Hydrologists track every drop that enters, leaves or is stored in a catchment. The water budget turns the water cycle into numbers.
⚖️ The water balance
For a catchment over a period: precipitation (P) = evapotranspiration (ET) + runoff (R) + change in storage (ΔS). Evapotranspiration is evaporation plus water released by plants. Over many years, ΔS is near zero, so R = P − ET. Rainfall depth in mm over an area in km² converts to volume: 1 mm over 1 km² is 1000 m³.
P = 800 mm, ET = 500 mm, ΔS = 0
R = 800 − 500 = 300 mm
catchment 50 km²: 300 mm · 50 · 1000 m³ = 15 000 000 m³ per year
runoff ratio = R/P = 300/800 = 0.375
🖼️ See it
Only about 2.5% of Earth’s water is fresh, and most of that is frozen or underground.
🌊 Rivers and floods
Discharge Q = A × v (cross-sectional area × mean velocity), in m³/s. A hydrograph plots discharge against time. After a storm, the peak discharge arrives after a lag time. Urban surfaces, steep slopes and saturated soil shorten the lag and raise the peak, increasing flood risk. Infiltration falls when soil is wet or paved.
channel 20 m wide, 2 m deep: A = 40 m²
v = 1.5 m/s
Q = 40 · 1.5 = 60 m³/s
volume in 1 hour = 60 · 3600 = 216 000 m³
Urbanisation makes “flashy” rivers: the same rain gives a higher, earlier peak.
✏️ Quick check · 1 of 7
Water balance
In the long term, runoff in a catchment equals:
P − ET.
✏️ Quick check · 2 of 7
Lag time
The lag time on a hydrograph is the delay between:
Rain → river peak.
✏️ Quick check · 3 of 7
Urban flooding
Urban areas increase flood peaks mainly because:
Impermeable.
✏️ Quick check · 4 of 7
Evapotranspiration
Evapotranspiration includes:
Two parts.
✍️ Type your answer · 5 of 7
A catchment gets 800 mm of precipitation and loses 500 mm to evapotranspiration. Storage does not change.
What is the runoff, in mm?
Enter an exact answer, without rounding.
mm
P − ET.
✍️ Type your answer · 6 of 7
A river channel is 20 m wide and 2 m deep (rectangular). The mean speed is 1.5 m/s.
What is the discharge, in m³/s?
Enter an exact answer, without rounding.
m³/s
Q = A · v.
✍️ Type your answer · 7 of 7
A river carries 60 m³/s.
How many cubic metres flow past in 1 hour (3600 s)?
Enter an exact answer, without rounding.
m³
Multiply.
📝 Lesson quiz · 5 questions
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Question 1 of 5
A hydrograph shows:
Question 2 of 5
Saturated soil during rain leads to:
Question 3 of 5
The runoff ratio is:
Question 4 of 5
Which land cover reduces flood peaks?
Question 5 of 5
Discharge is measured in:
Lesson 2 · Meteorology
🌬️ Atmospheric Circulation & Weather Systems
Uneven heating of the Earth drives a global pattern of winds. Weather systems form within this circulation.
🌐 Global circulation
The equator is heated most, so air rises there, spreads toward the poles, cools and sinks near 30° latitude, forming a Hadley cell. Further cells: the Ferrel cell (30°–60°) and the polar cell. The surface winds are the trade winds (easterly, 0°–30°), the westerlies (30°–60°) and the polar easterlies. The Coriolis effect from Earth’s rotation turns moving air to the right in the Northern Hemisphere and to the left in the Southern.
rising air at the equator → low pressure → rain (ITCZ)
sinking air near 30° → high pressure → deserts (Sahara)
cells per hemisphere: 3 (Hadley, Ferrel, polar)
total = 3 · 2 = 6
🖼️ See it
Air rises at low pressure near 0° and 60° and sinks at high pressure near 30° and the poles. The spinning Earth bends surface winds, giving the prevailing winds.
🌪️ Cyclones and pressure
Air spirals counter-clockwise into a low in the Northern Hemisphere (clockwise in the south), rising and forming cloud and rain. A high spirals out clockwise (north) with sinking, dry air. Closer isobars mean stronger winds. In the hydrostatic atmosphere, pressure falls about 1 hPa for every 8 m near sea level.
sea level 1013 hPa; at 800 m up, drop ≈ 800/8 = 100 hPa
pressure ≈ 1013 − 100 = 913 hPa
isobars 2 hPa/100 km vs 4 hPa/100 km → second has stronger wind
Deserts cluster near 30° N and S because dry air sinks there. The Sahara and Australian deserts follow this pattern.
✏️ Quick check · 1 of 7
Hadley cell
In a Hadley cell, air rises at the:
Hottest region.
