How flood models work

The seven steps of a flood model

Each step answers one question and hands its result to the next. The open-source Oasis framework for running catastrophe models splits a model the same way: a hazard part and a damage part that share one measure of the water, usually its depth, with the insured buildings and the policy terms around them.

1. 01

   Weather

   Question

   What falls, where, and for how long?

   Covers

   Rain over an area and a duration, temperature, and snow on the ground and how fast it melts. Past weather comes from rain gauges, weather radar and gridded reconstructions such as the European ERA5 record, which is hourly from 1940. A full catastrophe model also generates synthetic weather: thousands of simulated years of storms that could happen but have not.

   Example

   150 mm of rain in 72 hours over the upper part of a river basin, on soil that is already wet.

   Output

   Rain and snowmelt for each place and each hour, for real past storms or simulated ones.

2. 02

   Hydrology

   Question

   How much of the rain reaches the rivers, and when?

   Covers

   Water soaking into the soil, how wet the soil was before the storm, snow stored and melting, water running off slopes into streams, the flow down the river network, and reservoirs that hold water back. The European Commission's Joint Research Centre runs an open model for this step, LISFLOOD.

   Example

   The same 150 mm gives a small rise on dry soil and a large flood on saturated soil, because saturated soil sends almost all of the rain on to the streams.

   Output

   River flow over time at points along the river, in cubic metres per second.

3. 03

   Frequency

   Question

   How often is a flow of this size, or a rain of this size, exceeded?

   Covers

   Statistics of long gauge records, or a count in a long simulation. The result is a chance per year or, written the other way round, a return period.

   Example

   Q100, the river flow that has a 1 % chance of being exceeded in any one year at that place.

   Output

   Design flows such as Q10, Q100 and Q1000 for each stretch of river, or a catalogue of simulated events with the year in which each one happens.

4. 04

   Hydraulics

   Question

   Where does the water go on the ground, how deep does it stand and how fast does it move?

   Covers

   The river channel, the terrain of the floodplain, dykes, walls, bridges, culverts and buildings, and for rain floods the water running over the ground itself. A one-dimensional model computes water levels along surveyed cross-sections of the river. A two-dimensional model spreads the water over a grid of terrain cells. Many models do the channel in one dimension and the floodplain in two.

   Example

   The Q100 flow overtops a low bank and the water stands 90 cm deep in the street behind it.

   Output

   Maps of flood extent, water depth and, where it is computed, velocity, one per return period or one per simulated event. Official hazard maps under the EU Floods Directive must show the extent, the depth or water level and, where appropriate, the velocity.

5. 05

   Exposure

   Question

   What is insured, and where does it stand?

   Covers

   The location of each building, its use, its construction, the number of floors, whether it has a basement, the height of the ground floor above the street, and the sum insured.

   Example

   A two-storey house with a basement, its ground floor 40 cm above the street.

   Output

   A list of insured buildings with the details the damage step needs.

6. 06

   Vulnerability

   Question

   How much damage does a given depth do to this kind of building?

   Covers

   Depth-damage curves, which give the damage as a share of the rebuild cost at each depth of water, sometimes adjusted for how fast the water flows or how long it stays. The Joint Research Centre publishes such curves for most countries, with the expected damage and its spread at each depth. A test of seven damage models on two real floods found the results most sensitive to the assumed cost of total damage, and almost as sensitive to the shape of the curve.

   Example

   The 90 cm in the street stands 50 cm over the ground floor of the house above. That water ruins the floors, plaster, wiring and heating on that level, and the curve turns the depth into a share of the rebuild cost.

   Output

   The damage in money for each building in each event, before any policy terms. Insurers call it the ground-up loss.

7. 07

   Financial

   Question

   What does the insurer pay, and how much of that does its reinsurance pay?

   Covers

   The deductible, the limit and the layers of each policy, then the reinsurance contracts, applied event by event.

   Example

   The house's damage, less its deductible and capped at its limit, is added to the claims of the other insured buildings flooded by the same storm. The reinsurance pays the part of that total above the level at which it starts.

   Output

   The average annual loss, and the loss exceedance curve, which gives the loss reached with each chance per year. Solvency II capital is set on the loss with a 0.5 % chance per year, the 1-in-200-year loss.

