Masters of Engineering Design Project Presentation

1. Masters of Engineering Design Project Presentation Jamison Hill Dr. Lou Albright, advisor

2. Dynamic Modeling of Tree Growth and Energy Use in a Nursery Greenhouse Using MATLAB and Simulink

3. Introduction • In the forestry industry, there is a growing push towards the use of transplants for reforestation, as management becomes more intensive. • Planting transplants offer several advantages of the more traditional self-sowing approach: • Faster site establishment • Year-round availability • Larger size • Better control over form and genetics and species mix

4. Introduction cont… • To meet demand for high quality seedlings, CEA production techniques are used. • Energy costs especially lighting often the determining factor when deciding on production methods. • Simulation provides a means of predicting the costs and energy consumption statistics for different control strategies before carrying them out in the real-world.

5. Simulation Requirements • To make sense, results must be interpreted from the plant’s point of view. • For an accurate cost/benefit analysis, the model of the greenhouse must be coupled with a model of the plant.

6. Model Requirements • To be useful, model should be general: • Apply to all situations in which it would be used • Help the user gain an understanding of the process • Be complex enough to capture all the needed details and no more. • More of an art than a science

7. Examples of Good Models • Researchers have done this in the past with a variety of horticultural crops • ROSEGRO • HORTSIM • TOMGRO • Problem: most of them aren’t applicable to trees. • Same underlying process but different results

8. Special requirements for seedlings • Landis: no current models exist for greenhouse grown tree seedlings • Trees growth is modeled differently: assumed to be continuous as opposed to discrete basis • Tree Growers have a different set of objectives • Total Biomass • Height • Caliper • Root: Shoot ratio • Cold hardiness • And others (although these aren’t as easy to model)

9. + GUESS = GUESS • Thus, for my design project I created a new greenhouse-crop model: • GREENHOUSE USE OF ENERGY & SEEDLING SIMULATION • or GUESS for short.

10. Goal of GUESS: • To model the effects of greenhouse climate upon the growth of the seedlings. • To predict the costs associated with controlling climate at a particular set point • The hope is this models could help growers rationally weigh projected productions decisions in terms of their energy cost and their benefit to the plant.

11. Other Goals • Create a general purpose mechanistic model adaptable for a variety of tree species. • Create a model that is easy for an end user to understand and modify

12. Goal of GUESS Project • Personal goals • To understand the relative importance of the different processes occur and how to explain them in a mechanistic manner • To learn about how mathematics can be used as a tool to model the natural world.

13. What does GUESS do? • GUESS predicts the following: • The indoor climate characteristics or state (light, temperature, humidity, CO2) • The effect of state upon tree yield and development • The ability of the control system to maintain the indoor climate or state within a prescribed tolerance about pre-defined setpoints • The costs associated with control

14.   What does GUESS do • More specifically: • Given a raw weather data file, and a series of parameters • GUESS calculates and then produces graphs of costs, and environmental conditions (temp., CO2, rel H%, light), and growth rate (biomass, height, and diameter). • Show example

15. How does GUESS work • A two part answer • The mathematical models • The organization of the GUESS software • How the equations are expressed in computer code • First lets describe GUESS

16. Technically speaking • GUESS is a dynamic lumped-parameter simulation coupling a heat/mass transfer model of the greenhouse climate and control processes with a process based model of tree seedlings.

17. Why Lumped? • The equations for heat and mass transfer are 2nd order PDE’s. Lumping(ignoring spatial variation) equations to 1st order ODE’s with respect to time. Simple mass/energy balances that can be solved with standard numerical methods. Good enough when gradients are small and average values are most important.

18. Dynamic Model • In a dynamic model of greenhouse climate: • State variables represents the current conditions within the greenhouse. • At each time step: current outdoor conditions, external/internal fluxes and the previous state are used to calculate state derivatives. • Previous state derivatives are integrated to yield current state. • We are provided with a record of the states and the rates of change

19. Why Dynamic? • In the past, most energy modeling was done using the stepwise steady state method: • We would neglect storage, and calculate the steady state value for temp, etc.. (dT/dt = 0) • Relatively easy when time steps are large • Problems: • Can’t be used with small time steps or to predict instantaneous values. • Won’t tell you how we get from one state to another? • Most steady models were formulated years ago when computers were slow. Now that processors have improved, why not build better models?

20.   GUESS Structure • GUESS is composed of three parts • Weather data preprocessor • Interpolates needed weather: rel H, temp, wind, and solar • Calculates derived values humidity ratio, wind pressure • Core Simulink model • Output Graph routine

21. Core GUESS Model • In the core GUESS model we have: • 3 lumped parameter balances for indoor conditions • Temperature • Humidity • CO2 • 1 lumped parameter balance for the plant • Carbon (biomass) • And a cost calculator • Represented using block diagrams

22. Greenhouse Energy Balance • An object’s temperature is equal to the amount of heat stored in a object divided by its heat capacity (ρCPV). • In the simplest models we consider everything inside the greenhouse to be at the same temperature: air temperature, and to figure this one out, we perform an energy balance: • Change in Energy Stored = Gain from internal sources + gain from solar – losses due to conduction through the cover – losses due to longwave radiation – latent losses (evaporation) – losses due to air exchange

