The concept on which the FAO Penman - Monteith method for computing ET_{o} is based requires that weather data be measured in environmental conditions that correspond to the definition of reference evapotranspiration. In other words, the weather data are to be measured above an extensive grass crop that is actively evapotranspiring, or in an environment with healthy vegetation not short of water ^{1}. Under these reference conditions, the energy available at the surface (R_{n} - G) is partitioned between sensible and latent heat (H and l E, respectively) in such a way that, in general, the ratio (3 = H/l E_{ref} £ 0.5. The subscript *ref* indicates reference conditions.

^{1}More detailed discussions are given in Allen (1996) and Allenet al(1996).

Environmental conditions of arid lands that surround a non reference (arid) weather site do not allow for the reference rate of evapotranspiration to be attained. This is generally caused by lack of well-watered conditions. Thus, l E_{n/ref} < l E_{ref} (subscript *n/ref* for non reference conditions). If the available energy (R_{n} - G) is the same, then the partitioning among sensible and latent heat changes, with H_{n/ref} > H_{ref} and, often, b _{n/ref} > 0.5. Consequently, since air temperature increases with increasing H, the air temperatures measured at non reference sites are higher than those that would have been measured if reference conditions had existed, i.e. T_{n/ref} > T_{ref}. On the contrary, humidity measured at a non reference site is lower than that which would have occurred under reference conditions, thus e_{a n/ref} < e_{a ref} and VPD_{n/ref} > VPD_{ref}.

When computing ET_{o} using standard estimates for R_{n} - G, r_{a} and r_{s}, ET_{o} will be overestimated when calculated using T_{n/ref} and VPD_{n/ref}. A correction is therefore required to bring temperature and humidity data closer to the reference conditions.

In an environment having healthy vegetation and adequate soil moisture (reference conditions), minimum air temperature T_{min} usually approaches dew point temperature, T_{dew}, (see Figure 6.2 for Kimberly, Idaho, the United States)^{2}. This especially occurs if the wind dies down by early morning and when soil moisture is high (illustrated through the ratio precipitation/ET_{o}, in Figure 6.1). Air temperatures decrease during night time due to surface cooling caused by long-wave emission and evaporation when VPD is positive. When near surface air temperature T approaches T_{dew}, T is prevented from decreasing below T_{dew} by condensation of vapour from the air and the correspondent heating effect of released latent heat. Thus, for reference conditions the relationship (T_{min})_{ref} = (T_{dew})_{ref} is generally valid.

^{2}However, air temperature may not decrease to the dew point when large amounts of warm and dry air are transported to the surface by wind.

**FIGURE 6.1. Comparison of differences between the monthly
values of minimum and dew point temperature (T**_{min}** -
T**_{dew}**) corresponding to monthly ratios of precipitation/ET**_{o}**
Sudan, Africa and the United States**

For non reference sites, soil moisture and/or vegetation limitations make l ET_{n/re}f < l ET_{ref} or ET_{n/ref} < ET_{o}. Thus T_{min} may remain above T_{dew}. One cause of this phenomenon is the large "reservoir" of sensible heat created during daytime in the atmosphere (H_{n/ref} > H_{ref}, as suggested before), which is transferred towards the surface during the night, reducing the effect of cooling by long wave radiation. Another cause is the lack of soil moisture for evaporative cooling during night time.

This phenomenon can be observed in Figure 6.1, where monthly means for T_{min} - T_{dew} are plotted for weather stations operated by national governments of two countries, Sudan and the United States. The data are plotted against the monthly ratios of precipitation to reference ET_{o}. The P/ET_{o} ratios indicate the availability of adequate soil water to support reference (well-watered) conditions in the absense of irrigation. As illustrated by the data, T_{min} approaches T_{dew} for nearly all stations when the ratio P/ET_{o} approaches and exceeds 1. When P/ET_{o} < 1, then the aridity of the station causes T_{min} to substantially exceed measured T_{dew} The exception is for those weather stations that have P/ET_{o} < 1, but are irrigated or have adequate soil water reserves from a prior month. The similarity between data of Sudan and the United States indicates that this is a general phenomenon.

An additional comparison is given in Figure 2, where T_{min} - T_{dew} are compared for two semiarid locations in Idaho, the United States that are separated by 200 km. One location, Kimberly, is a reference site in the middle of a large irrigated area. The other, Boise, is a non reference site, located at an airport and surrounded by a mixture of irrigated and non irrigated rangeland. It can be seen that T_{min} approaches T_{dew} frequently for the irrigated site at Kimberly, with only small differences occuring during months where a dry climate occurs (low precipitation/ET_{o} ratio). On the contrary, T_{min} was as much as 10°C higher than T_{dew} for the nonreference Boise station. From this graphical comparison, one can conclude that data for the nonreference Boise site require appropriate correction before being utilized to compute ET_{o} using the FAO - PM method. This is necessary to avoid overestimation of ET_{o} due to overestimation of air temperature and VPD.

