Precipitation is one of the typical variables in the hydrological cycle, a process that has inevitably been affected by global climate change due to increasing atmospheric and other greenhouse gas concentrations and anthropogenic activities (Kong et al., 2021; Liu et al., 2018). General circulation models (GCMs) have been considered as primary tools for climate change scenarios and a very important basis for precipitation prediction (Zhao et al., 2020; Chen et al., 2014; Hasson and Pascale., 2016). Incomplete theoretical understanding and certain simplifying assumptions mean GCMs are not perfect (Georgescu et al., 2021; Reichler and Kim, 2008), particularly the greater errors in the local resolution. The World Climate Research Program (WCRP) developed the Coupled Model Intercomparison Project (CMIP), which provides an opportunity for model comparison and multi-model ensemble strategy development (Knutti and Sedláček, 2013; Li et al., 2011). The Coupled Model Intercomparison Project Phase 5 (CMIP5), coordinated by the WCRP with the support of the IPCC AR5, is still the current activity before the AR6. There are 59 GCMs in the CMIP5 (https://www.wcrp-climate.org/wgcm-cmip/wgcm-cmip5) in total, covering a large number of more complex models run at higher resolution, more complete “representative concentration pathways” (RCPs) of external forcing, more scenarios, and more saved diagnostics (Taylor et al., 2012). The models tended to be selected according to the availability, resolution, or initial analysis of their applicability (Huang et al., 2013; Knutti and Sedláček, 2013; Sabeerali et al., 2015; Sun and Ding, 2015; Li et al., 2018). It has been a focus of intense international attention to assess and correct GCMs in different regions all over the world (Maurer and Pierce, 2014; Wang C. et al., 2014; Toreti and Naveau., 2015). Given the variations in the GCM structure and hypothesis simplification, each model has its own level of performance and shows vast differences, especially at the local scale. Thus, based on the reliability and credibility exploration, models’ evaluation and selection play a very important role in future water projection.

Water resources in the Yellow River, one of China’s mother rivers, has caused extensive concern for the water resources issue (Miao et al., 2010; Zhou et al., 2018) due to the historical flow interruption in the last century. The huge stress on supplies in the middle and lower reaches is a major issue for economic and social development planning strategies in these regions. Meanwhile, climate change and the underlying surface change (e.g., land-use change and city or hydraulic engineering) caused by human activities are affecting the future water resources (Xia et al., 2014). Precipitation is the major source of the Yellow River water resources, and any future change will directly impact water resource utilization (Wang et al., 2018). Application of GCM scenarios has addressed the simulated and projected precipitation under climate change (Kang et al., 2015; Chen et al., 2016; Wei et al., 2016). The current research mainly imports several GCMs to try predicting precipitation or other related indexes such as the runoff change in spatio-temporal changes for future climate scenarios (Wang G. Q. et al., 2014; Yang et al., 2017). There has been some analysis of the performance of GCM simulation (Lin et al., 2018), but few studies comprehensively assess the uncertainty and credibility of GCMs. Decision-makers or other stakeholders might be very confused facing the quite different or even opposite results from the multi-model ensemble. Therefore, due to the well-known huge uncertainty of the GCMs (Friedlingstein et al., 2014; Lee et al., 2021), it is a key problem how much confidence could be provided if the future projection is imported into decision-making or planning.

