Modeling structural change in spatial system dynamics: A Daisyworld example
Identifieur interne : 000048 ( Pmc/Checkpoint ); précédent : 000047; suivant : 000049Modeling structural change in spatial system dynamics: A Daisyworld example
Auteurs : C. Neuwirth [Autriche, Allemagne] ; A. Peck [Canada] ; S. P. Simonovi [Canada]Source :
- Environmental Modelling & Software [ 1364-8152 ] ; 2015.
Abstract
System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems’ spatial dependencies, most applications have been restricted to the simulation of diffusion processes; this is especially true for models on structural change (e.g. LULC modeling). To address this shortcoming, a Python program is proposed to tightly couple SD software to a Geographic Information System (GIS). The approach provides the required capacities for handling bidirectional and synchronized interactions of operations between SD and GIS. In order to illustrate the concept and the techniques proposed for simulating structural changes, a fictitious environment called Daisyworld has been recreated in a spatial system dynamics (SSD) environment. The comparison of spatial and non-spatial simulations emphasizes the importance of considering spatio-temporal feedbacks. Finally, practical applications of structural change models in agriculture and disaster management are proposed.
Url:
DOI: 10.1016/j.envsoft.2014.11.026
PubMed: 26109906
PubMed Central: 4461191
Affiliations:
- Allemagne, Autriche, Canada
- Angleterre, Bavière, District de Haute-Bavière, Grand Londres
- Londres, Munich
- Université Louis-et-Maximilien de Munich
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Neuwirth</name><affiliation wicri:level="1"><nlm:aff id="aff1">Doctoral College GIScience, University of Salzburg, Salzburg, Austria</nlm:aff><country xml:lang="fr">Autriche</country><wicri:regionArea>Doctoral College GIScience, University of Salzburg, Salzburg</wicri:regionArea><wicri:noRegion>Salzburg</wicri:noRegion></affiliation><affiliation wicri:level="4"><nlm:aff id="aff2">Department of Geography, University of Munich (LMU), Munich, Germany</nlm:aff><country xml:lang="fr">Allemagne</country><wicri:regionArea>Department of Geography, University of Munich (LMU), Munich</wicri:regionArea><placeName><region type="land" nuts="1">Bavière</region><region type="district" nuts="2">District de Haute-Bavière</region><settlement type="city">Munich</settlement></placeName><orgName type="university">Université Louis-et-Maximilien de Munich</orgName></affiliation></author><author><name sortKey="Peck, A" sort="Peck, A" uniqKey="Peck A" first="A." last="Peck">A. Peck</name><affiliation wicri:level="3"><nlm:aff id="aff3">Department of Civil and Environmental Engineering, University of Western Ontario, London, Canada</nlm:aff><country xml:lang="fr">Canada</country><wicri:regionArea>Department of Civil and Environmental Engineering, University of Western Ontario, London</wicri:regionArea><placeName><settlement type="city">Londres</settlement><region type="country">Angleterre</region><region type="région" nuts="1">Grand Londres</region></placeName></affiliation></author><author><name sortKey="Simonovi, S P" sort="Simonovi, S P" uniqKey="Simonovi S" first="S. P." last="Simonovi">S. P. Simonovi</name><affiliation wicri:level="3"><nlm:aff id="aff3">Department of Civil and Environmental Engineering, University of Western Ontario, London, Canada</nlm:aff><country xml:lang="fr">Canada</country><wicri:regionArea>Department of Civil and Environmental Engineering, University of Western Ontario, London</wicri:regionArea><placeName><settlement type="city">Londres</settlement><region type="country">Angleterre</region><region type="région" nuts="1">Grand Londres</region></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">26109906</idno><idno type="pmc">4461191</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4461191</idno><idno type="RBID">PMC:4461191</idno><idno type="doi">10.1016/j.envsoft.2014.11.026</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000145</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000145</idno><idno type="wicri:Area/Pmc/Curation">000145</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000145</idno><idno type="wicri:Area/Pmc/Checkpoint">000048</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">000048</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Modeling structural change in spatial system dynamics: A Daisyworld example</title><author><name sortKey="Neuwirth, C" sort="Neuwirth, C" uniqKey="Neuwirth