Abstract

A perturbed physics Hadley Centre climate model ensemble was used to study changes in drought on doubling atmospheric CO2. The drought metrics analyzed were based on 1) precipitation anomalies, 2) soil moisture anomalies, and 3) the Palmer drought severity index (PDSI). Drought was assumed to occur 17% of the time under single CO2. On doubling CO2, in general, PDSI drought occurs more often than soil moisture drought, which occurs more often than precipitation drought. This paper explores the relative sensitivity of each drought metric to changes in the main drivers of drought, namely precipitation and available energy. Drought tends to increase when the mean precipitation decreases, the mean available energy increases, the standard deviation of precipitation increases, and the standard deviation of available energy decreases. Simple linear approximations show that the sensitivity of drought to changes in mean precipitation is similar for the three different metrics. However, the sensitivity of drought to changes in the mean available energy (which is projected to increase under increased atmospheric CO2) is highly dependent on metric: with PDSI drought the most sensitive, soil moisture less sensitive, and precipitation independent of available energy. Drought metrics are only slightly sensitive to changes in the variability of the drivers. An additional driver of drought is the response of plants to increased CO2. This process reduces evapotranspiration and increases soil moisture, and generally causes less soil moisture drought. In contrast, the associated increase in available energy generally causes an increase in PDSI drought. These differing sensitivities need to be taken into consideration when developing adaptation strategies.

1. Introduction

Drought develops during or following periods of low accumulated precipitation relative to normal conditions and is exacerbated by high temperatures. Direct impacts include reduced crop yields, reduced water resources, and increased fire risk. These lead to many indirect and wide-ranging socioeconomic impacts. Drought events are carefully monitored in order to help manage impacts and to mitigate any associated losses. There are a wide range of drought metrics available that are commonly used for drought monitoring (Keyantash and Dracup 2002; http://drought.unl.edu/dm/monitor.html; Shukla et al. 2011). They usually depend on some combination of precipitation, temperature, potential evaporation, soil moisture, and runoff, and are more or less relevant depending on the drought impact of interest. Although the severity of a drought event can be quantified using a relevant drought metric, the impact of any particular event on society is not simply related to its severity and depends on the vulnerability of the community to dry conditions. The Drought Impact Reporter (http://droughtreporter.unl.edu/) is a first attempt at quantifying the socioeconomic impact of droughts in the United States and can be viewed alongside the Drought Monitor (http://drought.unl.edu/dm/monitor.html).

To develop mitigation and adaptation strategies, it is important to investigate how drought might change under future climate change scenarios. Global climate models (GCMs) project possible future changes in hydroclimatology (Meehl et al. 2007). GCMs can generally produce good simulations of present-day air temperature simulations (Meehl et al. 2007). However, the majority of GCMs have difficulty producing precipitation simulations consistent with observations (Covey et al. 2003; Koutsoyiannis et al. 2008). Moving from global scale to regional scale increases the uncertainty (Blöschl et al. 2007). One method of incorporating knowledge of this uncertainty is to use ensembles of climate model simulations that identify a range of possible GCM outputs (Murphy et al. 2004, 2007). Burke and Brown (2008) used output from two ensembles of climate model simulations—a large perturbed physics ensemble and a smaller multimodel ensemble—and found large uncertainties in projected changes in drought on doubling atmospheric CO2, particularly in regions where there is large uncertainty in the precipitation change. Wang (2005) used a multimodel ensemble to show an increase in agricultural drought in most parts of the northern subtropics and midlatitudes, but also found a large spread of values.

Internal climate variability can be large in some regions. For example, over Australia, there are multidecadal epochs with lots of drought events and multidecadal epochs that are wet (Verdon-Kidd and Kiem 2010, 2009). Stott (2003) utilized several centuries of climate model simulations in a stable climate and showed that the decadal variability in modeled regional temperatures is generally consistent with observations. However, Zhang et al. (2007) suggested that the models may also underestimate precipitation variability. Model ensembles are increasingly being combined to increase the sampled internal climate variability (e.g., Christidis et al. 2011). Since the majority of climate model simulations assessed are usually only a few tens of years long, they will only encompass a reduced range of multidecadal natural variability.

This paper uses a perturbed physics GCM ensemble to develop an understanding of the uncertainty in projections of changes in regional drought in the future. Ten tropical and midlatitude regions are discussed (see Fig. 2). Uncertainties in drought projections are shown to be a consequence of 1) the initial climate, 2) changes in the drivers of drought (mainly precipitation and available energy) in the future climate, and 3) the sensitivities of the drought indices to changes in the drivers. Section 2 describes the perturbed physics global climate model ensemble used to define the different drought metrics discussed in section 3. Section 4 derives the approximations used to define the relationships between changes in drought and its drivers. Section 5 uses these approximations to understand differences between the drought metrics under increased CO2.

2. Perturbed physics model ensemble

The perturbed physics model ensemble uses the Hadley Centre Atmospheric Model, version 3 (HadAM3) global circulation model (Pope et al. 2000) coupled to a 50-m nondynamic mixed-layer (“slab”) ocean [Hadley Centre Slab Climate Model, version 3 (HadSM3)]. Atmospheric resolution is 300 km with 19 levels. HadAM3 incorporates the Met Office Surface Exchange Scheme (MOSES) land surface scheme, which has a four-layer soil model with depths chosen to capture the important temperature cycles (Cox et al. 1999). The model ensemble consists of 225 members, which is the same as that analyzed by Betts et al. (2007). For each ensemble member, the steady state climate was simulated for 20 years under the preindustrial concentration of CO2 (1 × CO2; 280 ppm) and under a doubled concentration (2 × CO2; 560 ppm). A selection of 31 uncertain parameters was perturbed in combination, resulting in multiple parameter perturbations that influence the following processes: large-scale cloud, convection, radiation, boundary layer, dynamics, land surface processes, and sea ice (Murphy et al. 2007; Webb et al. 2006; Rougier et al. 2009; Collins et al. 2010), thus sampling uncertainties in all the major surface and atmospheric processes within the model. The use of a perturbed physics ensemble enables the modeling uncertainty in the predicted climate response to doubling CO2 to be incorporated. The impact of internal model variability on the results was assessed using 2000 years of the third climate configuration of the Met Office Unified Model (HadCM3) coupled climate control simulation (Johns et al. 2003; Burke et al. 2006).

