Water balance equation

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Method synopsis

Comprehensive approach calculating potential evapotranspiration using three established methods (Thornthwaite, Hargreaves, Penman-Monteith) and actual evapotranspiration using the Budyko model. Provides robust estimates of water balance components for drought analysis.

Synthesized from method descriptions across 3 papers using this protocol.

Procedure from a recent peer-reviewed implementation

Steps below were extracted from the most recent peer-reviewed implementation of this protocol in the corpus — Statistical framework to assess long-term spatio-temporal climate changes: East River mountainous watershed case study (2022), Stochastic environmental research and risk assessment. The protocol was originally introduced by Estimation of Evapotranspiration Rates and Root Water Uptake Profiles From Soil Moisture Sensor Array Data (2021), Water Resources Research. Implementations in other papers (listed below) may differ.

1. Calculate potential evapotranspiration using multiple methods
   Calculate ET₀ using three different equations: (1) Thornthwaite formula using monthly average temperature with empirical coefficients, (2) Hargreaves formula using temperature and radiation with ET₀ = 0.0135Rs(Tm + 17.8) where Rs is global solar radiation, and (3) Penman-Monteith equation combining turbulent transfer and energy-balance models. The Penman-Monteith equation used reference evapotranspiration from hypothetical grass surface with calculations provided using the SPEI library in R.
   Quantities: Calculations performed for all 17 stations using monthly dataDuration: Applied to entire 1966-2021 monthly datasetConditions: Standard meteorological conditions with day length determined using DayLength function from solrad library
   Equipment: SPEI library in R, solrad library, DayLength function
2. Calculate actual evapotranspiration using Budyko model
   Apply the Budyko model which hypothesized that functional relationship between actual evapotranspiration, precipitation, and ET₀ is given by ET/P = {AI tanh(1/AI)[1−exp(−AI)]}^0.5 where AI is the Aridity Index given by AI = ET₀/P. The Budyko model provides concise and accurate representation of the relationship between annual evapotranspiration and long-term-average water and energy balance at catchment scale.
   Quantities: Applied to all 17 meteorological stations

Typical Equipment

• SPEI library in R
• solrad library
• DayLength function
• Budyko model equation

Output Measurements

• potential evapotranspiration
• actual evapotranspiration
• aridity index

Papers Using This Protocol (3)

Species Studied With This Protocol

Places Where Used