AnnouncingFAO Manual on Aquaponics available now in resources!
FeaturesPricingSupportSign In

Chapter 11 Aquaponics Systems Modelling

5 months ago

12 min read

Karel J. Keesman, Oliver Körner, Kai Wagner, Jan Urban, Divas Karimanzira, Thomas Rauschenbach, and Simon Goddek

Abstract Mathematical models can take very different forms and very different levels of complexity. A systematic way to postulate, calibrate and validate, as provided by systems theory, can therefore be very helpful. In this chapter, dynamic systems modelling of aquaponic (AP) systems, from a systems theoretical perspective, is considered and demonstrated to each of the subsystems of the AP system, such as fish tanks, anaerobic digester and hydroponic (HP) greenhouse. It further shows the links between the subsystems, so that in principle a complete AP systems model can be built and integrated into daily practice with respect to management and control of AP systems. The main challenge is to choose an appropriate model complexity that meets the experimental data for estimation of parameters and states and allows us to answer questions related to the modelling objective, such as simulation, experiment design, prediction and control.

Keywords Modelling · Recirculating aquaculture system · Anaerobic digestion · Hydroponic greenhouse · Multi-loop aquaponic system · Tools


K. J. Keesman · S. Goddek

Mathematical and Statistical Methods (Biometris), Wageningen University, Wageningen, The Netherlands

O. Körner

Leibniz-Institute of Vegetable and Ornamental Crops (IGZ), Grossbeeren, Germany

K. Wagner

Institut für physikalische Prozesstechnik, University of Applied Sciences Saarbrücken, Saarbrücken, Germany

J. Urban

Laboratory of Signal and Image Processing, Institute of Complex Systems, South Bohemian

Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and

Protection of Waters, University of South Bohemia in Ceske Budejovice, Nove Hrady, Czech Republic

D. Karimanzira · T. Rauschenbach

Fraunhofer IOSB-AST, Ilmenau, Germany

© The Author(s) 2019 267

S. Goddek et al. (eds.), Aquaponics Food Production Systems,


Badiola M, Mendiola D, Bostock J (2012) Recirculating Aquaculture Systems (RAS) analysis: main issues on management. Aquac Eng 51:26—35. 004

Batstone DJ, Keller J, Angelidaki I, Kalyuzhnyi SV, Pavlostathis SG, Rozzi A, Sanders WTM, Siegrist H, Vavilin VA (2002) The IWA Anaerobic Digestion Model no 1 (ADM1). Water Sci Technol 45:65—73

Boote KJ, Jones JW (1987) Equations to define canopy photosynthesis from given quantum efficiency, maximum leaf rate, light extinction, leaf area index, and photon flux density. In: Biggins J (ed) Progress in photosynthesis research. Martinus Nijhoff, Dordrecht, pp 415—418

Bot GPA (1993) Physical modelling of greenhouse climate. In: Hashimoto Y, Bot GPA, Day W, Tantau HJ, Nonami H (eds) The computerized greenhouse. Academic Press, San Diego, pp 51—74

Buck-Sorlin G, De Visser PHB, Henke M, Sarlikioti V, Ven der Heijden G, Marcelis LFM, Vos J (2011) Towards a functional—structural plant model of cut-rose: simulation of light environment, light absorption, photosynthesis and interference with the plant structure. Ann Bot 108:1121—1134

Challa H, Bakker M (1999) Potential production within the greenhouse environment. In: Stanhill G,

Enoch HZ (eds) Ecosystems of the world 20 — Greenhouse ecosystems. Elsevier, pp 333—347

Colt JEK (2013) Impact of aeration and alkalinity on the water quality and product quality of transported tilapia—-a simulation study. Aquac Eng:46—58

Corominas L, Riegler L, Takács I (2010) New framework for standardized notation in wastewater. J Int Assoc Water Pollut Res 61(4):S841—S857

Dahl O-J, Nygaard K (1966) SIMULA: an ALGOL-based simulation language. Commun ACM 9

