• Mechanisms responsible for delivering water to streams and rivers.
• River/streamflow: The movement of water in channels toward the ocean.
• Riverflow is typically quantified as discharge: volume of water per unit time \frac{m^3}{s}.

biologyreader.com: Components involved in runoff.

• A continuous record of streamflow is called a hydrograph.
• Peak/storm flow: Water present in a stream during and immediately after a significant rainfall event.
• Globally controlled by rainfall intensity and duration; at catchment scale, affected by catchment size, slope, shape, soil characteristics, vegetation type and cover, degree of urbanisation, and antecedent soil moisture.
• Periods between peaks are referred to as baseflow (distinct from low flow), typically understood to be supplied by groundwater.

• Rising limb: Steep section leading up to peak flow.
• Contributed by: Channel precipitation (rain falling directly into the stream) and rapid runoff.
• Recession limb: Follows the peak and shows a gradual decline in streamflow.
• Influenced by stormwater arriving from upstream and contributions from subsurface flow.

The exact proportion of precipitation that becomes channelized flow is difficult to determine.

Each is set by the same physical properties: size, slope, shape, hydraulic length, drainage density, soil, geology, land cover, and antecedent wetness.

• Overland flow: Water flowing over the land surface after precipitation.
• Horton (1933): Overland flow occurs when rainfall intensity exceeds the infiltration capacity of the soil.
  Excess water then flows as a shallow surface layer.
  Infiltration capacity acts as a threshold.

• However, in most cases, infiltration rates exceed typical rainfall intensities.

Continuous sheets of overland water flow are rarely observed in nature.

• However, in most cases, infiltration rates exceed typical rainfall intensities.

Selby (1970) measured 60–600 mm/hour on short grazed pasture in the central North Island of New Zealand. Almost nothing rains that hard.

• Hursh (1944) coined subsurface stormflow, recognising that flows other than surface flow matter. Cook (1946) proposed that overland flow can also be water that has been underground and re-emerges.
• Betson (1964): Introduced the concept of partial contributing areas — only specific parts of a catchment produce overland flow.
  The importance of infiltration is retained, but the idea of uniform thin flow is questioned.
• Hewlett & Hibbert (1967): Overland flow occurs when the water table rises to the surface due to infiltration and throughflow.
  This results in saturated areas near channels and lower slopes where return flow and direct precipitation dominate.
• Confirmed by the field study of Dunne & Black (1970).

Basher & Ross (2001), market gardens in the North Island of New Zealand: infiltration capacity of 400 mm/hour, rising to 900 mm/hour in the growing season — but as low as 0.5 mm/hour in the wheel tracks of the same site.

Hewlett and Hibbert placed the saturated areas next to the channel. Later work (Dunne & Black 1970; Anderson & Burt 1978) found four other geometries that force water back to the surface:

• panel a — convergence of subsurface flow into a hillslope hollow,
• panel b — a slope break that reduces the hydraulic gradient,
• panel c — a local thinning of soil over an impermeable base,
• panel d — a drop in hydraulic conductivity, producing a perched saturated zone.

In each case the soil volume receiving the throughflow is too small for the water arriving, so it returns to the surface. This is what the boggy patches at valley heads and slope bases actually are.

• The variable source area model proposes that only parts of the catchment contribute to the hydrograph.
• Overland flow alone can’t explain total discharge observed in hydrographs.
• The gradual decline in the hydrograph’s recession limb suggests a subsurface flow component.
• Tracer studies show significant presence of older water during stormflow.
• This points to throughflow and groundwater contributions.

The rain that falls during a storm is largely not the water that arrives in the river during that storm.

These are not alternatives to each other. At Maimai all three appear together.

