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Nima Asgharbeygi, Pat Langley, Stephen Bay Center for the Study of Language and Information Stanford University Kevin Arrigo Department of Geophysics Stanford University Computational Revision of Ecological Process Models Thanks to S. Dzeroski, J. Sanchez, K. Saito, J. Shrager, and L. Todorovski for their contributions to this research, which is funded by the US National Science Foundation.

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Data Mining vs. Scientific Discovery induce predictive models from large (often business) data sets; induce predictive models from large (often business) data sets; represent models in notations invented by AI researchers. represent models in notations invented by AI researchers. There exist two computational paradigms for discovering explicit knowledge from data. The data mining movement develops computational methods that: This talk focuses on applications of the second framework to environmental and ecosystem modeling. constructing models from (often small) scientific data sets; constructing models from (often small) scientific data sets; stated in formalisms invented by scientists themselves. stated in formalisms invented by scientists themselves. In contrast, computational scientific discovery focuses on:

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Observations from the Ross Sea

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A Model of Ross Sea Ecosystem model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue d[nitro,t,1] = phyto residue

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Inductive Revision of Ecosystem Models Revision observations initial model revised model model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue zoo residue d[nitro,t,1] = phyto residue model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue zoo residue d[nitro,t,1] = phyto residue

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A Space of Ecosystem Models Model revision requires ways to constrain search through this space.

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Phytoplankton Loss in Ross Sea Ecosystem model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue d[nitro,t,1] = phyto residue Phytoplankton loss is a process that affects two variables; no model should include one influence without the other.

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Grazing in the Ross Sea Ecosystem model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue d[nitro,t,1] = phyto residue We can view an ecosystem model as a set of processes that provide an alternative way to encode its assumptions.

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Process Model of Ross Sea Ecosystem model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro process phyto_loss equations:d[phyto,t,1] = phyto equations:d[phyto,t,1] = phyto d[residue,t,1] = phyto process zoo_loss equations:d[zoo,t,1] = zoo equations:d[zoo,t,1] = zoo d[residue,t,1] = zoo process zoo_phyto_grazing equations:d[zoo,t,1] = zoo equations:d[zoo,t,1] = zoo d[residue,t,1] = zoo d[phyto,t,1] = zoo process nitro_uptake equations:d[phyto,t,1] = phyto equations:d[phyto,t,1] = phyto d[nitro,t,1] = phyto process nitro_remineralization; equations:d[nitro,t,1] = residue equations:d[nitro,t,1] = residue d[residue,t,1 ] = residue

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Inductive Revision of Process Models Revision initial model observations revised model model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue zoo residue d[nitro,t,1] = phyto residue model RossSeaEcosystem variables: phyto, zoo, nitro, residue observables: phyto, nitro d[phyto,t,1] = phyto zoo phyto phyto d[zoo,t,1] = zoo zoo d[residue,t,1] = phyto zoo zoo residue zoo residue d[nitro,t,1] = phyto residue process exponential_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1, ] P equations: d[P,t] = [0, 1, ] P process logistic_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1, ] P (1 P / [0, 1, ]) equations: d[P,t] = [0, 1, ] P (1 P / [0, 1, ]) process constant_inflow variables: I {inorganic_nutrient} variables: I {inorganic_nutrient} equations: d[I,t] = [0, 1, ] equations: d[I,t] = [0, 1, ] process consumption variables: P1 {population}, P2 {population}, nutrient_P2 variables: P1 {population}, P2 {population}, nutrient_P2 equations: d[P1,t] = [0, 1, ] P1 nutrient_P2, equations: d[P1,t] = [0, 1, ] P1 nutrient_P2, d[P2,t] = [0, 1, ] P1 nutrient_P2 d[P2,t] = [0, 1, ] P1 nutrient_P2 process no_saturation variables: P {number}, nutrient_P {number} variables: P {number}, nutrient_P {number} equations: nutrient_P = P equations: nutrient_P = P process saturation variables: P {number}, nutrient_P {number} variables: P {number}, nutrient_P {number} equations: nutrient_P = P / (P + [0, 1, ]) equations: nutrient_P = P / (P + [0, 1, ]) generic processes

