Multi-Model Ensemble Projection of Precipitation Changes over China under Global Warming of 1.5 and 2°C with Consideration of Model Performance and Independence

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  • A weighting scheme jointly considering model performance and independence (PI-based weighting scheme) is employed to deal with multi-model ensemble prediction of precipitation over China from 17 global climate models. Four precipitation metrics on mean and extremes are used to evaluate the model performance and independence. The PI-based scheme is also compared with a rank-based weighting scheme and the simple arithmetic mean (AM) scheme. It is shown that the PI-based scheme achieves notable improvements in western China, with biases decreasing for all parameters. However, improvements are small and almost insignificant in eastern China. After calibration and validation, the scheme is used for future precipitation projection under the 1.5 and 2°C global warming targets (above preindustrial level). There is a general tendency to wetness for most regions in China, especially in terms of extreme precipitation. The PI scheme shows larger inhomogeneity in spatial distribution. For the total precipitation PRCPTOT (95th percentile extreme precipitation R95P), the land fraction for a change larger than 10% (20%) is 22.8% (53.4%) in PI, while 13.3% (36.8%) in AM, under 2°C global warming. Most noticeable increase exists in central and east parts of western China.
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  • Fig. 1.  Topography (m) and location of surface weather stations (gray dots) in China.

    Fig. 2.  The fraction of cases for four indices when the actual outcomes of the perfect model tests are in the 5th–95th range weighted by all other models. For all indices, the minimum value of σd for the fraction is expected to exceed 90%.

    Fig. 3.  The models’ weights obtained by the PI-based weighting scheme (black squares) and the rank-based weighting scheme (gray circles) over (a) western and (b) eastern China.

    Fig. 4.  The regional relative biases simulated by PI-based, rank-based, and AM schemes against observations for four precipitation indices during the period of 1986–2005. Color bars are the mean biases and whiskers represent the first and third quartiles (%).

    Fig. 5.  Spatial distributions of relative bias (%) for R95P from (a) PI-based, (b) rank-based, and (c) AM schemes against observations during the period 1986–2005. Warm and cool colors indicate dry and wet bias, respectively.

    Fig. 6.  Taylor diagram showing the four precipitation indices under the three weighting schemes during the period 1986–2005. The solid and hollow markers represent western and eastern China, respectively.

    Fig. 7.  Boxplots for relative changes (%) of total precipitation and extreme indices (compared to the period of 1985–2005) from PI-based, rank-based, and AM schemes over China under 1.5 and 2°C global warming.

    Fig. 8.  The spatial cumulative distribution functions (CDFs) of changes weighted by PI-based, rank-based, and AM schemes under 1.5 and 2°C global warming for the precipitation indices over China. The abscissa displays the changes of precipitation indices while the left ordinate shows the CDF values and the right ordinate shows the complementary values (1 − CDF). The changes are expressed by percentages (%) compared to the period of 1985–2005.

    Fig. 9.  Percentage changes of PRCPTOT for the 1.5°C (first column), 2°C (second column) global warming under RCP8.5 scenario compared to the period 1985–2005, and the additional 0.5°C warming (third column) from simulations of PI-based (top), rank-based (middle) weighting schemes, and AM (bottom). Areas with significant changes above the 95% confidence level are marked with black dots.

    Fig. 10.  Percentage changes of the three extreme precipitation indices: (a–c) RX5DAY, (d–f) RX1DAY, and (g–i) R95P, projected by PI-based weighting scheme for the 1.5°C (first column), 2°C (second column) global warming under RCP8.5 scenario compared to the period 1985–2005, and the additional 0.5°C warming (third column). Areas with significant changes above the 95% confidence level are marked with black dots.

    Table 1.  Model name, modeling center and country, institution identification (ID), and atmospheric resolution of 17 CMIP5 global climate models (expansions of acronyms are available at http://www.ametsoc.org/PubsAcronymList)

    Model nameModeling center and countryInstitution IDAtmospheric resolution
    (lat × lon)
    BCC-CSM1-1Beijing Climate Center, China Meteorological Administration, ChinaBCC2.81258° × 2.81258°
    BCC-CSM1-1-M1.125° × 1.12°
    BNU-ESMCollege of Global Change and Earth System Science, Beijing Normal University, ChinaBNU2.8° × 2.8°
    CanESM2Canadian Centre for Climate Modelling and Analysis, CanadaCCCMA2.8° × 2.8°
    CCSM4NCAR, United States of AmericaNCAR1.25° × 0.94°
    CNRM-CM5Centre National de Recherches Météorologiques–Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, FranceCNRM–CERFACS1.4° × 1.4°
    CSIRO-Mk3-6-0Commonwealth Scientific and Industrial Research Organisation, AustraliaCSIRO-QCCCE1.875° × 1.875°
    GFDL-CM3NOAA/Geophysical Fluid Dynamics Laboratory, United StatesNOAA/GFDL2.5° × 2.0°
    IPSL-CM5A-LRL’Institut Pierre-Simon Laplace, FranceIPSL3.75° × 1.895°
    IPSL-CM5A-MR2.5° × 1.27°
    MIROC5National Institute for Environmental Studies, The University of Tokyo, JapanMIROC1.40625° × 1.40625°
    MIROC-ESM2.815° × 2.815°
    MIROC-ESM-CHEM2.815° × 2.815°
    MPI-ESM-LRMax Planck Institute for Meteorology, GermanyMPI-M1.875° × 1.875°
    MPI-ESM-MR1.875° × 1.875°
    MRI-CGCM3Meteorological Research Institute, JapanMRI1.125° × 1.125°
    NorESM1-MNorwegian Climate Centre, NorwayNCC1.8725° × 2.5°
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Multi-Model Ensemble Projection of Precipitation Changes over China under Global Warming of 1.5 and 2°C with Consideration of Model Performance and Independence

