{"id":1202,"date":"2023-12-07T08:29:10","date_gmt":"2023-12-07T13:29:10","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/eweguide\/?post_type=chapter&p=1202"},"modified":"2024-05-30T17:51:19","modified_gmt":"2024-05-30T21:51:19","slug":"environmental-productivity","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/eweguide\/chapter\/environmental-productivity\/","title":{"raw":"Environmental Productivity","rendered":"Environmental Productivity"},"content":{"raw":"

Primary Production<\/h1>\r\nFor primary producers the production is estimated as a function of the producers\u2019 biomass, Bi<\/sub><\/em>, from a simple saturating relationship\r\n\r\n<\/a>[latex]f(B_i)=\\frac{r_i \\ B_i}{1+B_i \\ h_i} \\tag{1}\\label{1}[\/latex]\r\n

where, ri<\/sub> is the maximum production\/biomass ratio that can be realized (for low Bi<\/sub>\u2019s), and ri<\/sub>\/hi<\/sub> is the maximum net primary production when the biomass is not limiting to production (high Bi<\/sub>\u2019s). For parameterization it is only necessary to provide an estimate of ri<\/sub>\/(P\/B)i<\/sub>, i.e., a factor expressing how much primary production can be increased compared to the base model state. If a forcing function is applied to primary production, it multiplies the r parameter in (1<\/a>).<\/p>\r\n\r\n

Nutrient Cycling and Nutrient Limitation in Ecosim<\/h1>\r\nEcosim uses a very simple strategy to represent nutrient cycling and potential nutrient limitation of primary production rates.\u00a0 It is assumed that at any instant in time the system has a total nutrient concentration NT<\/sub>, which is partitioned between nutrient \u2018bound\u2019 in biomass versus free in the environment (accessible to plants for nutrient uptake).\u00a0 That is, T is represented as the sum\r\n

[latex]N_T=\\sum\\limits_i \u014b_i \\ B_i + N_f\\tag{2}\\label{2}[\/latex]<\/p>\r\n,where \u014bi is (fixed) nutrient content per unit of group i biomass, and Nf is free nutrient concentration.\u00a0 Then assuming that NT varies as dNT<\/sub>\/dt = I - v<\/sub>NT<\/sub>, where I is total inflow rate to the system from all nutrient loading sources and v is total loss rate from the system due to all loss agents (volume exchange, sedimentation, export in harvests, etc.), and that v is relatively large, NT is approximated in Ecosim by the (possibly moving) equilibrium value NT = I\/v.\r\n\r\nChanges in nutrient loading can be simulated by assigning a time forcing function number to NT<\/sub>on the Ecosim > Input > Ecosim parameters form, in which case NT<\/sub> is calculated as NT<\/sub> = ft<\/sub> NTo<\/sub>where NTo<\/sub> is the Ecopath base estimate of NT<\/sub> (at the start of each simulation) and ft is a time multiplier (ft<\/sub>\u00a0 = 1 implies Ecopath base value of >NT<\/sub>) supplied by the user the same as any other time forcing function.\u00a0 Note that under the moving equilibrium assumption, changes in ft can be viewed as caused by either changes in input rate I or nutrient loss rate v.\r\n\r\nThe Ecopath base estimate NTo<\/sub> of total nutrient is entered by specifying the base free nutrient proportion \u03a1f<\/sub> = Nf <\/sub>\/ NTo<\/sub> on entry to Ecosim (at Ecosim >Input > Ecosim parameters), from which the Ecosim initialization can calculate NTo<\/sub> as simply,\r\n

[latex]N_{To} = \\sum\\limits_{i} \u014b_i \\ B_i\/(1-p_f)\\tag{3}\\label{3}[\/latex]<\/p>\r\nNote here that the units of nutrient concentration are contained in the per-biomass relative nutrient concentrations \u014bi<\/sub>, and these need not be specified in any particular absolute units.\u00a0 During each simulation, Nf<\/sub> is varied dynamically by setting it equal at any time to\r\n

[latex]N_{T} - \\sum\\limits_i I \\ \u014b_i \\ B_i\\tag{4}\\label{4}[\/latex]<\/p>\r\nso that accumulation of nutrient in any biomass pool(s) can reduce free nutrient available to promote primary production.\r\n\r\nPrimary production rates for producer pools j are linked to free nutrient concentration during each simulation through assumed Michaelis-Menten uptake relationships of the form\r\n

[latex]P\/B_{j} =P\/B_{max,j} \\ N_f\/(k_j+N_f)\\tag{5}\\label{5}[\/latex]<\/p>\r\nwhere the parameters P\/Bmax,j <\/sub>and Kj<\/sub> are calculated as part of the Ecosim initialization using input estimates by the user of the ratios P\/Bmax,j<\/sub> \/ P\/BEcopath,j<\/sub> (Ecosim > Input > Group info\u00a0form).\u00a0 The Michaelis constant Kj<\/sub> is set so that P\/Bj<\/sub> =P\/BEcopath,j<\/sub> when Nf<\/sub> is at the initial concentration determined by\r\n

