The WadBOS ecosystem model as an example for building
Contents
1. Extend training material for SPICOSA provided by Joachim Maes SPICOSA WP8 VITO contact joachim maes vito be The WadBOS ecosystem model as an example for building block design and model documentation Accompanying Extend material e WadBOSEcosystemModel_v1 mox e WadBOSEcosystemModel_v3 mox e WadBOSEcosystem lix 1 Introduction Model formulation is the step where conceptual system knowledge is written in a more formal mathematical form A mathematical description can subsequently be implemented in a programming language The translation from a conceptual and mathematical description of the dynamics of an ecosystem into the simulation software Extend is presented in this manual A next objective of this chapter are to illustrate how a model that was made in Extend can be documented for submission In between we will show how returning processes can be stored in an Extend model block so as to facilitate the practice of modelling This manual is implemented as Chapter 8 in the SPICOSA deliverable D8 4 Model building blocks and it forms a direct link to the WP4 system formulation report In fact the same example will be used 2 The WadBOS model concepts and formulation 2 1 What is WadBOS WadBOS features an integrated system dynamic model representing the ecological and the economic functions of the Wadden Sea Engelen 2004 The Wadden Sea is part of a coastal system extending from the North of the Netherlands2. ee See kn half saturation constant of the nitrogen limited algae growth OS gram nitrogen per m3 Light Light incidence W per m2 forcing function Nee fie kL half saturation constant of the light limited algae growth W per m2 Dynamics of detritus in the water E i it pee SRS ast m X Phytopankton i x X Detritusy ier dt h Extend model Units gram carbon per m Parameters Phytoplankton a mortality E i i DetritusWat ma mortality rate of phytoplankton per month el g C kw mineralisation rate of detritus in the water per month Sedimentation of Denes vater v sedimentation of detritus m per month S Water detritus h water depth m Mineralisation of 7 dynamics detritus in the water Dynamics of detritus on the seabed E i dDetrit uan EWS seabed L Y y Detritus yare x Phytoplankton dt h h Extend model E k Kaeni x Detritus seapea Units gram carbon per m Parameters mgae el E Sedimentation of Ej Algae Hi j to d 0 i v sedimentation of detritus and of the i d i aia h phytoplankton m per month ee Detritus Seabed kp water depth m ea Kaeni mineralisation rate of detritus on the seabed per month denitrification rate of detritus on the seabed per month Sedimentation r DetritusVVater L Sedimentation of o Detritus Water Water depth Sedimentation r Mineralisation of detritus on th
3. Carrying capacity C kmax 1 Resource kK Resource Comments Help L__ visi a Fig 4 Dialog of the Extend Block with name RateLimitingProcess The new block has been saved under a new library that needs to be installed saved in toe Extend libraries folder The name of the library is WadBOSEcocystem lix 3 2 Building in hierarchy for better readability and increased intuitive understanding of the model The conceptual model is a good guide for hierarchy building Intuitively it seems interesting to group model blocks that calculate the dynamics of the different state variables of the model Probably this is a good tactic of any type of model State variables are excellent candidates to create a hierarchical structure in the model Open the WadBOS_EcosystemModel_v3 and explore how hierarchical blocks were constructed Fig 5 17 Af WadBOS_EcosystemModel_v3 mox Wadden Sea Ecosystem Model v3 a Light incidence Solar zi Per ie ve Deposition Solar jz DetritusWater DetritusSeabed Algae Nitrogen Nitrogen o Mussels y gt a Algae Phytoplankton Birds rhe lt asia a Mussels Mussels DetritusWWater a Algae ema DetritusSeabed Detritus Seabed a Detrituswater a Algae Detritus Water Nitrogen DetritusSeabed Algae DetritusWWater Mussels About this model Conceptual scheme Fig 5 Hierarchical blocks represe
4. Under button label type About this model Next enter the following button equation OpenEnclosingHBlock2 MyBlockNumber Now select the clone tool and clone the button About this model which is situated just above the Button label and drag it onto the Extend model pane Close the button block and the hierarchical text block Open the structure of the hierarchical text block and resize the icon so that it becomes a small rectangle that can be hidden under the About this model button Close the hierarchical block select the clone tool and drag the About this model button over the hierarchical block icon so that it is hidden by the About this model button Aroun eoon ATE Provides a button that executes an equation Clone this to the model worksheet Cancel About this model Button label About this model Button equation OpenEnclosingHBlock2 MyBlockNumberg Built in buttons Open H block a Comments Hep Fig 9 Dialog of the buttons block 25
