Summer heat sources changes over the Tibetan Plateau in CMIP6 models

The monthly CMIP6 data used in this study are downloaded from the Earth System Grid Federation data replication centers (https://esgf-node.llnl.gov/projects/cmip6/). Table S1 (available online at stacks.iop.org/ERL/16/064060/mmedia) lists the information of 22 models adopted in this study. The CMIP6 historical simulations (1850–2014) and the future projections under the SSP2-4.5 (SSP245) scenario (2015–2100) are utilized. The SSP245 scenario represents the medium-level emission pathway, and several other MIPs adopt it as a reference scenario (O'Neill et al 2016). The last 20 year average of the SSP245 experiment (i.e. 2081–2100) will be compared with its historical counterpart (1995–2014) to quantify the future change, which minimizes the uncertainties arising from the models' internal variability (Wang et al 2020).

We use the two-tailed Student's t-test to see whether the projected 2081–2100 means are significantly different from the historical 1995–2014 means. This test yields the probability measuring how the projected future multi-model ensemble mean (MME; ${\bar S_{\text{M}}}$ from equation (1a )) differs from the simulated present-day MME (${\bar H_{\text{M}}}$ from equation (1b )). The variances used in the Student's t-test representing the intermodel spreads are calculated from equation (1c ) and (1d )

$$\begin{equation}\begin{array}{*{20}{c}} {{{\bar S}_{\text{M}}} = \sum\limits_{i = 1}^N {{\bar S}_i} = \sum\limits_{i = 1}^N \left( {\sum\limits_{t = 2081}^{2100} {S_{t,i}}} \right),} \end{array}\end{equation} \tag{ 1a }$$

$$\begin{equation}\begin{array}{*{20}{c}} {{{\bar H}_{\text{M}}} = \sum\limits_{i = 1}^N {{\bar H}_i} = \sum\limits_{i = 1}^N \left( {\sum\limits_{t = 1995}^{2014} {H_{t,i}}} \right),} \end{array}\end{equation} \tag{ 1b }$$

$$\begin{equation}{\text{Var}}\left( S \right) = \frac{{\sum\nolimits_{i = 1}^N {{{\left( {{{\bar S}_i} - {{\bar S}_{\text{M}}}} \right)}^2}} }}{{N - 1}},\end{equation} \tag{ 1c }$$

$$\begin{equation}{\text{Var}}\left( H \right) = \frac{{\sum\nolimits_{i = 1}^N {{{\left( {{{\bar H}_i} - {{\bar H}_{\text{M}}}} \right)}^2}} }}{{N - 1}},\end{equation} \tag{ 1d }$$

where ${\bar S_i}$ and ${\bar H_i}$ denote the 20 year averages of the SSP245 (S) and historical (H) simulations of each model, and N is the number of models.

The monthly precipitation and surface (∼2 m) air temperature data are obtained from the CN05.1 gridded daily observation dataset developed by Wu and Gao (2013). This dataset (1961–present) is based on more than 2400 meteorological stations in China and has been interpolated into a high resolution of 0.25° × 0.25°. The monthly SH flux data over the TP in 1984–2016 is provided by Xie and Wang (2019). This new estimate of the SH is generated by merging several bias-corrected top-quality reanalysis datasets covering the entire TP region. These observational data are employed to evaluate the CMIP6 models' historical products, using several statistical methods such as model bias and pattern correlation coefficient (PCC). The boreal summer season (June–August, i.e. JJA) from 1979 to 2014 is chosen for the present-day analysis. The study domain is the TP region (TP; 26°–42° N, 70°–105° E) within a boundary defined by elevation higher than 2500 m (figure 1(a)). Since most of the Chinese Meteorological Administration stations are located in the eastern part of the plateau (dots in figure 1(a)), the following investigations of both CMIP6 simulations and observations are limited to the eastern TP (east of 90° E). To facilitate the model validation against observation, we interpolate all data's horizontal resolutions to 1° × 1°.

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The LH released from precipitation is calculated by ${\text{LH}} = Pr \times {L_{\text{w}}} \times {\rho _{\text{w}}}$, where $Pr$ is the total precipitation (mm d⁻¹), ${L_{\text{w}}}$ = 2.5 × 10⁻⁶ J kg⁻¹ is the condensation heat coefficient, and ${\rho _{\text{w}}}$ = 10³ kg m⁻³ is the density of liquid water (Duan and Wu 2008). Since the LH is solely proportional to precipitation, we apply precipitation to represent the LH for subsequent analyses.