C" first="C." last="Neuwirth">C. Neuwirth</name><affiliation wicri:level="1"><nlm:aff id="aff1">Doctoral College GIScience, University of Salzburg, Salzburg, Austria</nlm:aff><country xml:lang="fr">Autriche</country><wicri:regionArea>Doctoral College GIScience, University of Salzburg, Salzburg</wicri:regionArea><wicri:noRegion>Salzburg</wicri:noRegion></affiliation><affiliation wicri:level="4"><nlm:aff id="aff2">Department of Geography, University of Munich (LMU), Munich, Germany</nlm:aff><country xml:lang="fr">Allemagne</country><wicri:regionArea>Department of Geography, University of Munich (LMU), Munich</wicri:regionArea><placeName><region type="land" nuts="1">Bavière</region><region type="district" nuts="2">District de Haute-Bavière</region><settlement type="city">Munich</settlement></placeName><orgName type="university">Université Louis-et-Maximilien de Munich</orgName></affiliation></author><author><name sortKey="Peck, A" sort="Peck, A" uniqKey="Peck A" first="A." last="Peck">A. Peck</name><affiliation wicri:level="3"><nlm:aff id="aff3">Department of Civil and Environmental Engineering, University of Western Ontario, London, Canada</nlm:aff><country xml:lang="fr">Canada</country><wicri:regionArea>Department of Civil and Environmental Engineering, University of Western Ontario, London</wicri:regionArea><placeName><settlement type="city">Londres</settlement><region type="country">Angleterre</region><region type="région" nuts="1">Grand Londres</region></placeName></affiliation></author><author><name sortKey="Simonovi, S P" sort="Simonovi, S P" uniqKey="Simonovi S" first="S. P." last="Simonovi">S. P. Simonovi</name><affiliation wicri:level="3"><nlm:aff id="aff3">Department of Civil and Environmental Engineering, University of Western Ontario, London, Canada</nlm:aff><country xml:lang="fr">Canada</country><wicri:regionArea>Department of Civil and Environmental Engineering, University of Western Ontario, London</wicri:regionArea><placeName><settlement type="city">Londres</settlement><region type="country">Angleterre</region><region type="région" nuts="1">Grand Londres</region></placeName></affiliation></author></analytic><series><title level="j">Environmental Modelling & Software</title><idno type="ISSN">1364-8152</idno><idno type="eISSN">1873-6726</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems’ spatial dependencies, most applications have been restricted to the simulation of diffusion processes; this is especially true for models on structural change (e.g. LULC modeling). To address this shortcoming, a Python program is proposed to tightly couple SD software to a Geographic Information System (GIS). The approach provides the required capacities for handling bidirectional and synchronized interactions of operations between SD and GIS. In order to illustrate the concept and the techniques proposed for simulating structural changes, a fictitious environment called Daisyworld has been recreated in a spatial system dynamics (SSD) environment. The comparison of spatial and non-spatial simulations emphasizes the importance of considering spatio-temporal feedbacks. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Environ Model Softw</journal-id><journal-id journal-id-type="iso-abbrev">Environ Model Softw</journal-id><journal-title-group><journal-title>Environmental Modelling & Software</journal-title></journal-title-group><issn pub-type="ppub">1364-8152</issn><issn pub-type="epub">1873-6726</issn><publisher><publisher-name>Elsevier Science</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">26109906</article-id><article-id pub-id-type="pmc">4461191</article-id><article-id pub-id-type="publisher-id">S1364-8152(14)00352-1</article-id><article-id pub-id-type="doi">10.1016/j.envsoft.2014.11.026</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Modeling structural change in spatial system dynamics: A Daisyworld example</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Neuwirth</surname><given-names>C.</given-names></name><email>Christian.Neuwirth@lmu.de</email><xref rid="aff1" ref-type="aff">a</xref><xref rid="aff2" ref-type="aff">b</xref><xref rid="cor1" ref-type="corresp">∗</xref></contrib><contrib contrib-type="author"><name><surname>Peck</surname><given-names>A.</given-names></name><xref rid="aff3" ref-type="aff">c</xref></contrib><contrib contrib-type="author"><name><surname>Simonović</surname><given-names>S.P.