A synonym for “deadweight loss triangle” is “welfare loss triangle”.
Apropos nothing, Harberger (?) showed that welfare loss triangles can be surprisingly small, in the antitrust context.
Within the pollution context, permit me to present a model:
.
P.
. MD
. x x
. x x
. x x
. x x
. x x
.. x x
P1. x x DWL
. x x
. x x
. x x
. x x MB
P0 .x_____________________ x__________________
E1 E0 Emissions
Above, I try to indicate the CO2 emissions over a wide area - perhaps the US or the world. Damages per initial ton of C02 increase as the stock of CO2 increases in the atmosphere. So MD is an increasing curve. Emissions reductions are cheaper in the beginning, then get more expensive. So the marginal benefits of an additional ton of CO2 emitted decline.
If there were a market in CO2 emissions, that is, if those suffering damages from global climactic change could charge the users of fossil fuels (for example), the price would settle at P1. Alas, there is no market in CO2 (yet) so the price is at P0. In other words, you can emit CO2 for free.
In the absence of a tax on CO2 emissions, the free market will emit E0. A tax of P1 would cause a decline in emissions to E1.
Now for your question. The total benefit enjoyed by emitters of pollution is indicated by the area under the MB curve. The total losses from this is indicated by the area under the MD curve. Here, the dead weight loss is rather large (mainly because P1-P0 is large). It is the triangle MD-MB-“those 4 Xs in the middle of the diagram”.
OK, actually that wasn’t your question. It appears that you want to know what happens when there is some emissions reduction, but less than is optimal. To work that out, find a point between E0 and E1 and draw a line upwards. The resulting triangle is the “Welfare loss triangle from insufficient emissions reduction”.
Of course, you can also complicate matters by drawing a couple of interacting diagrams that model different regions of the world (eg, “the US” and “everyone else”). But let’s leave it here for now.