Applied hydrology 1

What is the process of evaporation?

Evaporation is the transfer of liquid water into a gaseous state and its diffusion into the atmosphere.

What is the formula for evapotranspiration (ET) in terms of evaporation (E) and transpiration (T)?

ET = E + T, where E is evaporation from soil or water surfaces and T is transpiration from plant surfaces.

Globally, what is the approximate contribution of transpiration to terrestrial evapotranspiration (ET)?

Transpiration accounts for about 60% of terrestrial ET (land only).

How does a higher Leaf Area Index (LAI) affect the ratio of transpiration (T) to evapotranspiration (E+T)?

A higher LAI increases canopy shading and root water supply, causing transpiration (T) to rise while soil evaporation (E) drops.

In semi-arid regions, what is the long-term relationship between precipitation (P) and evapotranspiration (ET)?

Over long periods, precipitation approximately equals evapotranspiration ($P \approx ET$), meaning most rainfall returns to the atmosphere.

What is net evaporation the result of?

Net evaporation is the balance between the evaporation flux (molecules escaping the surface) and the condensation flux (molecules re-entering the surface).

What is the term for the partial pressure exerted by water vapour molecules in the air?

This is termed the water vapour pressure.

When is the air considered to be saturated with water vapour?

The air is saturated when the number of water molecules leaving a water surface equals the number re-entering it, which occurs at the saturated vapour pressure (SVP).

According to Dalton's Law, the evaporation rate (E) is a function of what two primary factors?

The evaporation rate is dominated by wind speed (u) and the vapour pressure deficit ($es - ea$).

What is the formula for evaporation rate (E) according to Dalton's Law?

$E = u(es - ea)$, where u is a function of wind speed, $es$ is saturation vapour pressure, and $ea$ is actual vapour pressure.

How is the vapour pressure deficit calculated?

The vapour pressure deficit is calculated as the difference between the saturation vapour pressure and the actual vapour pressure ($es - ea$).

What is the key difference between Potential Evapotranspiration (PET) and Actual Evapotranspiration (AET)?

PET is the amount of ET that would occur if water supply were unlimited, whereas AET is the actual amount that occurs regardless of water availability.

List four key meteorological factors that control the rate of evapotranspiration (ET).

Humidity, temperature, sunshine, and wind speed.

What are the three primary energy sources for evapotranspiration?

The primary energy sources are solar energy (radiation), stored heat (from soils/water), and advective energy (from warm, dry air).

In the energy balance equation $R_n = H + \lambda E + G + \Delta Q$, what does the term $\lambda E$ represent?

$\lambda E$ represents the latent heat flux, which is the energy required to change water from a liquid to a vapour phase.

The ability of a soil to _, retain, and release moisture is a key determinant in the hydrological response of catchments.

absorb

What is the definition of Field Capacity (FC) in soil science?

Field Capacity is the state where the soil is wet and contains all the water it can hold against the force of gravity (soil water potential $\psi \approx$ -10 to -33 kPa).

What does the Permanent Wilting Point (PWP) of a soil represent?

The PWP is the point at which the soil is so dry that a plant can no longer extract any more water (soil water potential $\psi \approx$ -1500 kPa).

What is hydraulic conductivity a measure of?

It measures the ease with which water moves through soil, typically expressed in units of length per time (e.g., cm/h).

How does unsaturated hydraulic conductivity ($K_u$) change as soil moisture content ($\theta$) decreases?

Unsaturated hydraulic conductivity ($K_u$) decreases strongly as the soil moisture content ($\theta$) becomes lower.

Which force is responsible for holding water in soil pores against gravity?

Capillary (matric) forces, which arise from surface tension and adsorption.

What does a lower (more negative) soil water potential ($\psi$) indicate?

A lower or more negative soil water potential ($\psi$) indicates a stronger suction force holding water in the soil.

Which soil type, sand or clay, has stronger capillary forces (higher $\psi$) but lower hydraulic conductivity (K)?

Clay has stronger capillary forces but lower hydraulic conductivity.

List three factors that influence the rate of infiltration into soil.

Soil texture and structure, antecedent soil moisture, and land use/vegetation.

What is the name of the empirical equation for infiltration rate given by $f = fc + (f0 - f_c)e^{-kt}$?

This is the Horton Equation (1939).

In the Philip equation for infiltration, the term 'A' is the transmissivity term, which is approximately equal to what soil property?

The transmissivity term 'A' is approximately equal to the saturated hydraulic conductivity ($K_s$).

