By the end of this lecture, you should be able to:

• Describe the structure and properties of water relevant to hydrology
• Understand the concept and components of the hydrological cycle
• Explain the global distribution of water and its limited availability
• Distinguish a store from a flux, and estimate a residence time
• Define the water balance equation and interpret each term
• Be able to recognise a surface catchment
• Identify challenges in applying hydrological concepts at different scales

• Hydrology comes from Greek hydor (water) and Latin logia (study).
• Despite the name, it focuses on fresh water, not all water.
• Oceanography is the science of saline water.
• Hydrology examines:
  • Distribution and movement of water
  • Interactions with land, atmosphere, and ecosystems

One of the oldest recognisable descriptions of the water cycle (paraphrased from De architectura, Book VIII):

Precipitation falling in the mountains infiltrates the Earth’s surface and feeds the streams and springs of the lowlands.

after Vitruvius, Roman architect, 1st century BC

“The total quantity of fresh water on earth could satisfy all the needs of the human population if it were evenly distributed and accessible.” — Stumm (1986: 201)

• Hydrology explains uneven water distribution
• Serves as:
  • A pure science – explaining why the disparities exist
  • An applied science – acting to lessen their impact
• But hydrology is more than supplying water to people:
  • floods as natural hazards
  • lakes and rivers as ecological habitat

• Two main traditions:
  • Engineering hydrology – design-focused, quantitative
  • Earth science hydrology – process-focused, explanatory, rooted in geomorphology
• This course adopts a quantitative Earth science perspective
• Related fields:
  • Geohydrology – groundwater systems
  • Ecohydrology – water–ecosystem interactions

ETH-Zurich

• Covers more than 70% of Earth’s surface
• Essential to:
  • Human survival
  • Agricultural production
  • Ecological functioning
• For Indigenous Australians, water is integral to Country, ceremony, and responsibility

Physical properties of water

• Water: H_2O two hydrogen atoms covalently bonded to oxygen

• It is a bipolar molecule:

  • Positive hydrogen, negative oxygen

• Bonds:

  • Covalent within molecules
  • Hydrogen between molecules

• Leads to:
  • High surface tension
  • Strong cohesion
  • Exceptional solvent capability

Density

• Water is most dense at 3.98°C
• Ice is less dense → floats on water
• Implications: - Lakes freeze from top-down - Standing water thermally stratifies, with 4°C water sinking to the bottom - Aquatic ecosystems persist in cold conditions

Specific Heat

• Water has high specific heat capacity (4.2 kJ/kg/K)
• It takes 4,200 J to warm 1 kg (\approx 1 litre) of water by 1 K
• Slows temperature change
• Buffers climate and daily temperature swings, which is why maritime climates have cooler summers and milder winters than continental ones
• Comparison with other materials:

• The high energy required to break hydrogen bonds makes water an ideal climate stabiliser.
• Water changes state:
  • Solid ↔ Liquid ↔ Gas
• Processes include:
  • Melting, freezing
  • Evaporation, condensation
  • Sublimation, desublimation (deposition)
• Involves latent heat: energy absorbed on evaporation is carried with the vapour and released as sensible heat on condensation, often thousands of km away

• Water vapour is also the dominant greenhouse gas

Let’s switch from micro to macro! Where do we look?

A spatial unit to study the water cycle?

• A catchment (or river basin) is a land area where surface water drains to a common point
• Defined by topographic divides, assuming all water flows downhill
• Sizes range from hectares to millions of km²
• Every catchment is made of nested sub-catchments

• Surface water divides ≠ groundwater divides
• Groundwater can flow across topographic boundaries
• Important for:
  • Integrated water resource management
  • Understanding flow connectivity

Given only a contour map and a chosen outlet, everything you need is already on the page:

• Water flows down the steepest slope, so flow lines cross contours at right angles
• Ridges separate one catchment from the next — water cannot cross them
• The boundary must close on itself, at the outlet

Test of a correct boundary: everything inside drains to the outlet, everything outside drains elsewhere.

• The hydrological cycle describes water movement between Earth and atmosphere as gas, liquid, or solid.
• It is a conceptual model — useful but simplified.
• Hydrology begins with the global scale, then zooms into catchments.

• Most of Earth’s water is stored in:
  • Oceans/seas: 96.5%
  • Ice/glaciers: 1.74%
  • Groundwater: 1.69%
• Rivers and lakes make up tiny fractions of total volume.

• Key global processes:
  • Evaporation from oceans/lakes
  • Precipitation over land and sea
  • Run-off moves water back to oceans
• Oceans evaporate more than they receive.
• Continents receive more precipitation than they lose.
• Ironically, the terrestrial component, the part we care most about, is by far the smallest.

This diagram is not decoration. It is the water balance equation drawn to scale, and every unit that leaves must arrive somewhere (km³ per year):

• Globally, precipitation = evaporation = 577,000 km³/yr
• Mass is conserved, so this had to close. It is worth doing once anyway, because it tells you the diagram is a budget, not an illustration.

From flux to depth

• The 110,000 km³/yr of land precipitation falls on the externally draining land, 119 \times 10^6 km², a mean depth of \approx 920 mm/yr
• The internally draining basins take a further 9,000 km³/yr, so averaged over all 149 \times 10^6 km² of land it is \approx 800 mm/yr
• Match the numerator to the denominator, or the answer is meaningless

• A store is a volume (km³); a flux is a rate (km³/yr). They are not comparable quantities.
• Divide one by the other and you get the mean residence time, being how long a typical water molecule stays put:

• This is what makes the 96.5% figure meaningful. The atmosphere holds only 0.0009% of Earth’s water, yet every drop of rain passes through it, because it turns over every eight days.