The pertinent parameters perturbed within the land surface scheme are the dependence of plant responses to CO2 (a switch determining whether or not the plants respond physiologically to increased CO2) and the number of soil levels accessed for evapotranspiration (Rdepth). The number of soil layers accessed for evapotranspiration (Rdepth = 2, 3, or 4) significantly impacts the available soil water content, which has consequences on the hydrological cycle. The ensemble members with the deepest root depth simulate the most accurate global precipitation distribution under single CO2 (Rowell 2009). Therefore, as in Rowell (2009), only the ensemble members with the deepest root depth (Rdepth = 4) were used. A 37-member ensemble with no plant response to increased CO2, denoted RAD, is assessed in this paper. The plant physiological response to increased CO2 results in a decrease in stomatal conductance, a local decrease in evapotranspiration, a local increase in soil water content, and an additional increase in global mean temperature (Betts et al. 2007). The impact of this mechanism on drought under increased CO2 is explored by comparing RAD with a 48-member ensemble with plant physiological response to increased CO2, which is denoted RADPHYS.

3. Definition of drought

The drought metrics discussed here are based on time series of precipitation, available soil moisture, and the Palmer drought severity index (PDSI). The available soil moisture is defined as the amount of water in the root zone available for access by the plant. Both the precipitation and the available soil moisture are output directly by the GCM.

The PDSI was created by Palmer (1965) to provide the “cumulative departure of moisture supply” from the normal and is still commonly used as an operational drought index. Full details of the PDSI calculation can be found at the National Agricultural Decision Support System (http://greenleaf.unl.edu/downloads/). The PDSI is a hydrologic accounting scheme that uses a simple two-layer, bucket-type land surface scheme to partition the incoming precipitation into the components of the water balance. However, it does not account for the wide range of environmental conditions that may in reality occur such as frozen soil, snow, and the presence of roots and vegetation (Alley 1984). These processes are included within the land surface scheme in the GCM used to calculate the available soil moisture. The PDSI was calculated from the time series of precipitation and potential evaporation derived from the GCM, following the method described by Burke and Brown (2008) and Burke et al. (2006).

Another key difference between the calculation of the available soil moisture and the PDSI is the way in which feedbacks are incorporated. The available soil moisture is calculated within a fully coupled system, and as such provides feedbacks to the atmosphere that subsequently affect the precipitation and available energy. These changes lead to further changes in the GCM-output soil moisture. In contrast, the PDSI feels the effect of these feedbacks via the precipitation and available energy, but does not include the same processes that influence these feedbacks.

The aim of this paper is to develop a simple understanding of the drivers of drought under increased atmospheric CO2 for the three different drought metrics. To simplify the analysis as much as possible, time series of the annual drought metric were assessed. These represent long-term drought. In the quest for simplicity, possible effects on drought from changes in the seasonality of the drivers are not addressed here. In a single CO2 climate, a grid cell is assumed to be in drought during any year when the drought metric is one standard deviation or more below its long-term mean. Therefore, a threshold for drought (DT) can be defined as

 
formula

where σX(1xCO2) is the standard deviation of the annual drought metric and is the long-term mean of the annual drought metric in 1 × CO2. Anytime the drought metric falls below DT there is drought during that year; DT is defined independently for each location, drought metric, and ensemble member and, as in Burke et al. (2006), projected changes in drought are generally independent of its definition. It was assumed that the annual time series of precipitation, available soil moisture, and PDSI are normally distributed. This was tested using the 2000-year simulation of HadCM3, which provides a more robust sample of internal model variability. Given normal distributions, the likelihood of drought in a single CO2 climate can be found by converting to a standard normal and using lookup tables. This is, by construction, 0.17. This might not be a realistic approximation of actual drought occurrence for all of the regions studied, but the conclusions of this study are the same when a threshold of either 0.06 or 0.3 is used.

In a 2 × CO2 climate, the mean and standard deviation of the drought metric and, hence, the likelihood of drought will change in response to the increase in CO2. Since drought conditions are assumed to occur at the same threshold value (DT) the likelihood of drought in 2 × CO2 is found from the following standard normal variate:

 
formula

where σX(2xCO2) is the standard deviation of the annual drought metric and is the long-term mean of the annual drought metric in 2 × CO2 climate. After substituting Eq. (1) into Eq. (2) and simplifying:

 
formula

where is the change in the mean drought metric and Δσ is the change in the standard deviation of the drought metric on doubling CO2. The dependence of these two changes ( and Δσ) on changes in the two main drivers of drought (i.e., precipitation and available energy) is defined in the next section. This will then enable the changes in drought in 2 × CO2 to be directly related to changes in these drivers.

