Can radar measure river discharge? Methods, uncertainty budgets and what a station can honestly report
Non-contact radar gives you river stage and surface velocity. Turning those into flow takes a surveyed channel, a calibrated coefficient and an honest uncertainty. Here is how the methods compare and how to plan for each.
A question we are often asked is: can your radar measure how much water is flowing in the river? The honest answer is: it measures two of the three things you need, and the third has to come from a survey. Understanding why helps you plan a station that gives numbers you can trust, and know how far to trust them.
What discharge is
River discharge is the volume of water passing a cross-section each second, in cubic metres per second. It is the quantity water managers, flood forecasters and reservoir operators ultimately want. It is never read directly from the water. It is computed as the sum, across the channel, of the local velocity multiplied by the local area:
Q = Σ ( v_i · A_i ) ≈ V_mean · A(h)| Ingredient | What it is | How you get it |
|---|---|---|
Water level (stage), h | How high the water is | Measured by radar |
Cross-section area, A(h) | The area of the channel filled at that level | A survey of the channel, combined with the stage |
Mean velocity, V_mean | The average speed through the cross-section | Measured by radar at the surface, then converted with a coefficient |
What non-contact radar measures
Non-contact radar methods measure river stage and surface velocity from above, without touching the water. The WMO Manual on Stream Gauging describes the motive: non-contact methods have the potential to make streamflow measurement less costly and safer, by not having instrumentation in the water or requiring personnel to be in or above it, though "cost-effective and reliable instrumentation is needed" to realise that potential [1]. The sensor stays safe during floods, which is exactly when discharge matters most and the river cannot be approached.
Pravaah does this with two radars on one controller:
- a 61 GHz FMCW radar for water level, 0 to 50 m (customisable), ±1 mm, explained in how FMCW radar measures water level
- a 24 GHz Doppler radar for surface velocity, 0.02 to 20 m/s, ±1 % of the measured velocity, explained in surface velocity radar for rivers
The two missing ingredients
1. A surveyed cross-section
The radar tells you how high the water is. To know how much water that represents you need the shape of the channel beneath it, from a survey of the bed and banks. The survey matters most at low flow. Take a trapezoidal channel with side slopes of 2:1 and a bottom width of 20 m. If the survey is wrong by 2 m in bottom width (10 %), the area error is:
| Stage | Area with 20 m bottom width | Area with 22 m bottom width | Error in area |
|---|---|---|---|
| 1 m | 22 m² | 24 m² | 9.1 % |
| 2 m | 48 m² | 52 m² | 8.3 % |
| 3 m | 78 m² | 84 m² | 7.7 % |
| 5 m | 150 m² | 160 m² | 6.7 % |
Channels also change. In hill rivers the bed scours and fills with floods, so the cross-section behind last year's stage-area relation may no longer be there. Cross-sections are surveyed with a total station or satellite positioning, with an echo sounder or a wading survey below the water line, and in some research work with ground-penetrating radar, which has been used with surface velocity radar to measure flow without touching the river [2]. Resurvey after major floods.
2. A surface-to-average velocity relationship
Radar measures the speed of the water surface. Water near the bed moves more slowly, so the mean velocity over the whole cross-section is lower than the surface speed. A coefficient converts one to the other. About 0.85 is the commonly used default and the WMO Manual uses "about 0.85" [1]. A USGS study that compared radar with conventional measurement found the mean velocity to be approximately 0.85 times the measured surface velocity, with agreement within about 5 % on two rivers [2]. A field assessment of portable surface velocity radars confirmed 0.85 as a valid default but recommended site calibration, because the right value depends on the roughness of the channel relative to its depth, and reported discharge within about 10 % for low and intermediate roughness flows when the coefficient was calibrated [3].
