Tree rings and Drought Indices

21 11 2012

Kevin Anchukaitis

On November 14, Nature published a paper by  Justin Sheffield and colleagues with the title ‘Little change in global drought over the past 60 years’.  The paper describes the consequences of a bias in an index of drought, the Palmer Drought Severity Index (PDSI), which incorporates precipitation, temperature, and soil moisture storage into a single measure of drought severity.  The index is designed so as to indicate ‘normal’ (average) conditions at zero, with negative values indicating drought and positive values indicating pluvial (wetter) conditions.  Sheffield et al. note that the bias they identify arises from ‘a simplified model of potential evaporation [Thornthwaite model] that responds only to changes in temperature’. Indeed, this is something that scientists in the drought community have been aware of — For example, Aiguo Dai published a paper last year in the Journal of Geophysical Research in which he noted that

Another major complaint about the PDSI is that the [potential evaporation] calculated using the Thornthwaite equation (Thornthwaite,1948) in the original Palmer model could lead to errors in energy‐limited regions [Hobbins et al., 2008], as the Thornthwaite PE (PE_th) is based only on temperature, latitude, and month.

Similar to the Sheffield et al. paper, Dai looked at variants of the PDSI, including one calculated using the Penman-Monteith equation, which incorporates radiation, humidity, and wind speed as well as precipitation and temperature.  As their headline results, Sheffield et al. write that:

More realistic calculations, based on the underlying physical principles that take into account changes in available energy, humidity and wind speed, suggest that there has been little change in drought over the past 60 years.

While Dai came to a different conclusion:

The use of the Penman-Monteith PE and self-calibrating PDSI only slightly reduces the drying trend seen in the original PDSI.

This is one of those times to be wary of what Andrew Revkin has called ‘single study syndrome‘. As I am quoted saying in a ScienceNews article, I think the jury’s still out on the reason for the differences between the two groups and the implications.   Certainly, and as Sheffield et al. note, some of the difference is likely in part due to the treatment of uncertainties in the data for radiation, humidity, and wind speed that go into the Penman-Monteith equation.  Another solid resource on this issue is this Carbon Brief article by Freya Roberts.  In a larger sense, too, this is about what we actually mean by the term drought and how we chose to define and measure it.  John Fleck has this aspect extremely well-covered here, here, here, and here (also here, here, and here).

I wanted to address here, however, a question that arose in a Twitter string between journalists John Fleck and Keith Kloor, and climate scientists Jonathan Overpeck, Simon Donner, Ben Cook, Richard Betts, and myself — namely, since many tree-ring drought reconstructions are reconstructions of the PDSI, what does this mean for our understanding of past megadroughts?

Despite some of its weaknesses, the PDSI (even with the Thornthwaite model) still has some desirable characteristics.  First, it attempts to capture the influence of temperature on evapotranspiration, and so reflects more than just precipitation.  Second, since it describes dimensionless anomalies, it is theoretically comparable over large regions.  Third, since it simulates soil moisture storage, it can capture the importance of a previous season’s rain (or snow) on subsequence moisture availability. Finally, the Thornthwaite model can be calculated using precipitation and temperature, climate data that are more readily available back in time compared to the radiation, humidity, and wind speed data needed for  Penman-Monteith.  I should note that not all the assumptions implicit or explicit in the above hold true at all times or over all places.  Still, one is tempted to paraphrase Churchill on democracy.  Or was that Mark Twain?

So does the fact that many tree-ring reconstructions of drought — particularly the North American and Monsoon Asia Drought Atlases — use the Palmer Drought Severity Index as their ‘target’ (predictand) field mean that we have to re-evaluate our ideas about past megadroughts?  Not yet.  The first thing to keep in mind is that all the information we have about past drought comes from proxy measurements like tree-ring width (and lake sediments and speleothems and ice cores, to name a few) and not from observations of PDSI.  To put it another way, it is the sustained narrowness of growth rings in many trees over many decades and at many sites that leads us to infer something about the timing, extent, and relative magnitude of past droughts.  When we reconstruct the PDSI (or precipitation or temperature), we are in essence taking the part of the instrumental PDSI record that overlaps with the tree-ring record and using that period of overlap to calibrate and validate a statistical model that translates tree-ring width into an estimate of PDSI.  We are taking the tree-ring measurement data and putting them into units of climate.