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Generic Processes for Aquatic Ecosystems generic process exponential_lossgeneric process remineralization variables: S{species}, D{detritus} variables: N{nutrient}, D{detritus} variables: S{species}, D{detritus} variables: N{nutrient}, D{detritus} parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] equations:d[S,t,1] = 1 S equations:d[N, t,1] = D equations:d[S,t,1] = 1 S equations:d[N, t,1] = D d[D,t,1] = Sd[D, t,1] = 1 D generic process grazinggeneric process constant_inflow variables: S1{species}, S2{species}, D{detritus} variables: N{nutrient} variables: S1{species}, S2{species}, D{detritus} variables: N{nutrient} parameters: [0, 1], [0, 1] parameters: [0, 1] parameters: [0, 1], [0, 1] parameters: [0, 1] equations:d[S1,t,1] = S1 equations:d[N,t,1] = equations:d[S1,t,1] = S1 equations:d[N,t,1] = d[D,t,1] = (1 ) S1 d[S2,t,1] = 1 S1 generic process nutrient_uptake variables: S{species}, N{nutrient} variables: S{species}, N{nutrient} parameters: [0, ], [0, 1], [0, 1] parameters: [0, ], [0, 1], [0, 1] conditions:N > conditions:N > equations:d[S,t,1] = S equations:d[S,t,1] = S d[N,t,1] = 1 S

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A Method for Process Model Revision 1. Find all ways to instantiate available generic processes with specific variables, subject to type constraints; 2. Generate candidate model structures by deleting the current processes and adding new ones, subject to complexity limits; 3. For each generic model, carry out search through parameter space to find good coefficients [difficult]; 4. Return a list of revised models ordered by their overall scores. We have implemented RPM, an algorithm that revises an initial process model in four main stages: The evaluation metric can be squared error or description length based on error and distance from the initial model.

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Observations from the Ross Sea

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Revised Model of Ross Sea Ecosystem model RossSeaEcosystem variables: phyto, zoo, nitro, residue, light, G, growth_rate, nitro_rate, light_rate observables: phyto, nitro, light d[phyto,t,1] = phyto G zoo + growth_rate phyto d[zoo,t,1] = G zoo d[residue,t,1] = phyto G zoo residue d[nitro,t,1] = 1 n_to_c growth_rate phyto n_to_c residue G = (1 – exp( – phyto) growth_rate = r_max min(nitro_rate, light_rate) nitro_rate = nitro / (nitro ) light_rate = light / (light ) n_to_c = 0.251, r_max = 0.194, remin_rate =

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Initial Results on Ross Sea Training Data The best revised model reproduces the observations quite well.

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Initial Results on Ross Sea Test Data But the model predicts nearly the same behavior for both years.

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Revised Results on Ross Sea Test Data Refitting initial values for zooplankton gives better generalization.

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Results on Data from Protist Study

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Results on Data from Rinkobing Fjord

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specify a quantitative process model of the target system; specify a quantitative process model of the target system; display and edit the models structure and details graphically; display and edit the models structure and details graphically; simulate the models behavior over time and situations; simulate the models behavior over time and situations; compare the models predicted behavior to observations; compare the models predicted behavior to observations; invoke a revision module in response to detected anomalies. invoke a revision module in response to detected anomalies. Because few scientists want to be replaced, we are developing P ROMETHEUS, an interactive environment that lets users: The environment offers computational assistance in forming and evaluating models but lets the user retain control. Interfacing with Scientists

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Viewing and Editing a Process Model

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computational scientific discovery (e.g., Langley et al., 1983); computational scientific discovery (e.g., Langley et al., 1983); theory revision in machine learning (e.g., Towell, 1991); theory revision in machine learning (e.g., Towell, 1991); qualitative physics and simulation (e.g., Forbus, 1984); qualitative physics and simulation (e.g., Forbus, 1984); languages for scientific simulation (e.g., STELLA, MATLAB ); languages for scientific simulation (e.g., STELLA, MATLAB ); interactive tools for data analysis (e.g., Schneiderman, 2001). interactive tools for data analysis (e.g., Schneiderman, 2001). Intellectual Influences Our approach to computational discovery incorporates ideas from many traditions: Our work combines ideas from machine learning, AI, programming languages, and human-computer interaction.

