Angular modeling of the components of net radiation in agricultural crops and its implications on energy balance closure

Fernando Paz, Ma Isabel Marín, Jaime Garatuza, Christopher Watts, Julio Cesar Rodríguez, Enrico A. Yepez, Antoine Libert, Martín Alejandro Bolaños*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Efficient water management in agricultural crops is necessary to increase productivity and adapt to climate change. Evapotranspiration (ET) data are key in determining the water requirements of crops and set efficient irrigation schedules. Estimating ET at the regional scale (for example, in irrigation districts) is a technically complex task that has been tackled by using data acquired by remote sensors on satellites that can be validated with scaled up field measurements when area sources are matched. Energy and matter flux measurements using the eddy covariance (EC) technique are challenging due to balance closure issues, claimed to be due to the different footprints of the energy-balance components. We describe net radiometer footprints in terms of the sun-sensor geometry to characterize the bidirectional distribution functions of albedo and thermal emissions. In this context, we describe a one-parameter model of the components of net radiation that can be calibrated with a single data point. The model was validated in an experiment with five agricultural crops (bean, sorghum, chickpea, safflower, and wheat) at Valle del Yaqui, in Sonora, Mexico, using different sun-sensor geometry configurations. The results from the experimental fits were satisfactory (R2 > 0.99) and support the use of the model for albedo and radiative (surface) temperature in order to estimate net radiation. The analysis of the implications regarding a mismatch among footprints of the components of the energy balance showed that net radiometer fluxes are overestimated most of the time, implying that the closure problem could be solved by using a similar footprint as the aerodynamic components of the energy balance.

Original languageEnglish
Article number3028
JournalWater (Switzerland)
Issue number21
StatePublished - 1 Nov 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


  • Albedo
  • Eddy covariance
  • Footprint
  • Radiative temperature


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