how can one study the collapses - cnr can one study the collapses of societies “scientifically”?...
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How can one study the collapses of societies “scientifically”?
Main Question in “Collapse”
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J. Diamond’s 5 point Framework
1. Damage that people inadvertently inflict on their environment
2. Climate Change
3. Hostile Invasions
4. Decreased support by “friendly” neighbors
5. Societies responses to its problems
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Extreme deforestation- Loss of wood, soil,agriculture, wildlife,Etc…
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Anasazi – [U.S. Southwest]
Maya – [Central Americas]
Polynesian settlers – [Mangareva, Picairn, and Henderson Islands]
Vikings [Greenland]
Other collapses [first 2 points]
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Regarding the first 2 points:
Scientific knowledge may assist in forecasting changes in the Earth's biotic environment - a logical first step.
All aspects of this forecasting problem are beyond the scope of a single course.
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Water-Vegetation Interactions and Biodiversity in Changing Environments
Gaby Amilcare Ignacio
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Spatial scales resolved
Four hierarchical scales:
•Leaf
•Plant
•Canopy
•Landscape
Canopy embedded in a turbulent air stream -extracting momentum and releasing/uptaking scalars at the solid-fluid interface.
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Leaf Mass and Energy ExchangePart - I
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Photosynthesis: Basics
Of all the organisms in the natural world, green plants are the only ones that manufacture their own food.
This process is called photosynthesis and begins when light strikes the plant's leaves (both sunlight and artificial light can power this process).
Cells in the plant's leaves, called chloroplasts, contain a green pigment called chlorophyll, which interacts with sunlight to split the water in the plant into its basic components.
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Photosynthesis: Basics
Carbon dioxide enters the leaf through holes called stomata and combines with the stored energy in the chloroplasts through a chemical reaction to produce a simple sugar.
The biochemical reaction is often expressed as:
CH2O - represents the carbohydrate such as sucrose (e.g. sugar) or starch.
2 2 2 2CO H O light CH O O+ + → +
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Photosynthesis: Basics
Plants often produce more food than they need, which they store in stems, roots, seeds or fruit.
We can obtain this energy directly by eating the plant itself or its products (e.g. carrots, rice or potatoes).
Photosynthesis is the first step in the food chain, which connects all living things
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Photosynthesis: Basics
The oxygen that is released by the process of photosynthesis is an essential exchange for all living things.
Forests have been called the "lungs of the earth" because animals and humans inhale oxygen and exhale carbon dioxide in the process of breathing, and plants take in carbon dioxide and give off oxygen in the process of photosynthesis
2 2 2 2CO H O light CH O O+ + → +
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Photosynthesis: Basics
The sugar is then transported through tubes in the leaf to the roots, stems and fruits of the plants.
2 2 2 2CO H O light CH O O+ + → +
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Leaf Scale: Photosynthesis
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Photosynthesis: Basics
Some of the sugar is used immediately by the plant for energy; some is stored as starch; and some is built into a more complex substance, like plant tissue or cellulose.
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Photosynthesis & Light
The light driving this reaction is known asPhotosynthetically Active Radiation (PAR) –this is part of the solar radiation electromagnetic spectrum in the visible range (400-700 nanometers).
2 2 2 2CO H O light CH O O+ + → +
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Solar
Median Wavelengthof PAR ~ 550 nm
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Photosynthesis & Radiation
The radiation per photon is given by
median
h ceλ
=Planck’s constant
346.63 10h J s−= ×
Speed of light 10 13 10c m s−= ×
34 8 119
7
(6.63 10 ) (3 10 ) 3.6 105.5 10
J s m se Jm
− −−
−
× × ×= = ×
×
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Photosynthesis & Radiation
The energy content of a mole of photons
23 19
5
(6.023 10 ) (3.6 10 )
2.17 10
photons Jmol photon
Jmol
−× × × =
×
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Photosynthesis & Radiation
From the Electro-magnetic Spectrum, PAR contains about 50% of the short-wave.
