Transcript DISCHARGE RATING VERIFICATION

INTRODUCTION TO
DISCHARGE RATING
CURVES
‘Hydrographic Basics’ Training
May 2011
What is a ‘Control’?
“The physical element or
combination of elements that
controls the stage-discharge
relation”
‘Natural’ Controls
‘Natural’ Controls
Stable and sensitive
control
Control enhanced to
improve sensitivity
‘Natural’ Controls
Broad and insensitive
Control
Unstable control
‘Artificial’ Controls – Thin Plate
Weirs
‘V’-Notch
Cipolletti
‘Artificial’ Controls–Compound
Weirs
Sharp crested
compound
gauging weir with
dividing walls
between notches
Sharp crested
compound gauging weir
without dividing walls
Sharp crested compound
gauging weir with aeration
piers between notches
‘Artificial’ Controls–Compound
Weirs
Sharp crested
compound gauging
weir with dividing
walls between
notches
Horizontal Crump
(triangular) compound
gauging weir with
dividing walls between
notches
‘Artifical’ Controls – Parshall Flumes
Weir and Flume Combination
Sharp crest/Hydro flume combination gauging weir
Low Flow Control – ‘Drowning’
Formulae for Weir and Flume Design:
What is a Discharge Rating?
• Discharge Rating is a function of the downstream
•
•
•
•
•
physical features of the stream – i.e. the ‘control’
Relates gauge height (i.e. stage) and discharge (i.e.
flow)
Allows discharge to be estimated at any gauge height
Non-linear at some gauge heights (e.g. backwater
effects, hysteresis)
Required constant verification – over a wide range of
gauge heights
Can be estimated from mathematical formulae
(normally for ‘man-made’ structures such as weirs &
flumes)
Discharge Curve
Example
Sydney Water Hydrometric Services
8
6
Sydney Water Hydrometric Services
06/08/1986
06/08/1986
06/08/1986
06/08/1986
07/08/1986
07/08/1986
06/08/1986
06/08/1986
3
06/08/1986
06/08/1986
2.75
4
2
0
0
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
50000
100000
150000
200000
141 - Stream Discharge in Megalitres/Day
250000
170 - Sewage Effluent Level in Metres
100 - Stream Water Level in Metres
10
HYGPLOT V111 Output 10/10/2006
212260
KOWMUNG RIVER AT CEDAR FORD
Gaugings from 06/08/1986 to 07/08/1986
Rating Table 14.02 M14 10/04/1992 to Present
2.25
2
1.75
1.25
1
29
295
293
294
292
31
291
30
32
209
26
27
210
212
211
193
213
214
28
112
173
138
139
110
109
140
147
26/07/1977
05/05/2005
05/05/2005
05/05/2005
05/05/2005
26/07/1977
05/05/2005
26/07/1977
26/07/1977
08/11/2000
10/06/1977
10/06/1977
08/11/2000
08/11/2000
08/11/2000
14/11/1996
08/11/2000
08/11/2000
10/06/1977
06/10/1988
16/05/1996
20/09/1995
20/09/1995
06/10/1988
06/10/1988
20/09/1995
20/09/1995
146
141
142
143
145
144
20/09/1995
20/09/1995
20/09/1995
20/09/1995
20/09/1995
20/09/1995
3
249
278
216
250
80
195
43
217
6
251
280
44
5
1
218
77
38
277
35
40
36
41
76
06/05/1977
23/01/2002
08/06/2004
08/11/2000
23/01/2002
23/10/1980
14/11/1996
15/12/1977
08/11/2000
06/05/1977
23/01/2002
08/06/2004
15/12/1977
06/05/1977
06/05/1977
08/11/2000
23/10/1980
26/07/1977
08/06/2004
26/07/1977
26/07/1967
26/07/1977
26/07/1977
23/10/1980
0.75
0.25
0
HYGPLOT V111 Output 10/10/2006
802105
NGR S/M AT ROBERTS AVENUE
Gaugings from 26/07/1967 to 30/06/2006
Rating Table 2.01 M2 01/01/1991 to Present
100
82
81
79
85
4
75
151
174
150
23/10/1980
23/10/1980
23/10/1980
23/10/1980
06/05/1977
23/10/1980
20/09/1995
16/05/1996
20/09/1995
267
15
227
19
311
296
18
297
307
310
306
268
309
308
298
21
300
299
305
22
31/05/2003
16/05/1977
08/11/2000
18/05/1977
21/06/2005
05/05/2005
18/05/1977
05/05/2005
21/06/2005
21/06/2005
21/06/2005
31/05/2003
21/06/2005
21/06/2005
05/05/2005
18/05/1977
05/05/2005
05/05/2005
05/05/2005
18/05/1977
301 05/05/2005
302 05/05/2005
114 22/05/1991
304 05/05/2005
113 22/05/1991
303 05/05/2005
17 18/05/1977
159 20/09/1995
189 27/06/1996
158 20/09/1995
127 28/06/1991
198 27/11/1997
126 28/06/1991
106
208
242
103
102
270
95
104
96
99
101
271
98
97
272
24
58
314
25
60
274
275
312
289
313
273
23
59
105
165
164
166
167
168
19/02/1981
25/05/2000
16/11/2000
19/02/1981
19/02/1981
31/05/2003
19/02/1981
19/02/1981
19/02/1981
19/02/1981
19/02/1981
31/05/2003
19/02/1981
19/02/1981
31/05/2003
20/06/1977
06/10/1978
30/11/2005
63
55
67
64
66
65
56
68
243
244
54
129
246
245
06/10/1978
05/01/1978
06/10/1978
06/10/1978
06/10/1978
06/10/1978
05/01/1978
06/10/1978
16/11/2000
