**3. Time model for global warming**

As it can be seen from (1), an estimation of the atmospheric CO2 concentration ratio through time will give a time model for the global warming. This estimation can be done by linear regression of the annual average ratio for CO2, using the NASA dataset [20]. This leads to the following no-climate-mitigation model *r*0*,* applicable from the year 2000 (i.e., *t* = 0)

$$\begin{aligned} r\_0(t) &\approx a\_0 t + b\_0\\ a\_0 &\approx 0.0076, \quad b\_0 \approx 1.3176 \end{aligned} \tag{3}$$

Such a linear regression was found to be statistically highly significant (*p*< 10�21) and extremely strong (*r*<sup>2</sup> ≈0*:*99). By composing the energy-balancebased model Δ*T* (given in (1)) with *r*0, one gets the following climate-policy-free model *w*<sup>0</sup> for global warming, applicable from the year 2000 (i.e., *t* = 0)

$$\begin{aligned} w\_0(t) = \Delta T(r\_0(t)) &\approx \theta \frac{t + \lambda\_0}{t + \mu\_0} \\ \lambda\_0 &= (b\_0 - 1)/a\_0, \mu\_0 = (b\_0 - k)/a\_0 \\ a\_0, \ b\_0 &\text{ as in (3), } \notin \text{ as in (1)} \end{aligned} \tag{4}$$

The estimations based on this model, for the period 2005–2015, appear to be very close to the annual averages calculated using the NASA data [3] for the same period. According to (4), the rise in global average temperature will be estimated at

**Figure 1.** *Estimated global warming since 2000 and expected trend in case of no global climate mitigation.*

*Mathematical Model for CO2 Emissions Reduction to Slow and Reverse Global Warming DOI: http://dx.doi.org/10.5772/intechopen.88961*

1.19°C by 2020. Then, under the assumption of no climate mitigation, it will reach 1.5°C by 2041 and 2°C by 2084. More generally, any climate target L Lð Þ <*β* will be hit by the year 2000 þ ½ � *h* where *h* is the hitting time:

$$h \approx \frac{\mu\_0 \mathcal{L} - \lambda\_0 \beta}{\beta - \mathcal{L}} \qquad (\lambda\_0, \mu\_0 \text{ as in (4)}) \tag{5}$$

which makes the year *d* ¼ 1999 þ ½ � *h* the deadline for the implementation of the *2015 Paris Agreement*. See **Figure 1** for graphical estimation of *h*.

For the rest of the paper, L denotes any UN climate target 1ð Þ *:*5≤L< 2 *,* and *h* is its hitting time as formulated in (5).
