Watercourse Profile

Open Watercourse Profile

Extract the long-profile along the main watercourse from GIS, CAD, spreadsheet, or DEM data; compute length, elevation drop, and four standard slope values; and feed the results directly into the Time-of-Concentration calculator. This guide covers supported data sources, file formats, the four slope methods (with a worked example for a ~20 km river reach), DEM provenance, and how to clean up real-world profile artefacts.

Overview

The Watercourse Profile tool lets you import, analyse, and characterise the longest flow path in a catchment — a river, stream, or drainage channel — for use in Time of Concentration ($T_c$) and peak-flow estimation. It accepts data from a wide range of sources including GIS packages (QGIS, ArcGIS), CAD drawings (AutoCAD, Civil3D), GPS surveys, spreadsheets, and the HydroDesign Watershed Delineation tool.

Once a profile is loaded, the tool automatically calculates the watercourse length and — when elevation data is present — computes four different slope values using industry-standard hydrological methods. Saved profiles can be linked directly to the $T_c$ Calculator so that length and slope are consistent between the geometry step and the runoff-timing step of a design-flood workflow.

Why the watercourse profile matters

Every lumped rainfall-runoff method in HydroDesign (Rational, SCS, SDF, Unit Hydrograph) uses the watercourse length L and slope S to compute $T_c$, which in turn sets the design-rainfall duration. A 20% error in slope propagates into a ~10% error in $T_c$ (via the S^0.5 or S^0.385 exponent in most formulas), and then into a ~5% error in design intensity — small, but systematic and avoidable. The profile tool exists to remove that error source.

Getting Started

1. Create a new profile from the Watercourse Profiles list page.
2. Choose your data source: upload a file, paste distance-elevation data, or select a watercourse from a saved watershed delineation.
3. Review the profile. If elevation is present, review the elevation chart, slope calculations, and basic statistics. If elevation is missing, fetch it from ESRI or enter a known slope manually.
4. Select a slope method appropriate for your catchment (see the Slope Methods section) and save the profile.
5. Link to the $T_c$ Calculator using the Use in Tc Calculator button — or, from within the $T_c$ calculator, click Link watercourse profile below the length/slope inputs.

Data Sources

The tool supports three loading modes. Pick the one that matches the artefact you have in hand.

Upload File

Drag and drop a file, or click to browse. The tool auto-detects the file format (GeoJSON, Shapefile, KML, GPX, DXF, CSV, Excel) and whether the data contains geospatial coordinates, elevation, or just chainage. Geospatial sources are plotted on the map and sampled for elevation; chainage-only data produces an elevation profile without a map overlay.

Typical sources: QGIS/ArcGIS exports, Civil3D alignment elevations, GPS track logs from field surveys, and watercourse traces drawn in Google Earth.

Paste Data

Paste distance-elevation pairs directly from a spreadsheet. The expected layout is one point per line, with tab-, comma-, or space-separated values. The first column is distance (m) and the second column is elevation (m). Lines starting with # are treated as comments.

# distance_m   elevation_m
0              1245.3
250            1243.1
500            1239.8
...

This is the fastest path when you have profile data in Excel (HEC-RAS exports, survey field sheets, 1D model stations) and no need for a geospatial context.

From Watershed Delineation

Select the longest watercourse from a saved watershed delineation — typically produced by the HydroDesign delineator from MERIT-Hydro or a user-supplied DEM. This provides watercourse geometry and length directly, but usually no elevation data because the delineator returns a 2D polyline. You can then fetch elevation from ESRI or enter slope manually.

This is the canonical starting point for catchments that have already been delineated in HydroDesign — the length is guaranteed to match the delineated drainage network.