5. and connectors are explained The titles have a text size that is larger than the regular text while the dialog choice names and the connector names are in bold 19 lolx RateLimitingProcess Virtual Memory MB 1 237 7 This block can be used to calculate a rate limiting terms Such terms modulate the interaction between a resource and its consumer Dialog choices Maximum rate kmax rate of growth or decay of a state variable Half saturation constant kS It is the value of the resource where the rate is 50 of its maximal value Ithas the same units as the resource Shape factor p Value for the power relation Only for a functional response type3 Carrying capacity Value above which the growth is negative Processes can be chosen using the radio buttons Afunctional type 1 response relates the consumption rate to the resource availability In a functional type response the consumer rate kis proportional to the resource R In the functional type 2 response the consumption rate rises with resource availability but gradually decelerates until a plateau is reached at which the rate remains constant To describe this kind of functionality an extra parameter is needed ks often referred to as half saturation constant Itis the concentration where the rate is 50 ofits maximal value This response is equal to the Monod equation or the Michaelis Menten equation In a functional type 3 response the rate initially increases more tha
6. block The block s icon is given in the upper left corner Some introductory text is given in the upper right corner More documentation is needed there but this will be the focus of paragraph Under the model icon two names relate to the connectors ResourceIn and VarOut They represent the input value into the block and the output value out of the block respectively The pane situated in the lower left corner contains the dialog names The block s dialog contains four parameters HalfSatCont Shapefactor MaxRate CarCap one parameter with option display only DisplayResource two buttons OK Cancel four radio buttons Response Response23 CaryingCapacity Inhibition and edible text Comments and finally 12 static text items which were not given names On the right hand site the model code is presented The code calculates the value for VarOut based on the parameters and the Resourceln for four different options of rate limitation Defaults are presented under the code 16 A 1 RateLimitingProcess ale ae This block calculates a process with rate limitation Maximum rate kmax og Cancel ERAS Half saturation constant kS E Shape factor p 1 Carrying capacity K Choose a process Display Resource 550 Functional response type 1 C kmax Resource Functional response type 2 or 3 kmax Resource p Resource p kS p Inhibition kmax k5 p Resource p kS p e
7. block that calculates the bird population size By using the cloning tool a user interface can be built so that new users can enter parameters without the need of opening the Extend blocks 22 3 3 5 How to include push buttons to enter general model information The clone tool can also be used to add buttons to the model pane so as to include general model information text figures and so one We illustrate this procedure for the WadBOS ecosystem model We want to add a push button to the model pane with the following documentation that is based on the information that SSA teams will need to submit to the SPICOSA model database using the Model Documentation and Submission system Basic information Model name WadBOS Full model name Wadden Sea Ecosystem Model version 3 Model version and status version 3 tutorial model Latest date of revision 12 January 2007 Does the model use a non standard custom made Extend library YES WadBosEcosystem lix Institutions VITO Contact person Joachim Maes Contact address VITO Integrated Environmental Studies Boeretang 200 B 2400 Mol Belgium Phone number 32 14 335963 Fax number 32 14 321185 E mail address joachim maes vito be URL none Technical support Level of knowledge needed to operate model EASY Remarks None System design Policy issue Ecosystem dynamics Study site no study site tutorial model Model description summary This model simulates the flow o