4. Dependence of changes in drought on its drivers

a. Precipitation drought

The only driver of changes in precipitation drought is a change in the nature of the precipitation—that is, long-term mean and standard deviation, location, frequency, and intensity of rain events, etc. Only changes in its long-term mean and standard deviation are considered here. These changes can be directly related to the likelihood of drought by substituting them into Eq. (3).

b. Soil moisture drought

Soil moisture is calculated by the complex land surface scheme within the GCM. This means that any relevant feedbacks from the atmosphere are taken into account. To more readily understand the relationship between soil moisture drought and its drivers, a simplified representation of the land surface scheme was derived. This was designed to replicate the behavior of the land surface within the GCM and is based on the work of Gedney et al. (2000).

1) Characteristics of the land surface

The relatively small range of available soil moisture within the land surface scheme enables both the runoff and evaporative fraction to be parameterized as a linear function of the available soil moisture (Gedney et al. 2000). The parameterization for runoff is given by

 
formula

where Y is the total runoff in mm day−1, Yc and Y′ are fitted parameters, and μ is the available soil moisture given by

 
formula

where β is the root zone soil moisture and is dependent on the depth of the root zone; βwilt is the soil permanent wilting point, below which there is no evapotranspiration; and βcrit is the soil critical point above which the evapotranspiration is not constrained by soil moisture. Both βwilt and βcrit are soil parameters defined from observations of soil properties (Cox et al. 1999).

The parameterization for evaporative fraction is given by

 
formula

where fc and f′ are fitted parameters and f is the evaporative fraction given by

 
formula

where E is the evapotranspiration (mm day−1) and Ae is the effective available energy (mm day−1):

 
formula

where RN, G, L, and Ei are the net radiation (W m−2), ground heat flux (W m−2), latent heat of vaporization (J kg−1), and the evaporation from the canopy (mm day−1), respectively. Equations (4) and (6) define the characteristics of the land surface in terms of four parameters: fc, Yc, f′, and Y′. These parameters were found independently for each ensemble member. In each case, a linear regression curve was fitted to the monthly runoff versus monthly available soil moisture relationship and to the seasonal evaporative fraction versus seasonal available soil moisture relationship. All data were output by the GCM and were fitted using both 1 × CO2 and 2 × CO2 data.

2) Soil moisture in a single CO2 climate

In a stable climate, on multiannual time scales a simple water balance for a land surface in equilibrium can be written as

 
formula

where Pe is the throughfall precipitation, E is evapotranspiration, and Y is runoff (all in mm day−1). The bars denote the multiannual means. The multiannual mean soil moisture availability can be derived by substituting versions of Eqs. (4), (6), and (7) into Eq. (9):

 
formula

Equation (10) defines the soil moisture availability in 1 × CO2 ().

The available soil moisture can be separated into a long-term mean component and a fluctuating component, where, in this example, the fluctuating component is the standard deviation of available soil moisture (Koster and Suarez 1999). The standard deviation is found from the time derivative of Eq. (10):

 
formula

where σP and σA are the standard deviations of the annual precipitation and annual available energy, respectively; is the value of the evaporative fraction at the long-term mean soil moisture availability (); and ζ is given by

 
formula

Equation (11) defines the standard deviation of soil moisture availability in 1 × CO2 climate [σX(1xCO2)].

3) Change in soil moisture on doubling CO2

An analogous equation to Eq. (11) gives the response of soil moisture availability to an increase in CO2 [ in Eq. (13) below and in Eq. (3)]:

 
formula

where and are the changes in the long-term mean precipitation and available energy, respectively. Similarly, the change in the standard deviation of the soil moisture availability [Δσμ in Eq. (14) and Δσ in Eq. (3)] under increased CO2 can be approximated by

 
formula

where ΔσP and ΔσA are the changes in the standard deviation of precipitation and available energy, respectively. Higher order terms are assumed to be negligible.

These highly simplified relationships can be used to determine the change in soil moisture drought on doubling CO2 as a function of 1) the standard deviation of precipitation and available energy in 1 × CO2, 2) changes in the characteristics of precipitation and available energy on doubling CO2, and 3) the four parameters describing the behavior of the land surface (fc, Yc, f′, and Y′).

4) Impact of stomatal response to increased atmospheric CO2

Equations (11), (13), and (14) only hold if the parameters fc, Yc, f′, and Y′ are independent of CO2 level. However, if plants close their stomata in response to increased atmospheric CO2, there is a reduction in transpiration and more water available at the land surface (Field et al. 1995). This changes the relationship between evaporative fraction and soil moisture [Eq. (6)]. Figure 1 shows the relationship between evaporative fraction and soil moisture availability for 1 × CO2 and 2 × CO2. In Fig. 1a the plants do not respond to increased atmospheric CO2 and fc and f′ are not significantly different for the two simulations. However, in Fig. 1b the plants are allowed to respond to increased atmospheric CO2 and the relationship is clearly dependent on CO2 concentration. It was assumed that the effect of the stomatal closure impacts the relationship between evaporative fraction and soil moisture equally at all values of the available soil moisture. Therefore, the slope of the relationship (f′) is independent of CO2 concentration, while the intercept (fc) decreases with increasing CO2 concentration. This mechanism is an additional driver of soil moisture drought.

Fig. 1.

The impact of the plant response to increased CO2 on the relationship between seasonal evaporative fraction and seasonal soil moisture for a sample ensemble member for Amazon (AMZ, see Fig. 2).

Fig. 1.

The impact of the plant response to increased CO2 on the relationship between seasonal evaporative fraction and seasonal soil moisture for a sample ensemble member for Amazon (AMZ, see Fig. 2).

To explore the sensitivity of drought to this mechanism, the dependence of fc on atmospheric CO2 concentration needs to be included in the derivative of Eqs. (10) and (11). When this is included, Eqs. (13) and (14) become

 
formula
 
formula

where Δfc is the change in fc on doubling CO2.

