After Mid Sem Notes Flashcards
Why is a water table not flat?
Because it varies spatially due to topographic effects, spatial variation, permeability and bed rock topography
What is the capillary fringe?
The area above a water table with decreasing saturation
What forms where topography intersects the water table?
Wetlands, waterways and groundwater windows
What is water potential? and what happens in response to water potential?
phi (L^2/T^2), is the potential energy per unit mass of water in the system compared to that of pure, free water at atmospheric pressure.
Water flows from states of high energy to states of low energy in response to gradients in water potential
What is the energy of water equation?
ø = øv + øp +øg
What is hydraulic head equal to?
the sum of the pressure head and the elevation head
What does a piezometric well measure?
A point measurement of pressure (screened over a short interval only)
What is Darcy’s Law?
Q = - Ks A ∆H/∆x
What is storativity equal?
S = bSs
What is transmissivity?
T = bKs
What is interception loss?
Precipitation that is stored and then evaporated due to its interaction with vegetation
What is interception store?
Precipitation that is retained on vegetation and therefore prevented from contributing to runoff
What is throughfall?
The rain that passes through a vegetation canopy, including water that drips from leaves
What is stemflow/trunkflow?
water that originates as precipitatio that travels down tree trunks or plant stems
What is hortonian runoff?
Soil has saturated from rainfall and excess rain moves downslope to the stream as overland flow
What is rejected recharge?
Saturation overland flow
What are the four situations where overland flow may arise?
- Convergence of downslope subsurface flow
- Downslope change in gradient where flow slows and accumulates
- Local thinning of soil cover
- Downslope subsurface flow slows due to lower permeability zone, accumulates and exfilitrates to become runoff
What is transmission loss?
The loss of water from streamflow when water infiltrates into the streambed or floodplain.
What enchances downslope pathways?
Macropores
What is shallow water theory?
Theory that streamlines roughly follow the bed such that we can assume the pressure distribution is hydrostatic
What is a flood wave?
Non symmetric where advancing front is normally steeper than the receding tail
What is a rating curve?
A fixed and constant relationship between river level (stage) and discharge is required at a gauging station.
What does a stage- discharge relationship look like? With receding tail and advancing front
A loop
What is average velocity taken as?
60% of the depth
What is the mean section method?
Q=∑Vidi∆bi
What is stage?
The water level in reference to chosen height
What are the difference stages?
- Visual
- Float
- Pressure Sensor
- Electrical Resistance
What are the different discharge?
- Flowmeters - propellor acoustic doppler
- Weirs, flumes and orificies
- Floats
- Dilution
What is the dilution?
Dye released at upstream point and measured at downstream point (theory used to estimate V then Q
What is a float used?
Released and is timed over a set distance to estimate V
What is quickflow?
The rapid component of catchment runoff that occurs in response to rainfall
What is baseflow?
the slow component of catchment runoff that occurs in response rainfall. Baseflow is usually a results of groundwater discharge to a stream
What is recession?
The decline in streamflow that occurs after the passage of a flow peak
What is a hydrograph?
A graph of discharge vs time - usually continuous
What direction does water flow?
In the direction of decreasing energy
What is St Venant equation?
Dynamic Wave equation
What are the assumptions of St Venant?
- Pressure and inertial forces are not important
- Gravity and friction forces balance
- Basically: Water Surface (y) is parallel to bed
What is the rational method?
estimating peak discharges for small drainage areas in which no significant flood storage appears.
What is runoff typical mean?
Overland flow but may be simply a ‘lumped’ fast response which can include piped interflow as well as overland flow
What are the key catchment characteristics that can influence hydrograph response?
- Length to width ratio
- Length : Width ratio
- Slope
- Land use types
- Soil Type
What type of hydrograph does a storm moving downcatchment towards the recording point produce?
A more pronounced peak in the hydrograph - flashy response
What type of hydrograph does a storm moving upcatchment towards the recording point produce?
Streched hydrograph less flashy
What type of hydrograph does a steep profile result in?
Flashy response
Fast response
What type of hydrograph does a slower profile result in?