    Corresponding author: Zhihong JIANG, zhjiang@nuist.edu.cn
  • 1. Joint International Research Laboratory of Climate and Environmental Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing 210044, China
  • 2. Key Laboratory of Meteorological Disaster, Ministry of Education (KLME)/CIC-FEMD, Nanjing University of Information Science & Technology, Nanjing 210044, China
  • 3. Laboratoire de Météorologie Dynamique, L’Institut Pierre-Simon Laplace (IPSL), Centre National de la Recherche Scientifique (CNRS), Sorbonne Université, Ecole Normale Supérieure, Ecole Polytechnique, Paris 75005, France
Funds: Supported by the National Key Research and Development Program of China (2017YFA0603804, 2016YFA0600402, and 2018YFC1507704)

Abstract: A weighting scheme jointly considering model performance and independence (PI-based weighting scheme) is employed to deal with multi-model ensemble prediction of precipitation over China from 17 global climate models. Four precipitation metrics on mean and extremes are used to evaluate the model performance and independence. The PI-based scheme is also compared with a rank-based weighting scheme and the simple arithmetic mean (AM) scheme. It is shown that the PI-based scheme achieves notable improvements in western China, with biases decreasing for all parameters. However, improvements are small and almost insignificant in eastern China. After calibration and validation, the scheme is used for future precipitation projection under the 1.5 and 2°C global warming targets (above preindustrial level). There is a general tendency to wetness for most regions in China, especially in terms of extreme precipitation. The PI scheme shows larger inhomogeneity in spatial distribution. For the total precipitation PRCPTOT (95th percentile extreme precipitation R95P), the land fraction for a change larger than 10% (20%) is 22.8% (53.4%) in PI, while 13.3% (36.8%) in AM, under 2°C global warming. Most noticeable increase exists in central and east parts of western China.

    • Climate change under global warming is a major challenge for many natural ecosystems on the earth and for human societies (IPCC, 2013; WMO, 2019). The global average temperature is on the increase and expected to continue increasing over the 21st century with a projected global temperature change of about 1.4–4.8°C under the medium and high emissions scenarios representative concentration pathway (RCP) 6.0 and RCP8.5 at the end of the century (IPCC, 2013). Changes resulting from global warming may include rising sea levels due to the melting of glaciers and ice sheets, as well as an increase in severe climate events, such as extreme temperatures, extreme precipitation, droughts, etc. (Xu et al., 2013; Aslam et al., 2017; Guirguis et al., 2018). These extreme climate events provoke substantial economic losses and civilian casualties, which raises the urgency of searching adaptation and mitigation measures to combat climate change (Jones et al., 2014; Li et al., 2018; Zhan et al., 2018; Chen et al., 2020). The Paris Agreement on climate change sets an ambitious target of holding the increase of global average temperature to well below 2°C above preindustrial levels and recommends all efforts to limit the temperature increase to 1.5°C above preindustrial levels (UNFCCC, 2015). Recognizing this would significantly reduce the risks and impacts of climate change (Schleussner et al., 2016; James et al., 2017; King and Karoly, 2017).

      Climate models play a crucial role in studying the potential impacts of climate change, and the ability of global climate models (GCMs) to reproduce observed features of current climate and past climate change increases our confidence to correctly make projections (Palmer et al., 2005; Zhou et al., 2007; Semenov and Stratonovitch, 2010; Wang et al., 2018; Ren et al., 2019). Multi-model arithmetic mean (AM) is widely used to reduce multi-model uncertainties and to make climate projections more reliable (Knutti, 2010; Knutti et al., 2010). The underlying assumption of the multi-model ensemble mean practice is that all models are reasonably independent, equally plausible, and distributed around the reality (Sanderson et al., 2015a, b; Knutti et al., 2017). It also assumes that the range of models’ projections is representative of what we believe is the uncertainty. But these are all strong assumptions, not always satisfied, and the reality is that some models are worse than others in how well they represent the observed mean climate and trend (Eyring et al., 2016; Baumberger et al., 2017). Therefore, weighting schemes were proposed based on the performance of climate models. The common practice is using the ability of model’s simulated patterns against observations as a measure of model’s skill (Perkins et al., 2009; Qi et al., 2017).