Supported File Formats

Format	Extensions	Common sources
GeoJSON	.geojson, .json	QGIS, ArcGIS, web tools
Shapefile	.zip containing .shp	ArcGIS, QGIS, Civil3D
KML / KMZ	.kml, .kmz	Google Earth, QGIS
GPX	.gpx	GPS devices, field surveys
DXF	.dxf	AutoCAD, Civil3D, MicroStation
CSV / TSV	.csv, .tsv	Excel, Google Sheets
Excel	.xlsx	Microsoft Excel

Auto-detection

The tool automatically detects whether your data is geospatial (lat/lng coordinates) or chainage-based (distance along the watercourse). Geospatial data is displayed on a map; chainage data produces a profile chart only. If auto-detection mis-classifies your file, inspect the first few rows — most problems stem from missing headers or swapped column order.

Slope Calculation Methods

When elevation data is available, the tool reports four slope values. All are returned in m/m (dimensionless). Different methods suit different catchment shapes, and it is good practice to review all four before selecting the one you use downstream in $T_c$.

Conventional Average Slope

The simplest definition of watercourse slope: total elevation drop divided by total length.

$$S \;=\; \frac{\Delta H}{L} \;=\; \frac{Z_\text{upstream} - Z_\text{downstream}}{L}$$

Conventional average slope

Where $\Delta H$ is the elevation drop between the most upstream and most downstream points of the watercourse and $L$ is the total length. Quick and easy, but sensitive to the exact location of the start and end points — a single anomalous elevation at the headwater or outlet can bias the result significantly.

10-85 Slope ($S_{10\text{-}85}$)

The slope computed between the points at 10% and 85% of the watercourse length, measured from the downstream outlet upstream.

$$S_{10\text{-}85} \;=\; \frac{H_{85} - H_{10}}{L_{85} - L_{10}} \;=\; \frac{H_{85} - H_{10}}{0.75\,L}$$

10-85 slope

Where $H_{10}$ and $H_{85}$ are the elevations at 10% and 85% of the total length from the outlet, and $L_{10}$, $L_{85}$ are the corresponding chainages. The denominator is always 75% of the total length.

Why 10-85 is preferred for flood hydrology

The 10-85 method exists precisely to address the weaknesses of the conventional average slope. Two features of real watercourses distort the simple ΔH / L value:

• Headwaters are anomalously steep. The upper 10–15% of a main channel often includes first-order tributaries, gullies, or headwater springs on hillslopes — gradients that do not represent the main-stem channel flow regime.
• Outlets are anomalously flat. The lower 5–15% often flows across an alluvial fan, floodplain, or backwater reach where the channel grade is controlled by a downstream baselevel (confluence, weir, estuary) rather than by sediment transport dynamics.

By trimming both ends and computing slope only over the central 75% of the channel, the 10-85 method weights the central channel reach — the reach that actually governs the travel time of the flood wave — and de-emphasises the unrepresentative tails. For this reason it is the slope definition recommended by the SANRAL Drainage Manual (2013), Chapter 3 for $T_c$ calculation in South African practice, and it is the default in most national standards worldwide. Use it unless you have a specific reason to choose otherwise.

Equal-Area Slope

The slope of the straight line drawn through the downstream outlet such that the area between the line and the actual profile above the line equals the area below it. Found iteratively (bisection on the line’s upstream intercept).

$$\int_{0}^{L} \bigl[\, z_\text{line}(x) - z_\text{profile}(x) \,\bigr]\, dx \;=\; 0$$

Equal-area slope — geometric definition

This is the best purely-geometric representation of the average profile slope because the fitted line is not biased by any particular point — it minimises signed error across the whole length. It is less sensitive to noise than the conventional average and less aggressive in trimming than 10-85.

Taylor-Schwarz Weighted Slope

The Taylor-Schwarz slope divides the profile into segments and weights by the inverse square root of each segment’s slope, giving more influence to flat reaches that control travel time. It is the most hydraulically representative of the four methods because it emulates how the kinematic wave propagates.

$$S_\text{T-S} \;=\; \left[\; \frac{L}{\displaystyle \sum_i \frac{d\ell_i}{\sqrt{S_i}}} \;\right]^{2}$$

Taylor-Schwarz weighted slope

Where $d\ell_i$ is the length of segment $i$, $S_i$ is the local slope of segment $i$, and $L = \sum_i d\ell_i$ is the total length. Derived from equating travel time on the actual profile to travel time on an equivalent uniform-slope channel.

