Ensembles of climate change models for risk assessment of nuclear power plants

Climate change affects technical systems, structures and infrastructures, changing the environmental context for which systems, structures and infrastructure were originally designed. In order to prevent any risk growth beyond acceptable levels, the climate change effects must be accounted for into risk assessment models. Climate models can provide future climate data, such as air temperature and pressure. However, the reliability of climate models is a major concern due to the uncertainty in the temperature and pressure future projections. In this work, we consider five climate change models (individually unable to accurately provide historical recorded temperatures and, thus, also future projections) and ensemble their projections for integration in a probabilistic safety assessment, conditional on climate projections. As case study, we consider the passive containment cooling system of two AP1000 nuclear power plants. Results provided by the different ensembles are compared. Finally, a risk-based classification approach is performed to identify critical future temperatures, which may lead to passive containment cooling system risks beyond acceptable levels.


INTRODUCTION
The Intergovernmental Panel on Climate Change (IPCC) has underlined the need of placing increasing emphasis on the assessment of the impact of global climate change on the reliability of critical Systems, Structures and Infrastructures (SSIs) [1]. Climate change must be embedded into risk assessment to take into account the changing environmental context, and avoid or mitigate unexpected and undesirable operational conditions that were not considered in the SSIs design phase.
Current climate change seems to go beyond the bounds of the natural cyclic changes and how the natural, social and technical systems can tolerate this is a major issue [2]. To mention one phenomenon that might affect the cooling capability of risk-relevant SSIs, (like Nuclear Power Plants (NPPs)), a global average surface temperature increase of about 0.8°C has been recorded since 1900, and is expected to reach even 6.4°C by 2100 (depending on future Green House Gas (GHG) emissions and human activity [3; 4; 5; 6]), endangering cooling capability of SSIs.
The large uncertainties on the impact of climate change on the operational risk of SSIs rises significant challenges and methods are needed that allow assessing the possible impact of climate change with a transparent and feasible treatment of the involved uncertainties [1] Risk assessment methods typically rely on probabilistic-based approaches, wherein uncertainties are propagated into the rise model output [7]. In this framework, the uncertainty in the climate change projections, i.e. the uncertainty of the future values given by a climate model [8], plays an important role because it may lead either to over-or to under-estimation of the risk. In this respect, a pool of climate change models is available, each one addressing a specific problem (for example, the causeeffect relationship between climate change and GHG emissions), but none can be identified as the single best climate model [3]. The problem is, then, one of model uncertainty [9]. The difficulty in quantifying and managing this source of uncertainty is a challenge. Bayesian approaches have been proposed [9; 10; 11; 12; 13], but in the climate change modelling problem, the lack of comprehensive climate models, which treat all the specific issues addressed by the individual models, calls for aggregating the different models into an ensemble [14]. In this paper, three ensemble approaches are investigated to aggregate the projections of five climate models to improve the robustness and the accuracy of the projection of the future climate conditions [15; 16; 17; 18; 19; 20]. We aggregate the climate projections of five models (under one climate pathway of global future development (RCP 6.0)) from the open-source database Climate Change Health Impact Profiles project (ClimateCHIP, www.climatechip.org). The ensemble approaches of aggregation differ in the way they score the different models with respect to the monthly Mean Absolute Error (MAE), which is computed (for each climate model) by assessing the difference between the recorded and computed air temperature recorded (from 1981 to 2005). The following weighting strategies are considered for the aggregation [15; 16; 21]: i) weight proportional to the inverse of the MAE; ii) weight proportional to the logarithm of the inverse of the MAE; iii) weight proportional to a Borda count-based ranking [15]. We consider the Passive Containment Cooling System (PCCs) of AP1000 NPPs as case study [22] because: i) nuclear power is an energy option considered to reduce greenhouse gas emissions [23; 24]; ii) it has been shown that the safety and reliability of NPPs are significantly influenced by changes of air temperature, precipitation, river flows, sea level, shoreline erosion, coastal storms, floods, heat waves, etc., that affect cooling water supply [2; 8; 25; 26; 27].
The proposed ensemble methods are used to aggregate the forecasts of the climate change models in order to assess the Conditional Functional Failure Probability (CFFP) of the PCC by performing for, an integrated probabilistic safety assessment conditional on climate projections [22; 28] and to classify the temperature conditions that lead the PCCS to unexpected and dangerous scenarios [28].
The CFFP is the probability that the pressure of the containment exceeds a safety threshold, and it is computed by carrying out a Monte Carlo (MC) sampling of all input variables of the thermo-hydraulic model, which simulates the PCCS after a Loss Of Coolant Accident (LOCA). The results provided with the ensemble of temperature projections are compared with those retrieved using the individual climate change models. On the other hand, the great benefit of the risk-based classification approach consists in that once the air temperature projections of the different climate models (ensemble or not) are compared to the risk-relevant temperature interval, the risk assessment and the climate projections are simultaneously provided.
The remaining of this paper is organized as follows: Section 2 introduces the characteristics of the PCCS, and its behaviour following a LOCA; the climate models and their ensemble alternative strategies are described in Section 3; the theoretical description of the proposed risk assessment analyses is provided in Section 4; results of the risk assessment are presented in Section 5; conclusion and remarks are discussed in Section 6.