      In the same line of weighting models based on their performance, the rank-based scheme is widely applied in the evaluation of models and projection of future climate change (Chen et al., 2011). It consists simply of sorting models with well-defined criteria and using their rank to determine their weightings. This approach was shown to be quite efficient in reducing uncertainty from individual models and it usually outperforms any single model and the multi-model mean (Jiang et al., 2015; Li et al., 2016). Most methods formulate weights based on the performance of the model. They constitute an improvement to the simple AM, but they ignore the problem of models’ interdependence (Abramowitz and Bishop, 2015; Sanderson et al., 2015a, b). Various studies have pointed out that some model pairs are closely related due to the increasing replication of code across institutions and even sharing common module of model is natural (Knutti et al., 2013; Masson and Knutti, 2013). For example, some models are submitted by the same institution only with different resolutions (e.g., MPI-ESM-MR and MPI-ESM-LR); most institutions produce different models with similar configurations, or options for interactive atmospheric chemistry or carbon cycle (e.g., CMCC-CESM and CMCC-CM). Thus, it is important to consider the models’ interdependence in multi-model ensemble projections of climate change. However, few studies relative to this ensemble strategy are reported for future climate projection in China.

      In this paper, a weighting scheme proposed by Knutti et al. (2017), which considers both model performance and independence (PI-based weighting scheme), is applied to construct projections of mean and extreme precipitation over China under the 1.5 and 2°C global warming scenarios. In Section 2, we describe the study area and datasets used. Section 3 introduces the PI-based weighting scheme and the rank-based scheme. Followed in Section 4 are the performance comparison and projected changes in climatology and climate extremes indices. Finally, a summary of the major findings and conclusions are provided in Section 5.

    2.   Data
    • The daily gridded precipitation dataset CN05.1, covering a period of 1961–2005 with 0.25° × 0.25° resolution is used in this study for evaluation of ensemble performance of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) models (Taylor et al., 2012). The CN05.1 dataset is merged from 2416 weather observing stations in China. The station data are quality controlled by the China Meteorological Administration (CMA). More details concerning the data can be found in Xu et al. (2009) and Wu and Gao (2013).

      Since climate in China is complex and atmospheric circulations over eastern and western China are quite different (Zhang et al., 1984; Jiang et al., 2015), the entire multi-model ensemble weighting procedure is carried out separately in eastern (east of 105°E) and western China (west of 105°E) in this work. In the western area, observation stations are scarce and models generally have difficulties to take into account the complex topography. One should be precautionary in using the results of reproduction and projection of climate over this area. The topography and location of surface weather observation stations across China are shown in Fig. 1, in which the lines of 105°E and 40°N are drawn to help indicate geographic divisions defined in this paper.

      Figure 1.  Topography (m) and location of surface weather stations (gray dots) in China.

      Seventeen CMIP5 models’ historical simulations and future projections from RCP8.5 are used to generate 1.5 and 2°C warming. These models were selected on the sole criterion of data availability for our purpose, especially with daily precipitation for our warming targets at 1.5 and 2°C. All the datasets are retrieved through data portals of the Earth System Grid Federation, which can be obtained from https://esgf-node.llnl.gov/search/cmip5/. Some basic characteristics of the models used are listed in Table 1. The situation is somehow heterogeneous: some institutions providing single model version while others multiple versions of their model with different resolutions, different physical packages, or different complexity of the earth system. We can thus expect to have a huge diversity for the CMIP5 multi-model ensemble simulations, and at the same time there is also a strong interdependence among them. Of the 17 CMIP5 models that we selected following the sole criterion of data availability for our analysis, three models come from BCC, two models from IPSL, three models from MIROC, two models from MPI, and other seven models from seven different institutions. In our present work, we use only one realization from each model or model version, and we are aware that a full exploitation of the ensemble realizations would create a stronger interdependence.

      Model nameModeling center and countryInstitution IDAtmospheric resolution
      (lat × lon)
      BCC-CSM1-1Beijing Climate Center, China Meteorological Administration, ChinaBCC2.81258° × 2.81258°
      BCC-CSM1-1-M1.125° × 1.12°
      BNU-ESMCollege of Global Change and Earth System Science, Beijing Normal University, ChinaBNU2.8° × 2.8°
      CanESM2Canadian Centre for Climate Modelling and Analysis, CanadaCCCMA2.8° × 2.8°
      CCSM4NCAR, United States of AmericaNCAR1.25° × 0.94°
      CNRM-CM5Centre National de Recherches Météorologiques–Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, FranceCNRM–CERFACS1.4° × 1.4°
      CSIRO-Mk3-6-0Commonwealth Scientific and Industrial Research Organisation, AustraliaCSIRO-QCCCE1.875° × 1.875°
      GFDL-CM3NOAA/Geophysical Fluid Dynamics Laboratory, United StatesNOAA/GFDL2.5° × 2.0°
      IPSL-CM5A-LRL’Institut Pierre-Simon Laplace, FranceIPSL3.75° × 1.895°
      IPSL-CM5A-MR2.5° × 1.27°
      MIROC5National Institute for Environmental Studies, The University of Tokyo, JapanMIROC1.40625° × 1.40625°
      MIROC-ESM2.815° × 2.815°
      MIROC-ESM-CHEM2.815° × 2.815°
      MPI-ESM-LRMax Planck Institute for Meteorology, GermanyMPI-M1.875° × 1.875°
      MPI-ESM-MR1.875° × 1.875°
      MRI-CGCM3Meteorological Research Institute, JapanMRI1.125° × 1.125°
      NorESM1-MNorwegian Climate Centre, NorwayNCC1.8725° × 2.5°