Sluggish response
Less peaky hydrograph
Slower response
What is a isochrones?
Contours of equal travel time to outlet
What is time of concentration?
Travel time from the most remote point in the catchment to the outlet
What are the rainfall run-off estimation?
- Simplest method: Rational Method
- Unit Hydrograph Method
- Runoff routing modelling
- Physics based modelling
What is the rational method used to calculate?
Used to estimate the peak flow of design ARI from an average rainfall intensity of the same ARI
How are run off coefficients obtained?
From gauged catchment for different ARI
Steps:
1. A corresponding design storm intensity is obtained from IDF curve for the area
2. A Corresponding Qy determined from a flood frequency analysis of relevant discharge data.
What do the IDF curves show?
show that I decreases as duration increases (so we want shortest time whole catchment contributes)
How is tc estimated?
tc = 58L/A^(0.1)*Se^(0.2)
When is the rational method used?
In ungauged catchments where we do not know Cy from data
What is master baseflow curve method?
Requires a good set of historical hydrograph data for a given catchment
What is the straightline method?
straight line drawn from the point at which direct runoff begins (B) to the intersection with the recession limb.
Fixed base method?
surface runoff is assumed to end a fixed time (N) after the hydrograph peak
Variable slope method?
the baseflow curve before the surface runoff begin is extrapolated forward to the time of peak discharge
The baseflow curve after sruface runoff ceases is then extrapolated backward to the time of the point of inflection on the recession limb
What is the formula for constant loss method?
∑Q∆t = A ∑ (Ri - ø) ∆t
Does direct run off component include abstractions and losses?
No. Abstractions and losses are terms used to described the rainfall which ends up infiltrating into the ground or removed from the catchment through evapotranspiration
What is a T hour unit hydrograph?
A T-hour unit hydrograph is defined as the hydrograph resulting from unit depth of surface runoff (i.e. 1mm evenly over catchment area) produced by a storm of uniform intensity and duration of T hours
provides a relationship between excess or effective rainfall and direct runoff hydrograph
What are the assumptions of T hour unit hydrographs?
- Excess rainfall & effective runoff only
- Catchment responds linearly
- Superposition - many storms can be added to produce complex catchment response
- Catchment response is time invariant
What does the Application of TUH require?
- A design storm
- Estimation of losses or abstractions to determine excess rainfall resulting from the storm
- The TUH to be then used to generate a direct runoff hydrograph due to the storm
- An estimate of baseflow to add to the TUH estimate of the direct runoff hydrograph at the design point
What are the steps for calculating a T hour unit hydrograph?
A. A hydrograph of stream flow at a catchment outlet is examined to identify single peak flows
B. These are then matched with individual storms from a hyetograph for the catchment
C. Separate baseflow from hydrograph –> direct runoff hydrograph
D. Calculate volume of direct runoff (∑Qi∆ti)
E. Divide runoff volume by catchment area to obtain equivalent depth
F. Assuming constant loss rate (ø index), determine duration of excess rain, T, from hyetograph
G. Divided runoff hydrograph ordiantes by excess rain depth –> runoff hydrograph from unit (1mm) excess rain
How is an average TUH determined?
By averaging the TUH by averaging the peaks and the times to peak and then shaping the average by eye
What is convolution?
The application of the TUH to multi-period storm
What is deconvolution?
The process of deriving the TUH when we have a multi period storm
When will a TUH graph be bumpy?
if our UH is not sufficiently larger in duration than T, the linear combination used to generate the response to a multi-period storm will be bumpy
Is a unit hydrograph lagged by the same time interval that the TUH ordinates are in?
No, it is lagged by the duration of the excess runoff
What happens to baseflow when you are deriving a TUH and a hydrograph for a design storm?
Base flow is initially removed to obtained a direct runoff value and then once the direct run off hydrograph values have been obtained, base flow must be added back into
What happens when there is no discharge data to produce a SUH?
- Given the catchment area we can determine the volume of direct runoff a Unit Hydrograph ( = area (m^2) x 0.001m)
- We will assume the Unit Hydrograph has the shape of a triangle
- Now area is just hb/2 so we can estimate one of these we can create our synthetic unitgraph
What are the advantages of the TUH method?
