Part 02 · Precipitation
WASR 4500/6500
WASR 4500/6500 · Lecture Part 02 · Interactive Companion

Precipitation

Every water balance you will ever write starts with P — and P is the moodiest term in hydrology. It forms only when air is lifted and cooled, it falls in bursts that vary wildly in space and time, and turning a handful of rain gauges into one number for a whole watershed is a craft of its own. Click a part of the storm below (or a chapter card) to explore, experiment, and test yourself.

Companion to the Part 02 lecture slides · Evaristo Critical Zone Hydrology Lab, University of Georgia. Scores are self-assessment only — nothing is recorded, and progress resets if you reload.

Learning objectives — what you should be able to do
  1. Explain the atmospheric processes involved in the formation of precipitation (our focus here is almost entirely on rainfall).
  2. Assess the factors influencing the spatial and temporal variability of rainfall.
  3. Implement various ways of estimating areal average rainfall.
  4. Quantify interannual variability by calculating and interpreting standard deviation, coefficient of variation, and normalized annual precipitation.
  5. Apply circular statistics to quantify and interpret intra-annual (seasonal) variability in rainfall patterns.
Chapter 1 · From vapor to raindrop

How Rain Forms

Rain is not water that the sky “had lying around.” Every drop has to be manufactured — condensed from vapor onto a speck of dust, grown a million-fold in volume, and made heavy enough to beat the updraft holding it aloft. This chapter builds one from scratch.

1 · The assembly line

Four stages: from saturated air to precipitation

Start with a volume of air that is saturated — holding all the water vapor it can at its temperature. Scattered through it are condensation nuclei: tiny particles of dust, smoke, or salt (aerosols, roughly 10−3 to 10 μm across) that give vapor a surface to condense on. Cool the air to its dew point and vapor condenses on the nuclei as droplets; droplets then grow by coalescence — colliding and merging — and by further condensation (freshly formed droplets act as nuclei themselves). Around 0.1 mm, drops become heavy enough to fall through the atmosphere. Step through the chamber, then run the two experiments below it.

The two gatekeepers: no nuclei, no droplets — condensation needs a surface to start on. And no fall until a drop’s weight beats the updraft: small droplets are kept aloft by air motion, which is why clouds can hang overhead all day without raining. Some falling drops never land at all — they evaporate on the way down.
2 · The elevator

Three ways to lift an air mass

Condensation needs cooling, and in the atmosphere cooling means lifting: raise an air mass and it expands and cools, and some of its moisture condenses. Nature runs three main elevators. Frontal lifting pushes warm air up and over cooler air at a front. Orographic lifting forces air up a mountain range — wet on the windward side, a dry rain shadow on the leeward side. Convective lifting draws air upward over locally heated ground — the thunderstorm machine. Pick each tab and watch the parcel rise, cool, and rain out.

Fronts come in two speeds. A cold front wedges under warm air and shoves it up abruptly — cumulonimbus, heavy, short-lived rain. A warm front slides up a long gentle ramp over cool air — widespread, lighter, day-long drizzle. Same mechanism, very different hyetographs (Chapter 2 makes that word precise).
3 · The field test

Name that storm

A hydrologist should be able to hear a weather story and name the lifting mechanism behind it. Six storms, three mechanisms — tag each one, then check yourself.

Chapter 1 quiz

Test yourself: how rain forms

Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.

Chapter 2 · When the rain falls

Rain in Time

Two storms can drop the same depth of water and be utterly different events — one a violent hour, the other a gray, soaking day. The tools that tell them apart are the hyetograph and its running total, the rainfall mass curve.

1 · Two views of one storm

Hyetographs and mass curves

A rainfall hyetograph plots rainfall depth or intensity against time — the storm’s rhythm, bar by bar. Add the bars up as you go and you get the rainfall mass curve: cumulative depth versus time. The two are one dataset wearing two outfits, and the dictionary between them is slope: the slope of the mass curve at any moment is the bar height of the hyetograph — steep means pouring, flat means dry.

Below are three real storms from April 2023 at the USCRN Watkinsville 5 SSE station — the station just down the road from campus, and the same three days plotted in lecture. Sweep your cursor across a storm and watch the two views track each other; then try the reading questions.

Same month, three personalities: April 8 was the wettest (45.0 mm) — a long, steady soaker. April 30 dumped nearly all of its 38.6 mm before 10 a.m., then quit. April 27 barely rained at all until a single ferocious burst at 4 p.m. delivered most of its 17.3 mm. One station, one month — and that is temporal variability.
2 · Your turn at the controls

Build your own storm

The fastest way to internalize the hyetograph–mass-curve dictionary is to draw one and watch the other respond. Paint hourly bars below (click or drag across the chart) and the mass curve updates live. Then try the three challenges.

3 · Storms made to order

The SCS synthetic storm hyetograph

Rainfall–runoff analysis needs the time sequence of rainfall, not just the total — but design problems (“size this culvert for the 25-year storm”) come with only a depth. The standard fix: a synthetic storm hyetograph. The USDA SCS distilled thousands of real storms into dimensionless 24-hr (and 6-hr) mass curves — Types I, IA, II, and III — that you scale by your design depth. Each type belongs to a region of the country: I and IA on the Pacific coast, III along the Gulf and Atlantic seaboard, II across the interior — including inland Georgia; coastal Georgia is Type III.