0.46PAR SR=
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Photosynthesis & Radiation
Hence, the maximum photosynthetic photon flux density (PPFD) =
This estimate is close to the maximum observed PAR in clear sky conditions
2 1 3 2 15 2
1500 2.1 10 21002.17 10
mol molJ m s mol m sJ m s
µ− − − − −× ≈ × =×
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Photosynthesis: Biochemical Models
Gross Photosynthesis to be minimum of 3 rates:
minE
c
s
JA J
J
⎧⎪= ⎨⎪⎩
Light-limited
Rubisco-limited
Sucrose-limited
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Photosynthesis Models
( )*
*
*
2
( )
1
12
p m iE
i
m ic
oai c
o
s m
e PAR CJ
C
V CJCC KK
J V
α −Γ=
+ Γ
−Γ=
⎛ ⎞+ +⎜ ⎟
⎝ ⎠
=
G. Farquhar
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Photosynthesis – Model parameters
( )*
*2p m i
Ei
e PAR CJ
C
α −Γ=
+ ΓLeaf absorptivity for PAR ~ 0.8
Maximum quantum efficiency ~ 0.08
Compensationpoint (ppm)
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Photosynthesis – Model parameters
*( )
1
m ic
oai c
o
V CJCC KK
−Γ=
⎛ ⎞+ +⎜ ⎟
⎝ ⎠
Maximum carboxylation capacity (20-100 micromol m-2 s-1)
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Photosynthesis – Model parameters
( )*1
2
in
i
CA
C
α
α
−Γ=
+
( )n iA f C=Mathematical Form
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Photosynthesis - Model Parameters
max maxp mJ e PARα=
2 12100 mol m sµ − −:Leuning (2002)
Duke Forest
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Photosynthesis – Model parameters
Pinus taeda
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Photosynthesis – Model parameters
From Leuning (2002, PCE)
Cotton
ScotsPine
Tobacco
R. Leuning
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Tleaf=25oC
( )*1
2
in
i
CA
C
α
α
−Γ=
+
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Ci/Ca=0.66
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Ci/Ca=0.66
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Photosynthesis - Transpiration
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Stomatal Conductance
Collatz et al. (1991): Semi-empirical
2
ns
A RHg m bCO
= +
In the absence of soil moisture stress
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Duke Forest FACE-FACILITIES
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Pinus taeda
Well-wateredconditions
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Leaf Equation for CO2/H2O
( )*1
2
in
i
CA
C
α
α
−Γ=
+
2n
sA RHg m bCO
= +
( 2 )n s iA g CO C= −
Farquhar model
Collatz et al. model
Fickian diffusion
3 unknowns: An, gs, Ci
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Leaf Transpiration
[ ]s i aTranspiration c g e e′= −
( )i le f T=If leaf stomata are saturated, then
Clausius-Clapeyron
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Leaf equations: A parsimonious model for well-watered soils
*Given atmospheric state outside the leaf: CO2, PAR, ea (or RH) & Tl
*Given physiological properties of the leaf: Vcmax, m & b
Solve for: Ci, An, gs, and transpiration
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Under-story
Naumberg et al. (2001; Oecologia)
sunfleck
MODEL TESTING
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Plant Hydrodynamics
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Plant Hydraulics -
Up to this point, the photosynthesisand leaf level processes are Discussed with little regards to Plant Hydrodynamics.
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Photosynthetic Apparatus (~3.5 Billion years)
Land Plants (~350 million years; need for hydraulic apparatus)
From D. Christian (2004)
Photosynthesis and Terrestrial Plants
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Plant Hydraulics: Background
The evolution of land plants required hydraulic adjustments that permitted the display of the photosynthetic machinery within a desiccating atmosphere.
A productive display of this machinery necessitates a vertical distribution of chlorophyll so that the light-use efficiency of the organism is increased relative to a concentrated display of chlorophyll.
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Background:
This vertical distribution required certain “engineering solutions” to permit water to be supplied to leaves enclosed in an envelope that permits a controlled exchange of CO2 for water vapor.
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Spatial Scales in Water TransportLeaf-Air ExchangeThrough Stomata
Xylem WaterTransport
Ecosystem scaleBiosphere-atmosphere Water Exchange
Meso-ScaleLandscape-AtmosphereExchange
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Xylem – An Engineering Solution
Xylem has three main functions:1. Transport: They allow the passage of water from one conduit to another, but they must also prevent the spreading of air.
FromSperry
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Xylem – An Engineering Solution
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Xylem – An Engineering Solution
2. Storage
Xylem contains many living cells. These cells store large amounts of starch, which can be mobilized during leaf expansion.
Some of the cells release sugar into xylem conduits, which may play a role in embolism reversal
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Xylem – An Engineering Solution
3. Structural Support:
Xylem conduits provide structural support to the plant body.
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Data from Hubbard et al. (2001)
Relationship betweenstomatal conductance (gs) and photosynthesis (A) and plant hydraulicconductivity (KL).
KL = Soil to leaf
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J. Sperry
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From Hacke et al. (2000): Pinus taeda
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Leaf pressure
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Leaf-level Equations - Modified
2
( )ns leaf
A RHg m f bCO
ψ= +
leafψ
( )leaff ψCavitation occurs
1.0
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Plant-Hydrodynamics
leafψ
soilψrootψ
xylemψ
To connect soil Water status to leafPressure, the root-xylem system must Be resolved.
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Two-way interactions:
•Soil pressure -> leaf pressure,But leaf pressure affects transpiration And hence soil moisture/pressure.
•Atmospheric CO2 affects leafPhotosynthesis affects atmospheric CO2
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Two-way Interactions
Relative humidity affects leaf Transpiration affects relative humidity
Transpiration & air temperature affectLeaf temperature photosynthesis
Leaf conductance and transpiration
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A Problem in Biosphere-Atmosphere Exchange
•Given the state of the atmosphere above the canopy, and given the physiological, radiative, and drag properties of the canopy,
•Can we predict sources, sinks, Concentrations, and fluxes within and Above the canopy?
