Drought & Precipitation Cycle Simulator: The Soil-Moisture Bucket

A bucket model of the water balance

The simplest useful model of a landscape's water supply treats the root zone as a single bucket of soil with a finite storage capacity. Rain fills it, plants and bare soil empty it through evapotranspiration, and once it's full any extra rain simply runs off instead of soaking in. One line of bookkeeping captures the whole thing:

dS/dt = P(t) - ET(S, t) - R(S)

S  = soil moisture storage (mm of water held in the root zone)
P  = precipitation input (stochastic, see below)
ET = actual evapotranspiration, limited by how much water S has left
R  = runoff, only nonzero once S reaches field capacity

Crude as it looks, this "bucket model" (going back to Budyko-style water balance work in the mid-20th century) reproduces the qualitative behaviour of real catchments remarkably well, because the two things that matter most for drought — a finite reservoir and a moisture-limited loss term — are both in there.

Stochastic rainfall: why real rain isn't a sine wave

Real precipitation is not a smooth seasonal curve — it's a sequence of discrete events separated by dry runs of unpredictable length. Weather generators built on this idea, following the approach Richardson formalised in 1981, use two coupled random processes: a Markov chain decides whether a given day is wet or dry (with the probability of rain depending on whether yesterday was wet or dry, which reproduces realistic clustering of storms), and on wet days a gamma or exponential distribution decides how much rain fell. The result looks like real climate records — long dry runs interrupted by clusters of storms — instead of the unrealistically regular rainfall a simple sine wave would produce.

Evapotranspiration draws the bucket down

Potential evapotranspiration (PET) — how much water the atmosphere could pull out, set by temperature, humidity and solar radiation — is usually far higher than what a drying landscape can actually deliver. Actual ET is throttled by available moisture, often modelled as scaling roughly linearly with S/S_capacity once storage drops below a threshold: a full bucket evaporates near the potential rate, a nearly empty one evaporates almost nothing, because there is simply no water left near the surface for roots and soil to give up.

How droughts emerge from short-term variance

A single dry month is weather. A drought is what happens when a run of below-average months accumulates into a storage deficit the system cannot recover from quickly — which is exactly why indices like the Standardized Precipitation Index (SPI) are computed over multi-month rolling windows rather than single observations. In the bucket model this falls out naturally: because S integrates P − ET − R over time, it has memory. A dry season doesn't reset to zero the moment the rain returns; it takes as long to refill the deficit as it took to build it, sometimes longer once vegetation stress has reduced infiltration.

Feedback loops that turn a dry spell into a heat wave

Soil moisture doesn't just record drought — it amplifies it. A wet surface spends a large share of incoming solar energy evaporating water (latent heat), which cools the surface; once the bucket runs dry that cooling pathway disappears and the same energy instead heats the air directly (sensible heat). Research on land-atmosphere coupling "hot spots" (Koster et al., 2004) identified transition zones — regions neither always wet nor always dry — where this soil-moisture-temperature feedback is strongest, and where a drought is most likely to escalate into an especially severe heat wave. It's a slow feedback loop hiding inside a fast-looking weather system.

Reading the simulation

Watch the storage trace, not just the rainfall trace: a year can look ordinary in the rain record while the storage line keeps sliding downward, because the deficit from a previous dry spell hasn't been repaid yet. Push the storm-probability parameter down and you should see runs of low soil moisture get longer and deeper, not just more frequent — that non-linear lengthening of dry runs, rather than a simple proportional drop in total rain, is the signature of a real drought cycle.

Frequently asked questions

Try it live

Everything above runs in your browser — open Drought & Precipitation Cycle Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.