Chapter 4. Atmospheric Temperature and Stability 4.1 The temperature structure of the atmosphere Most people are familiar with the fact that the temperature of the atmosphere decreases with altitude. The temperature outside a commercial airliner at 12 km (36,000 ft) is typically -40°C or colder. Mountains are often capped with snow and ice, while adjacent valleys are green and lush. In this section we introduce students to the physical principles that explain the decline of atmospheric temperatures aloft and examine the condensation process in clouds and its effects on atmospheric temperature. We then study the concept of stability: what determines whether air is buoyant and convection can take place, or whether the atmosphere is stable and air parcels tend to return to their original altitude when displaced. The circulation in the atmosphere, which is driven to a large extent by convective motions, is discussed in Chapter 5; radiative processes (absorption and reflection of sunlight, thermal radiation (radiant heat)), which also play important roles in determining temperature and climate, are discussed in Chapter 6. Latitude=30N mesosphere Fig. 4.1 Average observed temperature distribution with altitude. The temperature of the stratosphere atmosphere on average in summer is shown for 30° N latitude, along with the names given to the major regions of the atmosphere (troposphere, stratosphere, mesosphere). The upper boundaries of the Altitude (km) troposphere and stratosphere ("tropopause", "stratopause", respectively) are indicated as horizontal lines. troposphere 0 102030405060 220 240 260 280 300 T (K) The lowest region of the atmosphere, up to the first temperature minimum at 12 - 16 km, is known as the troposphere, a name derived from the Greek words tropos, turning, and spaira, ball. The troposphere is relatively unstable because of the decrease of temperature with altitude. Air in the troposphere is poised to over-turn (to convect) much like water in 1 a kettle heated from below. Most of the weather of the planet is confined to the troposphere. The upper boundary of the troposphere, the altitude corresponding to the temperature minimum, is known as the tropopause. Temperature increases with altitude in the stratosphere (tropopause to 45 km), from the Latin word stratus meaning stretched out or layered. Vertical motions are strongly inhibited in the stratosphere as a consequence of the increase of temperature with altitude; an air parcel that is pushed upwards becomes denser than the air it seeks to displace and is driven back to its point of origin as we discuss below. The temperature maximum near 45 km (the stratopause) marks the upper boundary of the stratosphere. As we shall see, most of the world's ozone (O3) is contained in the stratosphere. Stratospheric ozone is vitally important to life because it absorbs harmful ultraviolet light from the sun, preventing it from reaching the earth's surface. Stratospheric ozone has been studied intensively for the last 30 years, reflecting concerns that global-scale changes have been caused by human activities (Chapter 7). The region of decreasing temperature above the stratopause is known as the mesosphere (from the Greek word mesos, middle). Above the mesopause (85 km) there is a region of very rapidly increasing temperature called the thermosphere (not shown in the figure), which attains the highest temperatures observed anywhere in the atmosphere. Densities are extremely low, and satellites orbit Earth for extended periods of time in the thermosphere. Thousands of kilometers above the surface, the atmosphere merges slowly with the interplanetary medium. 4.2 Displacement of an air parcel with altitude: work done by an air parcel on the atmosphere We now examine one of the basic factors causing atmospheric temperatures to decrease with altitude in the troposphere: work must be done on the atmosphere by a rising air parcel. (The other major factor, atmospheric radiation, is discussed in Chapter 6). Consider taking a parcel of air and moving it vertically from altitude Z1 to Z2 (see Fig. 4.2), not allowing heat or mass to exchange between the parcel and the environment. If we initially keep the volume fixed, then the pressure remains equal to P1. From the barometric law, we know that the ambient pressure P2 at Z2is lower than the initial pressure P1 that the parcel had at Z1, and we therefore allow the parcel at Z2 to expand until the pressure inside is equal to the ambient pressure. As the air parcel expands, it pushes against the force due to the pressure of the surrounding atmosphere, doing work (Chapter 2). To do this work, the parcel requires energy, but we have not allowed heat to be added to the parcel. Where does this energy come from? The only source is the kinetic energy of the molecules inside the air parcel. We know from Chapter 2 that this internal energy is related directly to temperature, E = 3/2 kT. Since energy is conserved ("1st Law of Thermodynamics") the work done by the parcel on the atmosphere must be accompanied by a drop in temperature. This is a fundamental reason why atmospheric temperature decreases with altitude. 