**Adjustment of T**_{max}**, T**_{min}** and T**_{dew}

The empirical method described herein intends to correct the observed temperatures, T_{max} and T_{min} in proportion to the difference (T_{min} - T_{dew}), which works as an indicator of the overestimation of (T_{n/ref} - T_{ref}). Since T_{dew} defines the actual vapour pressure (e_{a} = e° (T_{dew})), correcting T_{dew} also provides an adjustment for VPD.

The methodology proposed is the following:

1. Compare T_{min}- T_{dew}(T_{dew}measured or computed from e_{a}using equations (11) or (12) in Annex 3) from a non reference site with those from a reference site using a graphical procedure such as in Figure 6.2 and using monthly ratios of Precipitation/ET_{o}as the abcissa. Daily or monthly data are utilized to compute T_{min}- T_{dew}.2. When differences T

_{min}- T_{dew}for the non reference site are systematically higher than about 2°C relative to the reference site, then compute the average differencesD T = T_{min}- T_{dew}(6-1)for the months which require correction (in general this will occur when the monthly ratio Precipitation/ET

_{o}does not exceed 0.5).Or, if comparing T

_{min}- T_{dew}from the nonreference sets to T_{min}- T_{dew}from the reference site, then calculate D T as:D T = (T_{min}- T_{dew})_{n/ref}- (T_{min}- T_{dew})_{ref}(6-2)3. Correct temperatures for each month (or day) by:

_{}(6-3)

_{}(6-4)for D T > K

_{o}, where subscriptscorandobsrefer to corrected and observed values, respectively. K_{o}is a "conservative" factor equal to 2°C when the nonreference station is not compared to a reference station (D T is from Equation (1)). K_{o}= 0 when D T is from Equation (6-2).4. Correct T

_{dew}for the same months or days as:

_{}(6-5)where K

_{o}has the same value as for Equations (6-3) and (6-4), and utilizing either the observed or the calculated values for T_{dew}(equations (3-11) or (3-12) in Annex 3). The user should always insure that (T_{min})_{cor}³ (T_{dew})_{cor}.5. Compute ET

_{o}with the corrected values for T_{max}, T_{min}and T_{dew}.

**FIGURE 6.2. Comparison of differences between the monthly values of minimum and dew point temperature (T**_{min}** - T**_{dew}**) corresponding to monthly ratios of precipitation/ET**_{o}** for a reference site (Kimberly, Idaho, the United States) and for a non reference site (Boise, Idaho, the United States) in the same region**

**Adjustment of T**_{dew}** only**

When RH, e_{a}, or T_{dew} data are not dependable or where "correction" of T_{max} and T_{min} as is done in the previous section is undesireable, a second means for "correcting" the weather data set for station aridity is possible. This second method is to merely set

T_{dew}= T_{min}- K_{o}(6-6)

in the calculation for ET_{o} where K_{o} = 0°C for humid and subhumid climates and K_{o} = 2°C for arid and semiarid climates. The result of this procedure is to increase T_{dew} to reflect the higher humidity anticipated under reference conditions. It is noted that in a nonreference setting, the measured T_{min} may be too high, as compared to T_{min} expected for a reference setting, so that Equation (6-6) may result in values for T_{dew} that are overestimated, even for a reference condition. However, since the computation of vapor pressure deficit, VPD, in the ET_{o} equation, where VPD = 0.5 (e°(T_{max}) + e°(T_{min})) - e°(T_{dew}), utilizes values for air temperature and dew point temperature that may both be too high, the upward bias in all temperature parameters will tend to cancel, thereby presenting a VPD that is representative of a reference condition.

**Index for station aridity**

For non reference sites, when humidity data are available, one can compute an** aridity bias index** A_{bi} (for monthly time scales)

_{}(6-7)

between the ET_{o} computed from the observed (non-corrected) data (subscript obs) and, for the same period, using T_{min} as an estimate of T_{dew}. If there is not a large difference between T_{min} and T_{dew}, then A_{bi}^{~}0*.* When D T = T_{min} - T_{dew} is large (i.e., for a nonreference condition), then the aridity bias index A_{bi} becomes > 0.

The user should compare aridity bias indices for the dry and humid months and decide whether higher values for A_{bi} result from aridity or from other causes. A correction may be required when A_{bi} are consistently greater than 0.05. The correction of temperature and humidity data can be performed as indicated in the previous sections.

It is important for the user to realize that these corrections are to improve the calculations of ET_{o} only, since ET_{o} is defined for a well-watered environment. For hydrology studies where actual ET is required, then no adjustment should be made to air temperature and dew point temperature, since the ET_{o n/ref} characterises the natural evaporation demands of the climate.

Any corrected T_{max}, T_{min}, T_{dew} data should not be reintroduced into the original historical data series. Also, the user should note that all of the correction procedures presented here are only approximate attempts to bring the ET_{o} calculations closer to the "real" ET_{o} that reflects a well-watered environment. Any errors or uncertainties introduced by these adjustments at a specific site will remain largely unknown. Therefore the user is encouraged to use caution.