• Proposed by Horton & Hawkins (1965) — a different Horton from the one behind Hortonian overland flow.
• Water entering at the top of the soil column displaces older water at the bottom, which then enters the stream.
• Similar to a piston where top pressure pushes fluid at the bottom.
• The discharge can be viewed as a pressure wave, so it is modelled as pressure propagation rather than by tracking water particles.
• Though unconventional, the combination of rainfall above and impermeable bedrock below creates this piston effect. Demonstrated in laboratory soil columns by Germann & Beven (1981).
• The added water generates a hydraulic gradient that drives water movement along the base of the soil layer, which typically has higher conductivity (Brammer & McDonnell 1996).
• Analogy: A thatched roof—water moves quickly along aligned channels, especially in the downslope direction (Ward 1984, after Zaslavsky & Sinai 1981).

• Key pathway for rapid subsurface flow.
• Hydrological role: Enable fast water movement bypassing much of the soil matrix.
• Ongoing debate: Whether these pores form continuous flow networks or are limited by disconnected segments.
• Pipes are the continuous end-member (Jones 1981; Tanaka 1992). Where they exist they dominate hillslope hydrology, but they are not common.

• Historically, groundwater was thought to only contribute to baseflow.
• Sklash & Farvolden (1979) introduced the capillary fringe hypothesis to explain the groundwater ridge observed next to streams by Ragan (1968).
• Concept: A “groundwater ridge” forms near the stream during recharge.
• Added infiltration takes soil water next to the channel from tension (unsaturated) to positive pore pressure (saturated), generating hydraulic gradients that drive discharge to the stream.
• The water-saturation relationship in soils is nonlinear, so a small amount of water produces a large change in state.
• This increases both the rate of discharge and the size of the groundwater discharge area.
• Crucially, the ridge develops before any throughflow arrives from upslope.

A sequence of results, each overturning the last:

• Mosley (1979, 1982): dye tracing in cut soil faces suggested rainfall could reach the stream in under 3 hours via macropores.
• Pearce et al. (1986): isotopes showed the streamflow was mostly old water — so macropore flow was not the main mechanism.
• McDonnell (1990): groundwater ridging occurs, but there is not enough near-stream water to supply all the old water.
• McGlynn et al. (2002): a combined model — macropores deliver water fast to bedrock, then piston flow along the interface pushes old water out.

Hillslope scale (< 10 km²)

Runoff generation mechanisms control the hydrograph. Infiltration capacity, saturation, macropores and piston flow all matter, and they are measurable.

This is the scale of nearly every process study in this lecture, Maimai included.

Large basin scale

The timing of the peak and the shape of the hydrograph are set mostly by the channel drainage network and by the spatial and temporal pattern of the storm.

The hillslope mechanisms are still operating, but they are averaged over so much heterogeneity that they stop being the controlling factor.

In sharp contrast to the stormflow debate, there is general consensus here: the major source of baseflow is groundwater, with a smaller contribution from throughflow.

• Water infiltrates, reaches the saturated zone, then moves downslope towards the stream.
• A stream or lake often occurs where the regional water table intersects the surface — though not always.
• Baseflow is usually not visible. Springs are the exception. Most of it is slow seepage through the streambank and bed.
• The only way to detect it is repeated discharge measurement down a reach: if discharge grows with no tributary inflow, the reach is gaining.

Careful with two words

Baseflow is the slow, groundwater-fed component between storm peaks.

Low flow is a statistic of the flow record — how small the discharge gets in a dry period.

They are related but they are not the same quantity, and they are analysed with different tools.

Once water reaches the stream, the rate of flow depends on three things:

• the volume of water present,
• the gradient of the channel,
• the resistance at the channel bed.

This is described by uniform flow formulae — Chézy and, more commonly, Manning:

with A the cross-sectional area, R the hydraulic radius, S the energy slope, and n Manning’s roughness. Boulders and vegetation raise n and slow the flow.

Ephemeral channels

In arid regions many channels flow only during floods. The resistance problem there is complicated by infiltration through the bed.

The first flush of water fills the available pore space in the bed, so it:

• loses volume from the stream, and
• slows the flood front as it advances over a rough, dry surface.

