Tiêu chuẩn iso 01100 2 2010

ISO TC 113/SC 1 Reference number ISO 1100 2 2010(E) © ISO 2010 INTERNATIONAL STANDARD ISO 1100 2 Third edition 2010 12 01 Hydrometry — Measurement of liquid flow in open channels — Part 2 Determinatio[.]

General

The stage-discharge relationship, also known as a rating curve or rating, represents the connection between water stage and discharge at a gauging station Understanding this relationship is essential for accurate flow measurement and river management The principles governing the establishment and operation of gauging stations are outlined in ISO 1100-1, ensuring standardized procedures and reliable data collection.

Copyright International Organization for Standardization

Controls

The stage-discharge relationship at a gauging station is influenced by channel conditions downstream from the gauge, known as controls, which can be of two types: section control controlling low flows and channel control controlling high flows, with medium flows potentially governed by either Understanding the specific channel features that influence these controls is essential for accurate development of stage-discharge curves, especially when multiple controls occur or conditions change over time Accurate interpolation and extrapolation of measurements are critical, particularly when controls are temporary and prone to shift, causing changes in the stage-discharge relationship segments.

A section control is a specific cross-section of a stream channel located downstream from a water-level gauge, crucial for controlling the relationship between gauge height and discharge It can be a natural feature, such as a rock ledge or gravel bar, or a man-made structure like a small dam, weir, flume, or overflow spillway Visually, section controls are often identifiable in the field by observing a riffle or a pronounced drop in the water surface as the flow passes over it As flow increases and gauge height rises, the section control may become submerged, eliminating its influence on water discharge regulation; at this point, flow is instead controlled by downstream features or the overall hydraulic geometry and roughness of the channel.

Channel control refers to a combination of features—such as size, shape, curvature, slope, and roughness—that influence flow behavior at and downstream from a gauge The length of the reach that controls the stage-discharge relationship varies depending on channel characteristics; for example, a steep channel may be controlled by a shorter reach, while a flat channel might require a longer reach Additionally, the required control reach length depends on flow magnitude, and precise determination of this length is often unnecessary or impractical.

Stage-discharge relationships can be governed by a combination of section and channel controls, particularly within short transition zones where the control shifts from section to channel influence These transition zones are characterized by changes in the slope or shape of the stage-discharge curve and typically occur over limited stages along the rating curve Sometimes, a combination control involves multiple section controls exerting partial influence, though instances with more than two controls are rare These complex control zones usually can be accurately identified through plotting procedures, aiding in precise hydraulic analysis and flood management.

Governing hydraulic equations

Stage-discharge relationships are crucial hydraulic functions that depend on the type of control present Section controls, whether natural or artificial, are governed by weir or flume equations, which are essential for understanding flow behavior In their simplest form, these equations describe how the water stage relates to discharge, providing a fundamental basis for hydraulic modeling and flood management.

Q is the discharge, in cubic metres per second;

C D is a coefficient of discharge and includes several factors;

B is the cross-sectional width, in metres;

H is the hydraulic head, in metres; β is a power-law exponent, dependent on the cross-sectional shape of the control section

Stage-discharge relationships for channel controls with uniform flow are primarily determined by the Manning or Chezy equations, which relate flow characteristics to channel properties These equations apply to the reach of the controlling channel downstream from a gauge, enabling accurate prediction of flow rates based on water surface elevation The Manning equation, in particular, is widely used to quantify flow velocity and discharge in natural and engineered channels with uniform flow conditions Understanding these relationships is essential for river management, hydraulic modeling, and flood risk assessment.

A is the cross-sectional area, in square metres; r h is the hydraulic radius, in metres;

S f is the friction slope; n is the channel roughness

Q = CAr h 0,5 S f 0,5 (3) where C is the Chezy form of roughness

For steady or quasi-steady flows, the standard equations are generally applicable; however, in the case of highly unsteady flows like tidal or dam-break scenarios, the Saint-Venant unsteady-flow equations are required Despite their importance, these unsteady-flow equations are rarely used in developing stage-discharge relationships and are not addressed in this section of ISO 1100.

Complexities of stage-discharge relationships

Stage-discharge relationships for stable controls like rock outcrops, weirs, flumes, and small dams are straightforward to calibrate with proper maintenance However, challenges increase with unstable controls or variable backwater conditions, as segments of the stage-discharge relationship may shift temporarily or frequently These temporary shifts are common and can be managed effectively using the shifting-control method to ensure accurate discharge measurements.

Variable backwater significantly impacts the stage-discharge relationship in both stable and unstable channels Key sources of backwater include downstream reservoirs, tributaries, tides, vegetation, ice, dams, and other obstructions that affect flow conditions at the gauging station Understanding these backwater influences is essential for accurate flow measurement and hydraulic analysis.

Hysteresis, also known as loop rating curves, is a complex phenomenon in certain streams caused by rapid changes in water surface slope during quickly rising or falling water levels in a channel-control reach This effect is most noticeable in streams with relatively flat slopes, where the water surface slope on rising stages becomes significantly steeper than during steady-flow conditions, leading to increased discharge Recognizing hysteresis is essential for accurate streamflow measurement and management, especially in flood-prone or variable flow environments.

5 indicated by the steady-flow rating curve The reverse is true for falling stages See 5.8.3 for details of hysteresis rating curves

Flooding complexity arises when rivers are in flood, making it challenging to accurately define flood-plain storage and model flow patterns in the flood-plain rating curve The intricate interactions between the main channel and floodplain during flood events often lead to complex flow behaviors that are difficult to measure and represent accurately at specific sections.

5 Stage-discharge calibration of a gauging station

General

A stage-discharge gauging station's primary purpose is to record the flow of water in open channels or rivers by measuring water levels and converting these into discharge values using a stage-discharge relationship This relationship correlates water level (stage) with flow rate and is calibrated through direct measurements of discharge and corresponding water levels In some cases, additional parameters like index velocity or rate-of-change in stage between gauges can enhance the accuracy of calibration, guided by standards such as ISO 9123 and ISO 15769 The calibration process may also incorporate theoretical computations to shape and position the rating curve effectively Historical stage-discharge data should be considered to improve and refine the accuracy of current relationships.

Preparation of a stage-discharge relationship

The stage-discharge relationship is established by plotting discharge measurements against corresponding stage observations, considering whether the flow is steady, increasing, or decreasing, and noting the rate of stage change This can be performed manually on paper or automatically with computerized plotting tools Both arithmetic and logarithmic scales may be used, each offering specific advantages and disadvantages Typically, stage is plotted on the ordinate and discharge on the abscissa, but when deriving discharge from stage measurements, the stage is treated as the independent variable.