THE CASE STUDY
In this work, the Passive Containment Cooling System (PCCS) of the Westinghouse AP1000 Pressurized Water Reactor (PWR) is considered (Fig. 1) [29]. The AP1000 has been the first Generation III+ reactor to receive the final design certification by the Nuclear Regulatory   Following an accident, the PCCS cools the containment vessel in a passive way, which means that its operation is not triggered by electricity. The natural circulation of the air within the containment shield building enhanced by the evaporation of the water, which is drained by gravity from a pool situated on top of the containment shield building, removes heat from the containment vessel. If the pressure is effectively controlled within the safety limit of 0.4 MPa after 1000 seconds from the beginning of the accidental scenario, the removal of heat is successful and safety guaranteed [30].
The accident considered is a Loss of Coolant Accident (LOCA) [31] and it is modelled resorting to a Thermal Hydraulic (TH) model of literature [22; 29].
The evolution of a LOCA is typically described by four steps [32]: (1) blowdown, from the accident beginning to the time at which the primary circuit pressure is equal to the containment pressure; (2) refill, from the end of the blowdown to the time when the vessel lower plenum is completely refilled by the Emergency Core Cooling System (ECCS); (3) reflood, which is the interval of time in which the core is flooded by water; (4) post-reflood, which starts after the core is completely quenched and ends when the energy is released to the Reactor Coolant System (RCS). In the post-reflood phase, the steam produced in the RCS is cooled at the internal layer of the steel containment vessel and, then,

Ensembles of climate projection data
The AP1000 NPPs are design to operate for 80 to 100 years. It is, then, reasonable to investigate how the climate change and, in particular, the change of air temperature and pressure, might affect the reliability performance and the risk of these NPPs. assumption, which considers an equilibrium scenario of the total radiative force after the year 2100, due to a reduction of the GHG emission, has been adopted to retrieve the climate data [40].
A weighting strategy is utilized for aggregating future air temperatures [42], which are provided in terms of statistical indicators like the mean value (if the forecasts of the air temperatures were provided in the form of probability distributions, these could be aggregated by Bayesian model averaging [41]). The weighting is based on the difference between the predicted air temperature values and the real air temperature data in the time interval 1      To improve projection accuracy, a procedure of aggregation of the climate change models into an ensemble is introduced. Three ensemble approaches, which differ on the definition of the considered weighting strategies, are defined in order to obtain a projection that relies on the strengths of each weight proportional to the logarithm of the inverse of the MAE [42]: is the maximum error between the temperatures predicted by the climate change models and the real air temperature values, for each month.

c)
For each month, a weight proportional to a Borda count-based ranking [15] is assigned to each model. The ranking score S  [1,50] is equal to 1 for the (worst) model with the largest MAE, and 50 for the best performing climate change model with the smallest MAE. Consequently, the higher the rank, the higher the weight assigned to the climate model, allowing the best performing climate model to bring more information in the ensemble (more than for strategy b).
Once the weight, ij w , is defined, the air temperatures predicted by each climate change model are aggregated into the predicted temperature Ti, by computing the simple average:     [28].
Finally, it is worth pointing out that the ensemble strategies are expected to improve the accuracy with respect to the individual climate models, but not to address and quantify the epistemic uncertainty of the climate models used themselves. This is because, neither air temperature distributions nor ranges of temperature projections are available, which would allow propagating uncertainty, e.g. with probabilistic and possibilistic approaches [46,47]. Therefore, in what follows, we limit the analysis to the probabilistic uncertainty propagation of the design input variables of the TH model and of the environmental pressure, A, neglecting the uncertainty on the ensembled temperature projections.