[latex]N_{T} - \\sum\\limits_i I \\ \u014b_i \\ B_i\\tag{6}\\label{6}[\/latex]<\/p>\r\nwhen all Bi<\/sub> are at Ecopath base values. One can increase sensitivity to changes in nutrient concentration (make P\/Bj<\/sub> more variable with changes in NT<\/sub> and Nf<\/sub>) by increasing the input (P\/B)max,j<\/sub>)\u00a0\/ (P\/B)Ecopath,j<\/sub>\u00a0ratio.\r\n\r\nThe default free nutrient proportion pf is set at unity, which causes Nf <\/sub>to be virtually constant over time (and hence P\/Bj<\/sub>\u2019s to be virtually independent of nutrient concentration changes).\u00a0 Thus to \u201cturn on\u201d nutrient limitation effects, you must set a lower value for \u03c1f<\/sub>, (e.g., 0.3) on the Ecosim parameters form.\r\n\r\nBe aware that this simple approach to accounting for nutrient limitation can interact with the numerical method used to simulate very fast phytoplankton dynamics over time, to cause numerical instability or \u201cchattering\u201d in the values of phytoplankton biomass.\u00a0 This happens mainly in cases where \u03c1f<\/sub> is low, so that Nf<\/sub> is initially small.\u00a0 Then any biomass decline in the system (e.g., due to decline in zooplankton biomass) results in a relatively large increase in Nf<\/sub>, which can cause an over-response in the calculated phytoplankton biomass(es) Bj<\/sub>, which then drives Nf<\/sub> to near zero, which in turn causes too large a decrease in calculated Bj<\/sub> for the next monthly Ecosim time step.\r\n\r\nChattering can be reduced by using the Runge-Kutta integration option and\/or higher pf settings.\u00a0 Improved numerical integration procedures should allow us to avoid the problem entirely in future Ecosim versions, but at present the computational cost of avoiding the problem by \u2018brute force\u2019 (shorter simulation time steps) would be prohibitively expensive of computer time.\r\n\r\nNote further that the single free nutrient concentration Nf<\/sub>\u00a0is linked to all primary producer groups in the model (through the uptake kinetics-P\/B relationships), implying competition among all plant types in the model for free nutrients.\u00a0 This can cause major shifts in primary production structure over time, e.g., between benthic and pelagic primary production and between grazeable and non-grazeable algal types.","rendered":"

Primary Production<\/h1>\n

For primary producers the production is estimated as a function of the producers\u2019 biomass, Bi<\/sub><\/em>, from a simple saturating relationship<\/p>\n

<\/a>[latex]f(B_i)=\\frac{r_i \\ B_i}{1+B_i \\ h_i} \\tag{1}\\label{1}[\/latex]<\/p>\n

where, ri<\/sub> is the maximum production\/biomass ratio that can be realized (for low Bi<\/sub>\u2019s), and ri<\/sub>\/hi<\/sub> is the maximum net primary production when the biomass is not limiting to production (high Bi<\/sub>\u2019s). For parameterization it is only necessary to provide an estimate of ri<\/sub>\/(P\/B)i<\/sub>, i.e., a factor expressing how much primary production can be increased compared to the base model state. If a forcing function is applied to primary production, it multiplies the r parameter in (1<\/a>).<\/p>\n

Nutrient Cycling and Nutrient Limitation in Ecosim<\/h1>\n

Ecosim uses a very simple strategy to represent nutrient cycling and potential nutrient limitation of primary production rates.\u00a0 It is assumed that at any instant in time the system has a total nutrient concentration NT<\/sub>, which is partitioned between nutrient \u2018bound\u2019 in biomass versus free in the environment (accessible to plants for nutrient uptake).\u00a0 That is, T is represented as the sum<\/p>\n

[latex]N_T=\\sum\\limits_i \u014b_i \\ B_i + N_f\\tag{2}\\label{2}[\/latex]<\/p>\n

,where \u014bi is (fixed) nutrient content per unit of group i biomass, and Nf is free nutrient concentration.\u00a0 Then assuming that NT varies as dNT<\/sub>\/dt = I – v<\/sub>NT<\/sub>, where I is total inflow rate to the system from all nutrient loading sources and v is total loss rate from the system due to all loss agents (volume exchange, sedimentation, export in harvests, etc.), and that v is relatively large, NT is approximated in Ecosim by the (possibly moving) equilibrium value NT = I\/v.<\/p>\n

Changes in nutrient loading can be simulated by assigning a time forcing function number to NT<\/sub>on the Ecosim > Input > Ecosim parameters form, in which case NT<\/sub> is calculated as NT<\/sub> = ft<\/sub> NTo<\/sub>where NTo<\/sub> is the Ecopath base estimate of NT<\/sub> (at the start of each simulation) and ft is a time multiplier (ft<\/sub>\u00a0 = 1 implies Ecopath base value of >NT<\/sub>) supplied by the user the same as any other time forcing function.\u00a0 Note that under the moving equilibrium assumption, changes in ft can be viewed as caused by either changes in input rate I or nutrient loss rate v.<\/p>\n