16/11/2000
05/01/1978
10/02/1992
16/11/2000
16/11/2000
248
247
128
16/11/2000
16/11/2000
10/02/1992
53 05/01/1978
262 04/02/2002
261 04/02/2002
163 26/09/1995
260 04/02/2002
259 04/02/2002
258 04/02/2002
256 04/02/2002
257 04/02/2002
162
20/06/1977
06/10/1978
31/05/2003
31/05/2003
30/11/2005
02/10/2004
30/11/2005
31/05/2003
20/06/1977
06/10/1978
19/02/1981
23/10/1995
23/10/1995
23/10/1995
23/10/1995
23/10/1995
200
300
400
844 - Sewer Discharge in Megalitres/Day
26/09/1995
164 gaugings
could not be labelled.
500
Why Do We Need Gaugings?
• Shifting and changes to control
• Changes in downstream channel physical features (e.g.
vegetation)
• Backwater effects
• Channel bank instability
• Channel scouring
Continuity Equation
Q=A*V
Where:
Q = Discharge (flow)
A = Cross-sectional area
V = Mean Velocity
Rating Verification
Various Gauging Methods
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•
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•
•
Volumetric
Wading
Boat
Float
Bridge
Cableway – manned
Cableway – un-manned
Dyes (e.g. rhodamine)
Chemicals (e.g. sodium chloride)
Rating Curve Derivation
General Equation Method
• Mathematical Formulae
• Limited to ‘special design’ controls (e.g.: V-
•
notch, broad crested rectangular weirs)
Not suitable for complex control structures
(e.g.: natural controls)
Rating Curve Derivation
Linear Plot Method
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Gauge Height (GH) plotted on vertical axis
Discharge (flow) plotted on horizontal axis
Parabolic curve concave ‘downwards’
Low, medium and high flow curves plotted
Effects of irregular stream cross-sections
Linear Curve
(Example)
Sydney Water Hydrometric Services
100 - Stream Water Level in Metres
10
HYGPLOT V111 Output 10/10/2006
212260
KOWMUNG RIVER AT CEDAR FORD
Gaugings from 06/08/1986 to 07/08/1986
Rating Table 14.02 M14 10/04/1992 to Present
8
6
06/08/1986
06/08/1986
06/08/1986
06/08/1986
07/08/1986
07/08/1986
06/08/1986
06/08/1986
06/08/1986
06/08/1986
4
2
0
0
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
07/08/1986
50000
100000
150000
200000
141 - Stream Discharge in Megalitres/Day
250000
Linear Curve Method
Advantages
• Allows hydrographer to quickly identify changes
•
•
in stream discharge rating
Downstream effects on rating easily identified
Identifies different control effects throughout
flow range
Linear Curve Method
Disadvantages
• Rating curve extensions not easily undertaken
Rating Curve Derivation
Logarithmic Plot Method
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‘Gauge Height’ minus ‘Cease to Flow’ value plotted on vertical axis
Discharge (flow) plotted on horizontal axis
Plotted on log-log paper
Discharge curve plots as a ‘straight line’
Natural streams – logarithmic curve rarely a straight line over
entire flow range (e.g.: irregular cross-sections, downstream
features, ‘overbank’ flow)
• A number of ‘change points’ evident
Rating Curve Derivation
Determination of CTF
Include Velocity Head
Flow
Gauge Pool
Deepest
Point on
Control
Logarithmic Curve Method
Advantages
• Facilitates an ‘easy’ method of curve extension (for
BOTH low and high flow regimes)
• Gauging deviation from curve easily identified (straight
line analysis)
• Highlights changes in stream cross-section and control
changes throughout flow range (change points)
Logarithmic Curve Method
Disadvantages
• Gauge Height scale too open in LOW flow
•
regime
Gauge Height scale too compressed in HIGH
flow regime
Rating Curve Development
•Determine ‘Cease to Flow’ point
•Minimum of 10-12 ‘well spaced’ gaugings required
•Plot gaugings to BOTH linear and logarithmic curves
•Rising GH gaugings plot to the ‘right’ of the curve, falling gaugings tend to
plot to the ‘left’ of the curve
•Compute gaugings on site (if >5% deviation from current curve, second
gauging should be taken at an alternate section of the stream)
•Determine ‘Period of Applicability’
•Cross-sections at control, orifice and cableway required immediately AFTER floods
•Regular gauging required over a ‘wide’ range of Gauge Heights
•Ongoing monitoring of site required (i.e.: visual observation, gauging, survey)
Rating table changes and re-issues should be approved by a
suitably qualified and experienced person
Rating Curve Extrapolation
(When?)
