A clustering-based multi-model ensemble projection of near-term precipitation changes over East China and its uncertainty

The observational precipitation data covering mainland China on a 1° × 1° grid were obtained from the CN05.1 dataset, produced by the National Climate Center of the China Meteorological Administration from over 2400 observation stations over China (Wu and Gao 2013); this dataset has been widely used in previous studies (Yin et al 2014, Yang et al 2021, Gao et al 2023).

The monthly outputs of 28 CMIP6 models from historical and SSP2-4.5 scenario simulations were used. The models' detailed information is summarized in table 1. All datasets were interpolated into 1° × 1° grids using the bilinear interpolation method.

The models' performances in simulating the present-day (1995–2014) climatological annual mean precipitation over East China were evaluated with a Taylor diagram and the Taylor Skill score (TS score, figure 1). The simulated present-day precipitation patterns were comparable to the observations, with a pattern correlation coefficient exceeding 0.92 and TS score exceeding 0.79, suggesting that these models are suitable to project future changes in precipitation over East China.

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The near-future changes in annual mean precipitation over East China during 2046–2065, relative to 1995–2014, under the SSP2-4.5 scenario were projected with an ensemble of 28 models. Two kinds of MME mean approaches were employed: the simple arithmetic mean (AM), and rank-based weighting mean (Rank-mean). In the Rank-mean approach, the models were ranked by their performance and given different weights in simulating the present-day climatological precipitation measured by the TS score (Chen et al 2011). The uncertainty associated with the MME mean projection was tested using the signal-to-noise ratio (Zhou and Yu 2006, Li and Zhou 2010).

In addition to the MME mean projection, clustering-based MME probabilistic projections were employed, in which clustering analysis was performed on the 28 projected precipitation change patterns using Ward's agglomerative hierarchical clustering method (Ward 1963, Gong and Richman 1995). The principle of Ward's clustering method is to minimize the total within-cluster variance. The clustering process starts from 28 clusters (28 models in the ensemble), and the initial distance between clusters is set as the squared Euclidean distance between their spatial patterns. In implementation, the two-dimensional precipitation change field projected by each model was treated as the respective vector (41 × 35 = 1435 grid points). Then, in each step, the two closest clusters are merged, and the distances are updated using the algorithms described in Müllner (2011) and Gong and Richman (1995), as follows:

$$\begin{align}d\left( {u,v} \right) = & \left\{ \frac{{\left| v \right| + \left| s \right|}}{T}d{{\left( {v,s} \right)}^2} + \frac{{\left| v \right| + \left| t \right|}}{T}d{{\left( {v,t} \right)}^2}\right.\nonumber\\ & \,\,\,\,\,\left.- \frac{{\left| v \right|}}{T}d{{\left( {s,t} \right)}^2} \right\}^{1/2}\end{align} \tag{ 1 }$$

where $u$ is the newly merged cluster consisting of clusters $s$ and $t$, $v$ is an unused cluster, $\left| {{*}} \right|$ is the cardinality of its argument, $T = \left| v \right| + \left| s \right| + \left| t \right|$, and $d\left( {\cdot,\cdot} \right)$ is the distance between the two clusters. An objective method to determine the stopping level of the clustering process is to inspect the distance between merged clusters. The clustering process stops when this distance jumps markedly, i.e., when a 'kink' appears in the 'elbow method' (Thorndike 1953). After clustering, the ensemble mean within each cluster is calculated to represent this cluster. The occurrence probability of each cluster is defined using the relative frequency as the ratio of the number of models within this cluster to the total number of models.

The changes in annual mean precipitation over East China during 2046–2065, relative to 1995–2014, under the SSP2-4.5 scenario were projected by the 28 individual models. Obvious differences are found among the models, especially in South China (SC). Three typical projections by GISS-E2-1-G, HadGEM3-GC31-LL and GFDL-ESM4 are shown in figures 2(a)–(c). GISS-E2-1-G projects a north-increasing-south-decreasing pattern. HadGEM3-GC31-LL projects a more or less uniformly increasing pattern with stronger increases over the Yellow River basin and SC. GFDL-ESM4 projects a north-decreasing-south-increasing pattern, generally opposite to the GISS-E2-1-G projection.

