Enviro Sci 1CO3: Adiabatic Processes, Water Balance, and Global Circulation

Environmental Science 1CO3: Adiabatic Processes and Atmospheric Stability

Adiabatic processes describe the thermodynamic change in an air parcel when it rises or sinks without heat exchange with the surrounding environment. All work is performed internally within the parcel through expansion or contraction.

• Adiabatic Lapse Rates:

  • Dry Adiabatic Lapse Rate (DALR): A constant rate at which unsaturated air parcels cool as they rise or warm as they sink. It is always $10\,^{\circ}\text{C/km}$.
  • Moist Adiabatic Lapse Rate (MALR): Also known as the Saturated Adiabatic Lapse Rate (SALR), this applies once an air parcel reaches its dew point and saturation occurs, leading to condensation and cloud formation. LATENT heat released during condensation slows the cooling rate. In typical examples, this is approximately $6\,^{\circ}\text{C/km}$ or $5\,^{\circ}\text{C/km}$.
  • Environmental Lapse Rate (ELR): The actual rate at which the surrounding stationary air cools with height which varies by location and time.

• Atmospheric Stability Conditions:

  • Absolutely Stable Atmosphere: Occurs when $ELR < MALR < DALR$. A rising air parcel cools faster than the environment, becomes denser, and sinks back to the surface. This inhibits mixing.
  • Absolutely Unstable Atmosphere: Occurs when $MALR < DALR < ELR$. A rising parcel cools slower than the environment, remaining warmer and more buoyant, leading to natural ascent and the formation of clouds like Cumulonimbus.
  • Conditional Stability/Unstability: A situation where the atmosphere is stable for unsaturated parcels but becomes unstable if parcels reach saturation (the LCL).
  • Level of Free Convection (LFC): The altitude where a rising parcel becomes warmer than the surrounding air and begins to rise freely.

Numerical Applications of Air Parcel Behavior

Consider an initial surface temperature of $40\,^{\circ}\text{C}$ for both an air parcel and the environment.

• Scenario at $1000\,m$:

  • Parcel (DALR) cools by $10\,^{\circ}\text{C}$ to reach $30\,^{\circ}\text{C}$.
  • Environment (ELR at $8\,^{\circ}\text{C/km}$) reaches $32\,^{\circ}\text{C}$.
  • Condition: Stable (Parcel is cooler than environment).

• Scenario at $2000\,m$:

  • Parcel (DALR) reaches $20\,^{\circ}\text{C}$.
  • Environment (ELR) reaches $24\,^{\circ}\text{C}$.
  • Condition: Stable.

• Transition to Saturation at $5000\,m$:

  • If the parcel reached saturation at $4000\,m$ and switched to $\text{MALR} = 6\,^{\circ}\text{C/km}$, while the environment stayed at $\text{ELR} = 8\,^{\circ}\text{C/km}$.
  • At $4000\,m$, both are at $8\,^{\circ}\text{C}$.
  • At $5000\,m$, the parcel cools by $6\,^{\circ}\text{C}$ to reach $2\,^{\circ}\text{C}$. The environment cools by $8\,^{\circ}\text{C}$ to reach $0\,^{\circ}\text{C}$.
  • Condition: Unstable (Parcel $2\,^{\circ}\text{C}$ > Environment $0\,^{\circ}\text{C}$).

Orographic Uplift and Rain Shadows

Orographic uplift occurs when an air mass is forced to rise over a mountain chain.

• Process on the Windward Side:

  1. Air rises and cools at the DALR until it reaches the Lifting Condensation Level (LCL).
  2. Once at the LCL, the temperature equals the dew point, and the air cools at the MALR as moisture condenses to form clouds and precipitation.

• Process on the Leeward Side:

  1. As the air passes the summit, it has lost most moisture. It descends and warms at the DALR exclusively.
  2. This results in a warm, dry area known as a Rain Shadow.
  3. There is no such thing as a "dew point cooling rate."

Final Exam Level Calculation: Mountain Transit

Problem: An air parcel starts at sea level ($0\,m$) at $16\,^{\circ}\text{C}$. Its dew point is $10\,^{\circ}\text{C}$. It rises over a summit where the temperature is $-4\,^{\circ}\text{C}$ and descends to an interior basin at $100\,m$ above sea level.

1. Find Altitude of Dew Point:$\text{Change in Temp} = 16\,^{\circ}\text{C} - 10\,^{\circ}\text{C} = 6\,^{\circ}\text{C}$.     $\text{Altitude} = \frac{6\,^{\circ}\text{C}}{10\,^{\circ}\text{C/km}} = 0.6\,km\, (600\,m)$.

2. Find Change in Altitude from Dew Point to Summit:$\text{Using MALR of } 5\,^{\circ}\text{C/km}: 10\,^{\circ}\text{C} - (-4\,^{\circ}\text{C}) = 14\,^{\circ}\text{C}$.     $\text{Change} = \frac{14\,^{\circ}\text{C}}{5\,^{\circ}\text{C/km}} = 2.8\,km$.     $\text{Summit Total Altitude} = 0.6\,km + 2.8\,km = 3.4\,km$.

3. Find Temperature at Interior Basin ($100\,m$ or $0.1\,km$):$\text{Descent distance} = 3.4\,km - 0.1\,km = 3.3\,km$.     $\text{Warming at DALR} = 3.3\,km \times 10\,^{\circ}\text{C/km} = 33\,^{\circ}\text{C}$.     $\text{Final Temp} = -4\,^{\circ}\text{C} + 33\,^{\circ}\text{C} = 29\,^{\circ}\text{C}$.