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Directions for Future Research produce additional results on other ecosystem modeling tasks produce additional results on other ecosystem modeling tasks develop improved methods for fitting model parameters develop improved methods for fitting model parameters implement heuristic methods for searching the structure space implement heuristic methods for searching the structure space utilize knowledge of subsystems to further constrain search utilize knowledge of subsystems to further constrain search augment the modeling environment to make it more usable augment the modeling environment to make it more usable Despite our progress to date, we need further work in order to: Process modeling has great potential to aid model development in environmental science.

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Contributions of the Research a new formalism for representing scientific process models; a new formalism for representing scientific process models; an encoding for background knowledge as generic processes; an encoding for background knowledge as generic processes; an algorithm for revising process models with time-series data; an algorithm for revising process models with time-series data; an interactive environment for model construction/utilization. an interactive environment for model construction/utilization. In summary, our work on computational discovery has produced: We have demonstrated this approach to model revision on both ecosystem modeling and an environmental domain. The P ROMETHEUS modeling/revision environment is available at:

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End of Presentation

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The Challenge of Systems Science focusing on synthesis rather than analysis in their operation; focusing on synthesis rather than analysis in their operation; using computer modeling as one of their central methods; using computer modeling as one of their central methods; developing system-level models with many variables / relations; developing system-level models with many variables / relations; evaluating models on observational, not experimental, data. evaluating models on observational, not experimental, data. Disciplines like Earth science differ from traditional disciplines by: Constructing such models are complex tasks that would benefit from computational aids, but existing methods are insufficient.

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Why Are Process Models Interesting? they incorporate scientific formalisms rather than AI notations; they incorporate scientific formalisms rather than AI notations; that are easily communicable to scientists and engineers; that are easily communicable to scientists and engineers; they move beyond descriptive generalization to explanation; they move beyond descriptive generalization to explanation; while retaining the modularity needed to support induction. while retaining the modularity needed to support induction. Process models are a crucial target for machine learning because: These reasons point to process models as an ideal representation for scientific and engineering knowledge. Process models are an important alternative to formalisms used currently in machine learning.

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Advantages of Quantitative Process Models they embed quantitative relations within qualitative structure; they embed quantitative relations within qualitative structure; that refer to notations and mechanisms familiar to experts; that refer to notations and mechanisms familiar to experts; they provide dynamical predictions of changes over time; they provide dynamical predictions of changes over time; they offer causal and explanatory accounts of phenomena; they offer causal and explanatory accounts of phenomena; while retaining the modularity needed to support induction. while retaining the modularity needed to support induction. Process models offer scientists a promising framework because: Quantitative process models provide an important alternative to formalisms used currently in ecosystem modeling.

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Inductive Process Modeling Our response is to design, construct, and evaluate computational methods for inductive process modeling, which: represent scientific models as sets of quantitative processes; represent scientific models as sets of quantitative processes; use these models to predict and explain observational data; use these models to predict and explain observational data; search a space of process models to find good candidates; search a space of process models to find good candidates; utilize background knowledge to constrain this search. utilize background knowledge to constrain this search. This framework has great potential to aid environmental science, but it raises new computational challenges.

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Challenges of Inductive Process Modeling process models characterize behavior of dynamical systems; process models characterize behavior of dynamical systems; variables are continuous but can have discontinuous behavior; variables are continuous but can have discontinuous behavior; observations are not independently and identically distributed; observations are not independently and identically distributed; models may contain unobservable processes and variables; models may contain unobservable processes and variables; multiple processes can interact to produce complex behavior. multiple processes can interact to produce complex behavior. Process model induction differs from typical learning tasks in that: Compensating factors include a focus on deterministic systems and the availability of background knowledge.