An uncertainty budget
Discharge uncertainty is the combination of independent terms. A realistic budget for a radar station on a well-surveyed section might be:
| Term | Illustrative size | Notes |
|---|---|---|
| Stage (level radar) | 0.2 to 1 % | Small, except at very low flow |
| Cross-section area | 3 to 5 % | Survey quality, channel changes since the survey |
| Velocity measurement | 1 to 3 % | Radar accuracy, wind, noise, installation angle |
| Velocity coefficient α | 4 to 6 % | Calibration against gaugings, change with stage |
| Single-point representativeness | 2 to 5 % | One radar sees one place on the surface; the whole width may differ |
| Combined (root sum of squares) | about 7 to 10 % |
Combining 1 % (stage), 4 % (area), 2 % (velocity), 5 % (α) and 3 % (representativeness) gives √(1² + 4² + 2² + 5² + 3²) = 7.4 %. That is respectable. It is comparable with what the WMO Manual attributes to float measurements under favourable conditions, which "may be accurate to within ±10 per cent" [1], and with the roughly 10 % found in field tests of calibrated surface-velocity radars [3]. It is not the ±1 % of the velocity specification, and presenting the smaller number as the discharge uncertainty would be wrong. Terms that are not in the budget, because they are not random, include hysteresis in unsteady flow, backwater, and bed changes during a flood. See rating curves.
How the methods compare
| Method | What it needs | Typical use | Notes |
|---|---|---|---|
| Current meter, velocity-area | A person wading or on a bridge or cableway | The reference method for gaugings | Standard for rating curves, but cannot be used safely in a flood |
| Floats | Surface floats and a measured reach | Floods and places that cannot be waded | Surface float coefficient about 0.85; WMO notes ±10 % under favourable conditions [1] |
| Acoustic Doppler profiler | A boat, a tethered float or a fixed installation | Gaugings and continuous index velocity | Needs the sensor in the water |
| Surface velocity radar plus surveyed section | A fixed or portable radar and a survey | Noncontact gaugings and continuous index velocity | Agreement within about 5 to 10 % in published field tests [2][3] |
| Rating curve from stage | Gaugings across the range, a stable control | Continuous discharge from a stage record | Cheap to run; uncertainty large at the top of the range and in unsteady flow |
None of these is best everywhere. They are used together: gaugings (by current meter, float or radar) build and check the curve or index relation, and the continuous station extends them in time.
Four levels of what a radar station can honestly report
| Level | What you report | What you need | Use |
|---|---|---|---|
| 1. Stage | Water level and rate of rise | A level radar and a reference gauge | Thresholds, alarms, trends, early warning |
| 2. Stage and surface velocity | Level and surface speed, with quality flags | Level and velocity radar | Arrival-time estimates, behaviour of the river |
| 3. Index discharge | Discharge from a velocity-stage calibration | A survey and gaugings across the range | Water accounting, reservoir operation |
| 4. Discharge with uncertainty | Discharge, a stated uncertainty band, and flags for extrapolated values | All of the above, resurvey after floods, regular gauging | Reporting and long-term records |
Most stations deliver great value at Levels 1 and 2. Moving to Levels 3 and 4 is a project: a survey, a gauging campaign, and a maintenance routine.
What you can do with level and velocity alone
You do not need a discharge figure to benefit from velocity.
- Early warning: velocity shows how quickly a rise is travelling, which helps estimate when it will arrive downstream.
- Trends: changes in level and speed over hours show how a river is behaving.
- Verification: a rising level together with rising velocity is a stronger signal than either alone.
We describe this in more detail in Why surface velocity matters as much as water level.
Planning a station that can report discharge
- Choose a site with a stable, well-defined channel and a reach where the flow is reasonably straight and free of eddies, ideally under or beside a bridge.
- Survey the cross-section at the measuring point, with a datum tied to the level radar, and record the date.
- Take reference flow measurements across a range of levels, including as high a flood as can safely be reached, to calibrate the surface-to-average relationship. Floats and radar can reach into floods that a current meter cannot [1].
- Record level and velocity continuously with a station such as Pravaah, keeping the raw readings and quality flags.
- Apply the calibration in your analysis, store each version, and report discharge with its uncertainty.
- Resurvey and re-gauge after major floods and each season.
Our team can help you plan the site. Tell us about your river and what you need the numbers for.
References
- World Meteorological Organization, Manual on Stream Gauging, Volume I: Fieldwork, WMO-No. 1044 (2010), sections 8.9 and 8.10 and the discussion of float measurement. WMO publication page.
- J. E. Costa and others, Use of radars to monitor stream discharge by noncontact methods, Water Resources Research (2006). USGS.
- Field assessment of noncontact stream gauging using portable surface velocity radars (SVR), Water Resources Research (2016). HAL.
Illustrative values (area errors, the uncertainty budget and the combined figure) are computed from the stated assumptions. They show the scale of each term and are not guaranteed performance for any site.