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Little change in Palmer Drought Severity Index across global land under warming in climate projections

Abstract. Anthropogenic warming is reported to increase global drought for the 21st century when calculated using offline drought indices. However, this contradicts observations of greening and little systematic change in runoff over the past few decades and climate projections of future greening with slight increases in global runoff for the coming century. This calls into question the drought projections based on offline drought indices. To resolve this paradox, here we calculate a widely-used conventional drought index (i.e., the Palmer Drought Severity Index, PDSI) using direct outputs from 16 CMIP5 models (PDSI_CMIP5) such that the hydrologic consistency between PDSI_CMIP5 and CMIP5 models is maintained. Results show that the global PDSI_CMIP5 remains generally unchanged as climate warms, demonstrating that CMIP5 models do not actually project a general increase in PDSI drought (more reflecting soil moisture/agricultural drought) under future warming. Further analyses indicate that the projected increase in PDSI drought reported previously is primarily due to ignoring the vegetation response to elevated atmospheric CO2 concentration ([CO2]) in the offline calculations. On one hand, elevated [CO2] directly reduces stomatal opening; on the other hand, elevated [CO2] increases air temperature and thus vapor pressure deficit, which also causes partial stomatal closure. Finally, we show that the overestimation of PDSI drought can be avoided by directly using the relevant climate model outputs or by accounting for the effect of CO2 on evapotranspiration. Our findings refute the common warming leads to drying perception and highlight the importance of elevated CO2 in controlling future terrestrial hydrologic changes through vegetation responses.


Abstract. Anthropogenic warming is reported to increase global drought for the 21st century when calculated using offline drought indices. However, this contradicts observations of greening and little systematic change in runoff over the past few decades and climate projections of future greening with slight increases in global runoff for the coming century. This calls into question the drought projections based on offline drought indices. To resolve this paradox, here we calculate a widely-used conventional 25 drought index (i.e., the Palmer Drought Severity Index, PDSI) using direct outputs from 16 CMIP5 models (PDSI_CMIP5) such that the hydrologic consistency between PDSI_CMIP5 and CMIP5 models is maintained. Results show that the global PDSI_CMIP5 remains generally unchanged as climate warms, demonstrating that CMIP5 models do not actually project a general increase in PDSI drought (more reflecting soil moisture/agricultural drought) under future warming. Further analyses indicate that 30 the projected increase in PDSI drought reported previously is primarily due to ignoring the vegetation response to elevated atmospheric CO2 concentration ([CO2]) in the offline calculations. On one hand, elevated [CO2] directly reduces stomatal opening; on the other hand, elevated [CO2] increases air temperature and thus vapor pressure deficit, which also causes partial stomatal closure. Finally, we show that the overestimation of PDSI drought can be avoided by directly using the relevant climate 35 model outputs or by accounting for the effect of CO2 on evapotranspiration. Our findings refute the common "warming leads to drying" perception and highlight the importance of elevated CO2 in controlling future terrestrial hydrologic changes through vegetation responses.

