4. Consider the water balance in Figure 1 of Oki and Kanae (2006) as shown on th

Question

4. Consider the water balance in Figure 1 of Oki and Kanae (2006) as shown on the bottom of page 16 in the notes (the full article is posted in this Module). 4a. What percentage of global annual precipitation volume falls over oceans? Spatially averaged over the oceans, what is the depth of annual mean precipitation? 4b. Introduce the notation Eo for evaporation over ocean, Po for evaporation over ocean, and Pt for precipitation over land. If we write Eo = Po + P1-B, what is the numerical value and physical meaning of the term B?

Explanation / Answer

4a. Global annual precipitation volume is nothing but the volume of precipitation over land (PL) plus the precipitation on ocean (PO) = PL+PO = 391+111 = 502 * 103 km3/y

Percentage of global annual precipitation volume falling on ocean = (PO * 100) / (PO + PL) = 391*100 / (391+111) = 77.89%

WKT, the are of oceans = 360 * 106 km2

Therefore, depth of annual precipitation spatially averaged over oceans is nothing but the precipitation volume per year divided by the total area of oceans = 391 * 103 / 360 * 106 = 1.086 *10-3 km = 108.6 cm

4b. We know the value of Evaporation over ocean (EO), precipitation over land (PL) and the precipitation over ocean (PO), from the fig., given (There seems to be a printing mistake: PO is precipitation over ocean and not evaporation over ocean)

EO = 436.5   PL= 111 PO=391 (all units in 103 km3/y)

Therefore, in EO = PO + PL -B,

B = 65.5 * 103 km3/y

As it is clearly seen in the fig., this is the total terrestrial evapotranspiration. Conceptually also, since total evapotranspiration from land and ocean must be equal to the total precipitation over land and ocean (EO + EL= PO + PL), the missing term is total terrestrial evapotranspiration.

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