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.
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.
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.
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.
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.
Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.
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.
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.
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.
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.
Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.
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.
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.
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.
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.
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.
Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.
“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.
Line up Y years of annual precipitation totals py at a station, with mean P̂. Three statistics tell the whole story. The standard deviation measures the spread 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:
And the normalized annual precipitation restates any single year in units of standard deviations above or below its own long-term mean:
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.
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 P̂m as a vector length pointing that way. Add the twelve vectors tip-to-tail:
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.
Scored, with explanations after grading. Retake as many times as you like — questions reshuffle.