Characteristics of temporal-spatial potential evapotranspiration (ET0) distribution in Gansu Province were studied based on the Cloud model, which is a mathematical representation of qualitative concepts including expected value Ex, entropy En and hyper entropy He, integrates the fuzziness and randomness of qualitative concept in a unified way, and is a new method for the transformation between the qualitative and the quantitative. The values of ET0 were calculated by Penman-Monteith. The changes of ET0 in time were analyzed at monthly, seasonal and yearly intervals, respectively, and spatial changes were mainly divided into 4 parts: Hexi area, the middle, east and south area of Gansu. All data of 63 years (1951-2013) were collected at 29 meteorological stations involving the above districts in Gansu. All ET0 data were achieved by the soft Interactive data language. The indices of homogeneity and stability were used for reflecting characteristics of temporal-spatial distribution of ET0, which were achieved by Cloud mode, solving the uncertain conversion of qualitative concept and quantitative description. And the changes of ET0 in time (monthly, seaonal and annual) and space were analyzed by the linear change and the contour image. The results showed annual variation in ET0 had a fluctuation and increasing tendency, and the tendency rate was 2.11 mm/(10a) in all study area (P<0.05). The monthly change curve of ET0 for 63 years was single apex type, which was: ET0 in June and July was higher than that in other months. In homogeneity and stability aspects of ET0, from November to March of the next year was better than from April to August in the same year. At the same time, there was significant difference on the distribution of ET0 among seasons, and the maximum was summer, followed by spring, and the least was autumn and winter. The further analysis found that both homogeneity and stability of temporal-spatial distribution of ET0 had no consistency among seasons. The homogeneity of ET0 in autumn and winter was higher than that in spring and summer, but the stability in summer and autumn was better than that in spring and winter. Seen from the difference characteristics of the space, ET0 in the northwest area of Gansu Province were larger than that in the southeast, however, the annual changes of ET0 among areas were different for 63 years. Concretely speaking, the value of annual ET0 in Hexi area was keeping the highest from 1951 to 2013. Seeing the changes of ET0 in the space using the homogeneity and stability, we found ET0 of Hexi area was most discrete and instable, the east area of Gansu had the best homogeneity and stability, and the middle and south were between them. The homogeneity and stability of ET0 in the space was worse than that in the time. Generally, the homogeneity of the distribution of ET0 was increasing since 1981, namely, the homogeneity from 1981 to 2013 was better than that from 1951 to 1981, and at the same time, the stability was also increasing for 63 years. [ABSTRACT FROM AUTHOR]