Netherlands Against Flooding

Nathan Hungate, Brad Wilgus

Interfaces: Vol. 44, No. 1, January-February 2014, pp. 7-21Authors: Carel Eijgenraam, Jarl Kind, Carjin Bak, Ruud Brekelmans, Dick den Hertog, Matthis Duits, Kees Roos, Pieter Vermeer, Wim Kuijken

“Netherlands is faced with reclaiming, protecting, and developing land below sea level, and managing rivers flowing into the country to

protect its people and their economic interest.”

NL Flooding Dilemma:• 1953: Flood disaster in Southwest Netherlands, killing more than 1,800 people

and destroying (cropland) 10% of Netherlands GDP.

• 55% of the land area faces flood risk• 2/3 of the population at risk• 70% of GDP at risk

• West: country borders North Sea

• East: Rhine River enters the country from Germany, splitting into 3 branches towards the sea.

• Southeast corner: Meuse River enters the country from Belgium

In 1995: more than 250,000 people were evacuated as levees were at risk.

Contextualization:

• Dike: Slope of land to keep water out

• Dike-ring area: a flood-prone area surrounded by a closed ring of water defense or high grounds.

• For all 53 large dike-ring areas in Netherlands, the Water Act determines flood protection standards (yearly probability of flooding)

• These figures are related to the original 1958 figures in the Delta Act, based on 1953 data.

Key Issues:• US has flood probability standards of 1/100 (probability of flooding)

• Netherlands has standards of 1/10,000 (probability of flooding)

• Investment costs are high

Because a scientific basis for standards in other parts of the world are not available. This analysis and model framework can be of

great value for flood prone areas. • The solution to determine optimal dike heights done back in 1956 was

incorrect and analysis was incomplete in regards to timing of investments

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Water Implications….• Investments in Flood control have been around for over 5000 years in Ancient cities

such as Mesopotamia, which had a portion of the Euphrates river flowing through the city, similar to the Netherlands.

• Over 5000 years later, simulation modeling is being run, evaluating cost effectiveness of flood control measures.

Then: Utilization Now: Utilization/Prevention

Future: Disaster?

http://flood.firetree.net/

Investment was inadequate:• Population had doubled

• GDP had increased over 5 fold

• Increasing protection standards (ten fold) would:• Turn standards of 1/10,000 into

1/100,000 • keep in mind US standard is currently =

1/100Investments include:DamsSluicesStorm Surge BarriersLocksDikesLevees

What this operational science case is targeting….

Developing a Cost-Benefit Analysis (CBA)

Comparing the marginal societal costs of investing in water defenses against the marginal societal benefit of avoiding flood damage.

This model is different than inventory management models in that:

The investment cost of heightening a dike increases as the height of the existing dike increases. Making each subsequent heightening more expensive than the previous one.

Delta Works Development…

• “Developing efficient flood protection standards in a more objective

way.”

• A scientific basis for updating flood protection standards in the Water

Act by 2017.

• Utilized cost-benefit analysis and mixed-interger nonlinear programming

to demonstrate efficiency of increasing the legal standards in critical

regions.

• Monte Carlo analysis confirms the robustness of this recommendation.

In 2008, the Second Delta Committee recommended increasing legal flood protection standards at least 10 fold to compensate for population and economic growth since 1953.

Included dike improvement estimated at: (€11.5 billion ≈ $15,874,593,472 USD)

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Delta Works Framework:• Identify main dike ring areas• Assess cost of flooding • A human life is valued at €2.2 million (2008).• Using data from a purpose-built flood simulation lab and

empirical statistics regarding water wave properties and distribution. Seasonal changes and variation is taken into account.

• Salt-water flooding causes more damage to farmlands thus sea water flooding's have higher cost associations when modeling

• River flooding also has a longer warning time• Primary defenses must meet the requirements of the

“acceptable risk” models implemented by the CBA modeling

• Timing of investment• Height of Dike• Location of dike upgrades over a planning horizon of

atleast 300 years• The investment cost of heightening a dike increases as the

height of the existing dike rises, making each subsequent heightening more expensive than the previous one.