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In addition to individual model projections, the MME means obtained using the AM and Rank-mean (rank-based weights are shown in figure 1(b)) methods are shown in figures 2(d) and (e). Both MME means provide similar precipitation patterns featuring uniform increases with larger increase over SC. The uncertainty associated with the MME mean projection was tested with the signal-to-noise ratio. A precipitation increase of approximately 0.16 mm d⁻¹ is projected over North China (NC, 32° N–42° N, 110° E–120° E) by the MME mean with a relatively small inter-model spread from −0.07 mm d⁻¹ to 0.35 mm d⁻¹. However, this is not the case over SC (22° N–32° N, 110° E–120° E) owing to the large inter-model spread from −0.15 mm d⁻¹ to 0.74 mm d⁻¹ (figure 2(f)). Since a large inter-model spread exists over SC, neither the AM projection nor the Rank-mean projection is reliable, not exceeding the signal-to-noise ratio test. This suggests that alternative MME projection schemes need to be proposed instead of the MME mean.

To preserve the useful information in the MME and interpret it appropriately, we performed clustering-based MME probabilistic projection. Clustering analysis was performed on the precipitation patterns projected by the 28 individual models, and the models were finally classified into 4 clusters according to the 'elbow method' criterion. Future precipitation changes over East China exhibit four possible patterns (figure 3). Cluster 1, whose occurrence probability is 14.3%, projects a more or less uniformly increasing pattern with a larger increase over SC of approximately 0.51 mm d⁻¹. Cluster 2, whose occurrence probability is 25%, shows a distinctively north-increasing-south-decreasing pattern, projecting decreased precipitation over SC of approximately 0.01 mm d⁻¹. Cluster 3, whose occurrence probability is 35.7%, is similar to Cluster 1 but with an obviously weak magnitude, projecting a precipitation increase over SC of approximately 0.2 mm d⁻¹. Cluster 4, whose occurrence probability is 25%, is also a pattern of uniform increase but with larger increase over the Huai River basin, projecting increased precipitation over SC of approximately 0.23 mm d⁻¹. The differences in projected precipitation change over SC reflect large model uncertainty in future precipitation projections over the East Asian monsoon area. Next, we will explore the possible physical processes that result in the different precipitation changes over SC among the four clusters.

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To explore the physical processes responsible for the different precipitation changes over SC in the future, the annual mean precipitation was divided into extended summer mean precipitation from May to October (MJJASO) and extended winter mean precipitation from November to the following April (NDJFMA) respectively for further investigation. Remarkable differences are found among the four clusters in both the summer and winter precipitation results (figure 3(e)–(h)). In extended summer, the projected precipitation increases for 0.73 mm d⁻¹ in Cluster 1, 0.17 mm d⁻¹ in Cluster 2, 0.24 mm d⁻¹ in Cluster 3, and 0.35 mm d⁻¹ in Cluster 4, respectively. In extended winter, the projected precipitation increases for 0.32 mm d⁻¹ in Cluster 1, 0.15 mm d⁻¹ in Cluster 3, and 0.1 mm d⁻¹ in Cluster 4, while it decreases for 0.19 mm d⁻¹ in Cluster 2.

To investigate the physical processes associated with the different precipitation changes over SC, the atmospheric moisture budget was examined. According to the moisture budget equation, precipitation (Pre) is balanced by evaporation (Evap), the vertically integrated atmospheric moisture transport convergence (MC), and the residual term (Res) that includes sub-monthly transient eddies, and the surface boundary gradient term, which is usually neglected (Trenberth and Guillemot 1995, Seager and Henderson 2013). Moreover, the MC term can be decomposed into a dynamic component term (DY) due to changes in circulation, and a thermodynamic component term (TH) due to changes in specific humidity to facilitate studying the specific dynamic and thermodynamic effects, and the quadratic term of covariance between changes in humidity and winds (QT) (Li et al 2015):

$$\begin{align}\delta {\text{Pre}} - \delta {\text{Evap}} & = {\text{ }}\delta {\text{MC}} + \delta {\text{Res}} = \delta {\text{TH}}\nonumber\\ & \quad + {\text{ }}\delta {\text{DY}} + {\text{ }}\delta {\text{QT}} + {\text{ }}\delta {\text{Res}}.\end{align} \tag{ 2 }$$

Here, $\delta$ represents the changes of the future relative to the present-day.