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Generating Predictions and Explanations To utilize or evaluate a given process model, we must simulate its behavior over time: specify initial values for input variables and time step size; specify initial values for input variables and time step size; on each time step, determine which processes are active; on each time step, determine which processes are active; solve active algebraic/differential equations with known values; solve active algebraic/differential equations with known values; propagate values and recursively solve other active equations; propagate values and recursively solve other active equations; when multiple processes influence the same variable, assume their effects are additive. when multiple processes influence the same variable, assume their effects are additive. This performance method makes specific predictions that we can compare to observations.

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Generic Processes as Background Knowledge the variables involved in a process and their types; the variables involved in a process and their types; the parameters appearing in a process and their ranges; the parameters appearing in a process and their ranges; the forms of conditions on the process; and the forms of conditions on the process; and the forms of associated equations and their parameters. the forms of associated equations and their parameters. Our framework casts background knowledge as generic processes that specify: Generic processes are building blocks from which one can compose a specific process model.

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Estimating Parameters in Process Models 1. Selects random initial values that fall within ranges specified in the generic processes; 2. Improves these parameters using the Levenberg-Marquardt method until it reaches a local optimum; 3. Generates new candidate values through random jumps along dimensions of the parameter vector and continue search; 4. If no improvement occurs after N jumps, it restarts the search from a new random initial point. To estimate the parameters for each generic model structure, the IPM algorithm: This multi-level method gives reasonable fits to time-series data from a number of domains, but it is computationally intensive.

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A Process Model for an Aquatic Ecosystem model Ross_Sea_Ecosystem variables: phyto, nitro, residue, light, growth_rate, effective_light, ice_factor observables: phyto, nitro, light, ice_factor process phyto_loss equations:d[phyto,t,1] = 0.1 phyto equations:d[phyto,t,1] = 0.1 phyto d[residue,t,1] = 0.1 phyto process phyto_growth equations:d[phyto,t,1] = growth_rate phyto equations:d[phyto,t,1] = growth_rate phyto process phyto_uptakes_nitro conditions:nitro > 0 conditions:nitro > 0 equations:d[nitro,t,1] = growth_rate phyto equations:d[nitro,t,1] = growth_rate phyto process growth_limitation equations:growth_rate = 0.23 min(nitrate_rate, light_rate) equations:growth_rate = 0.23 min(nitrate_rate, light_rate) process nitrate_availability equations:nitrate_rate = nitrate / (nitrate + 5) equations:nitrate_rate = nitrate / (nitrate + 5) process light_availability equations:light_rate = effective_light / (effective_light + 50) equations:light_rate = effective_light / (effective_light + 50) process light_attenuation equations:effective_light = light ice_factor equations:effective_light = light ice_factor

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Generic Processes for Aquatic Ecosystems generic process exponential_lossgeneric process remineralization variables: S{species}, D{detritus} variables: N{nutrient}, D{detritus} variables: S{species}, D{detritus} variables: N{nutrient}, D{detritus} parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] equations:d[S,t,1] = 1 S equations:d[N, t,1] = D equations:d[S,t,1] = 1 S equations:d[N, t,1] = D d[D,t,1] = Sd[D, t,1] = 1 D generic process grazinggeneric process constant_inflow variables: S1{species}, S2{species}, D{detritus} variables: N{nutrient} variables: S1{species}, S2{species}, D{detritus} variables: N{nutrient} parameters: [0, 1], [0, 1] parameters: [0, 1] parameters: [0, 1], [0, 1] parameters: [0, 1] equations:d[S1,t,1] = S1 equations:d[N,t,1] = equations:d[S1,t,1] = S1 equations:d[N,t,1] = d[D,t,1] = (1 ) S1 d[S2,t,1] = 1 S1 generic process nutrient_uptake variables: S{species}, N{nutrient} variables: S{species}, N{nutrient} parameters: [0, ], [0, 1], [0, 1] parameters: [0, ], [0, 1], [0, 1] conditions:N > conditions:N > equations:d[S,t,1] = S equations:d[S,t,1] = S d[N,t,1] = 1 S

