Mathematical Modeling of Diurnal Patterns of Turbulent Heat Fluxes using Modified Aerodynamic Resistance Method


  • R. T. Akinnubi
  • O. O. Oketayo Department of Physics, Federal University Oye-Ekiti, Ekiti State
  • B. F. Akinwale
  • M. O. Ojo
  • A. Ikusika



Surface energy balance, aerodynamics surface layer resistances, radiometric surface temperature, Mean bias error


The development of improved methods for estimating turbulent heat fluxes is important in effective monitoring of the surface energy balance for climate change prediction. However, different  parameterized models carried out at the local site of Nigerian Micrometeorological site (NIMEX-1) did not consider the surface heat fluxes-aerodynamics resistance relationships, and these validated models cannot be incorporated into the Climate models because some of the input climate variables are not routinely available in some meteorological stations. This study therefore, aims at improving the diurnal patterns of surface heat fluxes estimates using radiometric surface temperature and aerodynamic surface-layer resistances. Hourly data of air temperature (Ta), soil temperature (Tsoil), global radiation (QL), surface temperature (Ts), wind speed (u), QH and QE were obtained from the NIMEX-1 at Ile-Ife (7.55 oN, 4.55 oE). The QH and QE were estimated using Aerodynamic Resistance Approach algorithm which was modified to reduce the large bias errors between the aerodynamic temperature and surface temperature above the ground level. The algorithms were validated and rated using the following error statistics: coefficient of determination (r2), Mean Bias Error (MBE) and Root Mean Square Error (RMSE). The RMSE and MBE for the modeled QE estimated using ARM and MAR reduced from 28.33Wm-2 to 14.33 Wm-2 and 36.93 to 10.74 Wm-2 respectively while for QH ,the RMSE and MBE reduced from 17.29 Wm-2 to 9.49 Wm-2 and 31.39 to 16.93 Wm-2 respectively. The r2 values ranged from 0.68 to 0.73 and 0.95 to 0.98 for QH and QE respectively. The MAR had the highest r2 and least error values.  Hence, the proposed modified Aerodynamic resistance models are estimated the diurnal and seasonal turbulent heat fluxes accurately for tropical regions.


]Akinnubi, R. T. and Adeniyi, M.O “Investigation of the surface energy budget at Nimex_3 site, Ibadan, using Bowen ratio energy balance methodâ€. International Journal of Engineering and Mathematical Intelligence, 3, pp 1-3, (2010).

Akinnubi. R. T and Adeniyi M.O “The Parameterization of Humid Tropical Surface-Layer Aerodynamic Resistance to Heat Transfer using Modified Louis Schemeâ€, Transaction of of Nigeria Association of Mathematical Physics,. 3(2), pp 395-398, (2017).

Ayoola, M. A. Olatona. G. I. and Oladiran.E. O. The March 29, “Solar Eclipse As Observed At Ibadan, Nigeriaâ€. paper Presented At NIP 30th Annual Conference, (2006).

Balogun, A. A., Jegede, O. O., Aregbesola, E. O., Ogolo, A. E., Ohamobi, S. and Sunmonu, K. E, “Evaluation of some surface layer characteristics during NIMEX-1. Paper presented at the Workshop on the Nigerian micrometeorological experiment (NIMEX-1)†Obafemi Awolowo University, Ile-Ife, Nigeria. 22nd, 2004 (2004):.

Castellvi, F. Martínez-Cob A., Pérez-Coveta, O “Estimating sensible and latent heat fluxes over rice using surface renewal. Agric Forest Meteorol., 139: pp 164–169, (2006).

Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebethal, C (2006). Some aspects of the Environmental Impact Assessment, International Centre for Theoretical Physics, Trieste, June 1990.

Jegede, O. O., Okogbue, E. C., and Balogun, E. E. “Proceedings of the workshop and the Nigeria Micrometeorological experiment (NIMEX-1)†July, 15, 2004, Ile-Ife, Nigeria. Comfort Press and Publishing Co. Lagos, Nigeria, pp 66, (2004).

Jia, L. “Modeling heat exchanges at land-atmosphere interface using multi-angular thermal infrared measurements†PhD Thesis, Wageningen University, pp 199, (2004).

Koloskov G., Mukhamejonav K.H., Tanto T.W Monin-Abukhov “Length as a cornerstone of the SEBAL calculations of evapotranspirationâ€. Journal of Hydrology, 10, (2007).