To ensure an accurate plotting stage versus discharge relationship, it is essential to prepare a comprehensive list of discharge measurements, verifying that the recorded stages are linked to a common datum and that discharge calculations are precise Typically, at least 15 measurements taken throughout the analysis period should be included, with additional data needed for complex rating curves involving multiple channels or extreme stage variations The measurements must be well distributed across the full range of gauge heights, incorporating low and high flow measurements to help accurately define and extrapolate the rating curve Including extreme low and high measurements, whenever possible, enhances the reliability of the discharge versus stage relationship.

Each discharge measurement should include a unique identification number, the date of measurement, and the gauge height at the time of measurement The recorded data must also specify the total discharge and specify the measurement's accuracy as determined by the hydrographer Incorporating these details ensures precise and reliable flow data essential for hydrological analysis and decision-making.

While additional measurements can be included, they are not compulsory Table 1 presents a typical list of discharge measurements, highlighting several items beyond the essential mandatory ones, to provide a comprehensive overview of the data collection process.

Table 1 — Typical list of discharge measurements made by a hydrographer using current meters and depth soundings

ID number Date (yy/mm/dd) Made by Width Area Mean velocity Gauge height Effective depth Discharge Method

Number of vertic als Gauge height change Rated m m 2 m/s m m m 3 /s m/h

MEF GTC AJB GMP HFR MAF MAF MAF MAF MAF MAF MAF MAF MAF MAJ MAF

GOOD GOOD POOR GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD GOOD

NOTE Discharge measurements made with acoustic Doppler current profilers require additional parameters, including the number of transects and the range of discharges measured during the transects (see ISO/TS 24154)

A straightforward plotting approach involves using an arithmetically divided scale, ensuring scale subdivisions encompass the full range of gauge height and discharge at the site Scales should feature uniform, easy-to-read, and interpolatable increments Selecting an appropriate scale is crucial to generate a rating curve that avoids being excessively steep or flat For large variations in gauge height or discharge, plotting the rating curve in multiple segments—such as low, medium, and high water—can improve readability and precision This segmented approach helps accurately represent the water conditions across different flow regimes.

Graph paper with arithmetic scales is user-friendly and easy to read, making it ideal for displaying rating curves and allowing zero values of gauge height or discharge to be plotted, unlike logarithmic scales However, for analytical purposes, arithmetic scales offer limited advantages, as stage-discharge relationships typically form curved, downwardly concave lines that are difficult to accurately plot with few data points Logarithmic scales provide significant analytical benefits by simplifying the shape of stage-discharge curves, as detailed in section 5.2.4 Therefore, it is recommended to initially plot the stage-discharge relationship on logarithmic paper for analysis and curve shaping, then transfer it to arithmetic paper for presentation if needed, enhancing accuracy and clarity.

X discharge, Q, in cubic metres per second

NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1

Figure 1 — Arithmetic plot of stage-discharge relationship

Logarithmic plotting is the most effective method for analyzing stage-discharge relationships, especially for specific segments To optimize this analysis, gauge height should be converted to the effective depth of flow by subtracting the zero discharge gauge height, resulting in a straight-line plot for a given control, as described in section 5.2.5.3 The slope of this line reflects the type of control (e.g., section or channel), aiding in accurate shape calibration of the rating curve This approach enables the calibration of stage-discharge relationships with fewer discharge measurements, as the slope—measured as the ratio of horizontal to vertical distance—is a crucial parameter, with discharge always plotted on the x-axis.

Rating curves for weirs and flumes follow Equation (1) in section 4.3 and display a logarithmic slope of 1.5 or higher, influenced by control shape, approach velocity, and minor variations in the discharge coefficient Most weir shapes produce logarithmic rating curves with slopes of 2 or greater, indicating a consistent relationship between flow and head However, the sharp-crested rectangular weir is an exception, with its logarithmic plot exhibiting a slope slightly greater than 2.

Rating curves for channel controls, described by Equation (2) or (3), typically have a slope between 1.5 and 2 when plotted as effective depth versus discharge Variations in the slope of these rating curves occur due to changes in roughness and friction slope as the water depth varies, affecting flow characteristics.

The control sections described in 5.2.2 to 5.2.4 apply to regular-shaped sections such as triangular, trapezoidal, and parabolic Significant changes in control shape, like transitioning from a trapezoidal section to a control with a small V-notch for extremely low water, result in a noticeable change in the rating-curve slope Similarly, shifting from section control to channel control causes a change in the slope of the logarithmic plot These transitions are characterized by short curved segments on the rating curve, which are crucial for accurate calibration, maintenance, and analysis of the rating curve Understanding the type and shape of control allows analysts to define the hydraulic shape of the rating curve more precisely, facilitating accurate extrapolation and identifying when extrapolation might lead to increased uncertainty.

Figure 2 illustrates how different channel and section controls influence the rating curve's shape and slope In Figure 2a, a trapezoidal channel with no floodplain and channel-control conditions produces a straight-line rating curve with a slope less than 2 when plotted with an effective gauge height of zero flow Figure 2b shows the addition of a floodplain, which also acts as a channel control, causing a change in the rating curve's shape above the bankfull stage; when re-plotted with the correct zero-flow gauge height, its slope remains less than 2 Figure 2c introduces a section control for low flow, altering the rating curve's shape; notably, the slope for the low-water segment often exceeds 2, reflecting a different flow-control mechanism.

Figure 3 presents a logarithmic plot of an observed rating curve based on measurements from Table 1, illustrating flow behavior in a stream with continuous section control across all flow ranges, including high-flow conditions The effective gauge height at zero flow (e) is 0.6 meters and is subtracted from gauge height measurements to determine the effective flow depth at control points The slope of the rating curve below 1.4 meters is approximately 4.3, indicating a section control consistent with the flow characteristics, while above 1.5 meters, the slope decreases to 2.8, reflecting a change in control shape The shift in slope around 1.5 meters results from a transition in the control cross-section's geometry—from a triangular shape below 1.4 meters to a trapezoidal form between 1.4 and 1.5 meters, and then a trapezoidal control shape above 1.5 meters.

The examples in Figures 2 and 3 demonstrate key principles of logarithmic plotting, which analysts should employ extensively However, it is important to recognize that certain sites may present exceptions or variations, requiring analysts to adapt these principles accordingly for accurate data interpretation.