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Inductive Process Modeling process exponential_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1, ] P equations: d[P,t] = [0, 1, ] P process logistic_growth variables: P {population} variables: P {population} equations: d[P,t] = [0, 1, ] P (1 P / [0, 1, ]) equations: d[P,t] = [0, 1, ] P (1 P / [0, 1, ]) process constant_inflow variables: I {inorganic_nutrient} variables: I {inorganic_nutrient} equations: d[I,t] = [0, 1, ] equations: d[I,t] = [0, 1, ] process consumption variables: P1 {population}, P2 {population}, nutrient_P2 variables: P1 {population}, P2 {population}, nutrient_P2 equations: d[P1,t] = [0, 1, ] P1 nutrient_P2, equations: d[P1,t] = [0, 1, ] P1 nutrient_P2, d[P2,t] = [0, 1, ] P1 nutrient_P2 d[P2,t] = [0, 1, ] P1 nutrient_P2 process no_saturation variables: P {number}, nutrient_P {number} variables: P {number}, nutrient_P {number} equations: nutrient_P = P equations: nutrient_P = P process saturation variables: P {number}, nutrient_P {number} variables: P {number}, nutrient_P {number} equations: nutrient_P = P / (P + [0, 1, ]) equations: nutrient_P = P / (P + [0, 1, ]) model AquaticEcosystem variables: nitro, phyto, zoo, nutrient_nitro, nutrient_phyto observables: nitro, phyto, zoo process phyto_exponential_growth equations: d[phyto,t] = 0.1 phyto equations: d[phyto,t] = 0.1 phyto process zoo_logistic_growth equations: d[zoo,t] = 0.1 zoo / (1 zoo / 1.5) equations: d[zoo,t] = 0.1 zoo / (1 zoo / 1.5) process phyto_nitro_consumption equations: d[nitro,t] = 1 phyto nutrient_nitro, equations: d[nitro,t] = 1 phyto nutrient_nitro, d[phyto,t] = 1 phyto nutrient_nitro d[phyto,t] = 1 phyto nutrient_nitro process phyto_nitro_no_saturation equations: nutrient_nitro = nitro equations: nutrient_nitro = nitro process zoo_phyto_consumption equations: d[phyto,t] = 1 zoo nutrient_phyto, equations: d[phyto,t] = 1 zoo nutrient_phyto, d[zoo,t] = 1 zoo nutrient_phyto d[zoo,t] = 1 zoo nutrient_phyto process zoo_phyto_saturation equations: nutrient_phyto = phyto / (phyto + 0.5) equations: nutrient_phyto = phyto / (phyto + 0.5) Induction training data generic processes process model

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The NPPc Portion of CASA NPPc = month max (E · IPAR, 0) E = 0.56 · T1 · T2 · W E = 0.56 · T1 · T2 · W T1 = · Topt – · Topt 2 T1 = · Topt – · Topt 2 T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] W = · EET / PET W = · EET / PET PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M if Tempc > 0 PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M if Tempc > 0 PET = 0 if Tempc < 0 PET = 0 if Tempc < 0 A = · AHI 3 – · AHI · AHI A = · AHI 3 – · AHI · AHI IPAR = 0.5 · FPAR-FAS · Monthly-Solar · Sol-Conver IPAR = 0.5 · FPAR-FAS · Monthly-Solar · Sol-Conver FPAR-FAS = min [(SR-FAS – 1.08) / SR (UMD-VEG), 0.95] FPAR-FAS = min [(SR-FAS – 1.08) / SR (UMD-VEG), 0.95] SR-FAS = (Mon-FAS-NDVI ) / (Mon-FAS-NDVI – 1000) SR-FAS = (Mon-FAS-NDVI ) / (Mon-FAS-NDVI – 1000)