      Table 1.  Model name, modeling center and country, institution identification (ID), and atmospheric resolution of 17 CMIP5 global climate models (expansions of acronyms are available at http://www.ametsoc.org/PubsAcronymList)

    • Three extreme precipitation indices are examined in this study, including the maximum 5-day precipitation (RX5DAY), maximum daily precipitation (RX1DAY), and strong precipitation events (R95P). In addition, the total precipitation (PRCPTOT) is used to represent the precipitation climatology. These indices are generally considered effective in extracting climate change information and have been widely used to identify and monitor extreme precipitation (Sillmann et al., 2013; Zhang et al., 2013; Zhou et al., 2016). All extreme indices of models were calculated based on the definitions from the Expert Team on Climate Change Detection and Indices (ETCCDI; Zhang et al., 2011).

      The extreme precipitation indices from different models and the observations were first calculated at their original grids. To facilitate model intercomparison and evaluation against the observations, all CMIP5 data and observations were interpolated onto the same 1° × 1° grid, by using bilinear interpolation.

    3.   Methodology
    • The weighting scheme used here was first proposed by Knutti et al. (2017), which considers both performance and independence of models (hereafter PI-based weighting scheme). It is based on two assumptions: models that agree poorly with observations for a selected set of diagnostics have less weight, and models that largely duplicate existing models also receive less weight.

      As proposed by Knutti et al. (2017), the single model weight wi for model i is defined as:

      $${w_i} = {e^{ - {{\left({{D_i}/{\sigma _d}} \right)}^2}}}/\left[{1 + \sum\nolimits_{j \ne i}^M {{e^{ - {{\left({{S_{ij}}/{\sigma _s}} \right)}^2}}}} } \right],$$ (1)

      where M is the total number of models, Di is the distance of model i to observations, and Sij is the distance between model i and model j. The parameters σd and σs determine how strongly the model performance and similarity are weighted, which can be determined through a cross-validation procedure. A large σd would effectively make the ensemble converge to the situation of model democracy, whereas a small σd puts important weights on only a few models; σs determines the typical distance by which a model would be considered similar to another. More details of the methodology can be found in Knutti et al. (2017).

      In this paper, model evaluation metrics include the assessment of both spatial pattern and temporal variability for precipitation, which allows us to deduce the distances Di and Sij in Eq. (1) by using the average of two normalized values: normalized root-mean-square error (RMSE) and normalized interannual variability score (IVS), with the normalization being realized by their respective median values.

      The spatial RMSE is defined as:

      $${\rm{RMSE}}(m,o) = \sqrt {\frac{1}{N}\sum\limits_{k = 1}^N {{{({M_k} - {O_k})}^2}} } ,$$ (2)

      where Mk and Ok denote the model pattern of a variable under investigation and the corresponding observed pattern, respectively; N indicates the number of spatial points. Smaller RMSE value represents a better agreement between the model and observation.

      The performance in interannual variation can be evaluated by a measure of the skill score IVS described by Chen et al. (2011) as follows:

      $${\rm{IVS}}(m,o) = {\left({\frac{{{\rm{ST}}{{\rm{D}}_m}}}{{{\rm{ST}}{{\rm{D}}_o}}} - \frac{{{\rm{ST}}{{\rm{D}}_o}}}{{{\rm{ST}}{{\rm{D}}_m}}}} \right)^2}, \hspace{18pt}$$ (3)

      where STDm and STDo denote the interannual standard deviation of model and observation, respectively. Smaller IVS value indicates a better agreement between the simulation and observation. Equations (2) and (3) are shown in the form of a measure between a model and the observation. They can be easily converted into inter-model measures between models i and j (not shown).

      Since multiple (four in this study) precipitation indices are used in this study, we define a comprehensive distance D of performance to combine the four individual distances Dv in Eq. (4). Our choice was based on the fact that the reliability of future climate projection relies on a comprehensive measure of the performance of climate models. The four precipitation indices PRCPTOT, RX1DAY, RX5DAY, and R95P represent different characteristics of precipitation. Therefore, an integrated (or comprehensive, or combined) distance should be a good choice. Coefficient wv is set as 1/4 to make their sum (v = 1, ..., 4) equal 1. Different coefficients can be taken into account based on the practical applications in follow-up studies.

      $$D = \sum\nolimits_{v = 1}^4 {{w_v}{D_v}} . \hspace{76pt}$$ (4)

      When the PI-based weighting scheme is used, its free parameters σd and σs can be determined through a cross-validation procedure. It is actually a perfect model test in which each model is, in turn, treated as the truth (Brunner et al., 2019). Note that our perfect model test uses two distinct periods in the past and in the future respectively: the calibration is done for the past period, but the cross-validation is evaluated for the future period. In ano-ther word, for each model (considered as truth in turn), a set of weights for the remaining models are calculated to mimic the past values of the true model. Once calibrated, the PI-based weighting scheme is used to deduce the future values of the true model. Such a cross-validation strategy allows us to test the future projection capability of the weighting scheme.

