Carbon export in upwelling regions. This problem will guide you through the solu lution of a box model to estimate how much carbon is produced and…

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4. Carbon export in upwelling regions. This problem will guide you through thesolulution of a box model to estimate how much carbon is produced and exported by thebiological pump in an upwelling region similar to the California Current.A schematic of the box model is shown at the end of the homework (Figure 2). Use it asyour guide. We consider a surface "upwelling box" located next to the coast, whichextends for 500 km in the north-south direction, and 50 km offshore. That is, the surfacearea of the upwelling region is 500 x 50 km2. The mean upwelling velocity (w) at thebase of the box is w = 3-10-5 m s1, typical of the California Current. The deep waterupwelling into the box has a nitrate (NO3) concentration NO3deep = 30 mmol m-3 andthe water within the box has a nitrate concentration NOssurf = 10 mmol m-3.(a) Calculate the total transport of water U upwelling into the box, and express youranswer in Sv (1Sv = 106 m3 s-1). (1 point)(b) Calculate the residence time of water in the upwelling box (relative to upwelling),assuming that the vertical thickness of the box is 100 m. Express your result in units ofdays. (1point)(c) Convince yourself that the conservation equation for nitrate in the box, NO3surf, is:d NOWAdt- = U . NOdeep – U . NOWf – nWhere V is the volume of the box (you won’t need the actual value), U is the water fluxupwelling into the box and exiting from the offshore side, and /7 is the export of organicnitrogen sinking out of the box by the biological pump. Assume steady state and find anexpression for the export of organic nitrogen /7 (1 point).(d) Plug in the numerical values for the upwelling rate U and the nitrate concentrationsNO3deep and NO3surf and determine the value of the organic nitrogen export /1,expressing it in units of mol s-1. (1 point)(e) Calculate the residence time of nitrate in the box, relative to the organic nitrogenexport //. Express your result in units of days. How does it compare to the residencetime of water you found in (b)? (1 point)(f) Calculate how much organic carbon is exported from the surface box, assuming thatit follows a Redfield Ratio (106:16) with organic nitrogen export you found in (d).Express your answer in units of g s-1. (1point)(e) California’s carbon emissions as CO2 to the atmosphere are approximately 120 Mt Cy-1, where 1 Mt = 106 g. How much higher (or lower) would the upwelling rate need tobe,, so that carbon sequestration by the biological pump in the upwelling region could