Watercourse profile and Time of Concentration

Every Time-of-Concentration formula takes watercourse length $L$ and slope $S$ as primary inputs. The two parameters have very different sensitivities:

• Length enters linearly or near-linearly (exponents 0.5 – 0.8 depending on formula). A 10% error in $L$ propagates to a 5 – 8% error in $T_c$.
• Slope enters through a square root (most formulas) or a 0.385 exponent (SA SCS / SANRAL). A 10% error in $S$ propagates to a ~5% error in $T_c$ for square-root forms, or a ~4% error for the SANRAL form.

The profile tool exists to compute both parameters consistently from a single source of truth. When a profile is linked to a $T_c$ calculation, the calculator’s length and slope inputs are auto-filled and locked. Unlinking returns the inputs to manual entry.

Which slope for which Tc formula?

• SANRAL SA SCS formula — use 10-85 slope. This is what the formula was calibrated against.
• Kirpich, NRCS Lag, FAA — either 10-85 or equal-area is appropriate. Conventional-average slope tends to overestimate $T_c$ for steep headwater catchments.
• Taylor-Schwarz — most defensible for long, compound profiles with strongly varying local gradient (e.g. alluvial valleys with a steep upper reach and a flat lower reach). Not required for well-behaved uniform-grade channels.
• FHWA 3-component — use the local slope of each flow segment (sheet, shallow-concentrated, channel) rather than a whole-watercourse slope.

See the $T_c$ Calculator guide for full details on each formula.

Elevation data

If your imported watercourse lacks elevation data (e.g. a 2D shapefile or a watercourse from a watershed delineation), you have two options:

• Fetch from ESRI. Uses the ESRI ArcGIS Online elevation service to sample elevations along the watercourse geometry. Requires geospatial coordinates (lat/lng). The underlying DEM is a global composite — suitable for most design-flood work, but review results in known terrain before trusting them for sensitive projects.
• Manual slope. Enter a known slope value (m/m) directly. Useful when you have an independent survey-derived slope and do not need to store an elevation profile.

DEM sources — choosing the right one

The provenance of your elevation data matters for watercourse-profile work, especially in flat or low-relief catchments where small elevation errors dominate the computed slope.

DEM	Native resolution	Best for	Caveats
MERIT-Hydro (Yamazaki et al. 2019)	~90 m (3 arc-sec)	Regional / national-scale watercourse extraction; catchments > 10 km²	Hydrologically-conditioned (pits filled, flow directions derived). Ideal default for South African work. Not suitable for small urban catchments.
SRTM (NASA, 2000)	30 m (1 arc-sec)	Medium catchments (~1 – 100 km²); general-purpose terrain	Not hydro-conditioned — pits, spikes, and vegetation bias common. Noisy profiles require smoothing.
Local LiDAR (national/municipal)	1 – 5 m	Small urban catchments, detailed design, flat terrain	Best accuracy when available (typically ±0.15 m vertical). Coverage is uneven — often only near cities or large infrastructure corridors.
ESRI World Elevation (tool default)	10 – 30 m (composite)	Quick profile sampling	Global mosaic of multiple sources — vertical accuracy varies by region. Good for screening, verify against authoritative DEM for final design.

MERIT-Hydro is the default for a reason

For catchments larger than a few km² in South Africa, MERIT-Hydro is almost always the right default. It is hydrologically conditioned (flow paths and catchments are consistent with a corrected DEM), globally consistent, and free. The HydroDesign Watershed Delineation tool uses it natively, so using the watershed delineator as your watercourse source automatically gives you MERIT-Hydro-consistent geometry. Only switch to local LiDAR when you have coverage of the whole catchment and the design is sensitive to sub-metre vertical precision (urban design-storm work, small detention basins).