The summertime physical processes were investigated first. Precipitation increases over SC are projected in all 4 clusters but with significantly different magnitudes (figure 4(a)–(d)). The largest increase is projected in Cluster 1 for 0.73 mm d⁻¹, followed by a moderate increase in Cluster 4 for 0.35 mm d⁻¹, and weak increases in Cluster 2 for 0.17 mm d⁻¹ and in Cluster 3 for 0.24 mm d⁻¹. In Cluster 1, the change of MC contributes 69% of the precipitation increase, whilst in Cluster 2, Cluster 3 and Cluster 4, the evaporation change dominates the precipitation increase, contributing 81%, 61% and 67%, respectively (figure 4(u)). Although evaporation is an important contributor to the precipitation increase, they show similar changes among the four clusters (figures 4(e)–(h)). By contrast, vast differences are found in MC changes among the four clusters (figures 4(i)–(l)), with comparable spread to the precipitation spread (figure 4(u)). That indicates that the different magnitudes in precipitation increases over SC could be attributed mainly to the difference in moisture transport convergence and, secondarily, to the difference in evaporation changes.

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Furthermore, MC term is decomposed into DY and TH contributions (figures 4(m)–(t)). Although the TH terms mainly contribute to the MC increases in all 4 clusters, they show relatively difference among four clusters. By contrast, huge spreads are found in DY terms among four clusters, which agree well with the corresponding different MCs between clusters. Thus, the different MCs are mainly the result of the difference in DY terms and secondarily the result of the difference in TH terms. Combined, the above results show that the dynamic effect resulting from different circulation changes predominates the different precipitation increases over SC. This is consistent with the previous study about the uncertainty source of projected SC precipitation change (Seager et al 2010, Zhou et al 2017, Tian et al 2019, Chen et al 2020b). Quantitatively, the DY terms over SC in the four clusters agree well with the corresponding precipitation changes. These changes in DY are 0.22 mm d⁻¹ in Cluster 1, corresponding to a strong precipitation increase, 0.01 mm d⁻¹ in Cluster 4, corresponding to a moderate precipitation increase, and −0.09 mm d⁻¹ in Cluster 2 and −0.09 mm d⁻¹ in Cluster 3 that combined with evaporation and TH effect contributes to a weak precipitation increase (figure 4(u)).

To demonstrate the four different circulation changes that are responsible for the different summertime precipitation changes over SC, four clusters of changes in summer 850 hPa horizontal winds are shown in figures 5(a)–(d). In Cluster 1 (figure 5(a)), an anomalous anti-cyclonic circulation is found over the western North Pacific (WNP), which transports moisture from the South China Sea (SCS) by the anomalous south-westerly winds along its north-western edge and leads to moisture convergence over SC; this condition is favorable to increased precipitation over SC. Similar anomalous anti-cyclonic circulation is found in Cluster 4 but with a weak magnitude over WNP (figure 5(d)), resulting in a moderate precipitation increase over SC. In contrast, in Cluster 2 and Cluster 3 (figures 5(b) and (c)), anomalous cyclonic circulation is found over WNP, which is associated with the anomalous north-easterly winds along its north-western edge, preventing moisture transport and suppressing precipitation over SC.

