Assessing the Risk of Persistent Drought Using Climate Model Simulations and Paleoclimate Data
| By Meko, David M | |
| Proquest LLC |
ABSTRACT
Projected changes in global rainfall patterns will likely alter water supplies and ecosystems in semiarid regions during the coming century. Instrumental and paleoclimate data indicate that natural hydroclimate fluctuations tend to be more energetic at low (multidecadal to multicentury) than at high (interannual) frequencies. State-of-the-art global climate models do not capture this characteristic of hydroclimate variability, suggesting that the models underestimate the risk of future persistent droughts. Methods are developed here for assessing the risk of such events in the coming century using climate model projections as well as observational (paleoclimate) information. Where instrumental and paleoclimate data are reliable, these methods may provide a more complete view of prolonged drought risk. In the U.S. Southwest, for instance, state-of-the-art climate model projections suggest the risk of a decade-scale megadrought in the coming century is less than 50%; the analysis herein suggests that the risk is at least 80%, and may be higher than 90% in certain areas. The likelihood of longer-lived events (>35 yr) is between 20% and 50%, and the risk of an unprecedented 50-yr megadrought is nonnegligible under the most severe warming scenario (5%-10%). These findings are important to consider as adaptation and mitigation strategies are developed to cope with regional impacts of climate change, where population growth is high and multidecadal megadrought-worse than anything seen during the last 2000 years-would pose unprecedented challenges to water resources in the region.
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1. Introduction
Information recorded in paleoclimate archives reveals that the twentieth century does not represent the full range of drought variability experienced in western
Prolonged droughts have happened during the instru- mental era and include the 1930s Dust Bowl (Fye et al. 2003), drought in sub-Saharan Africa (e.g., Charney 1975; Folland et al. 1986), and the recent ''Big Dry'' in
This paper estimates future prolonged drought risk using information from instrumental records, paleo- climate archives, and climate model simulations in simple
1) Coupled global climate model simulations of the twenty-first century present a realistic view of the direction, magnitude, and uncertainty in forced pre- cipitation changes, relative to today.
2) Paleoclimate records and observational data can empirically describe the distribution of variance across the frequency spectrum from interannual to multidecadal time scales in regional hydroclimate.
3) Simple models of time series are adequate for simulating the local statistical characteristics of hy- droclimate across interannual to multidecadal time scales, regardless of whether these characteristics are externally forced or internally generated.
Justifications for statements 1 and 2 are straightfor- ward: state-of-the-art models agree that semiarid sub- tropical regions throughout the world will tend to dry under climate change (e.g., Diffenbaugh and Giorgi 2012), and paleoclimate records, especially tree rings, are reasonably well validated and widely used to char- acterize variations of the past for a wide range of water resource management applications (Meko et al. 2012).
Assumption 3 in the list above deserves further elab- oration. We begin by noting that in western
The scenario delineated above is shown schematically in Fig. 1. Here, an idealized time series of some hydro- logical variable (say P 2 E) has been generated with unit variance and a mean of zero for the first 100 ''years'' (Fig. 1a). At year 101 the mean is shifted by 20.25s and an additional 50 years of data are generated while the variance stays the same. Figures 1b and 1c show re- alizations of 50 yr of data with the same mean and var- iance as the final 50 yr of the series in Fig. 1a. Although both the time series in Figs. 1b and 1c have the same mean and variance, a prolonged period of time with low values (a ''megadrought'') is found in the first re- alization (Fig. 1b), whereas in the second realization (Fig. 1c) it is not.
Implied by Fig. 1 is the possibility that deterministic simulations of climate change using state-of-the-art numerical models may be insufficient for estimating megadrought risk because the ensemble sizes of such experiments are relatively small (tens of realizations per model at most), and the statistics of infrequent events such as megadroughts might not be robust. Using a multimodel ensemble does not completely guard against this limitation because model simulations disagree on the expression of forced changes in hydroclimate at re- gional scales (e.g., Diffenbaugh and Giorgi 2012). In- stead, we use large ensembles of stochastic variables to emulate the statistics of interannual to decadal vari- ability, and output from global climate models to esti- mate how precipitation is expected to change this century. The limitations and possible implications of this assumption are discussed in section 4.
