthivorous Fish Pelagic Invertebrate Predators Micro- Phytoplankton (>20  m) Seabirds Deposit-feeding Benthos Suspension- feeding Benthos Detritus Ammonia Fishing R Micro- Zooplankton (2-200  m) Meso- Zooplankton (>200  m) Nitrate Nano- Phytoplankton (<20  m) Planktivorous Fish Piscivorous Fish Pre-recruits Marine Mammals spawning recruitment

BiBi NiNi Losses from System due to inefficiency, e i External Inputs, K i N i = e i (  a ij N j ) + K i 0 < e i < 1.0, “Ecopath type” solution; specify e i, a ij K i solve for N i There are an equal number of variables and equations A unique solution exists

Benthivorous Fish B: 0.88 Pelagic Invertebrate Predators Sullivan & Meise Phytoplankton Seabirds Deposit-feeding Benthos Suspension- feeding Benthos DOC 638 Detritus 2.2x10^6 mg at N s^ -1 Ammonia Fishing Lobsters: 0.9 Shellfish: 0.9 Fish: Phyto 501 R Zoo ? 285 Micro- Zooplankton 202 Meso- Zooplankton 4.8x10^5 mg at N s^ -1 Nitrate+Nitrite 2793 Nano- Phytoplankton Planktivorous Fish B: 9.85 Piscivorous Fish B: Pre-recruits Marine Mammals 6.0 from fish & Squid 1.8 from Zoo 7.8 total spawning recruitment 900 Bacteria

BiBi NiNi External Inputs, K i N i = e i (  a ij N j ) + K i “Inverse” solution: set bounds on e i,, and solve for N i = b i. B i where b i is turnover rate Losses from System due to inefficiency, e i Problem: There are more variables than equations There is no unique solution

To obtain a unique solution the introduction of an objective function is needed. The maximization or minimization of this function provides a unique solution. Vezina and Platt, 1988 Question ecological; how appropriate is this function? Alternative maximize resilience

Phyto Microz mesoZ Detritus NO3 Pel.F. Dem.F Regn. S.P. L.P.

Phyto Microz mesoZ Detritus NO3 Pel.F. Dem.F Regn. S.P. L.P.

Phyto Microz mesoZ Detritus NO3 Pel.F. Dem.F Regn. S.P. L.P.

N1 Phyto N2 Microz N3 mesoZ N4 Detritus NO3 Pel.F. Dem.F S.P. L.P. R3 R2 R1 R4 Fluxes Regn Losses Reg n Graz

Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration / / M <= 1 (Resilience / Sum of squares) Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration / / M <= 1 (Resilience / Sum of squares)

Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration / / / / / / M <= 1 (Resilience / Sum of squares) Proportion of intake to Z, D to higher levels F-ratioFraction of detritus regeneration / / / / / / M <= 1 (Resilience / Sum of squares)