Observational constraints on future climate change
When considering future climate changes, we require standardized plural scenarios on the climate control target to compare the model results. The climate research community has, therefore, developed four possible greenhouse gas concentration pathways under different climate control policies. These are known as representative concentration pathways (RCPs) (Collins et al. 2013; Vuuren et al. 2011) where the radiative forcing in 2100 is constrained to 8.5 W/m2 (RCP8.5), 6.0 W/m2 (RCP6.0), 4.5 W/m2 (RCP4.5) and 2.6 W/m2 (RCP2.6). However, future climate change projections contain intrinsic uncertainties. A method was proposed to constrain the uncertainty in ΔT by evaluating GCMs’ climate simulations and comparing them with the historical observations of surface air temperature (Allen et al. 2000; Stott and Kettleborough 2002). This is named Allen–Stott–Kettleborough (ASK) method. Its basic idea is simple: if GCM overestimates the observed magnitude of historical climate change, it will overestimate future climate change by a proportional amount, and vice versa. The future projections of ΔT are scaled up or down by this proportional amount, and the uncertainty ranges due to the internal climate variability are estimated.
Shiogama et al. (2016) considered simulations of the Coupled Model Intercomparison Project Phase 5 (CMIP5) (CMIP 2017; Collins et al. 2013) as pseudopast and future observations and applied the ASK method to estimate how fast and in what way the ΔT uncertainties can decline when the current observation network of surface air temperature is maintained. Shiogama et al. (2016) investigated the rate of decline of the ΔT uncertainty until the end of this century for each of RCPs, and found that more than 60% of the ΔT uncertainty in the 2090s (2090–2099) can be resolved by the observation until 2049.
We apply the same method as Shiogama et al. (2016) to estimate the future decline of the ΔT uncertainty in the 2090s using all the four RCPs, whereas Shiogama et al. (2016) analyzed each of four RCPs, respectively. Figure 1 shows the decline of ΔT uncertainty by the 2090s thanks to the update of observations. The uncertainty range of ΔT rapidly decreases as the more observation data accumulate. We can accurately reduce more than 60% of the ΔT uncertainty in the 2090s by 2039 and about 80% by 2089. The reduction rate of the ΔT uncertainty is improved because of the increase in the analyzed GCM data size. Shiogama et al. (2016) concluded that 60% of the ΔT uncertainty will be reduced by 2049, but that occurs by 2039 in this study. Although Shiogama et al. (2016) proposed a method for how observations reduce the future temperature rise uncertainty, they did not touch upon the mitigation strategies and actions. The present paper investigates the pathways of mitigation option implementations and evaluates the value of observation applying the expanded ATL method to the integrated assessment model MARIA.
ATL decision-making
We applied the above uncertainty-decreasing process to multi-stage decision-making. This is known as the Act Then Learn (ATL) procedure, and was first applied to the GLOBAL 2100 model (Manne and Richels 1992). Figure 2 shows the decision-making frames under uncertainties of (a) perfect ex ante information [Learn Then Act (LTA)] decision-making, (b) single-stage decision-making without learning and (c) multi-stage decision-making the ATL learning process. If the future uncertainty is completely resolved prior to the decision-making at the initial time, then the decision maker can select the optimal strategy corresponding to the foreseeable future [case (a)]. On the contrary, if no opportunity to revise the plan arises after the decision-making, the policy maker must select the initial action that maximizes a given objective function such as the expected discounted utility [case (b)]. If the policy maker can change the action based on the learning procedure at an intermediate time t*, as in case (c), the opportunity for change will be considered when deciding the action before t*.
We formulate the model description to address the above decision-making procedure. Let x(t) and a be the control variable at time t and parameter with uncertainty, respectively. We define the uncertainty as a set of discrete scenarios S = {s}, where each scenario s has a probability P(s) at t = 0 and a(s) represents the parameter a in a scenario s. The objective function to be maximized is represented by f(x(t) | a(s)). If the perfect ex ante information is available at t = 0, then we need only to determine the optimal decision under the certain scenario s*. This is represented by the case (a) of Fig. 2. The optimal behavior x*(t | s*) is given by the optimal solution of
$$\mathop {\hbox{max} }\limits_{{{\mathbf{x}}(t)}} .\quad f({\mathbf{x}}(t|s*)|{\mathbf{a}}(s*)).$$
(1)
By contrast, if we know only the future occurrence probability of the scenario s, i.e., P(s), and the decision can be given only once at t = 0, we must explore the optimal pathway x(t) considering all future possible scenarios. In this case, control variables x(t) should be identical across the future scenarios as shown in the case (b) of Fig. 2. When we maximize the expected objective function, the optimal pathway x***(t) is obtained by solving
$$\mathop {\hbox{max} }\limits_{{{\mathbf{x}}(t)}} .\quad \sum\nolimits_{{\,s}} {P(s)f({\mathbf{x}}(t)|{\mathbf{a}}(s))} .$$
(2)
Although other decision criteria (e.g., minimax regret strategy and maxmax strategy) are also applicable (Mori et al. 2013), we focus herein on the maximum expected value similar to Manne and Richels (1992).