2. Data and methods
To establish benchmarks for decadal drought and multidecadal megadrought, we use instrumental pre- cipitation data (Fig. 2; Mitchell and Jones 2005), and several recent reconstructions of hydroclimate including the Palmer drought severity index (PDSI) for the southwestern
a. Standardizing hydroclimate indicators
Here we develop a systematic approach to normali- zing hydroclimate fluctuations so that they retain their essential meaning whether they originate from cli- mate model simulations, observational datasets, or paleoclimate reconstructions. We further seek to dis- tinguish between decadal droughts, which have been experienced during the instrumental era (e.g., the 1930s Dust Bowl), and multidecadal megadrought events that are outside the range of variability experienced during the twentieth century. To begin, we consider two of the worst decade-scale droughts during the twentieth cen- tury: the 1930s Dust Bowl and the 1950s Southwest drought. Both of these intervals can be identified as 20.5s departures in the decadal (11-yr) running mean of precipitation (Fig. 2).
Identifying 20.5s events in the 11-yr means of paleo- climate records requires us to normalize these time series to exhibit unit variance over the twentieth cen- tury, so that fluctuations in the past are scaled relative to this baseline period. To that end we represent the entire
... (1)
where F(t) is reconstructed flow and m^ and s^ are the mean and standard deviation, respectively, of the annual data over the reference period of 1950-2000 CE. The time series of Z^(t) is a modified z score of F(t), and its values through time are shown in Fig. 3a. Identifying intervals of 20.5s departures in the running 11-yr mean highlights the 1150s, as well as several other low-flow decades, which occur about once per century (gray vertical bars). Time series from other recent drought studies (Cook et al. 2004; Stahle et al. 2011), normalized in the same way, are also shown in Figs. 3b and 3c. They suggest that the preindustrial rate of comparable decade-long droughts is ;1.5% century21, which is quite consistent with the literature-based estimate of 1%-2% century21 of Woodhouse and Overpeck (1998).
Our definition of decadal drought captures major in- tervals of aridity during the twentieth century as well as others during the last millennium (Figs. 3 and 2). We employ a second and more stringent criterion to identify multidecadal megadrought. In this case, 20.5s de- partures in the 35-yr mean are identified. Although this definition is somewhat arbitrary, it is useful because the thresholds employed are both longer in time and greater in magnitude than the descriptions of Meko et al. (2007) and Cook et al. (2007) used to characterize the worst droughts of the past millennium in
b.
With the definitions of ''decadal drought'' (an 11-yr, 20.5s event) and ''multidecadal megadrought'' (a 35-yr, 20.5s event) that we have outlined above, we now de- velop ''null'' expectations for the rate at which these events would occur from random chance under a station- ary climate, but with three different assumptions about the underlying frequency characteristics of hydroclimate variability on interannual to centennial time scales.
We begin by examining the statistics of prolonged drought when interannual hydroclimate fluctuations are simulated as normally distributed white noise with unit variance and standard deviation. An example of one such time series, Xw(t) is shown in Fig. 5. The decadal drought statistics of this type of noise, obtained from 1000 white noise realizations (each of length 100 years), are summarized in Fig. 6. If the distribution of variance across the hydroclimatic continuum were indeed white, then decadal droughts would be expected to occur at a rate of slightly , 1 (100 yr)2 1 (Fig. 6a), and the risk of such an event occurring during any given 50-yr period would be around 45% (Fig. 6b). The likelihood of a multidecadal megadrought during any given 50-yr period would be only about 0.45% (Fig. 6b). This pre- liminary
Although raw precipitation tends to have a white spectrum on interannual time scales (e.g., Vasseur and Yodzis 2004; Ault and St George 2010), the underlying continuum of hydroclimate may be somewhat ''redder'' in WNA (Cayan et al. 1998; Ault and St George 2010; Ault et al. 2012, 2013). Moreover, drought indices typi- cally have a source of built-in autocorrelation to ac- commodate the reality that surface moisture stores depend on their prior states (i.e., they have ''memory''). For example, PDSI models the surface water balance using a simplified approximation of soil moisture, and has a built-in autocorrelation function (e.g., Alley 1984; Wells et al. 2004). Similarly, the standardized pre- cipitation index (SPI) integrates anomalies over a num- ber of predefined lags to measure how aggregated rainfall anomalies deviate from their long-term averages.
In a simplistic sense, year-to-year persistence can be described as a first-order autoregressive [AR(1)] process [XAR(1)(t)]:
... (2)
where a is the lag-1 (i.e., 1 yr) autocorrelation coefficient and is derived empirically from data, XAR(1)(t) is au- toregressive red noise, and Xw(t) is the white noise input. In WNA, the value of a is about 0.3 on interannual time scales for the three (tree ring based) paleoclimate re- constructions shown in Fig. 3, as well as for many other hydroclimate indicators (Ault et al. 2013). A single re- alization of this type of noise (normalized to exhibit unit variance overall) is shown in Fig. 5, and the statistical characteristics of megadroughts in this type of noise are shown in Fig. 6.