Plants may also respond to increased atmospheric CO2 concentration by increasing their leaf area index through CO2 fertilization (Owensby et al. 1999). There is some debate as to the magnitude of this effect and whether it is offset by the reduced stomatal conductance (Levis et al. 2000; Kergoat et al. 2002). In this paper it is assumed that the closure of the stomata in response to increased CO2 is the dominant factor and CO2 fertilization effects are negligible.

c. PDSI

The PDSI was calculated from the time series of precipitation and potential evaporation derived directly from GCM data. It is an “offline” model, which means that it is driven by the GCM data but does not feed back onto the GCM. The sensitivity of changes in PDSI drought to changes in the precipitation and available energy was evaluated by perturbing the drivers and recalculating the PDSI. The mean and standard deviation of the time series of precipitation [P(t)] were systematically perturbed as follows:

 
formula
 
formula

where α is a change in the mean precipitation and β is a multiplier used to rescale the standard deviation of precipitation. Similar equations can be written to perturb the time series of potential evaporation. The means and standard deviations of precipitation and potential evaporation were perturbed independently using realistic values of either α or β. These perturbations cause a change in both the mean and standard deviation of the calculated PDSI. After visual inspection, least squares regression techniques were used to fit linear relationships between changes in the mean and standard deviation of the PDSI and each of the four perturbations. The regression fits have R2 values of greater than 80%. These relationships were then substituted into Eq. (3) to calculate the dependence of the PDSI drought on changes in its drivers. This approach does not consider the second order effects of changes in PDSI drought as a result of interactions between the drivers.

A relationship between the change in potential evaporation and the change in available energy was derived so that the sensitivity of PDSI drought to atmospheric demand can be compared with the sensitivity of soil moisture drought to atmospheric demand. This was again (after visual inspection) done using a least squares regression between the changes in the mean GCM-calculated available energy and the changes in the mean GCM-derived potential evaporation (see also Gedney et al. 2000). Given these relationships, the sensitivity of PDSI drought projections to changes in precipitation and available energy were evaluated.

5. Results

a. Future projections of drought

Equation (3) was used to calculate the likelihood of drought in a double CO2 climate for the subset of the Giorgi and Francisco (2000) regions shown in Fig. 2. Giorgi and Francisco (2000) selected these regions subjectively based on size and climate. However, other regional configurations could be devised that might be more applicable to drought studies. Figure 3a shows a box-and-whisker plot of the percentiles of changes in the likelihood of drought across the model ensemble on doubling CO2 for each of the three drought metrics. The likelihood of drought in a single CO2 climate is, by construction, 0.17, but the changes in the likelihood of drought are similar when a threshold of 0.06 or 0.3 is used. Overall, there is considerable uncertainty in the likelihood of drought under double CO2, which, in some regions, can cover nearly the whole range of possible drought occurrence [e.g., the Amazon (AMZ), South Africa (SAF), and the Mediterranean (MED)]. Differences between the ensemble members are large, as are differences between the drought metrics. However, in general, the mean likelihood of PDSI-based drought under 2 × CO2 is significantly larger than the other measures of drought with, for some regions and for some ensemble members, drought occurring 100% of the time. Soil moisture and precipitation drought occur less frequently than PDSI drought, with a tendency for soil moisture drought to be more frequent than precipitation drought.

Fig. 2.

The subset of Giorgi and Francisco (2000) regions used within the analysis: CNA = central North America; CAM = Central America; AMZ = Amazon; WAF = western Africa; SAF = South Africa; MED = Mediterranean; SAS = southern Asia; SEA = Southeast Asia; NAU = northern Australia; SAU = southern Australia.

Fig. 2.

The subset of Giorgi and Francisco (2000) regions used within the analysis: CNA = central North America; CAM = Central America; AMZ = Amazon; WAF = western Africa; SAF = South Africa; MED = Mediterranean; SAS = southern Asia; SEA = Southeast Asia; NAU = northern Australia; SAU = southern Australia.

Fig. 3.

(a) The likelihood of dry years under a double CO2 climate for precipitation, available soil moisture, and PDSI found using the perturbed physics ensemble; and (b) the range of internal model variability found using the HadCM3 control simulation. The box represents the 25th to 75th percentile, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile of the ensemble spread. The horizontal line at 0.17 represents the likelihood of drought in the base climate—changes in drought are the same when a threshold of 0.06 or 0.3 is used. The gray lines across (b) show the range of internal model variability when 100-year-long simulations are evaluated.

Fig. 3.

(a) The likelihood of dry years under a double CO2 climate for precipitation, available soil moisture, and PDSI found using the perturbed physics ensemble; and (b) the range of internal model variability found using the HadCM3 control simulation. The box represents the 25th to 75th percentile, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile of the ensemble spread. The horizontal line at 0.17 represents the likelihood of drought in the base climate—changes in drought are the same when a threshold of 0.06 or 0.3 is used. The gray lines across (b) show the range of internal model variability when 100-year-long simulations are evaluated.

Figure 3b shows a similar analysis using the 2000-year HadCM3 control simulation to provide an estimate of internal climate variability. Two subsets of 37 20-year periods were randomly sampled and the proportion of time in drought is shown. As would be hoped, the ensemble mean shows little difference in drought between the two subsets (~0.17 for all cases). However, internal climate variability is relatively large, with time in drought for any particular region ranging from less than 0.05 to greater than 0.4. Comparing Fig. 3a and Fig. 3b suggests that, while for the majority of regions and ensemble members the changes in drought under 2 × CO2 are distinguishable from the internal climate variability, this is not universally the case.