There is an inherent hypothesis in climate model evaluation that good model performance evaluated from the historical and present climate guarantees higher reliability or credibility in future climate projections. This hypothesis has been widely accepted in the absence of a better alternative, for example, a comprehensive understanding of the climate cycle and more accurate downscaling techniques. Many studies have attempted to assess the performance of climate models in terms of goodness-fit to present-day climate and to predict the future climate on continental and regional scales (Mahlstein I et al., 2012; Grainger et al., 2013; Hertig et al., 2014; Mehran et al., 2014; Hui et al., 2018). Through extensive work and improvement in the representation of the atmospheric oceanic process, various models have been developed and shown to increasingly perform well in simulating climate changes (Van den Hurk et al., 2013; Ahmadalipour et al., 2017). But climate simulations and forecasts are inevitably uncertain (Allen et al., 2000; Eghdamirad et al., 2017). To reduce the simulation uncertainty and improve the credibility of climate models, multi-model ensemble techniques have been adopted (Thibeault et al., 2012; Ongoma et al., 2018). Multi-model ensembles are believed to perform better than single simulations, particularly in terms of reliability amid the huge uncertainty of climate models. This is because the multi-model approach involves different physical parameterization methods and structures that surmount the limitations of the single simulation (Wang et al., 2017). Thus, the technique of the multi-model ensemble (MME), defined as the average of simulation results from the multiple models, has been widely used on account of the better large-scale agreement with observations (Cubasch et al., 2001; Kumar et al., 2012). The extensive use of the MME has been considered a successful way to provide higher quality and more consistent future climate change projections, by means of constraining projections using observations (Lu and Fu et al., 2009; Strategy, 2014). However, since the future projections may vary widely among the different models, utilizing an average of all the models for the MME is not necessarily the best way to obtain more reliable projections without looking into the reliability of the individual models (Sun and Ding., 2009; Knutti, 2010; Lee and Wang, 2014). Therefore, the weight of individual simulation becomes crucial when deducing the multi-model ensemble result, rather than the simple average. Moreover, a multi-model ensemble does not necessarily involve all models. It has been recognized that poorly performing models degrade the overall skill of weather and climate forecasts in an ensemble mean approach (Krishnamurti et al., 2000); for further assessment of future changes, selecting some best models is needed (Huang et al., 2013; Seo and Ok, 2013; Lee and Wang, 2014; Vasconcellos et al., 2020).

The reliability ensemble averaging (REA) methodology, proposed by Giorgi and Mearns (2002) , provides a weighted average of climate change ensemble results based on the “reliability” of each model. “Reliability” defines the ability of a particular model to simulate the observed climate and its degree of convergence in predicted climate change compared with other ensemble members (Sun et al., 2015). Another similar averaging method is Bayesian model averaging (BMA) proposed by A. E. Raftery and coworkers as a formal framework. BMA conditions simulations of the entire ensemble of models and optimally combines their predictive capabilities. The weights are the estimated posterior model probabilities, representing each model’s relative forecast skill in the training period with observations (Vrugt and Robinson, 2007). Moreover, this BMA methodology can assess the models’ joint predictive uncertainty, which is an advantage in the face of huge uncertainty in climate model projections compared with other weighted methods such as REA. Since the model averaging simply requires a numerical representation of each model, there are no restrictions on the diversity of conceptual and numerical models. Many studies have demonstrated that BMA produces more accurate and reliable predictions than other available multi-model techniques (Raftery and Zheng, 2003; Ajami et al., 2007; Duan et al., 2007; Demirel and Moradkhani, 2016; Ma et al., 2018). However, due to normally providing only one weight group, BMA is not a perfect solution to variations in models, much less the defects of a large basin without allowing for spatial differences. Thus, a framework for the full assessment process of GCM simulation and projection is a necessary one that consists of uncertainty analysis, individual model evaluation, and then weight setting up.

There is a growing need among policymakers and even stakeholders to identify a future projection mode reliable enough to inform decision-making for adaptation and mitigation purposes, but the reliability assessment of projections is a challenge (Collins et al., 2012; Zhao et al., 2017). When a future projection is provided to policymakers and stakeholders, there are usually questions about how much confidence or even probability can be associated with it. Here, we addressed “credibility”, which is defined as the self-evaluation of molders or researchers when they submit the results to the government based on the MME projection or individual model skill. Credibility is more easily accepted than reliability by policymakers and stakeholders because it explicitly expresses the confidence or probability.

Thus, the goal of this study is to propose a framework to identify the uncertainty and credibility of GCMs for projected future precipitation. As a main component of the framework, a new grid-based BMA approach is also presented. Applying the CMIP5 to the Yellow River basin, this study assesses the performance and inherent uncertainties of the CMIP5 GCMs in simulating precipitation variation and projecting the precipitation change in future periods with credibility. Section 2 describes the data and methodology. Section 3 presents the performance of the grid-based weighted Bayesian model averaging (GBMA) method and uncertainties in CMIP5 models with historical observations over the Yellow River and the future projections with credibility quantification. Conclusions and discussions are provided in section 4.

The development of GCMs enables projections of future climate and even water resource trends. The main challenge is that it is difficult, especially for decision-makers, to trust the predictions, given the huge uncertainty and even opposing results of GCMs. There have been plenty of publications on the evaluation and uncertainty in GCM models, including the Coupled Model Intercomparison Project of CMIP5. Normally climate researchers will suggest several models that are more reliable based on comparative analysis with observations in space and time for the specified basin. However, it is not still simple or used directly if the output of GCMs is imported into further analysis, such as the projected precipitation for future water resources. The current analysis usually focuses on one point or some aspects of the uncertainty and credibility of GCMs, but it lacks an overall operational process to deal with these problems. Thus, this study proposed a framework for an ensemble result generation process in a more credible manner for the future-projected precipitation, in which a new BMA model based on a grid is built to express spatial differences of models for long-span basins.