Steps 1 to 4 are the hazard and steps 5 to 7 are the loss. Public hazard maps stop after step 4, because exposure, damage curves and policy terms are needed only by someone who wants the loss in money rather than in water depth.

A hazard map gives one extent and one depth per return period. That is enough to price one building and to estimate its average annual loss. It cannot give the loss curve of a portfolio, because each map puts the same return period on every river at the same time. Real floods are not like that: in a very extreme flood the highest flows occur over a small core area, and the same flood is far less rare elsewhere. A loss curve needs simulated events that are extreme in some places and ordinary in others.

River floods

A river flood is a river or stream rising over its banks onto the land beside it. Most official flood maps in the EU show river floods. This is how each step works for them.

• Weather. Days of rain over a whole river basin, often thousands of square kilometres, sometimes on top of melting snow. What matters is the total over one to several days across the basin, more than the intensity of any one hour.
• Hydrology. The water collects in streams and travels downstream as a wave. On a large river the wave takes days to pass, and a town far downstream can flood after the rain has stopped. How high the wave is at each place depends on how wet the soil was, whether the tributaries peak at the same time and how much the reservoirs hold back.
• Frequency. Counted on the river flow, from long gauge records. Hydrologists take the largest flow of each year at a gauge, fit a statistical distribution of extremes to that series and read off the flows with a 10 %, 1 % and 0.1 % chance a year: Q10, Q100 and Q1000. Regional formulas carry the results to stretches of river without a gauge. A gauge record rarely covers more than a century, so a 1,000-year flow is read from the fitted curve far beyond the measured years.
• Hydraulics. The design flow runs through a model of the channel and the floodplain, with the surveyed river bed, the terrain, dykes, bridges, weirs and buildings. Dykes need a choice. A model can leave them out, keep them standing up to their design flow and remove them above it, let water flow over their crest as built, or run a breach as a separate scenario. The four choices give four different maps behind the same dyke.
• Loss. One storm hits many places at once. A large river flood can reach towns along hundreds of kilometres of river in the same week, so an insurer's losses across a region rise together. That is why reinsurance and capital need simulated events that are consistent along and across rivers. A set of separate hazard maps, one per return period, does not show which places flood together.

Rain floods (surface water)

A rain flood, also called a surface-water or pluvial flood, happens when rain falls faster than the ground and the drains can take it. The water runs over the surface and gathers in low places, and it can flood a house far from any river. River maps do not show it, and the EU Floods Directive allows member states to leave floods from sewerage systems out of their maps.

• Weather. Short, intense, local rain: a thunderstorm that drops most of its water in 15 to 60 minutes over a small area. A rain gauge a few kilometres away can miss the worst of it.
• Hydrology. Reduced to two questions: how much of the rain soaks into the ground, and how much the drains carry away. Roofs and asphalt let almost none of it soak in, and drains are built for a given rain, so a heavier one overloads them. There is no river network to route.
• Frequency. Usually taken from rain statistics: intensity-duration-frequency curves, which give the rain that falls in a given duration with a given chance per year, for example the rain in one hour that is exceeded once in 100 years on average. A 1-in-100 rain does not give a 1-in-100 depth at a house. The depth also depends on how wet the ground was, whether the drains were blocked and where exactly the storm sat. The plain label for such a map is "depth from a 1-in-100 rain of a stated duration".
• Hydraulics. Modelled as "rain on grid": the design rain is placed on every cell of the terrain, and the model lets it run downhill, collect in hollows and flow along streets. The result is very sensitive to small terrain detail. A kerb, a garden wall, a raised doorstep, a road embankment or an underpass changes where the water goes, so the terrain grid has to be fine enough to show them, and the buildings have to be in it.
• Loss. More frequent and more local. A thunderstorm floods a few streets rather than a region, and the claims are many and mostly small: basements, ground floors and garages, often in places that no river map marks.

Is frequency just the weather?

No. Weather is one storm: so many millimetres in so many hours, on soil that is dry or wet that day. Frequency is a count over many years: the chance that a given flow, rain or depth at a given place is exceeded in any one year. Hydrology links the two, and it links them loosely, because the same rain makes different floods.