These transmission losses are why an arid-zone flood peak can shrink dramatically as it travels downstream.

Measuring hillslope runoff

• Overland flow varies enormously in space and time, so several plots are needed to characterise one slope.
• A rainfall simulator can be used to impose a controlled, repeatable input instead of waiting for a storm.

Alternative: subsurface tracing with a conservative tracer that does not bind to soil — sodium chloride, bromide, or fluorescent dyes such as Rhodamine WT.

• The velocity–area method multiplies stream velocity by cross-sectional area to estimate discharge.
• Black dots: locations of velocity readings.
• Dashed lines: triangular/trapezoidal cross sections.

The velocity–area method of streamflow measurement. The black circles indicate the position of current meter velocity readings. Dashed lines represent the triangular or trapezoidal cross-sectional area through which the velocity is measured.

• The velocity–area method requires the assumption that the velocity measured is representative of the entire cross-sectional flow.

• Since multiple measurements across the depth are rarely feasible, adjustments are needed to account for velocity variations.

• Water flows faster near the surface than near the bed due to bed friction.

• A general guideline: measure velocity at 60% of depth from the surface (or 40% above the bed).

• For deeper rivers, average readings at 20% and 80% of depth for better accuracy.

• If no velocity meter is available, a float method can provide rough estimates by timing surface travel over a measured distance.

• Surface floats overestimate true velocity since they ride faster-flowing surface water.

• The velocity–area method works well for small rivers, but its accuracy depends on sampling strategy.
• It becomes less reliable in turbid, shallow, or rough-bedded streams (e.g., mountain creeks).
• In such cases, consider alternative methods like dilution gauging. Illustration of float-based surface velocity measurement

• Stage = water level or height at a specific point in a river.

• Discharge = volumetric flow rate (e.g. \frac{m^3}{s}).

• Repeated discharge measurements (via velocity–area method) enable creation of a rating curve.

• A rating curve relates stage to discharge and allows continuous discharge estimation from simple stage measurements.

• Developed by pairing stage readings (e.g. using a stilling well) with discharge data.

• Rating curves are typically non-linear, reflecting the geometry of riverbanks:
  As rivers fill between banks, more water is required to raise stage than at low flows.

• Assumes a stable riverbed. Changes (e.g. due to flood scouring or deposition) will invalidate the curve.

• This is why flumes or weirs are often installed to stabilize the control section.

Limitations:

• Few high-flow measurements → less reliable for peak floods.
• High-flow events are dangerous and infrequent.
• Thus, errors increase at the upper end of the curve.

Remember: discharge is inferred from measured stage — not directly observed.

• In principle the same as stage-discharge relationship, but with a control section.
• Flumes and weirs are stream gauging structures that extend the stage–discharge method by imposing control over stream velocity and cross-sectional area.
• By doing so, they provide a continuous record of stream discharge.
• The key is to standardize flow through a known cross-sectional area so that velocity becomes predictable or known.
• This is especially useful because stream velocity varies with depth, but gauging structures enforce a consistent flow regime.
• These structures are designed so that discharge becomes a function of stage alone.

• Discharge through weirs is determined by known formulas based on weir shape.
• For a V-notch weir (Very accurate for low-flow rates):
  Q = 0.53 \sqrt{2g} \, C \, \tan\left(\frac{\theta}{2}\right) b^{2.5}
• Where:
  • Q = discharge (\text{m}^3/\text{s})
  • g = gravity (9.81 \text{m}/\text{s}^2)
  • C = discharge coefficient (depends on \theta)
  • \theta = notch angle
  • b = stage height (m)
• For a 90° V-notch, C = 0.578, and: Q = 1.366\ b^{2.5}
• These equations follow ISO 1438 standards for gauging structures.

• The shape of the gauging structure affects sensitivity to changes in flow:
  • V-notches are excellent for low flows due to higher sensitivity.
  • As discharge increases, cross-sectional area expands nonlinearly.
• Under high flows, it’s crucial that water doesn’t bypass the structure.
• V-notches are commonly used with 90° or 120° angles based on application needs.
• Stilling ponds slow down water before measurement but can trap sediment.