Risk assessment of the NPP
The air temperature projections provided by climate models and ensemble strategies for the time intervals t2, t3 and t4 are used as input data of two risk assessment approaches to assess the risk of the NPP of Section 2 [28], namely the integrated probabilistic safety assessment and the risk-based classification approach. These approaches have been selected because, although, both approaches rely on the same assumptions and are based on the probabilistic assessment of a dynamic system model, they differ in how uncertainty in output is quantified and, thereby, communicated. On one hand, the integrated probabilistic risk assessment has been shown in [28] to be useful when the knowledge available is strong enough for uncertainty to be quantified as conditional probabilities given a future air temperature [49] (although these probabilities do not capture the uncertainty in climate data). On the other hand, the risk-based classification of projected temperatures communicates uncertainty as statements associated to a future state, as either safe or non-safe, and differences between different climate projections. The difference with the probabilistic risk assessment is that no probabilities are shown, only the projected temperatures, and it may be easier for a decision maker to relate to a temperature than to a probability.
In details, the approaches can be summarized as follows:  In what follows, we show that the air pressure A is correlated to T. Without loss of generality, let us consider the Sanmen NPP: Fig. 8 shows that real i T (solid line in Fig. 8) and the corresponding air pressure (dashed line in Fig. 8), which have also been collected in a weather station nearby the NPP, are negatively correlated, that is, an increase of T leads to a decrease of A.

Fig. 8 Monthly mean of air temperatures (solid) and air pressures (dashed) based on observations collected by a Chinese weather station.
For this reason, A is here sampled from the joint distribution of the air temperature and the air pressure. Regarding the Sanmen NPP, the joint distribution of air temperature and pressure is approximated by the monthly specific Gaussian bivariate distribution shown in Fig. 9. Fig. 10 shows that, in this way, samples of A at different future air temperatures projected i T are also negatively correlated to T. Fig. 9 The joint distribution of temperature and pressure based on data collected by a Chinese weather station (circles).

Results
Hereafter, without loss of generality, we show and discuss the results of the application of the two alternative risk assessment approaches to site 1 (the NPP in Samen County, Zhejiang Province, China) and to site 11, (the Duke's Lee NPP, in Gaffney, South Carolina, USA). These NPPs are selected because of their significance: the former has already been studied in different environmental conditions and climate change scenarios [22; 28], and it is interesting to investigate how risk assessment might be affected by the information carried by the ensembles of climate models, rather than by the individual models [28]; the latter, instead, is interesting to be analysed because, as shown in Fig. 7, it shows the best results in predicting the real historical air temperature by adopting the proposed ensemble strategies.

Approach 1: The integrated probabilistic safety assessment conditional on climate projections
In order to assess the CFFP of the PCCS, the MC procedure is performed for each individual climate Similarly, Fig. 12 shows the FMMs of the containment pressure of 5 months (from May to September during the time periods from 1981 to 2099). Although good agreement of the FFMs retrieved by using climate models and ensemble strategies is shown in the hottest months (June, July and August), with the exception of the HadGem climate model which leads to more likely high containment pressure (crosses line in Fig. 12), the influence of the climate models on the probability distribution of the containment pressure is confirmed by the FMMs of September: in particular, the CFFP of the PCCS largely deviates when the HadGem and NORES climate models are adopted (crosses and squares lines, respectively, in Fig. 12), leading the average containment pressure close to the safety limit of    In all cases, we claim that the risk assessment performed with the ensemble strategies of the air temperature models can give more reliable (robust) results than that performed with the individual modes, because the ensemble strategies show larger accuracy than the individual climate models in predicting the air temperature, as described in Section 3. A more insightful uncertainty analysis of the CFFPs projections would have been allowed if the uncertainty on the climate projections would have been provided either in terms of probabilistic or possibilistic terms, as already discussed in Section 3.4.