9 a) Trapezoidal channel with no flood plain and with channel-control conditions b) Flood plain added c) Section control for low flow added Key

1 channel control (no flood plain, no section control) 4 flood plain 7 channel control

2 channel-control rating curve 5 flood-plain rating curve 8 section control

3 channel control (no section control) 6 transition curve

Figure 2 — Relationship of the channel and control properties to the rating-curve shape

(the left-hand drawing in each pair shows the channel shape, the right-hand drawing the rating-curve shape)

NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1

Figure 3 — Logarithmic plot of stage-discharge relationship

5.2.5.2 Gauge height of zero flow

The zero flow gauge height, also known as the cease-to-flow (CTF) value, is measured at the lowest point in the control cross-section of a section control In natural channels, this value can be determined by measuring the flow depth at the deepest part of the control section and then subtracting the combined velocity head from the gauge height at the time of measurement Accurate determination of the zero flow gauge height is essential for flow measurement and hydraulic analysis.

The effective gauge height of zero flow is the value, subtracted from mean gauge heights of discharge measurements, that causes the logarithmic rating curve to appear as a straight line, and it should be determined for each rating-curve segment For controls with regular shapes, this value is close to the actual gauge height of zero flow, but a more precise determination can be achieved using a trial-and-error plotting method By assuming a value and plotting measurements accordingly, if the curve appears concave upward, a larger value is needed; if it appears concave downward, a smaller value should be used Typically, only a few trials are necessary to find the effective gauge height of zero flow, also known as the logarithmic-scale offset.

The equation for a rating curve that plots as a straight line on logarithmic plotting paper is:

Curve fitting

The stage-discharge relationship curve-fitting process involves drawing, positioning, and shaping the rating curve to accurately represent flow data Hydraulic analysis and line-fitting tools assist in developing the rating curve, but final calibration measurements must be reflected in the curve It is essential that the rating curve remains hydraulically correct, recognizing that not all calibration measurements will fit perfectly due to shifting control conditions The curve-fitting process should produce a curve shape that adapts to control changes, ensuring reliable and accurate stage-discharge data for hydrological assessments.

Stage-discharge relationships are defined through hydraulic equations, including Equations (1), (2), and (3) When section control is present, the weir equation (Equation 1) is used to calculate rating-curve points accurately Discharge coefficients (C_D) are established in international standards for specific weir and flume types, enabling precise hydraulic-based rating curve computations For natural section controls like rock outcrops or gravel bars, the discharge coefficient can be estimated through calibration measurements Cross-section widths and depths are determined from surveyed data of the control section to ensure accurate stage-discharge modeling.

The shape of the rating curve in channel segments influenced by control can be defined using Equation (2) or Equation (3) Key channel characteristics, such as cross-sectional area and hydraulic radius, are determined from surveys of typical cross-sections in the control reach Field observations provide estimates for Manning's roughness coefficient, n, or the Chezy coefficient, C The friction slope is derived from channel surveys, maps, or calibration measurements Using these parameters, Equation (2) or (3) allows calculation of discharge at selected gauge heights to establish the rating curve, assuming steady, uniform flow For more complex, non-uniform flow conditions, advanced backwater curve analysis techniques and computer programs are available for detailed assessment.

The rating curve for both section and channel control is initially computed using hydraulic equations to define its hydraulic shape However, the accurate position of the rating curve is determined through calibration measurements, ensuring precise flow assessments This calibration process also helps identify when new measurements indicate a shift in the rating curve's position, maintaining reliable flow monitoring and control.

The stage-discharge relationship is established through mathematical methods like regression analysis and maximum-likelihood techniques, ensuring accurate flow predictions When dealing with complex channel geometries, multiple equations may be necessary to accurately define the rating curve Special attention should be paid to segment transitions to maintain the reliability of the data It is essential that the shape of the rating curve aligns hydraulically with the channel conditions to ensure precise discharge estimations.

Combination-control stage-discharge relationships

Combination-control rating curves, also known as compound-control rating curves, involve two section controls that govern different flow segments, such as a rock riffle controlling low flows and a downstream cross-section controlling medium flows when the riffle becomes submerged The resulting rating curve often shows a change in slope, indicating a shift in the effective gauge height at zero flow as control transitions between sections A transition curve typically appears between these segments, representing partial control from both sections Effective analysis requires separate logarithmic plots for each segment to accurately identify straight-line relationships and compute the slope, which is generally greater than 2 for each segment.

A compound rating curve combines section control for low flows with channel control for medium to high flows, providing a comprehensive flow measurement model Graphical analysis involves creating separate plots for the section-control and channel-control segments, with a transition curve illustrating the flow range where partial control occurs from both methods For optimal analysis, the slope of the section-control segment should be greater than 2, while the slope of the channel-control segment should be less than 2, ensuring clear differentiation between flow regimes This approach enhances accuracy in flow measurement and river discharge assessments.

A compound rating curve combines multiple channel controls to accurately represent flow conditions across different stages Typically, it includes a control for medium and high flows, and a separate control when water overflows the banks The transition between these segments reflects the shift from channel-controlled flow to floodplain-controlled flow, where vegetation and floodplain geometry influence the stage-discharge relationship As water levels rise, floodplain effects become dominant, causing the rating curve to change slope, which remains less than 2 when re-plotted with an effective gauge height of zero flow.

Stable stage-discharge relationships

A stable stage-discharge relationship remains consistent over time, indicating steady channel and control conditions In natural channels, this stability is a relative concept, as they are often affected by scour, sediment deposition, and vegetation growth, which can cause changes in the relationship Despite these natural variations, a stable relationship signifies reliable predictions of flow based on water stage measurements.

For stable channels and controls, the stage-discharge relationship is typically characterized by fitting a curve to calibration measurements, ensuring accurate flow estimation An example illustrated in Figure 3 demonstrates a stable stage-discharge relationship at a natural rock outcrop, which remains unchanged over time However, shifts in this rating curve can occur due to debris accumulation on the control, potentially affecting flow measurements and requiring periodic reevaluation.

Unstable stage-discharge relationships

Unstable stage-discharge relationships are characterized by frequent shifts and changes in position These variations are driven by evolving channel geometry and friction properties, which influence the control characteristics over time Such fluctuations are most prominent during floods, ice formation, or periods of vegetative growth Additionally, scour and deposition of sediment can alter the bed and bank materials, causing the rating curve to shift periodically Vegetation, including weeds and trees, can also impact the stage-discharge relationship during specific times of the year, contributing to the instability of the relationship.

In unstable channels and control conditions, it is often impossible to accurately define all variations of the rating curve solely through discharge measurements Therefore, shifting-control techniques are essential for estimating the position of the rating curve during periods between measurements These methods help ensure reliable flow measurements when continuous data collection is not feasible, as detailed in section 5.7.