What decides how big a flood the same rain makes:

• Soil wetness. On dry soil much of the rain soaks in. On soil that is already saturated almost all of it runs off to the streams.
• Snow. Rain on melting snow adds the melt water to the rain, and frozen ground lets little of either soak in.
• Where in the basin the rain falls. Rain over the upper part of a basin passes every town downstream on its way out. The same rain near the mouth reaches only the last stretch.
• Whether tributaries peak together. Two flood waves that reach a confluence in the same hours add up; a day apart, they do not. In September 2024 SHMÚ, the Slovak hydrometeorological institute, reported that at Thebnerstrassl, the last Austrian gauge on the Danube above the mouth of the Morava, the Danube's two flood waves merged under the influence of the Morava.
• Reservoirs. In the same flood, reservoirs on the Czech side of the Morava and Dyje basins held back a large part of the rain, which lowered the flood wave and made it last longer, according to the same report.

Viglione, Merz and Blöschl worked this through with a simplified catchment model. The return period of a flood came out much higher than that of the storm behind it: of the order of hundreds of times higher in a catchment that is dry on average, and never more than a few times higher in one that is wet on average, because a wet catchment cannot get much worse than it normally is. The usual design method assumes that a 1-in-100 rain makes a 1-in-100 flood. In their study that only works if the method assumes that a larger share of the rain runs off than in a typical yearly flood, which means soil wetter than usual.

There are two routes to frequency.

Statistics of measured river peaks. Take the largest flow of each year at each gauge, fit a distribution of extremes, read off Q10, Q100 and Q1000, and carry them to ungauged stretches with regional formulas. The weather never enters: the measured peaks already contain the soil states, the snowmelt and the reservoir operation of every year on record. This is how official design flows are usually set.

Simulated weather, run through hydrology and then counted. Generate thousands of years of synthetic weather, run each storm through the hydrology and the hydraulics, and count how often each flow, depth or loss is exceeded. A research chain at GFZ, the German geosciences research centre, did this for the Mulde basin and produced 10,000 years of river flow, flooding and damage. In that chain one event has different return periods in different places, as real floods do. The costs are computing time and calibration, and the rarest results depend on the weather generator, so they are still checked against the gauge statistics.

A third approach keeps the gauge statistics and adds a model of how the flows at many gauges rise together. It produces events that span a region without simulating the weather.

What is a return period, and why is it called that?

A return period is the average time between floods of at least a given size at one place. The 100-year flood is the flood with a 1 % chance of being reached or exceeded in any one year. The name comes from that average: over a very long record, floods of that size come back once every 100 years on average.

It is a chance per year, and it keeps no schedule. A 100-year flood can come two years running, and a place can go 300 years without one. The chance is the same every year, whatever happened the year before.

Over many years the chance grows. The chance of at least one 100-year flood in 30 years, the length of a long mortgage, is 1 minus 0.99 to the power of 30, about 26 %. Over 100 years it is about 63 %.

Hydrologists write the flow with a 100-year return period as Q100, Q being the usual symbol for river flow. The EU Floods Directive asks for maps of a low probability flood, a medium probability flood with a return period of 100 years or more and, where appropriate, a high probability flood. Each state picks the return periods it maps, such as Q10, Q100 and Q1000.

A return period always belongs to one quantity at one place: the flow at one gauge, the rain over one duration at one point, or the water depth at one building. The 100-year rain, the 100-year flow and the 100-year depth at a house are three different events, and a map should say which one it shows.

Does a real flood have return periods?

Yes, as a label given afterwards, one for each river and each place. After a flood the hydrological service takes the peak flow measured at each gauge and reads where it falls on that gauge's frequency curve. One storm therefore gets many return periods. Storm Boris in September 2024 shows how far apart they can be:

The labels differ because each one answers a narrower question than "how big was the storm": how rare was this peak flow at this gauge, measured against that gauge's own record. A small mountain basin that took some of the heaviest rain of the storm produced a flow far beyond its usual floods. The Danube collects water from a very large basin, much of which had far less rain, and reservoirs on the Dyje lowered the wave of the Morava.

Two things follow for anyone who reads such a label. A storm has no single return period, so "a 300-year flood" in a headline describes one place. And the label can move: figures published during and just after a flood are operational and are revised when the hydrological office verifies them, and the new peak joins the gauge record, which changes the frequency curve used for the next estimate.