23. Cover Conductance • Sum of conductances to/ from cover • Includes longwave & convection • Strong functions of indoor & outdoor temperatures, cloud cover, and wind speed • But can be treated as a constant over standard operating conditions since they partially cancel

24. Humidity in the Greenhouse • Humidity is measured 3 ways • Vapor pressure • Partial pressure of H2O in the air • Used to calculate potential driven flows • Relative humidity • Measure of potential to do work or humidity difference • VP/VPsat • Humidity ratio or absolute humidity • Kg H2O/kg air • Used in air mixing problems

25. Vapor Pressure • VPD = driving force for most transfers • Difference between saturated and current air • 2 basic kinds of transfers • Evaporation • Condensation • VPsat: exponential func. of T • Condensation • Occurs when T ≤ Tdewpoint • Dewpoint: temp. at which VPsat = VP (current) • Evaporation requires energy • Wet bulb: min. temp. one can cool to by evaporation

26. Humidity Balance • We need 3 types of units • Humidity Ratio • Vapor Pressure Deficit: VPsat-VP • Rel H • Rate of Change of absolute humidity = Ventilation + Infiltration * (Humidity Difference with Outside) + Fogging + Cooling Pads + ET - Condensation

27. Condensation, Foggers, and Pads • All are driven by VPD • Because of cooling, foggers take VPsat at wet bulb • Pads operate by changing Tout and Hout usually within 80% of wet bulb

28. Evapotranspiration • Modeled by Penman-Monteith EQ • Sum of two terms • One driven by humidity gradient • One driven by radiation But since air resistance is so great in the greenhouse, we ignore the gradient term

29. Plant Carbon Balance • View growth as mass balance • Measured in dry units (g dry weight) • Change in dry weight = Conversion Factor * (Net Photosynthesis – Respiration) • Conversion factor: go from moles CO2 to g dry weight

30. Is catalyzed by Rubisco Farquhar et. al recognized: Rate governed by the limiting substrate: RuBP CO2(inside the leaf) Rate of RuBP production determined largely light reaction Can be modeled as minimum of two saturation curves Classical Michaelis-Menten: CO2 Light reaction curve Take in account photorespiration and dark respiration Photosynthesis

31. Respiration • 2 forms • Maintenance: • CO2 released during maintenance of existing biomass • Temperature dependent • Includes dark respiration • Growth: • Temperature independent • CO2 released during the synthesis of new tissue • Usually constant * (Photo-Maintenance respiration) • Constant about 0.25

32. Allometry • How do we go from biomass to height and diameter, which are more interesting? • By using a series of simple power laws, see right panel

33. Structure of Model:Block Diagram Notation • The core model in GUESS was written in Simulink using block diagram notation: • Graphical programming language used by Simulink. • Allows modeler to focus primarily on equations, and ignore interface construction and numerical methods • Each block is viewed as a little black box where data is fed in at the output, and results leave at output • The type of model used by Simulink to characterize the block is the state-space or machine model, in a minute, we’ll see why its so useful

34. Structure of Model:The State Machine • In Simulink, each block is viewed as a state machine, a black box whose output depends only upon its current conditions aka state variables • Parameters: • Input (what we give the block) • Output (what we want from the block) • State (current conditions within the block) • Another property of the state machine is that the rate of change of the state depends only two things: the inputs and the previous states. • Because of this we can use these state machines as mass balances, thus making Simulink a good choice for models where dynamics are more important than the spatial distribution.

35. Demonstration • Now that I discussed how GUESS works • Lets see what it can do

36. Model Verification Strategy • Due to budget, time, etc…, an actual validation with a real greenhouse and was infeasible • So, next best thing • Phone interviews with various growers • See if my results at least qualitatively support common growing practices.

37. Model Simulation • A test case was set up to validate the model. • We experimented with different lighting targets to see which one offered the most growth per unit energy cost • The model was parameterized for Douglas fir production in Corvallis, OR • Seedlings were started at 0.57g d.w and were harvested at 1.7 g dw • Temperature regulated to 68.5±6.3°F

38. Simulation Results • Given the targets and parameters we initially used: • 3 growing seasons could be had only if supplemental lighting is used. 100 molar required! • But Weyerhaeuser achieves 3 seasons/yr with only 10 molar photoperiodic lights!

39. Comparison: New conversion Factor

40. Comparison: Old Conversion Factors

41. Simulation Results • Light levels required: • 75 micromolar (with CO2 enrichment) • 100 micromolar without • Values higher than recc’d • Found to be highly dependent on W/m2 solar to mol/m2 PAR • Initial conversion factor of 2.2 changed to 2.34 to reflect data from Langhans, now no supplemental lighting is required! • Problem: conversion factors are for 350-700 nm band only not for entire solar or artificial spectrum. PAR:NIR split approx 50:50 but can vary greatly

42. Results Continued • Growth rate highly sensitive to sunlight/PAR conversion factor. • A need for better data for unit conversion. • Growth rate could be highly sensitive to carbon content conversion as well.

43. Room for future improvements • Obtain better conversion factor data • Separate model for shoot and root temperature. • In full sunlight, leaves and soil surface approx 2-5K warmer than surrounding air. Include dynamic storage effects of soil and cover on air temperature.

44. Wrapping It Up • Models can be very useful as simulation tools, but their utility depends highly upon the data used to parameterize them. • A mechanistically correct model may produce meaningless results when given inappropriate data and asked inappropriate questions.

45. THE END