Hydrological Redistribution of Fixed Global Water: A Linear Volumetric Flux Model for Local Precipitation Change in Ethiopian Watersheds

Overview. This preprint proposes a linear master equation for understanding local precipitation change in Ethiopia as a redistribution of Earth's fixed water supply, not as creation of new water: Pfuture = Pinitial ± S(n) where S(n) = S0 + rs·n is the net storage change over n years, S0 is the initial storage imbalance, and rs is the linear net storage rate. The sign is positive when storage releases water to the atmosphere (local precipitation rises, global precipitation falls) and negative when storage captures water (local precipitation falls, global precipitation rises). Background. Ethiopia's water security depends on reliable precipitation. Land-use change, population growth, groundwater pumping, and deforestation are altering local water budgets. The principle of conservation of mass states that total water on Earth is constant. Water moves between oceans, atmosphere, ice, groundwater, forests, and human biomass. Temperature and humidity are thermodynamic drivers of these movements — not volumetric sources of water. Methods. Two linear models are developed and validated in three Ethiopian watersheds: Abbay (Blue Nile), Awash, and Rift Valley. Storage-flux variables include net human water change (births/deaths), deforestation, afforestation, and groundwater depletion. The system is subject to the fixed global water constraint: Plocal(n) + Pglobal(n) = Wtotal = constant Validation. Hold-out design: calibration 1980–2010, validation 2011–2024. Local accuracy is assessed with R², RMSE, NSE, and PBIAS against EMI observed precipitation. The inverse global relationship is tested by regressing independent GPCC/IPCC global precipitation on S(n), expecting a slope of −1 ± 0.30. Conservation compliance is checked as |Plocal + Pglobal − Wtotal| ≤ 5%. Robustness is confirmed via ±20% parameter sensitivity and 5-fold cross-validation. Expected outputs. A validated linear master model, a decision-support tool (Excel/Python/GIS), two peer-reviewed journal articles with EWTI affiliation, a policy brief for MoWE and regional water bureaus, a training manual for EWTI short courses, and a final technical report. Abbreviations. EMI = Ethiopian Meteorological Institute; MoWE = Ministry of Water and Energy; CSA = Central Statistical Agency; EEFRI = Ethiopian Environment and Forest Research Institute; AWTI = Arba Minch University Water Technology Institute; EIWR = Ethiopian Institute of Water Resources; GPCC = Global Precipitation Climatology Centre; GRACE = Gravity Recovery and Climate Experiment; EWTI = Ethiopian Water Technology Institute; VIF = Variance Inflation Factor; NSE = Nash–Sutcliffe Efficiency; PBIAS = Percent Bias; RMSE = Root Mean Square Error. Reuse. This work is released under CC BY 4.0. All validation code will be archived on Zenodo with a DOI, and a Jupyter validation notebook will be included so reviewers can reproduce every metric.