Pools & Fluxes

The four pieces

• Pool (a stock, the rectangle) holds an amount: g C m⁻², kg N ha⁻¹, number of hares. You give it a starting value.
• Flux (the pipe with a valve) moves material into or out of a pool. Its equation gives a rate, amount per unit time. A cloud at the end of a pipe means the material comes from, or goes to, somewhere outside the model.
• Converter (the circle) holds a parameter, such as a rate constant, or a calculation built from other quantities.
• Connector (the thin red arrow) carries information, not material. An equation may use a quantity only if a connector runs from that quantity to it. A decomposition flux of k * Soil_C therefore needs two connectors: one from k and one from the pool Soil C that it drains.

Building a model

• Pick Pool and click the canvas. Pick Flux and drag from a pool to another pool, or from empty space into a pool. Pick Connector and drag from a quantity to the flux or converter that uses it.
• Click anything to edit it on the right. Drag pools and converters to move them, drag a cloud onto a pool to attach the pipe, drag a connector to bend it. Delete removes the selected item.
• In equations, spaces in names become underscores: the pool Soil C is written Soil_C. Capitals do not matter.

Equation language

+ - * / ^ and parentheses; exp ln log10 sqrt abs min max sin cos mod int round; IF a > b THEN x ELSE y with < <= > >= = <> AND OR NOT; TIME, DT, PI; STEP(height, t) switches on at time t; RAMP(slope, t) rises from time t; PULSE(amount, t, interval) moves an amount in a single step at time t, repeating every interval if one is given.

Predict, then run

Results stay hidden until you press Run, and they hide again whenever you change the model. Before each run, choose what to plot by clicking names above the graph, and write down or sketch what you expect. Tick Rerun on every edit to watch the graph change as you type or drag a slider instead.

What the computer does

Each pool's equation is d(pool)/dt = inflows − outflows; the Equations tab lists them. With Euler, each step computes every flux from the current pools, then sets pool(t + DT) = pool(t) + DT × (inflows − outflows). Because the fluxes are held fixed for the whole step while the pools change, a large DT overshoots. Runge–Kutta 4 evaluates the fluxes four times inside each step and averages them, so it is far more accurate at the same DT. A practical test: halve DT and run again. If the graph changes, DT was too large.

A non-negative pool cuts its outflows when they would drain it below zero within a step. A one-way flux never runs backwards: a negative result is treated as zero.

Saving

Your model is kept in this browser between visits. Save writes a .json file you can hand in or share; Open reads one back. Copy model puts the same text on the clipboard; pasting that text anywhere on this page (outside a text box) opens it. Copy graph copies the graph, with a legend, as a picture for a document or slide.