Turbidity Plume Calculator

Calculator Inputs

Enter site conditions and compute centerline and cross-stream turbidity.

Units: NTU, m, m/s, m²/s, 1/s

Baseline turbidity (NTU)

Background reading upstream of the activity.

Source excess at x=0 (ΔNTU)

Increase above baseline at the discharge location.

Flow rate (m³/s)

Used for mass-rate estimate if conversion is provided.

Current velocity (m/s)

Controls travel time and downstream attenuation.

Water depth (m)

Depth affects settling loss term (vs/H).

Transverse mixing Ky (m²/s)

Higher values spread the plume wider.

Settling velocity vs (m/s)

Represents particle settling and deposition tendencies.

Additional decay k (1/s)

Optional decay from aggregation, filtration, or removal.

Compliance threshold (NTU)

Used to estimate plume width above the limit.

Distance downstream x (m)

Where you want the point concentration estimate.

Cross-stream offset y (m)

0 is centerline. Positive values move laterally outward.

TSS conversion (mg/L per NTU)

Optional; set to 0 if you don’t need TSS.

Profile max distance (m)

Generates a centerline table from 0 to max.

Profile step (m)

Smaller step = more rows and detail.

Tip: Keep Ky, vs, and k aligned with field or literature values for your sediment class.

Example Data Table

Sample centerline outputs for a typical scenario (baseline 5 NTU, source excess 120 NTU, velocity 0.45 m/s, depth 3 m, Ky 0.35 m²/s).

Distance (m)	Travel time (hr)	σy (m)	Centerline turbidity (NTU)	Width at 25 NTU (m)
0	0	0	125	0
100	0.06	12.49	112.94	53.2
250	0.15	19.75	98.65	74.9
500	0.31	27.93	81	93.6
1000	0.62	39.51	55.35	96.2

Example values are illustrative. Use measured site parameters for permitting decisions.

Formula Used

This estimator applies a simplified steady plume approach with downstream advection, transverse spreading, and exponential loss terms.

Transverse spread

σy(x) = √( 2 · Ky · x / u )

Ky is the transverse mixing coefficient (m²/s) and u is current velocity (m/s).

Downstream attenuation

atten(x) = exp( - (k + vs/H) · x / u )

k is optional decay (1/s), vs is settling velocity (m/s), and H is depth (m).

Turbidity at any point

ΔT(x,y) = ΔT0 · atten(x) · exp( - y² / (2·σy²) )

T(x,y) = Tbaseline + ΔT(x,y)

ΔT0 is the source excess turbidity above baseline. The width at a threshold is found by solving for y where T(x,y) equals the limit.

Important: This model is a screening-level tool. Complex bathymetry, stratification, tide reversals, or near-field jet mixing may require specialized modeling and field validation.

How to Use This Calculator

Enter baseline and source excess. Use upstream monitoring for baseline and the expected turbidity rise at the release point for ΔNTU.
Set hydraulic conditions. Input velocity, depth, and a reasonable mixing Ky based on site observations or references.
Add loss terms. If settling is relevant, set vs. Include decay k if aggregation or treatment reduces turbidity.
Choose a compliance threshold. The tool estimates the plume width above this limit at each distance.
Pick a point and profile range. Use x and y for a specific location, and max/step to generate a centerline table.
Export results. After calculation, download CSV for spreadsheets or PDF for quick reporting.

Practical Guide to Turbidity Plume Estimation

1) Why plume screening matters on construction sites

Turbidity plumes can affect aquatic habitat, visibility, and downstream intakes. For dredging, trenching, cofferdams, and dewatering returns, a fast screening estimate helps plan controls, monitoring locations, and work windows. This calculator is designed for early-stage decisions and quick scenario comparison.

2) Baseline and source excess define the starting condition

Two values drive the initial signal: upstream baseline turbidity (NTU) and the excess increase at the release point (ΔNTU). Baseline is typically measured with a handheld meter or fixed station. Source excess can be estimated from pilot runs or similar projects, then refined with field data.

3) Flow and velocity control travel time and dilution timing

Velocity (m/s) sets how quickly the plume moves. Many rivers and channels operate in the 0.1 to 2.0 m/s range, but localized jets or backwaters can differ. Flow (m³/s) is used here to estimate a mass rate when a site-specific NTU-to-TSS conversion is available.

4) Mixing coefficient Ky governs how fast the plume widens

Ky (m²/s) represents lateral spreading from turbulence and shear. Screening values are often in the 0.05 to 1.0 m²/s band depending on channel roughness, bends, and velocity gradients. Higher Ky increases σy and produces a wider plume footprint at the same distance.

5) Settling and decay reduce turbidity with distance

Settling velocity vs (m/s) and decay k (1/s) act as removal terms. Fine silt and clay may have vs around 1e-5 to 1e-3 m/s, while coarser particles can be higher. Depth matters because the settling loss term uses vs/H, making shallow reaches more sensitive.

6) Threshold width supports compliance planning

The calculator estimates the plume width where turbidity exceeds a chosen threshold. If the centerline value drops below the limit at a given distance, the reported width becomes zero. Use the width output to place downstream monitoring points, set buffer distances, and evaluate controls like silt curtains.

7) Profiles, exports, calibration, and limitations

The centerline profile table shows how turbidity, σy, and threshold width evolve from 0 to the selected maximum distance. Export CSV for sensitivity checks and export PDF for a consistent field package. Calibrate with monitoring whenever possible. NTU-to-TSS conversion can vary widely by sediment type; values from 0.5 to 5 mg/L per NTU are common in practice, but must be verified locally carefully. Complex bathymetry, stratification, tides, and near-field jets may require detailed modeling.

FAQs

1) What does “source excess ΔNTU” represent?

It is the turbidity increase above baseline at the discharge location. Use pilot tests, return-water sampling, or historical project data to estimate it, then refine with monitoring.

2) How should I choose Ky?

Start with a screening range (about 0.05–1.0 m²/s) and adjust based on channel roughness, bends, and observed lateral spreading. Calibrate Ky using measured plume widths when available.

3) Why does water depth affect results?

Depth appears in the settling removal term vs/H. Shallower water increases vs/H, which reduces turbidity faster with distance, all else equal.

4) Why is the “width at threshold” sometimes zero?

If the centerline turbidity at that distance is below your threshold, there is no cross-stream location that exceeds the limit, so the estimated exceedance width is zero.

5) Can I apply this to tidal or reversing flows?

Only as a rough screening tool. If currents reverse, the assumption of steady downstream advection breaks down. Consider time-varying methods and field validation for tidal systems.

6) How do I set the NTU-to-TSS conversion?

Collect paired samples: measure NTU and lab TSS for the same water, then fit a site-specific factor. Use that factor in mg/L per NTU for the most representative sediment conditions.

7) What should I export for a field package?

Export CSV for internal checks and trend plots, and export PDF for a concise summary of assumptions and outputs. Include baseline source, monitoring plan, and any calibration notes.