2.2 Water balance equation and its applications

The water balance equation is a key tool in hydrology, helping us track water movement through ecosystems. It's based on the simple idea that water in equals water out, plus any change in storage. This concept is crucial for understanding how water cycles through our environment.

Applying the water balance equation lets us calculate changes in water storage and estimate unknown components of the water cycle. This is super useful for managing water resources, predicting droughts or floods, and assessing human impacts on water systems.

Water balance equation

Components and principles

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• The water balance equation is a mathematical expression that describes the flow of water in and out of a system based on the principle of conservation of mass
• The basic form of the water balance equation is: $Change in Storage = Inflows - Outflows$
• Inflows to a hydrologic system can include:
  • Precipitation (rainfall, snowfall)
  • Surface water inflow (streamflow from upstream areas)
  • Groundwater inflow (subsurface flow from adjacent aquifers)
  • Anthropogenic inputs (wastewater discharge, interbasin transfers)
• Outflows from a hydrologic system can include:
  • Evapotranspiration (water loss to the atmosphere through evaporation and transpiration)
  • Surface water outflow (streamflow leaving the system)
  • Groundwater outflow (subsurface flow to adjacent aquifers)
  • Anthropogenic withdrawals (water abstraction for irrigation, industrial use, or domestic supply)

Spatial and temporal scales

• The water balance equation can be applied to various spatial scales, ranging from a small catchment (few hectares) to a large river basin (thousands of square kilometers) or even global scale
• The time scale over which the water balance is considered can vary from short-term to long-term depending on the purpose of the analysis
  • Short-term: daily, weekly, or monthly water balance (useful for operational water management)
  • Long-term: annual or multi-year water balance (useful for strategic planning and assessing sustainability)

Applying water balance

Calculating changes in water storage

• Changes in water storage within a hydrologic system can be calculated by rearranging the water balance equation to solve for the storage term: $Change in Storage = Inflows - Outflows$
• Positive changes in storage indicate an increase in the amount of water stored within the system
  • Examples: rising groundwater levels, increasing reservoir storage, soil moisture accumulation
• Negative changes in storage indicate a decrease in the amount of water stored within the system
  • Examples: falling groundwater levels, decreasing lake levels, soil moisture depletion
• To calculate changes in storage, accurate measurements or estimates of the inflows and outflows to the system over the time period of interest are required
  • Inflows and outflows can be measured directly (streamflow gauging, precipitation measurements)
  • Inflows and outflows can be estimated using hydrologic models or remote sensing techniques (satellite-based precipitation estimates, evapotranspiration models)

Estimating unknown water balance components

• The water balance equation can be used to estimate the magnitude of unmeasured or unknown components of the hydrologic cycle by solving for the unknown term
• Example: if precipitation, streamflow, and change in storage are known, evapotranspiration can be estimated as the residual of the water balance equation: $Evapotranspiration = Precipitation - Streamflow - Change in Storage$
• This approach is commonly used to estimate components that are difficult or costly to measure directly, such as groundwater recharge or actual evapotranspiration

Watershed water balance

Factors influencing watershed water balance

• Analyzing the water balance of a watershed or hydrologic system involves quantifying the major inflows, outflows, and changes in storage over a specified time period
• The relative importance of different water balance components can vary depending on the climate, geology, land use, and other characteristics of the watershed
  • Climate: precipitation amount and seasonality, temperature, humidity
  • Geology: soil type, aquifer properties, topography
  • Land use: vegetation cover, urbanization, agricultural practices
• In humid regions, precipitation is often the dominant inflow, while evapotranspiration and streamflow are the major outflows
  • Example: tropical rainforest watersheds (Amazon basin)
• In arid regions, evapotranspiration may exceed precipitation, resulting in a negative water balance and depletion of water storage
  • Example: desert watersheds (Mojave desert)

Temporal variability in watershed water balance

• Seasonal variations in the water balance can be significant, with different components dominating at different times of the year
  • Example: snowmelt-driven streamflow in spring, high evapotranspiration rates in summer
• Inter-annual variability in the water balance can be influenced by large-scale climate patterns
  • Example: El Niño-Southern Oscillation (ENSO) can cause wet or dry years in different regions
  • Example: North Atlantic Oscillation (NAO) can influence winter precipitation and streamflow in Europe and eastern North America
• Analyzing the water balance can help to identify the key processes and drivers of hydrologic variability within a watershed, and inform water resources management decisions
  • Example: understanding the relative contributions of snowmelt and rainfall to streamflow can help to predict and manage water supply

Human impact on water balance

Land use change and water infrastructure

• Human activities such as land use change, water abstraction, and dam construction can significantly alter the water balance of a region
• Deforestation or urbanization can reduce infiltration and increase surface runoff, leading to higher peak flows and reduced baseflow in streams
  • Example: conversion of forests to agricultural land in the Amazon basin
  • Example: urban expansion and increased impervious surfaces in cities
• Irrigation can increase evapotranspiration rates and reduce downstream water availability, particularly in water-scarce regions
  • Example: intensive groundwater-based irrigation in the High Plains aquifer of the central United States
• Dams and reservoirs can alter the timing and magnitude of streamflow, with impacts on downstream ecosystems and water users
  • Example: the Three Gorges Dam on the Yangtze River in China

Groundwater depletion and climate change

• Groundwater pumping can lower water tables and reduce baseflow to streams, leading to depletion of aquifers and subsidence of land surface
  • Example: overexploitation of the Central Valley aquifer in California
• Climate change, which is largely driven by human activities, can affect the water balance through changes in precipitation patterns, temperature, and evapotranspiration rates
  • Example: increased frequency and intensity of droughts in the Mediterranean region
  • Example: accelerated melting of glaciers in the Himalaya, affecting downstream water availability
• Evaluating the impact of human activities on the water balance requires a comprehensive understanding of the complex interactions between human and natural systems, and the use of integrated hydrologic models and decision support tools