For gauging stations with unstable channel conditions, installing a weir or flume can be an effective solution to stabilize the rating curve When variable backwater causes instability, combining a velocity index gauge with a stage gauge is a common method to accurately define the rating curve, utilizing acoustic velocity meters mounted on the streambed or channel side to measure index velocity, as detailed in ISO 15769 Additional methods for unstable rating curves include the stage-fall method with two stage gauges, the electromagnetic method using a full-channel-width coil, and the ultrasonic method, which are described in ISO 9123, ISO 9213, and ISO 6416, respectively.

Shifting controls

Shifting controls happen when channel conditions are unstable, causing discharge measurements taken at different times to represent different positions of the rating curve To accurately define the stage-discharge relationship during such periods, frequent discharge measurements are necessary to capture the magnitude and timing of shifts However, if measurements are infrequent, a reasonable estimate of the stage-discharge relationship can still be achieved by combining available discharge data with an understanding of shifting-control behavior, ensuring reliable flow assessments even under changing conditions.

When discharge measurements show a shift in the rating curve, it is essential to determine whether the shift is temporary or permanent If the change is expected to last several months or longer, creating a new rating curve is recommended For temporary shifts likely to change soon, a temporary shift curve should be used to define discharge during the shift period until new data indicates another change Relying on experience and knowledge of each control is the best approach to assess whether rating-curve shifts are temporary or permanent.

Shift curves typically resemble the original rating curve, emphasizing the importance of accurately establishing the base rating curve based on stream hydraulics Changes such as scour or deposition at a natural section control alter the gauge height at zero flow, often producing a shift curve parallel to the original when plotted on arithmetic paper, with a consistent gauge height difference across the stage range When plotted on logarithmic paper, deposition shifts the curve upward and makes it concave upward, while scour causes the curve to lie below the original and appear concave downward, reflecting the impact of bed changes on flow measurement accuracy.

Table 2 and Figure 4 illustrate the application of shift curves, with measurements 366 to 368 and 372 to 375 from Table 1 representing distinct hydrological events The data indicate a +0.05 shift from the lower end of the base rating curve during a weed growth or sediment deposition period between August 21 and November 26, 1973, and a -0.06 shift during channel scour between July 10 and November 11, 1974 Measurements 369 to 371, taken between these periods, show no shift in the transition zone, confirming that the shifts are specific to the identified events These measurements define the shift curves, and detailed hydrographic analysis of stage and discharge data will determine the exact timing of deposition, weed growth, and scour events.

Table 2 — List of discharge measurements modified from Table 1

(yyyy/mm/dd) Effective depth m Discharge m 3 /s

NOTE The effective depths of measurements 366 to 368 were modified to represent deposition in the stream channel and the effective depths of measurements 372 to 375 were modified to represent channel scour

NOTE 1 The upper shift curve (measurements 366 to 368) represents deposition in the channel section that controls the lower segment of the relationship (measurements 367 to 368)

NOTE 2 The lower shift curve (measurements 372 to 375) represents scour of the channel section that controls the lower segment of the relationship

Figure 4 — Logarithmic plot of a stage-discharge relationship and shift curves representing changes in the stage-discharge relationship

For streams with continuous flow variations, shifting the rating curve requires defining shift curves based on discharge measurements, gauge height zero flow determinations, and hydraulic properties, then adjusting these curves over time Such adjustments can be uniform, proportional, or abrupt depending on specific control changes, like debris deposits, which may cause sudden shifts detectable through gauge height records If no clear cause is identifiable, gradual shifts—such as seasonal growth of aquatic vegetation—are assumed, leading to time-based adjustments of the shift curve This approach ensures accurate flow measurements and effective stream gauge calibration under varying conditions.

Shifting-control procedures are complex and often difficult to interpret, as multiple logical explanations or interpretations may exist Experience with a specific stream is essential for understanding shift characteristics and conducting accurate analysis, ensuring safe and efficient operations.

Variable-backwater effects

Variable backwater conditions in the downstream reaches of a stream can lead to apparent changes in the stage-discharge relationship by causing control submergence or partial submergence These conditions complicate the analysis of stage-discharge relationships, requiring more advanced methods to accurately model flow dynamics Understanding how backwater effects influence stream stages is essential for precise hydrological assessments and flood management strategies.

Variable backwater can result from downstream influences such as reservoirs or tributary streams, from ice, from vegetation growth or from dynamic conditions known as hysteresis

Downstream conditions can sometimes cause water levels to rise sufficiently to submerge channel controls, impairing their effectiveness in defining stage-discharge relationships A downstream reservoir filling enough to submerge the control or tributary inflows entering below or within the control reach can create backwater effects that hinder accurate flow measurement Additionally, obstructions such as beaver dams or other channel blockages downstream may lead to partial submergence, invalidating the stage-discharge relationship and affecting flow data accuracy.

For certain short-duration and infrequent downstream backwater conditions, shifting-control methods provide an effective approach for analyzing discharge records A graphical plot of the stage record can help determine the extent and magnitude of backwater by estimating the non-backwater stage during backwater events This method offers a practical solution for assessing backwater effects in hydrological studies.

For significant and sustained variable-backwater conditions, analyzing discharge records requires specialized methods Typically, a stage gauge coupled with an auxiliary index velocity gauge is used Index velocity is commonly measured using acoustic velocity meters based on Doppler principles, which determine flow velocity in specific segments of the channel By combining measurements of stage and index velocity, an accurate discharge relationship can be established This approach is thoroughly detailed in ISO 15769, ensuring reliable flow measurement under complex backwater conditions.

Various approaches for flow measurement include the stage-fall method, ultrasonic technique, electromagnetic full-channel-width coil method, and one-dimensional unsteady-flow models These methods are standardized and detailed in ISO 9123, ISO 6416, ISO 9213, and ISO/TR 11627, ensuring accurate and reliable flow measurement across different applications.

5.8.3 Hysteresis effects, or loop rating curves

The stage-discharge relationship at a gauging station indicates the normal or steady-flow discharge for a specific water stage Discharge during rising stages may exceed the normal flow, while during falling stages, it can be lower due to variations in water surface slope This phenomenon, known as hysteresis or a loop rating curve, is most evident in mildly sloped rivers where dynamic flow conditions caused by passing flood waves influence discharge readings.