Precipitation Forms and Temperature Profiles

• Rain: Snow falls from a cold cloud, reaches a layer above freezing, melts into water droplets, and hits the ground above $0\,^{\circ}\text{C}$.
• Snow: The entire atmospheric profile remains below freezing point. Snowflakes reach the ground without melting.
• Sleet: Snow melts into rain in a warm layer (temperature inversion) but refreezes into ice pellets while falling through a deep freezing layer near the ground.
• Freezing Rain (Glaze): Snow melts into rain in a warm layer and then encounters a shallow freezing layer just above the ground. The water becomes supercooled and freezes instantly upon contact with cold surfaces (e.g., the 1998 Ice Storm in Kingston and Montreal).
• Supercooled Water: An intermediate, gel-like state where water remains liquid below $0\,^{\circ}\text{C}$ because it has not had time to crystallize. It is common in cloud formation at high altitudes.

Acid Rain Neutralization and Calculations

• Soil buffering: Soils in the Prairies and Southern Ontario are rich in Limestone (calcium carbonate, $CaCO_3$), providing high buffering capacity. Igneous/metamorphic rocks like Granite, Feldspar, and Tephra have low buffering capacity.
• Neutralization Formula Example:
  • Neutralize $400\,mm$ rain on $0.75\,ha$ at pH 2.
  • $\text{Volume} = 0.4\,m \times (0.75 \times 10,000\,m^2) = 3,000\,m^3 = 3,000,000\,L$.
  • $\text{Conc of } [H^+] = 10^{-2} = 0.01\,mol/L$.
  • $\text{Total Moles } H^+ = 3,000,000 \times 0.01 = 30,000\,moles$.
  • Neutralization: $1\,mole\, CaCO_3\, (100\,g/mol)$ has a valence of 2.
  • $\text{Amount Required} = \frac{30,000\,moles \times 100\,g/mol}{2} = 1,500,000\,g = 1,500\,kg$.

The Water Balance and Climate Indicators

• Hydrologic Cycle Distribution: $97\%$ of Earth's water is in oceans. Freshwater is $<3\%$. Most freshwater is trapped in ice/glaciers (Antarctica and Greenland).
• Water Balance Equation: A local-scale description of the cycle: $\text{Precipitation} = \text{Evapotranspiration} + \text{Runoff} + \text{Change in Storage}$.
• Potential Evapotranspiration (PE): Atmospheric demand for moisture, primarily a function of temperature.
• Actual Evapotranspiration (AE): The actual amount of water released, limited by available precipitation and soil storage.

Regional Climate Graphs:

• Kingsport, Tennessee (Maritime Influence): High precipitation throughout the year ($>1000\,mm$). Soil storage recharge occurs in winter; a slight deficit occurs in high-demand summer months.
• Ottawa, Ontario (Continental Climate): Showcases PE of $0$ during winter months because it is below freezing. Significant moisture supply in winter/spring, high demand in summer, and recharge in autumn.
• San Juan, Puerto Rico (Maritime Tropical): Temperatures year-round above $25\,^{\circ}\text{C}$. High precipitation fluctuations due to the Intertropical Convergence Zone (ITCZ).

Water Management and Human Interaction

• Agriculture: $80\%$ of the world\'s almonds are grown in California. This requires flood irrigation, consuming $40\%$ of the state\'s water supply. Canada is not food self-sufficient and depends on California for two-thirds of its fruits/nuts and one-third of its vegetables.
• Urban Flooding: Impervious surfaces (asphalt, concrete) reduce Soil Storage. This leads to:
  1. Increased stream discharge.
  2. A shorter lag time between rain events and peak discharge (Peak occurs much sooner).
• Urban Solutions:
  • Rain Gardens: Revegetate sidewalks to restore natural infiltration.
  • Green Roofs: Capture water at the source and reduce the Urban Heat Island effect.
  • Permeable Pavement: Encourages latent heat flow and groundwater recharge.
  • Downspout Disconnects: Routes roof water to lawns rather than sewer systems.

Global Atmospheric Circulation and Toxins

• Mercury ($Hg$) Pollution: The only liquid metal at room temperature. It has a boiling point near water, allowing it to evaporate and travel with moisture.

  • Grasshopper Effect/Long-Range Transport: Pollutants bounce from low/mid-latitudes to the poles by evaporating and precipitating repeatedly.
  • Methylation: Bacteria in sediments convert inorganic mercury into Methylmercury, which enters the food web.
  • Bioaccumulation/Biomagnification: Mercury concentrations increase at each trophic level. Highest levels are found in apex predators like Polar Bears and humans (specifically pregnant mothers in the Arctic, with some blood levels reaching $40\,\mu g/L$, far exceeding the WHO limit of $2.5\,\mu g/L$).

• Wind Generation Forces:

  1. Pressure Gradient Force (PGF): Moves air from High to Low pressure. Stronger where isobars are closely packed.
  2. Coriolis Force: Caused by Earth's rotation; deflects winds to the right in the Northern Hemisphere. It acts at a 90-degree angle to the wind direction.
  3. Friction: Occurs only at the surface (below $700\,m$), slowing wind and dragging it across isobars.
  4. Geostrophic Winds: Occur at high altitudes where PGF and Coriolis are balanced, resulting in winds flowing parallel to isobars.

• Global Wind Systems:

  • ITCZ: Permanent low pressure at the equator where air rises and cools.
  • Hadley Cells: Circulation between the equator and $30\,^{\circ}$ latitude.
  • Jet Streams: High-altitude geostrophic winds located at the Polar Front (where Westerlies meet cold polar air). The core is located where the pressure gradient is greatest.
  • Rossby Waves: Large-scale undulations in the jet stream that can cause cold air capsules to break off into mid-latitudes.