A logistics firm is developing a simulation to monitor the battery 'State-of-Health' (SoH) for its fleet of electric delivery vans. The simulation begins with a new battery at $100\%$ SoH and assumes a baseline degradation of $0.00005$ (i.e., $0.005\%$) for every kilometer driven. The fleet manager uses this model to schedule vehicle replacements and estimate the long-term resale value of the fleet.

The automated management system of a hydroelectric dam uses a computer-based simulation to regulate water flow and safety. For example, the system:

• controls the positioning of the main intake valves, the turbine speeds, and the spillway gates
• allows the operator to switch between different operational modes, such as maximum power generation or flood mitigation.

The simulation software processes high-frequency data from a network of physical sensors to maintain a real-time model of the reservoir's status.

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The rise in global temperatures has led to the melting of the sea ice in polar regions. Scientists have developed a number of computer models that can be used to make predictions about the rate of sea ice melting in these polar regions and its effect on coastal areas globally. In order to create a computer model a number of variables are identified.

A computer model of the effects of the melting of the sea ice in the Arctic Ocean may include the following variables:

• average ocean surface temperature (°C)
• albedo of the ocean (the proportion of light reflected from the ocean surface)
• precipitation (mm)
• salinity of the ocean (grammes of salt in one kilogramme of water)
• area of sea ice (km²)

In this model the following rules have been determined:

• for every 0.01 °C increase in ocean surface temperature, the area of sea ice decreases by 1 %
• for every 1 % decrease in the area of the sea ice, the sea level rises by 20 mm

The initial values are:

• area of sea ice = 1 000 000 km²
• average surface temperature of the ocean is 0.00 °C

For the next iteration, assume there is an increase of 0.04 °C in the ocean surface temperature.

The scientists observed when running the model numerous times using historical data there were significant differences between observed and expected results.

A second model was developed that included new variables and rules.

The surface of the ocean reflects the heat from the sun. The ratio between the area covered by the sea ice and the area where there is no sea ice (open ocean) affects the value of the average albedo. The lower the albedo, the quicker the sea ice will melt.

The average albedo is calculated using this formula:

$$\text{Average albedo}=\frac{(\text{area of sea ice}\times \text{albedo of sea ice})+(\text{area of open ocean}\times \text{albedo of open ocean})}{(\text{area of sea ice}+\text{area of open ocean})}$$

Note:

• area of sea ice = 1 000 000 km²
• area of open ocean = 1 000 000 km²
• albedo of sea ice = 0.6
• albedo of open ocean = 0.1

The average albedo will change with every iteration of the model. Each iteration is 2 years after the previous.

The rules for the model are:

• the initial albedo is 0.35
• the rate of decrease in sea ice every 2 years is $\frac{0.3}{{\text{average albedo}}^2}$
• the starting year is 2019
• the sample rate is every 2 years

Urban planning and infrastructure development increasingly rely on computational models to handle the complexities of modern transportation. Traffic flow simulations are used to design efficient road networks and minimize congestion in growing cities.

A regional water authority manages a primary reservoir currently containing $180$ million cubic meters ($m^3$) of water. Due to a predicted drought, engineers need to simulate the depletion of the reservoir over the next $120$ days to determine if emergency restrictions are necessary. The current estimated daily outflow for residential and industrial use is $1.5$ million $m^3$.