Abstract

The aridity of a terrestrial climate is often quantified using the dimensionless ratio of annual precipitation (P) to annual potential evapotranspiration (PET). In this study, the climatological patterns and greenhouse warming responses of terrestrial P, Penman–Monteith PET, and are compared among 16 modern global climate models. The large-scale climatological values and implied biome types often disagree widely among models, with large systematic differences from observational estimates. In addition, the PET climatologies often differ by several tens of percent when computed using monthly versus 3-hourly inputs.

With greenhouse warming, land P does not systematically increase or decrease, except at high latitudes. Therefore, because of moderate, ubiquitous PET increases, decreases (drying) are much more widespread than increases (wetting) in the tropics, subtropics, and midlatitudes in most models, confirming and expanding on earlier findings. The PET increases are also somewhat sensitive to the time resolution of the inputs, although not as systematically as for the PET climatologies.

The changes in the balance between P and PET are also quantified using an alternative aridity index, the ratio , which has a one-to-one but nonlinear correspondence with . It is argued that the magnitudes of changes are more uniformly relevant than the magnitudes of changes, which tend to be much higher in wetter regions. The ratio and its changes are also found to be excellent statistical predictors of the land surface evaporative fraction and its changes.

1. Introduction

Our everyday experience tells us that precipitation (P) is one of the factors that determines the effective wetness or dryness of a terrestrial climate, but not the only one. For example, the “emerald city” of Seattle, Washington, receives ~950 mm yr−1 of P on average. Yet the environment of Dallas, Texas, which also averages ~950 mm yr−1 of P, seems much drier. This is because its more intense sunshine and warmer, drier air evaporate plant and soil water more effectively.

Therefore, when characterizing climatic aridity, it makes sense to consider P relative to potential evapotranspiration (PET; e.g., Hartmann 1994), the rate at which the climate demands water from well-watered vegetation. PET is best computed from climate data using the Penman–Monteith equation (see section 2), which is just the solution to the physical equations for the energy balance that would hold over a wet surface in given climatic conditions (e.g., Monteith 1981; Allen et al. 1998, 2005). According to one standard dataset (FAO 2004), PET in Seattle is mm yr−1, but PET in Dallas is mm yr−1, far more water than can actually be supplied by P. Of course, an extensive wet area would cool and moisten those climatic conditions, lowering the PET estimates, but plants in a given environment experience its actual (hot, dry) climate, so for ecological purposes it is sensible to use the actual climate when computing PET. The concept of PET is also known as reference evapotranspiration, potential evaporation, or evaporative demand, and is very closely related to pan evaporation.

The simplest measure that accounts for the relative magnitudes of P and PET is the ratio of their climatological annual mean values, the aridity index (e.g., Transeau 1905; Budyko and Miller 1974; Middleton and Thomas 1997; Feng and Fu 2013), which can be thought of as a nondimensionalized precipitation. The value of indicates whether evapotranspiration should be water-limited or energy-limited , and a difference in between two climates implies a difference in limiting-factor importance. From the above data, is in Seattle, but only in Dallas. Budyko and Miller (1974) and earlier workers noted that the same values of correspond to similar vegetation densities and runoff ratios across widely varying temperature, radiation, and PET regimes on Earth. This observation has led to the use of as the main moisture variable in several prominent terrestrial biome classification schemes (e.g., Middleton and Thomas 1997; Holdridge 1967). In the Middleton and Thomas (1997) scheme, which has been adopted by the United Nations (UN; e.g., Mortimore 2009), is defined as hyperarid, as arid, as semiarid, as dry subhumid, and as humid. The climate of Dallas is thus dry subhumid while that of Seattle is quite humid, even though P is the same.

Global climate models (GCMs) are often used to generate hydroclimatic responses to various forcings. However, these responses have usually been characterized in terms of individual dimensional quantities such as P, actual evapotranspiration (E or ET), runoff, and/or soil moisture (e.g., Collins et al. 2014; Meehl et al. 2007), or in terms of complicated metrics of local drought relative to some reference period, such as the Palmer drought severity index (PDSI) (Cook et al. 2014; Dai 2013). The characterization of the models’ mean states has been similarly concerned with individual variables, and has often focused on features over the oceans, especially for P (e.g., Flato et al. 2014). In contrast, very few studies have tried to quantify the patterns of general land aridity in climate models, or of the response of aridity to forcing. Here we propose to build on the work of Feng and Fu (2013) by mapping , its response to greenhouse warming, and its contributing factors across a wide range of modern GCMs over global land.