</given-names></name><xref rid="aff3" ref-type="aff">c</xref></contrib></contrib-group><aff id="aff1"><label>a</label>Doctoral College GIScience, University of Salzburg, Salzburg, Austria</aff><aff id="aff2"><label>b</label>Department of Geography, University of Munich (LMU), Munich, Germany</aff><aff id="aff3"><label>c</label>Department of Civil and Environmental Engineering, University of Western Ontario, London, Canada</aff><author-notes><corresp id="cor1"><label>∗</label>Corresponding author. Department of Geography, University of Munich (LMU), Munich, Germany. Tel.: +49 89 2180 4135. <email>Christian.Neuwirth@lmu.de</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>1</day><month>3</month><year>2015</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on .</pmc-comment>
<pub-date pub-type="ppub"><month>3</month><year>2015</year></pub-date><volume>65</volume><fpage>30</fpage><lpage>40</lpage><history><date date-type="received"><day>21</day><month>5</month><year>2014</year></date><date date-type="rev-recd"><day>26</day><month>11</month><year>2014</year></date><date date-type="accepted"><day>26</day><month>11</month><year>2014</year></date></history><permissions><copyright-statement>© 2014 The Authors</copyright-statement><copyright-year>2014</copyright-year><license license-type="CC BY-NC-ND" xlink:href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><license-p>This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).</license-p></license></permissions><abstract><p>System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems’ spatial dependencies, most applications have been restricted to the simulation of diffusion processes; this is especially true for models on structural change (e.g. LULC modeling). To address this shortcoming, a Python program is proposed to tightly couple SD software to a Geographic Information System (GIS). The approach provides the required capacities for handling bidirectional and synchronized interactions of operations between SD and GIS. In order to illustrate the concept and the techniques proposed for simulating structural changes, a fictitious environment called Daisyworld has been recreated in a spatial system dynamics (SSD) environment. The comparison of spatial and non-spatial simulations emphasizes the importance of considering spatio-temporal feedbacks. Finally, practical applications of structural change models in agriculture and disaster management are proposed.</p></abstract><abstract abstract-type="author-highlights"><title>Highlights</title><p><list list-type="simple"><list-item id="u0010"><label>•</label><p>Simulation of evolving spatial structures has been widely neglected so far in SSD.</p></list-item><list-item id="u0015"><label>•</label><p>The simulation requires bidirectional and synchronous interaction between System Dynamics and GIS applications.</p></list-item><list-item id="u0020"><label>•</label><p>Daisyworld is used to illustrate the tight coupling approach.</p></list-item><list-item id="u0025"><label>•</label><p>Results highlight the importance of considering spatio-temporal feedbacks.</p></list-item></list></p></abstract><kwd-group><title>Keywords</title><kwd>Spatial system dynamics</kwd><kwd>Tight coupling</kwd><kwd>Process and structure</kwd><kwd>Structural feedback</kwd></kwd-group></article-meta></front><floats-group><fig id="fig1"><label>Fig. 1</label><caption><p>Schematic representation of a (a) causal loop diagram; (b) stock and flow diagram.</p></caption><graphic xlink:href="gr1"></graphic></fig><fig id="fig2"><label>Fig. 2</label><caption><p>SD model on farming intensities and infrastructure.</p></caption><graphic xlink:href="gr2"></graphic></fig><fig id="fig3"><label>Fig. 3</label><caption><p>Association of process (time) and structure (space) in a structural change model.</p></caption><graphic xlink:href="gr3"></graphic></fig><fig id="fig4"><label>Fig. 4</label><caption><p>Schematic representation of synchronized operations between SD and GIS.</p></caption><graphic xlink:href="gr4"></graphic></fig><fig id="fig5"><label>Fig. 5</label><caption><p>Code sequence of coupling tool.</p></caption><graphic xlink:href="gr5"></graphic></fig><fig id="fig6"><label>Fig. 6</label><caption><p>Daisyworld as stock and flow diagram; variables which have been added to the original model are shown in bold.</p></caption><graphic xlink:href="gr6"></graphic></fig><fig id="fig7"><label>Fig. 7</label><caption><p>Schematic representation of spatio-temporal landscape changes in Daisyworld</p></caption><graphic xlink:href="gr7"></graphic></fig><fig id="fig8"><label>Fig. 8</label><caption><p>Non-spatial simulation compared to 5 spatial simulations with randomly generated landscapes; model settings: black daisies 100 ha, white daisies 100 ha, fertile soil 500 ha, barren land 300 ha, luminosity drop from 1 to 0.9 after 50 time steps.