The gray lines in Fig. 3b show that this range is approximately halved when 100-year simulations are used instead of 20-year simulations. This is because more dry periods are sampled, leading to an improved estimate of internal climate variability and more robust statistics. However, computational limitations mean that the GCM ensemble members are temporally limited.

The differences between ensemble members, regions, and drought indices shown in Fig. 3a are thus a consequence of 1) the nature of the single CO2 climates and their natural variability, 2) changes in the drivers of drought on doubling CO2, and 3) the sensitivities of the drought indices to changes in the drivers. These three factors are discussed in further detail below.

b. Drivers of drought and their change on doubling CO2

The main drivers of drought are the precipitation and available energy characteristics of a region. Figure 4 shows the 20-yr mean and standard deviation of annual precipitation ( and σP) and available energy ( and σA) for the single CO2 climate. The different regions encompass a range of climatologies with between 1.5 and 6 mm day−1 and between 2.5 and 5 mm day−1; σP is between 0.1 and 0.6 mm day−1. Regions with larger tend to have a larger σP and vice versa. As might be expected, σA is much smaller and relatively independent of region, with values around 0.05 mm day−1. Observed and σP for the period 1979–98 are also shown (Xie and Arkin 1997). The observations generally fall within the spread of the model ensemble, with the mean of the model ensemble wetter than the observations for six of the regions.

Fig. 4.

The multiannual mean precipitation (), standard deviation of annual mean precipitation (σP σP), multiannual mean available energy (), and standard deviation of annual mean available energy (σA) for the model ensemble under a single CO2 climate. The box represents the 25th to 75th percentile of the ensemble spread, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile. The line across the plots represents the observations for the period 1979–98.

Fig. 4.

The multiannual mean precipitation (), standard deviation of annual mean precipitation (σP σP), multiannual mean available energy (), and standard deviation of annual mean available energy (σA) for the model ensemble under a single CO2 climate. The box represents the 25th to 75th percentile of the ensemble spread, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile. The line across the plots represents the observations for the period 1979–98.

In Fig. 4, the ensemble spread is caused by a combination of uncertainties arising from the perturbed physics methodology and from internal model natural variability. As for Fig. 3b, the influence of natural variability was examined by subsampling the 2000-year HadCM3 control run. Available energy is not readily available from this simulation, so only precipitation was assessed. The impact of natural variability on precipitation is arguably greater than on available energy because GCMs find it easier to recreate regional temperature than regional precipitation (Koutsoyiannis et al. 2008). A subset of 37 20-year periods was randomly sampled. The spread in resulting from natural variability is only 10% of that in Fig. 4a, whereas the spread in σP is 75% of the spread in Fig. 4b. This suggests that the spread in is dominated by the physics perturbations, whereas natural variability has a more important role in the spread in σP.

Figures 5a,b show the changes in and σP on doubling CO2. The gray lines encompass the spread of precipitation values that might be expected from natural variability alone calculated in the same way as for Fig. 3b. The value of increases in CNA, WAF, SEA, and SAS and decrease in AMZ, SAF, and MED. In NAU, SAU, and CAM, any changes in are not readily distinguished from natural variability. Changes in σP generally fall within natural variability, although in CAM, SEA, and SAS, the increase in σP falls outside the range suggested by natural variability alone. Figure 5c shows an increase in for all regions and all ensemble members by between 0.1 and 0.3 mm day−1. This increase is expected to be much larger than any plausible increase from natural variability alone. In contrast, the change in σA is small and not significantly different from zero in any region. Its range is likely to be comparable with the range of natural variability. These drivers and their changes are related to the likelihood of drought on doubling CO2 via the simple linearization tools evaluated below.

Fig. 5.

The change in the multiannual mean precipitation, standard deviation of annual mean precipitation, multiannual mean available energy, and standard deviation of annual mean available energy for the model ensemble on doubling of CO2. The box represents the 25th to 75th percentile of the ensemble spread, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile. The gray lines represent the spread from natural variability.

Fig. 5.

The change in the multiannual mean precipitation, standard deviation of annual mean precipitation, multiannual mean available energy, and standard deviation of annual mean available energy for the model ensemble on doubling of CO2. The box represents the 25th to 75th percentile of the ensemble spread, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile. The gray lines represent the spread from natural variability.

c. Evaluation of linearization tools

1) Soil moisture drought

The ability of the simplified relationships to estimate the GCM output of [Eq. (10)], σμ [Eq. (11)], [Eq. (13)], and Δσμ [Eq. (14)] is shown in Fig. 6. Comparisons for all selected ensemble members and all regions are shown on one plot. Clearly there is excellent agreement between the modeled and estimated , with a RMSE of 0.037 and a bias of 0.018. Despite the simplifying assumptions the agreement for σμ is still good, with a RMSE of 0.017 and a bias of 0.004. The simplification is equally good for all regions. Both and Δσμ are small but adequately predicted by the simplified models, with RMSE of 0.022 and 0.013 and a bias of −0.004 and −0.006, respectively. Sources for the scatter in these three later relationships are discussed in detail in Koster and Suarez (1999) but it should be noted that interannual variations in storage are assumed to be negligible. As discussed earlier, estimating the standard deviations from just 20 years of data is another source of uncertainty.

Fig. 6.

The mean and standard deviation of soil moisture in a single CO2 climate and their changes on doubling CO2 using the simple linearization compared with the GCM output.

Fig. 6.

The mean and standard deviation of soil moisture in a single CO2 climate and their changes on doubling CO2 using the simple linearization compared with the GCM output.

