Estimating downward long-wave radiation on the Andean Altiplano

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.