2. Methods

Given values of near-surface air temperature , water vapor pressure , wind speed , and net downward broadband radiation , the Penman–Monteith equation for PET is

 
formula

where is the saturation vapor pressure at , is a standard notation for the local slope of the saturation vapor pressure curve, is the assumed bulk stomatal resistance of well-watered vegetation, is an assumed scalar transfer coefficient, is the air density, is the air specific heat, is the heat of vaporization of water, , is the air pressure, is the ratio of molar masses of water vapor and dry air, and G is the heat flux into the ground or soil (usually ignored or parameterized).

In a previous study (Scheff and Frierson 2014, hereinafter SF14), the authors computed 1981–99 and 2081–99 annual PET climatologies for 13 GCMs in phase 5 of the Coupled Model Intercomparison Project (CMIP5) multimodel ensemble (Taylor et al. 2012), using 3-hourly surface output from the historical and business-as-usual RCP8.5 scenarios in a procedure closely adapted from the American Society of Civil Engineers’ (ASCE) standardized tall-crop version of (1) for hourly data (Allen et al. 2005). Here we make use of those same PET climatologies, expanded to include the three additional CMIP5 GCMs that have since archived output satisfying the SF14 criteria. The resulting 16 models are listed in Table 1 along with any exceptions to the SF14 procedures. Note that the GCM’s land surface skin temperature (as opposed to ) is not used in (1); instead, the derivation of (1) uses the often much cooler skin temperature of a wet surface, consistent with the definition of PET. Thus, the conceptual problem with GCM internal “PET” fields identified by Milly (1992) is explicitly avoided by using the Penman–Monteith approach. See Milly (1992) and section 1b of SF14.

Table 1.

CMIP5 models analyzed in this study.

CMIP5 models analyzed in this study.
CMIP5 models analyzed in this study.

In addition, we apply the SF14 procedures to 3-hourly, 1°, 1981–99 meteorological data from the Global Land Data Assimilation System 2.0 (GLDAS; Rodell et al. 2004) to obtain a comparable observational estimate of climatological PET. These data come directly from the widely used Sheffield et al. (2006) meteorological forcing dataset, except for the upward energy fluxes used to compute , which inevitably have some influence from the Noah land model used in GLDAS.

We also compute all of these PET climatologies using monthly-mean instead of 3-hourly output, with a procedure closely adapted from the ASCE standardized tall-crop version of (1) for daily data. This is very similar to the 3-hourly SF14 procedure; the main differences (after Allen et al. 2005) are that is estimated as the average of and , where and are the monthly-mean daily minimum and maximum values of ; that is somewhat differently estimated as , where is the average of and ; and that is set to a constant 45 s m−1. (The only other difference is that the monthly average of is archived directly by the models as the variable sfcWind, not computed from the vector components.) This is much less computationally intensive than using 3-hourly output, and many previous studies (e.g., Feng and Fu 2013; Cook et al. 2014; Dai 2013) have also used monthly-mean output, so the comparison is of considerable interest. However, contrary to their stated method (Allen et al. 1998) and to Allen et al. (2005), those studies simply estimated as , so we also do another set of monthly PET computations using this nonstandard estimate for comparison to our main results. (For the GLDAS observations, we only use this nonstandard method, since and are not included in the GLDAS monthly product.)

Finally, P (unlike PET) is one of the variables directly saved by the GCMs, so we compute its annual climatologies using monthly-mean output, for simplicity. We also use gauge-based observational estimates from the Global Precipitation Climatology Centre (GPCC) 1951–2000 climatology product (Schneider et al. 2014), for comparison. [The 1981–99 mean of the less comprehensive Climatic Research Unit TS3.21 P product (Harris et al. 2014) is nearly identical.]

3. Results and discussion

a. Basic states

Figure 1 maps the 1981–99 terrestrial P climatologies for each GCM in Table 1, with the GPCC observational product also shown for reference and five key regions (defined in Table 2) outlined with rectangles. One can immediately see that while in many places the models are quite similar to each other and to the observations (e.g., much of Eurasia and northern Africa), in many other places they differ greatly. Perhaps the most dramatic model-to-model differences are in the outlined region of northern South America (as well as neighboring Central America), where many models simulate only 1–2 mm day−1 of precipitation (red and orange, similar to the Sahel or the interior western United States) across the same vast areas where other models (and the observations) have 5–8 mm day−1 or more (blue), and dense tropical rain forests are found. The same situation, where some models have near-observed large-scale P but other models have a great deal less, also occurs across the central Amazon basin and the (outlined) southeast of the continent; Malhi et al. (2009) noted similar behavior in the CMIP3 models. This type of difference is also particularly stark for the Indian Peninsula (also outlined), where some models have 0–1 mm day−1 yet most other models (and the observations) have 3 mm day−1. Conversely, through large portions of southern Africa (outlined) and central Africa, several models simulate roughly double the observed P amounts, while many other models are closer to observed. Southern and central China and much of central North America (outlined) also have striking intermodel P disagreements.