Handling profile artefacts

Real-world DEM-derived profiles are rarely clean. Typical artefacts and how to handle them:

• Pits (local depressions along the channel). Appear as “notches” in the profile where the DEM has a single-pixel hole. MERIT-Hydro has these filled by default; raw SRTM does not. Fix: use a pit-filled / hydro-conditioned DEM, or post-process by running a monotonic filter (force elevation to be non-increasing downstream).
• Spikes (noise peaks). Single-pixel elevation overshoots, usually from radar layover in steep terrain or vegetation returns. Fix: apply a median filter over a moving window (5 – 11 points) or manually delete the offending point in the paste-data editor.
• Flat segments at DEM pixel resolution. When the watercourse follows a single DEM contour for several pixels, the profile appears stair-stepped. Fix: use a higher-resolution DEM, or apply light smoothing (low-pass filter) before slope calculation — note that the 10-85 method is largely insensitive to this.
• Vegetation bias in SRTM. SRTM is a C-band radar product and returns the canopy top, not the bare earth, under dense forest. Profiles through riparian vegetation show a spurious elevation lift. Fix: use MERIT-Hydro (which corrects for this) or a local bare-earth LiDAR product.
• Profile reversed (upstream-to-downstream swapped). The elevation chart should descend from left to right. If it ascends, the watercourse was digitised in the wrong direction — click Reverse profile to flip it.

Smoothing is a double-edged sword

Heavy smoothing cleans up noise but can also erase real knickpoints (headcuts, grade changes at confluences, waterfalls) that are hydrologically important. Always compare the smoothed profile to the raw data before accepting it. A good rule of thumb: smooth only enough to make the slope calculations stable across the four methods — if your conventional-average and 10-85 slopes differ by less than ~20%, you are smooth enough.

$T_c$ Calculator integration

Saved watercourse profiles can be linked to $T_c$ calculations in two ways:

• From the profile page — click Use in Tc Calculator to navigate to a new $T_c$ calculation with length and slope pre-filled.
• From the $T_c$ calculator — click Link watercourse profile below the length/slope inputs to select a saved profile.

When a profile is linked, the flow-length and slope inputs are auto-filled from the profile. Unlinking returns the inputs to manual entry. The linkage is persistent: if you re-open the $T_c$ calculation later, the inputs still reflect the currently saved state of the linked profile (changes to the profile propagate to downstream calculations).

Worked example — 20 km river reach

Consider a main watercourse draining a 350 km² rural catchment in KwaZulu-Natal. The extracted profile has the following chainage-elevation points (abridged from a MERIT-Hydro extraction at 90 m resolution):

Chainage (m)	Chainage (% from outlet)	Elevation (m)
0	0% (outlet)	320.0
2 000	10%	340.0
5 000	25%	415.0
10 000	50%	560.0
15 000	75%	720.0
17 000	85%	790.0
20 000	100% (headwater)	905.0

Total length $L = 20{,}000$ m (20 km). Total elevation drop $\Delta H = 905 - 320 = 585$ m.

Step 1 — Conventional average slope.

$$S \;=\; \frac{\Delta H}{L} \;=\; \frac{585}{20{,}000} \;=\; 0.02925 \ \mathrm{m/m}$$

Step 2 — 10-85 slope. $H_{10} = 340$ m (at 2 000 m), $H_{85} = 790$ m (at 17 000 m).

$$S_{10\text{-}85} \;=\; \frac{H_{85} - H_{10}}{0.75\,L} \;=\; \frac{790 - 340}{0.75 \times 20{,}000} \;=\; \frac{450}{15{,}000} \;=\; 0.0300 \ \mathrm{m/m}$$

