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A Modified Fu (1981) Equation with a Time-varying Parameter that Improves Estimates of Inter-annual Variability in Catchment Water Balance

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Abstract

Fu’s equation has been widely adopted to examine the regional (inter-catchment) variability of the water balance at the catchment scale due to the simplicity and effectiveness of the Budyko framework. Fu’s equation has also been used to analyze the temporal (inter-annual) variability of the water balance, but ignoring inter-annual storage changes is a recognized weakness. The regional variability of the water balance was examined through application of Fu’s equation to long-term (1951–2000) observations of climate and runoff in 194 Model Parameter Estimation Experiment catchments across the contiguous United States. A set of hydroclimatic metrics was used to simulate spatial variability in the partitioning of precipitation for the study catchments using the free parameter \(\omega\) of Fu’s equation. Through the use of a stepwise regression model, it was found that four widely available variables, namely, seasonality of precipitation and potential evapotranspiration, seasonal synchronicity between moisture and energy, and the soil moisture storage index, explained 59.2% of the variability in \(\omega\). Application of the empirical formula of \(\omega\) to Fu’s equation explained 96.5% of the spatial variability in long-term runoff for an independent set of catchments. To explore the inter-annual variability of the water balance, a modified Fu equation was developed by incorporating inter-annual water storage changes into the estimation of evaporation and total water supply. The time-varying functional forms of the parameter \(\omega\), in terms of one or more of the selected environmental factors for each of 194 catchments, were also established at the annual scale. The results indicated that the modified Fu equation with time-varying parameter (MFETP), which accounted for the impacts of inter-annual changes in water storages and the time-variation process of \(\omega\), greatly improved estimates of inter-annual variability in the water balance compared to the conventional model. The MFETP offers an improved model for assessment of the inter-annual responses of runoff to changes in climate and watershed properties at the catchment scale.

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Data Availability

Data, models, and codes generated or used for this study are available from the corresponding author upon reasonable request.

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Funding

This research was funded by the National Natural Science Foundation of China (NSFC Grant 52109024), and the National Key Research and Development Program of China (No. 2019YFC0408903).

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Authors and Affiliations

  1. Operation and Administration Center for River Basin Hydro Complex, China Three Gorges Corporation, Yichang, 443133, China

    Shuai Li

  2. Bureau of Hydrology, Changjiang Water Resources Commission, Wuhan, 430010, China

    Tao Du

  3. Australian Rivers Institute, Griffith University, Nathan, QLD, 4111, Australia

    Christopher James Gippel

Authors
  1. Shuai Li
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  2. Tao Du
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  3. Christopher James Gippel
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Shuai Li, Tao Du, and Christopher James Gippel. The methodology was proposed by Shuai Li. The first draft of the manuscript was written by Shuai Li and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Shuai Li.

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Highlights

• The regional and temporal variabilities of the water balance in 194 MOPEX catchments were investigated using the Budyko framework.

• A modified Fu equation was developed by incorporating inter-annual water storage changes into the estimation of evaporation and total water supply.

• The modified Fu equation with time-varying parameter (MFETP) was applied to explore the inter-annual variability of the water balance.

• The MFETP greatly improved the estimates of inter-annual variability in the water balance.

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Li, S., Du, T. & Gippel, C.J. A Modified Fu (1981) Equation with a Time-varying Parameter that Improves Estimates of Inter-annual Variability in Catchment Water Balance. Water Resour Manage 36, 1645–1659 (2022). https://doi.org/10.1007/s11269-021-03057-1

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  • DOI: https://doi.org/10.1007/s11269-021-03057-1

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