(9):671—678. de Zwart HF (1996) Analyzing energy-saving options in greenhouse cultivation using a simulation model. Wageningen Agricultural University, Wageningen, p 236

Delaide B, Goddek S, Keesman, KJ, Jijakli MH (2018). A methodology to quantify the aerobic and anaerobic sludge digestion performance for nutrient recycling in aquaponics. https://popups. 22, 12

Drayer GE, Howard AM (2014) Modeling and simulation of an aquatic habitat for bioregenerative life support research. Acta Astronaut 93:S.138—S.147. 07.013

El-Mashad H (2003) Solar Thermophilic Anaerobic Reactor (STAR) for renewable energy production PhD thesis Wageningen University. ISBN: 9058089533-238

Emerenciano M, Carneiro P, Lapa M, Lapa K, Delaide B, Goddek S (2017) Mineralizacão de sólidos. Aquac Bras 21—26

Emrich S, Suslov S, Judex F (2007) Fully agent based. Modellings of epidemic spread using anylogic. In: Proceedings of the EUROSIM

FAO (2016) The State of World Fisheries and Aquaculture 2016. Contributing to food security and nutrition for all. Food and Agriculture Organization of the United Nations, Rome

Ficara E, Hassam S, Allegrini A, Leva A, Malpei F, Ferretti G (2012) Anaerobic digestion models: a comparative study. In: Proceedings of the 7th Vienna international conference on mathematical modelling 2012, p 1052

Fortmann-Roe S (2014) Insight maker: a general-purpose tool for web-based modeling & simulation. Simul Model Pract Theory 47:28—45

Frantz JM, Hand B, Buckingham L, Ghose S (2010) Virtual grower: software to calculate heating costs of greenhouse production in the United States. HortTechnology 20:778—785

Galí A, Benabdallah T, Astals S, Mata-Alvarez J (2009) Modified version of ADM1 model for agro-waste application. Bioresour Technol 100(11):2783—2790

Goddek S (2017) Opportunities and challenges of multi-loop aquaponic systems. Wageningen University.

Goddek S, Delaide BPL, Joyce A, Wuertz S, Jijakli MH, Gross A, Eding EH, Bläser I, Reuter M, Keizer LCP, Morgenstern R, Körner O, Verreth J, Keesman KJ (2018) Nutrient mineralization and organic matter reduction performance of RAS-based sludge in sequential UASB-EGSB reactors. Aquac Eng 83:10—19. ISSN: 0144-8609

Goddek S, Keesman KJ (2018) The necessity of desalination technology for designing and sizing multi-loop aquaponics systems. Desalination 428:76—85. 11.024

Goddek S, Körner O (2019) A fully integrated simulation model of multi-loop aquaponics: A case study for system sizing in different environments. Agric Syst

Goddek S, Delaide B, Mankasingh U, Ragnarsdottir K, Jijakli H, Thorarinsdottir R (2015) Challenges of sustainable and commercial aquaponics. Sustainability 7:4199—4224. https://

Goddek S, Espinal CA, Delaide B, Jijakli MH, Schmautz Z, Wuertz S, Keesman KJ (2016) Navigating towards decoupled aquaponic systems: a system dynamics design approach. Water (Switzerland) 8:303.

Graber A, Junge R (2009) Aquaponic systems: nutrient recycling from fish wastewater by vegetable production. Desalination 246:147—156

Halamachi I, Simon Y (2005) A novel computer simulation model for design and management of re-circulating aquaculture systems. Aquac Eng 32(3—4):S443—S464. aquaeng.2004.09.010

Hassan J et al (2016) Transient accumulation of NO2-and N2O during denitrification explained by assuming cell diversification by stochastic transcription of denitrification genes. PLoS Comput Biol 11(1):e1004621

He E, Wurtsbaugh W (1993) An empirical model of gastric evacuation rates for fish and an analysis of digestion in piscivorous brown trout. Trans Am Fish Soc 122(5):S.717—S.730