Step 3 — Equal-area slope (approximate). The equal-area line through the outlet (320 m) has an upstream intercept $z_L$ chosen so the area above/below is balanced. For this profile the line rises more steeply than the conventional-average line because the upper reach is concave (steepening headwater). Numerically, bisection yields $z_L \approx 935$ m, giving:

$$S_\text{eq-area} \;=\; \frac{z_L - z_0}{L} \;=\; \frac{935 - 320}{20{,}000} \;=\; 0.0308 \ \mathrm{m/m}$$

Step 4 — Taylor-Schwarz slope. Break the profile into six segments (between consecutive listed points), compute local slope $S_i$ and $d\ell_i / \sqrt{S_i}$ for each, sum, and square:

Segment	$d\ell_i$ (m)	$\Delta z_i$ (m)	$S_i$ (m/m)	$d\ell_i / \sqrt{S_i}$
0 – 2 000	2 000	20	0.0100	20 000
2 000 – 5 000	3 000	75	0.0250	18 974
5 000 – 10 000	5 000	145	0.0290	29 361
10 000 – 15 000	5 000	160	0.0320	27 951
15 000 – 17 000	2 000	70	0.0350	10 690
17 000 – 20 000	3 000	115	0.0383	15 323
Sum	20 000	585	—	122 299

$$S_\text{T-S} \;=\; \left(\frac{20{,}000}{122{,}299}\right)^{2} \;=\; (0.1635)^{2} \;=\; 0.0267 \ \mathrm{m/m}$$

Step 5 — compare and choose.

Method	Slope (m/m)	% vs 10-85
Conventional average	0.0293	-2%
10-85 (recommended)	0.0300	—
Equal-area	0.0308	+3%
Taylor-Schwarz	0.0267	-11%

All four values agree within ~15% — a well-behaved profile. The 10-85 slope of 0.030 m/m is the defensible choice for SANRAL-method $T_c$ (the lower Taylor-Schwarz reflects the disproportionate weight given to the mild outlet reach, which is appropriate for travel-time routing but more than SANRAL’s empirical calibration expects).

Substituted into the SANRAL SA SCS formula (see the Rational Method guide):

$$T_c \;=\; \left(\frac{0.87 \cdot L^{2}}{1000 \cdot S_\text{avg}}\right)^{0.385} \;=\; \left(\frac{0.87 \cdot 20^{2}}{1000 \cdot 0.030}\right)^{0.385} \;=\; \left(11.60\right)^{0.385} \;\approx\; 2.58 \ \mathrm{h}$$

A $T_c$ of approximately 2.6 hours — a reasonable value for a 350 km² rural catchment in moderately steep terrain.

References

• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 3 — Hydrology: Section 3.5 (Time of Concentration) and the definition of the 10-85 slope method used for all SANRAL peak-flow calculations.
• Yamazaki, D., Ikeshima, D., Sosa, J., Bates, P.D., Allen, G.H., Pavelsky, T.M. (2019). MERIT Hydro: A high-resolution global hydrography map based on latest topography dataset. Water Resources Research, 55(6), 5053 – 5073. The hydrologically-conditioned DEM used as the default basis for HydroDesign watershed delineation and watercourse extraction.
• Chow, V.T. (1959). Open-Channel Hydraulics. McGraw-Hill, New York. Classical treatment of watercourse geometry, slope definitions, and the relationship to channel flow hydraulics.
• Taylor, A.B. & Schwarz, H.E. (1952). Unit-hydrograph lag and peak flow related to basin characteristics. Transactions of the American Geophysical Union, 33(2), 235 – 246. Original derivation of the inverse-square-root length-weighted slope that bears their name.
• USGS / NASA. (2000). Shuttle Radar Topography Mission (SRTM) Digital Elevation Data. U.S. Geological Survey, EROS Data Center. Global 30 m DEM; primary input to many national hydrography products.

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Open Watercourse Profile