A trapezoidal flume helps flush sediment

• Flumes and weirs both allow continuous measurement of stream discharge but have key differences:
  • Weir: Water flows over a structure (like a small waterfall).
  • Flume: Water flows through a structure without dropping.
• Flumes tend to produce less sedimentation, making them suitable for high-energy environments.

• Trapezoidal flumes can flush out sediment efficiently, avoiding stilling pond build-up.
• Both are suitable for small streams but not large rivers, due to structural stress.

Streamflow from space

Everything on the last few slides needs a person to stand in, or beside, a river.

• The global gauge network is shrinking, and many national records are not shared.
• Whole basins in Africa, central Asia and South America have no publicly available discharge record.
• The measurements we most want — the flood peaks — are the ones that are dangerous to make and that destroy the gauge. In Mozambique in 2000, most gauges were inundated or washed away, so the return period of the flood could not be established afterwards.

The awkward fact

A satellite cannot measure discharge.

Discharge is a volume flux through a cross-section. Nothing in a reflected radar pulse carries velocity or bed geometry.

What a satellite can see is:

• water surface extent — where the water is,
• water surface elevation — how high it is,
• and, if it sees enough of the reach, the water surface slope.

A radar altimeter sends a pulse straight down and times the return. Range plus precise orbit determination gives the height of the surface above a reference ellipsoid.

• Designed for the ocean: TOPEX/Poseidon (1992), the Jason series, Sentinel-3, Sentinel-6 Michael Freilich, CryoSat-2.
• Repurposed over land. Where a ground track crosses a river, we get a time series of water height: a virtual station.
• Repeat cycles: ~10 days (Jason, Sentinel-6), ~27 days (Sentinel-3).

What nadir altimetry cannot do

• The tracks are fixed. Most rivers are never crossed, and the crossing is rarely where you want a gauge.
• The footprint is kilometres across, so the return from a narrow river is contaminated by the banks and the floodplain.
• You get a height at a point, not a slope along a reach, so the flow gradient is unknown.

Surface Water and Ocean Topography — NASA and CNES, with CSA and UKSA. Launched 16 December 2022.

The instrument is KaRIn, a Ka-band radar interferometer: two antennas on a 10 m boom. The phase difference between the two returns gives the height of every pixel, so it maps elevation over an area rather than along a line.

• Two 50 km swaths either side of a 20 km nadir gap: 120 km total.
• Pixels roughly 10–70 m across track, ~20 m along track.
• 21-day repeat, with 2–4 looks per cycle at mid latitudes.
• Requirement: rivers wider than 100 m (goal 50 m); lakes larger than about 250 m × 250 m.

Why the swath matters

For the first time we obtain, for the same reach and the same overpass:

• the width W of the water surface,
• the water surface elevation,
• and the slope S along the reach.

Slope is the quantity nadir altimetry could never give, and it is the one that Manning’s equation demands.

Products are reported on ~10 km reaches defined in the SWORD river database.

Recall the uniform flow law from the channel flow slide:

SWOT supplies W, S, and the change in cross-sectional area \delta A between overpasses.

It does not supply:

• Manning’s n, the roughness, and
• A_0, the unobserved cross-sectional area beneath the lowest water surface ever seen.

Both must be estimated from many repeat passes, from prior information, or from a model.

The same caution, one more time

On the rating curve slide we said: discharge is inferred from measured stage, not directly observed.

Nothing about being in orbit changes that. A SWOT discharge value is the output of an inversion with two unknowns, constrained by observations of the water surface.

Floods

A working definition: inundation of land adjacent to a river, caused by a period of abnormally large discharge.

Every word of that is negotiable.

• Flooding also comes from the sea and from lakes.
• “Abnormal” depends entirely on the length of record you happen to hold.
• Floods reach our attention through damage, so they are usually rated in dollars, not in cumecs.