In sites where the hysteresis effect is significant, instantaneous discharge values based on steady-state rating curves can substantially deviate from the true discharge To improve accuracy, auxiliary equipment may be necessary to complement gauge height records Methods such as a twin-gauge approach utilizing the stage-fall-discharge relationship (ISO 9123) or an unsteady-flow model (ISO/TR 11627) can be employed Alternatively, in certain cases, the use of a velocity index relationship (ISO 15769) provides a practical solution for more precise discharge measurement.

When hysteresis effects are moderate and require correction, a single-gauge stage record combined with the rate of change in the stage can be used to estimate flow discharge accurately Under specific conditions, it is possible to calculate the true discharge (Q) of unsteady flow from the steady-state discharge (Qo) using an appropriate mathematical equation, enhancing the precision of flow measurements.

S o is the water surface slope corresponding to steady, non-uniform flow;

V w is the velocity of the flood wave; d d h t is the rate of change of the stage with time

The slope, S o , can be determined from observation of gauges during conditions of steady flow Alternatively, it can be computed approximately from Manning's or Chezy's equation

The rate of change of the stage, dh/dt, can be obtained from the recorded observations of the stage at the gauge

The wave velocity, V w , is given by the equation: w d 1 d d d

A is the cross-sectional area;

B is the surface width at the cross-section; d d

Q h can be approximated from the stage-discharge relationship

The conditions described are applicable when the stream's rise and fall occur gradually, allowing the acceleration head and velocity head to be neglected due to minimal changes in velocity It is also important that the flow velocity remains low to ensure the velocity head can be safely ignored With a sufficient number of discharge measurements, a gauging site can be calibrated using a family of curves by evaluating the combined parameter 1/(S₀ Vw), simplifying the analysis and improving accuracy.

Extrapolation of the stage-discharge relationship

A stage-discharge relationship should only be applied within the range of measurements it is based on When flow estimates are needed outside this range, careful extrapolation of the rating curve is necessary, ideally using methods that accurately define its shape and position Before extrapolating, it is essential to thoroughly inspect the channel and control areas upstream and downstream of the gauge, noting any obstructions, contractions, expansions, debris, or changes in channel shape If abnormal channel conditions cannot be accounted for, extrapolating the rating curve is not recommended.

The logarithmic plotting method is a straightforward approach for extrapolating rating curves, but it requires a solid understanding of control conditions and plotting techniques to avoid significant errors To ensure accuracy, the effective gauge height scale should be chosen so that the rating curve appears as a straight line, especially in the portion requiring extrapolation Knowing whether the control is a section or a channel, and understanding the control shape across the extrapolation range, are crucial for proper application When the control shape remains consistent and channel roughness is stable, linear extrapolation of the logarithmic plot is appropriate, particularly for medium and high flows under channel-control conditions However, this method should not be used to extrapolate beyond approximately 1.5 times the highest measured discharge, and special caution is needed when estimating flows below the lowest measurement For very low flows with section control, understanding the control shape and the gauge height of zero flow is essential; plotting on arithmetic paper can facilitate accurate determination of zero flow gauge height, especially when extrapolating the rating curve to zero discharge.

The stage-discharge relationship can often be described using the weir, Manning, or Chezy equations, which are applicable above or below measured discharges through cross-section surveys, high-water marks, and estimates of roughness and discharge coefficients Accurate application requires careful consideration when the cross-section shape varies significantly, as friction slope may also change notably Additionally, during overbank flow, the friction slope for flows exceeding bankfull conditions can differ substantially from that during in-bank flow, impacting flow calculations and flood predictions.

Estimates of high discharges can sometimes be made that will aid in the extrapolation of the high end of a stage-discharge relationship The slope-area method is one such technique (see ISO 1070) Another method can be used when another gauging site exists on the same stream, either upstream or downstream By careful accounting of additions, withdrawals and channel storage, the peak discharge can be estimated for the site where an extrapolation is required

The velocity-area method is used to extrapolate a rating curve by establishing a stage-area relationship from cross-sectional surveys and a stage-velocity relationship within the measured range While accurate where discharge measurements are available, estimating the stage-velocity relationship above the highest measured stage is challenging, making extrapolation less reliable Consequently, this method is generally considered inferior to techniques based on Manning’s or Chezy’s equations, which offer more precise flow estimations.

One effective method for estimating discharge at higher water stages is utilizing one-dimensional flow models, as outlined in ISO/TR 11627 These models can leverage parameters derived from measurements at lower stages, providing a practical approach for flow prediction However, it's important to recognize that one-dimensional flow models share limitations with traditional hydraulic equations, especially when the river cross-sectional shape experiences significant changes, potentially affecting the accuracy of discharge estimates at higher stages.

It is advisable to utilize at least two different methods for extrapolating data whenever possible, as this allows for comparison of results and enhances the reliability of the extrapolated section of the rating curve Combining multiple approaches improves confidence in the accuracy of the extrapolated data, ensuring more dependable and precise hydrological assessments.

6 Methods of testing stage-discharge relationships

Regularly verify the stage-discharge relationship at least six times per year through check discharge measurements, ensuring accuracy and reliability The frequency and timing of these measurements should be tailored based on factors like the stability of the rating curve, hydrological events such as floods, and any indications of changes in the rating curve During critical periods like floods or droughts, additional measurements are recommended to minimize the need for extrapolation and to assess the impact of backwater or hysteresis effects If a discharge measurement significantly deviates from the expected rating curve or previous readings, an immediate follow-up measurement is essential to confirm the data's accuracy.

When a check discharge measurement plot falls within a small percentage of the rating curve, it is assumed that the existing rating curve remains valid, and no correction is necessary The acceptable deviation percentage is typically determined by the measurement's uncertainty, as outlined in ISO 748, which details the calculation of discharge measurement uncertainty This approach ensures accurate water flow assessments while maintaining the integrity of the rating curve when deviations are within acceptable limits.

5 % uncertainty, then shifting-control techniques will not be employed unless a check measurement plots further than 5 % from the rating curve

A key approach involves performing a statistical analysis of the rating curve to determine the dispersion, typically using the standard deviation of measurements around the curve When multiple measurements show deviations exceeding two standard deviations, a shift curve or a new rating curve is established to improve accuracy Standard deviations are generally calculated separately for each segment of the rating curve, ensuring precise assessment of measurement variability.

A bias check is conducted to identify periods when the rating curve may have shifted, even if check measurements fall within the acceptable uncertainty or within two standard deviations of the discharge measurement For example, multiple measurements that are within 5% of the rating curve, yet all lie consistently on the same side, can indicate potential bias Several statistical tests are employed to detect such biases and ensure the accuracy of flow measurements.