In the Green-Ampt infiltration model, the cumulative infiltration (F) is related to the wetted depth (L) and the change in moisture content ($\Delta\theta$) by what equation?

$F = L \times \Delta\theta$

What is the definition of 'ponding time' during a rainfall event?

Ponding time is the elapsed time between the start of rainfall and the moment water begins to pond on the soil surface.

What is the equation to calculate the time to ponding ($t_p$) using the Green-Ampt model parameters?

$tp = \frac{Ks \psi \Delta\theta}{i(i - K_s)}$, where i is rainfall intensity.

What is 'interception' in the context of the hydrological cycle?

Interception is the process by which falling precipitation is trapped by vegetation surfaces.

What is 'depression storage'?

Depression storage is rainfall that is intercepted by surfaces like flat roofs or natural depressions and remains there until it evaporates, not contributing to runoff.

Name the three main components of precipitation that has been intercepted by vegetation.

The three components are throughfall, stemflow, and litter interception.

How does rainfall intensity affect the percentage of water that is intercepted?

The percentage of intercepted water decreases as rainfall intensity increases.

Generally, what percentage of precipitation might be 'lost' to interception in a forest?

Interception loss in forests is generally at least 10% to 20% of total precipitation.

What is the Leaf Area Index (LAI)?

LAI is the total one-sided area of leaf tissue per unit of ground surface area.

What is the relationship between the maximum canopy storage ($S_{max}$) and the Leaf Area Index (LAI)?

Maximum canopy storage is directly proportional to the Leaf Area Index, often expressed as $S_{max} = k \times LAI$.

How is the Interception Ratio calculated?

Interception Ratio = (Interception loss) / (Precipitation).

What is soil moisture?

Soil moisture is the water stored in the pores of the unsaturated (vadose) zone between the soil surface and the water table.

How is Plant Available Water ($\theta_{paw}$) calculated from other soil water content properties?

Plant Available Water is the difference between Field Capacity and Permanent Wilting Point: $\theta{paw} = \theta{fc} - \theta_{wp}$.

What is the Soil Moisture Deficit?

It is the amount of water (in mm depth) required to fill the soil up to its field capacity.

What term describes the phenomenon where a soil has a different moisture content for a given soil potential depending on whether it is being wetted or dried?

This phenomenon is called hysteresis.

What is the simple water balance equation for calculating the change in soil moisture ($\Delta S$)?

$\Delta S = P - ET - G - Q$, where P is precipitation, ET is evapotranspiration, G is percolation, and Q is runoff.

Using a simple water balance for a catchment with an area of 2800 km², mean annual precipitation of 1200 mm, and mean annual discharge of 40 m³/s, how would you estimate the mean annual evapotranspiration?

First, convert discharge to mm/year, then use the long-term water balance equation $ET = P - Q$. ($Q = 509$ mm/year, so $ET = 1200 - 509 = 691$ mm/year).

In the hydrological cycle, what are the primary processes that prevent precipitation from leaving a catchment as discharge?

The main processes are interception by vegetation, depression storage, evaporation/evapotranspiration, and infiltration into the soil.

What is the difference between runoff and discharge?

Runoff is the movement of water towards a stream (above or below ground), while discharge (or streamflow) is the volume of water flowing in the stream itself past a certain point per unit time.

What is a Flow Duration Curve (FDC)?

A Flow Duration Curve is a cumulative frequency curve that shows the percentage of time a particular discharge was equalled or exceeded during a given period.

How would catchment storage (e.g., from lakes or groundwater aquifers) impact the shape of a Flow Duration Curve?

High catchment storage results in a flatter FDC, indicating less variation between high and low flows, while low storage leads to a steep FDC with large flow extremes.

What is the conceptual basis of the Rational Method for estimating peak discharge?

The Rational Method estimates peak discharge based on the idea that the maximum runoff rate occurs when the entire catchment area is contributing to flow at the outlet, which happens after a duration equal to the time of concentration.

What equation is used in the Rational Method to calculate peak discharge?

$Q_p = 0.278 C i A$, where C is the runoff coefficient, i is rainfall intensity (mm/h), and A is catchment area (km²).

List three key assumptions of the Rational Method.

1. Peak flow occurs after the time of concentration. 2. Rainfall intensity is constant during the storm and uniform over the catchment. 3. The runoff coefficient C is constant during the storm.

What is the purpose of a rating curve in hydrology?

A rating curve establishes a relationship between water level (stage) and discharge at a specific point in a river, allowing discharge to be estimated from continuous stage measurements.