The precipitation attribution analysis (Jin et al 2020) is adopted to examine the contributing factors to the future change of the eastern-TP precipitation. The expression of the moisture budget in a vertical column is:

$$\begin{equation}\begin{array}{*{20}{c}} {P - E = - \left\langle\dfrac{{\partial q}}{{\partial t}} + {\mathbf{V}} \cdot \nabla q + \omega \dfrac{{\partial q}}{{\partial p}}\right\rangle,} \end{array}\end{equation} \tag{ 2 }$$

where 〈〉$= \frac{1}{g}\int\limits_{{p_{\text{T}}}}^{{p_{\text{s}}}} \left( {} \right){\text{d}}p$ denotes the vertical integration. Here P and E are the precipitation rate and surface evaporation rate (kg m⁻² s⁻¹), respectively. ${\mathbf{V}}$ is the horizontal wind velocity, ∇ is the horizontal gradient operator, q is the specific humidity, ω is the vertical p velocity, and p is the pressure. The tropopause pressure ${p_{\text{T}}}$ is set to 100 hPa, and the surface pressure ${p_{\text{s}}}$ is set to 600 hPa over the eastern TP. For monthly or seasonal mean motion, the local rate of change ($\frac{{\partial q}}{{\partial t}}$) can be neglected. A two-layer approximation is applied to the troposphere over the TP to estimate the moisture transport terms. Considering that the TP surface is around 600 hPa, we set the mid-level interface to 400 hPa and assume that the lower-layer mean specific humidity is equal to the specific humidity at 500 hPa, while the upper-layer specific humidity is negligible. Thus, the horizontal and vertical moisture transports can be approximated by

$$\begin{equation}\begin{array}{*{20}{c}} { - \langle {\mathbf{V}} \cdot \nabla q\rangle \approx - \frac{1}{g}\left( {{u_{500}}\frac{{\partial {q_{500}}}}{{\partial x}} + {v_{500}}\frac{{\partial {q_{500}}}}{{\partial y}}} \right)\Delta p,} \end{array}\end{equation} \tag{ 3a }$$

$$\begin{align}\begin{array}{*{20}{c}} { - \omega \frac{{\partial q}}{{\partial p}} \approx - \frac{1}{g}{\omega _{400}}{q_{500}},} \end{array}\end{align} \tag{ 3b }$$

where $\Delta p$ = 200 hPa is the thickness of the lower layer. Therefore, the precipitation change could be attributed to the changes in surface evaporation, low-level horizontal moisture advection, and vertical moisture transport, as expressed by the following equation:

$$\begin{align} \Delta Pr^* = & \ \Delta Ev + \underbrace {\Delta \left( { - \frac{{\Delta p}}{{{\rho _w}g}}{{\mathbf{V}}_{500}} \cdot \nabla {q_{500}}} \right)}_{\Delta \left[ { - {\mathbf{V}} \cdot \nabla q} \right]}\nonumber\\ & + \underbrace {\Delta \left( { - \frac{1}{{{\rho _w}g}}{\omega _{400}}{q_{500}}} \right)}_{\Delta \left[ { - \omega q} \right]}, \end{align} \tag{ 4 }$$

where $Pr = P/{\rho _w}$ and $Ev = E/{\rho _w}$ (mm d⁻¹). The operator $\Delta$ represents the difference between the SSP245 projection (2081–2100 mean) and the historical simulation (1995–2014 mean). $\Delta P{r^*}$ denotes the diagnosed precipitation change that is the sum of the three terms on the right-hand side of equation (4).

Figure 1(a) shows that the observed JJA mean precipitation generally decreases from the southeast to the northwest over the TP because the South Asian monsoon transports abundant water vapor primarily to the southeastern TP. The regional-mean rainfall for the eastern TP is 3.3 mm d⁻¹ or 302 mm during JJA. The historical precipitation simulated by the MME is higher than the observation in most parts of the TP region (figure 1(b)). The largest bias and intermodel spread (measured by one standard deviation of multiple models' simulations) appear at the southern and eastern edges, indicating the models' poor skills in simulating the monsoon rainfall amount over the southeastern TP. All models overestimate the observed precipitation with the relative biases ranging from 7.6% to 112.6% over the eastern TP. Thus, the 22 models' MME has a notable wet bias of 2.1 mm d⁻¹ or 64.8% of the mean plus a great intermodel spread of 1.6 mm d⁻¹. To quantify the discrepancy among models, we further calculate the PCC and normalized root-mean-square error (NRMSE) of each model compared with observation (figure 1(c)). Since the wet biases are substantial, both PCC and NRMSE need to be considered for choosing high-performance models. The best eight models with high PCC (greater than the mean) and low NRMSE (smaller than the mean) are selected (upper left quadrant in figure 1(c)). The MME of the best eight models ('Best 8 MME') is better than the MME of all 22 models ('22 MME') in capturing the observed pattern. The corresponding five poor models—PCC (NRMSE) lower (higher) than the mean value—are also picked out as a contrast group. The mean bias of the best group is 59.1%, which is significantly smaller than that of the poor group (89.6%). In addition, both observation and MME historical simulations exhibit no significant trend in the TP summer precipitation (figure not shown).

