1. Critical Zone Science InTeGrate Teaching Team (Washburne)
Water & Energy Fluxes – Integrative Concepts: Effective Energy & Mass Transfer Eq.
Critical Zone Science
InTeGrate Teaching Team
(Washburne)

2. Effective Energy & Mass Transfer (EEMT) Model
Is there a common measure that ties the energy and water budget together? Some have tried to define this.
SOM=soil organic matter.
Figure Modified from Chorover, J., R. Kretzschmar, F. Garcia-Pichel, and D. L. Sparks.  2007.  Soil biogeochemical processes in the critical zone.  Elements 3, (artwork by R. Kindliman) see permission ref pg. 3
artwork by R. Kindliman
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3. The two components are basically the energy to heat water from cloud to surface temperatures and the energy related to photosynthesis.
Foc is ecosystem productivity, which can be measured in kg/m2/yr
Modified from Chorover, J., R. Kretzschmar, F. Garcia-Pichel, and D. L. Sparks.  2007.  Soil biogeochemical processes in the critical zone.  Elements 3, (artwork by R. Kindliman) see permission ref pg. 3
Image Source:
Figure 2. Climatic forcing of CZ evolution is quantified on the basis of effective precipitation (EPPT = FW . CW . ΔT , where FW is water mass flux, CW is water heat capacity, ΔT is Tambient K) and fixed carbon (EBIO = FOC . hBIO, where FOC is reduced C mass flux and hBIO is the Gibbs energy of biomass C).
artwork by R. Kindliman
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4. Rn  λE + H + G + ∆SH (∆Ts) + λbio
Inputs
Outputs
Recharge
artwork by R. Kindliman
Balance Equations
Rn  λE + H + G + ∆SH (∆Ts) + λbio
Ppt  ET + RO + Rchg + ∆Sm (∆SM) + bio
CO2  GPP  Re + ∆SC (∆NEP)
Energy Uses
Latent heat changes
Warming rain
Driving photosynthesis
Slide from:
Figure 1. As an open, non-equilibrium system, the CZ receives energy and matter influx that is transmitted along evolving flow paths set up by tectonic/climatic forcing and subjected to internal gradients (Rasmussen et al., 2010). Evolution of internal structure is driven by system entropy dissipation in the form of water, heat and biogeochemical products of CZ erosion and weathering (sediments, solutes, and trace gases).
Figure Modified from Chorover, J., R. Kretzschmar, F. Garcia-Pichel, and D. L. Sparks.  2007.  Soil biogeochemical processes in the critical zone.  Elements 3, (artwork by R. Kindliman) see permission ref pg. 3
Modified from:

5. Sugars and other organic molecules
The Plant Carbon Cycle
PHOTOSYNTHESIS
CO2 + H2O  O2 + Sugars
O CO2
RESPIRATION
O2 + Sugars  CO2 + H2O
CO O2
Plants
Algae
Bacteria
Most Living Organisms
Sugars and other organic molecules
H2O
H2O
redrawn from Figure 3-10 Essential Cell Biology 2/e, Garland Science, 2004
Energy of SUNLIGHT
Useful Chemical BONDS
redrawn from Figure 3-10 Essential Cell Biology 2/e, Garland Science, 2004

6. artwork by R. Kindliman
Actually, things could get more complicated, but lets just focus on EEMT for now.
Figure Modified from Chorover, J., R. Kretzschmar, F. Garcia-Pichel, and D. L. Sparks.  2007.  Soil biogeochemical processes in the critical zone.  Elements 3, (artwork by R. Kindliman) see permission ref pg. 3
Figure 1. As an open, non-equilibrium system, the CZ receives energy and matter influx that is transmitted along evolving flow paths set up by tectonic/climatic forcing and subjected to internal gradients (Rasmussen et al., 2010). Evolution of internal structure is driven by system entropy dissipation in the form of water, heat and biogeochemical products of CZ erosion and weathering (sediments, solutes, and trace gases).
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7. Example Calculation 𝐸𝑝𝑝𝑡 = ∆𝑇∗ 𝐹 𝑝𝑝𝑡 ∗ 𝑐 𝑤
Let ∆T=20 oK, Fppt=500 mm, cw= MJ/kg/oK
𝐸𝑝𝑝𝑡 = ∆𝑇∗ 𝐹 𝑝𝑝𝑡 ∗ 𝑐 𝑤
=20 𝑜 𝐾 ∗500 𝑚𝑚 𝑦𝑟 ∗ 𝑚 1000 𝑚𝑚 ∗1000 𝑘𝑔 𝑚 3 ∗ 𝑀𝐽 𝐾𝑔 − 𝑜 𝐾
=41.8 𝑀𝐽 𝑚 2 −𝑦𝑟
Let Foc=500 g/m2/yr, hbio=22 MJ/kg
𝐸𝑏𝑖𝑜 = 𝐹 𝑜𝑐 ∗ ℎ 𝑏𝑖𝑜
500 𝑔 𝑚2−𝑦𝑟 ∗ 𝑘𝑔 1000 𝑔 ∗22 𝑀𝐽 𝐾𝑔 =11 𝑀𝐽 𝑚 2 −𝑦𝑟
EEMT = 𝐸𝑝𝑝𝑡 + 𝐸𝑏𝑖𝑜 =
53 𝑀𝐽 𝑚 2 −𝑦𝑟 * 𝑦𝑟 𝑀𝑠 = 𝑊 𝑚 2

8. top row: DEM of Catalina’s and Jemez basin
bottom row: EEMT variations – notice significant elevation component.
Image source:
Figure 3. The Jemez River Basin - Santa Catalina Mountains Critical Zone Observatory (JRB-SCM CZO) comprises two research sites - JRB in north central New Mexico and SCM in southern Arizona.  Top panels show digital elevation models of SCM and Valles Caldera in JRB.  Lower panels show EEMT calculations for annual flux (MJ m-2 yr-1) at 10 m resolution for the SCM (d) and Valles Caldera of JRB. Instrumented sites are outlined.
see permission ref pg. 2
Source

9. EEMT – CJCZO site
Aspect (related to radiation exposure) is also a factor.
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see permission ref pg. 2
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