      In practice, we followed the procedure of Knutti et al. (2017) and Brunner et al. (2019), and calculated the percentage of cases falling down to the 5th–95th percentiles range obtained from the true model. The good value of σd was then empirically determined as its minimum value making this percentage equal to 90%. Figure 2 shows the percentage of cases, in function of prescribed σd values (with an incremental bin of 0.01), where the actual outcomes of the perfect model tests are in the 5th–95th percentiles range. This cross-validation is repeated for each of the four variables, as represented by the four curves in Fig. 2. By choosing the minimum value of the four curves when the threshold of 90% is reached, σd is estimated to be 0.54 in western China, and 0.46 in eastern China. These values are quite consistent with that obtained by Knutti et al. (2017) who also normalized their Euclidean distance by the median value. The dependence on the value of σs is rather weak relative to σd, so the value of σs is set as 0.5 as suggested in Knutti et al. (2017). The PI-based weighting scheme is now fully established after its free parameters are calibrated.

      Figure 2.  The fraction of cases for four indices when the actual outcomes of the perfect model tests are in the 5th–95th range weighted by all other models. For all indices, the minimum value of σd for the fraction is expected to exceed 90%.

    • In order to assess the proposed weighting scheme, we evaluate it against two largely-used algorithms, the rank-based weighting scheme (Chen et al., 2011; Jiang et al., 2015; Li et al., 2016) and AM, with the latter serving as a baseline. To ensure a fair comparison, the rank-based weighting scheme uses the same evaluation metrics based on the spatial pattern and interannual variability of relevant precipitation indices. If Ri is the rank for model i after evaluation that can be based on multiple criteria, we can then calculate a performance indicator Pi and it can be ultimately converted into weight wi after normalization:

      $${P_i} = \frac{{\sum\nolimits_{i = 1}^M {{R_i}} }}{{{R_i}}},$$ (5)

      and

      $${w_i} = \frac{{{P_i}}}{{\sum\nolimits_{i = 1}^M {{P_i}} }}.$$ (6)

      Equation (6) can guarantee that the sum of all weights is equal to 1.

    • For all the three weighting schemes (PI-based, rank-based, and AM scheme), their calibration period is from 1961 to 1985. The validation is performed with independent samples from 1986 to 2005. After the calibration and validation, the three weighting algorithms are applied to future precipitation projection under the framework of 1.5 and 2°C global warming targets.

      To determine the timing of the two warming targets, a 40-yr period from 1861 to 1900 is firstly selected as the preindustrial reference. For each of the models in our investigation, the time series of annual global mean temperature is smoothed by a 21-yr running average, and we can then find the year when 1.5°C (2°C) warming is reached. A 21-yr window centered on this year is then used to define the 1.5°C (2°C) world. The reference pe-riod 1985–2005 is used to represent nowadays to assess the changes in precipitation climate.

    4.   Results
    • The final weights obtained by the two weighting schemes, sorted by descending order of PI-based scheme are shown in Fig. 3. For both western and eastern China, the PI-based weighting shows a larger range from strong weights to weak ones, which means that models with a good performance and a large independence from others are more prominent in the PI algorithm.

      Figure 3.  The models’ weights obtained by the PI-based weighting scheme (black squares) and the rank-based weighting scheme (gray circles) over (a) western and (b) eastern China.

      Although σd in western China is larger than its counterpart in eastern China, models closer to observation obtain higher weights, which indicates that the inconsistency among models in the west is more significant. For both areas, we can see that models from the same institution have generally closer weights, but they are not among the highest, which may be the direct consequence of the PI algorithm with interdependence of models taken into account. We can observe that the models IPSL-CM5A-LR and IPSL-CM5A-MR, both from IPSL, have a better performance above the average. In an idealized condition, if a second member happens to be identical to the first (that is, sij = 0), the two members would have half their original weight. We can generalize the example into the case of N identical members, and each would have a weight scaled by 1/N. In reality, CMIP5 members are not perfectly independent and our work presented here uses only the first run from each model, which makes the members in our ensemble have a relatively weak repeatability from each other.

    • Figure 4 shows relative biases (areal mean in shaded bar, first and third quartiles in bar with whiskers) of the four indices reproduced by three weighting strategies, PI-based, rank-based, and AM, against observations during the evaluation period 1986–2005 in western and eastern China, respectively. We can see that areal-mean biases in the western area are (about 2 to 3 times) larger than those in the eastern area for all precipitation indices. This can be explained by the fact that most models have mediocre performance in reproducing extreme events related to the complex topography in western China (Jiang et al., 2015; Chen et al., 2017).