✏️ Quick check · 2 of 7
Coriolis
In the Northern Hemisphere the Coriolis effect turns moving air to the:
Right.
✏️ Quick check · 3 of 7
Deserts
Deserts are common near 30° latitude because:
High pressure.
✏️ Quick check · 4 of 7
Low pressure
In the Northern Hemisphere, winds around a low blow:
Spiral in.
✍️ Type your answer · 5 of 7
Pressure falls about 1 hPa for each 8 m climbed. Sea-level pressure is 1013 hPa.
What is the drop in hPa at 800 m?
Enter an exact answer, without rounding.
hPa
Divide by 8.
✍️ Type your answer · 6 of 7
Sea-level pressure is 1013 hPa, and at 800 m it drops by 100 hPa.
What is the pressure at 800 m, in hPa?
Enter an exact answer, without rounding.
hPa
Subtract.
✍️ Type your answer · 7 of 7
There are three circulation cells (Hadley, Ferrel, polar) in each hemisphere.
How many are there in total?
Enter an exact answer, without rounding.
Multiply.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The trade winds blow toward the:
Question 2 of 5
The ITCZ is a belt of:
Question 3 of 5
A high pressure system brings:
Question 4 of 5
Westerlies dominate between:
Question 5 of 5
Closely spaced isobars mean:
Lesson 3 · Oceanography
🐋 Ocean Circulation & Climate
The ocean stores and moves enormous amounts of heat. Its currents shape climate and its changes can shift weather around the world.
🔥 Heat and density
Water has a very high specific heat capacity (4200 J per kg per °C), so oceans heat and cool slowly. Seawater density rises as it gets colder and saltier. Cold, salty water sinks near the poles and drives thermohaline circulation, the global “conveyor belt” that takes about 1000 years to complete a loop. Surface gyres are driven by wind and the Coriolis effect.
Q = m · c · ΔT
1 kg water warmed by 2 °C: 1 · 4200 · 2 = 8400 J
air c ≈ 1000, water c = 4200: water stores 4.2 times more per kg per °C
🖼️ See it
Thermohaline circulation moves heat around the planet. Freshwater from melting ice could weaken it.
🌎 Upwelling and El Niño
Upwelling brings cold, nutrient-rich water to the surface, supporting rich fisheries (Peru). In an El Niño, trade winds weaken, warm water spreads east across the Pacific and upwelling fades, shifting rain and causing drought or flood in many regions. La Niña is the opposite phase. The cycle repeats every 2–7 years (ENSO).
normal: trade winds push warm water WEST
El Niño: winds weaken → warm water moves EAST → upwelling weakens
event every 4 years → in 20 years: 20/4 = 5 events
The oceans have absorbed over 90% of the extra heat trapped by greenhouse gases, which slows surface warming but raises sea level.
✏️ Quick check · 1 of 7
Density
Sea water is densest when it is:
Cold and salty.
✏️ Quick check · 2 of 7
Upwelling
Upwelling brings:
Rising.
✏️ Quick check · 3 of 7
El Niño
During El Niño the trade winds:
Weaker.
✏️ Quick check · 4 of 7
Heat store
Oceans moderate climate because water has:
Slow to change.
✍️ Type your answer · 5 of 7
Water has c = 4200 J/(kg·°C).
How many joules to warm 1 kg of water by 2 °C?
Enter an exact answer, without rounding.
J
Q = m · c · ΔT.
✍️ Type your answer · 6 of 7
A 5 kg sample of water is warmed by 10 °C (c = 4200).
How many joules?
Enter an exact answer, without rounding.
J
Q = m · c · ΔT.
✍️ Type your answer · 7 of 7
El Niño occurs about once every 4 years.
How many events in 20 years?
Enter an exact answer, without rounding.
Divide.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The thermohaline circulation is driven by differences in:
Question 2 of 5
La Niña is characterised by:
Question 3 of 5
Which current warms northwest Europe?
Question 4 of 5
Ocean gyres are driven mainly by:
Question 5 of 5
Which holds more heat per kg for each °C?
Lesson 4 · Geophysics
📉 Seismology & Earth’s Interior
Earthquake waves are like X-rays of the planet. How they speed up, slow down, bend and stop reveals what lies beneath our feet.
🌊 Seismic waves
P-waves are compressional and travel through solids and liquids. S-waves are shear waves and cannot pass through liquids. Surface waves travel along the ground and do the most damage. Waves bend (refract) where the speed changes and reflect at boundaries. The Mohorovičić discontinuity (Moho) separates crust and mantle; S-waves vanish at the outer core, showing that it is liquid, and the shadow zone maps the core’s size.
time lag between S and P: Δt
d = Δt / (1/vS − 1/vP)
vP = 6 km/s, vS = 3 km/s: 1/3 − 1/6 = 1/6
Δt = 40 s → d = 40 · 6 = 240 km
🖼️ See it
S waves cannot travel through liquid, which is how seismologists proved the outer core is molten.