Despite the intuitive and simple representation of hydroclimate as an AR(1) process-moisture deficits tend to persist through time-there is some evidence that such an approximation misses key characteris- tics of variability on longer time scales (Pelletier and Turcotte 1997; Kantelhardt et al. 2006; Koscielny- Bunde et al. 2006; Ault et al. 2013). As a complemen- tary approach, we also simulate hydroclimate as a process with underlying frequency characteristics that are described by a weak power-law relationship between frequency f and variance S( f ), such that S( f ) } f2b. Power spectra with higher values of b cor- respond to time series that exhibit more variance at lower frequencies. To generate time series with this type of frequency behavior, we employ a method similar to the one described by Pelletier and Turcotte (1997) and explained thoroughly in Pelletier (2008). First, we calculate the discrete Fourier transform of a white noise time series Xw( t), and filter it to conform to a predefined value of b:
... (3)
where k are the standard Fourier frequencies and N is the length of the time series. The term ck rescales the Fourier coefficients so that they are approximately power-law distributed:
... (4)
Here the value of b is divided by 2 because it is being applied to the raw Fourier coefficients, which have am- plitudes proportional to the square root of the power spectrum.
The rescaled Fourier series X~ p (k) is then used to generate power-law time series Xp(t) by taking the real part of the inverse Fourier transform of X~ p (k):
... (5)
Finally, the mean and variance are restored to the values of the original white noise data (zero and unity, in this case).
We used a value of 0.5 for b to rescale each realization of Xw(t), which was suggested as an appropriate estimate by Ault et al. (2013) from synthesis of tree-ring re- constructions of precipitation, PDSI, and streamflow as well as non-tree-ring estimates of hydroclimate. As a check, we calculated the power laws of the noises after they had been rescaled. We found that the actual values of b varied from one realization to the next, but were generally between 0.4 and 0.6. This range agrees well with instrumental and paleoclimate estimates of this parameter for the region, and is certainly within the observational uncertainty (Ault et al. 2013). Impor- tantly, time series with spectra scaled by power laws of ;0.5 will also appear to exhibit autocorrelation of about 0.3, which in turn implies that the AR(1) and power-law realizations will behave very similarly on short time scales, but not necessarily on longer ones (e.g., Pelletier and Turcotte 1997; Ault et al. 2013). Finally, our use of power-law noises does not make any assumptions about the underlying climate dynamics governing the shape of the power spectrum of hydroclimate: linear and non- linear processes alike may produce such spectral distri- butions (Milotti 1995; Penland and Sardeshmukh 2012).
Table 1 highlights a few key features of the two models employed here. In particular, the noise models used to estimate drought risk use parameters that do not vary across space, and all are scaled to the twentieth- century mean and variance. The autocorrelation parameter of 0.3 is a middle-of-the-road value from the time series shown in Fig. 3, and is well within the range of estimates for autocorrelation in the region from other paleo- climate and observational datasets (Ault et al. 2013). The value used for b (0.5) is from the analysis of proxy records in
Sample time series and statistics of power-law re- alizations of drought (Figs. 5 and 6, respectively) reveal the importance of low-frequency variability in shaping prolonged drought risk. Over the time scale of 50 years, the white, AR(1), and power-law noises are all re- markably similar to each other [because the initial re- alization of Xw(t) is rescaled to produce both XAR(1)(t) and Xp(t)]. On the time scale of a millennium (Fig. 5b), the low-frequency differences are more apparent. The running 11-yr mean of each noise type (Fig. 5b)makes the implications for risk clear: the AR(1) and power- law time series spend more time in drought and depict higher levels of risk for megadrought. In Fig. 6a,itis also clear that the fraction of time spent in decadal drought conditions is about 17% for the power-law noise realizations, as opposed to 10% for the AR(1) simulations, and less than 5% for the white noise time series. Although the AR(1) and power-law time series exhibit similar likelihoods that a single decadal drought will occur during any given 50-yr period, the power-law series yields events that persist for longer. Drought risk on longer time scales, however, is clearly far higher for the power-law distributed time series than for the other two, with the risk of a 35-yr (20.5s) megadrought being greater than 16% for any given 50-yr segment. We stress that these risks apply to a stationary climate with no local feedbacks or externally forced changes. They are therefore our most conservative baseline estimates of prolonged drought risk during the coming century.
c. Projected risk of persistent drought in CMIP5 simulations
Our definition of megadrought is easily extended to climate model data. For instance, projected pre- cipitation at the jth position of each grid of a given model can be transformed as
... (6)
where m^ j and s^j are the late twentieth-century (1950- 2000 CE) mean and standard deviation, respectively. The subscript j is used as a spatial index (i.e., a point on a grid).