Five models from CMIP5 are addressed in this study due to the evaluation of the Yellow River basin from the China Meteorological Administration. In the historical period of 1986–2005, the models show a significant spread in space and time. The variations are mostly around ‒50 to 50 mm and demonstrated a great difference in space and even opposite trends in some regions. For different-class precipitation, the uncertainties of the five models are small in relatively weak rainfall but large in heavy rainfall, indicating more risk in future projections and the necessity to explore their credibility. It is quite hard to select the best or most reliable model, given the large uncertainty. However, it is worth noting that the spatial complementary could be expected for less deviation in amplitude. The MME should be a way to reduce the simulation uncertainty and improve GCM predictions.

In contrast with BMA, the grid-based BMA generally represents the spatial differences and performances of each GCM, resulting in a more reliable projection for each grid. It could somehow overcome individual differences and address relatively creditable information from more models on a grid-scale, which could avoid the leveling effect errors in a spatial scale from BMA. This is very critical for a large and long-span basin. However, real improvement still depends on better GCM models. If all the selected models fail in one grid, it is still impossible to get the correct projection even on such a grid scale.

The future precipitation of the YRB in 2021–2051 and 2061–2090 is calculated based on the grid-based BMA, which presents an increasing trend all over the YRB. The regions of rainfall lower than 200 mm will shrink progressively and other higher rainfall areas will expand, even for 800 mm, which is more remarkable for a further future period of 2061–2090. The 400 mm isohyet will also move to the north and west, which might have a deep impact as the geographical marker of semi-arid and semi-humid regions in China. Moreover, the monthly precipitation anomaly generally also shows an increasing trend, and the risk of heavy rainfall might increase in Shanxi, Henan, and Shandong provinces.

If taking the 40% as the accepted probability of projections, in the near future period of 2021–2050, precipitation in most of the Yellow River basin will increase by 0–25 mm and 25–50 mm and by 50–100 mm for the northern parts of Shaanxi and Shanxi. The probability goes up even higher than 80% for some parts for 0–25 mm and 25–50 mm, and the area with a probability higher than 40% extends to a larger region. The increasing trend and amplitude will be more concrete in the far future period of 2061–2090.

According to the signal-to-noise ratios, the middle parts of the YRB such as Qinghai, Gansu, and Ningxia provinces, the south and middle of Inner Mongolia, the north of Shaanxi, and Shanxi present higher values and credibility, which means that the projections in these regions have high credibility. While the other projections are less reliable, the risk exists in the higher precipitation regions in the southern part of the YRB, which will bring new challenges for flood control and mitigation. It is also worth noting that the credibility of 2061–2090 is higher in the larger scope, which is due to the similar assumptions in all GCMs, allowing for the more inherent uncertainty in the far future scenarios rather than better credibility. It ultimately requires more evidence-based data, in-depth understanding, and exact mapping in GCMs to improve the credibility of future projections.

The proposed framework here consists of downscaling, uncertainty analysis (model spread and Taylor diagram), ensemble analysis (a grid-based BMA), credibility analysis (signal-to-noise ratio), and probability projection. It provides a whole chain and novel way for identifying uncertainty and credibility. In particular, the new proposed GBMA method could help produce a more reliable ensemble projection, given the current capabilities of GCMs. This issue is very crucial for assessing risks for disaster and water resource management strategy on the basis of future precipitation projection.

GCMs mainly lie in the spatial differences in performance, especially for local regions, given the different settings of boundary conditions, parameters, and dynamical mechanisms. Quite a few studies find the different GCMs show significant differences in reproducing the historical climate and weather for large areas all over the world, which could be relative to the geography, land cover, etc., Thus, the grid scale or other similar representative units shall be involved to do multi-model ensemble rather than model evaluation on a whole large basin. Though the fundamental improvements of projections rely on more accurate GCMs, the ensemble way could first go further for a more positive spatial expression. As the new GCMs of CMIP6 improve and uncertainties reduce, this proposed framework could play a powerful role in a more credible ensemble projection in the future.