The Ecopath base estimate NTo<\/sub> of total nutrient is entered by specifying the base free nutrient proportion \u03a1f<\/sub> = Nf <\/sub>\/ NTo<\/sub> on entry to Ecosim (at Ecosim >Input > Ecosim parameters), from which the Ecosim initialization can calculate NTo<\/sub> as simply,<\/p>\n

[latex]N_{To} = \\sum\\limits_{i} \u014b_i \\ B_i\/(1-p_f)\\tag{3}\\label{3}[\/latex]<\/p>\n

Note here that the units of nutrient concentration are contained in the per-biomass relative nutrient concentrations \u014bi<\/sub>, and these need not be specified in any particular absolute units.\u00a0 During each simulation, Nf<\/sub> is varied dynamically by setting it equal at any time to<\/p>\n

[latex]N_{T} - \\sum\\limits_i I \\ \u014b_i \\ B_i\\tag{4}\\label{4}[\/latex]<\/p>\n

so that accumulation of nutrient in any biomass pool(s) can reduce free nutrient available to promote primary production.<\/p>\n

Primary production rates for producer pools j are linked to free nutrient concentration during each simulation through assumed Michaelis-Menten uptake relationships of the form<\/p>\n

[latex]P\/B_{j} =P\/B_{max,j} \\ N_f\/(k_j+N_f)\\tag{5}\\label{5}[\/latex]<\/p>\n

where the parameters P\/Bmax,j <\/sub>and Kj<\/sub> are calculated as part of the Ecosim initialization using input estimates by the user of the ratios P\/Bmax,j<\/sub> \/ P\/BEcopath,j<\/sub> (Ecosim > Input > Group info\u00a0form).\u00a0 The Michaelis constant Kj<\/sub> is set so that P\/Bj<\/sub> =P\/BEcopath,j<\/sub> when Nf<\/sub> is at the initial concentration determined by<\/p>\n

[latex]N_{T} - \\sum\\limits_i I \\ \u014b_i \\ B_i\\tag{6}\\label{6}[\/latex]<\/p>\n

when all Bi<\/sub> are at Ecopath base values. One can increase sensitivity to changes in nutrient concentration (make P\/Bj<\/sub> more variable with changes in NT<\/sub> and Nf<\/sub>) by increasing the input (P\/B)max,j<\/sub>)\u00a0\/ (P\/B)Ecopath,j<\/sub>\u00a0ratio.<\/p>\n

The default free nutrient proportion pf is set at unity, which causes Nf <\/sub>to be virtually constant over time (and hence P\/Bj<\/sub>\u2019s to be virtually independent of nutrient concentration changes).\u00a0 Thus to \u201cturn on\u201d nutrient limitation effects, you must set a lower value for \u03c1f<\/sub>, (e.g., 0.3) on the Ecosim parameters form.<\/p>\n

Be aware that this simple approach to accounting for nutrient limitation can interact with the numerical method used to simulate very fast phytoplankton dynamics over time, to cause numerical instability or \u201cchattering\u201d in the values of phytoplankton biomass.\u00a0 This happens mainly in cases where \u03c1f<\/sub> is low, so that Nf<\/sub> is initially small.\u00a0 Then any biomass decline in the system (e.g., due to decline in zooplankton biomass) results in a relatively large increase in Nf<\/sub>, which can cause an over-response in the calculated phytoplankton biomass(es) Bj<\/sub>, which then drives Nf<\/sub> to near zero, which in turn causes too large a decrease in calculated Bj<\/sub> for the next monthly Ecosim time step.<\/p>\n

Chattering can be reduced by using the Runge-Kutta integration option and\/or higher pf settings.\u00a0 Improved numerical integration procedures should allow us to avoid the problem entirely in future Ecosim versions, but at present the computational cost of avoiding the problem by \u2018brute force\u2019 (shorter simulation time steps) would be prohibitively expensive of computer time.<\/p>\n

Note further that the single free nutrient concentration Nf<\/sub>\u00a0is linked to all primary producer groups in the model (through the uptake kinetics-P\/B relationships), implying competition among all plant types in the model for free nutrients.\u00a0 This can cause major shifts in primary production structure over time, e.g., between benthic and pelagic primary production and between grazeable and non-grazeable algal types.<\/p>\n","protected":false},"author":1909,"menu_order":20,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1202","chapter","type-chapter","status-publish","hentry"],"part":441,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapters\/1202","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/wp\/v2\/users\/1909"}],"version-history":[{"count":12,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapters\/1202\/revisions"}],"predecessor-version":[{"id":1736,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapters\/1202\/revisions\/1736"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/parts\/441"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapters\/1202\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/wp\/v2\/media?parent=1202"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/pressbooks\/v2\/chapter-type?post=1202"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/wp\/v2\/contributor?post=1202"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/eweguide\/wp-json\/wp\/v2\/license?post=1202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}