Model Assumptions:• A flooding incident occurs when the load on a dike is greater than the strength of that dike,

resulting in a breach. • The flood probability is the outcome of the comparison of two stochastic variables: hydraulic load

and strength.• Load factors are dependent on water level, wave height, and wave period.• There are many more variables taken into account such as wind direction, duration, basin geometry,

etc..• Variables indicating the strength of the dike are crest height, seaside slope, thickness of stone

revetment. • The occurrence of failures leads to the quantification of the overall failure probability of a dike ring. • Uncertainties about loads are much greater than the uncertainty about strength.• The weakest dike segment will fully determine the flood probability of the dike ring.• Each dike ring is dependent, therefore flooding of other dike-ring areas doesn’t affect the status of

another ring.

Investment cost functionDiscountingEconomic GrowthWater-level rise

Formulation:• The probability of failure of segment l at time t, resulting in a complete

breach of the dike, is given by

• The flood probability of the dike ring at time t is given by

• The expected damage cost at time t is given by the product of the flood probability and the damage costs; hence, it becomes

• For homogenous dike-rings a discretized version of the model can be solved using dynamic programming (DP)

The task is to rapidly find the optimal solution, allowing the user to run multiple scenarios for all 53 dike rings within a reasonable time. Using heuristic approaches to solve the MINLP.

Continued Formulation.…• The formula for the legal

standard probability is the quotient of an efficient level of expected damage and the current potential loss from such damage.

• Damage is defined as the log (mean) of expected damage just before the next optimal upgrade at the optimal moment and the expected damage just after that upgrade.

• For an optimal investment, it holds that the optimal damage cost for a certain time k…

• Also….

MINLP Model:• The time frames in the planning horizon are

discretized

• Binary variables indicate whether an upgrade should occur at these times

• The upgrade heights are continuous variables

• Investment costs and expected damage costs depend nonlinearly on both the upgrades and their timing

• We are left with a large-scale MINLP model

A mixed-interger nonlinear model used for non-homogenous dike rings.

Example of Investment Evaluation:Expected loss gradually increases as the combined result of economic growth, climate change, and soil subsidence.

When a high level of expected loss is reached, a new investment action becomes profitable and is executed.

Dividing the values for the expected loss in the optimal strategy by the corresponding values for the potential damage yields the values for the flood probability.

CBA Optimization Advantages:The successful application of operations research yields both a highly significant increase in protection for each region with approximately

€7.8 billion in cost savings ≈ $10.77 billion

• The model interface produces optimal results for all 53 dike-rings in < 1 day.

• Study shows the highest standards should be set along rivers rather than the coast.• Flood risk is highest in areas where maximum flood depth is highest,

this is seen much more along rivers.

• For a 90% confidence interval with the Monte Carlo Simulation, the upper and lower bound estimates range is 10%. Damage is hard to calculate precisely.

• Optimal cost estimates were €3.7 billion instead of €11.5 billion

Monitoring Importance:

A faster change in water levels would require more frequent investment (high importance)

Also in the Monte Carlo Analysis, the constantly changing uncertainty in potential damage is by far the most important cause of the uncertainty in Pefficient2050

Questions?

10-25 years lead time expected

• Data Gathering:• Dikes were divided into ≈ 652 (5km) sections.

• Researched the lowest costs for a range of 20 heightenings, up to atleast 2 meters higher than the existing height.

• Checked dike sections for special problems (& applied special constructions or solutions)

• Decision Support System:• HKV Consultants implemented the optimization model in a user-friendly

software package (OptimaliseRing)• Includes database for all dike-ring areas• User interface• MINLP optimization algorithm• Postprocessing module transforming output into tables, graphs, and maps