Certain limitations make estimating megadrought risk in the CMIP5 archive more complicated than simply calculating how often these events occur in climate projections. First, the number of ensemble members available from each model is small (Fig. 4), and the role for internal variability may be substantial on decadal to multidecadal time scales (Hawkins and Sutton 2009; Deser et al. 2012). This makes it difficult to reliably es- timate risks stemming from the combined influences of forced changes and internal variability. Second, the distribution of variance across time scales is different in observational data than in models. In particular, models tend to exhibit power spectra resembling white noise in WNA, even when run for many centuries or forced with the time-evolving boundary conditions of the last mil- lennium (Ault et al. 2012, 2013). To illustrate this point further here, we show power-law estimates from ob- servations and CMIP5 data in Fig. 7. In this case, the power-law coefficients are calculated from each model individually and then averaged together to produce this map. Importantly, the results of individual models ap- pear similar to this ensemble average, supporting recent findings that the continuum of hydroclimate in WNA appears to be considerably redder in observations than in models (Ault et al. 2013, 2012).
We address the aforementioned challenges by de- veloping a
... (7)
where Z^ij (t) is normalized precipitation of the ith model at the jth point on a grid, and Xw(t) is a normally dis- tributed time series of white noise with unit variance. The quantity .^ij/s^ ij scales the white noise by normalizing the twenty-first-century standard deviations (.^ij ) from a given model grid point by the corresponding twentieth-century reference standard deviation (s^ ij). Twentieth- to twenty-first-century differences in mean precipitation at each point in each model are repre- sented by the random, normally distributed variable jij, with expected mean of Dm^ ij (the change in precipitation) and variance (s2m ), estimated from ensembles of runs mij when possible, and otherwise set to zero. Finally, to generate
We estimate decadal drought and multidecadal meg- adrought risk in three climate change scenarios (RCP2.6, RCP4.5, and RCP8.5) for each of the 27 CMIP5 models considered here by generating 1000 stochastic (white noise) realizations, each 1000 years long, of WNA hydroclimate using Eq. (7), as well as the AR(1) and power-law rescaling procedures. In each model, and for each RCP, estimates of s^ are made using the 1950-2000 portion of the model's historical simulation, and .^ is es- timated over the 50-yr interval spanning 2050-2100. Likewise, Dm^ and s2m , are estimated from the differences between historical (1950-2000) and late twenty-first- century (2050-2100) precipitation means. We then identify the percentage of all 1000 realizations that ex- perience decadal drought or multidecadal megadrought conditions in each RCP, model, and type of noise.
3. Results
In the CMIP5 control runs, rates of decadal drought occurrence (the average number of events per century) are spatially uniform and close to one (Fig. 8a). Similarly, white noise realizations also tend to produce about one event per century. Under climate change, rates of decadal drought occurrence show more regional diversity than in the controls (Figs. 8b-d). In the northern part of WNA, rates are close to zero, whereas throughout much of the U.S. Southwest they are between 1.5 and 1.75. Multi- decadal megadrought rates are close to zero in the control runs of the CMIP5 archive (Fig. 8e). Under climate change, these rates are closer to 0.5 (or 1 event per 200 yr), but they are still quite rare (Figs. 8f-h).
The risk of a single decade-long drought over any given 50-yr period in the control runs is about 50% (Fig. 9a), which is intuitive because the corresponding rate is about one per century. Decadal drought risk in the climate change scenarios, estimated over the period 2050-2100, depicts a decrease in the northern regions, and an increase to between 60% and 80% (Figs. 9b-d)in the U.S. Southwest. Moreover, risk increases in the U.S. Southwest with the intensity of the warming; the highest levels are found under the RCP8.5 scenario.
In the unforced control runs, the risk of a multidecadal megadrought is less than 1% throughout the region (Fig. 9e). Under climate change, however, risks in the U.S. Southwest increase to10%-20% inRCP2.6 (Fig.9f), 20%-40% inRCP4.5(Fig.9g),and30%-50%inRCP8.5 (Fig. 9h).