2 We can determine the temperature change of an air parcel with altitude when the parcel moves verticall without exchanging any heat with its surroundings. This quantity, ∆T/∆Z, is called the adiabatic lapse rate. (The term adiabatic refers to the fact that the parcel is not permitted to exchange heat with the atmosphere.) Consider an air parcel with mass m Pressure and work on a vertically-displaced air parcel Figure 4.2 Vertical displacement of an air parcel. The parcel does work on This diagram illustrates the atm expanding from schematically the upward P1->P2 at Z2 displacement of an air parcel in the atmosphere, from altitude Z1 to Z2.. No exchange of heat or mass is allowed with the environment. Since pressure decreases with height (left panel, Z (km) barometric law), the parcel will P2,Z2 P2,Z2 P1,Z2 P1,Z2 expand in volume and pressure will drop inside; in the process, the parcel does work on the P1,Z1 P1,Z1 atmosphere at Z2, and the temperature of the parcel 0 5 10 15 decreases by an amount given by 0.0 0.4 0.8 the adiabatic lapse rate. P (bar) that is raised distance ∆Z, for example, due to the wind blowing over a mountain. As our parcel goes up the mountain, another parcel goes down. Let us suppose that the distribution of temperature and pressure in the atmosphere is so arranged that no energy has to be supplied to effect the switch--the parcel that is falling gains just enough energy to pull the other parcel up, like a perfectly matched pair of cable cars. What will be the relationship between temperature and pressure, given that pressure and altitude obey the barometric law? Since no energy needs to be supplied to exchange the parcels, and work is done against gravity by the rising parcel, there must be an exact trade between internal energy and gravitational energy. That means that the sum of these two is same in all parcels with the same mass at any altitude. The work done against gravity (mg∆Z, see work defined in Chapter 2) must exactly balance the amount of energy extracted from the internal kinetic energy of the air molecules in the air parcel. The extracted energy is defined as -m cp ∆T, where cp is the specific heat of air, the amount of energy required to raise the temperature of 1 kg of air by 1°C (cp 1005 J/kg). We therefore know that the two quantities are equal (work against gravity and energy extracted from molecules): mg ∆Z=-m cp∆T Eq. 4.1a which can be re-arranged to yield the remarkably simple ∆T / ∆Z = -g / cp = -9.8° C / km. Eq. 4.1b ∆T / ∆Z, the adiabatic lapse rate, is the temperature change for an air parcel (cools if it moves up, warms if it moves down) when it suddenly moves from one altitude to another. 3 Our special atmosphere, where all parcels move up or down freely without exchanging energy with the environment, is said to be neutrally stable as discussed below. There are many ways that an air parcel can be forced to move adiabatically in the real atmosphere. If the air blows over an obstacle, such as a mountain, the upward motion on the front side and downward motion on the rear side occur too rapidly for heat or mass to be exchanged with the surroundings. If air near the ground is heated, for example by absorption of sunlight by the ground, then the scale height H increases and the whole air column will be pushed upwards. Air parcels forced to move in this way have no way to know if their motion is balanced by that of other air parcels, or if they are being push up or down some other way. Therefore, air parcels forced to move up or down adiabatically and which maintain pressure equal to the surrounding atmosphere, change temperature with altitude as given by the adiabatic lapse rate (Eq. 4.1b). Note that the ambient atmosphere need not have this lapse rate (usually the atmosphere is not neutrally stable), so the parcel that has moved will usually be at a different temperature than the surrounding air. It will therefore have a different density (Perfect Gas Law). This distinction, between the temperature change in a parcel forced to move vertically and the temperature change with altitude in the ambient atmosphere, represents a key concept in the discussion that follows. 4.3 Stability adibatic A stable B Fig 4.3 Ambient lapse rates and parcel unstable temperature changes.