Understanding the underlying reasons for the plot of stage-discharge relationships is essential during testing and analysis Without this insight, there is a risk of misapplying or misinterpreting statistical tests Analysts must consider changes in stream characteristics and base their decisions on hydraulic principles rather than solely relying on statistical results, ensuring accurate and meaningful interpretations.

7 Uncertainty in the stage-discharge relationship

General

This clause presents the theoretical background and statistical equations essential for estimating uncertainties in the stage-discharge relationship and daily mean discharge It provides practical numerical examples demonstrating how to apply these procedures to assess the accuracy of stage-discharge estimates Detailed calculations and examples are included in Annex A to facilitate understanding and implementation of uncertainty estimation methods.

Assess the uncertainty in a single discharge measurement following ISO 748, with calculations based on ISO 5168 to ensure accuracy Evaluate the uncertainty in the stage-discharge relationship and continuous discharge measurements using the principles outlined in this clause, which adhere to the guidelines specified in ISO/TR 7066-1 Proper uncertainty assessment is essential for reliable flow measurement and data integrity.

Definition of uncertainty

ISO/TS 25377 establishes standardized concepts, terminology, and methods for assessing the uncertainty of hydrometric measurements, ensuring consistency and accuracy in data analysis This technical specification clarifies distinctions in terminology from previous ISO 1100 editions, emphasizing precise communication in measurement practices Uncertainty, as defined by ISO/TS 25377, is a parameter related to measurement results that characterizes the likely dispersion of possible values, reflecting the precision and reliability of the measurement process.

Uncertainty in measurement is quantified using parameters such as standard deviation or a specified multiple of the standard deviation, with the standard uncertainty defined as "uncertainty expressed as a standard deviation." Expanded uncertainty provides an interval around the measurement result that is expected to include a large portion of the possible values attributed to the measurand, calculated by multiplying the standard uncertainty by a coverage factor, k, typically ranging from 2 to 3 The level of confidence indicates the probability that the true value lies within this interval, with coverage factors of 1, 2, and 3 corresponding approximately to confidence levels of 68%, 95%, and 99.8%, assuming a normal distribution.

The expanded uncertainty and level of confidence are not to be confused with the statistical quantities

“confidence interval” and “confidence level” These quantities are computed using statistical procedures and assumptions that do not always apply to the uncertainty of flow measurement In particular, the term

“confidence level” should not be used, but rather the term “level of confidence”

Previous editions of ISO 1100 referred to the "uncertainty" as expanded relative uncertainty with a coverage factor of 2, while also using the terms "standard error" and "standard deviation" to describe standard uncertainty.

Statistical analysis of the stage-discharge relationship

Uncertainty analysis in hydrology involves comparing concurrent discharge and gauge height measurements, known as gaugings, with discharge values derived from the stage-discharge relationship at corresponding gauge heights This process determines uncertainty through statistical analysis of measurement scatter around the rating curve Since the stage-discharge relationship is a line of best fit, it generally provides a more accurate estimate than individual gaugings The relationship's equation is calculated as described in section 5.2.5.3, assuming it plots as a straight line on logarithmic paper If necessary, the rating curve should be segmented into sections that can be accurately approximated by straight lines on logarithmic paper, ensuring precise discharge estimations.

It is recommended that several current meters be used to establish the stage-discharge relationship to avoid systematic bias in the relationship

Uncertainties in stage-discharge rating curves are conceptually similar to the standard errors used in regression analysis within statistical theory However, while regression theory relies solely on curve-fitting via the least-squares method, stage-discharge relationships are typically developed through hydraulic reasoning combined with mathematical fitting techniques Therefore, the term "uncertainty" is preferred over "standard error" to better reflect the broader scope and practical considerations involved in these relationships.

The uncertainty in the overall rating-curve relationship is characterized by the standard error of estimate (S), which reflects the dispersion of stage-discharge data around the curve This measure, also known as the standard deviation of residuals, is used to quantify the confidence in discharge values derived from the rating curve The uncertainty for a specific discharge value, u(Q c(h)), is calculated based on this standard error When multiple straight-line segments are present in the stage-discharge relationship, this process is repeated for each segment to ensure accurate assessment of uncertainty across the entire curve.

The standard error of estimate, S, is calculated from the following equation:

Q c is the corresponding discharge calculated from the rating-curve equation or rating-curve table;

N is the number of gaugings in the rating-curve segment; p is the number of rating-curve parameters estimated from the N gaugings

The value of p reflects the number of parameters adjusted to fit the rating curve to gauging data When all three parameters—Q₁, β, and e—are tuned, p equals 3 If the effective gauge height at zero flow, e, is predetermined and only Q₁ and β are adjusted, p equals 2 Conversely, when the slope β is fixed based on hydraulic principles and only Q₁ is estimated, p equals 1.

Note 2: The quantity N − p is known as the number of degrees of freedom, representing the number of effective observations that define the variability around the rating-curve relationship Specifically, it indicates how many data points contribute to establishing the scatter in the observations, with p observations being accounted for in the model This concept is essential in statistical analysis, as it influences the accuracy of the regression and the reliability of the results Understanding degrees of freedom helps in assessing the precision of the rating curve and ensures valid interpretations in hydrological and environmental studies.

“used up”, in effect, to establish the position of the rating curve

The standard uncertainty in the calculated value of lnQ c at gauge height h, u(lnQ c (h)), is found from the following equation (see ISO/TR 7066-1):

An expanded uncertainty, U(lnQ c (h)), can be calculated from:

The uncertainty in the measurement is expressed as U(lnQ_c(h)) = k ⋅ u(lnQ_c(h)), where k is a coverage factor that ensures a specified level of confidence The expanded uncertainty creates an uncertainty interval around the calculated value of lnQ_c(h), which is expected to include the majority of possible discharge values This interval is represented as lnQ_c(h) ± U(lnQ_c(h)), providing a reliable range for the measured parameter.

The uncertainties and the limits of the uncertainty interval are expressed in natural-logarithmic units The corresponding uncertainty interval for discharges is found by taking anti-logarithms:

Q h ± ≈Q h ±U Q h (11) where the approximate equality holds when U(lnQ c (h)) is small enough so that the linear approximation to the exponential holds

For the expanded uncertainty, the coverage factor (k) is typically determined using Student's t-correction based on the desired confidence level for N − p gaugings When the confidence level is set at 95%, a coverage factor of approximately 2 is used for 20 or more gaugings A coverage factor of 1 corresponds to a confidence level of about 68%, providing a practical guideline for uncertainty estimation in measurement processes.