What is the standard three-parameter equation for a simple curved rating curve?

$Q = K(G + \Delta G)^A$, where Q is discharge, G is gauge height, and K, A, and $\Delta G$ are constants.

In the rating curve equation $Q = K(G + \Delta G)^A$, what does the parameter $\Delta G$ represent?

$\Delta G$ is a correction to the gauge datum, representing the theoretical water level at which zero flow occurs for that specific rating equation.

Why is getting a good value for the power 'A' in a rating curve critical for flood estimation?

The power 'A' governs the shape of the curve, and a good value is critical for accurately extrapolating the relationship to estimate discharge during extreme floods, which are often beyond the measured range.

In normal flow conditions, what is the typical rating power 'A' for a channel that can be approximated as a rectangle?

For a rectangular channel, the rating power 'A' is expected to be between 1.5 and 1.667.

The assumption that the underlying processes causing changes in a system have not significantly changed over time is known as _.

stationarity

What are three examples of factors that can cause non-stationarity in hydrological data records?

Land-use change, construction of a reservoir, and climate change.

What is the Base Flow Index (BFI)?

The Base Flow Index measures the proportion of a river's runoff that originates from stored sources, such as groundwater.

What is a 'mass curve' in the context of water resources?

A mass curve is a plot of the cumulative volume of flow (often monthly mean flows) over time, used in reservoir storage analysis.

What information does a D-day Flow Duration Curve provide?

It shows the exceedance probability for the average flow over 'D' consecutive days (e.g., a 10-day mean flow), which is useful for assessing sustained low-flow conditions.

When comparing frequency histograms from two different catchments, what two standardisation rules must be applied?

The y-axis (frequency) must be standardised, and the class intervals and number of classes must be identical for both histograms.

What is the primary advantage of using a logarithmic scale for the flow axis on a Flow Duration Curve?

A logarithmic scale linearises the often log-normally distributed flow data, making it easier to interpret and extrapolate, especially at the low-flow end.

What is the primary difference between a Confidence Interval and a Prediction Interval in statistical analysis?

A Confidence Interval estimates the range for a population parameter (like the mean), whereas a Prediction Interval estimates the range for a single future observation.

Name the four main methods used to fit a probability distribution to extreme value data like annual maximum floods.

The four methods are Least Squares, Method of Moments, L-Moments, and Maximum Likelihood.

What is a major advantage of L-Moments over the standard Method of Moments for analysing flood data?

L-Moments are less sensitive to the influence of very large outliers because they are linear combinations of ranked data, not powers of the data.

The General Extreme Value (GEV) distribution family consists of what three types?

Type 1 (EVI or Gumbel), Type 2 (EVII or Fréchet), and Type 3 (EVIII or Weibull).

How does an EVII (Fréchet) distribution typically appear when plotted on a Gumbel (EVI) probability plot?

An EVII distribution appears as an accelerating, upward-curving line, indicating a faster growth rate for larger events.

How does an EVIII (Weibull) distribution typically appear when plotted on a Gumbel (EVI) probability plot?

An EVIII distribution appears as a decelerating, downward-curving line, indicating that the growth rate of floods slows and approaches an upper bound.

In GEV analysis, the shape parameter 'k' is used to transform the EV1 plotting positions $E(yi)$ into GEV plotting positions $w(yi, k)$. What is the formula for this transformation?

$w(yi, k) = \frac{(1 - \exp(-k \cdot E(yi)))}{k}$

What physical catchment characteristic often leads to an EVIII (Weibull) distribution for annual maximum floods?

The presence of large, flat floodplains that significantly attenuate the peak flows of large floods.

To convert point rainfall measurements to an average value over a catchment, what are the three main methods used?

The three main methods are the Arithmetic Mean, Thiessen Polygons, and the Isohyetal method.

How are influence zones for each rain gauge determined in the Thiessen Polygon method?

Polygons are constructed using the perpendicular bisectors of the lines connecting each station to its closest neighbours, assigning an area of influence to each gauge.

What is an isohyet?

An isohyet is a line on a map connecting points that receive equal amounts of rainfall over a given period.

Which method for calculating areal rainfall is generally considered the most accurate, especially when there are many gauges or significant topographical variation?

The Isohyetal method is considered superior as it accounts for the spatial variation of rainfall between gauges.

What is a Double Mass Curve used for in precipitation analysis?

It is used to check the consistency of a single rainfall station's record over time by plotting its cumulative rainfall against the cumulative average of several nearby stations.

