SOEE1401 Lecture 2: Definitions and Atmospheric Structure

Units

• Meteorology uses a mix of S.I. (Systeme International) units for scientific purposes and older, non-SI units for historical reasons, convenience, or public communication.
• Always specify the units used for a given value.

Temperature

• Kelvin (K): SI unit, essential for many calculations.
• Degrees Celsius (°C): Non-SI unit, commonly used for general temperature reporting due to familiarity and convenient range.
  • $0 K = -273.15 °C$
  • Conversion formula: $T<em>{Kelvin} = T</em>{Celsius} + 273.15$
• Degrees Fahrenheit (°F): Non-SI unit, widely used in America.
  • Conversion formula: $T<em>{Fahrenheit} = \frac{9}{5} T</em>{Celsius} + 32$

Pressure

• Pascal (Pa): SI unit for pressure. Atmospheric pressure is typically measured in hectopascals (hPa).
  • $1 hPa = 100 Pa$
• Millibar (mb): Non-SI unit, commonly used for pressure.
  • $1 mb = 1 hPa$
• Mean sea-level pressure: $1013.25 mb$

Wind Speed

• Metres per second (m s^{-1}): SI unit, used in scientific contexts and increasingly in general communication.
• Knots (kt): Nautical miles per hour (non-SI).
  • $1 kt = 0.514 m s^{-1} \approx 0.5 m s^{-1}$
• Kilometres per hour (kph).
  • $1 kph = 0.278 m s^{-1}$
• Miles per hour (mph).
  • $1 mph = 0.447 m s^{-1}$
• Wind speeds are reported using various units.

Wind Direction

• Convention: Wind direction indicates where the wind is coming FROM.
  • Expressed as a bearing in degrees from north (compass bearing while facing the wind).
  • Due to wind variability (gustiness), often only a general direction is given (e.g., northerly, south-westerly).

Humidity

• Relative Humidity (RH): Percentage (%) (non-SI unit).
  • Represents the ratio of the actual water vapor content to the maximum possible water vapor content at a given temperature.
  • Closely related to perceived comfort (how humid it feels).
  • Determines cloud and fog formation: condensation occurs when RH reaches 100%.
  • Formula: $RH = 100 \times \frac{P<em>V}{P</em>S}$, where $P<em>V$ is the actual vapor pressure and $P</em>S$ is the saturation vapor pressure.
  • The Clausius-Clapeyron curve relates vapor pressure to temperature.

Dew Point

• Definition: The temperature to which an air parcel must be cooled at constant pressure and water vapor content to reach saturation.
• Dew Point Depression: The difference between the actual air temperature and the dew point temperature.

Other Humidity Measures

• Mixing Ratio: Ratio of the mass of water vapor to the mass of dry air. $q = \frac{M<em>v}{M</em>a}$, where $M<em>v$ is the mass of water vapor and $M</em>a$ is the mass of dry air. Also expressed as Mixing ratio = $\frac{M<em>v}{M</em>v + M_a}$.
• Specific Humidity: Ratio of the mass of water vapor to the mass of moist air.
• Absolute Humidity (Vapor Density): Mass of water vapor per unit volume of moist air. Vapor pressure is proportional to vapor density at a given temperature.

Time

• Time is usually reported in 24-hour format and in Coordinated Universal Time (UTC), which is nearly equivalent to GMT.
  • Example: 1800 UTC.
• Using UTC is essential for meteorological analysis and forecasting, as it ensures consistent timing of measurements across different time zones worldwide.

Vertical Structure of the Atmosphere

Layers

• Troposphere
• Stratosphere
• Mesosphere
• Thermosphere

Troposphere

• Lowest layer of the atmosphere.
  • Depth: ~8 km at the poles, ~16 km at the equator (varies spatially and temporally).
  • Contains most of the atmosphere's water vapor.
  • The layer where almost all "weather" occurs.
  • Temperature generally decreases with altitude (but with significant variability).
  • Capped by the tropopause: a region of increasing temperature (temperature inversion) or an isothermal layer.
  • The tropopause acts as a "lid," inhibiting air exchange between the troposphere and stratosphere.

Boundary Layer

• A sub-layer of the troposphere.
  • In direct contact with the surface every day.
  • Experiences the direct effects of surface friction.
  • Dominated by turbulence and surface exchange processes (heat, moisture, momentum).
  • Exhibits large diurnal changes in properties like depth and temperature.
  • Depth: Varies from a few tens of meters (in stable conditions) to ~2 km over tropical oceans; typically a few 100 m to ~1 km.
  • Temperature decreases with altitude.
  • Usually capped by a temperature inversion that inhibits mixing with the air in the free troposphere above.
  • A well-defined boundary layer is not always present.

Stratosphere

• Extends from the top of the troposphere to ~50 km.
  • Temperature generally increases with altitude during summer; more complex structure in winter.
  • Contains the majority of atmospheric ozone (O3).
  • Absorption of ultraviolet radiation by ozone leads to a maximum temperature at the stratopause (sometimes exceeding 0°C).
  • Interaction with the troposphere is limited and poorly understood.

Vertical Structure: Pressure

• Pressure at any point is the result of the weight of all the air in the column above it.
• Upward force of pressure exactly balances downward force of the air's weight above.
• Pressure decreases approximately logarithmically with altitude.
  • Deviations from a logarithmic profile are due to changes in air density resulting from temperature and moisture content variations.
  • Near the surface, a 1 mb change in pressure is equivalent to approximately an 8 m change in altitude.

Horizontal Scales in the Atmosphere

Local (Microscale/Boundary-Layer Scale)

• Time: Few hours to ~1 day.
• Distance: <2 km.
• Phenomena: Local convection, small cumulus clouds, fog, hill/valley drainage flows, variations in surface wind.

Regional (Mesoscale)

• Time: Hours to days.
• Distance: A few to several 100 km.
• Phenomena: Thunderstorms, fronts, land-sea breezes.

Large Scale (Synoptic Scale)

• Time: Up to ~10 days.
• Distance: Several 100 to several 1000 km.
• Phenomena: High and low-pressure systems.

Planetary Scale

• Time: Days to months.
• Distance: Several 1000 km to global scale.
• Phenomena: Storm tracks, polar vortices, Hadley circulation.

Vertical vs. Horizontal Gradients

• Horizontal gradients are typically much smaller than vertical gradients for most quantities of interest.
• Example:
  • Pressure vertical gradient: ~$0.1 hPa m^{-1}$
  • Pressure horizontal gradient: < $0.1 hPa km^{-1}$ (typically ~$0.01 hPa km^{-1}$)

Example values of vertical and horizontal gradients

• Pressure gradient ~$4 hPa$ per $100 km$ ($0.04 mb km^{-1}$)
• Temperature vertical gradients: typically ~$0.01 °C m^{-1}$ (can be larger locally, e.g. boundary layer temperature inversion up to ~$0.2 °C m^{-1}$)
• Temperature horizontal gradients: On a large scale typically < $1°C$ per $100 km$ ($0.01 °C km^{-1}$), up to ~$5 °C$ per $100 km$ within frontal zones. Local effects may result in larger gradients on small scales.

Summary

• The atmosphere is divided vertically into distinct layers.
• The troposphere is the lowest layer and is closely connected to "weather."
• The boundary layer is a shallow sub-layer of the troposphere directly influenced by the surface and dominated by turbulent mixing.
• Large-scale horizontal gradients of pressure and temperature are generally much smaller than vertical gradients.
• Vertical gradients are offset by gravity, so the forcing processes driving synoptic weather systems are almost horizontal, and large-scale vertical motions are usually slow.