  Previous works have analysed the relationship existing between reference
evapotranspiration (ET0) and other climatic variables under a one-at-a-time
perturbation condition. However, due to the physical relationships between
these climatic variables is advisable to study their joint influence on ET0.
The box-counting joint multifractal algorithm describes the relations between
variables using relevant information extracted from the data singularities.
This work investigated the use of this algorithm to describe the simultaneous
behaviour of ET0, calculated by means of Penman-Monteith (PM) equation, and
relative humidity (RH) and air temperature (T), influencing on it in the middle
zone of the Guadalquivir river valley, Andalusia, southern Spain. The studied
cases were grouped according to the fractal dimension values, which were
related to their probability of occurrence. The most likely cases were linked
to smooth behaviour and weak dependence between variables, both circumstances
were detected in the local multifractal analysis. For these cases, the rest of
Penman Monteith (PM) equation variables, neither the T nor the RH, seemed to
influence on ET0 determination, especially when low T values were involved. By
contrast, the least frequent cases were those with variables showing high
fluctuations and strong relationship between them. In these situations, when T
is low, the ET0 is affected by the rest of PM equation variables. This fact
confirmed T as main driver of ET0 because the higher T values the lesser
influence of other climate variables on ET0. Joint multifractal analysis shows
some limitations when it is applied to large number of variables, the results
reported are promising and suggest the convenience of exploring the
relationships between ET0 and other climatic variables not considered here with
this framework such as wind speed and net radiation.
