After Mid Sem Notes Flashcards
1
Q
Why is a water table not flat?
A
Because it varies spatially due to topographic effects, spatial variation, permeability and bed rock topography
2
Q
What is the capillary fringe?
A
The area above a water table with decreasing saturation
3
Q
What forms where topography intersects the water table?
A
Wetlands, waterways and groundwater windows
4
Q
What is water potential? and what happens in response to water potential?
A
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
5
Q
What is the energy of water equation?
A
ø = øv + øp +øg
6
Q
What is hydraulic head equal to?
A
the sum of the pressure head and the elevation head
7
Q
What does a piezometric well measure?
A
A point measurement of pressure (screened over a short interval only)
8
Q
What is Darcy’s Law?
A
Q = - Ks A ∆H/∆x
9
Q
What is storativity equal?
A
S = bSs
10
Q
What is transmissivity?
A
T = bKs
11
Q
What is interception loss?
A
Precipitation that is stored and then evaporated due to its interaction with vegetation
12
Q
What is interception store?
A
Precipitation that is retained on vegetation and therefore prevented from contributing to runoff
13
Q
What is throughfall?
A
The rain that passes through a vegetation canopy, including water that drips from leaves
14
Q
What is stemflow/trunkflow?
A
water that originates as precipitatio that travels down tree trunks or plant stems
15
Q
What is hortonian runoff?
A
Soil has saturated from rainfall and excess rain moves downslope to the stream as overland flow
16
Q
What is rejected recharge?
A
Saturation overland flow
17
Q
What are the four situations where overland flow may arise?
A
- 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
18
Q
What is transmission loss?
A
The loss of water from streamflow when water infiltrates into the streambed or floodplain.
19
Q
What enchances downslope pathways?
A
Macropores
20
Q
What is shallow water theory?
A
Theory that streamlines roughly follow the bed such that we can assume the pressure distribution is hydrostatic
21
Q
What is a flood wave?
A
Non symmetric where advancing front is normally steeper than the receding tail
22
Q
What is a rating curve?
A
A fixed and constant relationship between river level (stage) and discharge is required at a gauging station.
23
Q
What does a stage- discharge relationship look like? With receding tail and advancing front
A
A loop
24
Q
What is average velocity taken as?
A
60% of the depth
25
What is the mean section method?
Q=∑Vidi∆bi
26
What is stage?
The water level in reference to chosen height
27
What are the difference stages?
1. Visual
2. Float
3. Pressure Sensor
4. Electrical Resistance
28
What are the different discharge?
1. Flowmeters - propellor acoustic doppler
2. Weirs, flumes and orificies
3. Floats
4. Dilution
29
What is the dilution?
Dye released at upstream point and measured at downstream point (theory used to estimate V then Q
30
What is a float used?
Released and is timed over a set distance to estimate V
31
What is quickflow?
The rapid component of catchment runoff that occurs in response to rainfall
32
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
33
What is recession?
The decline in streamflow that occurs after the passage of a flow peak
34
What is a hydrograph?
A graph of discharge vs time - usually continuous
35
What direction does water flow?
In the direction of decreasing energy
36
What is St Venant equation?
Dynamic Wave equation
37
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
38
What is the rational method?
estimating peak discharges for small drainage areas in which no significant flood storage appears.
39
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
40
What are the key catchment characteristics that can influence hydrograph response?
- Length to width ratio
- Length : Width ratio
- Slope
- Land use types
- Soil Type
41
What type of hydrograph does a storm moving downcatchment towards the recording point produce?
A more pronounced peak in the hydrograph - flashy response
42
What type of hydrograph does a storm moving upcatchment towards the recording point produce?
Streched hydrograph less flashy
43
What type of hydrograph does a steep profile result in?
Flashy response
| Fast response
44
What type of hydrograph does a slower profile result in?
Sluggish response
Less peaky hydrograph
Slower response
45
What is a isochrones?
Contours of equal travel time to outlet
46
What is time of concentration?
Travel time from the most remote point in the catchment to the outlet
47
What are the rainfall run-off estimation?
1. Simplest method: Rational Method
2. Unit Hydrograph Method
3. Runoff routing modelling
4. Physics based modelling
48
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
49
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.
50
What do the IDF curves show?
show that I decreases as duration increases (so we want shortest time whole catchment contributes)
51
How is tc estimated?
tc = 58L/A^(0.1)*Se^(0.2)
52
When is the rational method used?
