Mathematical Modeling of Floods: Natural Hazards and Human Impact

In today's era of climate change, it is essential to understand hazards. This project uses mathematical models to analyze environmental challenges and promote critical thinking.

Students will receive information about natural disasters and calculate the intensity and effect of human impact on natural resources.

Two activities were completed with the students.

1.What is the probability of a flood?

Goal : Probability of a flood occurring within a 100-year period.

(What did the students do?): Calculate the increase in hazard over time.

Mathematical problem: Given p = 0.01 (1%), calculate the  hazard over 4 years.

Solution:P(at least once) = 1 - (1 - p)ⁿ = 1 - (1 - 0.01)⁴ = 0.0394, or 3.94%.

Conclusion: Although 1% seems quite small, the probability increases over time. If we calculate the probability over 30 years, the hazard rises to 26%.

2.Urbanization and Flooding : What are the consequences of flooding?

Goal: Calculate water volume on natural and urban surfaces and how it affects flooding.

(What did the students do?): Two problems were calculated on the same area during the same heavy rain. This determined the amount of water absorbed by the ground and that running off into the streets.

Mathematical problem: Calculate the volume of water (V) over a 1 km² area with 50 mm² of rainfall in two environments:

• Forest: The soil absorbs 80% of the water, only 20% leaks out (C = 0.2).
• Concrete: The surface absorbs nothing, 100% leaks out (C = 1.0).

Solution: Forest: V = A · h · C= 1,000,000 m² * 0.05 m * 0.2 = 10,000 m³                                                                                                                                                    Concrete: V = A · h · C = 1,000,000 m² * 0.05 m * 1 = 50,000 m³, area, h - height of the rain, and C -  runoff coefficient.

Conclusion: We can conclude that concrete produces five times more surface water than forests do. Students discovered that urban flooding is a direct result of human impact on nature.

What did the students learn?

Students gained insights that changed their perspective on science and ecology:

• Students learned how to analyze and predict natural disasters using statistics.
• Direct Connection between Human and Nature: The second activity demonstrated that urbanization can increase water runoff by up to 500%.
• Students developed critical thinking skills by analyzing real-life problems. They thought critically and asked questions "Where and what is the boundary between urbanization and environmental safety?" and "How does urban construction affect community safety?"

Why is this important for the future? In an era of climate change, fostering environmental awareness is crucial. Mathematically literate students can use data to design sustainable cities and apply modeling as a tool to reduce natural hazard risks and protect the planet.