Wody Polskie: flood risk reduction programme for the Nysa Kłodzka basin, February 2025. SHMÚ: report on the September 2024 flood in the Morava, Danube, lower Váh and Nitra basins, operational data.

What is river flow: height or speed?

Neither on its own. River flow, or discharge, is the volume of water passing a cross-section of the river each second, in cubic metres per second (m³/s). It equals the area of the wet cross-section times the average speed of the water through it. A river 50 m wide and 3 m deep on average, flowing at 2 m per second, carries 50 times 3 times 2, which is 300 m³ every second.

Gauges measure height. A gauge records the water level, called the stage, every few minutes. Flow is measured only from time to time, by measuring the speed of the water across the whole section, and each measurement gives one pair of a height and a flow. The pairs are fitted into a rating curve, and from then on the flow is read from the height through that curve.

The same flow can stand at different heights. A bridge that narrows the river, debris or ice caught against its piers, plants growing in the channel, or gravel that raises the bed all lift the water for the same flow, and the rating curve then has to be measured again. A river downstream can also hold water back. In September 2024 the high Danube backed water up into the lower Morava, and SHMÚ linked the Morava's sharp rise there to that backwater. Where water is backed up, the height no longer tells the flow.

The curve is least certain in the floods that matter most, because the largest floods are rarely measured directly. In September 2024 the gauge at Lądek-Zdrój on the Biała Lądecka in Poland was damaged when the water stood at 366 cm. The peak, 515 cm, was found afterwards by levelling in the field, and Wody Polskie estimated the peak flow by extending the rating curve up to that height.

A flood model needs both quantities. The frequency step works on flow, because flow is what the river carries whatever the shape of its channel. The hydraulic step turns that flow back into a height and a depth on the ground, with today's bridges and dykes in place.

How is a flood map tested against a real flood, and what does that prove?

The usual test is a replay. The hydraulic model is given the river flows or levels measured during a real flood at gauges upstream of the area, and the water it spreads is compared with what satellites saw. The Copernicus Emergency Management Service maps flooded areas from satellite images, usually radar, when an authorised national body asks for it during a disaster.

A replay tests the water-placement step, the hydraulics: the terrain, the channel, the dykes and bridges, and the physics of the model. The model is given the flows that really happened, so errors in hydrology and frequency are taken out of the comparison, and a mismatch with the satellite outline is a hydraulics mismatch.

It does not test whether the 100-year flow is right. A model that reproduces 2024 when it is given 2024's flows has not shown that its Q100 is correct, whether a flood like 2024 is a 1-in-50 or a 1-in-500 event, or how losses in two towns move together in the same year. Those answers come from the frequency step, and a replay cannot check it.

Four rules keep a replay fair:

• The input flows come from gauges upstream of the area being scored. Gauges and high-water marks downstream are kept back as checks; a model that is fed a level and then scored against the same level proves nothing.
• Gauge readings during an extreme flood are provisional, and the verified figures published later are the ones to use.
• The satellite outline is incomplete. The service itself warns that the first image may be taken after the water has gone down, that water under trees and in built-up areas is hard to see, and that in dense urban areas floods may not be visible in streets.
• Where a dyke failed, a replay without the breach misses the water behind it that the satellite shows.

The match is usually scored with the Critical Success Index (CSI). Take all the ground that either the model or the observation calls flooded. The CSI is the share of that ground that both call flooded. If they agree on 80 hectares, the model alone floods another 10 and the observation alone shows another 10, the CSI is 80 divided by 100, or 0.8. A score of 1 is a perfect match. Ground that both call dry does not count, so a model cannot score well just by getting the large, easy dry areas right.

Bates and colleagues write that reasonable local models built on good data routinely score 0.7 to 0.8, and that 0.9 is an effective upper limit for the measure, because river flow measurements and the other inputs carry errors that cannot be removed. A score also depends on its rules: which areas were scored, when the image was taken, and whether the model was tuned on the same flood it is scored on.

Who does what

Public bodies produce most of the hazard steps. The loss steps sit mostly with insurers, reinsurers and the catastrophe models they use, while EU bodies supply open parts and set the capital rules.