Yes, this has been proven. Please refer to the link below.

https://iopscience.iop.org/article/10.1088/1748-9326/ac153e#:~:text=First%2C%20we%20show%20that%20many,dependent%20social%20and%20ecological%20systems.

Regards

You can see something about it here in researchgate:

Article Sensitivity of Catchment Transit Times to Rainfall Variabili...

One might think so. But if one takes the TP40 rainfall frequency map of the USA, or average annual rainfall of the landscape of interest, and overlaid the catchment, watershed, basin mapping, it would become pretty clear that topography, elevation, orientation to common wind and storm patterns, location and aspect related to mountain systems, locations affected by Gulf and Atlantic cyclonic event, etc., there are many factors that can affect rainfall variability. It is likely one might find more variability in rainfall in larger hydrologic units such as basins, portions get intense rain, other portions moderate or nothing. But it isn’t the size of the hydrologic unit that affects this variability, it is the variability of the moisture laden atmospheric currents as it moves across a variable physiographic areas, topography and landscape. But one might find specific areas or even regions where rainfall tends to be more uniform, as well as areas with more variability. Smaller catchments and watersheds may well receive the most extreme unit area storm events, because they are so small that slow moving, localized extreme storms engulf the entire area for a significant period of time, while larger hydrologic units are not completely covered or have substantial delays as local storm cell pass over select areas. Watching the Doppler radar as storm pass over the landscape can be informative, and helpful perhaps to show catchments, watersheds and basins as a background.

Of course. Bigger catchments have rather diverse climates and so rainfall diversity. Big catchments, like Volga, Dunai, Nile has rather diverse rainfall patterns.

Sorry, don't have a quick answer for this question

Yes, usually as the size of the area (around a central point) increases, the variations in areal rainfall decrease (expressed as a decrease in the variance of normalized areal precipitation as the area increases; where normalized precipitation is defined as the amount of precipitation for any one time period divided by the mean amount of precipitation across all time periods considered in the analysis). That is, as area increases around a point, there is a 'smoothing out' of spatial variations in point precipitation.

There were some publications in Water Resources Research (in the 1970s, if I remember correctly) that address this directly--let me know if you are interested, and I can dig up the citations for you.

Dear James C.Trask,

Thank you for your explanation, but still, need your help for the publication that you mentioned. I cannot find latest papers on that too.

Shimelash--I'll dig up the references (cited in my 2007 PhD dissertation) this weekend and post the citations in this thread.

Shimelash--the 2 research articles are by Rodriguez-Iturbe and Mejia (1974a,b) in the journal Water Resources Research, Vol. 10 #4. My dissertation (linked on my ResearchGate profile) has the full citations in the "References Cited" section on page 376. In Section 1A (and associated appendices) of the dissertation, I describe how the variance of normalized point precipitation data (from point precipitation gages) is adjusted downward to form areal precipitation estimates for Lake Tahoe and also for the surrounding watershed in the Tahoe Basin.

We have worked on characterizations, I hope you find our papers useful:

https://www.researchgate.net/publication/343981824_Analysis_of_climate_types_Main_strategies_for_sustainable_decisions_in_agricultural_areas_of_Carabobo_Venezuela

https://www.researchgate.net/publication/327729823_Tropical_rainfall_conditions_in_rainfed_agriculture_in_Carabobo_Venezuela?_sg%5B0%5D=iLncYXZKrZzBNwVQkvbhHok9JWV4N3-1ksqewLS57ymncpPOVql-LoaKry2-xqXJHIPWW5Rkd7_l8xtemfIKDa2-UwILma0aQQnE9K3-.862F1DxH0c7xCGSNyX98JpOMPDzE4Kp1l55g_GDMjrk3xuZ0mh0hwIw8oyAXRwHxinEhrLPLiJXSMWXaXupm7g

https://www.researchgate.net/publication/322335584_Caracterizacion_de_los_patrones_de_precipitacion_en_el_estado_Anzoategui_Venezuela_Characterization_of_precipitation_patterns_in_the_Anzoategui_state_Venezuela?_sg%5B0%5D=cTTLjmH7J3PgjeFMg1kKSKhEJ6VmvSFOOoYCLj8zdedmJcQiZ3k2audwO2Er1bALqQ8f3ykJJSQd45YjX5DDbIKf2ItALIVmX-1r0z8t.TgDO3X6mDfsSY8GYjKJOLHINfMeq4qS-w6xp3VpLfvvt0FKpcL7DU7TDzaLaQKHfp2CG9JTP9Vyeievegdt6SA