      Figure 4.  The regional relative biases simulated by PI-based, rank-based, and AM schemes against observations for four precipitation indices during the period of 1986–2005. Color bars are the mean biases and whiskers represent the first and third quartiles (%).

      In the western area, the areal-mean biases of PI-based scheme for the four indices PRCPTOT, RX5DAY, RX1DAY, and R95P are 32%, 79%, 46%, and 150%, respectively. Biases of the PI-based scheme are much lower than those from the other two schemes, and the regional interquartile bias ranges are also smaller. Take the most noticeable index R95P as example, on the basis of AM, the areal-mean relative bias decreases by 101%, and decreases by 78% if compared to the rank scheme. The 25th and 75th percentile errors of AM are 81% and 327%, while only 32% and 195% are reproduced by PI-based scheme. However, biases’ differences among indices in eastern China are not very prominent. From the 25th and 75th percentiles, we can see that the higher dry and wet biases of extreme precipitation are better reduced in the weighting schemes.

      Among the four precipitation indices, the relative bias for R95P is the most noticeable; even the best performing PI scheme shows a relative bias of 150% and 29% in western and eastern China, respectively. Thus, spatial distributions of R95P’s biases is illustrated in Fig. 5 for the three weighting strategies respectively to find more spatial details. It can be seen that large biases (> 50%) are located in western China to the south of 40°N, especially in the periphery of the Tibetan Plateau where biases are about 150% to 300%. In eastern China, an underestimate lower than 50% exists in south of the Yangtze River. Most areas in the north of the Yangtze River have wet biases of about 100%. Comparing the three weighting schemes, we can find that areas with significant improvement in the PI-based weighting scheme are concentrated in the north and central Tibetan Plateau where we see the largest biases. They are largely reduced to a level below 50%. In other parts of China, especially in eastern areas, the improvement of PI-based scheme is relatively modest. Similar results are also found in other indices (figure omitted), with the largest biases concentrated in the periphery of the Tibetan Plateau. They are nevertheless smaller compared to the case of R95P. Biases in the western area are reduced the most. Although the relative bias reduction is large over the Tibetan Plateau, it should be noted that observation stations are sparse and unevenly distributed over the plateau, which can generate spurious results with improperly-designed interpolation algorithm. One should be precautionary in using the results of reproduction and projection of climate over this area.

      Figure 5.  Spatial distributions of relative bias (%) for R95P from (a) PI-based, (b) rank-based, and (c) AM schemes against observations during the period 1986–2005. Warm and cool colors indicate dry and wet bias, respectively.

      Taylor diagram is now used to present a concise statistical analysis of the three weighting schemes in the evaluation period 1986–2005 (Fig. 6). It can display three pieces of information: pattern correlation coefficient, ratio of the centered standard deviations, and root-mean-square error, with two of them being independent and used to deduce the third one. There is generally a weak performance with the AM (gray markers). In western China, the spatial correlation coefficients of major indices between the simulations and observations are less than 0.8 and the maximum does not exceed 0.85; the standard deviations are also large. In eastern China, all markers representing the AM are the most distant from the ref-point. It is easy to see that the performance reproducing the spatial pattern by the weighted schemes is improved, and PI (red markers) is the best with pattern correlation coefficients higher than 0.85 and ratios of spatial variance closer to 1 for all the four precipitation indices in western China. In eastern China, the performance of three strategies are similar, with all markers concentrated together, spatial correlation coefficients between 0.85 and 0.9, and standard deviation ratios between 0.5 and 0.6. Again, R95P shows its weakest score compared to other indices.

      Figure 6.  Taylor diagram showing the four precipitation indices under the three weighting schemes during the period 1986–2005. The solid and hollow markers represent western and eastern China, respectively.

      In brief, the PI-based weighting strategy effectively enhances our capability of reproducing the precipitation spatial characteristic in China, especially in western China. All precipitation indices with the PI-based scheme show significant improvement. In eastern China, however, the improvements are small and insignificant.

    • In view of the added value of combining multi-model results, especially by the PI-based scheme, a projection of future climate corresponding to 1.5 and 2°C warming targets (relative to preindustrial) under RCP8.5 emission scenario was produced with the above weighting strategies. Figure 7 displays boxplots showing the spatial distributions of relative changes for the four precipitation indices and for the three weighting schemes, respectively. Each boxplot allows to present the 10%, 25%, 50%, 75%, and 90% percentiles of relevant field across all spatial grids, and for the two warming targets at 1.5 (blank boxes) and 2°C (hatched boxes), respectively. As a conventional practice, the plotted change is relative to 1985–2005, a common reference period, while the target warming levels (1.5 and 2°C) are relative to preindustrial. Compared with the rank-based scheme (blue box and whisker) and the AM scheme (gray box and whisker), the PI-based scheme (red box and whisker) shows larger dispersions (boxes and whiskers are longer), which means that the projected fields have larger inhomogeneity in their spatial distribution, with more pronounced wet and dry conditions. The areal-mean values (gray dots) are relatively close to each other, with bars of those from the PI-based scheme slightly higher.