Note 2 explains that the uncertainty interval limits are symmetrical in logarithmic units but typically not in discharge units When the natural-logarithmic uncertainties, U(lnQ c(h)), are small, they can be approximated as equal to the relative uncertainties in discharge units, providing a practical approach for assessing measurement accuracy.

The expanded uncertainty, U(lnQ_c(h)), should be calculated for each observation of (h − e) using a coverage factor k equal to 2 This results in uncertainty limits on lnQ_c(h) that form curved lines around the stage-discharge relationship, with the limits reaching their minimum at the mean value of ln(h − e) These uncertainty bounds provide a reliable measure of variability and assist in assessing the accuracy of discharge estimations Proper calculation of these limits ensures precise evaluation of measurement uncertainties, enhancing the robustness of hydrological measurements and analyses.

Note 3 highlights that the uncertainty in the calculated lnQₙ value arises from the variability in possible rating curve positions, which depends on the limited number of gaugings and their measurement accuracy This dispersion reflects the inherent variability and potential error in the gauging data used to determine flow rates, emphasizing the importance of precise and reliable measurements for accurate hydraulic analysis.

Dispersed around the rating curve with a standard error of estimate (S), it is expected that future discharge measurements will also vary similarly, which must be considered when assessing the accuracy of discharge predictions using the rating curve This inherent dispersion impacts the reliability of flow estimates, highlighting the importance of accounting for the standard error in flood forecasting and water resource management.

When the stage-discharge relationship consists of multiple straight-line segments, it is essential to calculate S and U(lnQ c (h)) separately for each segment Additionally, the appropriate degrees of freedom (N − p) should be applied to each segment to ensure accurate statistical analysis This approach ensures precise modeling and reliable interpretation of the stage-discharge data across different segments of the relationship.

It is desirable that at least 20 observations be available in each segment in order to achieve a statistically reliable estimate of S and u(lnQ c (h)).

Uncertainty of predicted discharge

The rating curve is essential for calculating discharge values based on gauge height measurements recorded at gauging stations These computed discharges serve as predictions of the actual flow that would be observed during direct gauging The difference between the predicted discharge and the true observed value is significant for practical applications, with the variability in this difference known as the uncertainty of prediction This uncertainty is represented by the standard uncertainty (u(Qp)) or the expanded uncertainty (U(Qp)), reflecting the potential dispersion around the predicted discharge.

Expanded uncertainty, or related terms involving the logarithms of discharge, reflects the range of possible measurement errors Although the predicted discharges (Qp) and the computed discharges (Qc) from the rating curve at recorded gauge heights share the same values, their interpretation differs: Qp is compared with the distribution of plausible individual observed discharges, whereas Qc is evaluated against the distribution of potential positions of the rating curve.

There are three key reasons why the predicted discharge may differ from actual measurements: changes in control conditions affecting the rating curve, measurement errors in gauged discharge, and errors in recorded gauge height The first two reasons impact the gaugings used to establish the rating-curve relationship, with their combined influence quantified by the standard error of estimate, S The third source of error pertains to inaccuracies in the recorded gauge height, which are not reflected in the initial gaugings because auxiliary reference gauges are used to verify the correct reading Assuming the rating curve is nearly linear over the relevant range and applying the logarithmic rating-curve equation, the standard uncertainty in predicted discharge resulting from gauge height measurement errors can be calculated using a specific mathematical formula.

(ln p( )) (ln( )) u Q h = ⋅β u h e− (12) where u(ln(h − e)) is the uncertainty in the effective depth

The standard uncertainty of prediction is calculated by combining the uncertainty with the standard error of estimate, denoted as S, and the uncertainty in the calculated discharge, U(lnQ c (h)) These components are integrated using root-sum-squares (RSS) to provide an accurate measure of overall prediction uncertainty, ensuring reliable and precise flow estimations.

Prediction uncertainties, including expanded uncertainty limits and relative (percentage) prediction uncertainties, are calculated using the same methods outlined in section 7.3.3 When the standard uncertainties of natural-logarithmic quantities are minimal, they directly correspond to the relative (percentage) uncertainties of the related stages and discharges, ensuring accurate and reliable measurement confidence.

At certain gauging stations with rock-ledge or well-maintained artificial controls, the standard error of estimate primarily reflects the measurement uncertainty of the gaugings used to establish the rating curve In these cases, measurement errors do not significantly impact the accuracy of predicted flows Consequently, the standard error of estimate, S², can be omitted from the calculation of prediction uncertainty, leading to more precise flow estimations.

Uncertainty in the daily mean discharge

The daily mean discharge is the most commonly required value for design and planning purposes It is calculated by averaging the discharge observations taken over a 24-hour period For example, measuring 24 instantaneous discharges at 30-minute intervals throughout the day allows for the computation of the daily mean discharge, effectively representing the flow using the rectangular rule of numerical integration of the discharge hydrograph.

The relative (percentage) standard uncertainty in the daily mean discharge is determined by calculating the discharge-weighted mean of the relative prediction uncertainties for individual discharges This approach involves using a specific equation that accounts for the variability in discharge estimates, ensuring accurate quantification of uncertainty in hydrological data Such precise assessment of discharge uncertainty is essential for improving the reliability of water resource management and hydrological modeling.

The article discusses the relative (percentage) standard uncertainties associated with daily mean discharge measurements, denoted as u r (Q dm) It also addresses the prediction uncertainties in discharge estimates derived from the rating curve, represented as u r (Q p (h)), which is equivalent to u(lnQ p (h)) as calculated in section 7.4.

Q c is the calculated value of the discharge from the rating-curve table or rating-curve equation used to calculate the daily mean discharge

The measurement structure's corresponding equation aligns with Equation (14), where \( u_r(Q_p(h)) \) represents the percentage standard prediction uncertainty of the discharge predicted from the structure rating curve This uncertainty quantifies the reliability of flow estimates derived from the rating curve, ensuring accurate hydrological assessments.

2 2 r( ) r( ) u h e u C β − + D 2 u r (C D ) being the percentage uncertainty in the coefficient of discharge for the structure

NOTE 1 The percentage uncertainty, u r (b), in the length of the crest (the width of the throat) has been neglected NOTE 2 The value of e in this case is usually zero

Uncertainty in the stage-discharge relationship and in a continuous measurement of discharge

The uncertainty in a single discharge measurement should be assessed according to ISO 5168, ensuring accuracy and reliability This annex addresses the challenges of evaluating uncertainty in the stage-discharge relationship as outlined in ISO/TR 7066-1 Additionally, it covers methods for assessing uncertainty during continuous discharge measurements to maintain consistent data quality.