Fig. 1.

1981–99 climatological annual-mean precipitation P in mm day−1 for each CMIP5 model in Table 1, with Global Precipitation Climatology Centre (GPCC) gauge-based observational product as described in section 2. Values in a few color-saturated regions greatly exceed those on the scale. Regions in Table 2 are outlined.

Fig. 1.

1981–99 climatological annual-mean precipitation P in mm day−1 for each CMIP5 model in Table 1, with Global Precipitation Climatology Centre (GPCC) gauge-based observational product as described in section 2. Values in a few color-saturated regions greatly exceed those on the scale. Regions in Table 2 are outlined.

Table 2.

Region definitions.

Region definitions.
Region definitions.

Figure 2 shows the corresponding climatologies of annual Penman–Monteith PET (computed using the 3-hourly output) on the same scale. (This is simply an expansion and rescaling of SF14’s Fig. 1, plus an observational panel.) In many of the same low- to midlatitude areas where the models strongly disagree on P, they also strongly disagree on PET, and the high-P models are often also the low-PET models in a given area. For example, in much of South America, the two MRI models (and ACCESS1.0 and HadGEM2-ES to a lesser extent; see Table 1 for model expansions), which all showed high, realistic P in Fig. 1, also have much lower, more realistic PET, just 3–4 mm day−1 (light blue) where most of the other models have 5–7 mm day−1 (yellow to red), much greater than observed. Similar patterns of very large, opposite biases in PET and P are also common in the southern African and Indian peninsular regions. This negative intermodel relationship is somewhat to be expected, since rainier simulated climates also likely have less sunshine, higher relative humidity, and (in the tropics and/or warm seasons) cooler daytime temperatures, all of which mean lower Penman–Monteith PET (e.g., Allen et al. 2005; SF14; see also Brutsaert and Parlange 1998). However, there are also strong PET intermodel differences in Fig. 2 that do not show such a clear association with P differences. For example, maximum PET values in the central Sahara, where , range from 6 to over 8 mm day−1 (Fig. 1 of SF14 shows that some of these models exceed 10 mm day−1, in fact).

Fig. 2.

1981–99 annual-mean potential evapotranspiration (PET) in mm day−1 for each model and for the Global Land Data Assimilation System 2.0 (GLDAS) observation-based product as described in section 2.

Fig. 2.

1981–99 annual-mean potential evapotranspiration (PET) in mm day−1 for each model and for the Global Land Data Assimilation System 2.0 (GLDAS) observation-based product as described in section 2.

Figure 3 distills these relationships by taking area-weighted means of Figs. 1 and 2 over all land in each region, and plotting the regional P and PET against each other. (These means are taken by nearest-neighbor interpolating each model onto a common 0.25° grid and using only those 0.25° grid points which get assigned to an analyzed grid box for every model, so that the same set of points is used in each model despite the different coastlines.) The negative intermodel relationship between mean-state P and PET is always visually clear, and the correlation is always stronger than −0.6. The dramatic, zeroth-order differences between many models and the observational estimates are also made clear: some models have barely half observed P for the two South American regions (or nearly twice observed P for the southern African region) and/or an order of magnitude less P than observed for the Indian peninsular region. The large scale of the defined regions means that somewhat smaller-scale differences (e.g., across the north coast of South America) are even greater.

Fig. 3.

1981–99 annual-mean regional-land-mean P vs PET for each model (numbers) and for the observational products (asterisks), plotted for each region in Table 2. Values in parentheses are simple correlations of the 16 model points.

Fig. 3.

1981–99 annual-mean regional-land-mean P vs PET for each model (numbers) and for the observational products (asterisks), plotted for each region in Table 2. Values in parentheses are simple correlations of the 16 model points.

Figure 4 shows the percent differences between the Penman–Monteith PET climatologies computed using monthly-mean output (with the standard estimate) and those computed using 3-hourly output just shown in Fig. 2. Throughout much of the low- to midlatitudes the monthly-computed PET is higher than the 3-hourly value by about 10%–30%, with the exact magnitude and extent of the difference varying somewhat among models. At high latitudes the difference typically takes the opposite sign and is somewhat smaller. (In the two IPSL models, the discrepancy is much larger and consistently positive.) The discrepancy turns out to be largely explained by a rather uniform 20%–50% (50%–150% in the IPSL models) overestimation of the aerodynamic (i.e., right hand) term of Eq. (1) by the monthly method. Similar magnitude discrepancies, albeit with different signs and patterns, are found for the observational estimates using the nonstandard for the monthly computations; equivalent plots for the models look similar (not shown). Thus, the discrepancies are not a simple artifact of the choice of estimate. We conclude that monthly-computed PET, which does not account for the diurnal cycle of most variables or for weather variability, is not usually representative of more carefully computed climatological PET. So, we use the 3-hourly-computed PET, except where indicated.

