Introduction to ecosystem modelling (continued)

Transcription

1 NGEN02 Ecosystem Modelling 2015 Introduction to ecosystem modelling (continued) Uses of models in science and research System dynamics modelling The modelling process Recommended reading: Smith & Smith Environmental Modelling, Chapter 2

2 Models in science and research An idealised or simplified conceptual or formal representation of a phenomenon or item of interest, usually from the real world... the purpose is to describe, explain or study the real-world phenomenon the model represents enabling conclusions to be drawn about its properties or behaviour part of the scientific method brings existing knowledge and new observations together to build an explicit and coherent proposal to account for a real-world phenomenon a hypothesis

3 Models have the potential to: Uses of models Make predictions about the response of a system to change in its drivers Compare the results of two alternative theories Describe the effect of complex factors, such as random variation in inputs Explain how the underlying processes contribute to the result Extrapolate results to other situations Predict future events Translate knowledge and results into a form that can be easily used by non-experts In short, models are tools for prediction interpretation communication

4 System dynamics modelling Model and system are closely-related concepts. Both: strive to depict knowledge and ideas in a simple, transparent or efficient way strive to describe or explain how something works can help predict how something may change in response to a perturbation in external driving forces, i.e. to relate cause to effect or input to output many though not all models can be broken down into a number of elements with links between them, i.e. they represent a system

5 System dynamics modelling Developed in 1960 s by Jay Forrester initially to describe how interactions between actors and inputs in economic systems govern oscillations like the business cycle Describe a system in terms of stocks (elements), flows (links) and inputs or drivers Time-dependent equations govern the dependency of flows on stocks and inputs e.g. Simple population model births + population N food + offspring per adult + deaths

6 Ecosystem modelling Numerical ecosystem models are generally system dynamics models: Ecosystem compartments as stocks (state variables) e.g. C, N, P in biomass and detritus pools population density of organism groups water storage in soil, snow pack, canopy Ecosystem fluxes as flows into system (e.g. photosynthesis) out of system (e.g. respiration, evapotranspiration) between compartments (e.g. litter transfer from vegetation to soil) External drivers e.g. temperature, solar insolation, rainfall, N deposition Time-dependent equations describe processes controlling (rates of) fluxes depending on state variables and external drivers

7 A typical Ecosystem model Drivers - Temperature - Radiation - Precipitation Processes - Light interception - Photosynthesis - Respiration - Hydrology State variables - Carbon stocks - Leaf area - Soil water - Soil moisture Fluxes - Exchange of energy and matter between the system and its surrounding - Exchange of energy and matter between the stocks of the system

8 The modelling process steps to getting from question to answer type of model? verification conceptual structure? mathematical/ logical formulation Question calibration validation simulation protocol? technical implementation Answer! model experiment

9 Choosing the right model for the right task Principle of parsimony (also known as Ockham s razor): given a choice between two explanations for something, we should choose the simplest one that accounts for the facts This leads to the Golden Rule of Modelling: A model should be as simple as possible, but no simpler

10 e.g. Light interception by a forest canopy

11 Smith & Smith Section 1.4 Choosing the right model for the right task

12 Choosing the right model for the right task Less complex Static Describes an average or steady state relationship between input and output Qualitative Few possible outcomes, or just yes/no Deterministic Average result with no explicit treatment of uncertainty Descriptive Applicable within the domain of observations used to define the model = not for extrapolation Functional Describes relationship between input and output but not the underlying causes = can explain what but not why More complex Dynamic Output and maybe input change over time, accounts for lead and lag effects due to system internal feedbacks Quantitative Results on a scale, many possible outcomes Stochastic Accounts for randomness and uncertainty in input, internal dynamics and output Predictive Applicable outside the temporal and spatial domain of the observations = robust to extrapolation Mechanistic Accounts for relationship between input and output in terms of processes and feedbacks of the linking system = can explain why

13 Examples. A model to: estimate the leaf area index of a land surface pixel from satellite data static, quantitative, deterministic, descriptive, functional describe the spread of an invasive weed from point of contamination dynamic, quantitative, stochastic, descriptive, mechanistic determine based on air particle counts whether critical levels for health risks are exceeded static, qualitative, deterministic, descriptive, functional predict the net ecosystem exchange of a forest under a future climate and emissions scenario dynamic, quantitative, deterministic, predictive, mechanistic

