How Does Maths Help Predict Rain And Temperature?

Before we get to the maths, here are the basics on temperature and rainfall.

Temperature is a measure of how cold or hot something is. It is usually measured in degrees Celsius (°C) or degrees Fahrenheit (°F). The temperature of an object or substance is a measure of the average kinetic energy of the particles that make up the object or substance. The higher the temperature, the more energetic the particles are, and the faster their movement. If the temperature is low, the particles are less energetic and move slower.

Rainfall is the amount of water that falls from the sky as precipitation, such as rain, snow, sleet, or hail. It is measured in millimetres or inches and is typically recorded over a specific period of time, such as a day, week, month, or year. Rainfall is an important factor in the water cycle, necessary for agriculture and an important source of freshwater. The amount of rainfall that an area receives varies greatly depending on its location, climate, and weather patterns.

Process Of Rainfall

Rainfall is a vital part of the Earth's water cycle, which plays a crucial role in maintaining the Earth's climate and supporting life on the planet. The process of rain begins with evaporation, in which the sun's energy causes water to evaporate from the surface of the Earth, from water bodies, soil, and plants. The water vapour rises into the atmosphere, cooling along the way. It condenses into droplets which, eventually, form clouds.

Once the clouds become dense and heavy, the water droplets will combine and grow until they become too heavy to stay suspended. At this point, the water droplets will fall from the clouds as precipitation.

Precipitation can take different forms depending on the temperature of the air and the altitude at which the clouds are located. If the air is cold and the clouds are high in the atmosphere, the precipitation will be in the form of snow. In other words, if the dew point is less than 0 degrees celsius, then precipitation may fall as snow. If the air is warmer,and the dew point is more than 0 degrees celsius, then precipitation may fall as rain. Hail is a type of precipitation that forms when thunderstorms produce strong updrafts that carry raindrops up into the freezing upper levels of the atmosphere.

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Correlation Between Rainfall And Temperature

Temperature and rainfall are closely linked and play important roles in the climate and Earth's water cycle. Temperature plays a key role in the water cycle as it determines the rate of evaporation and also the type of precipitation that forms.

For example, if the air is warm and the temperature is high, more water will evaporate from the Earth's surface, and the atmosphere will be more saturated with water vapour. This can lead to precipitation in the form of rain. If the air is colder, less water will evaporate, and the atmosphere will be less saturated with water vapour. If there is precipitation, it could be snow or sleet.

Temperature can also affect the amount of rainfall in an area. In general, warmer temperatures are associated with more rainfall, while colder temperatures are associated with less rainfall because warmer air can hold more moisture.

Rainfall, Temperature, And Mathematics

We know that in a linear equation y = mx + c, if we give the value of x we can calculate the value of y. If we know the constants m and c, this equation can be written for multiple parameters on which rain and temperature are dependent.

y = m₁x₁ + m₂x₂ + .......... m_nx_n + c

Here m₁, m₂, ...........m_n, and c are constants. x₁, x₂, ........x_n represent different parameters such as humidity, temperature, months, evaporation, sunshine, and wind-speed.

Using different sensors we record the data for the different parameters at the meteo weather station. A meteorological weather station is a facility on land or on the sea with instruments to record the weather conditions. This data is processed with the help of data analytics. Using exploratory data analysis, we can find correlations between different parameters and rainfall. These correlations are known as features. In India, in the months of June to September, there is more chance of train which is an example of a feature. Another example of a feature is if high evaporation rate then there is a high chance of rainfall.

These features are used in different models to predict rainfall. The different models work on the concept of the equation given above. In this equation, different parameters are given as input and according to the value of y rainfall can be predicted. The following diagram details the different steps in the prediction of rain and temperature.

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There are various mathematical models that can be used to predict the weather. Indian Meteorological Department (IMD) uses Numerical Weather Prediction (NWP) model for weather forecasting. Some of them are detailed below.

Numerical Weather Prediction (NWP) Models

NWP models can be used to make short-term weather forecasts, as well as long-term climate predictions. These models use complex mathematical equations to simulate the physical processes that affect the atmosphere and weather.

Statistical Models

There are many different statistical models that can be used such as linear regression and decision trees. These models use probability and statistics for the prediction of rain and temperature. These models also use statistical analysis and historical data to make predictions about future temperatures. For example, a model might use data on past temperatures, humidity, atmospheric pressure, and other factors to predict future temperatures.

Machine Learning Models

These models are based on mathematical algorithms that can automatically learn patterns in data and make predictions based on those patterns. They can be trained on large datasets of weather and climate data to make accurate temperature predictions. It is important to carefully evaluate the performance of any machine learning model before using it for weather forecasting, as some models may perform better than others depending on the specific dataset and prediction task. There are many different machine learning models that can be used for the prediction of rain and temperature such as neural networks, random forests, decision trees, etc.

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Physical Models

These models use the laws of physics, complex mathematical equations, and a wide range of data including observations from weather stations, satellites, and other sources to simulate the behaviour of the atmosphere and predict temperature. Physical models can be used to make both short-term and long-term temperature predictions.

Hydrological Models

These are mathematical models that are used to simulate the movement, distribution, and management of water through the Earth's surface, in the soil, and in the atmosphere, and can be used to predict the amount of rainfall that will reach the ground and be available for use.