To see if there is an improvement compared to CMIP5, we refer to Su et al (2013)'s results that examined the annual mean precipitation over the eastern TP in 24 CMIP5 models. They found an overestimation range of 61.9% to 183.4%, with a mean bias of 116.6% in CMIP5 models. Through our calculations, the CMIP6 simulated annual mean precipitation has a mean bias of 99.0%, with a range from 44.3% to 142.8%. We find that the CMIP6 models' mean wet bias in annual mean precipitation is reduced by 18%, and the intermodel spread range is reduced by 23% compared to CMIP5. The improvement is statistically significant at the 90% confidence level. Considering that a fair comparison requires the same group of models or at least the same number of models, the comparison of ours and Su et al (2013) results is not ideal but arguably reasonable.

The period 1984–2014 is selected for the evaluation of the SH owing to the limited availability of reliable observational data. The observed summer SH is stronger in the western-central and northern TP (figure 2(a)) due to sparse vegetation, semiarid surface condition, and higher altitude. The mean SH in the eastern TP is 48.4 W m⁻². The distributions of the 22 MME's bias and the intermodel spread (figure 2(b)) generally resemble that of the SH climatology (figure 2(a)) with larger negative bias over the western and northern TP. The MME has a bias of −6.1 W m⁻² or −12.7% over the eastern TP, and the area-averaged intermodel spread is 14.7 W m⁻². The relative biases of all models range from −61.8% to 35.7%, in which most of them (15 out of 22) underestimate the SH. Twelve out of 22 models with PCC above 0.75 suggest their good spatial correspondence with the observation, while other models have PCC lower than 0.62 (figure 2(c)). Since the model biases are relatively small, we use PCC as the primary criterion to select 12 models as a good-model group, and the other ten models form a poor-model group. It can be seen that the good models for the SH do not precisely match those for the precipitation, indicating the model's inconsistent skills in simulating different variables. For the SH, the 'Good 12 MME' has the optimal performance with the highest PCC (0.90) and almost the lowest NRMSE (0.57). Considering the uncertainties in the SH datasets (Duan et al 2014), we also compared the model simulations with two other advanced TP SH observational datasets provided, respectively, by Yang et al (2011) for the period 1984–2006 and Duan et al (2018) for the period 1979–2016 to verify the reliability of the above result. It turns out that the same 12 good models are selected (figure S1). Moreover, the MME historical simulations can capture the weakening trend in the observed SH (figure not shown), which is mainly due to the reduced surface wind speed over the eastern TP (Duan and Wu 2008), despite that the declining rate of the modeled SH is lower than the observed value.

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3.2.1. Projected changes of the TP precipitation and sensible heat and their influencing factors

We use the difference between the 2081–2100 average in the SSP245 experiment and the 1995–2014 average in historical simulation to quantify the projected change in the 21st century and utilize the percentage of this difference to the 1995–2014 climatology to represent the expected relative change. The precipitation attribution analysis shows that the enhancement of vertical moisture transport and surface evaporation are the major contributors to the simulated precipitation increase. In contrast, the horizontal moisture advection term is relatively small and has a negative contribution (figure 3). This conclusion is valid for all models in general. However, the relative contributions between the vertical transport and evaporation differ among the three MME groups. In 'Best 8 MME,' the increase in evaporation is much larger than the increase in vertical moisture transport, while in 'Poor 5 MME,' the substantial vertical moisture transport enhancement is the primary contributor to the precipitation increase. Thus, the contributions by these two terms are comparable in '22 MME.' Compared to '22 MME' and 'Poor 5 MME,' the 'Best 8 MME' diagnosed precipitation change ($\Delta P{r^*}$) seems to a bit overestimate the projected change ($\Delta Pr$). The reason for this overestimation needs further investigation.