• Required when range required for computation is
•
outside range of ‘gauged’ flows
Likely causes are: - control change
- scouring of bed
- backwater effects
- change in downstream stream
geometry
Rating Curve Extrapolation
(How?)
• Recommended that more than one method
•
used
Main methods are: -
Logarithmic extension
Gauge Height - Velocity
Stevens Method (A√d)
Manning's Formula
Logarithmic Method
• A rating curve plotted on log-log coordinates will plot as
a straight line
Q = K (GH - ctf)↑n
Where Q = discharge
K = a constant
GH = Gauge Height
ctf = Cease to flow GH
n = a function of the shape of the cross-section
Typical Log - Log Graph Paper
Logarithmic Method
(Example)
Logarithmic Method
·
·
Depth
above
CTF
Change Point 2
·
Change Point 1
··
·
·
Discharge
= gauging
Log-Log showing breakpoints at
weir notch and floodplain
Logarithmic Method
•If the log-log extension exceeds the maximum
measured flow by approximately 20%, other
methods such as Mannings or velocity – area
should be used.
Velocity - Area Method
• Based on ‘Continuity Equation’
Q=AV
Where Q = Discharge
A = Cross-sectional area
V = Mean velocity
• Requires an accurate cross-section surveyed up to the highest gauge
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•
•
•
•
•
height required for the rating extension
Area can be plotted against gauge height and an area for any gauge
height can be determined
Mean velocity of the stream is derived directly from gauging results
(provided gaugings are taken at the prime gauge section)
The mean velocity is plotted against the gauge height
At higher stages the rate of increase in the velocity through the
measurement section will diminish rapidly.
The Gauge height-Velocity curve is then extended to the desired stage
Discharge then computed from product of Area and Velocity
Graphical Representation of
Velocity-Area Extension
Stevens (or A√d ) Method
•
Requires an accurate cross-section
•
Should not be used where ‘over-bank’ flow conditions exist
•
Has little value for extrapolation of curve to cover lower flow regime
•
Based on an adaption of ‘Chezy’s Formula’
Q = KA√d
Where
Q = Discharge
K = a constant
A = Cross-sectional area (from cross-section)
d = mean depth at cross-section (area / width)
•
‘Q’ and ‘GH’ are each plotted against A*√d (straight line which is extended)
•
This will plot as a straight line which can be extended to extrapolate discharge
above maximum recorded GH
Stevens (or A√d ) Method
(continued)
MANNINGS FORMULA
•
•
•
Requires an accurate cross-section
Should not be used where ‘overbank’ flow conditions exist
Based on Manning's Formula:
Q = A (r↑0.6667) √s
n
Where
•
Q = Discharge
A = Cross-sectional area (from cross-section)
r = hydraulic radius (area/wetted perimeter)
s = slope
n = Manning’s n*
As √s becomes constant at higher gauge heights, the formula becomes:
n
V = k(r↑0.6667)
Where:
V = Mean velocity
k = constant
r = hydraulic radius (area/wetted perimeter)
* Can range from 0.010 (smooth concrete banks) to 0.035 (weedy banks)
Mannings Formula
(continued)
• As ‘r’ can be computed from cross-sections, ‘V’
can be taken from the GH-Velocity curve, ‘k’
can be computed from the above equation
• When ‘k’ is plotted against GH the curve should
reach a constant value at higher stages
• This straight line portion may be extended to
give the value of ‘k’
Manning’s Formula
(continued)
•Straight reach of channel should be at least 60m in length, free of
rapids, abrupt falls and sudden contractions and expansions
•Slope is determined by dividing the difference in water surface level
at the start and finish of the reach by the length of the reach
•Hydraulic radius is the area of the cross-section divided by the wetted
perimeter
•The Mannings co-efficient of roughness is dependent on characteristics of
channel and can be derived from following table:
Type of Channel
Manning ‘n’ Value
Clean and straight with no deep pools
0.030
As above with more stones and weeds
0.035
Some deep pools
0.040
Questions?