14 Defining the conceptual structure List the available inputs and required outputs Identify the state variables $ Decide on the currency of the model the fluxes that will link the compartments of the model List the processes that (i) affect the state variables and (ii) are affected by the inputs or state variables Draw a causal loop diagram:

15 From concept to mathematical formulation Clarify the units for all inputs, state variables, fluxes and outputs A mathematical or logical expression is needed for every flux, link from an input or link to an output (every arrow in the causal loop diagram) These expressions are the processes of the model Two parts to this functional form parameters y Linear Power function Logistic function y y >0 0<p<1 <0 p>1 x x y = α + βx y = βx p y = eα+βx 1 + e α+βx x

16 From concept to mathematical formulation Functional form is known for many common ecosystem processes read the literature! If observations of x and y are available, standard curve-fitting tools and techniques can fit parameters to data Model-data fusion techniques exist for calibrating interacting processes and multiple parameters simultaneously (beyond the scope of this course)

17 Technical implementation of the model When the equations and parameters are set, the model is finished but for all but the simplest models we still need a tool to solve the model Typically, we encode the model in a programming platform such as MATLAB, Java, C++, FORTRAN Strictly speaking this is not the model but a tool to solve the model = compute the output given the input Not a model... Model... A min{ J E, J C } J E [CO2] APAR α [CO ] 2 i Γ* 2Γ i * J C V max [CO [CO ] K 2 i 2 C ] i Γ* (1 K 1 O [O 2 ]) [CO 2 ] i [CO 2 ] a 1.6A g c

18 Verification Verification = confirming that the technical implementation correctly solves the model Several tests, ranging from the purely technical to the partly scientific: does the source code compile? does the model execute to completion without crashing? Laugh test: is the output sane compared to general knowledge of the system the model represents? does the model reproduce known benchmarks (relationships between input and output known from previous work)?

19 Calibration Some though not all models can be calibrated against observational (measurement) data For a system dynamic model, calibration generally involves tuning parameters of individual equations (processes) based on emergent outputs e.g. photosynthesis (single process) based on NEE (emergent output) this raises the tricky question of which of several parameters to tune (often a subjective choice)

20 Validation A model is valid if it is suitable for addressing the hypothesis of a study Several aspects to this: sensitivity of the outputs to inputs and parameters parameter uncertainty = uncertainty in the outputs related to uncertainty as to the correct values of the model parameters structural uncertainty = uncertainty stemming from the choice of processes and interactions in the model bias and error in the output of the model when compared with observational data Validation = quantifying sensitivity, uncertainty, bias and error and judging whether the model is still useful (valid) in the light of the results

21 Sensitivity analysis of a photosynthesis model

22 Temperature change ( C) Temperature ( C) Frequency (% of model runs) Parameter-based uncertainty: Future climate change according to different parameterisations of the same GCM Temperature change ( C) Frequency (% of model runs) Stainforth et al Nature 43:

23 Modelled versus observed ecosystem fluxes RMSE = root mean square error roughly: average difference between the observed and modelled values

24 Simulation protocol and model experiment Designing a model experiment is similar to designing a field or lab experiment. Elements are: control (sometimes called the baseline in modelling) treatment = change relative to control in drivers or model assumptions (sometimes called the scenario in modelling) result = change or difference in output in scenario relative to baseline (treatment relative to control) Simulation protocol = rules for carrying out the model experiment input data time step spatial domain time slices to simulate under baseline and scenario assumptions

25 Simulation protocol and model experiment Typical protocol for a future climate experiment with a DGVM (global biosphere model)

26 Net primary production (kgc m 2 yr 1 ) Result of a model experiment Northern Sweden Scenario Southern Sweden T+P+R+C T+P+C T P R C T = change i temperature P = change in precipitation R = change in radiation C = change in CO 2 Year in climate projection

27 Keywords from this lecture system dynamics stocks & flows compartments & fluxes Golden Rule of Modelling model scope static v dynamic qualitative v quantitative deterministic v stochastic descriptive v predictive functional v mechanistic conceptual model causal loop diagram functional form, parameters technical implementation v model verification validation sensitivity, uncertainty, bias, error simulation protocol model experiment