      Figure 7.  Boxplots for relative changes (%) of total precipitation and extreme indices (compared to the period of 1985–2005) from PI-based, rank-based, and AM schemes over China under 1.5 and 2°C global warming.

      To better illustrate the impact of weighting schemes on the projection of precipitation, results can also be displayed in the form of a cumulative distribution function (CDF) across China, as shown in Fig. 8. Such a graphic presentation is very useful since the CDF can be directly interpreted as the fraction of the national territory where changes are inferior to the corresponding value of the abscissa. On the right side of the ordinate, we also indicated the complementary values (1 − CDF) of what is shown on the left side. It can be interpreted as the fraction of the national territory where changes are superior to the corresponding value of the abscissa. Each panel in Fig. 8 represents one of the four precipitation indices with curves corresponding to the three weighting schemes and to the 1.5 and 2°C warming targets, respectively. For all indices, the rank-based CDFs are almost congruent with the basic AM’s, while obvious distinctions can be detected for PI.

      Figure 8.  The spatial cumulative distribution functions (CDFs) of changes weighted by PI-based, rank-based, and AM schemes under 1.5 and 2°C global warming for the precipitation indices over China. The abscissa displays the changes of precipitation indices while the left ordinate shows the CDF values and the right ordinate shows the complementary values (1 − CDF). The changes are expressed by percentages (%) compared to the period of 1985–2005.

      First, we examine the changes of PRCPTOT, relative to present day (1985–2005). The PI-based scheme shows that half of China would experience an increase larger than 3.8% and 5.7% in the 1.5 and 2°C warmer climates, respectively. Under the same conditions, a quarter of China would experience an increase larger than 7.1% and 10.2%. Compared with the PI-based scheme, the increases in PRCPTOT are slightly smaller in AM, projecting that half of China would increase by 2.5% and 3.9%, and quarter of China by 4.6% and 6.8%, respectively. These characteristics show some similarity among the four precipitation indices, with a trend to larger values in the order of PRCPTOT, RX5DAY, RX1DAY, and R95P. We remark large increases and large dispersions for R95P; under the 1.5°C (2°C) warming target, half of China may experience changes larger than 17.1% (25.7%) in PI’s projection while 13.7% (21.3%) in AM’s.

      The CDF curves in Fig. 8 can also be examined from the vertical perspective, which gives the land fraction for a given change threshold. If we use a threshold of 10% for PRCPTOT, we can see that the fraction of national territory where PRCPTOT changes exceed the threshold of 10%, under the 1.5°C (2°C) global warming target, is 10.6% (22.8%) with the PI-based scheme, while around 3.9% (12.5%) with the rank-based scheme, and 2.8% (13.3%) with AM. Similarly, for R95P with a 20% threshold, the fraction of national territory is 26.7% (53.4%), 13.2% (37.8%), 9.7% (36.8%) for the three weighting schemes (PI, rank, and AM), respectively. If we use the threshold 0 for PRCPTOT, we can then evaluate the fraction of the national territory with mean rainfall increasing (or decreasing). It is certainly fortuitous to observe that the three weighting schemes and the two warming targets all converge to a situation of two-thirds of China with rainfall increased and the remaining one-third with rainfall decreased. If we apply the threshold 0 to extreme indices, the majority of the national territory shows increases with RX5DAY by 86.4% (92.7%), RX1DAY by 92.5% (97.7%), and R95P by 91% (95.8%), respectively, for the warming target 1.5°C (2°C).

      The spatial distributions of PRCPTOT changes weighted by the three schemes are depicted in Fig. 9. Consistent with what is shown by the boxplots and CDF curves, the spatial structure has a larger range with the PI-based scheme. Robust increases are detected in the central and east parts of western China in all three projections, but the increase amount projected by the PI-based model exceeds 20% in the 1.5°C global warming. Especially in the northern Tibetan Plateau, it is twice bigger than that projected by AM (about 10%). Under 2°C global warming, the increase with the PI-based model exceeds 25%, while it is about 10% in AM. For the half-a-degree additional warming (right column), the difference among the three weighting models is not significant except for the central and eastern Tibetan Plateau and Inner Mongolia area, where the change amplitude is more noticeable with the PI-based model. Similar results can be found in RX5DAY, RX1DAY, and R95P, but R95P shows more significant increases especially in the Tibetan Plateau and in northeastern China.

      Figure 9.  Percentage changes of PRCPTOT for the 1.5°C (first column), 2°C (second column) global warming under RCP8.5 scenario compared to the period 1985–2005, and the additional 0.5°C warming (third column) from simulations of PI-based (top), rank-based (middle) weighting schemes, and AM (bottom). Areas with significant changes above the 95% confidence level are marked with black dots.