Fig. 4.

Percent differences between the 1981–99 annual-mean PET computed using monthly vs 3-hourly output, for each model and for the GLDAS observation-based product. For the observations only, the nonstandard is used in the monthly computation.

Fig. 4.

Percent differences between the 1981–99 annual-mean PET computed using monthly vs 3-hourly output, for each model and for the GLDAS observation-based product. For the observations only, the nonstandard is used in the monthly computation.

Having examined the climatological terrestrial P and PET in the models and observations, Fig. 5 plots their ratio, the aridity index , with the UN dryland categories (Middleton and Thomas 1997) on the color scale. The large, reinforcing P and PET differences highlighted above generate similarly stark model-dependent biases in terrestrial aridity. Vast areas of South America may be simulated as anything from semiarid/arid to extremely humid depending on the model, particularly in the humid northern and southeastern regions where observed is and respectively. The central Amazon basin, at least, is usually humid in the models, but it is still much more so in some than others, again consistent with estimates for CMIP3 models in Malhi et al. (2009). There is also strong disagreement on aridity in central North America: some models depict a very large semiarid area reaching up into the central/western United States and Canada, with as low as 0.3 or so, while others keep the vast majority of the United States and Canada humid, outside of the far southwest. The observations, in contrast, have a sharp west–east gradient in aridity across the highlighted region. Similarly, the Indian subcontinent in some models is a large, nearly hyperarid desert similar to the Arabian Peninsula, while in others it contains regions that range from arid to humid, in line with observations. There are also interesting large-scale differences in southern to central Africa, Australia, eastern China, and many other areas. These all may be of more immediate consequence to applications than the P disagreements over tropical oceans highlighted by more general reviews such as Flato et al. (2014).

Fig. 5.

1981–99 aridity index for each model and for the observational products, where P and PET are the climatologies shown in Figs. 1 and 2. The dryland categories from Middleton and Thomas (1997) are indicated on the scale (HA = hyperarid; DSH = dry subhumid; above 0.65 is considered humid).

Fig. 5.

1981–99 aridity index for each model and for the observational products, where P and PET are the climatologies shown in Figs. 1 and 2. The dryland categories from Middleton and Thomas (1997) are indicated on the scale (HA = hyperarid; DSH = dry subhumid; above 0.65 is considered humid).

b. Responses to greenhouse warming

Figure 6 maps the model changes in annual terrestrial P between the 1981–99 base state described above and the 2081–99 RCP8.5 future. As found in more general studies (e.g., Collins et al. 2014; Scheff and Frierson 2012a,b), P increases are generally widespread in high latitudes. However, the responses over mid- to low-latitude land do not neatly fit the typical description of deep-tropical increases and subtropical decreases found in those studies, which focused largely on P responses over the oceans because they tend to be more robust. Instead, these regions generally show patterns of both increase and decrease in P that vary widely from model to model with little zonal structure. For example, in many models the region of strongest absolute terrestrial P decline is tropical northern South America, not the subtropics. In some models (e.g., the two GFDL-ESM models) declines in P actually predominate throughout low- to midlatitude land, while in others (e.g., CNRM-CM5) increases in P predominate, with few declining regions. Most models are between these two extremes, but with widely varying, nonzonal patterns, particularly in South America, Africa, Australia, and southern to eastern Asia, and with no particular preference for P increases or decreases outside of the high latitudes.

Fig. 6.

Changes in annual precipitation P in mm day−1 between 1981–99 (historical scenario) and 2081–99 (RCP8.5 scenario), for each model.

Fig. 6.

Changes in annual precipitation P in mm day−1 between 1981–99 (historical scenario) and 2081–99 (RCP8.5 scenario), for each model.

Interestingly, these P changes do not tend to be positively related to climatological P, , or (not shown) across models; that is, the models that reduce P in a given location are not generally the drier ones, contrary to a “wet-get-wetter” expectation (e.g., Held and Soden 2006). For example, in northern South America HadGEM2-ES, ACCESS1.0, and the two MRI models are very humid in the mean yet have huge declines in P with greenhouse warming, and in India the two BCC and two MRI models are very arid in the mean yet show marked P increases. Figure 7 plots regional-mean change in P against basic-state to emphasize this; substantial positive correlations are absent (central North America comes closest at +0.47, although some of the driest models there still increase P the most.) All the correlation magnitudes are much less than in Fig. 3. The x axes of Fig. 7 span multiple UN aridity categories, again highlighting the zeroth-order model disagreements and biases in aridity discussed above.