</p></caption><graphic xlink:href="gr8"></graphic></fig><fig id="fig9"><label>Fig. 9</label><caption><p>Stress test scenario for a non-spatial and a spatial simulation; model settings: black daisies 190 ha, white daisies 10 ha, fertile soil 500 ha, barren land 300 ha, luminosity drop from 1 to 0.9 after 10 time steps.</p></caption><graphic xlink:href="gr9"></graphic></fig><fig id="fig10"><label>Fig. 10</label><caption><p>Land cover response scenario for a non-spatial and a spatial simulation; model settings: black daisies 100 ha, white daisies 100 ha, fertile soil 500 ha, barren land 300 ha, luminosity is increased from 1 to 1.1 between time step 50 and 100.</p></caption><graphic xlink:href="gr10"></graphic></fig><fig id="fig11"><label>Fig. 11</label><caption><p>Simulation of the same landscape with 4 different raster resolutions; model settings: black daisies 100 ha, white daisies 100 ha, fertile soil 500 ha, barren land 300 ha, luminosity drop from 1 to 0.9 after 50 time steps.</p></caption><graphic xlink:href="gr11"></graphic></fig><table-wrap id="tbl1" position="float"><label>Table 1</label><caption><p>Daisyworld equations (<xref rid="bib35" ref-type="bibr">Watson and Lovelock, 1983</xref>).</p></caption><table frame="hsides" rules="groups"><thead><tr><th>#</th><th>Description</th><th>Equations</th></tr></thead><tbody><tr><td>(1)</td><td>Planetary Albedo</td><td><inline-formula><mml:math id="M6" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:msub><mml:mi>α</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>w</mml:mi></mml:msub><mml:msub><mml:mi>A</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></td></tr><tr><td>(2)</td><td>Planetary Temperature</td><td><inline-formula><mml:math id="M7" altimg="si2.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>∜</mml:mo><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>σ</mml:mi><mml:mo>)</mml:mo><mml:mo>−</mml:mo><mml:mn>273</mml:mn></mml:mrow></mml:math></inline-formula></td></tr><tr><td>(3)</td><td>Local Temperature</td><td><inline-formula><mml:math id="M8" altimg="si3.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>q</mml:mi><mml:mo>'</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></td></tr><tr><td>(4)</td><td>Growth Rate</td><td><inline-formula><mml:math id="M9" altimg="si4.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mn>0.003265</mml:mn><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>22.5</mml:mn><mml:mo>−</mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></td></tr><tr><td>(5)</td><td>Area Change</td><td><inline-formula><mml:math id="M10" altimg="si5.gif" overflow="scroll"><mml:mrow><mml:mrow><mml:mrow><mml:mo>ⅆ</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>ⅆ</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>g</mml:mi></mml:msub><mml:msub><mml:mi>β</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:mi>γ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula></td></tr></tbody></table><table-wrap-foot><fn><p>Planetary albedo A; proportion of total area α; subscripts: fertile soil g, black daisies b, white daisies w; planetary temperature <inline-formula><mml:math id="M11" altimg="si6.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in [°C]; solar input S, 917 Wm<sup>−2</sup>; dimensionless measure of the luminosity of Daisyworld's sun, 0–1; Boltzmann constant, 5.67032 E<sup>−8</sup>; proportional constant q′, 20 °C, daisy growth rate β; area in absolute numbers <italic>x</italic>; death rate per unit of time <inline-formula><mml:math id="M12" altimg="si7.gif" overflow="scroll"><mml:mi>γ</mml:mi></mml:math></inline-formula>, 0.3.</p></fn></table-wrap-foot></table-wrap><table-wrap id="tbl2" position="float"><label>Table 2</label><caption><p>Detailed description of the Daisyworld stock and flow elements (based on descriptions in <xref rid="bib8" ref-type="bibr">Ford, 2010</xref>); modifications to this model are referenced by footnotes.