Water Balance

The circulation of the global oceans is pretty complex.  The rate of ocean heat transport impacts the rate of atmospheric heat transport which feedback on the rate of ocean heat transport.  While that is going on, the rate of polar sea ice growth changes in response to both the rate of atmospheric heat transport and ocean heat transport which provides separate feedbacks to both transports.  There is no obvious simple way to solve all the responses, but you can isolate portions to illustrate parts of the interactions.

			Factor	0.6
			System	Circuit 1	Circuit 2
		Flow	100	60	40
		supply T	25	25	25
		return T	3	2.2	4.2
		delta T	22	22.8	20.8
		Capacity	2200	1368	832
	Circuit 1 total	Circuit 1a	Circuit 1b	Circuit 1c		Circuit 2 total	Circuit 2a	Circuit 2b
Flow	60	30	20	10	Flow	40	20	20
supply T	25	25	25	25	supply T	25	25	25
return T	2.2	1	4.6	1	return T	4.2	2	6.4
delta T	22.8	24	20.4	24	delta T	20.8	23	18.6
Capacity	1368	720	408	240	Capacity	832	460	372

This is a simple spread sheet of a hypothetical ocean circulation.  The total flow is 100 units and the "factor" is the ratio of the flow to two primary circuits, the Southern Hemisphere and the Northern Hemisphere.  The pump providing the flow will be the Coriolis effect.  Circuit 1 has three branch circuits.  Imagine 1a is the Pacific circuit, 1c is the Atlantic circuit and 1b is the India Ocean Circuit.  1a and 1c have the same return temperature while 1b has a higher return because of restricted flow. Circuit 2 has two branches.  Circuit 2a would be the Pacific and 2b the Atlantic.  Circuit 2b has a higher return temperature also because of restricted flow.All of the circuits/branches have the same supply water temperature and the Capacity listed is just flow times delta T.

			Factor	0.5
			System	Circuit 1	Circuit 2
		Flow	100	50	50
		supply T	25	25	25
		return T	3.32	2.44	4.2
		delta T	21.68	22.56	20.8
		Capacity	2168	1128	1040
	Circuit 1 total	Circuit 1a	Circuit 1b	Circuit 1c		Circuit 2 total	Circuit 2a	Circuit 2b
Flow	50	20	20	10	Flow	50	25	25
supply T	25	25	25	25	supply T	25	25	25
return T	2.44	1	4.6	1	return T	4.2	2	6.4
delta T	22.56	24	20.4	24	delta T	20.8	23	18.6
Capacity	1128	480	408	240	Capacity	1040	575	465

Update: Now imagine I balanced the flow between the two main circuits.  With the same flow, the capacity is slightly reduced.  Circuit 1 obviously would have a lower capacity because of the reduction of flow, but circuit two would have a higher capacity.  I haven't adjusted the return temperatures to reflect the changes, but circuit 1 should have a lower return temperature, which would offset some of the capacity lost with the reduction in flow and circuit two should have a higher return temperature, but the total capacity will change.  That will change the average return temperature and with circuit 2b have some restriction, the total "head" of the system would increase cause a reduction in total system flow.  Each circuit should vary proportionally with the circuit flow variation, but there will be additional loses of overall system efficiency relative to the first condition.  For this example, 2168/2200=98.5 or a 1.5% reduction in efficiency.

That is not much loss right?  Well, it is in the same order of magnitude as a CO2 doubling is currently estimated.  If the total system capacity is "fixed", the this change would require an increase in the supply T to compensate.  Since the return water temperature is relatively "fixed" at 0 C degrees or a bit less due to the heat of fusion, a change is the percentage of hemispheric flow distribution will impact climate. No external forcing required.

Now lets consider some real numbers.  Using the Reynold's Oiv2 data, the SST between 30S and 30N has an average temperature of 26.2 C which is close to the supply temperature in the examples, 11.2 C is the average temperature of the southern circuit which we can call our circuit 1 return temperature, measured from 30S to 60S.  The Northern circuit 2 has an average temperature of 14C, measured from 30N to 60N. 

	Factor	0.5
	System	Circuit 1	Circuit 2
Flow	100	50	50
supply T	26.2	26.2	26.2
return T	12.6	11.2	14
delta T	13.6	15	12.2
Capacity	1360	750	610
	Factor	0.45
	System	Circuit 1	Circuit 2
Flow	100	45	55
supply T	26.2	26.2	26.2
return T	12.74	11.2	14
delta T	13.46	15	12.2
Capacity	1346	675	671

Using those temperatures, there would be a load imbalance of about 10% or a flow imbalance of about the same percentage.  Since the "average" atmospheric effect is ~160 Wm-2 which would need to be balanced by internal meridional flux in an equilibrium condition, the imbalance in terms of energy would be about 16 Wm-2. 

I will leave this here, but this is the rough ballpark of the potential impact of changes in ocean heat transport (OHT) which can vary with surface winds (atmospheric oscillations) and sea ice extent (termination of OHT) which is explored in this paper by Brian Rose et al. The role of Oceans and Sea Ice in Abrupt Transitions between Climate States.