Fig. 7.

Regional-land-mean 1981–99 aridity index vs twenty-first-century P change, for each model and region. Values in parentheses are simple correlations of the model points. The dashed line is observational regional-land-mean . For reference, less than 0.05 is defined as hyperarid, 0.05 to 0.2 as arid, 0.2 to 0.5 as semiarid, 0.5 to 0.65 as dry subhumid, and more than 0.65 as humid (Middleton and Thomas 1997); see the scale of Fig. 5.

Fig. 7.

Regional-land-mean 1981–99 aridity index vs twenty-first-century P change, for each model and region. Values in parentheses are simple correlations of the model points. The dashed line is observational regional-land-mean . For reference, less than 0.05 is defined as hyperarid, 0.05 to 0.2 as arid, 0.2 to 0.5 as semiarid, 0.5 to 0.65 as dry subhumid, and more than 0.65 as humid (Middleton and Thomas 1997); see the scale of Fig. 5.

In contrast, annual PET increases moderately but very robustly across all of the models and across all of global land, as shown in Fig. 8. This is just an expansion of Fig. 3 from SF14, but is shown here for reference. As shown by SF14, this is because the direct response of the Penman–Monteith equation to temperature at constant relative humidity dominates the responses to the other factors, and must always be positive. The physical mechanisms for this response are the widening of the vapor pressure deficit and the increase of the equilibrium evaporative fraction, both of which come directly from the Clausius–Clapeyron equation. The percentage increases tend to be larger at higher latitudes because the percent sensitivity of (1) to temperature is much larger at cooler background temperatures, due to the lower evaporative fraction (SF14). Also, although the physical increases shown in Fig. 8 are mostly due to warming, they are much smaller than the huge, fictitious increases in PET projected by empirical temperature-based methods like the Thornthwaite equation (used in the most common version of the PDSI) and the Croley method (used in Great Lakes studies), which are clearly invalid under climate change (e.g., Hoerling et al. 2012; Lofgren et al. 2011; Hobbins et al. 2008; McKenney and Rosenberg 1993; Sheffield et al. 2012). For more details on all of this, see SF14.

Fig. 8.

Percent changes in annual PET between 1981–99 and 2081–99, for each model.

Fig. 8.

Percent changes in annual PET between 1981–99 and 2081–99, for each model.

Figure 9 shows the difference between the percent changes in monthly-computed PET (using the standard estimate; results with the nonstandard estimate are nearly identical) and the percent changes in 3-hourly-computed PET just shown in Fig. 8. SF14 had posited that methods not explicitly resolving the diurnal cycle (such as the use of monthly output) might strongly overestimate the PET increase, because total PET is much more sensitive to conditions during the daytime, which is when greenhouse warming is generally below its diurnal average. However, with a few high-latitude exceptions in certain models, the differences (Fig. 9) are quite small compared to the increases themselves (Fig. 8), perhaps because the diurnal dependence of greenhouse warming is not actually that large outside the high latitudes (see Fig. 10.11b of Meehl et al. 2007). This lends further confidence to the results of Feng and Fu (2013), Cook et al. (2014), Dai (2013), and other studies driven by twenty-first-century changes in monthly-computed Penman–Monteith PET.

Fig. 9.

Differences between the percent changes in annual PET over the twenty-first century computed using monthly vs 3-hourly output.

Fig. 9.

Differences between the percent changes in annual PET over the twenty-first century computed using monthly vs 3-hourly output.

Finally, Fig. 10 maps the changes in the aridity index between the two epochs. The moderate, consistent Penman–Monteith PET increases (Fig. 8) combine with the more muddled terrestrial P changes (Fig. 6) to yield widespread declines in the supply-to-demand ratio (i.e., aridification) outside of the high latitudes, with generally fewer areas of increases in . In each model, there are large areas where raw annual P (Fig. 6) increases with greenhouse warming, yet when normalized by annual PET (Fig. 10) it declines instead. Figure 10 presents a very different story than the widespread “wet get wetter, dry get drier” mnemonic: terrestrial drying is dominant in the wet tropics and midlatitudes, not just in the dry subtropics.

Fig. 10.

Changes in the aridity index between 1981–99 and 2081–99, for each model.

Fig. 10.

Changes in the aridity index between 1981–99 and 2081–99, for each model.

