BIOGEOCHEMICAL CYCLES as treated in BOX MODELS
Definitions:
- Reservoir - entity defined by characteristic physical,
chemical, or biological properties that are relatively uniformly
distributed. (examples include ocean, atmosphere, biosphere, etc.); an
amount of material defined by certain physical, chemical, or biological
characteristics that, under the
particular consideration, can be considered reasonably homogeneous
(reservoir is considered well-mixed), and is available as
"stock"
- Flux - amount of a specific material entering or leaving
a reservoir per unit time (example: rain into the ocean); the amount of
material transferred from one reservoir into another per unit time
(also: flux density as being flux per reference unit, usually area)
- Source - rate of creation of a specific material within a
reservoir per unit time (example: chemical formation of ozone within
the stratosphere); can be a flux into the reservoir or creation inside
the reservoir
- Sink - rate of destruction of a specific material within
a reservoir per unit time (example: chemical destruction of ozone
within
the stratosphere)
- Cycle - system of connected reservoirs that transfer and
conserve a specific material (example: energy cycle, hydrocycle, carbon
cycle, nitrogen cycle, etc.)
- Residence time - τres = Mass in reservoir / Fluxout
= M/Fout (often referred to as lifetime, average time spent
in reservoir); average amount of time a molecule will remain in a
reservoir
- Replacement time - τrep = M/Fin ;
average amount of time it takes to replace the stock in the reservoir
- Steady State or SS- when dM2/dt = F1->2
- F1<-2 = 0; when a flux into a reservoir equals the flux
out of the reservoir, leaving its stock unchanged
- Turnover time at steady state τ = M/Fout =
M/Fin = mass/(mass/time) = time
- Change in M1 with time dM1/dt = -F1->2
+ F1<-2
- Often (not always) F is a first order process (depends linearly
on M) F = k×M, k = transfer rate constant (s-1)
then τ = M/F = M/(k×M) = l/k
- Characteristic response time - time to reduce a
disturbance from equilibrium to l/e of the initial perturbation value
- For a first order process (F=k×M ,similar to chemical
kinetics), τe = l/k. τe is the same as the
residence time, often called lifetime
- Budget - A balance sheet of all fluxes into and out of a
reservoir