Lecture 12: System Cycles

Reservoirs - Physical boundaries or holding tanks (the ocean is a reservoir)

• A reservoir is also thought of by the mass of material in it, (the ozone, the fish in the ocean)
• You must be the one that defines a reservoir when doing your study, (the pesticides in a hawk is a reservoir)

Cycles Can Be Portrayed Visually, Graphically, or Mathematically

• When we construct a portrayal of the characteristics and functioning of a cycle or any characteristics of a cycle or any other environmental process, it's called a model
• Models of natural cycles and other processes can be:
• Physical models
• Landscape drawings
• Box models
• Mathematical models

Physical Model

• Landscape drawing
• Basic water cycle drawing

Box Model

• Reservoirs are portrayed as boxes connected with arrows
• Even simpler cycle drawing
• Has units and %s along with the process on each arrow (Ocean$\rightarrow$ evaporation 86%$\rightarrow$ Atmosphere)
• Reservoirs -Boxes
• Contents - Numbers in that box
• Transfer processes - Arrows
• Fluxes - Numbers on the arrows
• Box models are the first step in developing math and computer models
• Each process is described by a math equation

The Content of a Reservoir is a Function of Both Concentration and Overall Size

Content (or burden) of a reservoir = total mass of substance in reservoir = concentration $\ast$ mass of physical unit

E.G. Content of Sodium in Sea Water

$=$ $10.78 g/kg$ ($Na$ concentration of seawater) $\ast$ $1.4 \times 10^{21} kg$ (total mass of ocean)

$=$ $15.1 \times 10^{21} kg$ (burden of Na in seawater)

Am I Going to Sample Every Fish in Lake Ontario? Once I Get a Fish, How Do I Find Mercury Content? (Put It In a Blender)

• There are not really any boundaries that exist on their own, we as researchers point out and make boundaries.

Fluxes are Flows of Matter Into and Out of Reservoirs

Flux - Amount of material transferred, described in terms of mass or volume per unit of time

• Evaporation of water from the ocean surface to atmosphere ~$~383*10^{18}g/yrH_2{O}$
• Fluxes are controlled by the rates of transfer processes and capacities of reservoirs

Source - Where the flux is coming from; a source gives out more than it takes in

Sink - Where the flux is going; a sink takes in more than it gives out

• If source - sinks $\rightarrow$ steady state

Can a Source Also Be a Sink?

• Yes the atmosphere! (it evaporates water, and rain water)
• If the source and sink are running at the same rate it will stay the same
• How long will it take to use up a reservoir is a calculation?
• When source is way more than sink, it is called "burden is increasing"?

Turn over time - The time it takes to empty or fill a reservoir.

What if a Material of Interest Enters a Reservoir?

• Multiple possibilities
• Can go from source to sink (the amount of time it goes from source to sink is called residence time)

Feedback Loops

Positive Feedback - Self reinforcing, self perpetuating "vicious" cycle

Negative Feedback - Self regulating, homeostatic