This is the same basic picture already described by Feng and Fu (2013), Cook et al. (2014), and Dai (2013), and strongly confirms their results. However, it also has the advantages of both using a very simple, transparent aridity metric and showing spatial results for many different individual GCMs. In particular, one can see that some models tend to aridify more than others. Fu and Feng (2014) suggest that such global-scale disagreements on future aridity trends stem from the different phases of unforced land P variability sampled by each independent model run. However, Fig. 10 makes it clear that at least some of these differences stem from fundamental differences in the forced model response, since pairs of related models (e.g., MRI, IPSL, BCC, GFDL-ESM) look extremely similar to each other. It seems highly unlikely in light of these close similarities between independent runs that, for example, the MRI models aridify less than the others because they both happen to sample an unusually wet period of natural variation during 2081–99. Further investigation would augment this “poor man’s ensemble” by evaluating multiple runs for each model, when possible.

4. Two alternative metrics

One disadvantage of a plot like Fig. 10, which depicts absolute changes in as in Feng and Fu (2013), is that very wet regions (e.g., the high latitudes, the Amazon, Southeast Asia) are disproportionately highlighted because the magnitude of is so much larger there already. Equivalently, as can be seen from the scale on Fig. 5, the same absolute change is much more consequential in dry climates than in wet ones: a change from 0.6 to 0.1 implies a wholesale ecoclimatic shift from subhumid savanna or forest to arid desert, while a change from 1.6 to 1.1 is merely from rather humid forest to fairly humid forest (Budyko and Miller 1974; Holdridge 1967). This makes Fig. 10 “unfair” in some sense. Using the reciprocal , as those older studies do, merely causes the opposite, worse problem: a change from, say, 100 to 97 in a hyperarid desert is obviously much less important than a change from 3.5 to 0.5 (semiarid to very humid.) This suggests that we might look at the relative changes in or , in the form of percent changes [as in Fu and Feng (2014)] or ratios [as suggested by the scale in Holdridge (1967)]. However, this still “unfairly” highlights tiny changes in very arid regions with : a chance increase from to 0.0002 is depicted as boldly as an increase from 0.5 to 1 elsewhere, leading to rather meaningless features in places like the Sahara. [This occurs frequently in plots of percent change in P; see Fig. 12.22 of Collins et al. (2014) for examples.]

Therefore, it would be useful to employ an aridity change metric whose practical meaning does not depend so strongly on the base climate. The metrics and are each fundamentally unbalanced because they approach infinity on one side but 0 on the other. One way to portray the relative magnitudes of climatic water supply P versus demand PET in a more balanced (yet still nondimensional) fashion is to use the ratio , which just ranges between 0 and 1 . Like the division of P and PET in the traditional index, the addition of P and PET in the denominator is not physical in and of itself but just helps us numerically assess the relative magnitudes. A similar approach is sometimes taken in terrestrial plant modeling (e.g., Medvigy et al. 2009).

Our new index is a one-to-one function of or ,

 
formula

so it preserves exactly the same information: always corresponds to , to , and so on. However, as desired, change magnitudes are not one-to-one: the above change from 0.6 to 0.1 corresponds to a change from 0.38 to 0.09, while the “equal” change from 1.6 to 1.1 corresponds to a change from just 0.62 to 0.52, nearly 3 times smaller than the first change. Essentially, to 0.1 represents a more dramatic change in our assessment of whether , , or than does to 1.1.

Inspired by this reasoning, Fig. 11 plots this alternate aridity index for each model, using the 1981–99 climatologies. As expected, it is in a one-to-one relationship with Fig. 5 (as shown on the scale), with the same spatial patterns and model-to-model differences apparent. However, the boundaries between UN dryland categories now occur at somewhat more regular intervals, and the scale is now able to saturate at more humid climates ( rather than 1.5) due to the compression, allowing more information to be retained without sacrificing any detail in the drier climates. The scale also provides a handy reference for converting between the two indices.

Fig. 11.

1981–99 alternate aridity index (right-hand scale) for each model and for the observations. The corresponding values (left-hand scale) and dryland categories are also shown for reference. Compare to Fig. 5.

Fig. 11.

1981–99 alternate aridity index (right-hand scale) for each model and for the observations. The corresponding values (left-hand scale) and dryland categories are also shown for reference. Compare to Fig. 5.