Read the curves like a hydrologist: Type IA is the gentle maritime drizzle — early, low peak. Type II is the violent interior thunderstorm — nearly half the storm’s water arrives in the two hours around hour 12. That single steep step is why Type II design storms produce the scariest runoff peaks.
Chapter 2 quiz

Test yourself: rain in time

Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.

Chapter 3 · Where the rain falls

Rain in Space

A rain gauge samples an area about the size of a dinner plate — and we routinely ask a handful of them to speak for a watershed of many square miles. This chapter is about doing that honestly: turning point measurements into an areal average rainfall.

1 · The big picture

Rain is patchy — globally, nationally, locally

At planetary scale, precipitation spans two orders of magnitude: tropical belts like the Amazon, the Congo, and Southeast Asia soak under 2,500–10,000+ mm yr−1, while the Sahara, the Gobi, and the polar deserts sit under 250. Across the U.S. the same story plays out: green, wet coasts (the Pacific Northwest catches 40–160 inches a year) against a brown interior West (parts of the desert Southwest see less than 8), with the Southeast — Georgia included — comfortably wet at 40–60. Sort the places below into wet and dry, then meet the watershed where the real work happens.

2 · One storm, three answers

The nine-gauge watershed

Here is the classic worked example from Mays: a 15.5 mi² watershed, nine rain gauges in and around it, one 24-hr storm. The recorded depths range from 0.74″ at Emmetville to a drenching 9.10″ at Wyatt — a twelve-fold difference across a few miles. What is the rainfall on this watershed? That depends on whom you ask:

The arithmetic mean simply averages the gauges — fine when gauges are uniformly spread and rainfall is tame. The Thiessen method gives each gauge a polygon of influence (every point in the watershed is assigned its nearest gauge, so polygon boundaries are the perpendicular bisectors between neighbors) and weights each depth by its polygon’s area Aj inside the watershed. The isohyetal method draws contours of equal rainfall (isohyets) from the gauge values, then weights the average depth between successive isohyets by the area between them — the most accurate of the three where data allow, and the method your X1 assignment automates.

areal average   = ΣAjPj / ΣAjone formula behind both weighted methods — only the meaning of the pieces changes

Work all three tabs — and stay sharp in the isohyetal one: the published table hides a genuine arithmetic error, and you are going to catch it.

3 · Mission briefing

X1 assignment: make your own isohyetal maps

Everything in this chapter becomes hands-on in X1: you will build precipitation (isohyetal) maps of Georgia from real daily data — the 2023 records of the four USCRN stations in the state. The briefing below walks the workflow; tick items off as you complete them.

Chapter 3 quiz

Test yourself: rain in space

Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.

Chapter 4 · Putting numbers on the mood swings

How Variable Is the Rain?

“It varies” is an observation. How much it varies — year to year, and month to month within a year — is a calculation, and it decides how big your reservoirs, your error bars, and your worries need to be.

1 · Year to year

Interannual variability: σ̂, CV, and the normalized year

Line up Y years of annual precipitation totals py at a station, with mean . Three statistics tell the whole story. The standard deviation measures the spread of the annual totals:

σ̂P = [ 1/(Y−1) · Σy=1..Y (py)² ]1/2the sample standard deviation of the annual totals

The coefficient of variation divides that spread by the mean, giving a relative variability you can compare between wet and dry places:

CV ≡ σ̂P / dimensionless — the great equalizer between climates

And the normalized annual precipitation restates any single year in units of standard deviations above or below its own long-term mean:

y ≡ (py) / σ̂P“that year was 1.8 standard deviations dry” — comparable anywhere on Earth

Click any year in the records below to normalize it, and toggle between the two stations — one humid and steady, one semi-arid and jumpy — to see why CV, not σ̂, is the fair comparison.

2 · Within the year

Intra-annual variability: the seasonality clock

Months are circular data — December sits next to January, and an average computed the ordinary way would put a station that rains in December and January at… June. Circular statistics fixes this by treating each month as a direction on a circle (its mid-month day-of-year, converted to an angle φm) and each month’s normal precipitation m as a vector length pointing that way. Add the twelve vectors tip-to-tail:

S = Σ m sin φmC = Σ m cos φmPR = (S² + C²)1/2the resultant vector: its length is the “clumpiness” of the rain calendar
ISPR / Σm    φ̅ = atan2(C, S)seasonality index (0 = evenly spread, 1 = all in one month) and average time of occurrence

Months on opposite sides of the year pull in opposite directions and cancel; months piled in one season reinforce. A long resultant arrow means strong seasonality; a stubby one means rain spread all year — in which case φ̅ still computes, but means little. Drag the monthly bars (or use the presets from lecture: winter-wet San Francisco vs. anytime-wet Boston) and watch S, C, PR, IS, and φ̅ respond. Then take the three challenges.

From lecture: San Francisco — IS = 0.662, φ̅ = 22° ≈ late January: strongly seasonal, winter-wet. Boston — IS = 0.047: rain in every month, essentially no seasonality, so its φ̅ (8°, early January) is not very meaningful. Same tools, opposite climates.
Chapter 4 quiz

Test yourself: quantifying variability

Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.