📐 Locating earthquakes and magnitude
Three seismograph stations each give a distance circle from the S–P lag; the circles intersect at the epicentre (triangulation). Magnitude measures energy released; each step of 1 on the moment-magnitude scale is about 32 times more energy and 10 times more ground motion.
magnitude 6 → 8: 2 steps
energy ratio = 32 · 32 = 1024
ground motion ratio = 10 · 10 = 100
3 stations needed to fix a position on a map
The Earth rings like a bell after a great earthquake. Its oscillations were recorded for weeks after the 2004 Sumatra event.
✏️ Quick check · 1 of 7
Liquid core
S-waves are not detected on the far side of Earth because they:
Not liquids.
✏️ Quick check · 2 of 7
Moho
The Moho is the boundary between the:
Top of the mantle.
✏️ Quick check · 3 of 7
Triangulation
How many stations are needed to locate an epicentre?
Three circles.
✏️ Quick check · 4 of 7
Surface waves
Which waves usually cause the most damage?
On the ground.
✍️ Type your answer · 5 of 7
A seismograph records an S–P lag of 40 s. vP = 6 km/s and vS = 3 km/s, so d = Δt · 6.
What is the distance, in km?
Enter an exact answer, without rounding.
km
Multiply.
✍️ Type your answer · 6 of 7
Each magnitude step is about 10 times the ground motion. An event is 2 magnitude units larger.
How many times greater is the ground motion?
Enter an exact answer, without rounding.
Multiply by 10 twice.
✍️ Type your answer · 7 of 7
Each magnitude step is about 32 times the energy. A magnitude 7 event versus magnitude 6.
How many times more energy?
Enter an exact answer, without rounding.
Single step.
📝 Lesson quiz · 5 questions
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Question 1 of 5
P-waves are described as:
Question 2 of 5
The shadow zone shows that Earth has a:
Question 3 of 5
Which is fastest?
Question 4 of 5
The epicentre is found by:
Question 5 of 5
Magnitude measures:
Lesson 5 · Materials
🔬 Mineralogy & Petrology
Minerals are classified by their chemistry and structure. Rocks are classified by how they formed, and their textures tell their histories.
🧊 Mineral groups and structure
Most rock-forming minerals are silicates, built from silica tetrahedra: one silicon atom bonded to four oxygen atoms (SiO₄). The way tetrahedra link (isolated, chains, sheets, frameworks) controls properties: olivine (isolated), pyroxene and amphibole (chains), mica (sheets, splits easily) and quartz and feldspar (frameworks). Non-silicates include carbonates (calcite CaCO₃), oxides (haematite Fe₂O₃) and sulphides (pyrite FeS₂).
SiO₄: 1 Si + 4 O = 5 atoms
calcite CaCO₃: M = 40 + 12 + 3·16 = 100 g/mol
Ca fraction = 40/100 = 40%
quartz SiO₂: M = 28 + 32 = 60 g/mol; Si = 28/60 = 46.7%
🖼️ See it
Slow cooling gives crystals time to grow. Rocks are named from their mineral content and their texture.
🌋 Igneous textures and Bowen’s series
Magma composition ranges from mafic (low silica, rich in Fe and Mg, dark, such as basalt and gabbro) to felsic (high silica, light, such as rhyolite and granite). Slow cooling gives coarse (phaneritic) texture; fast cooling gives fine (aphanitic) texture; very fast cooling gives glass (obsidian). Minerals crystallise in a set order, Bowen’s reaction series: olivine crystallises at the highest temperature, quartz at the lowest.
mafic: ~50% SiO₂ (basalt, gabbro)
intermediate: ~60% (andesite, diorite)
felsic: ~70% (rhyolite, granite)
basalt and gabbro have the same composition; gabbro cools slowly underground (coarse)
Pairs to remember: extrusive/intrusive twins: basalt/gabbro, andesite/diorite, rhyolite/granite.
✏️ Quick check · 1 of 7
Silicates
The basic building block of silicate minerals is the:
Four oxygens.
✏️ Quick check · 2 of 7
Granite
Granite is an:
Coarse and light.
✏️ Quick check · 3 of 7
Obsidian
Obsidian is a volcanic glass because it:
Fast.
✏️ Quick check · 4 of 7
Bowen
Which mineral crystallises first from cooling mafic magma?
High temperature.
✍️ Type your answer · 5 of 7
Quartz is SiO₂ (Si = 28, O = 16).
What is its molar mass, in g/mol?
Enter an exact answer, without rounding.
g/mol
Add atomic masses.
✍️ Type your answer · 6 of 7
Calcite is CaCO₃ (Ca = 40, C = 12, O = 16).
What is its molar mass, in g/mol?