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PARU,C,RH,T aa
RE
dzS
Atmospheric Forcing
Soil
)z(a
INPUT FORCING VARIABLES
Gs
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cSzq
tC
+∂∂
−=∂∂
∫∫= coo StztzpC ),|,(
bs
ic
rrCCzaS
+−
= )(ρ
,....,),|,( woo Utztzp σ>−−
Time-averaged Equations
Time averaging ~ 30 minutes
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Include all three scalars: T, H2O, and CO2
3 conservation equs. for mean conc.3 equations to link S conc. (fluid mech.)3 equations for the leaf state
3 scalars 9 unknowns (flux, source, and conc.)
3 “internal” state variables (Ci, qs, Tl)1 additional unknown - stomatal resistance (gs)
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Farquhar/Collatz model for A-Ci, gs (2 eq.)
Assume leaf is saturated (Claussius-Claperon – q & Tl, 1 equ.)
Leaf energy balance – (Tl, 1 equ.)
PROBLEM IS Mathematically tractable
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Hokusai “The big wave”
The Fluid Mechanics?PART - II
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jijii dtuxbdttuxadu Ω+= ),,(),,(
Linking concentrationto source strength:
Lagrangian Fluid Mechanics
,i ija b Determined from Thomson’s (1987) model -Require first and second momentsof the turbulent velocity
,....,),|,( woo Utztzp σ>−−
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Oak-Hickory standDuke Forest
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Modeling the Fluid Flow
Navier-Stokes equations, which describe the conservation of fluid momentum, are very high dimensional.largest scale - 1 km ~ ABLsmallest scale ~ 0.1 mm ~ viscous dissipation (or Kolmogorov scale).Some sort of averaging is required
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Averaging & Canopy Turbulence
Navier-Stokes equations are averaged in space and time
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Spatial Averaging and Canopy Effects on the Airflow
The spatial averaging excludes the solid plant parts, causing the averaging volume to be a “multiply-connected” space.
The effect of the solid plant part on the air flow can be formally described via closure models, analogous to standard closure models in turbulence
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FLUME EXPERIMENTS
•To understand the connection between energetic length scales, spatial and temporal averaging, start with an idealized canopy.
•Vertical rods within a flume.
•Repeat the experiment for 5 canopy densities (sparse to dense) and 2 Re
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PLAN Open channel
Test sectionFlow direction9 m
1 m
1 m
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FLUME EXPERIMENTS
Weighted scheme
Rods positions
hwdr
Canopy sublayer
2h
2 cm
1 cm
h
+++++++++++++++
SECTIONVIEW
• PLAN• VIEW
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How Leaf Area Density Affects the Flow Statistics
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xU
Kelvin-Helmholtz Instability
Mixing Layer
U2
U1
Canopy Flow - Mixing Layer
yω
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Canonical Form of the CSL
THE FLOW FIELD IS A SUPERPOSITION OF THREE CANONICAL STRUCTURES
d
Displaced wall
Real wallREGION I
REGION II
REGION IIIBoundaryLayer
MixingLayer
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Structure of Turbulence in Model Plant Canopy
Lowest Layers in the Canopy:
Flow Visualizations
Laser Sheet
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SHOW MOVIE
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Flow Visualization
Flow visualization supports the hypothesis that the structure of turbulence in the deeper layers of the canopy is dominated by Von Karman streets periodically interrupted by sweep events from the top layers.
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The flow field is dominated by small vorticity generated by von Kàrmàn vortex streets.Strouhal Number = f d / u = 0.21 (independent of Re)
REGION I: FLOW DEEP WITHIN THE CANOPY
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Region – II: Attached Eddies /Kelvin-Helmholtz Instabilities
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REGION II: Combine Mixing Layer and Boundary Layer
LBL= Boundary Layer Length = k(z-d)LML = Mixing Layer Length = Shear Length Scalel = Total Mixing Length Estimated from an eddy-diffusivity
MLBL LLl αα +−= )1(
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inu w′ ′
outu w′ ′
2( )d dF C a z U=
a(z)
Toy Model for Momentum Transport
2( )d
du w C a z Udz′ ′
= −
1 equ. 2 unknowns
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t
t
dUu w Kdz
dUK l ldz
′ ′ = −
⎛ ⎞= ×⎜ ⎟⎜ ⎟
⎝ ⎠
Toy Model for Momentum Transport
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Toy Model for Momentum Transport
2( )t d
d dUK C a z Udz dz
⎛ ⎞− = −⎜ ⎟⎝ ⎠
2nd order nonlinear & non-homogeneous ODE
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DragCoefficient
From Poggi, Porporato,
Ridolfi, et al. (2004, BLM)
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Second-order closure models