The likelihood of soil moisture drought in 2 × CO2 was calculated using the output from the simple characterization and Eq. (3). Table 1 shows the adequate agreement between the GCM-derived and the simple characterization-derived soil moisture drought. The RMSE and bias for the ensemble are both of the order 0.1 or less. In general, the approximation accurately estimates soil moisture drought in NAU and WAF. There is some noise in the estimates over AMZ, CAM, MED, and SEA but little bias. This is partly because the changes in drought are generally larger in these regions (Fig. 3). In SAU, SAF, and SAS, drought is slightly underestimated by the approximation and in CNA it is slightly overestimated. Table 1 shows the errors in the simplified estimate of soil moisture drought fall within the spread of projected changes in drought.

Table 1.

The minimum and maximum soil moisture drought in 2 × CO2 derived directly from the GCM ensemble. Also shown is the RMSE and bias between the GCM model output and the linearization for the ensemble members. A positive bias means that the simplification underestimates drought and vice versa.

The minimum and maximum soil moisture drought in 2 × CO2 derived directly from the GCM ensemble. Also shown is the RMSE and bias between the GCM model output and the linearization for the ensemble members. A positive bias means that the simplification underestimates drought and vice versa.
The minimum and maximum soil moisture drought in 2 × CO2 derived directly from the GCM ensemble. Also shown is the RMSE and bias between the GCM model output and the linearization for the ensemble members. A positive bias means that the simplification underestimates drought and vice versa.

2) PDSI drought

The linearization of the relationship between change in PDSI drought and change in its drivers was evaluated. This was done independently for each driver (, σP, , and σA) by comparing with the output from the PDSI calculation forced by the appropriately perturbed driver. Table 2 shows that changes in σP and σA have little effect on drought—ensemble mean drought under 2 × CO2 is very similar to its 1 × CO2 value. However, the increase in shown in Fig. 5 results in a large increase in drought, and the changes in result in some change in drought with the sign the same as the sign of the change of . Table 2 shows that the RMSE and bias between the two methods of calculating the PDSI drought are small for σP and σA. This should be expected because of the small changes in drought. Errors in the estimation of drought with changes in are similar to those shown in Table 1 for soil moisture drought. Errors associated with changes in are larger not only because the changes in drought are larger, but also because there is a two-step approximation involved between the change in , the change in potential evaporation, and the change in PDSI drought. Although some errors are introduced by these approximations, this methodology is accurate enough to compare the sensitivity of PDSI drought with that of the other drought metrics.

Table 2.

The impact of each driver of drought on the ensemble mean PDSI drought in 2 × CO2. The mean drought in 2 × CO2 is shown. Drought in 1 × CO2 is 0.17. Also shown is the RMSE and bias between the GCM drought and the linearized drought calculated by assuming only the named driver changes in 2 × CO2. A positive bias means that the linearization underestimates drought and vice versa.

The impact of each driver of drought on the ensemble mean PDSI drought in 2 × CO2. The mean drought in 2 × CO2 is shown. Drought in 1 × CO2 is 0.17. Also shown is the RMSE and bias between the GCM drought and the linearized drought calculated by assuming only the named driver changes in 2 × CO2. A positive bias means that the linearization underestimates drought and vice versa.
The impact of each driver of drought on the ensemble mean PDSI drought in 2 × CO2. The mean drought in 2 × CO2 is shown. Drought in 1 × CO2 is 0.17. Also shown is the RMSE and bias between the GCM drought and the linearized drought calculated by assuming only the named driver changes in 2 × CO2. A positive bias means that the linearization underestimates drought and vice versa.

d. Sensitivity of drought to its drivers

The sensitivity of drought to each of its drivers was found by systematically adjusting the driver of interest and setting the changes in all of the other drivers to zero. Figure 7 shows all of the ensemble members for a representative region: SAF. In general, a decrease in , increase in σP, increase in , and decrease in σA all result in an increase in drought. The spread shown in Fig. 7 is independent of the magnitude of the change in the drivers and is dependent on a combination of modeling uncertainty and natural variability in the 1 × CO2 climate.

Fig. 7.

The sensitivity of precipitation, soil moisture, and PDSI drought to changes in the mean and standard deviation of precipitation and available energy characteristics for a representative region: SAF. The gray lines represent the different ensemble members and the black line represents the member with the largest standard deviation of precipitation in 1 × CO2.

Fig. 7.

The sensitivity of precipitation, soil moisture, and PDSI drought to changes in the mean and standard deviation of precipitation and available energy characteristics for a representative region: SAF. The gray lines represent the different ensemble members and the black line represents the member with the largest standard deviation of precipitation in 1 × CO2.

Changes in precipitation drought are solely dependent on changes in the precipitation characteristics. Figures 7a,b shows that precipitation drought is most sensitive to changes in and only slightly sensitive to changes in σP. Under increased CO2, Fig. 5 shows an increase in that will result in an increase in other forms of drought, so precipitation drought under 2 × CO2 is less than the other types of drought that are sensitive to available energy. Figures 7c,d show that the sensitivity of soil moisture drought to changes in and Δσμ is comparable to the sensitivity of precipitation drought. However, soil moisture drought is also relatively sensitive to changes in (Fig. 7e). The sensitivity of soil moisture drought to changes in σA (Fig. 7f) is small, but has a consistent direction of response. As is the case for soil moisture drought, PDSI drought is mainly sensitive to changes in the means of the drivers and minimally sensitive to changes in the standard deviations. Figure 7 suggests that PDSI drought may be more sensitive to changes in than it is to changes in . Its sensitivity to changes in the standard deviation is very small, and an increase in standard deviation can cause either a slight increase or a slight decrease in PDSI drought, depending on ensemble member. The overall pattern of sensitivities shown in Fig. 7 (i.e., a high sensitivity to any change in the mean and a low sensitivity to any change in the standard deviation) is independent of region.