A.2 Example of uncertainty calculations for individual gaugings

The standard error of estimate, S, for the rating curve can be calculated using Equation (7) outlined in section 7.3.2 By substituting the relevant values from Table A.1 and assuming the gauge height at zero flow, e, is known in advance, which results in p = 2, the calculation of S becomes straightforward This method provides an accurate measure of the prediction accuracy for the rating curve, ensuring reliable flow measurements.

The expanded uncertainty of a rating-curve segment reflects the overall measurement variability and is determined by multiplying the standard deviation (S) by a coverage factor (k) When points follow a Gaussian distribution, a coverage factor of k=2 encompasses approximately 95% of the data, indicating a high level of confidence, while k=1 covers about 68% For example, with k=2, the expanded uncertainty provides a range that encloses around 95% of the dispersed points around the fitted line.

The uncertainty \( U = 2S = 0.063 \) is measured in natural logarithm (ln) units, indicating the variability in the measurement The uncertainty limits are expressed as \( \ln Q_c \pm U \), and converting back to the original scale via anti-logs yields \( Q_c \exp(1 \pm U) \), which is approximately equal to \( Q_c \pm U Q_c \) This relationship shows that \( U \) in natural-log units can be interpreted as a relative uncertainty, representing the percentage variation relative to the rating curve value \( Q_c \) Therefore, both \( U \) and \( S \) can be expressed as percentages of the rating-curve value \( Q_c \), providing a clear understanding of the uncertainty's magnitude relative to the measured flow rate.

S = 3,16 % (68 % level of confidence) U = 6,32 % (95 % level of confidence)

In logarithmic coordinates, the equation lnQ c ± U represents two parallel straight lines positioned on either side of the rating-curve segment, separated by a distance U (which equals 2S) These lines define the confidence limits within which approximately 95% of observations are expected to fall, with an average containment of 6.3%.

When the dispersion around the fitted line is not negligible, the standard uncertainty in the calculated value of lnQ_c, denoted as u(lnQ_c(h)), can be determined for individual lnQ_c values at any stage (In(h − e)) This calculation is based on Equation (8) in section 7.3.3, ensuring accurate measurement of uncertainty when data points exhibit larger deviations from the fit.

Substituting the values for observation No 1 in Table A.1 and using a coverage factor of 2 gives the following:

= 0,0198 ln-units = 1,98 % of Q c (rounded to 2,0 % in Table A.1)

Table A.1 — Tabulated values required to calculate S

Table A.1 presents similar computations for each observation, with the percent uncertainty indicated in the last column These uncertainties can be visualized as symmetric limits around the stage-discharge curve for each observed (h − e) value Plotting these uncertainties on logarithmic paper highlights the 95% confidence interval, with the narrowest limits occurring at the mean value of In(h − e).

A.3 Example of calculating the uncertainty of the daily mean discharge

The percentage standard uncertainty for the daily mean discharge (u r (Q dm)) can be determined using Equation (14) in section 7.5 To estimate the expanded uncertainty (U r (Q dm))) at approximately 95% confidence level, the standard uncertainty is multiplied by a coverage factor (k) of 2 This approach provides a comprehensive measure of measurement uncertainty, ensuring accuracy and reliability in flow data analysis.

Therefore, the daily mean discharge = 161,815 m 3 /s ± 2,1 % (expanded uncertainty, k = 2, level of confidence approximately 95 %)

Table A.2 illustrates this calculation, using hourly values of discharge

The rating-curve exponent, β, is established at 1.530 It is assumed that the control remains highly stable, ensuring that the standard error of estimate reflects only measurement uncertainty Consequently, there is no need to include the standard error of estimate in the prediction uncertainty, simplifying the accuracy assessment of the model.

Table A.2 — Typical computation of the uncertainty in the daily mean discharge, using hourly values of the discharge

[1] ISO 1070, Liquid flow measurement in open channels — Slope-area method

[2] ISO 1088, Hydrometry — Velocity-area methods using current-meters — Collection and processing of data for determination of uncertainties in flow measurement

[3] ISO 1100-1, Measurement of liquid flow in open channels — Part 1: Establishment and operation of a gauging station

[4] ISO 1438, Hydrometry — Open channel flow measurement using thin-plate weirs

[5] ISO 3846, Hydrometry — Open channel flow measurement using rectangular broad-crested weirs

[6] ISO 3847, Liquid flow measurements in open channels by weirs and flumes — End-depth method for estimation of flow in rectangular channels with a free overfall

[7] ISO 4359, Liquid flow measurement in open channels — Rectangular, trapezoidal and U-shaped flumes

[8] ISO 4360, Hydrometry — Open channel flow measurement using triangular profile weirs

[9] ISO 4362, Hydrometric determinations — Flow measurement in open channels using structures —

[10] ISO 4369, Measurement of liquid flow in open channels — Moving-boat method

[11] ISO 4373, Hydrometry — Water level measuring devices

[12] ISO 4374, Liquid flow measurement in open channels — Round-nose horizontal broad-crested weirs

[13] ISO 4377, Hydrometric determinations — Flow measurement in open channels using structures —

[14] ISO 6416, Hydrometry — Measurement of discharge by the ultrasonic (acoustic) method

[15] ISO/TR 7066-1, Assessment of uncertainty in calibration and use of flow measurement devices — Part 1: Linear calibration relationships

[16] ISO 8333, Liquid flow measurement in open channels by weirs and flumes — V-shaped broad-crested weirs

[17] ISO 9196, Liquid flow measurement in open channels — Flow measurements under ice conditions

[18] ISO/TR 9210, Measurement of liquid flow in open channels — Measurement in meandering rivers and in streams with unstable boundaries

[19] ISO 9213, Measurement of total discharge in open channels — Electromagnetic method using a full- channel-width coil

[20] ISO 9825, Hydrometry — Field measurement of discharge in large rivers and rivers in flood

[21] ISO 9826, Measurement of liquid flow in open channels — Parshall and SANIIRI flumes

[22] ISO/TR 11627, Measurement of liquid flow in open channels — Computing stream flow using an unsteady flow model

[23] ISO/TS 25377, Hydrometric uncertainty guidance (HUG)

[24] ISO 80000-1, Quantities and units — Part 1: General

Tiêu đề	Determination of the stage-discharge relationship
Trường học	International Organization for Standardization
Chuyên ngành	Hydrometry
Thể loại	Tiêu chuẩn
Năm xuất bản	2010
Thành phố	Geneva

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Số trang	34
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