In case (c) in which two-stage decision-making is available, the control variables x(t) should be identical before t* but can diverge after t*. If the uncertainty set S is partitioned into K subsets after t*, the optimal solution can be formulated as follows:
$$\begin{aligned} & \mathop {\hbox{max} .}\limits_{{{\mathbf{x}}(t)}} \;\sum\nolimits_{{{\kern 1pt} s}} {P(s)f({\mathbf{x}}(t|s)|{\mathbf{a}}(s))} , \\ & {\text{subject}}\;{\text{to}}\;{\mathbf{x}}(t|s)={{\mathbf{x}}_1}(t)\quad {\text{for}}\quad t \leqslant {t^*}, \\ & \quad \quad \quad \quad {\mathbf{x}}(t|s)={{\mathbf{x}}_2}(t|{\mkern 1mu} {R_k}(s))\quad {\text{for}}\quad t>{t^*}\quad k=1,2, \ldots K. \\ \end{aligned}$$
(3)
where R
k
(s) represents the kth subinterval of S. Let x**(t|s) denote the optimum solution of Eq. (3).
For example, future population growth rates up to 2100 are categorized into S = {very low, low, middle, high, very high}, but information on the actual rate is lacking. In 2050, the future population growth might be recognized as R = {{very low, low}, {middle}, {high, very high}}. If the future population post-2050 is narrowed to {very low, low}, the decision-making can exclude the other possibilities.
We define the value of “information” or “scientific knowledge” by comparing the simulated GDPs in the above three cases in this study according to Manne and Richels (1992).
For instance, the difference between the expected optimal GDP under ex ante perfect information and the expected GDP of the single-stage decision-making gives the “value of perfect information”. Let Y(x(t) | a(s)) be the GDP of period t under the future scenario s. The expected value of perfect information at period t, namely VPI(t), and the discounted summation of the differences, namely TVPI, are defined as
$${\text{VPI}}(t)=\sum\nolimits_{{\,s*}} {P({s^*})Y({{\mathbf{x}}^*}(t|{s^*})|{\mathbf{a}}({s^*}))} - \sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} .$$
(4)
$${\text{TVPI}}=\sum\nolimits_{t} {{{(1 - d)}^t}\left[ {\sum\nolimits_{{\,s*}} {P({s^*})Y({{\mathbf{x}}^*}(t|{s^*})|{\mathbf{a}}({s^*}))} - \sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} } \right]} .$$
(5)
where d denotes the discount rate.
The ratio of VPI(t) to GDP, namely VPIR(t), and ratio of TVPI to the discounted summation of GDP in case (c), namely TVPIR are, respectively, defined as
$${\text{VPIR}}(t)=\frac{{{\text{VPI}}(t)}}{{\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} }}$$
(6)
$${\text{TVPIR}}=\frac{{{\text{TVP}}I}}{{\sum\nolimits_{t} {{{(1 - d)}^t}\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} } }}$$
(7)
which represent the ratio of that economic gain of perfect information to the economic output without learning under the initial information.
Similarly, the difference between the GDPs calculated by the optimal solutions of Eq. (3) in case (c) and Eq. (2) gives the accumulated knowledge value of the learning process, namely VLP(t):
$${\text{VLP}}(t)=\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{**}}(t|s)|{\mathbf{a}}(s))} - \sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} .$$
(8)
The discount summation of VLP(t), namely TVLP, represents the total value of learning.
$${\text{TVLP}}=\sum\nolimits_{t} {{{(1 - d)}^t}\left[ {\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{**}}(t|s)|{\mathbf{a}}(s))} - \sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} } \right]} .$$
(9)
Similar to Eqs. (6) and (7), we can define the value of learning as follows:
$${\text{VLPR}}(t)=\frac{{{\text{VLP}}(t)}}{{\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)\,|\,{\mathbf{a}}(s))} }}$$
(10)
$${\text{TVLPR}}=\frac{{{\text{TVLP}}}}{{\sum\nolimits_{t} {{{(1 - d)}^t}\sum\nolimits_{{\,s}} {P(s)Y({{\mathbf{x}}^{***}}(t)|{\mathbf{a}}(s))} } }}$$
(11)
In previous applications of this approach to integrated assessment models (Manne and Richels 1992; Mori et al. 2013), the uncertainty was eliminated by hypothetical processes. Herein, we investigate the impact of knowledge accumulation on the policies adopted for energy technology. We apply the learning process of Fig. 1 to an integrated assessment scheme named the Multiregional Approach for Resource and Industry Allocation (MARIA) (Mori et al. 2013). We also analyze the economic benefits of the knowledge accumulation.
It should be noted that the concept of “value of information” or “value of scientific knowledge” is extremely broad. It extends from conventional cost-and-benefit analysis approach employed herein to technological and societal innovation as yet unknown. For instance, few people in the previous century could have imagined today’s progress in the information technology or artificial intelligence. Such new knowledge or a big innovation would substantially alter the policies on climate change. However, we cannot evaluate these values nor can we rely on such advance to provide today’s decision. However, there are some possible options with expected large potential and high barriers (e.g., nuclear fusion reactor, space solar power systems (SSPS), and geo-engineering options). The method described herein might be applicable to evaluating these “uncertain” options.