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Furthermore, what causes the different circulation changes over WNP among the four clusters? The four clusters of changes in sea surface temperature (SST) are shown in figures 5(e)–(h). In Cluster 1, anomalous warming is found over the equatorial eastern Pacific, known as the El Nino-like SST anomaly (SSTA). This typical El Niño-like SSTA could stimulate anomalous WNP anti-cyclonic circulations, as it has been indicated in previous studies (Zhang et al 1999, Weng et al 2007). In Cluster 4, similar SST warming was found but with a weak magnitude; this warming may have been responsible for the weak anomalous WNP anti-cyclonic circulation. In contrast, in Cluster 2 and 3, the El Niño-like SSTA obviously extends westward, i.e., causing anomalous warming over the equatorial central Pacific (CP). The warming magnitudes are 0.21 °C in Cluster 2 and 0.16 °C in Cluster 3, higher than those in Cluster 1 (0.11 °C) and Cluster 4 (0.002 °C). The CP-El Niño-like SSTA could stimulate anomalous cyclonic circulation over WNP through Gill-type responses (Yuan et al 2012, Chen et al 2020). In summary, the different circulation changes observed over WNP in extended summer among clusters may have been due to the different SST warming patterns over the equatorial Pacific.

The physical processes contributing to the spread in extended winter precipitation changes are analyzed and the results are shown in figure 6. Precipitation increases over SC are projected in Cluster 1 for 0.32 mm d⁻¹, 0.15 mm d⁻¹ in Cluster 3, and 0.1 mm d⁻¹ in Cluster 4, respectively, Cluster 2 shows markedly decreased precipitation for 0.19 mm d⁻¹ (figure 6(b)), and this difference is contributed by the MC effect (figure 6(j)). As shown in figure 6(u), the evaporation is projected to similarly increase across clusters, while obviously decreased MC in Cluster 2 is different from the other clusters, which agrees well with the spread of precipitation changes. Further, the MC is further decomposed into DY and TH terms. This decomposition shows that the TH contributes to the increased precipitation over SC (figures 6(m)–(p)) but the DY contributes to the decreased precipitation in the four clusters (figures 6(q)–(t)). Among then, the stronger negative contribution in DY is projected in Cluster 2, that mainly explains its different MC from the other clusters (figure 6(u)). Therefore, the comparison among the four clusters shows that the different winter precipitation changes over SC are attributed mainly to the dynamic effect associated with circulation changes. Quantitatively, the DY term is −0.33 mm d⁻¹ in Cluster 2 and it contributes to the precipitation decrease. The DY term is −0.15 mm d⁻¹ in Cluster 1 in combination with evaporation and TH effect contributes to a strong precipitation increase. The DY contribution of −0.08 mm d⁻¹ in Cluster 3 and −0.13 mm d⁻¹ in Cluster 4, respectively, in combination with evaporation and the TH effect, contribute to weak precipitation increase over SC (figure 6(u)).

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In addition, the residual term that mainly includes sub-monthly transient eddy has a negative contribution in Cluster 2 and Cluster 4 (figure 6(u)), which partly explains precipitation decreases over SC. The change of transient eddies is projected to decrease in the subtropics during winter half year that is mainly associated with the transient eddy moisture transport in response to global warming (Seager et al 2010, Wu et al 2011) due to the westerly jet weakening in the region (Liang and Zhang 2021). As demonstrated by He (2023), the weakened southern branch westerly jet on the southern side of the Tibetan Plateau plays a key role in suppressing winter precipitation in the subtropical East Asian.

To explore physical processes that are responsible for the different winter precipitation changes over SC, four clusters of changes in SST, and vertical motion are shown in figure 7. The precipitation decrease over SC observed in Cluster 2 is possibly associated with the notably zonal SSTA gradient between the SCS and adjacent WNP (figure 7(b)) driving an anomalous zonal circulation with a descending branch at the SCS and SC (figure 7(f)) and suppressing the precipitation over there (figure 6(r)). Similar SSTA gradients (figure 7(c)) and associated anomalous zonal circulations (figure 7(g)) are found in Cluster 3 but with a much weaker strength, resulting in weak precipitation suppression over SCS (figure 6(s)). Different from the zonal SSTA gradients observed in Cluster 2 and Cluster 3, meridional SSTA gradients over the WNP are found in Cluster 1 (figure 7(a)) and Cluster 4 (figure 7(d)), and these gradients drive anomalous meridional circulation with a descending branch at 20° N–30° N (figure 7(e) and (h)), suppressing the precipitation from southern coastal China extending to the WNP region (figures 6(q) and (t)). Overall, the different winter precipitation changes observed among the clusters may have been associated with the vertical motions stimulated by different SSTA gradients over the SCS and adjacent WNP.

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