      The reason resides certainly in the fact that the PI-based scheme has sharper transitions in the distribution of weights among models. That is, the final results are basically dominated by a few models having larger weights. In other words, “good” localized characteristics from these well-behaved models are less affected by other models. With the same argument, we can expect that the AM, which performs simple average over many models, would underestimate high-value regions. Sanderson et al. (2017) pointed out that some noticeable differences of the uncertainty range also exist with weighting of models, the underlying causes being the same as we evoked here. A similar conclusion is found in other studies on the weighting strategy: the projected changes made by weighted ensembles are generally comparable with each other on the spatial patterns, but with more pronounced amplitude in uncertainty regions (Langenbrunner and Neelin, 2017; Massoud et al., 2019).

      The projected changes with the PI-based strategy under the 1.5 and 2°C warming targets are depicted in Fig. 10 for the three extreme precipitation indices. It is obvious that all extreme precipitation indices increase across almost whole China. The mean increase for RX5DAY is by 5.8% and 9.3% under 1.5 and 2°C global warming. Similarly, RX1DAY increases by 7.1% and 10.4%. The increase of strong precipitation R95P is the most noticeable, with the national mean being by 17.5% and 26.6%, respectively. For all extreme indices, the Tibetan Plateau and northeastern China are areas with significant wetter conditions, especially in the 2°C warming, higher than other areas by about 5%. Meanwhile, there is no significant increase found in the middle reaches of the Yangtze River and the Yellow River, and even a slight decrease can be observed. An additional 0.5°C warming may lead to increases in heavy precipitation over most areas. The national mean increases of RX5DAY and RX1DAY are 3.5% and 3.4%, respectively, and the most significant response of R95P can reach 9.3%. The center and east of the Tibetan Plateau and the north of Inner Mongolia have been shown to be more significantly associated to the additional global warming. Although a precise comparison with previous works is out of scope of the present paper, most of our findings are consistent with what is reported in the current literature (Wu et al., 2015; Chen et al., 2017; Shi et al., 2018), showing reliable features, such as the increase of extreme precipitation indices in the Tibetan Plateau and Northeast China, and their insignificant change in central China.

      Figure 10.  Percentage changes of the three extreme precipitation indices: (a–c) RX5DAY, (d–f) RX1DAY, and (g–i) R95P, projected by PI-based weighting scheme for the 1.5°C (first column), 2°C (second column) global warming under RCP8.5 scenario compared to the period 1985–2005, and the additional 0.5°C warming (third column). Areas with significant changes above the 95% confidence level are marked with black dots.

    5.   Conclusions and discussion
    • A weighting scheme considering both model performance and independence (PI-based weighting scheme) is used to deal with multi-model ensemble simulation and projection of precipitation over China under the global warming of 1.5 and 2°C. To better appreciate its performance, a work of intercomparison with the performance-only (rank-based) scheme and a full-model-democracy scheme (AM) was carried out. Main conclusions are as the following.

      (1) Compared to the rank-based and AM strategies, the PI-based weighting scheme produces a better simulation of spatial patterns for the total precipitation and extreme indices, especially in western China over the Tibetan Plateau. Relative to the baseline of AM, the western China mean bias decreases by about 38% for PRCPTOT, 18% for RX5DAY, 32% for RX1DAY, and 101% for R95P. For all the four indices, the spatial pattern correlation coefficients are higher than 0.8, and the ratios of spatial variations are closer to 1. Nevertheless, no significant improvements are found in eastern China.

      (2) An intercomparison of future climate projections among the three schemes shows that their spatial patterns are highly correlated but PI has larger inhomogeneity in spatial distribution. A few results under the 2°C global warming target can be detailed here for the total precipitation PRCPTOT and strong precipitation R95P. Their critical change values, if dividing the whole China area into two equal halves under the 2°C global warming target, are 5.7% and 25.7% in PI, while 3.9% and 21.3% in AM. The land fraction of whole China’s territory with a change of PRCPTOT (R95P) larger than 10% (20%) is 22.8% (53.4%) in PI, while 13.3% (36.8%) in AM. The difference shows an increase of 9.5% (16.6%). In the central and east parts of western China, the increase for both PRCPTOT and R95P is the most noticeable in PI, which can exceed 20% and 40% for PRCPTOT and R95P respectively, twice bigger than in AM.

      Our results show an obvious improvement in western China for the PI-based ensemble scheme. However, both observation and simulation are less reliable in western China due to limited observation stations and the presence of complex topography including high mountains and the Tibetan Plateau. Thus, the results over this area should be regarded with precautions.

      It should be noted that any weighting scheme of models is inevitably related to the choice of distance metrics and variables used, which implies intrinsic uncertainties for the methodology. In the present work, we used a com-bined set of diagnostics (PRCPTOT, RX5DAY, RX1DAY, and R95P) and took the spatial and temporal features simultaneously into account to determine model performance and independence. Other performance metrics, not only for the mean state and extreme but also for trends or key physical process, should be explored in the future.

      The basic idea of PI-based scheme is generic and could be applied to a wider range of climate change issues by integrating a larger set of GCM simulations. It is particularly promising in the upcoming CMIP6 framework that includes larger members of a same model.

      Acknowledgments. We would like to acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP. We thank the climate modeling groups for producing simulations and making their model outputs available.

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