</p></caption><table frame="hsides" rules="groups"><thead><tr><th>#</th><th>Type</th><th>Init. or const. value</th><th>Condition or equation</th></tr></thead><tbody><tr><td>(1)</td><td>Function</td><td>–</td><td>Equation (2); <xref rid="tbl1" ref-type="table">Table 1</xref></td></tr><tr><td>(2)</td><td>Condition</td><td></td><td>Time dependent cond.: IF THEN ELSE(Time < <italic>x</italic>,<italic>y</italic>,<italic>z</italic>)</td></tr><tr><td>(3)<xref rid="tbl2fna" ref-type="table-fn">a</xref></td><td>Constant</td><td>0.5</td><td>–</td></tr><tr><td>(4)</td><td>Variable</td><td>–</td><td>Luminosity*(1-Average albedo)</td></tr><tr><td>(5)<xref rid="tbl2fna" ref-type="table-fn">a</xref></td><td>Constant</td><td>Scenario dependent</td><td></td></tr><tr><td>(6)</td><td>Constant</td><td>0.75</td><td>–</td></tr><tr><td>(7)<xref rid="tbl2fnb" ref-type="table-fn">b</xref></td><td>Variable</td><td>–</td><td>Equation (1); <xref rid="tbl1" ref-type="table">Table 1</xref></td></tr><tr><td>(8)</td><td>Constant</td><td>0.25</td><td>–</td></tr><tr><td>(9)</td><td>Constant</td><td>0.5</td><td>–</td></tr><tr><td>(10)</td><td>Variable</td><td>–</td><td>(20)*(Average albedo-White albedo)</td></tr><tr><td>(11)<xref rid="tbl2fnc" ref-type="table-fn">c</xref></td><td>Stock</td><td>Scenario dependent</td><td>White growth-White decay</td></tr><tr><td>(12)</td><td>Flow</td><td>–</td><td>Area white daisies*Decay rate</td></tr><tr><td>(13)</td><td>Stock</td><td>Scenario dependent</td><td>Black decay + White decay-Black growth-White growth</td></tr><tr><td>(14)</td><td>Flow</td><td>–</td><td>Area black daisies*Decay rate</td></tr><tr><td>(15)<xref rid="tbl2fnc" ref-type="table-fn">c</xref></td><td>Stock</td><td>Scenario dependent</td><td>Black growth-Black decay</td></tr><tr><td>(16)</td><td>Variable</td><td>–</td><td>(20)*(Average albedo-Black albedo)</td></tr><tr><td>(17)</td><td>Variable</td><td>–</td><td>Temperatures in Daisyworld + Temperature adjustment white daisies</td></tr><tr><td>(18)</td><td>Flow</td><td>–</td><td>Area white daisies*Actual white growth rate</td></tr><tr><td>(19)</td><td>Constant</td><td>0.3</td><td>–</td></tr><tr><td>(20)</td><td>Flow</td><td>–</td><td>Area black daisies*Actual black growth rate</td></tr><tr><td>(21)</td><td>Variable</td><td>–</td><td>Temperatures in Daisyworld + Temperature adjustment black daisies</td></tr><tr><td>(22)</td><td>Function</td><td>–</td><td>Equation (4), <xref rid="tbl1" ref-type="table">Table 1</xref></td></tr><tr><td>(23)</td><td>Spatial variable</td><td>–</td><td>Local availability of fertile soil for white daisies</td></tr><tr><td>(24)</td><td>Spatial variable</td><td>–</td><td>Local availability of fertile soil for black daisies</td></tr><tr><td>(25)</td><td>Function</td><td>–</td><td>Equation (4), <xref rid="tbl1" ref-type="table">Table 1</xref></td></tr></tbody></table><table-wrap-foot><fn id="tbl2fna"><label>a</label><p>New land type barren land.</p></fn></table-wrap-foot><table-wrap-foot><fn id="tbl2fnb"><label>b</label><p>See equation (6); barren land is involved as a fourth land type in the calculation of planetary albedo.</p></fn></table-wrap-foot><table-wrap-foot><fn id="tbl2fnc"><label>c</label><p>See <xref rid="tbl1" ref-type="table">Table 1</xref>, equation (5); the proportional area of fertile ground <inline-formula><mml:math id="M13" altimg="si8.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>α</mml:mi><mml:mi>g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the original version is replaced by a spatially explicit growth reduction multiplier <inline-formula><mml:math id="M14" altimg="si9.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mo>,</mml:mo><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> (see also modified equations (7) and (8)).</p></fn></table-wrap-foot></table-wrap></floats-group></pmc><affiliations><list><country><li>Allemagne</li><li>Autriche</li><li>Canada</li></country><region><li>Angleterre</li><li>Bavière</li><li>District de Haute-Bavière</li><li>Grand Londres</li></region><settlement><li>Londres</li><li>Munich</li></settlement><orgName><li>Université Louis-et-Maximilien de Munich</li></orgName></list><tree><country name="Autriche"><noRegion><name sortKey="Neuwirth, C" sort="Neuwirth, C" uniqKey="Neuwirth C" first="C." last="Neuwirth">C. Neuwirth</name></noRegion></country><country name="Allemagne"><region name="Bavière"><name sortKey="Neuwirth, C" sort="Neuwirth, C" uniqKey="Neuwirth C" first="C." last="Neuwirth">C. Neuwirth</name></region></country><country name="Canada"><region name="Angleterre"><name sortKey="Peck, A" sort="Peck, A" uniqKey="Peck A" first="A." last="Peck">A. Peck</name></region><name sortKey="Simonovi, S P" sort="Simonovi, S P" uniqKey="Simonovi S" first="S. P." last="Simonovi">S. P. Simonovi</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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