Hydrology: Water Balance, Precipitation, and Atmospheric Processes
Water Balance Fundamentals
The fundamental equation for water balance is:
I − O = ΔS
Where I = Inputs, O = Outputs, and ΔS = Change in Storage.
In hydrological terms, this is often expressed as:
(IE + IR) − (OO + OS) = ΔS
The change in storage (ΔS) can be calculated using the components of the hydrological cycle:
ΔS = Inputs – Outputs
= (P + Qin + Gin) – (Qout + Evt + Gout)
Water Storage Components
Atmospheric Water Storage
- Precipitation (e.g., Rain, Snow, Hail)
Surface Water Storage
- Lakes, Rivers, Streams, Ponds, and Oceans.
- Visible storage on the surface in liquid form.
Groundwater Storage
- Aquifers and (Un)Saturated Zones.
- Hidden below the surface within the ground.
- Represents huge quantities of stored water.
The Cryosphere (Ice Storage)
- Mountain glaciers and Polar Ice Caps.
- Water stored as ice in solid form.
Defining Watersheds and Catchment Areas
A Drainage Basin, also known as a Catchment or Watershed, is the total geographical area drained by a river and its tributaries.
Watershed Storage Change Equation
When analyzing a specific watershed, the change in storage (ΔS) is calculated based on local inputs and outputs:
ΔS = (P + Gin) – (Qsw + EVt + Gout)
Understanding Precipitation
Definition: Precipitation is any form of moisture originating in the atmosphere that is transferred to the Earth’s surface and exists as water in a condensed form.
Four Lifting Mechanisms of Precipitation
Convective Lifting
Lifting of a warm, buoyant air mass up into the atmosphere, where it cools and condenses into a cloud. Cooler air descends to replace the warm air being lifted.
Orographic Lifting
Lifting of an air mass caused by elevated topography (such as a mountain range), forcing the air upward and creating clouds.
Convergence Lifting
Lifting that occurs at the center of a low-pressure system, pushing warm air up into the atmosphere to create clouds.
Frontal Lifting
Lifting caused by cold air pushing warm air to higher altitudes, which results in cloud formation and precipitation events (P).
Main Sources of Atmospheric Moisture
- Evaporation from the oceans – nearly 90% of atmospheric moisture supply.
- Warm freshwater bodies (local sources such as the Great Lakes).
- Zones of lush vegetation (e.g., tropical rainforests) through evapotranspiration.
The highest amount of evaporation and moisture supply to the atmosphere occurs in the warmer areas near the equator.
Global Movement of Air Masses
Air mass movement around Earth is mainly driven by two factors:
Temperature Gradients
Temperatures are higher at the equator and lower at the poles. This difference transports air masses from warm to cold regions, creating planet-sized flow paths.
Earth’s Rotation (Coriolis Effect)
The planet’s rotation from west to east helps form large planetary circulation patterns. A ring of moist air moving towards the poles from the equator changes its radius and must accelerate to maintain angular momentum, leading to the development of westerly wind systems in certain locations.
Atmospheric Circulation Cells Explained
The global circulation system is divided into three major cells:
Tropical Cell (Hadley Cell)
Warm equatorial air rises and moves poleward. it cools, descends around 30° latitude (N or S), and branches into a return flow toward the equator and a continued flow toward the poles.
Middle Cell (Ferrel Cell)
This cell circulates air between the tropical and polar cells within the more temperate zones of the planet.
Polar Cell
Air rises around 60° latitude (N or S). As it flows northward toward the pole, it cools and descends near the ground surface at the pole.
Impact of Circulation Transition Zones
- When air is rising off the surface (e.g., at the equator), it creates large storm clouds and heavy precipitation.
- Where air is descending towards the surface from aloft, it is much drier, often causing the formation of dry lands and deserts (e.g., 30° latitude).
Six Steps of Cloud Formation
Evaporation and Transpiration
Moisture enters the atmosphere through evaporation from water bodies or is released by biological transpiration (evapotranspiration).
Adiabatic Cooling
This warm, moist air rises due to its reduced density (buoyancy). At a certain height, it begins to cool adiabatically—cooling without loss of heat, but through gas expansion at lower pressures.
Observed Lapse Rates:
- Dry air: Decrease of 1°C for every 100 meters of ascent.
- Wet (saturated) air: Decrease of 0.6°C for every 100 meters of ascent.
Reaching Saturation Point
As the warm, moist air parcels rise and the temperature drops, the relative humidity approaches its saturation point. At this critical point, condensation begins, switching the phase from gas/vapor to liquid water or ice nuclei, forming clouds.
This critical point is referred to as the Saturated Vapour Pressure, which is the total maximum amount of moisture the atmosphere can hold at a particular temperature.
Relative Humidity = Vapour Pressure / Saturated Vapour Pressure
Condensation Nucleation
At saturation, water begins to condense. The water molecules require a seed, known as a condensation nucleus, upon which they can attach.
Dust and sea salt act very well for this purpose, ranging in size from 10-3 to 10 µm (micrometers).
Droplet Growth
As condensation continues, smaller droplets increase in size through further condensation or through merging with other droplets via collisions in the turbulent air.
Precipitation Release
Eventually, these droplets become large enough to overcome the buoyant updrafts in the atmosphere. Gravity takes hold and pulls them back to the surface as precipitation.
Note: Droplets can be broken up or evaporated back into the atmosphere as they fall. The average size of a raindrop is typically 0.1 to 3 mm.
Challenges in Measuring Snowfall
Measuring snowfall accurately presents several difficulties:
- Snowfall is difficult to capture reliably in a collection gauge due to wind effects.
- The redistribution on the ground surface is irregular and heavily controlled by winds.
- The large variation in snow density or packing significantly impacts the total water content of the snow mass (Snow Water Equivalent).