Introduction
Drought is an intermittent disturbance of the water cycle that has profound impacts on regional water 40 resources, agriculture and other ecosystem services (Sherwood and Fu, 2014). By taking meteorological outputs from climate model projections as the inputs to offline drought indices/hydrological impact models, numerous studies have projected increases in future drought, in terms of both frequency and severity, mainly as a consequence of warming associated with anthropogenic climate change (Cook et al., 2014(Cook et al., , 2015Dai, 2011Dai, , 2012Dai et al., 2018;Huang et al., 2015Huang et al., , 2017Lehner et al., 2017;Liu et 45 al., 2018;Naumann et al., 2018;Park et al., 2018;Samaniego et al., 2018;Sternberg, 2011;Trenberth et al., 2013). The scientific basis underpinning this drying trend projected using offline drought indices/hydrological impact models is that the calculated increases in evapotranspiration (E) are larger than the projected increase in precipitation (P) in many places (Sternberg et al., 2011), which results in an increasing water deficit and thus increasing future drought. However, direct climate model outputs of 50 E exhibit a much smaller increasing trend (Supplementary Figure S1) and the global land mean P is actually projected to increase faster than its E counterpart (Greve et al., 2017;Dunne, 2016, 2017;Roderick et al., 2015;Yang et al., 2018) leading to very different conclusions.
Several recent studies have demonstrated that the drying bias in the offline calculated E trend is primarily due to neglecting the impact of increasing atmospheric CO2 concentration ([CO2]) on the 55 water use efficiency of vegetation (Lemordant et al., 2018;Dunne, 2016, 2017;Roderick et al., 2015;Swann et al., 2016;Yang et al., 2019). In existing hydrologic impact models/drought indices, P and potential evapotranspiration (EP; the rate of evapotranspiration that would occur with an unlimited supply of water) are the two key input variables, which respectively represent water supply to, and water demand from, the land surface. While P is a direct climate model output, EP is neither used 60 nor produced by climate models. The commonly adopted procedure is to calculate EP using the meteorological variables contained in the climate model output using an intermediate EP model. The calculated EP, together with the climate model projected P, are used to force an independent hydrologic impact model (or hydrologic calculations embedded in drought indices) that independently calculates E, runoff (Q), and storage change (∆S), for assessing hydrologic changes under future climate scenarios 65 (see Figure 1). Among various EP models, the open-water-Penman model (Shuttleworth, 1993) and the reference crop Penman-Monteith model (Allen et al., 1998)  coupled climate model output. For that reason, the consequent assessments of drought changes in existing offline hydrologic impact models/drought indices do not correctly represent the projections in the underlying fully-coupled climate models. Figure 1 illustrates the inconsistency in the hydrologic predictions (also see Milly and Dunne 2017) that have resulted in different trends in projected future drought between climate models and offline hydrologic impact models/drought indices. 80 Here, we re-assess changes in future global drought using climate model projections from 16 Coupled-Model-Intercomparison-Project-Phase-5 (CMIP5) models under historical  and Representative Concentration Pathway 8.5 (RCP8.5; 2006-2100) experiments (Taylor et al., 2012). The Palmer Drought Severity Index (PDSI; Palmer, 1965) is adopted here to quantify drought as it has been widely used for operational drought monitoring and is increasingly used in studies assessing drought 85 under climate change (Cook et al., 2014(Cook et al., , 2015Dai, 2011Dai, , 2012Dai et al., 2018;Lehner et al., 2017;Liu et al., 2018;Sheffield et al., 2012;Swann et al., 2016;Trenberth et al., 2013). To maintain consistency between the calculated PDSI and the CMIP5 models, we calculate PDSI using direct hydrologic outputs (i.e., P, E, Q, ΔS) from the CMIP5 models (PDSI_CMIP5; see Methods). This procedure minimizes the uncertainty in PDSI estimates caused by uncertainties in the hydrologic 90 simulations embedded in the original PDSI algorithm (Palmer, 1965). The original PDSI using reference crop Penman-Monteith EP (PDSI_PM-RC), as extensively used previously (e.g., Cook et al., 2014Cook et al., , 2015Liu et al., 2018), and is also presented for comparison (the right stream shown in Figure  (2006-2100) experiments (Taylor et al., 2012). We used monthly series of runoff, precipitation, soil moisture, sensible and latent heat flux at the land surface along with near-surface air temperature, air pressure, wind speed and specific humidity. All outputs from 16 CMIP5 models were resampled to a common 1 o spatial resolution by using the first-order conservative remapping scheme (Jones, 1999). 105