Henze M, Willi G, Takashi M, Mark L (2002) Activated sludge models ASM1, ASM2, ASM2d AND ASM3. IWA Publishing in its Scientific and Technical Report series, UK. ISBN: 1-900222-24-8

Heuvelink E (1996) Tomato growth and yield: quantitative analysis and synthesis. Department of Horticulture. Wageningen Agricultural University, Wageningen, The Netherlands, p 326

Jablonsky J, Papacek S, Hagemann M (2016) Different strategies of metabolic regulation in cyanobacteria: from transcriptional to biochemical control. Sci Rep 6:33024

Janka E, Körner O, Rosenqvist E, Ottosen CO (2018) Simulation of PSII-operating efficiency from chlorophyll fluorescence in response to light and temperature in chrysanthemum (Dendranthema grandiflora) using a multilayer leaf model. Photosynthetica 56:633—640

Karimanzira D, Keesman KJ, Kloas W, Baganz D, Rauschenbach T (2016) Dynamic modeling of the INAPRO aquaponic system. Aquac Eng 75:29—45.

Keesman KJ (2011) System identification: an introduction. Springer, London

Knaus U, Palm HW (2017) Effects of fish biology on ebb and flow aquaponical cultured herbs in northern Germany (Mecklenburg Western Pomerania). Aquaculture 466:51—63. 10.1016/j.aquaculture.2016.09.025

Körner O, Hansen JB (2011) An on-line tool for optimising greenhouse crop production. Acta Hortic 957:147—154

Körner O, Van Straten G (2008) Decision support for dynamic greenhouse climate control strategies. Comput Electron Agric 60:18—30

Körner O, Aaslyng JM, Andreassen AU, Holst N (2007) Modelling microclimate for dynamic greenhouse climate control. HortScience 42:272—279

Körner O, Warner D, Tzilivakis J, Eveleens-Clark B, Heuvelink E (2008) Decision support for optimising energy consumption in European greenhouses. Acta Hortic 801:803—810

Körner O, Gutzmann E, Kledal PR (2017) A dynamic model simulating the symbiotic effects in aquaponic systems. Acta Hortic 1170:309—316

Licamele JD (2009) Biomass production and nutrient dynamics in an aquaponics system. The University of Arizona

Liebig HP, Alscher G (1993) Combination of growth models for optimized COsub2/sub- and temperaturecontrol of lettuce. Acta Hortic 328:155—162

Lugert V, Thaller G, Tetens J, Schulz C, Krieter J (2014) A review on fish growth calculation: multiple functions in fish production and their specific application. Rev Aquac 8(1):30—42

Lupatsch I, Kissil GW (1998) Predicting aquaculture waste from gilthead seabream (Sparus aurata) culture using nutritional approach. Aquat Living Resour 11(4):265—268. 1016/S0990-7440(98)80010-7

Lupatsch I, Kissil GW, Sklan D (2003) Comparison of energy and protein efficiency among three fish species gilthead sea bream (Sparus aurata), European sea bass (Dicentrarchus labrax) and white grouper (Epinephelus aeneus): energy expenditure for protein and lipid deposition. Aquaculture:175—189

Macal CM, North MJ (2005) Tutorial on agent-based modeling and simulation. In: Simulation conference, 2005 proceedings of the winter. IEEE

Madsen LO, Møller-Pedersen B, Nygaard K (1993) Object-oriented programming in the BETA programming language. Addison-Wesley. ISBN 0-201-62430-3

Marcelis LFM (1994) Fruit growth and dry matter partitioning in cucumber. Department of Horticulture. Wageningen Agricultural University, Wageningen, p 173

McCarthy J, Levin MI (1965) LISP 1.5 programmer's manual. MIT Press, Cambridge, MA

Orellana JUW (2014) Culture of yellowtail kingfish (Seriola lalandi) in a marine recirculating aquaculture system (RAS) with artificial seawater. Aquac Eng:20—28