- Simply measure of catchment effects on rainfall excess
- Gives reasonable flood estimate (design) when applied correctly
- Synthetic unit hydrograph can be constructed where no hydrological data is available
What are the disadvantages of the TUH method?
- Not suitable for nonlinear catchments
- Unreliable if spatial distribution of excess rainfall not uniform
- Derivation from complex multi-period storms is difficult
What is muskingham method?
t
How is storage calculated for channel routing problems?
S = K (xI + (1-x)O)
What value must C1 + C2 + C3 equal?
1
What is level pool routing?
the part of hydrology that relates to direct runoff and how it moves through surface water flow paths
Is the water balance equation applied in continuous or discrete form? and why?
In discrete form
Because most hydrological data is collected as such
What is flood routing?
The calculation of a flood hydrograph at the outlet of a water body given the inflow hydrograph at the inlet of the same water body
What is translation?
Change in time that the flood peak occurs
What is attenuation?
Attenuation is the reduction in magnitude of flood peak
What happens to a flood going from location A to location B?
The flood wave becomes stretched due to friction and gravity as it moves from the inflow point, through the storage to the outflow point. Its peak is attenuated and translated.
What is point storage routing?
typically deep and wide. Water surface is considered to be horizontal as it pools behind the outlet.
What is the unique storage function?
S = f(O)
O = CWh^(3/2)
S = Ah
O = CW (S/A)^(3/2)
where C is the weir coefficient
W = the width of the spillway
h = height above spillway
What is the lumped system routing?
Based solely on the principle of mass water balance
How are the three variables of the mass balance equation determined?
- mass balance equation ODE
- constitutive relationship between O and S. This may be available as an algebraic equation or as a table or graph
- the inflow hydrograph usually tabular form
What are the two methods for lumped system routing application?
- Euler Explicits
- Midpoint Method
When using the reservoir spillway example with inflows and outflows plotted, where do they cross over? (point storage)
Intersection of I(t) and O(t) must coincide with the maximum in O(t) aka at peak outflow
When does the maximum storage occur for point storage?
When O(t) = I (t)
When does the maximum storage occur for level pool routing storage?
Maximum S corresponds to Max O and cuves cross at max O
What is the linear reservoir method?
Storage and outflow are linearly related:
O = ßS where ß [s-1]
What is the process for obtaining a linear analytical solution?
Find S = Ah
Find O term
When is the trapezoidal method used?
In natural reseroirs, there is no convenient explicit relationship between the depth above the spill level and storage so we used the trapezoidal method to calculate the storage volume elevation relationship
What are the steps for flood routing?
- Define the catchment boundary
- Define internal sub catchment boundaries. Sub catchments are typically based on the junctions in the stream network and are ideally the same size
- Catchment nodes are placed at a point in each sub catchment that either represents i) for a case where a stream is present - the point on the stream whihch is closest to the centroid of the sub-catchment or ii) where a stream is not present the approximate centroid of the sub catchment
- Nodes are placed on the stream at each subcatchment outlet. Placement is typically at stream junctions where appropriate
- Links are drawn between upstream and downstream nodes
- Links in which we need to perform routing are identified and labelled with triangles
In lumped system channel routing is S a unique function of O
No. but it can be assumed to have an average relationship
In channel routing , where does inflows and outflow curves intersect?
They intersect at the point of maximum storage which occurs before the peak Q
What is muskingham river assumption?
The storage is a linear function of I, O and can be thought of as comprising of a wedge and prism component. The river reach between our two sections is assumed to have a relatively uniform cross section
What is muskingham method?
Storage, S, is a function of both O and I Assumes stage (water depth) is proportional to discharge, Q = V.A
Wedge storage = fraction of L.(Au/s - Ad/s) = xL (I-O)/v
Prism storage = L.Ad/s = L.O/v
How is K determined for muskingham method?
By eye with it being the slope of the line of best fit
What is a common error of the muskingham method?
