# An atmospheric energy balance calculation

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There is a vast amount of existing information on most of the parameters needed to calculate cooling as a function of spray rate, but it is distributed between many computers around the world and has been saved in different formats with different spatial resolutions and sampling rates, using different recovery software and different access protocols. Most of this information has now been collected, decoded, interpolated, unified and stored in a database as 6596 equal-area (7.72 x 1010 m2) cells of a reduced Gaussian grid. This allows selective interrogation by an efficient parsing routine (Sortino 2006).

If there is to be double pre-industrial CO2 with no temperature change, then solar reflection needs to increase by approximately 3.7Wm-2, or 2000 Terawatts globally. This is about the electrical output of 1.8 million nuclear power stations of 1100 MW each. The question is how many spray vessels with how much spray equipment placed where at which season will be needed? Calculations can be done separately for each of the equal-area cells. The greatest uncertainties concern the estimates of the present number of cloud condensation nuclei at various times and places, and the drop lifetimes. This is because it is the fractional change in drop numbers in clouds that drives the change in albedo.

To demonstrate a spot test of equation (11.2) for reasonably typical conditions, let the cloud depth Z be 300 m, with a liquid water content L of 0.3 ml m-3 and use n = 65 cm -3 for the average mid-ocean drop concentration from the range of values suggested by Bennartz (2007) to calculate an albedo of A(Z, L, n) = 0.495.

The effect of injecting 30kgs-1 of seawater as 0.8 |xm drops but confining it to just one of the equal-area cells will be to increase the number of new nuclei per cell by 1.12 x 1017 s-1. It will take some time (perhaps 2 hours) for turbulence to disperse the evaporated spray residues through the boundary layer, but the cleanliness of the mid-ocean air and the hydrophilic nature of the salty residue will make them very effective condensation nuclei. A large fraction of those that reach the high humidity at the cloud base will form newer but smaller drops with the same total liquid water content as before. It will take some further time before they wash out or coalesce with large drops. The lowest estimate for drop life is approximately 1 day, giving an increase of 9.67 x 1021 in each cell to bring the total to 1.47 x 1022. The depth of the marine boundary layer is often between 500 and 1500 m. If we can take the depth of a cell of the reduced Gaussian grid to be

1000m, the new concentration of cloud drops will be 191 cm-3. This will make the new value of A(Z, L, n) = 0.584.

The mean 24-hour equinoctial solar input at the equator is 440 Wm-2, while at the latitude of Patagonia it is reduced to 240 W m-2. If spray sources can migrate with the seasons, atypical value of 340 W m-2 seems reasonable, even conservative. The resulting change of albedo will increase reflected power by 30.26 Wm-2 or 2.33 TW over the 7.72 x 1010 m2 area of one cell.

We cannot be sure that spray sources will always be under the right kind of cloud. The most conservative cooling estimate would be based on the assumption of completely random, non-intelligent deployment of spray vessels. This would reduce the 2.33 TW cooling by the fraction of cover of suitable low-level stratocumulus. This is given by Charlson et al. (1987) as 0.18 and would reduce reflected power from a single source of 30kgs-1 to 420 GW. However, a lower concentration of nuclei over a wide area is more effective than a high one over a small area and the lifetime of nuclei under clear skies should be much longer than in cloud. It may turn out to be better to release spray in air masses that are cloudless but are predicted to become cloudy after some dispersal has taken place.

These crude engineering lumped calculations should be performed with the actual values at a representative sample of times for every cell that has not been excluded on grounds of being downwind of land with dirty air, upwind of drought-stricken regions or too close to busy shipping routes. The wind speed data for each cell should be checked to ensure that there is enough input power for, as will be developed shortly, wind energy provides the principal source for driving the vessels and creating the spray. With an efficient generator, the 30 kg s-1 flow rate will be reached at 8 m s-1 wind speed. If the nucleus lifetime was the longest estimate of 5 days (Houghton 2004), this would bring the concentration up to levels found over land and lead to much reduced effectiveness. Cells will be placed in rank order to see how many are needed to achieve any target cooling and either how many vessels should be put in each cell or how many cells should be treated by one vessel. Vessel movements can be planned by looking at the best-cell list for the next month.