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Table 1 presents the projected changes of precipitation and their attributing terms over the eastern TP. The significance of these future changes has been examined using the two-tailed Student's t-test in which the intermodel spread (i.e. model uncertainty) is considered. The confidence level follows the likelihood scale assigned by the IPCC fifth assessment report on consistent treatment of uncertainties (Mastrandrea et al 2010). Precipitation projected by 'Best 8 MME' will 'likely' increase by 6.2% (0.33 mm d⁻¹), which is attributed to a 'very likely' enhancement of 12.1% in surface evaporation, a 'likely' intensification of 9.0% in vertical moisture transport, and a slight offset by the 'likely' decrease in horizontal moisture convergence. The 'virtually certain' increase of 21.4% in low-level specific humidity and the 'likely' weakening of 8.9% in ascending motion jointly induce the predicted strengthening in the vertical moisture transport. The relative change of the horizontal moisture advection term is quite large (40.5%) since this term's historical average (negative) is very small. The results of '22 MME' are similar to those of 'Best 8 MME,' except that the '22 MME' projected precipitation will 'very likely' increase owing to the less offset effect by the 'about as likely as not' decrease in the upward motion.

Table 1. 'Best 8 MME' and '22 MME' projected precipitation changes and their contributing factors over the eastern TP in summer. Results of '22 MME' are presented as a comparison. The *, **, and *** symbols indicate that the likelihood of the projected change is 'likely' (66%–100% probability), 'very likely' (90%–100% probability), and 'virtually certain' (99%–100% probability), respectively (under two-tailed Student's t-test). The value without the asterisks means its likelihood is 'about as likely as not' (33%–66% probability). Note that $- {\omega _{400}}$ is presented in the table because the summer-mean value of ${\omega _{400}}$ is negative over the eastern TP, which indicates the climatological ascending motion.

	$Pr$		$Ev$		$\left[ { - {\boldsymbol{V}} \cdot \nabla q} \right]$
	Change (mm d−1)	Relative change	Change (mm d−1)	Relative change	Change (mm d−1)	Relative change
'Best 8 MME'	0.33*	6.2%*	0.30**	12.1%**	−0.065*	40.5%*
'22 MME'	0.48**	8.7%**	0.28**	10.9%**	−0.061*	46.0%*
	$\left[ { - \omega q} \right]$		${q_{500}}$		$- {\omega _{400}}$
	Change (mm d−1)	Relative change	Change (g kg−1)	Relative change	Change (Pa s−1)	Relative change
'Best 8 MME'	0.18*	9.0%*	0.91***	21.4%***	−4.14 × 10−3*	−8.9%*
'22 MME'	0.31*	14.7%*	0.91***	20.8%***	−2.19 × 10−3	−4.4%

According to the bulk aerodynamic formula of surface SH flux, the SH is proportional to the surface (∼10 m) wind speed (${U_{\text{s}}}$) and the ground-air temperature difference (${T_{\text{s}}} - {T_{{\text{as}}}}$). The SH projected by 'Good 12 MME' will be 'likely' unchanged (i.e. 'unlikely' changed) in the future (table 2). Meanwhile, the surface wind speed will also 'likely' remain unchanged, and the ground-air temperature difference will 'about as likely as not' (i.e. insignificantly) decrease. The '22 MME' predicted SH will be 'very likely' unchanged (i.e. 'very unlikely' changed).

Table 2. 'Good 12 MME' and '22 MME' projected SH changes and their influencing factors over the eastern TP in summer. The ⁺⁺ and ⁺ symbols indicate 'very unlikely' (0%–10% probability) and 'unlikely' (0%–33% probability), respectively (under two-tailed Student's t-test). The value without the symbols means its likelihood is 'about as likely as not' (33%–66% probability).

	SH		${U_{\text{s}}}$		${T_{\text{s}}} - {T_{{\text{as}}}}$
	Change (W m−2)	Relative change	Change (m s−1)	Relative change	Change (°C)	Relative change
'Good 12 MME'	1.40+	3.3%+	−0.10+	−3.8%+	−0.25	−15.0%
'22 MME'	0.21++	0.5%++	−0.09+	−3.0%+	−0.16	−8.8%

Figure 4 shows the range of the projected relative changes, illustrating the large inter-model variability in 22 models. The box includes 66% of data that shows the range of 'likely' occurrence, and the dashed line between the 5th and 95th percentiles represents the 'very likely' range. Most models project enhancement in precipitation. Six of the best eight models are concentrated in the 'likely' box, and the '22 MME' projection is higher than the 'Best 8 MME.' Since the MPI-ESM1-2 h and MPI-ESM1-2-LR models predict negative changes, the projection range of the 'Best 8' group is quite large. The projected changes of the SH show great discrepancies among the models, and the 'likely' box is inclusive of zero, which induces the insignificant MME change. The spread of the good models for the SH is also broad, mainly due to the two notable positive outliers (CESM2 and CESM2-WACCM models).

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3.2.2. Precipitation sensitivity to local and global warming