Figure 12 then maps the changes in between the 2081–99 and 1981–99 periods. As desired, the magnitudes are more spatially comparable than in Fig. 10, with high-latitude changes in particular becoming much less saturated, and subtropical changes becoming less washed out. Of course, the signs of the changes are still the same. If anything, the reduction in distracting wet-zone “noise” makes the overall global trend toward aridity in most models, and the fact that some models somewhat buck that trend, even clearer. The uniformly applicable scale also makes the changes more striking: everywhere that the color saturates, the modeled P versus PET balance is moving or more of the way from to or vice versa, the same as a change from semiarid to arid, or alternatively from Seattle to Dallas . Aridification of this magnitude seems to occur particularly often in the Amazon, southern Europe, and Mexico and vicinity, but can happen in many diverse terrestrial locations depending on the model. Similarly, humidification of this magnitude is most commonly projected in parts of Siberia, but can also occur in parts of South America, Africa, or in subarctic North America, depending on the model. However, even the more ordinarily projected change magnitudes of 0.05 to 0.10 are clearly consequential on the scale of Fig. 11, and the wide prevalence of declines of this magnitude throughout the tropics, subtropics, and midlatitudes is a worrisome prediction.

Fig. 12.

Changes in the alternate aridity index between 1981–99 and 2081–99, for each model.

Fig. 12.

Changes in the alternate aridity index between 1981–99 and 2081–99, for each model.

Another common 0-to-1-valued terrestrial wetness metric is the evaporative fraction (e.g., Koster et al. 2009; Gentine et al. 2011), the proportion of total upward turbulent heat flux made up by evaporation or latent heat (LH) rather than sensible heat (SH). As with , values closer to 1 imply more well-watered conditions, while values closer to 0 are consistent with insufficient water. The ratio is also an exact nonlinear function of the better-known but worse-behaved Bowen ratio , just as is to . However, unlike , the evaporative fraction is not purely a climate metric: LH and SH are at least proximately determined by the vegetation and soil, although their sum is constrained by the surface radiation balance. Equivalently, GCM (and GLDAS) LH and SH fields are produced by the land model, not by the atmospheric model (or data), and GCM land models still have great difficulty reproducing realistic LH (e.g., Sheffield et al. 2013).

However, it is still instructive to compare the two metrics. Figure 13 plots for each GCM and for the GLDAS, where LH and SH are 1981–99 annual means. The broad spatial patterns are quite similar to Fig. 11, with higher values in the tropics and high latitudes and lower values in the subtropical dry zones, although there is an unexplained tendency for lower values in GLDAS than in the GCMs, especially at higher latitudes. By plotting regional means of the two metrics against each other, Fig. 14 shows that and also agree extremely well on which GCMs are drier versus wetter in a given location; the correlations are always at least +0.89. This reassuringly implies that the GCM land models are consistently responding to climate forcing, though the unusually low values in GLDAS for a given are still apparent.

Fig. 13.

1981–99 evaporative fraction for each model and for the GLDAS observation-driven land model estimate.

Fig. 13.

1981–99 evaporative fraction for each model and for the GLDAS observation-driven land model estimate.

Fig. 14.

1981–99 regional-land-mean alternate aridity index vs evaporative fraction for each model (numbers) and for the observational products (asterisks), for each region. Values in parentheses are simple correlations of the 16 model points. For reference, less than is defined as hyperarid, to ⅙ as arid, ⅙ to ⅓ as semiarid, ⅓ to as dry subhumid, and more than as humid; see the scale of Fig. 11.

Fig. 14.

1981–99 regional-land-mean alternate aridity index vs evaporative fraction for each model (numbers) and for the observational products (asterisks), for each region. Values in parentheses are simple correlations of the 16 model points. For reference, less than is defined as hyperarid, to ⅙ as arid, ⅙ to ⅓ as semiarid, ⅓ to as dry subhumid, and more than as humid; see the scale of Fig. 11.

Will greenhouse warming responses of also follow greenhouse warming responses of ? One might not expect so, since for a constant surface-wetness state, fundamentally increases with warming due to the Clausius–Clapeyron equation (e.g., Hartmann 1994). For example, is much higher over tropical oceans than over high-latitude oceans, even though they are equally “wet.” This could offset some of the expected drying-induced declines in . Indeed, Fig. 15 shows that unlike in Fig. 12, variously increases or decreases with projected warming in the GCMs, with no clear sign preference. However, this neutrality still implies drying with warming, since warming alone (without any surface drying) would lead to systematic increases in as explained above. Also, the geographic patterns of the responses in Figs. 12 and 15 appear quite similar, although the signs may be different. Figure 16 shows that regional intermodel disagreements are also very consistent between responses and responses, just as they were for the metrics’ mean states; intermodel correlations are at least +0.86 in each region. Thus, in GCMs, the atmosphere/hydroclimate response to greenhouse warming seems very relevant for the land hydrologic response, increasing our confidence in the land models.

Fig. 15.

Changes in evaporative fraction between 1981–99 and 2081–99, for each model.

Fig. 15.

