This manuscript generated a global 5km monthly potential evapotranspiration dataset (1982–2015) estimated by comprehensively considering interspecific differences in various vegetation-related parameters (e.g., plant stomatal resistance and CO2 effects on stomatal resistance) to calibrate and parametrize the Shuttleworth-Wallace (SW) model. It can be accepted after some revisions. The authors should carefully consider my comments and suggestions below.

• Lines 72. Maybe it is necessary to explain more clearly what is vegetation not “closed?
• Lines 74. “Heterogeneous” should be “homogeneous”?
• Line 97-98. “vegetation height” and “Leaf Area Index” should be “vegetation height datasets” and “Leaf Area Index datasets”, respectively?
• Figure 1. I suggest enlarging the size of the font in the legend and adjusting the position of the legend.
• Line 144-145. How did the authors consider the uncertainty from gap-filled heat fluxes? As far as I know, the MDS method was applied to fill the gap of ET measurements in the FLUXNET2015 datasets. Recently, Jiang et al. (2022) have developed a novel physical full-factorial scheme for gap-filling of EC-measured ET. Their scheme has been demonstrated to outperform the MDS and MDV gap-filling methods. The authors should introduce this new advance in the gap-filling of ET and at least discuss the possible uncertainty caused by using the MDS gap-filled ET.
• Line 149-154. How did the authors consider the effect of nighttime ET on daily ET? The authors seemed to take the daytime ET as a surrogate of daily ET.
• Line 163-164. In arid areas, a day may not be identified to have no water limits even when its corresponding EF exceeded the 95th percentile EF threshold.
• Line 170. The CO2 concentration observed at Mauna Loa cannot represent the spatial heterogeneity of CO2 concentration over the globe. How did the authors consider the uncertainty from this act?
• Lines 178. I suggest specifying the full name of CRUTS like the previous dataset. Please keep CRUTS consistent with the CRU TS below.
• Figure 2. I suggest adjusting the color configuration of the flow chart, such as reducing the color saturation.
• Lines 265. W/m2 should be corrected to W/m².
• Section 2.1.4. I suppose that the authors use the vegetation canopy height to estimate surface roughness length and further aerodynamic resistance. I have two questions. First, the authors have used multiple datasets as inputs or to obtain vegetation canopy height (h). How did the authors consider the difference between different datasets? Second, how to parameterize the spatially and temporally variable surface roughness length by using the time-invariant vegetation height? The authors are suggested to refer to the work of Peng et al. (2022) who developed for the first time a practical method for global estimates of 500 m daily aerodynamic roughness length with a combination of machine learning techniques, wind profile equation, observations from 273 sites and MODIS remote sensing data.
• Line 246, Eq. (2c). The extinction coefficient 0.6 is empirical and may not be suitable for all vegetation types and fractional vegetation coverages. How did the authors consider this uncertainty?
• Line 265-266. How did the authors consider the uncertainty from the minimum threshold (30 W/m² for forests and 100 W/m² for other vegetation)?
• Figure 5 was not referenced in the text.
• Line 428. “Figure 1b” should be “Figure 11b”?
• Line 440. “PE was the major contributor of PE”? Perhaps the later PE should be PET.

References

1. Jiang, Y., Tang, R., & Li, Z. L. (2022). A physical full-factorial scheme for gap-filling of eddy covariance measurements of daytime evapotranspiration. Agricultural and Forest Meteorology, 323, 109087.
2. Peng, Z., Tang, R., Jiang, Y., Liu, M., & Li, Z. L. (2022). Global estimates of 500 m daily aerodynamic roughness length from MODIS data. ISPRS Journal of Photogrammetry and Remote Sensing, 183, 336-351.