<p>Assessment of latent (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation>) and sensible (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation>) heat fluxes at the air–water interface is crucial for understanding heat and mass transfer in reservoirs and supporting effective water management. Despite extensive studies, reliable evaluation of these fluxes, especially in small reservoirs, remains challenging due to limited direct measurements, such as changes in water heat storage. This study develops and evaluates an innovative framework using nonlinear regression and dimensionless groups to reliably estimate <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation> in small reservoirs. Field data from two reservoirs in Iran are employed: Alavian dam (area <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\approx2.5\text{k}\text{m}^2\)</EquationSource> </InlineEquation>, study period May 21–August 21, 2016) and Ekbatan dam (area <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\approx2\text{k}\text{m}^2\)</EquationSource> </InlineEquation>, study periods May 22–August 22, 2019; May 21–August 21, 2020; and May 22–August 22, 2021). The values of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation> from the Bowen ratio energy balance (BREB) method serve as reference, with 2021 data used for independent model validation at the Ekbatan dam. Results show the model reliably estimates <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation>, with Willmott index (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(d\)</EquationSource> </InlineEquation>) <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(&gt;0.83\)</EquationSource> </InlineEquation> for all periods, agreeing well with BREB data. RMSE and MAE are within acceptable ranges, and independent validation at the Ekbatan dam confirms the model captures <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation> variability accurately. Regarding <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(H\)</EquationSource> </InlineEquation>, estimates obtained using the Bowen ratio and predicted <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(LE\)</EquationSource> </InlineEquation> values show appropriate accuracy; RMSE ranges from <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(2.8\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(6.8\text{W}/\text{m}^2\)</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(d\)</EquationSource> </InlineEquation> exceeds <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(0.96\)</EquationSource> </InlineEquation>, indicating satisfactory alignment with reference values. Overall results highlight that a dimensionless, physically based framework is a practical tool for water resource management and energy balance assessment in small reservoirs.</p>

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A Physically-Based Framework for Estimating Latent and Sensible Heat Fluxes in Small Water Bodies

  • Amir Rezazadeh,
  • Ghorban Mahtabi,
  • Amir Amiri Roshkhar,
  • Amir Parsa Khoshahang,
  • Fatemeh Farboudi

摘要

Assessment of latent ( \(LE\) ) and sensible ( \(H\) ) heat fluxes at the air–water interface is crucial for understanding heat and mass transfer in reservoirs and supporting effective water management. Despite extensive studies, reliable evaluation of these fluxes, especially in small reservoirs, remains challenging due to limited direct measurements, such as changes in water heat storage. This study develops and evaluates an innovative framework using nonlinear regression and dimensionless groups to reliably estimate \(LE\) and \(H\) in small reservoirs. Field data from two reservoirs in Iran are employed: Alavian dam (area \(\approx2.5\text{k}\text{m}^2\) , study period May 21–August 21, 2016) and Ekbatan dam (area \(\approx2\text{k}\text{m}^2\) , study periods May 22–August 22, 2019; May 21–August 21, 2020; and May 22–August 22, 2021). The values of \(H\) and \(LE\) from the Bowen ratio energy balance (BREB) method serve as reference, with 2021 data used for independent model validation at the Ekbatan dam. Results show the model reliably estimates \(LE\) , with Willmott index ( \(d\) ) \(>0.83\) for all periods, agreeing well with BREB data. RMSE and MAE are within acceptable ranges, and independent validation at the Ekbatan dam confirms the model captures \(LE\) variability accurately. Regarding \(H\) , estimates obtained using the Bowen ratio and predicted \(LE\) values show appropriate accuracy; RMSE ranges from \(2.8\) to \(6.8\text{W}/\text{m}^2\) , and \(d\) exceeds \(0.96\) , indicating satisfactory alignment with reference values. Overall results highlight that a dimensionless, physically based framework is a practical tool for water resource management and energy balance assessment in small reservoirs.