## Estimation of ET0 with Limited Weather Data

For both daily and monthly calculations, data for some weather variables frequently are missing. This requires appropriate procedures to estimate such meteorological variables and then use these estimates in the FAO-PM calculations presented in the section entitled "Daily ET Calculations with FAO-PM Method," above.

### Case When Radiation Data Are Missing

Several alternative methodologies can be utilized to estimate shortwave incoming radiation Rs. These have been evaluated using several data sets, namely those for a large variety of climates in the world included in CLIMWAT [80] for a total of 918 weather stations in 20 countries [81].

Use ofRs/Ra Data from a Nearby Weather Station. This method relies on the fact that, for the same month, very often for the same day, the variables commanding incoming solar radiation Rs in a given region are similar. This assumption implies that a nearby station should be at a distance not greater than 300 km; the physiography of the region should be such that relief is negligible in influencing the movement of air masses, and the air masses governing rainfall and cloudiness are the same.

Much caution should be used when the method is to be applied to mountainous and coastal areas, where differences in exposure and altitude could be important or where rainfall is variable because of convective conditions.

Thus, for locations where a nearby weather station exists within the same homogeneous region, the best estimate for Rs is

where Ra is the daily extraterrestrial radiation (MJm-2 day-1) for the same location and (Rs/Ra)nt is the ratio of shortwave to extraterrestrial radiation ( ) obtained from observations at the nearest (subscript nt) weather station.

This estimation method is recommended for monthly and daily calculations. However, when using it for daily estimates, a more careful analysis of weather data in the importing and exporting meteorological stations has to be performed to verify if both stations are in the same homogeneous climatic region. That analysis should include the comparison of daily data from both stations, particularly concerning T^, Tmin, (Tmax - Tmm), RHmax,

RHmin, and (RHmax — RHmin). In fact, similar cloudiness (and similar n/N ratios) are related to similarities in temperature and humidity trends.

Use of a Relationship with the Temperature Difference (Tmax — Tm,n). It is known that the difference between maximum and minimum air temperature is related to cloudiness conditions. Clear-sky conditions correspond to higher Tmax because the atmosphere is transparent to the incoming radiation, and to low Tmin because long-wave radiation is returned only in a small fraction. On the contrary, overcast conditions correspond to a lower Tmax because a larger part of the radiation is absorbed and reflected upward by the clouds, whereas Tmin is higher because, reflected downward, long-wave radiation is increased. Therefore, the difference (Tmax — Tmin) can be used as an indicator of the fraction of extraterrestrial radiation that becomes available at an evaporative surface. This principle has been utilized by Hargreaves and Samani [82] to develop estimates of ET0 using only air-temperature data. Then [83],

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