Calculation of PDSI
The Palmer Drought Severity Index (PDSI) was used to quantify drought (Palmer, 1965). To minimize the impact of initial conditions on PDSI estimates, the first 40 years (1861-1900) are used for model spin-up with the analyses focused on the 1901-2100 period. Briefly, the PDSI model consists of two parts: (i) a two-stage bucket model that calculates the monthly water balance components (i.e., actual 110 evapotranspiration (E), runoff (Q) and soil moisture changes (∆S)) using P and EP as inputs, and (ii) a dimensionless index that describes the moisture departure between the actual precipitation and the precipitation needed to maintain a normal soil moisture level for a given time (i.e., the climatically appropriate for existing conditions values). Detailed descriptions of PDSI can be found in Palmer (1965). A drought event is identified with negative PDSI values, with a more negative PDSI indicating 115 a more severe drought, whereas moist events are associated with positive PDSI values.
We calculated PDSI following Palmer (1965) yet calculated EP using the reference crop Penman-Monteith model (PDSI_PM-RC). The Penman-Monteith model explicitly considers influences from both radiative and aerodynamic components and has been widely used in previous PDSI calculations (e.g., van der Schrier et al., 2011;Dai et al., 2011;Sheffield et al., 2012). In addition, we also used a

Calculation of Potential Evapotranspiration
Two potential evapotranspiration formulations were used to calculate EP. The first is the reference crop Penman-Monteith EP model, which computes EP (mm day -1 ) as (Allen et al., 1998

170
In applications, a PDSI < -3.0 is considered to be drought conditions while a PDSI > 3.0 is considered exceptionally moist (e.g., Palmer, 1965;Liu et al., 2018). We examined changes in the land area subject  (Figures 3a-c). A similar result that the increase in drought area is essentially the same as the increase in moist area is obtained when the PDSI thresholds are changed to PDSI < -2.0 and 185 PDSI > 2.0 (Supplementary Figure S2).
The above results clearly indicate an inconsistency between the PDSI_PM-RC that has been widely used in offline calculations for drought assessment studies and the underlying CMIP5 models, as the PDSI_CMIP5 used here is based on the direct hydrologic outputs (E, Q and ∆S) from CMIP5 models.
To give a global overview, we compare the time series of the three global average PDSI in Figure 4.  Figure S3).

The effect of warming on drought changes
Warming has been identified as the key driver of the overall future drought increase in numerous studies (Cook et al., 2014(Cook et al., , 2015Dai, 2011Dai, , 2012Dai et al., 2018;Huang et al., 2015Huang et al., , 2017Lehner et 205 al., 2017;Liu et al., 2018). To further understand the impact of warming on drought changes, we assessed changes in PDSI_CMIP5 at 1.5 o C and 2 o C warming above the pre-industrial level. The PDSI_PM-RC is also presented for comparison. Any substantial increase in drought is identified when PDSI for a future warming target decreased by 1.0 compared to PDSI during the 1986-2005 baseline (i.e., ΔPDSI < -1). Additionally, only places where the ΔPDSI < -1.0 threshold is reached in at least 8 210 CMIP5 model (out of the 16 CMIP5 models 50% and more) are considered to be robust projections and thus used herein. Based on the PDSI_CMIP5, our results show that almost nowhere on earth (only 0.06% of the global land area) is projected to have a substantial drought increase at the 1.5 o C warming target, and this number only slightly increases to 0.77% at the 2 o C warming target (Figures 5a and b). In comparison, substantial increase in drought is identified at 5.10 % and 13.41 % of the global land area 215 at the two warming targets, respectively, when PDSI_PM-RC is used (Figures 5a and c). More places are projected to have a substantial drought increase under future warming if we relaxed the threshold of PDSI change to -0.5 (i.e., ΔPDSI < -0.5) (Figure 5d-f). Nevertheless, the PDSI_CMIP5 still shows a considerable smaller percentage of drying lands (6.2% and 10.0%) than the PDSI_PM-RC (26.32% and 34.77%) under the two warming targets, respectively, particularly over North America, much of 220 Amazonia, Europe, the Congo basin and southeast China.

