Integrated Radiative Forcing
Researchers are aware of the limitations of RF and have been developing metrics that can express total climate response, including future impacts.
To express the future effects of GHGs, RFs of current (or future) GHG emissions over a chosen time frame can be summed (in mathematical terms: integrating emissions over time). The results incorporate future effects of GHGs. This method places an equal weight on impacts occurring at each point of time within the chosen time frame. See Figure 3 for a schematic illustration of integrated RF. Integrated RF is expressed in Watts per square meter year (W/m2y), i.e. it expresses the energy that is added to the system during a chosen time horizon due to the GHG emissions.
Figure 3: Integrated Radiative Forcing: the sum of RF over a chosen time period (area under the curve) measured in Watts per square meter year (W/m2 year)
Figure 4: Integrated RF of All Anthropogenic GHGs Emitted in the Year 2000 over Two Different Time Horizons.
Top graph: integrated RF over a 100-year time horizon, i.e. the bars express the cumulative energy that will be added or subtracted from the global energy balance over the next 100 years due to the different GHGs emitted in 2000.
Bottom graph: integrated RF over a 20-year time horizon.
(Source: IPCC, 2007, WG I, p 206)
Choosing the time frame for integrated RF greatly influences results. For example, as Figure 4 shows, integrated RF of CO2 is much larger over the 100-year time frame than over the 20-year time frame, whereas the contributions from short-lived gases stay the same over the two time horizons, because they decay much faster and do not cause additional forcing after the first 20 years.
Choosing the time horizon for integrated RF is not a scientific matter but a policy choice. If we are concerned about the long-term warming impacts of GHG emissions, we should choose a longer time horizon. If we are concerned about warming impacts in the short term that may lead to irreversible changes (‘tipping points’), we should choose a shorter time horizon.
Integrated RF can be calculated using different assumptions. Figure 4 uses a pulse emission (the emissions from the year 2000) and integrates RF as GHG emissions from that year decay over time. Short-lived GHGs will decay faster, long-lived gases more slowly.
Yet integrated RF could also be calculated assuming sustained emissions. For example, instead of using only the emissions from the year 2000, as in Figure 4, emissions over the chosen time frame (say 20 years) could be assumed to remain constant and cumulative integrated RF of these constant emissions could be calculated. The RF for short-lived emissions would then stay constant (not decay). The RF for long-lived gases would grow over time because these gases accumulate. Figure 5 is a simplified illustration of RF for a pulse emission and RF for constant emissions. If we expect that emissions will grow or decrease, we can also calculate integrated RF scenarios with growing or decreasing emissions.
The choice to calculate pulse or sustained emissions is a policy decision. As Figure 5 illustrates, the results can vary dramatically depending on which method is chosen. A pulse emission is suitable for air travel calculators, since the interest is in calculating the effects of a single flight. Sustained emissions would be appropriate for modeling, for example, the effects of future aviation: either constant emissions or the predicted emissions projections should be chosen in that case.
Figure 5: Atmospheric Concentration and Radiative Forcing Over Time for a Pulse Emission (top) and Constant Emission Levels (bottom).
Top left: A pulse emission of two hypothetical GHGs: a short-lived one (red) and a long-lived one (blue). The concentrations of both GHGs decrease over time: the short-lived GHGs decays much faster than long-lived GHG.
Top right: The total RF (blue line) of these two pulse emissions also decreases over time because both gases decay over time. Integrated RF is the area under the blue curve.
Bottom left: Constant emissions of two hypothetical GHGs: concentration of the short-lived GHG (red) stays constant; concentration of the long-lived GHG (green) accumulates over time.
Bottom right: The total RF of these two constant emissions (blue line) increases over time because the concentration of the short-lived GHG stays constant and the concentration of the long-lived GHG increases over time. Integrated RF for these two constant emissions is the area under the blue curve.
Temporal differences in warming
Integrated RF only sums the radiative forcings over a chose time horizon. It does not show at what point during that time horizon warming occurs. For example, short-lived GHGs with strong warming capacity, such as methane, will cause temperature changes early on, but will then decay and no longer cause warming. Long-lived gases with comparatively weaker warming capacities, such as CO2, will warm the climate more gradually, but for a much longer time. Figure 6 shows the same total integrated RF value for two very differently-acting GHGs. Despite the fact that they share the same value for integrated RF, their effect on the climate will play out quite differently. Neither integrated radiative forcing nor Global Warming Potential (see next section) takes these differences into account.
Figure 6: Identical Integrated Radiative Forcing of Two Hypothetical GHGs with Different Longevity and Warming Capacity.
The red line shows the RF of a short-lived GHG with a high warming capacity, such as methane. The green line shows the RF of a long-lived GHG with a weaker warming capacity, such as CO2. Both GHGs have the same integrated RF value (area under the curve) yet because the warming they cause occurs at different points in time and with different strengths, their effect on the climate will not be the same. Integrated RF does not reflect this difference.
Integrated RF does not account for the thermal inertia of the climate system. Thermal inertia refers to the delay in the change of Earth’s energy balance in response to climate forcing, or the imbalance caused by a lag between the effects of forcing and the return to energy equilibrium.
Integrated RF can be used to expresses the future effects of current aviation. The chosen time horizon greatly influences the results: short time horizons emphasize the warming due to short-lived emissions, whereas longer time horizons emphasize the warming of long-lived gases. The choice of pulse versus sustained emissions also influences the results: sustained emissions give more weight to short-lived effects than pulse emissions do.