In ungauged catchments where we do not know Cy from data
53
What is master baseflow curve method?
Requires a good set of historical hydrograph data for a given catchment
54
What is the straightline method?
straight line drawn from the point at which direct runoff begins (B) to the intersection with the recession limb.
55
Fixed base method?
surface runoff is assumed to end a fixed time (N) after the hydrograph peak
56
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
57
What is the formula for constant loss method?
∑Q∆t = A ∑ (Ri - ø) ∆t
58
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
59
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
60
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
61
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
62
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
63
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
64
What is convolution?
The application of the TUH to multi-period storm
65
What is deconvolution?
The process of deriving the TUH when we have a multi period storm
66
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
67
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
68
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
69
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
70
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
71
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
72
What is muskingham method?
t
73
How is storage calculated for channel routing problems?
S = K (xI + (1-x)O)
74
What value must C1 + C2 + C3 equal?
1
75
What is level pool routing?
the part of hydrology that relates to direct runoff and how it moves through surface water flow paths
76
Is the water balance equation applied in continuous or discrete form? and why?
In discrete form
| Because most hydrological data is collected as such
77
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
78
What is translation?
Change in time that the flood peak occurs
79
What is attenuation?
Attenuation is the reduction in magnitude of flood peak
80
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.
81
What is point storage routing?
typically deep and wide. Water surface is considered to be horizontal as it pools behind the outlet.
82
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
83
What is the lumped system routing?
Based solely on the principle of mass water balance
84
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
85
What are the two methods for lumped system routing application?
- Euler Explicits
| - Midpoint Method
86
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
87
When does the maximum storage occur for point storage?
When O(t) = I (t)
88
When does the maximum storage occur for level pool routing storage?
Maximum S corresponds to Max O and cuves cross at max O
89
What is the linear reservoir method?
Storage and outflow are linearly related:
| O = ßS where ß [s-1]
90
What is the process for obtaining a linear analytical solution?
Find S = Ah
| Find O term
91
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
92
What are the steps for flood routing?
1. Define the catchment boundary
2. Define internal sub catchment boundaries. Sub catchments are typically based on the junctions in the stream network and are ideally the same size
3. 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
4. Nodes are placed on the stream at each subcatchment outlet. Placement is typically at stream junctions where appropriate
5. Links are drawn between upstream and downstream nodes
6. Links in which we need to perform routing are identified and labelled with triangles
93
In lumped system channel routing is S a unique function of O
No. but it can be assumed to have an average relationship
94
In channel routing , where does inflows and outflow curves intersect?
They intersect at the point of maximum storage which occurs before the peak Q
95
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
96
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
97
How is K determined for muskingham method?
By eye with it being the slope of the line of best fit
98
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.
99
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
100
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
101
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
102
What is annual exceedance probability?
The probability that the event is equaled or exceeded in any one year.
AEP = 1/ARI = 1/T
103
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
104
When can a continuous probability function be used?
for a very large set of observations, we could reduce the class size
105
what does PDF stand for?
Probability density distribution
106
What is the probability that an annual maximum flow equals or exceeds X is given by?
P(Q≥X) = ∫ p(Q)dQ
107
What is the probability that an annual maximum flow is less than X is given by?
F(X) = 1- P(X)
108
What direction is negative skewed?
To the right
109
What direction is positive skewed?
To the left
110
What are the three main approaches that exist to fit our chosen distribution to our data?
1. Plotting position method
2. Method of moments
3. Method of maximum likelihood
111
What is the chi squared test?
A statistical test used to test the goodness of fit
112
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
113
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
114
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)
115
What is the Weibull Formula? and when is it used?
AEP = r/(N+1)
when N isnt too large
116
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
117
What are the steps for plotting method?
1. List flow in descending order and rank from 1 - N
2. Estimate P(Q≥X) for each X using e.g. Gringrten
3. Calculate complement F = P (Q
118
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)
119
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
120
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
121
What are statistics?
The parameters which characterise or summarise the population
122
What is variability?
The expected distance from the mean is given by the second moment about the mean
123
What is symmetry?
The skew of the distribution is measured by the third moment about the mean
Lambda is the coefficient of skewness
124
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
125
How is the standard normal variate z calculated?
z = (x-µ) / sigma
126
What is the null hypothesis generally state?
The data is adequately predicted by the fitted distribution
127
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
```
128
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
129
If the test value is less than the critical value do we accept of reject the null hypothesis?
We accept the null hypothesis