Kustas, W.P., Hatfield, J.L. and J.H. Prueger. “The soil moisture-coupling experiment (SMACEX): background, hydrometeorological conditions, and preliminary findings†J. Remote Sens. Environ., 74, pp 327–342, (2008).

Lhomme J.P. and E. Elguero, “Examination of evaporative fraction diurnal behaviour using a soil-vegetation model coupled with a mixed-layer model†Hydrol. Earth. Syst. Sci., 3 (2), pp 259-270, (1999).

Ma, Y., O. Tsukamoto, H. Ishikawa, Z. Su, M. Menenti, Wang, J., and Wen. J. “Determination of Regional land surface heat flux densities over heterogeneous landscape of HEIFE Integrating satellite remote sensing with field observations†Journal of Meteorological Society of Japan, 803, pp 485-501, (2002)..

Ma, Y., O. Tsukamoto, X. Wu, I. Tamagawa, J. Wang, H. Ishikawa, Z. Hu, and H. Gao, “Characteristics of energy transfer and micrometeorology in the surface layerâ€, (2000).

Mafouf, J. F., and J. Noilhan. (1991). Comparative study of various formulations of evaporation from bare soil using in situ data. J. Appl. Meteor., 30, 1354–1365.

Mauder, M., Jegede, O. O., Okogbue, E. C., Wimmer, F., and Foken, T “Surface energy balance measurement at a tropical site in West Africa during the transition from dry to wet seasonâ€, Theor. Appl. Climatol., 89, pp 171–183, (2007).

Nagar, S. G., Sectoramayya, Tyagi. A and Siingh. S. S. Estimation of daytime surface fluxes of radiation and heat at Anand during 13 – 17 May 1997. Current Science, 83 , pp 39 – 46, (1995).

Niclòs, R., Estrela, M.J., Valiente, J.A., Barberà , M.J “Clasificación periódica de coberturas terrestresaescala regional con imágenes MODISâ€. GeoFocus, 10, pp 1-17, (2009).

Oladosu, O R and Jegede, O.O “Thermal properties of an agricultural site in Ile- Ife, Nigeria†Nigeria J. Pure Appl. Phy. 4(1), pp 71-74, (2005)..

Stewart, J.B., Shuttleworth WJ, Blyth K, Lloyd CR: “FIFE: a comparison between aerodynamic surface temperature and surface radiometric temperature over sparse prairie grass†19th Conf. Agric Forest Meteorol, Charleston, South Carolina, March 1989, pp 144–146,(1989).

Su, Z. “The Surface Energy Balance System SEBS for estimation of turbulent heat fluxes†Hydrology and Earth System Sciences, 61, pp 85-99, (2002).

Su, Z., and Menenti M. “Mesoscale Climate Hydrology: The contribution of the new observing systems†Pre-Execution Phase, Final Report, BCRS NUSP-2, 99-05, pp 14, (1999).

Su, Z., M. Menenti, H. Pelgrum, B. J. Van den Hurk J. M., and Bastiaanssen W. G. M.. “Remote sensing of land surface heat fluxes for updating numerical weather predictionsâ€, In Nieuwenhuis, G.J.A., Vaughan, R.A., and Molenaar, M.eds, Operational Remote Sensing for Sustainable Development, Balkema, pp 393-402, (1998).

Sun, Y.-J., Wang, J.-F., Zhang, R.-H., Gillies, R.R., Xue, Y., Bo, Y.-C. “Air temperature retrieval from remote sensing data based on thermodynamics. Theory†Appl. Climatol., 80, pp 37–48, (2006).

Van den Hurk, B. J. J. M., (2001) “Energy balance based surface flux estimation from satellite Boundary-Layer†Meteorol. 82, pp 119–134.

Voogt, J. A. and Grimmond, C. S. B. “Modelling Surface Sensible Heat Flux Using Surface Radiative Temperatures in a Simple Urban Area†Journal of Applied Meteorology, 39, pp 1679-1699 (2000).

Wu, J., Wang, D. (2005) â€Estimating evaporation coefficient during two stage evaporation from soil surfaces†Soil Sci. 170, pp 235-243.




How to Cite

Akinnubi, R. T., Oketayo, O. O., Akinwale, B. F., Ojo, M. O., & Ikusika, A. (2018). Mathematical Modeling of Diurnal Patterns of Turbulent Heat Fluxes using Modified Aerodynamic Resistance Method. Asian Journal of Applied Sciences, 6(6).