Changes in evaporative fraction between 1981–99 and 2081–99, for each model.

Fig. 16.

Regional-land-mean twenty-first-century change vs change, for each model and region. Values in parentheses are simple correlations of the model points.

Fig. 16.

Regional-land-mean twenty-first-century change vs change, for each model and region. Values in parentheses are simple correlations of the model points.

5. Summary and conclusions

The aridity of a terrestrial climate is generally quantified using the relative magnitudes of precipitation P and potential evapotranspiration PET. This study evaluates the climatologies and greenhouse-warming responses of terrestrial P, Penman–Monteith PET (1), and their dimensionless ratio (the aridity index) in 16 different CMIP5 global climate models. The climatologies generally agree in much of Eurasia and North Africa, but they disagree dramatically in large areas of the Americas, sub-Saharan Africa, South Asia, and elsewhere, with the same areas represented as semiarid-to-arid or quite humid by different models (Figs. 1, 2, 3, 5, and 7). In many of these areas, P and PET are much closer to the observations in some models than in others, and PET is often high in the same models for which P is low, strengthening the disagreements and biases.

The terrestrial P responses to warming tend to be positive at high latitudes, but an inconsistent and complex mixture of positive and negative elsewhere, counter to both naive expectations of more P in a warmer climate and ocean-inspired theories of strongly zonal P response to warming (Fig. 6). Since the Penman–Monteith PET responses to warming are uniformly and substantially positive in contrast (SF14 and Fig. 8), aridification ( decline) generally dominates over humidification ( increase) in the tropics, the subtropics, and the midlatitudes (Fig. 10), with varying spatial patterns. This is in marked contrast to the expectation from a “wet get wetter, dry get drier” rule, but strongly agrees with more recent studies (Dai 2013; Feng and Fu 2013; Cook et al. 2014). However, this global drying tendency is much less apparent in certain models.

The PET climatologies are also found to be sensitive to the computation time scale: except at high latitudes, the aerodynamic (right-hand) part of (1) is uniformly 20%–50% higher when computed using monthly rather than 3-hourly GCM output, making total PET 10%–30% higher in large areas (Fig. 4). However, contrary to the authors’ earlier suggestion (SF14), the responses to greenhouse warming are not as sensitive to this choice of input time scale, though there are large local differences in some models (Fig. 9). The use of diurnally averaged temperature to estimate the monthly-mean saturation vapor pressure (as done by the above studies, counter to standard procedure) does not change the general magnitude of any of these comparisons, though the details for the climatologies differ.

The same change in is much more meaningful when is low than when it is high. Therefore, an alternative index (Fig. 11), which carries the same information as but only varies from 0 to 1 , is also used to quantify the model aridities and responses to warming. Indeed, the responses of (Fig. 12) are more spatially comparable than those of (Fig. 10), with a more uniform interpretation. This alternative method better highlights aridity changes in all terrestrial regions, rather than disproportionately focusing on changes in wet or very dry places. These climatologies and changes are also consistent in many ways with evaporative fraction climatologies and changes (Figs. 1316), though the latter are fundamentally biased positive by the warming itself apart from any water-availability change, obscuring the aridity-related signal (Fig. 15).

One problem with this study, and with all the cited studies that use PET to think about the terrestrial response to greenhouse warming, is that PET is just a notional flux: it is never actually realized, except in irrigated or very humid settings. The authors are in the process of developing a new framework for thinking about the effect of warming when actual ET < PET. Preliminary results suggest that if the actual evaporative fraction is much less than the notional evaporative fraction from a wet surface, then the actual ET requirement for plants will have a higher percentage sensitivity to warming than will PET, because it will be less energetically constrained. Thus, the warming/drying result may become even stronger in this framework. However, it is also important to note that ambient carbon dioxide increases might reduce plant ET requirements (e.g., Sellers et al. 1996), introducing the opposite effect. Much more work needs to be done.

Finally, it is often suggested in the paleoclimate literature that warm greenhouse climates of the past are well watered and cold climates such as the last glacial maximum are arid, contrary to the conclusions above. Could model biases, either in land parameterizations or atmospheric physics parameterizations, be exaggerating the global drying tendency? The authors have work planned and in progress attempting to reconcile these perspectives with a combination of paleoclimate model analysis, moisture proxy meta-analysis, and idealized climate modeling. The resolution of this dilemma could greatly improve our understanding of the future of terrestrial aridity.

Acknowledgments

We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. J. S. would also like to thank the two anonymous reviewers for suggestions that greatly strengthened this paper. This work was supported by NSF Awards AGS-0846641, AGS-0936059, AGS-1359464, AGS-1433551, and PLR-1341497.

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