Pagand P, Blancheton JP, Casellas C (2000) A model for predicting the quantities of dissolved inorganic nitrogen released in effluents from a sea bass (Dicentrarchus labrax) recirculating water system. Aquac Eng 22(1—2):S137—S153

Pavlostathis SG, Giraldo-gomez E (1991) Kinetics of anaerobic treatment: A critical review. Crit Rev Environ Control 21:411—490

Poorter H, Anten NP, Marcelis LFM (2013) Physiological mechanisms in plant growth models: do we need a supra-cellular systems biology approach. Plant Cell Environ 36:1673—1690

Rath T (1992) Einsatz wissensbasierter Systeme zur Modellierung und Darstellung von gartenbautechnischem Fachwissen am Beispiel des hybriden Expertensystems HORTEX. University of Hannover, Germany

Rath T (2011) Softwaresystem zur Planung von Heizanlagen von Gewächshäusern. Fachgebiet Biosystem- und Gartenbautechnik. Leibniz University Hannover, Germany

Reyes Lastiri D, Slinkert T, Cappon HJ, Baganz D, Staaks G, Keesman KJ, (2016) Model of an aquaponic system for minimised water, energy and nitrogen requirements. Water Sci Technol. wst2016127.

Richie M, Haley D, Oetker M (2004) Effect of feeding frequency on gastric evacuation and the return of appetite in Tilapia Oreochromis niloticus (L.). Aquaculture 234(1—4):S657—S673.

Rusten BE (2006) Design and operations of the Kaldnes moving bed biofilm reactors. Aquac Eng:322—331

Sánchez-Romero A, Miranda-Baeza A, Rivas-Vega M (2016) Development of a model to simulate nitrogen dynamics in an integrated shrimp—macroalgae culture system with zerowater exchange. J World Aquacult Soc 47(1):129—138

Sinha NK, Kuszta B (1983) Modelling and identification of dynamic systems. Von-Nostrand Reinhold, New York

Soukup J, Macháček P (2014) Serialization and persistent objects. Springer. 1007/978-3-642-39323-5

Sterman J (2000) Business dynamics: systems thinking and modeling for a complex world. McGraw Hill, Boston

Štys D, Stys D Jr, Pecenkova J, Stys KM, Chkalova M, Kouba P, Pautsina A, Durniev D, Nahlık T, Cısa P (2015) 5iD Viewer-observation of fish school behaviour in labyrinths and use of semantic and syntactic entropy for school structure definition. World Acad Sci Eng Technol Int

J Comput Electr Autom Control Inf Eng 9(1):281—285 van Ooteghem RJC (2007) Optimal control design for a solar greenhouse. Wageningen University, Wageningen, p 304

Vanthoor B (2011) A model-based greenhouse design method. Wageningen University, Wageningen, p 307

Waller U, Buhmann AK, Ernst A et al (2015) Integrated multi-trophic aquaculture in a zeroexchange recirculation aquaculture system for marine fish and hydroponic halophyte production. Aquac Int 23:1473

Weatherley LR, Hill RG, Macmillan KJ (1993) Process modelling of an intensive aquaculture system. Aquac Eng:215—230

Wik TEI, Lindén BT, Wramner PI (2009) Integrated dynamic aquaculture and wastewater treatment modelling for recirculating aquaculture systems. Aquaculture 287(3/4):361—370

Willems JC, Polderman JW (1998) Introduction to mathematical systems theory: a behavioral approach. Springer. ISBN: 978-1-4757-2953-5

Wolfram S (1991) Mathematica: a system for doing mathematics by computer. Wolfram Research, Champagne

Yogev U, Barnes A, Gross A (2016) Nutrients and energy balance analysis for a conceptual model of a three loops off grid, aquaponics. Water 8:589.

Zeigler BP, Praehofer H, Kim TG (2000) Theory of modeling and simulation, 2nd edn. Elsevier, London

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.