Figure 8 enables a further comparison of the sensitivities for the different regions and metrics. Since the sensitivities to changes in the standard deviations are relatively small, only sensitivities to changes in the means are shown. Figure 8 shows the increase in drought after 1) a 0.1 mm day−1 decrease in and 2) a 0.1 mm day−1 increase in for each of the different regions. The increase in drought as a result of a decrease in is fairly similar for all three drought metrics and all regions with a spread of ~0.2. Soil moisture drought is slightly more sensitive to changes in than is precipitation drought. This increased sensitivity is associated with the parameterization of the land surface. There is a small dependence of the different drought metrics on region. For example, drought in the MED is slightly more sensitive to changes in than drought in SEA. Figure 8b shows the sensitivity of drought to increased . Precipitation drought is independent of direct changes in . The increase in PDSI drought is significantly larger than the increase in soil moisture drought. This is because the PDSI calculation results in a faster loss of water in response to increased atmospheric demand than the land surface scheme within the GCM. There is some dependence of both PDSI and soil moisture drought on region and a small spread in values within each region.

Fig. 8.

The change in the three different drought metrics for (a) a 0.1 mm day−1 decrease in precipitation and (b) a 0.1 mm day−1 increase in available energy.

Fig. 8.

The change in the three different drought metrics for (a) a 0.1 mm day−1 decrease in precipitation and (b) a 0.1 mm day−1 increase in available energy.

The cause of the spread of the likelihood of drought within a region and differences between regions was explored further for precipitation and soil moisture drought. Figure 7 highlights the ensemble member with the largest σP under a 1 × CO2 climate in black. This member has low sensitivity to the change in driver, irrespective of the driver. Figure 9 shows the relationship between σP in 1 × CO2 and the likelihood of drought for the specified change in driver; the changes in all other drivers being set to zero. Three regions are shown (SAF, MED, and NAU). In the case of precipitation drought, any changes are solely a function of σP in 1 × CO2 and independent of region [by definition from Eq. (3)]. Figures 9a,b shows that a large σP in the 1 × CO2 climate results in smaller increase in precipitation drought, given a prescribed increase in either or σP. The value of σP in 1 × CO2 is a function of regional climate, modeling uncertainty, and internal model variability. In the case of soil moisture drought, Fig. 9 shows changes in drought are a function of both σP in 1 × CO2 and region, although the influence of σP in 1 × CO2 appears greater than any differences between regions. This is independent of whether the prescribed change is a change in precipitation or available energy characteristics. However, the contributions of both the land surface and σA in 1 × CO2 are obviously larger with a prescribed change in available energy.

Fig. 9.

The relationship between the standard deviation of annual precipitation in a single CO2 climate and the likelihood of drought for a prescribed change in each driver for the precipitation and soil moisture drought metrics.

Fig. 9.

The relationship between the standard deviation of annual precipitation in a single CO2 climate and the likelihood of drought for a prescribed change in each driver for the precipitation and soil moisture drought metrics.

The simple definitions of precipitation and soil moisture drought used here enable their sensitivity to a 1 × CO2 climate to be readily assessed. This is not the case for PDSI drought, and such a sensitivity analysis for PDSI drought is beyond the scope of this paper.

e. Plant response to increased CO2

The closure of stomata in response to increased atmospheric CO2, denoted the physiological forcing, is an additional mechanism that affects drought. This process results in a local reduction of transpiration and a local increase in water availability. The local responses feed back into the climate system and cause a further increase in global mean temperature (Betts et al. 2007). Any changes in precipitation and available energy characteristics may be modified by these large-scale feedbacks. This mechanism will impact all three drought metrics but in different ways. Table 3 shows the ensemble mean change in drought on doubling atmospheric CO2 for the RAD (no physiological forcing) and RADPHYS (physiological forcing) ensemble. There are only significant differences in drought for some of the regions and some of the metrics. Any difference in precipitation drought between RAD and RADPHYS is solely a result of the feedbacks to the climate system that modify changes in the precipitation characteristics. Differences in soil moisture drought between RAD and RADPHYS are caused by a combination of the local increase in water availability and the large-scale feedbacks that cause additional changes in the drivers of drought. The local increase in water availability at the land surface will lead to a reduction of soil moisture drought. Table 3 shows a significant decrease in soil moisture drought for several of the regions for RADPHYS compared with RAD. In other regions, the combination of additional feedbacks as a result of the physiological forcing and the local increase in soil water availability results in no significant differences between soil moisture drought in RAD and RADPHYS.

Table 3.

The ensemble mean change in drought in 2 × CO2 with (RADPHYS) and without (RAD) the plant response to increased atmospheric CO2. The regions and metrics where the RAD and RADPHYS ensembles are significantly different at >90% level are shown in bold.

The ensemble mean change in drought in 2 × CO2 with (RADPHYS) and without (RAD) the plant response to increased atmospheric CO2. The regions and metrics where the RAD and RADPHYS ensembles are significantly different at >90% level are shown in bold.
The ensemble mean change in drought in 2 × CO2 with (RADPHYS) and without (RAD) the plant response to increased atmospheric CO2. The regions and metrics where the RAD and RADPHYS ensembles are significantly different at >90% level are shown in bold.

