Masters of Engineering Design Project Presentation

Jamison HillDr. Lou Albright, advisor

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

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

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.

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.

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

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

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)

GUESS Thus, for my design project I created a

new greenhouse-crop model: GREENHOUSE USE OF ENERGY GREENHOUSE USE OF ENERGY

& SEEDLING SIMULATION& SEEDLING SIMULATION or GUESS for short.

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.

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

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.

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

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

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

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.

0d A

CVdt r

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.

2

2C k

t x

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

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?

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

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

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

:

:

:

:

1

inP in out r cover cover cover in cover

SHORTWAVECONDUCTION LONGWAVE COVER

r sky cover in sky P in outEVAPOTRANSPIRATION

VENTILALONGWAVE SKY

d TC V UA T T I h F T T

d t

h T T E HEAT nV C T T

TION INFILTRATION

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

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

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

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 ,

EVAPOTRAN-VENTILATION+INFILTRATION SPIRATION

inin out foggers in sat wetbulb conden sat

sation

dHnV H H k VP VP k VP VP E

dt

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

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

* *

{ }P sat air airnet

a

C VP T VPs RE

s r

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

Photosynthesis 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

2 2RUBISCOCO RuBP PGA

2min 0.5CO

net O dlight

WA V R

W

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

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

1.51

22

24

M K A

M K D H

A D

D

H

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

STATE

x

INPUT y OUTPUT

z

1,t tState f Input State

OUTPUT f State

In Out

Simulink Blockor

Subsystem

In Out

Simulink Blockor

Subsystem

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.

STATE

x

INPUT y OUTPUT

z

1, t

dStatef Input State

dt

OUTPUT f State

In Out

Simulink Blockor

Subsystem

In Out

Simulink Blockor

Subsystem

Demonstration

Now that I discussed how GUESS works

Lets see what it can do

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.

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

Parameter Value

Unit

U-Value 6.2 Wm-2-K-1

Infiltration 1.1 A.C. hr-1

Floor Area 581 m2

Enclosed Volume

3711 m3

Cover Area 790 m2Lighting Parameters  

Intensity Set pointBand-width

CO2 enrichment

No Lights  --  -- Yes

25 50 15 Yes

75 88 40 Yes

75 88 40 No

100 100 55 No

250 250 130 Yes

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!

Comparison: New conversion Factor

Tree GrowthNo supplemental lighting or CO2

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 50 100 150 200 250 300 350

Day

Am

ou

nt

Biomass(g) Height(cm) Diam.(mm)

Comparison: Old Conversion Factors

Tree GrowthNo CO2, No Lights

Old Conversion Factor

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 50 100 150 200 250 300 350Day

Am

ou

nt

Biomass(g) Height(cm) Diam.(mm)

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

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.

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.

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.

THE END