A qualitatively similar picture of risk to that in Fig. 9 is seen in Figs. 10 and 11, which summarize our
Thus far, we have only considered the risk of a pro- longed period of aridity using two somewhat narrow definitions of decadal drought and megadrought. To develop a more complete representation of drought risk across a wide range of time scales and magnitudes, we examine the two-dimensional probability density function of drought risk using the same time scale- independent definition employed by Ault et al. (2013). Specifically, a drought is defined as a period of time during which 3/5 of the antecedent years are below a particular threshold. These thresholds are the values of the x axes on the individual panels of Fig. 14, and the time scales are shown on the y axes of that figure. As in the earlier figures, risk is estimated from all
The results in Fig. 14 show that risk increases with GHG forcing intensity across all time scales in the raw CMIP5 archive (Figs. 14a-c), as well as for each type of noise. It also illustrates that the AR(1) and power-law distributions depict higher levels of risk on decadal and longer time scales than the white noise and CMIP5 en- sembles. To emphasize this point further, we show the differences in drought risk across time scales between each type of noise and the raw CMIP5 estimates in Fig. 15. From this figure, it is clear that the low-probability (but presumably consequential) ''tails'' of the distributions are far more likely in the AR(1) and power-law noises than in the raw CMIP5 archive. For instance, under the RCP8.5 scenario, the risk of a 0.5s event on 40-yr time scales is below 5% as estimated from CMIP5 runs (Fig. 14c), but closer to 10% in the power-law noise realizations (Fig. 14i).
We extend our analysis of megadrought risk in the western
We stress that our results have only used precipitation, yet temperature may play a substantial role in driving or exacerbating drought. Also, we used the low end of b estimates from Ault et al. (2013) to generate the power- law noises, but higher values might be realistic on long time scales, according to the preponderance of paleo- climate evidence considered in that study, and would raise the levels of risk. Hence, to the extent that the global climate models simulate future change realistically and our simple
4. Discussion and conclusions
In the current generation of global climate models, the risk of a decade-scale drought occurring this century is at least 50% for most of the greater southwestern
An obvious limitation of our work is that it is ''blind'' to certain aspects of dynamically driven changes in prolonged drought risk. For instance, changes in the magnitude, fre- quency, or teleconnection patterns of El Niño and La Niña (e.g., Coats et al. 2013a) may alter the statistics of in- terannual variability in ways that are not captured by our simple models. Further, megadrought statistics over the last millennium may be forcing dependent, as suggested by Cook et al. (2004), for instance, which shows that mega- droughts were more common during the medieval climate era of 850-1200 CE. Another very serious limitation is imposed by the reliability of the models themselves to make realistic predictions of changes in climatological precipitation for the end of the twenty-first century.
The projected increases in risk for the U.S. Southwest reflect forced changes in the global hydrological cycle (e.g., Held and Soden 2006; Solomon et al. 2007; Vecchi and Soden 2007; Seager et al. 2010). As such, the global picture of persistent drought risk in the CMIP5 archive (Fig. 16) bears a striking resemblance to the projected decreases in precipitation throughout many semiarid regions of the world (Diffenbaugh and Giorgi 2012; Knutti and Sedlacek 2013). It follows that prolonged drought risk is a function not only of forced changes in the global hydrological cycle and the severity of future warming, but also of the accuracy with which GCMs project large-scale changes in hydroclimate (e.g., Held and Soden 2006; Seager et al. 2007; Vecchi and Soden 2007; Seager et al. 2010). Moreover, we have based our analysis on precipitation projections, yet this variable has been notoriously challenging for GCMs to simulate accurately and large biases may remain in some models (e.g., Knutti and Sedlacek 2013; Jiang et al. 2012). Our estimates of risk are consequently only as accurate as climate model projections of changes in precipitation. An alternative approach, employed for instance by Seager et al. (2007, 2010), examines the role of large- scale dynamic and thermodynamic controls on pre- cipitation minus evapotranspiration (P 2 E). Such studies have found that drought conditions like the Dust Bowl will become normal in the Southwest and in other subtropical dry zones. If such transitions are indeed ''imminent,'' as stated in those studies, then the risk of decadal drought is 100%, and the risk of longer-lived events is probably also extremely high. By orienting our analysis around precipitation, the risks of prolonged drought we show here are in fact the lowest levels con- sistent with model simulations of future climates.
From Fig. 16 it is also clear that several other areas may be facing similar (or worse) levels of prolonged risk in the coming century. Synthesis of paleoclimatic, in- strumental, and model data for these regions may lead to improvements in projecting risks in these areas and preparing appropriate adaptation and mitigation strat- egies. For example, high-resolution tree-ring and cave records are available from
Despite the simplicity of our
5. Implications
Droughts in the past have had particularly notable human and financial costs. In
Acknowledgments. We thank
Denotes Open Access content.
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JULIA E. COLE AND
(Manuscript received
Corresponding author address:
E-mail: [email protected]
| Copyright: | (c) 2014 American Meteorological Society |
| Wordcount: | 7741 |
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