Routed inflow decreases initially.
The initial dip usually contributes to an overprediction of the peak magnitude which is not a bad thing for design purposes.
In the absence of hydrograph data, what can K be approximated to be?
K = L/c
where L is the channel length
and c is avearge speed of celerity
What is the equation for calculating x?
x = 0.5 [ 1- Q ave/(Bave.s.L.c)
where Qave is the discharge along the reach
Bve is the average channel width along the reach
s is the average bedslope along the channel
L is the length of the reach
c is the average speed of flood peak h
What is the average recurrence interval?
An annual maximum event has an ARI of T years if, on average, its magnitude is equaled or exceeded once every T years
What is annual exceedance probability?
The probability that the event is equaled or exceeded in any one year.
AEP = 1/ARI = 1/T
What is the aim of streamflow statistics? And what can it be used to do?
to correlate the magnitude of streamflow events to their frequency of occurence.
It can be used to predict the magnitude of extreme events with average recurrence intervals (ARI) that exceed the period of record (not recommended for ARI > 100 years)
It can be used to identify the magnitdue of streamflow for a prescribed reccurence interval
When can a continuous probability function be used?
for a very large set of observations, we could reduce the class size
what does PDF stand for?
Probability density distribution
What is the probability that an annual maximum flow equals or exceeds X is given by?
P(Q≥X) = ∫ p(Q)dQ
What is the probability that an annual maximum flow is less than X is given by?
F(X) = 1- P(X)
What direction is negative skewed?
To the right
What direction is positive skewed?
To the left
What are the three main approaches that exist to fit our chosen distribution to our data?
- Plotting position method
- Method of moments
- Method of maximum likelihood
What is the chi squared test?
A statistical test used to test the goodness of fit
What is the plotting position method?
Using an approximate probability graph (Q vs F) to produce for the different distributions.
The data should plot as a straight line if it obeys the corresponding probability distribution
What is plotting position method? and when is it used?
P(X) = r/N
When there is a very large set of observations, N
where r is the rank where rank 1st is highest flow
What is a weakness of the plotting position method?
The smallest flow with rank N has 100% chance of being equalled or exceeded, that is the smallest flow that can occur - simply not true)
What is the Weibull Formula? and when is it used?
AEP = r/(N+1)
when N isnt too large
What is Gringorten formula and when is it used?
AEP = r - alpha /(N+1 - 2*alpha)
It gives a better indication of AEP
alpha = 0.44
What are the steps for plotting method?
- List flow in descending order and rank from 1 - N
- Estimate P(Q≥X) for each X using e.g. Gringrten
- Calculate complement F = P (Q<X)
- Plot on desired probability paper and fit straight line
- Use fitted line to interpolate and extrapoloage data
What is the method of moments equation?
F (X) = exp ( -e ^ (-b(X-a)) )
where a = µ- lamda/b where lambda = 0.5772
where b = PI / (2.4495 s^2)
What is the probability of a 1 in T flood being exceeded at least once in the next N years?
P (Q ≥ X at least one in N years) = 1 - [1 - 1/T]^N
What is central tendency?
the mean µ is the expected value of X itself and is a measure of the centre point of X
This is the first moment of X about the origin
What are statistics?
The parameters which characterise or summarise the population
What is variability?
The expected distance from the mean is given by the second moment about the mean
What is symmetry?
The skew of the distribution is measured by the third moment about the mean
Lambda is the coefficient of skewness
Why do we fit PDFs?
If we know the PDF for our random variable X we can accurately determine probabilities as well as make predictions about the probability of the occurrence of events that are outside the scope of the original sample
How is the standard normal variate z calculated?
z = (x-µ) / sigma
What is the null hypothesis generally state?
The data is adequately predicted by the fitted distribution
What do the variables ni and ei mean in the chi squared test?
ni = observed number in interval i ei = expected number in interval i
What is the critical value of the chi squared test?
X ^2 (1-alpha, v)
where alpha is the level of significance
v is the degree of freedom
If the test value is less than the critical value do we accept of reject the null hypothesis?
We accept the null hypothesis
