Tidal and fluvial flood risk together: joint probability
On a tidal river the peak flow and the peak sea level rarely coincide, so design levels come from joint probability rather than from stacked worst cases. This sets out the method and the checks a reviewer should make.
Where a site sits on a tidal river, the flood risk assessment has to deal with two sources at once, and the peak of one rarely coincides with the peak of the other. Joint probability analysis of tidal and fluvial risk is the method for combining them into design levels that have a stated annual probability, rather than stacking two worst cases on top of each other and calling the result conservative. Reviewers see both errors. Stacked maxima produce a level nobody can defend, and independent addition produces a level that is too low.
The output you are looking for is a set of combinations with the same joint return period, and a statement of which combination governs each part of the scheme.
Where both sources act on one site
The zone of interest is the transition reach, between the tidal limit and the point upstream where water levels are set by river flow alone. Its length varies with channel gradient and tidal range. On a low-gradient estuary the transition can extend many kilometres inland, and sites that feel entirely riverine are still tidally influenced at the design event.
Signs that both sources are in play include a tidal flap or non-return valve on the outfall, historic flood records in both summer convective and winter surge conditions, and model schedules that quote both a peak flow in cubic metres per second and an extreme sea level in metres above ordnance datum.
Ask the Environment Agency for the modelling that underpins the mapping in the area. Where a detailed model exists, the joint probability work may already have been done for the reach, and repeating it with different assumptions creates an argument you do not need.
Why the two cannot be added
Extreme river flow and extreme sea level share a driver. The same Atlantic depression brings rainfall over the catchment and a surge up the estuary, so the two variables are positively dependent rather than independent. Treating them as independent understates the chance of both being high together.
But full dependence is also wrong. Rainfall takes time to translate into river flow, and the delay depends on catchment size and response. A small, steep catchment can peak within hours of the rain and line up with a surge. A large, slow catchment peaks days later, by which time several tides have passed.
So the correct treatment sits between the two, and the degree of dependence is a property of the location. Defra and Environment Agency research on joint probability, including the dependence mapping produced for estuaries around England and Wales, provides the dependence measures used in practice. Use the published values for the reach rather than a default.
Joint probability in practice
The usual approach tests several combinations that share the same joint annual exceedance probability. For a 0.5 per cent joint event you might run a near-extreme sea level with a modest river flow, a near-extreme river flow with a modest sea level, and two or three intermediate pairings. Each combination is a legitimate 0.5 per cent scenario, and each produces a different water surface profile along the reach.
The governing combination then varies with position. Downstream receptors are usually governed by the tide-dominated pairing, upstream receptors by the flow-dominated one, and the crossover sits somewhere in the middle of the site on a long frontage. On a site straddling that crossover, two different combinations govern two ends of the same building.
Record the matrix. A table of combinations against modelled level at each receptor is the single most useful page in this part of the Flood Risk Assessment, and it lets the reviewer follow the logic without rerunning anything.
Tide locking and what it does to drainage
A tidally influenced outfall stops discharging when the receiving water rises above the invert. During that period the site's surface water has nowhere to go, so the storage has to hold the whole of the runoff generated while the outfall is locked.
The duration of the lock is set by the tidal curve and the outfall level, not by the rainfall event. That means the critical storm for a tide-locked site is often a long-duration, lower-intensity event rather than the short summer storm that governs a free-draining site. Test durations out to the length of the lock, and state the lock duration used.
Where the required volume is unachievable, the options narrow to raising the outfall, pumping, or accepting managed surcharge within the site. Each of those has a maintenance consequence that belongs in the Drainage Strategy and, if it is to be relied upon, in a planning obligation or condition. Our note on culverts and the presumption against burying a stream covers the related point about conveyance through a site.
Climate change allowances, one epoch at a time
Sea level allowances and peak river flow allowances are published separately and are structured differently. Sea level allowances are given by region and by year. Peak river flow allowances are given by river basin district, management catchment and allowance category, and the category to apply depends on the vulnerability of the development and the flood zone.
Three rules keep this clean. Apply the same epoch to both sources, matched to the lifetime of the development, which for residential development is normally taken as 100 years. Do not blend the central allowance for one source with the upper end allowance for the other unless you are running that combination deliberately as a sensitivity test. And state the version of the allowances used with the date you accessed them, because the figures are revised.
Peak rainfall intensity allowances for the drainage design are a third set again, and they are not interchangeable with the river flow allowances.
What a reviewer should check
Working through a joint probability chapter, these are the questions that find real problems:
- Is the dependence measure stated, with its source, and is it appropriate to the reach?
- Do all the tested combinations share the same joint annual exceedance probability?
- Is the governing combination identified separately for each receptor rather than once for the whole site?
- Are the epochs for sea level and river flow the same, and do they match the stated development lifetime?
- Is the tide lock duration stated, and were storm durations tested out to it?
- Are breach and overtopping scenarios assessed where defences are present, with a hazard rating rather than depth alone?
- Do finished floor levels and freeboard relate to the governing scenario, and is safe access assessed in the same event?
A chapter that answers all seven in its own text needs very little correspondence afterwards. One that answers none of them usually generates three rounds.
Reporting the governing scenario
Write the conclusion so that a case officer who has never opened a hydraulic model can use it. Give the design level at each receptor, name the combination that produced it, state the freeboard, and say what happens in an event beyond the design case. Residual risk is where the tidal and fluvial distinction stops being academic, because a surge event arrives with warning while a flash fluvial event on a small catchment may not.
Where the scheme relies on the exception test, the flood risk side of the two limbs draws directly on this analysis, as set out in our note on the exception test evidence and the two limbs in practice. Keep the numbers consistent between the two documents.
This is general guidance, not legal advice. Flood modelling and joint probability analysis are work for a suitably qualified hydrologist or flood risk engineer, and PlanScope provides AI-assisted draft reports for planning applications. Reports should be reviewed before submission. We do not guarantee planning approval. For specialist technical reports, qualified professional input may be required.
Frequently asked questions
What is joint probability in a flood risk assessment?
It is the analysis of how likely two flood sources are to be extreme at the same time. For a tidal river it combines extreme sea level with river flow, using a measured degree of dependence for that reach. The output is a set of combinations that share one annual exceedance probability, each producing its own water level.
Why can tidal and fluvial peaks not simply be added?
Adding two maxima produces an event far rarer than the design standard, which cannot be defended in policy terms. Treating the sources as independent understates the risk, because the same weather system drives both. The dependence between them lies between those extremes and varies by estuary, so published dependence values are used.
What is tide locking and why does it matter?
Tide locking happens when the receiving water rises above the outfall invert and the site cannot discharge. Storage must then hold everything that falls during the locked period. Because the lock duration is set by the tidal curve, the critical storm is often long and moderate rather than short and intense, so longer durations must be tested.
Which climate change allowances apply to each source?
Sea level allowances are published by region and year. Peak river flow allowances are published by river basin district, management catchment and allowance category, with the category depending on vulnerability and flood zone. Peak rainfall intensity allowances are separate again and apply to drainage design. Use the same epoch across all of them.
Does a defended site still need this analysis?
Yes, and usually more of it. Flood zones are mapped ignoring defences, so a defended site sits in Zone 3 for policy purposes. Breach and overtopping scenarios then need assessing with a hazard rating that combines depth and velocity, alongside the undefended joint probability levels used to set floor levels and freeboard.
Sources and further reading
This article is general guidance about the planning system in England and, where stated, the rest of the UK. It is not legal or professional advice. Check your local planning authority’s validation requirements and take professional advice for your specific site.