RESEARCH PAPER
Net radiation estimation using the Brunt equation for clear sky emissivity and air and canopy temperatures for longwave radiation in well watered crops
 
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1
Institute of Agricultural and Technological Sciences, Federal University of Rondonópolis, Avenida dos Estudantes, 5055, Cidade Universitária, Rondonópolis, MT, Brazil
 
2
Texas A&M AgriLife Research and Extension Center at Uvalde, 1619 Garner Field Road, Uvalde, Texas 78801, United States
 
3
Dipartimento di Scienze Agrarie, Alimentati e Forestali, Università degli Studi di Palermo, Italy
 
 
Final revision date: 2026-06-09
 
 
Acceptance date: 2026-06-16
 
 
Publication date: 2026-08-24
 
 
Corresponding author
Thiago F. Duarte   

Institute of Agricultural and Technological Sciences, Federal University of Rondonópolis, Brazil
 
 
Int. Agrophys. 2026, 40(4): 423-435
 
HIGHLIGHTS
  • Rn estimates improve when using the Brunt model calibrated at the regional scale
  • Regionally calibrated Brunt model applies at local scale
  • In well-watered crops, daily Rn can use Tair instead of Tc
KEYWORDS
TOPICS
ABSTRACT
Net radiation (Rn) is commonly estimated using models that apply the Brunt equation to calculate incoming longwave radiation and use air temperature (Tair) to estimate outgoing longwave radiation under reference conditions. This study evaluated two previously calibrated Brunt models to estimate Rn without site-specific calibration and assessed whether Tair can substitute for canopy temperature (Tc ) under well-watered crop conditions. Measurements were collected in sesame and cotton fields during the first year and in a cotton field during the second year, when Tc was also measured. Net radiation was estimated at hourly and daily time scales. Across all methods, errors were higher at the hourly scale than at the daily scale. Daily-scale performance metrics showed RMSE values of 11.88 and 13.45 W m⁻² and KGE values of 0.91 and 0.74 for the first and second years, respectively. Both regionally calibrated Brunt models outperformed the Allen/FAO method. Although statistical differences were detected between Rn estimates derived from Tair and Tc , regression analyses and error metrics indicated that these differences were small, particularly at the daily scale. Therefore, the calibrated Brunt equations effectively improve Rn estimation, and Tair can reliably replace Tc for daily Rn calculations under well-watered conditions.
ACKNOWLEDGEMENTS
We appreciate Ray King, Bethany Speer, Sixto Silva, Dalton Thompson, Angela Jones, Joe Gonzalez and Randy Cox for assistance in crop management and field sample collection, and Christine Thompson and Liza Silva for administrative support. We thank the late Professor Dr. J. Tom Cothren for advice on cotton variety selection for the 2015 cotton trial and appreciate the help from Dale A. Mott for providing seeds for the 2025 cotton trial. We thank Dr. Charles Stichler for advice on sesame management.
FUNDING
This work was supported by Texas A&M AgriLife Research Cropping System Program (Leskovar), Sesaco Co. Uvalde Field Trial project (Dong and Leskovar), Cotton Incorporated/Texas State Support Committee project 20-557TX (Dong), USDA-NIFA Hatch project 9574-2 (Dong), USDA Multi-State Specialty Crop Project TX-SCMP-19-01 (Leskovar), and Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES/ PRAPG) Notice 14/2023 (Duarte). The work also received support from University of Palermo, Italy for Tortorici to visit Uvalde Research Center.
CONFLICT OF INTEREST
The authors have no conflicts of interest to disclose.
ADDITIONAL INFORMATION
CRediT authorship contribution statement. Thiago F. Duarte: writing – original draft, Writing – review and editing, conceptualization, data curation, visualization, software, methodology, investigation, formal analysis, validation, funding acquisition. Xuejun Dong: writing – review and editing, conceptualization, methodology, investigation, data curation, validation, supervision, resources, funding acquisition, project administration. Uzair Ahmad: writing – review and editing, data curation, investigation. Noemi Tortorici: writing – review and editing, data curation, investigation. Tonny J.A. Silva: methodology, validation, writing – review and editing. Edna M. Bonfim-Silva: methodology, validation, writing – review and editing. Daniel I. Leskovar: methodology, funding acquisition, writing – review and editing. All authors have read and agreed to the published version of the manuscript.
Data accessibility. The dataset in support of this work is available at https://zenodo.org/records/19118881
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