2. Transport of Pollutants - Box Models in Water

Okay, so, let’s consider two things, first thing to be considered is what is called as the temperature profile as a function of height. So, we are saying that vertical convection happens as a result of thermal forces which means there’s a temperature difference. So, what is the temperature difference that will result in vertical movement of air masses? So, which means that I need to know what is the temperature profile as a function of height. So let us say that this axis is temperature, it is also the ground. This is height Z.

The temperature profile describes how temperature changes with height in the atmosphere. When we refer to vertical convection, it means that differences in temperature can cause air to move up or down. For example, warmer air tends to rise because it is less dense, while cooler air sinks. To understand this movement, we need to measure the temperature at different heights. The ground temperature creates a baseline for how temperature typically changes as you go higher into the atmosphere.

Think of a hot air balloon. The hot air inside the balloon is warmer than the air outside. As the hot air rises, it takes the balloon along, just like warm air rising in the atmosphere. If we plotted the temperature on one axis and height on another, we would see the relationship between these two variables clearly.

During daytime the radiation heats up the soil or the land faster than it heats the air. So, the radiation directly heats the soil. As a result, this temperature of the soil is very high. You can see that normally, when you are in summer or in the peak daytime, the land is very hot. You can see that in summers, it is much hotter than what the temperatures in the air are.

During the day, the sun heats the ground more quickly than it heats the air above it. This creates a temperature difference where the ground is much warmer than the air. The heat from the soil begins to warm the air directly above it, which causes a vertical temperature gradient. As a result of this gradient, the air near the ground becomes less dense and starts to rise.

Imagine standing on hot sand at the beach. Your feet feel very warm because the sand absorbs the sun's heat quickly. The air above the hot sand is also warmer than the air at a higher point, leading to rising warm air and creating an upward draft.

What happens when there is no radiation, say at 7pm, 6:30 or 7pm, sun is set, no radiation, what then starts happening? The soil then starts cooling, it cools very rapidly; it is given up all its heat.

As the sun sets, the ground loses its heat rapidly because there is no incoming solar radiation. This cooling process means the air close to the ground remains warmer for a time, but eventually, the cooler ground affects the air above. As the ground cools faster than the air, the air starts to cool down too, but this process takes time.

At night, the warmth of your body can feel greater when wrapped in a blanket. The blanket prevents the heat from escaping quickly, but eventually, as the blanket cools, you feel colder. Similarly, the ground cools down quickly at night, affecting the air temperature above.

Then when you have morning 6am or 7am sun rises, it starts going reverse because now you will start seeing things like this (see in the picture). The reverse is happening, the land starts heating up very quickly and it then starts heating the air on top of it.

In the morning, when the sun rises, the ground begins to warm again rapidly. This heat is transferred to the air, reversing the cooling trend from the night before. The air close to the ground once again becomes warmer than the air above, leading to upward movement of air (thermal convection) as it warms up.

Think about a cold morning when you feel the warmth of the sun on your face. As the sun rises higher, it immediately warms the ground, just like a heater warming a room. The air near the heated ground becomes warm, causing it to rise and cool air to move in, creating a breeze.

This profile is called as an environmental lapse rate. It is called a lapse rate because it is the temperature profile as a function of height. The environmental lapse rate varies from place to place throughout the day, season to season.

The environmental lapse rate is the rate at which air temperature decreases with an increase in altitude. This rate is not constant and changes according to various factors such as location and time of year. Higher altitudes typically have cooler temperatures, but local conditions can alter this expected change.

Imagine hiking up a mountain. As you climb, you may start feeling cooler as you gain altitude, even on a warm day at the base. This phenomenon illustrates the environmental lapse rate – the temperature drops as you move higher up the mountain.

So this region is called as the temperature inversion. The temperature inversion means generally in the daytime temperature is reducing as a function of height, but here temperature is increasing as height.

Temperature inversions occur when a layer of warm air traps cooler air below it. This can happen during stable conditions when the ground cools at night and warm air settles above. Inversions can prevent pollutants from dispersing because the warmer air above can create a cap, trapping pollutants near the surface.

Consider a foggy valley in the morning. The warm air above traps cool air near the ground, where the fog collects. Until the warm air layer dissipates, the fog (and any pollutants within it) remain trapped, illustrating how inversions can hold pollution close to the ground.

If I release a parcel of air coming from a pollutant source, several things can happen to it depending on what is the condition in the environmental lapse rate.

When pollutants are released into the air, their behavior depends on their temperature relative to the surrounding air. If the pollutant is warmer, it will rise due to buoyancy. If the environmental lapse rate supports this upward movement, the pollutants can disperse. If not, they may remain trapped close to the source, causing concentration.

Imagine steam escaping from a hot cup of coffee. The steam rises because it is warmer than the surrounding air. If the air around is cooler (like when you are outside on a cold day), the steam will rise higher and disperse, just like pollutants that are warmer than their surroundings.

This is called atmospheric stability. So, if the temperature of this parcel is always going to be higher than that of the environmental surroundings, that means it has greater buoyancy.

Atmospheric stability refers to how likely air parcels are to rise or sink based on their temperature compared to the environment. When an air parcel is warmer than the surrounding air, it tends to rise. If it's cooler, it will sink. If temperatures are similar, the air parcel remains stable. This stability affects pollutant transport in the atmosphere.

Think of a feather and a rock. If you try to drop both at the same time, the feather might flutter down slowly due to air resistance (stable), while the rock drops straight down (sinking due to greater weight). Similarly, warm and cold air behave in this way concerning buoyancy.

If you have a stable environment, this height is very high, it has the opportunity to mix in a larger volume; therefore, the concentration of rho is going to be smaller in the case of an unstable environment.

In a stable atmospheric condition, pollutants tend to remain trapped close to their source, leading to higher concentrations. However, in an unstable environment, the mixing height increases, allowing pollutants to disperse over a larger area, which lowers their concentration. Wind plays a crucial role in this process by moving pollutants horizontally.

Imagine spraying perfume in a small closed room versus a large open space. In the closed room, the fragrance stays concentrated and strong; outside, it quickly disperses and becomes faint. Wind acts like the open space that helps spread out the pollution.

The definition of what people call as the mean mixing height which is the intersection of the adiabatic and environmental lapse rates.

Mean mixing height is the altitude at which the environmental lapse rate and adiabatic lapse rate intersect. This height is crucial for understanding how pollutants will behave after being emitted. A higher mixing height means better dispersion of pollutants, while a lower height means they will remain concentrated.

Think about a pot of boiling water. The steam rises until it reaches a point where it spreads out in the air. If the steam cannot rise far, it stays concentrated near the pot, just as pollutants will behave when mixing height is low.

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