Report

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 • • • • • • • • • 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 • • • • • 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 • • • • • ‘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 • • • • • • 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?