What does a distinct change in the slope of a Double Mass Curve indicate?

It indicates a change in the data-capturing characteristics of the station, such as a change in location, instrumentation, or local environment.

What does an Intensity-Duration-Frequency (IDF) curve show?

An IDF curve shows the relationship between rainfall intensity, its duration, and the frequency (or return period) of its occurrence for a specific location.

What does the 'return period' of a storm signify?

The return period is the average interval of time within which a storm of a given magnitude is expected to be equalled or exceeded once.

What is a Unit Hydrograph (UH)?

A Unit Hydrograph is the direct runoff hydrograph resulting from one unit (e.g., 1 mm or 1 cm) of effective rainfall generated uniformly over a catchment at a constant rate during a specified duration.

What are the three fundamental principles (or assumptions) of the Unit Hydrograph method?

The principles are Invariance (stationarity), Proportionality (linearity), and Superposition.

The principle of _ in Unit Hydrograph theory states that if an effective rainfall of R1 produces a hydrograph Q1, then an effective rainfall of cR1 will produce a hydrograph cQ1.

Proportionality

What is the first step in deriving a Unit Hydrograph from historical rainfall-runoff data?

Select several representative, single-peaked storm hydrographs from the flow record.

After selecting a storm hydrograph, what must be done to the total flow data before calculating the direct runoff volume?

The baseflow component must be separated from the total streamflow to isolate the direct runoff.

What are the three main mechanisms of runoff generation?

Overland flow ($Qo$), throughflow/lateral flow ($Qt$), and groundwater flow ($Q_G$).

What condition leads to Horton overland flow (infiltration-excess overland flow)?

Horton overland flow occurs when the rainfall rate is higher than the infiltration capacity of the soil.

What is saturated overland flow?

It is overland flow that occurs when the soil becomes saturated from below, causing the water table to rise to the surface, and consists of return flow and direct precipitation on saturated areas.

What is the partial areas concept in runoff generation?

The concept, proposed by Betson (1964), suggests that within a catchment, only limited, specific areas (rather than the entire catchment) contribute overland flow to a storm hydrograph.

What is the difference between a lumped and a distributed hydrological model?

A lumped model treats the entire catchment as a single unit, averaging parameters spatially, while a distributed model divides the catchment into smaller units (grids/sub-catchments) and considers spatial variability.

What is the difference between a conceptual (parametric) and a physically-based (mechanistic) model?

A conceptual model uses simplified storages (reservoirs) to represent processes, while a physically-based model uses equations representing the physics of water movement (conservation of mass, momentum, etc.).

What is the purpose of model calibration?

Model calibration is the process of adjusting model parameters to achieve the best possible agreement between the model's simulated output and observed data.

What is an objective function in hydrological modelling?

An objective function is a mathematical measure used to quantify the 'goodness-of-fit' between simulated and observed data during model calibration (e.g., Nash-Sutcliffe Efficiency).

What does a Nash-Sutcliffe Efficiency (NSE) value of 1 indicate?

An NSE of 1 indicates a perfect match between the simulated model output and the observed data.

What is the purpose of a model 'warm-up' period?

A warm-up period is used at the beginning of a simulation to allow the model's internal states (like soil moisture) to reach a realistic condition, ensuring the subsequent simulation is not biased by arbitrary initial values.

What is the key difference between weather and climate?

Weather describes the short-term state of the atmosphere at a specific location, while climate describes the long-term patterns and averages of weather over decades or longer.

What is the difference between a Global Climate Model (GCM) and a Regional Climate Model (RCM)?

GCMs simulate the climate system on a global scale with coarse resolution, while RCMs operate over a limited area with a higher resolution, using GCM outputs as boundary conditions.

What are Representative Concentration Pathways (RCPs)?

RCPs are scenarios that describe different possible future trajectories of greenhouse gas concentrations, used as inputs for climate models.

What non-parametric statistical test is commonly used to detect monotonic trends in time series data like temperature or rainfall?

The Mann-Kendall (MK) Test.

After a trend is identified using the Mann-Kendall test, what method is used to estimate the magnitude (slope) of that trend?

Sen's Slope Estimator is used to calculate the magnitude of the trend.

What is meant by the lag time on a hydrograph?

Lag time is the delay between the centre of mass of the effective rainfall hyetograph and the peak of the resulting runoff hydrograph.

On a hydrograph, what process is dominant after the inflection point on the recession limb?

After the inflection point, the flow is predominantly from water released from temporary storage in the soil, known as interflow.