As with rainfall, the frequency–magnitude relationship governs: small floods are common, the large ones are rare and do nearly all the damage.

Hydrological size and human cost are different quantities

China, 1998 — ~US$20 billion damage, 15 million people displaced, 3,000 lives lost.

Mississippi and Missouri, 1993 — US$15–20 billion, 48 lives lost. Hydrologically the far larger event: the highest in the record, with an average recurrence interval of 100–500 years.

Similar cost. A factor of sixty in lives. The difference is not hydrology, it is warning, infrastructure and wealth.

18 December 1999

27 February 2000

• Four floods in succession, January to March 2000.
• Preconditioning: rainfall at Maputo was 70 per cent above normal in October–November 1999, so the catchments were already saturated.
• Cyclones Connie, Eline and Glória each delivered record rainfall inland over Zimbabwe and northern South Africa.
• The Limpopo rose 3 m higher than any recorded flood. For the first time in the record, the Limpopo and Incomáti joined into a single inundation.
• 700 people died; 45,000 were displaced; ~US$450 million of infrastructure damage.
• Flood warnings were issued upstream by Zimbabwe and South Africa. Communications inside Mozambique had already been cut by the earlier floods.

• Brisbane River catchment, 13,570 km²; mostly grazing and forestry, but Brisbane (1.98 million) and Ipswich (200,000) sit in the lower reaches.
• A strong La Niña, with very warm sea surface temperatures off the Queensland coast, drove exceptional rainfall from late November 2010.
• Six large rainfall events made December 2010 the wettest December on record for southern Queensland. The soil was fully saturated.
• Rainfall for 10–12 January 2011 had an annual exceedance probability of 1 in 150 over the catchment, exceeding 1 in 500 in places.
• Peak in Brisbane City: 13 January 2011. Seventh highest river height since records began in 1840, highest since 1974.
• 37 people killed, 29,000 homes and businesses inundated, ~A$5 billion in insurance and recovery.

Despite the Inquiry’s finding, the public narrative fixed on Wivenhoe. Four reasons, and none of them hydrological:

• The summer of 2010–11 followed an extreme drought. A year earlier there were serious concerns Brisbane would run out of potable water, so the prevailing story was of empty dams.
• There had been no major flood since 1974, so flooding was outside the collective memory of most residents.
• Wivenhoe was built after 1974, which created a sense of security that flooding had been solved.
• Modern societies want an immediate scapegoat for a natural disaster.

Nathan (2012): lessons from large floods

1. Big rains cause big floods.
2. Communicating risk is difficult.
3. Hydrologic complexity cannot be ignored.

Deceptively simple, and worth pinning to a wall. Note that two of the three are not about hydrology at all.

Mapping floods from space

• Long archive (Landsat since the 1980s), familiar, easy to interpret.
• Fatal weakness: cloud. Floods arrive with the weather that caused them, so the optical sensor is blind at the moment of peak inundation. The Mozambique image of 27 February 2000 is patchy with cloud for this reason.

• False positives: smooth dry surfaces — tarmac, dry sand, salt pans — also look dark.
• False negatives: wind-roughened water scatters back and looks like land; flooded vegetation can look bright through double-bounce off trunks and the water surface.

The route water takes from raindrop to river largely determines its chemistry, because chemistry is set by contact time with the soil.

• Water arriving as overland flow has had little soil contact: low nutrient load, but often high suspended solids picked up from the surface. It looks dirty and is chemically clean.
• Water arriving as throughflow or groundwater has had long contact: higher nutrient load, but clear. It looks clean and is chemically loaded.

So “clear water” and “clean water” are not the same claim.

A consequence of piston flow

When groundwater responds to rainfall, it frequently responds as a pressure wave. The water that enters the stream is not the water that just infiltrated.

That water may be years or decades old, and therefore unaffected by any recent land-use change.