• Precipitation is partitioned into evaporation, run-off and groundwater recharge.
• The split varies by climate:
  • Humid temperate: roughly one third each
  • Semi-arid: about half to evaporation
  • Arid: evaporation dominates, recharge almost nil
• Most of Australia sits in the semi-arid to arid panels.

Take the 0.27% “available” share literally. 0.27\% of 1{,}385{,}984 \times 10^3 km³ is 3.74 \times 10^{18} L, which among 8 billion people is

• Enormous — but it is a store. An inheritance, not an income.
• Set it against what the world’s rivers carry in a year:

• The entire accessible store is worth about a century of run-off. Spend it faster than that and you are mining it.
• Read that as a comparison, not as a residence time. Almost all of this store is groundwater, and rivers are not what refills it. Rain soaking down to the water table replaces it over several hundred years.

What you may actually spend is the flux: river run-off, 42,600 km³/yr among 8 billion people.

• Sanity check: 5.3 \times 10^3 m³/cap/yr lands between the UK and the USA on the next slide, below Australia. That is where a global average belongs.
• It is also about 70 times Australian household use (\approx 200 L per person per day).
• So the answer to the question is yes, in total, and no, where and when it is needed. Scarcity is a problem of distribution, as Stumm said.

• Per capita water availability is misleading if population and use patterns are ignored.
• Australia looks water-rich by volume, but its high tropical north-west rainfall masks extreme scarcity elsewhere.
• Availability counts only rainfall within a country’s borders, ignoring rivers and groundwater that cross them, and food imported from elsewhere.
• Effective management depends on abstraction, storage, and equity.

• OECD countries vary widely in water abstraction.
• Largest user is the USA: ~1,730 m³/person/year
• Australia, Canada and New Zealand are also near the top
• Often driven by:
  • Agriculture
  • Industry
  • Irrigation infrastructure
• Water use ≠ water availability
• Australia’s 2005—2007 drought showed what happens when the two collide

approximately eleven per cent of non-renewable groundwater use for irrigation is embedded in international food trade, of which two-thirds are exported by Pakistan, the USA and India alone.

Dalin et al (2017), Nature

• Focuses on processes at basin scale:
  • Evaporation
  • Precipitation
  • Run-off
• Includes sub-processes:
  • Interception
  • Transpiration
  • Infiltration and through-flow

• The water balance equation represents the continuity of water mass in a system.
• It quantifies water input, output, and storage over time.
• In its most fundamental form:

• Often rearranged to estimate streamflow (Q)Q = P - E - \Delta S

Where P is precipitation, E evaporation, \Delta S the change in storage, and Q run-off. We write Q rather than R, because R usually means rainfall.

• The equation includes both fluxes and stores:
  • Fluxes: P, E, Q
  • Store: \Delta S (soil, groundwater, snow)
• Each term may be:
  • Positive (gain) — e.g. precipitation
  • Negative (loss) — e.g. evaporation or outflow
• Storage can increase or decrease depending on the balance.

• Used widely in:
  • Catchment hydrology
  • Water resource models
  • Climate impact studies
• Knowing three of the four terms allows you to estimate the fourth.
• Example: If P = 100, E = 40, \Delta S = 10, then Q = 100 - 40 - 10 = 50

• Difficulties in application include:
  • Spatial variability in rainfall
  • Temporal mismatch in data resolution
  • Estimating \Delta S is often hard
• Hydrological models often use the water balance to simulate run-off.
• Model example: Input daily rainfall and evaporation to calculate daily discharge using: Q = P - E - \Delta S

• The uncertainty is not in the equation. Mass is conserved.
• It is in applying it: every process operates over some area and some period, and those rarely coincide with the area and period we can actually measure.
• This mismatch of scale is why hydrology can look like an imprecise science, and it is the thread running through the rest of this course.

• Hydrological events vary by:
  • Magnitude (e.g. rainfall depth)
  • Frequency (how often)
  • Duration (how long)
• High magnitude, low frequency, and vice versa.

• Hydrological data are positively skewed, not normal. A few huge events drag the mean above the median, so quoting a “mean” flood tells you very little.
• Probability: p = \frac{n}{N}, and recurrence interval = 1/p
• A 1% annual chance event = the 1-in-100-year event

“We had our 1-in-100-year flood last year, so we’re safe for a while.”

• This is wrong, and it is the most common misunderstanding in hydrology.
• The chance of a flood of that size next year is still 1%. The river has no memory of last year.
• Two 1-in-100-year floods in consecutive years are unremarkable: unlikely in any given pair of years, but there are a great many pairs of years and a great many rivers.

• This is why we say recurrence interval, not “return period”: it is the average spacing between events of that magnitude, taken over a very long record.
• It is a statement about long-run frequency, never about when the next one arrives.
• Practical consequence: a 1% annual chance over a 30-year mortgage is a 1-(0.99)^{30} \approx 26% chance of at least one such flood.

• Every number in this lecture is an estimate. Nobody has ever measured global evaporation with a bucket.
• The scale problem is real: gauges measure points, we need catchments and continents.
• Over roughly the past 40 years, satellites have made the global distribution of precipitation, evaporation and storage observable for the first time.

Which term of P \pm E \pm \Delta S \pm Q = 0 can we see from orbit?

In this lecture, we covered:

• The definition and scope of hydrology as a science of fresh water
• The physical and molecular properties of water that influence climate and flow
• The structure and function of the hydrological cycle, from global to catchment scale
• Key concepts such as catchments, water availability, and store vs flux
• Residence time as the bridge between the two, and why a store is not a supply
• The water balance equation as a tool for understanding and modelling water movement
• Challenges in quantifying water fluxes, and why scale is hydrology’s central difficulty