Enter an exact answer, without rounding.
g/mol
Add atomic masses.
✍️ Type your answer · 7 of 7
Of the 100 g/mol of calcite, 40 g/mol is calcium.
What percent of calcite is calcium?
Enter an exact answer, without rounding.
%
Divide, ×100.
📝 Lesson quiz · 5 questions
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Question 1 of 5
Mica splits into thin sheets because its tetrahedra are arranged in:
Question 2 of 5
Basalt has a fine texture because it:
Question 3 of 5
Felsic rocks are generally:
Question 4 of 5
Which is a carbonate mineral?
Question 5 of 5
Gabbro is the intrusive equivalent of:
Lesson 6 · Structural geology
🧭 Geologic Maps & Structures
Rocks bend, break and tilt under stress. Geologists read maps and cross-sections to reconstruct those events.
🔧 Stress, folds and faults
Three kinds of stress: compression (squeezing), tension (stretching) and shear. Rock folds when it is hot and slow-stressed: an anticline is arch-shaped (oldest rock in the middle) and a syncline is trough-shaped (youngest rock in the middle). Rock fractures when it is cold and fast-stressed. A normal fault forms under tension (hanging wall moves down); a reverse fault forms under compression (hanging wall moves up); a strike-slip fault forms under shear.
tension → normal fault (crust gets longer)
compression → reverse fault (crust gets shorter)
shear → strike-slip fault (San Andreas)
anticline: oldest in the core syncline: youngest in the core
🖼️ See it
On a geological map the pattern of outcrops shows which structure lies beneath, and the dip direction tells you which is which.
📐 Strike, dip and cross-sections
The strike of a bed is the compass direction of a horizontal line on its surface; the dip is its angle of tilt below horizontal (0°–90°), measured at right angles to the strike. A geologic map uses colours for rock units and symbols for faults and dips. A cross-section shows what the layers look like in a vertical slice. An unconformity is a gap in the rock record where erosion removed layers.
bed dips 30° → thickness vertical ≈ true thickness / cos 30°
vertical depth of a bed dipping at 45° that outcrops 100 m horizontally away:
depth = 100 · tan 45° = 100 m
at 30°: depth = 100 · tan 30° ≈ 58 m
A fault cuts across layers, so it is younger than the layers it displaces. An unconformity shows time missing from the record.
✏️ Quick check · 1 of 7
Normal fault
A normal fault forms under:
Pulling apart.
✏️ Quick check · 2 of 7
Anticline
In an anticline, the oldest rocks are:
Arch shape.
✏️ Quick check · 3 of 7
Dip
The dip of a bed is its:
Slope.
✏️ Quick check · 4 of 7
Unconformity
An unconformity represents:
Missing time.
✍️ Type your answer · 5 of 7
A bed dips at 45° and outcrops 100 m horizontally from a well. depth = 100 · tan 45°.
What is the depth to the bed at the well, in m?
Enter an exact answer, without rounding.
m
tan 45° = 1.
✍️ Type your answer · 6 of 7
A bed dips at 30° and the horizontal distance is 100 m. depth = 100 · tan 30°, with tan 30° = 0.5774.
What is the depth, in m, rounded to one decimal place?
Round your answer as the question asks.
m
Multiply.
✍️ Type your answer · 7 of 7
A fault displaces a bed by 25 m vertically on one side and the bed is 5 m thick.
How many bed-thicknesses is the displacement?
Enter an exact answer, without rounding.
Divide.
📝 Lesson quiz · 5 questions
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Question 1 of 5
Compression produces a:
Question 2 of 5
A syncline is a fold that is:
Question 3 of 5
The San Andreas Fault is a:
Question 4 of 5
Which is younger?
Question 5 of 5
A geologic map shows:
Final Challenge
🏆 12-Question Challenge Quiz
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
0 / 12
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · Hydrology & the Water Budget
Over many years, the change in storage in a catchment is about:
Q2 · Hydrology & the Water Budget
Discharge is measured in:
Q3 · Atmospheric Circulation & Weather Systems
The Coriolis effect is caused by:
Q4 · Atmospheric Circulation & Weather Systems
Closely spaced isobars mean:
Q5 · Ocean Circulation & Climate
The “conveyor belt” of the ocean is driven mainly by:
Q6 · Ocean Circulation & Climate
Which holds more heat per kg for each °C?
Q7 · Seismology & Earth’s Interior
A typical earthquake focus shallower than 70 km is most likely at:
Q8 · Seismology & Earth’s Interior
Magnitude measures:
Q9 · Mineralogy & Petrology
Most of the Earth’s crust is made of:
Q10 · Mineralogy & Petrology
Gabbro is the intrusive equivalent of:
Q11 · Geologic Maps & Structures
Rocks tend to fracture rather than fold when they are: