Hydrology

Hydrology and the hydrological cycle

Hydrology is the science of the occurrence, circulation and distribution of water on the earth. Engineering hydrology applies it to the design and operation of water-resources projects — estimating floods, yields, storage and groundwater.

The hydrological cycle is the continuous circulation of water between the oceans, the atmosphere and the land, driven by solar energy and gravity:

1. Evaporation from oceans and water bodies, and transpiration from plants.
2. Condensation into clouds and transport by winds.
3. Precipitation on land and sea.
4. On land: interception, depression storage, infiltration into the soil, percolation to groundwater, surface runoff, interflow and baseflow back to streams and oceans.

The cycle has no beginning or end, and the total quantity of water is essentially constant.

Precipitation

Forms

Rainfall intensity is commonly classed as light (up to about 2.5 mm/h), moderate (about 2.5–7.5 mm/h) and heavy (above about 7.5 mm/h).

Types of precipitation (by the cause of air lifting)

• Convective — heated air near the ground rises, cools and condenses; intense, short-duration, local storms (common in tropical summers).
• Orographic — moist air forced up by mountain barriers; heavy rain on the windward side and a rain shadow on the leeward side (Western Ghats, Himalayan foothills).
• Cyclonic — lifting due to low-pressure systems: frontal (warm and cold fronts) and non-frontal (convergence into a low, e.g. tropical cyclones and monsoon depressions).

In India the south-west monsoon (June–September) brings the major part of the annual rainfall for most of the country; Tamil Nadu receives much of its rainfall from the north-east monsoon (October–December).

Measurement of rainfall

Other methods: radar (areal coverage), satellite estimation.

Siting a rain gauge: on level open ground; the distance from any obstruction should be at least about twice its height; the rim kept horizontal and a little above ground; enclosure protected by a fence.

Rain gauge network

The World Meteorological Organization recommends roughly: flat regions of temperate, Mediterranean and tropical zones — 1 station per 600–900 km² (ideal); mountainous regions — 1 per 100–250 km²; arid and polar zones — 1 per 1500–10 000 km². At least about 10% of gauges should be self-recording.

Preparation of rainfall data

Estimating missing data

For station X with missing record and neighbouring stations A, B, C (with normal annual precipitation $N$):

• Arithmetic mean method — if the normal annual precipitations of the neighbouring stations are within 10% of that of X: $P_x=\frac{P_A+P_B+P_C}{3}$.
• Normal ratio method — otherwise:

Consistency — double mass curve

A change in gauge location, exposure or observation method makes the record inconsistent. The accumulated annual rainfall of the station is plotted against the accumulated mean of a group of base stations. A break in slope reveals the inconsistency; the record is corrected by

($M_c$ = corrected slope, i.e. the slope of the period to be retained; $M_a$ = original slope of the period being corrected.)

Abstractions

Abstractions are the parts of precipitation that do not become direct runoff: evaporation, transpiration, interception, depression storage and infiltration. Rainfall minus abstractions gives effective (excess) rainfall.

Evaporation

Evaporation is the process by which water changes from liquid to vapour at a free water surface below its boiling point. It is a cooling process (latent heat is absorbed).

Factors affecting evaporation

Other approaches: water budget method, energy budget method and mass transfer method.

Evaporation pans

Lake evaporation = $C_p$ × pan evaporation. Pans evaporate more than lakes because of their small size, heat exchange through the sides and differences in exposure.

The ISI (IMD) standard pan is a copper pan 1220 mm in diameter and 255 mm deep, painted white, covered with a wire mesh and mounted on a wooden stand.

Reduction of reservoir evaporation

1. Reduction of surface area — deep reservoirs rather than wide, shallow ones.
2. Mechanical covers — only for small tanks.
3. Chemical films — monomolecular layers of cetyl alcohol (hexadecanol) or stearyl alcohol, which reduce evaporation without harming aquatic life.
4. Wind breaks — tree lines on the windward side.
5. Removing water-loving vegetation (phreatophytes) along the periphery.

Transpiration and evapotranspiration

• Transpiration — water taken up by plant roots and released as vapour through leaf stomata; measured on a single plant by a phytometer.
• Evapotranspiration (ET, consumptive use) — total evaporation from soil and water surfaces plus transpiration from vegetation.
• Potential evapotranspiration (PET) — ET when water supply to plants is unlimited.
• Actual evapotranspiration (AET) — ET under actual soil-moisture conditions; AET = PET only when soil moisture is at field capacity.
• Reference crop ET ($E{T}_0$) — PET of a standard grass (or alfalfa) surface; crop ET $=K_c\times E{T}_0$.

Measurement and estimation

• Lysimeter — a tank of soil with vegetation, isolated from the surroundings; ET found from the water balance (weighing or non-weighing).
• Field plots — water balance of an actual field.
• Blaney–Criddle (monthly consumptive use, cm):

($K$ = crop coefficient, $P_h$ = monthly percentage of annual daytime hours, $T_f$ = mean monthly temperature in °F.)

• Thornthwaite — temperature-based monthly PET.
• Penman (Penman–Monteith) — combines energy balance and aerodynamic terms; the most reliable physically based method (FAO recommended).
• Hargreaves — radiation and temperature based.

Interception and depression storage

• Interception — rainfall caught by vegetation and later evaporated; significant in forests and for light, short storms.
• Depression storage — water held in small surface depressions, later evaporating or infiltrating; must be filled before overland flow starts.

Infiltration

Infiltration is the entry of water into the soil surface; percolation is its downward movement through the soil towards the water table.

• Infiltration capacity $f_p$ — maximum rate at which a soil can absorb water at a given time.
• Actual infiltration rate $f=f_p$ if rainfall intensity $i\ge f_p$; $f=i$ if $i<f_p$.

Factors affecting infiltration capacity

Soil texture and structure; initial moisture content (dry soil infiltrates faster); vegetative cover (increases); compaction by rain impact, traffic and grazing (decreases); entrapped air; water temperature (viscosity); quality of water (suspended silt clogs pores); land use and surface crusting.

Measurement of infiltration

• Flooding-type infiltrometer — a ring (about 30 cm diameter) driven into the soil; water added to keep a constant head; rate of addition gives infiltration. The double-ring infiltrometer (inner about 30 cm, outer about 60 cm) reduces lateral-spread error — readings are taken in the inner ring.
• Rainfall simulator — sprinklers apply artificial rain over a small plot; infiltration = rain − runoff; represents rain-impact effects better.

Infiltration indices

The φ-index is widely used for large catchments and flood estimation.

Runoff

Runoff is the part of precipitation that flows towards streams, rivers and the sea as surface or subsurface flow.

• Direct runoff = surface runoff + prompt interflow; it forms the flood hydrograph.
• Natural flow (virgin flow) — runoff unaffected by human diversions and storage; observed flows must be corrected for upstream abstractions and return flows.

Types of streams

• Perennial — flow throughout the year; the water table stays above the stream bed (effluent streams fed by baseflow).
• Intermittent — flow during wet seasons only; water table above the bed in wet seasons.
• Ephemeral — flow only during and immediately after rain; the bed is always above the water table (common in arid zones).

Factors affecting runoff

Climatic: type, intensity, duration and areal distribution of precipitation; direction of storm movement; antecedent rainfall; evaporation and transpiration.

Physiographic (catchment):

• Area — total runoff volume increases, runoff per unit area and peak per unit area decrease.
• Shape — fan-shaped (compact) catchments give higher, earlier peaks than fern-leaf (elongated) catchments.
• Slope — steeper slopes give quicker, higher runoff.
• Soil and geology, land use and vegetation (forests reduce and delay runoff; urbanisation increases it), drainage density (stream length per unit area — higher density gives quicker response), storage in lakes and swamps.

Yield of a catchment

The yield is the total quantity of water that can be expected from a stream in a given period (usually a year). The dependable yield is the yield that is equalled or exceeded in a stated percentage of years — commonly 75% dependable yield for irrigation planning and higher dependability (about 90% or more) for hydropower and drinking water.

Rainfall–runoff relationships

Runoff coefficient and correlation

• Runoff coefficient $C=R/P$.
• A linear regression $R=aP+b$ (or exponential forms) is fitted to observed annual rainfall and runoff.

Empirical formulas and tables (Indian practice)

SCS curve number method

The hydrograph

A hydrograph is a graph of discharge against time at a stream section. A storm hydrograph has:

Time parameters:

• Time to peak $t_p$ — from the start of effective rainfall to the peak.
• Basin lag $t_L$ — from the centroid of effective rainfall to the peak (sometimes to the centroid of the hydrograph).
• Time of concentration $t_c$ — time for runoff from the hydraulically most remote point to reach the outlet.
• Time base $T_B$ — duration of direct runoff.

Factors affecting the hydrograph shape

• Catchment shape — fan-shaped catchments: high, sharp peaks; fern-leaf (elongated): flatter, delayed hydrographs.
• Size — large catchments have longer time bases and lower peaks per unit area.
• Slope — steep channels and land slopes give steep rising limbs.
• Drainage density — high density gives quicker, peakier response.
• Land use — forests and vegetation flatten the hydrograph; urban areas sharpen it.
• Storm characteristics — intensity, duration, areal distribution and direction of movement: a storm moving downstream gives a higher peak than one moving upstream.

Baseflow separation

To obtain the direct runoff hydrograph (DRH), baseflow is subtracted:

1. Straight-line method — join the start of the rising limb to a point on the recession limb $N$ days after the peak.
2. Fixed base method — extend the pre-storm recession to below the peak, then join to the point $N$ days after the peak.
3. Variable slope method — separate groundwater recession curves before and after the storm.

Recession curve: $Q_t=Q_0{K}_r^t$, with recession constant $K_r<1$ (separately for surface, interflow and baseflow storage).

Effective rainfall hyetograph

Effective rainfall (rainfall excess) = rainfall − losses (using the φ-index or other loss models). Its volume equals the volume of direct runoff. The ERH plotted against time is the input to unit hydrograph computations.

Unit hydrograph

Assumptions

1. Time invariance — the DRH for a given effective rainfall is always the same regardless of when it occurs.
2. Linear response — ordinates are proportional to the effective rainfall depth (proportionality), and hydrographs from successive storms can be added (superposition).
3. Effective rainfall uniformly distributed over the catchment and within the duration.

Limitations

• Precipitation must be nearly uniform — so the method is best for catchments of moderate size (large catchments are subdivided; the upper limit is often quoted as about 5000 km²).
• Not suitable when snowmelt or large channel storage dominate, or for very small plots.
• The effective rainfall must have a duration close to the unit duration used.

Area under the unit hydrograph

The volume of direct runoff equals 1 cm over the catchment:

Derivation from an isolated storm

1. Select an isolated, uniform storm of duration about D hours.
2. Separate baseflow → DRH.
3. Compute the effective rainfall depth = DRH volume ÷ catchment area.
4. UH ordinate = DRH ordinate ÷ effective rainfall depth (cm).
5. Average the unit hydrographs from several storms (average peak and time to peak; adjust shape to keep unit volume).

Using the unit hydrograph

For effective rainfalls of $R_1,R_2,\dots$ cm in successive D-hour blocks, the DRH is obtained by multiplying the UH by each depth, lagging each by D hours, and adding. Baseflow is then added to get the flood hydrograph.

Changing the unit duration

Method of superposition

A nD-hour UH (n integer) = sum of n D-hour UHs lagged successively by D hours, divided by n.

S-curve method

The S-curve method works for any T (larger or smaller than D, not necessarily a multiple).

Synthetic unit hydrographs

For ungauged catchments, UH parameters are related to catchment characteristics:

• Snyder's method: basin lag $t_p=C_t(L{L}_{ca}{)}^{0.3}$ ($L$ = main stream length, $L_{ca}$ = distance along the stream to the point nearest the catchment centroid, in km; $t_p$ in h); peak discharge $Q_p=\frac{2.78C_{p}A}{t_p}$ (m³/s per cm).
• SCS dimensionless unit hydrograph — time to peak $T_p=D/2+t_L$; peak $Q_p=\frac{2.08A}{T_p}$ (m³/s per cm, A in km², $T_p$ in h); time base ≈ 5$T_p$ for the curvilinear form (2.67$T_p$ for the triangular form).
• Regional methods — in India, the Central Water Commission's flood estimation reports give regional synthetic UH relations for hydro-meteorological sub-zones.

Instantaneous unit hydrograph (IUH)

The UH as $D\to 0$ — the response to 1 cm of effective rainfall applied instantaneously. It depends only on catchment characteristics. Conceptual models: Nash's cascade of linear reservoirs, Clark's model (time–area diagram routed through a linear reservoir). A D-hour UH is obtained by routing/averaging the IUH (or from its S-curve).

Worked examples

Frequently tested points

• Hydrograph: rising limb, crest, recession; recession depends only on catchment storage.
• Fan-shaped catchment and downstream-moving storm → higher peak.
• $N=0.83A^{0.2}$ days; recession $Q_t=Q_0{K}_r^t$.
• UH: 1 cm effective rain, uniform, D hours; assumptions of linearity (proportionality, superposition) and time invariance.
• Area under UH = 1 cm × A: $A=0.36\sum Q\Delta t$.
• S-curve equilibrium $Q_s=2.778A/D$; $U_T=(D/T)[S(t)-S(t-T)]$.
• Snyder $t_p=C_t(L{L}_{ca}{)}^{0.3}$; IUH is the UH with zero duration.