Approach 2: The risk classification based on an assessment of critical temperatures
The approach consists in assessing the T-Y profiles by simulating the system model given all uncertainties (i.e., design input variables D and air pressure A) with fixed T, where we define the distribution of Y conditional on temperature T (taking into account that air pressure A is conditionally dependent on air temperature T). The distribution of Y is derived by simulating the TH model for temperatures in the range 25°C to 45°C (i.e., the variability of the historical air temperatures on sites 1 and 11), with a fixed set of randomly sampled design variables D. In this way, the differences in Y for different values of T should only depend on T. Figure 15 shows that the relationship between Y and T is monotone: the larger T, the larger the probability of exceeding the safety limit of 0.4 MPa. It can be seen that when T is lower than 30°C the probability of Y to be lower than 0.   For site 1, as soon as the air temperature T exceeds 28.5 °C, the containment pressure Y increases. On the other hand, the analysis of the distribution of Y for site 11 shows that the containment pressure Y increases as the air temperature T exceeds 30 °C ( Table 2). The failure pressure threshold (Yh) of 0.4 MPa is overcome at different temperatures depending on the site: 35.5°C is identified as the failure critical temperature for site 1 (Fig. 16), whereas the failure critical temperature of site 11 is 36 °C (Fig. 17).  Fig. 17 The critical temperatures leading to the 95th percentile of Y exceeding the safety limit for site 11.
The risk classification based on the projections provided by both the climate models and the ensemble strategies is performed for the hottest months (for the NPPs located at sites 1 and 11). Fig. 18 shows the risk classification for the site 1: even if the forecasts of the air temperature are within the identified risk-relevant interval, the air temperature forecasts provided by the ensemble strategies (diamonds, backward-pointing and forward-pointing triangles in Fig. 18 for the a), b) and c) ensemble strategies, respectively) are very close to one another, whereas, those retrieved by using the individual climate models greatly differ from each other. For example, the projections of the HadGem and MIROC models (crosses and circles in Fig. 18, respectively) are higher than those provided by the NORES climate model (squares in Fig. 18).   Fig. 19 for the a), b) and c) ensemble strategies, respectively) give very similar air temperature forecasts, whereas the climate models provide different projections of the air temperature. For example, the HadGem model (crosses in Fig. 19) gives the highest forecasts of the air temperature, which are close to the failure critical temperature from the time period 2 (from 2011 to 2040). The climate models GFDL, IPCM, MIROC and NORES (pointing-up triangles, pointingdown triangles, circles and squares in Fig. 19, respectively) provide air temperature forecasts that are lower than those provided by the ensembles, and, thus, this may lead to underestimating the risk associated to the PCCS. For example, analyzing the time period 4 (from 2081 to 2099), it can be observed that the projections provided by these climate models are closer to the safety threshold of 36 °C than those provided by the ensemble strategies. Finally, it is worth highlighting the simplicity of application and the limited computational burden of the risk classification approach embedding climate change into the risk assessment: indeed, once that the air temperature projections of the different climate models (with and without the ensemble) are compared with the critical temperatures, the risk associated to that temperature is easily provided (without the need of building the CFFPs, as for approach 1). Limitations of the integrated probabilistic safety assessment conditional on climate projections are indeed overcome: while a probability distribution of the climate data is strongly required by the probabilistic safety assessment approach, this is not required by the risk-based classification approach. Since future climate data are pointwise projections, i.e., without probability distribution, the risk assessment approach might turn to be challenged as the number of system variables depending on the air temperature increases, whereas the risk-based classification approach would not.

Conclusions
Climate change must be considered for NPPs, in particular if passive safety systems are used. To support this claim, we have considered as case study a PCCS of an AP100 reactor. Several challenges with the integration of climate change have been identified and two alternative ways to investigate the potential impact of changing climate have been proposed: a fully probabilistic modelling based on climate projections and a risk classification-based on an assessment of critical temperatures. The probabilistic risk assessment quantifies the failure probability of the NPP, conditioned to a future air temperature. Conversely, the risk classification of projected temperatures provides a risk assessment of the NPP under future climate scenarios, by providing the future air temperatures which may lead the PCCS into failure. From a decision maker point of view, we expect this latter method to be preferred, because temperature is a physical variable more easy to understand than the concept and meaning of probability.
Three ensemble approaches, based on the aggregation of the projections of five climate models, have been proposed to be used within two alternatives ways of investigation. It has been demonstrated that, using a database of real recorded air temperatures, the three ensemble approaches give more accurate forecasts than the individual climate models. Results have shown that, whilst each individual climate model leads to a different risk assessment, the ensemble strategies lead to very similar risk assessment results and, consequently, the evaluation of the risk is more robust than that one obtained by using an individual climate model, due to the fact that the results do not depend on the particular climate change model.

Acknowledgment
Authors thank Dr. Sahlin Ullrika for her precious encouragement in initiating the research activity, for initially manipulating the climate change data, and for the fruitful exchanges of views that have greatly improved the manuscript.