8. dBirdsidt kmax 1 K Birds Birds m kS kS Mussels Birds State variables Birds the number of the total bird population Number Mussels the biomass of the mussel population gram C per m3 Parameters kmax maximum growth rate of the bird population per month K carrying capacity of the bird population numbers m mortality rate of the birds per month KS half saturation constant of the mussel inhibited bird mortality gram carbon per m3 Connectors BirdsOut Birds Musselsin Mussels Topics Next g i Bearch Cancel Fig 7 Left Hierarchical block that groups the processes that affect the dynamics of birds in the WadBOS ecosystem model Right Help tab of the hierarchical block All other blocks have been documented similarly Click on the help tab of each hierarchical block for details 3 3 4 How to make hierarchical blocks more accessible by providing a user interface The clone tool can be used to provide a user interface between the Extend model and the parameters that drive the model An example is presented here for the hierarchical block that represents the dynamics of the bird population Using the cloning tool all the parameters were copied and placed after user defined text items Now a user can modify the parameters without the need of opening the particular blocks 21 l 358 Birds E I Tt oo oe eo eB Fig 8 Screenshot of the hierarchical
9. into Northern Germany and Western Denmark In the Netherlands the sea is a protected nature reserve because of the important ecological functions that it fulfils At the same time the sea has important economic functions Fishing recreation transportation and mining are among the main economic activities It generates employment income leisure and food for many a household The management of the different activities and functions of the sea is distributed over a great number of institutions ranging from the municipal to the European When decisions are to be made or policies need to be developed relative to the exploitation or protection of the area incompatible views tend to slow down the decision making process In this manual selected parts of the WadBOS model are used to illustrate how an ecosystem model can be formulated based on a conceptual description For simplicity we do not consider spatial information at this point We assume a reservoir like sea with a constant surface area and a uniform distribution of dept 2 2 Conceptual model The conceptual model in Fig 1 describes the flow carbon and nitrogen through a coastal zone food web The ecosystem is represented by six state variables Dissolved inorganic nitrogen the stock of detritus in the water and on the sea bed phytoplankton mussels and birds These state variables are coupled to each other via 11 processes 1 mineralization of detritus in the water 2 denitrifi
10. System appraisal Calibration No calibration was performed Sensitivity analysis No sensitivity was performed Evaluation and validation Level 5 no evaluation at all System output Output quantities Bird population size User community SPICOSA References Engelen G 2004 Models in policy formulation and assessment The WadBOS Decision Support System In Environmental Modelling Finding simplicity in complexity J Wainwright and M Mulligan Eds John Wiley and Sons Ltd West Sussex England pp 257 271 Uljee I Engelen G 2002 WadBOS user manual This is the procedure to store this information in your Extend model and to make it available for other users using a button e Open the Extend model where you want to add information e Type insome dummy text on the model pane for instance text e Select the text and make a hierarchical block of the text item by right clicking and select the option Make hierarchical Name your block e Next open the block double click on the text item and replace the text with any other information that you copy from an editor or from MS Word You may firstly want to rescale or expand the text block and the hierarchical block e Leave the block open and open the utilities library 24 Drag the Extend button block into the open hierarchical block preferably below the text that you entered Double click on the button block to open the dialog Fig 9 Make the following choices
11. cation of detritus on the sea bed 3 uptake of nitrogen by algae 4 mineralization of detritus on the sea bed 5 atmospheric deposition of nitrogen 6 sedimentation of detritus and dead phytoplankton 7 grazing of algae by mussels 8 phytoplankton mortality 9 mussel mortality caused by bird predation 10 growth of the bird population 11 mortality of birds as a function of mussel biomass Detritus water phyto mortality mineralization rate deposition phyto growth Inorganic nitrogen denitrification Detritus sea bed Phytoplankton i mineralization i 3 sedimentation mussel grazing Mussels mussel mortality bird mortality Fig 1 Conceptual model of an coastal ecosystem model based on the WadBOS DSS Using the numbered processes the dynamics of this ecosystem are captured by the following set of equations dNitrogen dt dDetritUS water dt dDetritts sapea dt dPhytoplankton dt dMussels _ dt dBirds dt 1 4 24 5 3 8 1 6 6 2 4 3 8 6 7 7 8 10 11 2 3 Mathematical description and implementation in Extend Next the conceptual model is formulated using a set of coupled differential equations The mathematical model was implemented in Extend A first version of the model saved as WadBOS_EcosystemModel_v1 mox contains the explicit model code using Extend model blocks from the generic library only The following figures show the tra
12. dt O Rks El kad eo Af Structure of RateLimitingProcess WadBosEcosystem lix Views x Functions CHECKDATA w Includes Main i block can be used to calculate different rate limiting terms El ii i Resourcein Declare constants and static variables here VarOut This message occurs for each step in the simulation on simulate z 4 fa DisplayResource ResourcelIn Dalen Hames lt iE Response oK VarOut ResourceIn MaxRate Pacis if Response23 Rll gi VarOut MaxRate ResourceIn ShapeFactor ResourceIn ShapeFactor Hal fSatConst ShapeFactor ShapeFactor if Inhibition Late VarOut MaxRate HalfSatConst ShapeFactor HalfSatConst ShapeFactor ResourceIn ShapeFactor anran if CarryingCapacity CarCap VarOut MaxRate 1 ResourceIn CarCap ResourceIn Response23 CaryingCapacity Display Resource em pe SREDEBLEC Y If the dialog data is inconsistent for simulation abort DIALOGOPEN checkdata DIALOGCLOSE CHECKDATA STERSIZE f Initialize any simulation variables RESUMESIM aaa BLOCKRECEIVED BLOCKRECEIVE BLOCKRECEIVE BLOCKRECEIVES Greatebliock OPENMODEL ABORTSIM HBLOCKOPEN 0 ABORTDIALOGMESSAGE Defaults Z HBLOCKCLOSE ShapeFactor 1 CONNECTIONNMAKE Response true PLOTTEROCLOSE Marhata i PLOTTERICLOSE PLOTTER2CLOSE 7 ch E gt Line 20 Code Completion Fa _ Fig 3 Structure of the RateLimitingProcess Extend
13. e sea floor Seabed Detritus dynamics Dynamics of the phytoplankton Algae Equation j j q dPhytoplankton Si none x Laghi xPintoplanio dt ky Nitrogen k Light Extend model z m le x Musses x Phytoplankton 1 Units gram carbon per m Parameters Nitrogen ptake by a el p Algae Kmax maximum growth rate of phytoplankton per month i ajs Algae kn half saturation constant of the nitrogen limited algae growth i gram nitrogen per m3 Sedimentation of Light Light incidence W per m2 forcing function ngaa Phytoplankton kL half saturation constant of the light limited algae growth W per dynamics m2 yy Ponnan v sedimentation of detritus and of the dead fraction of the Mortality rate mortality h phytoplankton m per month Algae g grazing factor of mussels on phytoplankton m8 per gram carbon per month Mussels Grazing by mussels p Grazing rate Algae Dynamics of the mussel population Equation dMussels Phytoplankton mussel X x Mussels dt kp Phytoplankton Extend model mase G X Birds x Mussels Units gram carbon per m Parameters d d 5 Growth of Growth rate a ussels limited i j L Mussels Kkmussel maximum growth rate of the mussel jae FARE E wa Mussels population per month kp half saturation constant of the phytoplankton Pairk ann limited mussel growth gra
14. e is soon loaded with blocks Therefore it would be interesting to encode a single block that can substitute all of the above processes This block saves time and space This step is done a second version of the Extend code that simulates the Wadden Sea ecosystem WaddenSea_EcosystemModel_v3 mox We do not repeat how to make a new block This information is presented in the Extend User Manual and in the CoexistenceModel example Fig 3 shows the structure of the new block named RateLimitingProcess while the accompanying dialog is presented in Fig 4 14 Table 1 Rate limiting terms that modulate the maximum rate with mathematical description and implementation in Extend using the generic library and using a newly created Extend block that replaces generic blocks The new block saves time for the modeller and needs less space on the model pane Process Mathematical Extend code with generic Extend code with newly description blocks created block Unlimited dC _ k XC resource R dt Ta Carrying dc Kra x h _ e x C Consumer C capacity dt K Functional dC _ k XRXC response dt type 1 Functional dC R K nax X xC bd response dt R k oa ly type 2 eo mca i ely F 1 Reserce ia j P unctiona dC R dh 4 Cosas response u Re k xE z type 3 Consumer c i T P Inhibition dC k k ax X Xx C
15. f carbon and nitrogen through six compartments of the Wadden Sea ecosystem The model has six state variables Dissolved inorganic nitrogen the stock of detritus in the water and on the sea bed phytoplankton mussels and birds These state variables are coupled to each other by 11 processes 1 mineralization of detritus in the water 2 denitrification of detritus on the sea bed 3 uptake of nitrogen by algae 4 mineralization of detritus on the sea bed 5 atmospheric deposition of nitrogen 6 sedimentation of detritus and dead phytoplankton 7 grazing of algae by mussels 8 phytoplankton mortality 9 mussel mortality caused by bird predation 10 growth of the bird population 11 mortality of birds as a function of mussel biomass System formulation Model resolution time horizon 120 months but can be defined by the user temporal resolution 1 month 23 spatial extension of the model lumped model spatial scale is the WaddenSea spatial resolution State variables of the model Click on the help file of the hierarchical blocks for information Schemes Click on the help file of the hierarchical blocks for information Numerical solution technique Euler forward Data input Input data none Forcing functions Light and atmospheric deposition Click on the help file of the hierarchical blocks for information Boundary conditions none Initial conditions Click on the help file of the hierarchical blocks for information
16. ickly becomes clear that the explicit formulation of all these rate limitations is a time consuming task so we decided to construct a new Extend block that simply implements the basic rate limiting equations Secondly we made the first version of the model more accessible by combining blocks into hierarchical structures Both steps do not alter the model outcomes But they strongly improve the looks of the model so that non modellers are able to read the model in an intuitive way 3 1 Coding a new model block in Extend that enables faster modelling practice Rate limiting terms modulate the interaction between a resource and its consumer Many formulations exist but in ecology the most applied rate limiting terms are carrying capacity functional response and inhibition All rate limiting terms that are used in the WadBOS ecosystem model are presented using squared brackets in the differential equations 13 Table 1 lists the interactions between a consumer C interacts and a resource R at a rate kmax Each time the mathematical formulation and the implementation of that exact formulation in Extend are given Each time when a modeller wants to include any of these rate limiting terms he or she has to click and drag the appropriate blocks from the generic library to the model pane or copy the blocks and paste them for a second or third rate limiting process This is time consuming and no need to say boring Also the model pan
17. l Each of the state variables is solved in Extend and plotted to an I O output plotter block that resides in the Plotter library Fig 2 The modelled time step is set to 0 001 month and the model simulates 120 months Try to change the time step to see how this parameter affects the results When using a time step of 1 month the model explodes due to numerical errors A time step of 0 1 month already yields stable results 12 3 Model hierarchy and the design and application of model building blocks The ecosystem model as presented above works fine but it is hard to read for non modellers Also it requires a whole lot of clicking and dragging blocks from the generic library to the model pane which becomes a boring and time consuming task So we implemented two steps to facilitate the work for the modeller and the readability of the model for the non modeller Firstly we designed a new building block called rate limiting process As you probably noted the rate of ecological processes of the form dN dt rxN is often limited or even inhibited by resources The growth of a mussel population is limited by available food while a process such as denitrification is inhibited by the presence of oxygen Several mathematical expressions limit the rate of ecological processes The most applied are carrying capacity functional response and the reverse of functional response inhibition When translating the mathematical model into Extend it qu
18. m carbon per m3 Mussels population Mmussel mortality rate of the mussels per month G grazing factor of birds on mussels per bird per month amp E Fh vusemonatiyrate Mortality 4e 06 Grazing rate E4 Birds Mussels Dynamics of the mussel population 10 Dynamics of the bird population Equation aBirds _ kna X 1 Pirr T T EE l ky x Birds dt K k Mussels Extend model Units numbers Parameters 200000 s A Growth of the kvira maximum growth rate of the bird population per month pem atla ana fa K carrying capacity of the bird population numbers Birds Mbird mortality rate of the birds per month hos gle km half saturation constant of the mussel inhibited bird Dynamics of the mortality gram carbon per m3 Mussels l P Mortality of H iX he bird population Inhibition Mort rate Birds bird population 11 EE _ ox ELEL I Ele eAl le ue Plotter 1 0 n Nitrogen wenn Y2 Detritus Seabed Algae vor Detritus Water 0 x Value Y2 7 Plotter 1 0 40000 6 416667 36666 67 5 833333 33333 33 5 25 30000 4 666667 26666 67 4 083333 23333 33 35 20000 2 916667 16666 67 2 333333 13333 33 175 10000 1 166667 H 6666 667 0 5833333 3333 333 0 0 0 20 40 60 80 100 120 Y2 Bids s Green owe Fig 2 Monthly changes of the state variables of the WadBOS ecosystem mode
19. n linearly after which it levels off The most simple function is a sigmoid function using the shape factor p Topics Next Previous Print Search Cancel Fig 6 Screenshot of the Help tab for block RateLimitingProcess that resides in the Extend library WadbosEcosystem lix 3 3 3 How to document the hierarchical Extend blocks Hierarchical blocks have a help tab The help function can be used by opening the structure of the block by clicking on the block while holding the ALT key down and entering text in the upper right pane Fig 7 shows the help tab that was completed in order to document the hierarchical Birds block of the Wadden Sea ecosystem model The documentation starts with a concise description of the function of the block Next the conceptual formulation mathematical equations state variables and parameters are provided Also input and output connectors should be explained Check also the other blocks of the case study for documentation 20 lolx Population model for birds g 7 3 Growth of the e bird population Bids ne fe he bird population Help pa of rc olx Birds Virtual Memory MB 1 258 8 This block calculates the dynamics of the bird population Conceptual model The population increases due to growth towards carying capacity and decreases due to mortality and emigration as a function of the mussel population Mathematical formulation
20. nslation of the mathematical model into an Extend model In Extend each state variable is solved using the integrate block using the option Euler forward Each state variable is initialised with a particular value that can be filled in in the dialog of the integrate block Models can be downloaded from the internal SPICOSA website Notice that each process is only once coded in Model blocks In Extend each process was given a name and that name is used to repeat processes in other parts of the model Nitrogen dynamics Bqdaven dNitrogen yyX k x DetritusWater k K gjeni x Detritus 5 yea dt Extend model ae Yna XK max NOS Light lx Phytoplankton h f k Nitrogen k Light Units gram nitrogen per m Parameters rs conver Fat fifa Ntrogen YN factor converting carbon biomass of the detritus ash free dry eas ream weight of organisms to nitrogen Sopa aes kw mineralisation rate of detritus in the water per month p kp mineralisation rate of detritus on the seabed per month ores Hen oh Nitrogen dynamics Kaeni denitrification rate of detritus on the seabed per month Oopa AD Atmospheric deposition gram nitrogen per month per m sai forcing function EE h water depth m ay YNA factor converting carbon biomass of the algae ash free dry wae weight of organisms to nitrogen my i kmax maximum growth rate of phytoplankton per month
21. nt the state variables of the WadBOS ecosystem model 18 3 3 Documenting the model In a final step the model needs proper documentation so that it can act as a stand alone application Any user should be able to open this model and find all the relevant information to use the model in the data entity itself Extend offers several means of documenting generic Extend blocks self made Extend blocks or hierarchical Extend blocks 3 3 1 How to give a name to individual blocks Every Extend block can be given a name if you click on the block you can fill in a name in the lower left corner next to the help tab Check Fig 7 for the names that have been given to the blocks that make up the birds sub model 3 3 2 How to document the newly coded Extend block RateLimitingProcess Newly coded blocks have a help tab The help function can be used by opening the structure of the block by clicking on the block while holding the ALT key down and entering text in the upper right pane In case of documenting a newly made block it is essential to follow the guidelines that WP8 provides This means that there should be concise information on the function of the model block and an explanation of the possible dialog choices and connectors Fig 6 gives a screenshot with the documentation of the newly made model block for rate limiting processes The help tab starts with a very short explanation about the function of the block Next the possible dialog choices
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