The direct effect of the plant response to increased atmospheric CO2 and its impact on soil moisture drought can be parameterized by a change in the intercept of the relationship between soil moisture availability and evaporative fraction—that is, a change in fc in Eq. (6) (illustrated by Fig. 1b). Figure 10 shows a box plot of the change in fc for the RADPHYS ensemble on doubling CO2. These changes are usually decreases and cover a large range of values from zero to a decrease of ~30% in the value of fc. In general, the regions with the larger leaf area index (AMZ, WAF, and SEA) have the largest spread of Δfc and have ensemble members with the largest decrease. Figure 10 shows there are a wide range of modeled values of Δfc that are a function of different climates and different changes in climate. This spread falls within the wide range discussed in the literature (Bernacchi et al. 2007; Morison 1998; Medlyn et al. 2001). The sensitivity of soil moisture drought to Δfc was found using Eqs. (15) and (16) substituted into Eq. (3). Figure 11 shows this sensitivity for a representative region: SAF. Since fc is expected to reduce with increasing CO2, only these values are shown. A relatively small change in fc will result in a significant reduction of drought. As for Fig. 9, the spread of drought at any given value of Δfc is mainly dependent on σP in 1 × CO2 and less dependent on the region under consideration.

Fig. 10.

The change (usually decrease) in fcfc) along with its spread as a result of doubling CO2 concentration for the ensemble members that include plant response to increase CO2 for each region. The box represents the 25th to 75th percentile, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile.

Fig. 10.

The change (usually decrease) in fcfc) along with its spread as a result of doubling CO2 concentration for the ensemble members that include plant response to increase CO2 for each region. The box represents the 25th to 75th percentile, the line within the box represents the mean value, and the whiskers represent the 10th to 90th percentile.

Fig. 11.

The sensitivity of drought to changes in fc for SAF.

Fig. 11.

The sensitivity of drought to changes in fc for SAF.

Table 3 shows that the PDSI projects increased drought for nearly all of the regions for the RADPHYS ensemble compared with the RAD ensemble; this is statistically significant for three of the regions. The PDSI calculation does not include the response of stomata to increase atmospheric CO2 and consequent increase in water availability at the land surface. Therefore, any differences in PDSI drought between RAD and RADPHYS are solely a result of the large-scale feedbacks within the climate model that modify changes in both precipitation and available energy characteristics. The feedbacks cause an increase in global temperature and an increase in global available energy. This additional global increase results in available energy in an increased global PDSI drought occurrence in RADPHYS compared with RAD.

6. Discussion and conclusions

This paper follows a study by Burke and Brown (2008) that shows large ranges in the projected changes in drought under double atmospheric CO2. It shows that drought under increased CO2 is dependent on the characteristics of the present-day climate and its natural variability, any changes in climate, and the sensitivity of the drought metrics to these changes. In particular, a model that provides a good regional estimate of the variability of precipitation in the present-day climate will help reduce the uncertainty of drought projections under future climate change scenarios.

Simplistic approximations were made to determine the sensitivity of three different drought metrics (based on precipitation, soil moisture, and the PDSI) to the main changes in the drivers of drought: namely precipitation and available energy characteristics. Only changes in the means and standard deviations were considered, but other factors such as changes in intensity of precipitation or the sequence of wet and dry days may well be relevant. In general, drought increases when the mean precipitation decreases, the mean available energy increases, the standard deviation of precipitation increases, and the standard deviation of available energy decreases. All three drought metrics have similar sensitivity to changes in mean precipitation and are only slightly sensitive to changes in the standard deviation of either precipitation or available energy. However, the sensitivities of the different metrics to changes in the mean available energy, which is projected to increase under increased atmospheric CO2, are very different. Precipitation drought is independent of available energy. Soil moisture drought has some sensitivity and PDSI drought is highly sensitive to changes in available energy. This greater sensitivity of PDSI drought to changes in available energy may well explain the differences noted by Sheffield and Wood (2007) between a global soil moisture drought index and a global PDSI (Dai et al. 2004) over the period 1950–2000. They found a small wetting trend in global soil moisture, whereas the PDSI has a significant global drying trend. The sensitivity of soil moisture drought to its drivers is likely to depend on the land surface scheme used (Gedney et al. 2000) and will cause additional uncertainty when using different climate models.

The response of plants to increased atmospheric CO2 is an additional driver of drought. It causes a local increase in water availability and global feedbacks onto the drivers of drought. Precipitation and PDSI drought are not sensitive to the local increase in water availability caused by changes in this driver, but they are impacted by the feedbacks that modify the precipitation and available energy. In particular, these feedbacks generally act so as to increase available energy further and increase PDSI drought. Soil moisture drought is additionally sensitive to the local increase in water availability, which acts so as to reduce drought. Methods need to be developed to quantify the impact of this local increase in water availability on PDSI drought. This could be done, for example, by including the change in the stomatal response in the calculation of potential evaporation using the method proposed by Bell et al. (2011).

This paper demonstrates how more detailed knowledge of GCMs and their internal climate variability is important when developing methods to evaluate the impact of climate change on drought. Results are shown for several different regions and the methodology has not been optimized for any particular region. There will be better ways of defining and assessing drought given information on the variability and mechanisms of drought within any specific region. In addition, local knowledge on key vulnerabilities will enable the most relevant thresholds and metrics to be defined and assessed. For example, Verdon-Kidd and Kiem (2010) provide a comprehensive assessment of the mechanisms of drought (see also Barros and Bowden 2008) and the impacts of drought on the local community in southeastern Australia—a region of agricultural, social, and economic importance that has suffered three intense and protracted drought events over the past century (Verdon-Kidd and Kiem 2009). Such information, plus an assessment of key GCM uncertainties and consideration of the most appropriate drought metric, will help define a method for understanding and quantifying future drought risk.

Acknowledgments

This work was supported by the Joint DECC and Defra Integrated Climate Programme—DECC–Defra (GA01101). Acknowledgments to the QUMP team at the Met Office Hadley Centre who created the multiparameter ensemble and the two anonymous reviewers who provided some constructive insights.

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