Estimating downward long-wave radiation on the Andean Altiplano

Abstract The Andean Altiplano is a vast plateau lying at an average altitude of 4000 m above sea level, between Bolivia and Peru, and prone to radiative frost during the cropping season. Since the occurrence of radiative frost is generated by a deficit in long-wave radiation, accurate estimation of downward long-wave radiation is essential in models of frost prediction. However, most simple formulas tend to significantly overestimate this radiation in clear-sky conditions. From measurements made during two cropping seasons on two different sites on the Bolivian Altiplano, it is shown that the downward long-wave radiation can be more accurately estimated by means of an adjusted form of Brutsaert's [Brutsaert, W., 1975. On a derivable formula for long-wave radiation from clear skies. Water Resour. Res. 11, 742–744] equation, with a modified leading coefficient (1.18 instead of 1.24) multiplied by a cloudiness correction. The lower value of the leading coefficient apparently results from steeper vertical gradients of temperature and humidity in this high-altitude region. The cloud correction takes the form of a linear function of the ratio (s) between the observed magnitude of solar radiation and its clear-sky estimate, expressed as F(s) = −0.34s + 1.37. The formula was first calibrated on one measurement site (Condoriri) and then tested on the other site (Irpani). For daytime hours, the comparison between estimated and measured values is rather satisfactory. During nighttime hours the formula yields reasonably good estimates when the value of ratio s (not available at night) is replaced by its mean value calculated the previous day between 14 h and 16 h 30 min. Crawford and Duchon's [Crawford, T.M., Duchon, C.E., 1999. An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling long-wave radiation. J. Appl. Meteorol. 38, 474–480] cloud correction, based on the same ratio s, proves also to work fairly well under these particular conditions.

[1]  D. Brunt.  Notes on radiation in the atmosphere. I , 2007 .

[2]  A. C. Dilley,et al.  Estimating downward clear sky long‐wave irradiance at the surface from screen temperature and precipitable water , 1998 .

[3]  Donald R. Satterlund,et al.  An improved equation for estimating long‐wave radiation from the atmosphere , 1979 .

[4]  K. I. Kondratʹev.  Radiation in the atmosphere , 1969 .

[5]  L. S. Pereira,et al.  Revised FAO Procedures for Calculating Evapotranspiration: Irrigation and Drainage Paper No. 56 with Testing in Idaho , 2001 .

[6]  W. Brutsaert.  Evaporation into the atmosphere , 1982 .

[7]  H. Savijärvi,et al.  Comparison of surface radiative flux parameterizations Part II . Shortwave radiation , 2001 .

[8]  S. Idso.  A set of equations for full spectrum and 8- to 14-μm and 10.5- to 12.5-μm thermal radiation from cloudless skies , 1981 .

[9]  L. Alados-Arboledas,et al.  The estimation of thermal atmospheric radiation under cloudy conditions , 1995 .

[10]  John H. C. Gash,et al.  Longwave Radiation from Clear Skies in Niger: A Comparison of Observations with Simple Formulas , 1993 .

[11]  J. Lhomme,et al.  Modelling nocturnal heat dynamics and frost mitigation in Andean raised field systems , 2002 .

[12]  Lydie Guilioni,et al.  A simple model for minimum crop temperature forecasting during nocturnal cooling , 2004 .

[13]  Ronald L. Elliott,et al.  On the development of a simple downwelling longwave radiation scheme , 2002 .

[14]  J. Vacher.  Responses of two main Andean crops, quinoa (Chenopodium quinoa Willd) and papa amarga (Solanum juzepczukii Buk.) to drought on the Bolivian Altiplano: Significance of local adaptation , 1998 .

[15]  T. M. Crawford,et al.  An Improved Parameterization for Estimating Effective Atmospheric Emissivity for Use in Calculating Daytime Downwelling Longwave Radiation , 1999 .

[16]  Paul Berdahl,et al.  The thermal radiance of clear skies , 1982 .

[17]  W. Brutsaert.  On a derivable formula for long-wave radiation from clear skies , 1975 .

[18]  W. Brutsaert,et al.  Cloud effect in the estimation of instantaneous downward longwave radiation , 1993 .

[19]  M. Pérez-García.  Simplified modelling of the nocturnal clear sky atmospheric radiation for environmental applications , 2004 .

[20]  N. L. Dias,et al.  Assessing daytime downward longwave radiation estimates for clear and cloudy skies in Southern Brazil , 2006 .

[21]  A. Prata.  A new long‐wave formula for estimating downward clear‐sky radiation at the surface , 1996 .

[22]  W. Swinbank.  Long‐wave radiation from clear skies , 1963 .

[23]  D. O. Staley,et al.  Effective Atmospheric Emissivity under Clear Skies , 1972 .