Sheffield et al. talk briefly about the implications for paleoclimate reconstruction of drought and get this part right:

… the tree-ring data, which reflect real variations in climatic and non-climatic factors …

Or to put it another way, tree-ring width reflects climate, but PDSI might not accurately reflect drought severity because of the way temperature is used to calculate potential evapotranspiration.  As an example of this potential problem in the modern record, Sheffield et al. cite two papers they say show a diverging relationship (‘diverge from the instrumental-based PDSI_Th in recent decades’ between PDSI and ring width’) — unfortunately, this is where things start to go a bit wrong:

Fang, K. Y. et al. Drought variations in the eastern part of northwest China over the past two centuries: evidence from tree rings. Clim. Res. 38, 129–135 (2009).

deGrandpre,L.et al. Seasonal shift in the climate responses of Pinus sibirica,Pinus sylvestris, and Larix sibirica trees from semi-arid, north-central Mongolia. Can. J. For. Res. 41, 1242–1255 (2011)

Both papers describe climate and tree growth relationships in semi-arid regions of China and Mongolia.  The second, by deGrandpre and coauthors (which, in the interest of disclosure, includes some of my own coauthors on related projects), doesn’t actually discuss any divergence between PDSI and tree-ring width.  The first, by Keyan Fang and coauthors, does show a period of separation between ring width and PDSI, but only between 1997 and 2003, the end of their record:

Fang et al. Figure 5

The authors of Fang et al. discuss this feature of their study, saying:

The abnormally dry conditions from 1997 to 2003 (Fig. 5) might have been caused by the significant drying trend and a poor PDSI model fit (Liang et al. 2007). That is, the current PDSI model for this region might have overestimated the effects of the warming trend on the local moisture conditions since 1997, resulting in abnormally dry PDSI values.

So, they are essentially (briefly) worrying about the same phenomenon that Sheffield et al. describe — that higher temperatures are biasing the calculation of the PDSI here.  I’m hesitant to read any more into a single study of a single species in a single location, but it is interesting to note that, if Fang et al. are correct and the lower PDSI values after 1997 are indeed a reflection of ‘overestimated the effects of the warming’  on the PDSI, their tree-rings didn’t ‘fall for it’ — they don’t follow PDSI into biased territory.  This should give us more confidence that the trees are reflecting moisture conditions, but it gives us less confidence in the PDSI.

Strangely, Sheffield and coauthors also briefly speculate about the Divergence Problem in formerly temperature-sensitive trees at some northern treeline sites.  Unfortunately, they get this part rather wrong — the mechanism they describe for the influence of temperature on tree-ring width isn’t correct and PDSI is completely unrelated to the divergence problem in these trees.

In case you’re still concerned about the existence of megadroughts identified in tree-ring chronologies (and other proxies) from places like the western United States, it is important to point out that a lot of the evidence for these events doesn’t even involve reconstructions of the PDSI.  For instance, Scott Stine’s important 1994 megadrought study is based on the dates of now-drowned Medieval trees in the Sierra Nevada of California (indicating sustained and dramatically lower lake levels at times prior to the 14th century). Henri Grissino-Mayer’s amazing 2000+ year reconstruction of drought from El Malpais in New Mexico is of water year precipitation, not PDSI.  And Dave Meko, Connie Woodhouse, and other have reconstructed streamflow, not PDSI, in the Colorado River basin.    Evidence for megadroughts comes from the proxies themselves, not the modern instrumental data like PDSI.