The equations used for Figure 11.2, together with lumped assumptions about what is in reality a wide spread of values, allow the approximate prediction of global cooling as a function of spray rate from purely randomly placed spray sources as shown in Figure 11.3. The circle shows the approximate increase in positive forcing since the start of the industrial revolution. As the spraying rate is increased, the gain in reflected power evidently shows diminishing returns. But if these lumped assumptions are correct, the spray rate to cancel the 3.7 W m-2 effect of a doubling of pre-industrial CO2 is between 30 and 70 m3 s-1.

Assumptions and sources

Boundary layer depth 1000 m Cloud depth 300 m

Schwartz & Slingo (1996) Liquid water 0.3 ml m-3

Schwartz & Slingo (1996) Drop life 59 hours

Smith (1991)

Low not high cloud fraction 0.18 Charlson et al. (1987) Initial albedo 0.495

24 hour power in 340 W m-2

### Global spray rate m3 s-1

Figure 11.3 Global cooling as a function of spray rate for the assumptions in the right-hand side table, non-intelligent spraying and the range of initial nuclei concentration suggested by Bennartz (2007). The circle shows warming since the start of the industrial revolution. It could be reversed by spraying approximately 10 m3 s-1. The question mark is a guess for the effect of twice pre-industrial CO2. Assumptions obtained from Charlson et al. (1987), Schwartz & Slingo (1996) and Smith etal. (1991).

It is also useful to calculate the spray amount that would 'hold the fort' long enough for renewable energy technologies to be deployed by cancelling the annual increase in global warming, probably approximately 40mWm-2. The annual increase would be a spray rate of less than 150kg s-1, even with non-intelligent positioning.

Suitable sites for spraying need plenty of incoming sunshine to give something to reflect. They must have a high fraction of low-level marine stratocumulus cloud. They should have few high clouds because these will reduce incoming energy and send the reflected energy down again. There should be reliable but not extreme winds to give spray vessels sufficient thrust. There should be a low density of shipping and icebergs. It helps to have a low initial density of cloud condensation nuclei because it is the fractional change that counts. This suggests sea areas distant from dirty or dusty land upwind. Owing to a possible anxiety over the effect of extra cloud condensation nuclei on rainfall, areas upwind of land with a drought problem should be avoided.

In Figure 11.4 maps are for four seasons showing suitability of different sea areas based on the combination of one possible set of the selection criteria. Clearly, seasonal migration of the spray vessels is desirable and the southern oceans are particularly suitable for treatment in the southern summer. The very best all-year sites are off the coasts of California, Peru and Namibia. Regions in which marine

Global spray rate m3 s-1

Figure 11.3 Global cooling as a function of spray rate for the assumptions in the right-hand side table, non-intelligent spraying and the range of initial nuclei concentration suggested by Bennartz (2007). The circle shows warming since the start of the industrial revolution. It could be reversed by spraying approximately 10 m3 s-1. The question mark is a guess for the effect of twice pre-industrial CO2. Assumptions obtained from Charlson et al. (1987), Schwartz & Slingo (1996) and Smith etal. (1991).

Figure 11.4 Results of a parameter combination based on a set of selection criteria of sunshine, initial CCN concentration, cloud cover and wind speed for four quarters of 2001 from Sortino (2006). Red is best but yellow is fine. Seasonal migration is indicated. (a) January-March, (b) April-June, (c) July-September and (d) October-December. (See also colour plate.)

currents are flowing towards the Arctic are of special interest partly because cooling this water might contribute to preserving Arctic ice cover, which is itself a powerful reflector of solar energy, and partly because a reduction in the release rate of methane from the melting of Siberian permafrost might be achieved.