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Results of Revising the NPP Model Initial model: E = 0.56 · T1 · T2 · W E = 0.56 · T1 · T2 · W T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] T2 = 1.18 / [(1 + e 0.2 · (Topt – Tempc – 10) ) · (1 + e 0.3 · (Tempc – Topt – 10) )] PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M SR {3.06, 4.35, 4.35, 4.05, 5.09, 3.06, 4.05, 4.05, 4.05, 5.09, 4.05} SR {3.06, 4.35, 4.35, 4.05, 5.09, 3.06, 4.05, 4.05, 4.05, 5.09, 4.05} RMSE on training data = and r 2 = Revised model: E = · T · T · W 0.00 E = · T · T · W 0.00 T2 = 0.83 / [(1 + e 1.0 · (Topt – Tempc – 6.34) ) · (1 + e 1.0 · (Tempc – Topt – 11.52) )] T2 = 0.83 / [(1 + e 1.0 · (Topt – Tempc – 6.34) ) · (1 + e 1.0 · (Tempc – Topt – 11.52) )] PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M PET = 1.6 · (10 · Tempc / AHI) A · PET-TW-M SR {0.61, 3.99, 2.44, 10.0, 2.21, 2.13, 2.04, 0.43, 1.35, 1.85, 1.61} SR {0.61, 3.99, 2.44, 10.0, 2.21, 2.13, 2.04, 0.43, 1.35, 1.85, 1.61} Cross-validated RMSE = and r 2 = [ 15 % reduction ]

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Generic Processes for Photosynthesis Regulation generic process translationgeneric process transcription variables: P{protein}, M{mRNA} variables: M{mRNA}, R{rate} variables: P{protein}, M{mRNA} variables: M{mRNA}, R{rate} parameters: [0, 1] parameters: parameters: [0, 1] parameters: equations:d[P,t,1] = M equations:d[M,t,1] = R equations:d[P,t,1] = M equations:d[M,t,1] = R generic process regulate_onegeneric process regulate_two variables: R{rate}, S{signal} variables: R{rate}, S{signal} variables: R{rate}, S{signal} variables: R{rate}, S{signal} parameters: [ 1, 1] parameters: [ 1, 1], [0, 1] parameters: [ 1, 1] parameters: [ 1, 1], [0, 1] equations:R = S equations:R = S equations:R = S equations:R = S d[S, t,1] = 1 S generic process automatic_degradationgeneric process controlled_degradation variables: C{concentration} variables: D{concentration}, E{concentration} variables: C{concentration} variables: D{concentration}, E{concentration} conditions:C > 0 conditions:D > 0, E > 0 conditions:C > 0 conditions:D > 0, E > 0 parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] parameters: [0, 1] equations:d[C,t,1] = 1 C equations:d[D,t,1] = 1 E equations:d[C,t,1] = 1 C equations:d[D,t,1] = 1 E d[E,t,1] = 1 E generic process photosynthesis variables: L{light}, P{protein}, R{redox}, S{ROS} variables: L{light}, P{protein}, R{redox}, S{ROS} parameters: [0, 1], [0, 1] parameters: [0, 1], [0, 1] equations:d[R,t,1] = L P equations:d[R,t,1] = L P d[S,t,1] = L P

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A Process Model for Photosynthetic Regulation model photo_regulation variables: light, mRNA_protein, ROS, redox, transcription_rate observables: light, mRNA process photosynthesis; equations:d[redox,t,1] = light protein equations:d[redox,t,1] = light protein d[ROS,t,1] = light protein process protein_translationprocess mRNA_transcription equations:d[protein,t,1] = 7.54 mRNA equations:d[mRNA,t,1] = transcription_rate equations:d[protein,t,1] = 7.54 mRNA equations:d[mRNA,t,1] = transcription_rate process regulate_one_1process regulate_two_2 equations: transcription_rate = 0.99 light equations:transcription_rate = redox equations: transcription_rate = 0.99 light equations:transcription_rate = redox d[redox,t,1] = redox process automatic_degradation_1process controlled_degradation_1 conditions:protein > 0 conditions:redox > 0, ROS > 0 conditions:protein > 0 conditions:redox > 0, ROS > 0 equations:d[protein,t,1] = 1.91 protein equations:d[redox,t,1] = ROS equations:d[protein,t,1] = 1.91 protein equations:d[redox,t,1] = ROS d[ROS,t,1] = ROS

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