So why worry about the problems in the PDSI if you’re a paleoclimatologist like myself? It is possible that we’re on the cusp of this becoming a problem for the calibration of our statistical reconstruction models, although nothing like the ‘divergence’ seen in Fang et al. has thus far emerged (yet) at most tree-ring sites that I’m aware of.  Also, we’d like to be able to compare past droughts from the paleoclimate record with modern droughts from the instrumental data and future droughts from climate models.  But to do so, we need a metric that reliably will tell us the same thing across those epochs.  Evidence has been accumulating for years that PDSI presented a problem for this goal of integrating data and models and the past into understanding the future.  Our group has been looking into ways to deal with this for several years on issues including probabilistic drought forecasting and comparisons between models and paleoclimate data.  Hoerling and colleagues recently published a paper in the Journal of Climate looking at the PDSI and specifically predictions of imminent drying in the U.S. Great Plains.  They write  that:

PDSI is shown to be an excellent proxy indicator for Great Plains soil moisture in the 20th Century; however, its suitability breaks down in the 21st Century with the PDSI severely overstating surface water imbalances and implied agricultural stresses. Several lines of evidence and physical considerations indicate that simplifying assumptions regarding temperature effects on water balances especially concerning evapotranspiration in Palmer’s formulation compromise its suitability as drought indicator in a warming climate.

PDSI tracks soil moisture and precipitation well through the 20th century, but after that time becomes a biased indicator of drought conditions.

Hoerling et al. 2012 Figure 3

Richard Seager talked to John Fleck about this issue as well, pointing to this paper by Burke et al.

So what’s the solution for paleoclimatologists, if we’d still like to keep some of the attractive elements of the PDSI but enable better comparisons between past, present, and future droughts?  We might have to trade some of the desirable traits of the PDSI for potentially less-biased — but more uncertain or incomplete — drought metrics like modeled soil moisture. When comparing past climates and GCM simulations, we might utilize forward models to transform simulated climate into simulated tree-ring widths or other proxy measures, as opposed to the normal approach of transforming proxy data into climate variables.

In summary, the Sheffield et al. result doesn’t really cast any doubt on our knowledge of the existence, timing, during, and relative magnitude of past megadroughts.  What it does do — along with the other papers, particularly those by Hoerling and Dai, discussed above — is make us (dendroclimatologists) think about other drought metrics we might want to reconstruct to enable the most accurate comparisons across timescales and between paleoclimate data, instrumental observations, and climate model simulations.  Stay tuned.

UPDATE (via Skeptical Science): John Nielsen-Gammon, professor, atmospheric scientist, and Texas State Climatologist looks at the Sheffield paper and compares it with the earlier Dai article.  His summary:

So what’s the take-home message from all this?  It does indeed matter how you estimate evaporation, and better estimates do indeed correspond to smaller global drought trends over time, but those trends are probably not as small as Sheffield et al. calculates.  Drought is still getting worse on a globally-averaged basis.


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24 11 2012
Stewart Franks

Dear Kevin,

On Thornthwaite – “First, it attempts to capture the influence of temperature on evapotranspiration, and so reflects more than just precipitation.”

Drought indices based on precipitation alone are indeed inadequate.

Nonetheless the error in this statement is that air temperatures do not directly affect evapotranspiration – rather, they are a response to the partitioning of the suns radiant energy into ET and sensible heating (that warm the air).

The Sheffield PDSI formulation based on the PM equation encapsulates the physical driving factors (humidity, windspeed and net radiation). However even this is likely to produce an overestimate of actual evapotranspiration, as the potential ET rises when the actual ET decreases (as occurs during drought because soil moisture is by definition limited)

Temperature based estimates of evapotranspiration only exist because of the paucity of other data – they are used in hydrology as a proxy but they are biased during drought.

Hydrology is both a science and an engineering discipline – unfortunately, the practical requirements for estimation and the physics of the processes is very commonly misunderstood (even by many hydrologists)

Best wishes, S.

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