Discussion and concluding remarks
The above results clearly demonstrate an overestimation of drought severity and extent using PDSI in many previous assessments of future drought (e.g., Cook et al., 2014Cook et al., , 2015Dai, 2011Dai, , 2012Dai et al., 2018;Lehner et al., 2018;Liu et al., 2018). The overestimation is primarily caused by neglecting the 225 impact of elevated [CO2] on rs and consequently on EP in the offline calculation of drought indices. As important assumption that rs remains constant over time (Allen et al., 1998;Shuttleworth, 1993). This 230 assumption is in general valid for water surfaces and/or wet bare soils but proved to be problematic over vegetated surfaces. Over vegetated surfaces, on one hand, elevated [CO2] leads to a partial stomatal closure that increase rs (e.g., Ainsworth and Rogers, 2007) yet on the other hand, elevated [CO2] has "fertilized" vegetation resulting in an increased foliage cover (e.g., Donohue et al., 2013;Zhu et al., 2016), which also effectively suggests a reduction in rs. In addition, elevated [CO2] serves as the 235 ultimate driver of climate warming in the CMIP5 models and consequently leads to an increase in atmospheric vapor pressure deficit, which also tends to increase rs (Lin et al., 2018;Novick et al., 2016).  (Yang et al., 2019). This suggests that warming does not necessarily lead to a higher EP over vegetated surfaces and hence increased drought under [CO2] enrichment, which is consistent with CMIP5 model projections yet contradicts the perception that "warming leads to drying" in many previous studies (Cook et al., 2014, 245 2015; Dai, 2011Dai, , 2012Dai et al., 2018;Huang et al., 2015Huang et al., , 2017Lehner et al., 2018;Liu et al., 2018;Park et al., 2018;Samaniego et al., 2018;Sternberg, 2011;Trenberth et al., 2013). Additionally, it is worthwhile mentioning that the CMIP5 models do project topsoil moisture (within 10 cm) to decline similar to PDSI_PM-RC (Dai, 2012;Dai et al., 2018), but that since no systematic decline in runoff or in vegetation indicators (e.g., leaf area index and gross/net primary production) seems to result from it unchanged (Berg et al., 2017;Greve et al., 2017), consistent with PDSI_CMIP5 and PDSI_PM[CO2] ( Figures 3 and 4). 255 Here, we use PDSI as an illustrating case; similar results were also found in another commonly used drought index (i.e., the Standardized Precipitation-Evapotranspiration Index, or SPEI; Vicente-Serrano, 2010) (Supplementary Figure S4). Nevertheless, both PDSI and SPEI, as well as other drought/aridity metrics, are secondary offline impact models. Since climate models are fully-coupled land (and ocean) atmosphere models that are an internally consistent representation of the climate system (Milly and 260 Dunne, 2016), a scientific prior of applying any offline hydrological impact models is that the adopted model must be able to recover the hydrological simulations in climate models (Roderick et al., 2015;Milly and Dunne, 2017;Yang et al., 2019). Otherwise, any inconsistency in hydrological predictions between offline impact models and climate models themselves would lead to inconsistent predictions in other components of the climate system. Unfortunately, this important scientific prior has been largely 265 ignored in many previous drought assessment studies, leading to biased drought predictions that are actually inconsistent with climate model themselves.
In summary, we have shown that climate model projections of the global drought area remains more or less constant over a 200-year period under different scenarios for future warming. Our results demonstrate that the "warming leads to drying" perception is fundamentally flawed, primarily due to the 270 ignorance of the vegetation response to elevated [CO2] (also see Yang et al., 2019). However, despite a small overall trend globally, we find that both drying and wetting areas are simulated to increase towards the end of this century (Figures 3b-f), suggesting an increased spatial variability in surface hydrological conditions that will likely lead to increased droughts and/or floods at local/regional scales.

Data availability
The data that support the findings of this study are openly available (http://cmip-pcmdi.llnl.gov/cmip5/).

Author contribution
Y. Yang and M. Roderick designed the study. S. Zhang and Y. Yang performed the calculation and drafted the manuscript. All authors contributed to results discussion and manuscript writing; 285

Competing interests
The authors declare that they have no conflict of interest     respectively. The meteorological variables used to calculate EP depend on the adopted EP model but mainly include net radiation, near-surface air temperature, vapor pressure and wind speed. The biological factor here is the response of surface resistance to elevated [CO2] over vegetated lands.