Discussion of reading 4: Scientific graphics

Tufte, Visual display of quantitative information

Chapter 4: Data-ink and redesign

Chapter 8: Data density and small multiples

Page 183: Acessible Complexity

Go around table for plans for career exploration

What aspects of this graph

are consistent with Tufte?

Is it effective?

(SST) and sea-ice. The control simulations employ time-varying observed SST and sea-ice [in the spirit of, and

named after the Atmospheric Model Intercomparison Pro-

ject (AMIP), Gates 1992], and climate changes are pre-scribed by either uniformly increasing the SST by 4K or by

quadrupling the atmospheric CO2 concentration. We

compare results from the AMIP experiments with furtheridealized aquaplanet versions of the same models and the

same climate perturbations. The SST?4K warming

experiments explore the climate response and associatedclimate feedbacks (in the absence of SST feedbacks) in

analogy to a global warming scenario, as in Cess et al.

(1989, 1990, 1996). Increasing atmospheric CO2 providesinsight into the tropospheric adjustment to the direct radi-

ative forcing from CO2 (Hansen et al. 2002; Gregory and

Webb 2008).The idealized warming experiments with the AMIP

configuration capture much of the global response of the

fully-coupled projections. This point is illustrated with thehelp of Fig. 1 which compares the global equilibrium cli-

mate sensitivity (ECS) for several ocean-atmosphere cou-

pled models calculated by Andrews et al. (2012) with theclimate sensitivity parameter (k, defined by Cess et al.

1989) for the corresponding AMIP SST?4K experiments.

This comparison confirms other recent findings that AMIP

experiments contain similar feedbacks as experiments with

fully-coupled climate models (e.g. Tomassini et al. 2013;Brient and Bony 2013).

Aquaplanets are an idealized configuration in which theplanet’s surface is completely water-covered. This simpler

setting still allows a global model’s explicit dynamics and

parameterized physics to interact within an Earth-like cli-mate. The configurations used here, illustrated by Fig. 2,

are modeled after the AquaPlanet Experiment Project

(APE, Neale and Hoskins 2000; Williamson et al. 2012). Inparticular, the SST is prescribed using a simple analytic

profile (so-called ‘‘QOBS,’’ maximum on the Equator

reaching 0 !C at 60! latitude), sea-ice is neglected, andorbital parameters are defined as perpetual equinox con-

ditions (i.e., there is no seasonality, but the diurnal cycle is

retained). Aquaplanets are an attractive framework becausethey retain the dynamics and physics of more realistic

configurations while eliminating zonal asymmetries and

interactions with a more complex land-surface. Simplifyingthe lower boundary and orbital parameters, and hence

reducing the dimensionality, provides a conceptually sim-

pler configuration that facilitates analysis and allowsshorter integrations. These potential advantages are valid

for studies of both the mean climate and idealized climate

change experiments. Such simplifications may, however,introduce differences from more realistic model configu-

rations, and aquaplanet climate response might differ

among models more than Earth-like configurations, forinstance by accentuating certain biases. Blackburn et al.

(2013) have highlighted that some aspects of aquaplanet

simulations show more variation across models than Earth-like simulations, such as the structure of the ITCZ and

tropical precipitation variability. In the climate change

context, differences from the Earth-like configurations may

Fig. 1 Relationship between the AMIP global sensitivity parameterand equilibrium climate sensitivity inferred from coupled modelexperiments. Colors show the AMIP value of the tropical cloud effectparameter (see text); discrepancies between the colors and the verticalposition show the influence of extratropical climate responses. Twomodels not included by Andrews et al. (2012) are added to Fig. 1:CCSM4 and FGOALS-g2 (see Table 1 for a list models). Otherresults from those models are presented in the text, so the ECS wascalculated as in Andrews et al. (2012) (using the method of Gregoryet al. 2004). The CanAM4 results are presented in Fig. 1, butexcluded from the remainder of this discussion because no aquaplanetresults are available for that model

Fig. 2 Illustration of the left AMIP and right AQUA configurations.Color shading shows SST for ocean locations and topography for landlocations; streamlines show the annual mean flow at 925 hPa

B. Medeiros et al.

123

Medeiros, Stevens and Bony, Climate Dynamics, 2014

What aspects of this graph are consistent with Tufte?Is it effective?

Medeiros, Stevens and Bony, Climate Dynamics, 2014

Using aquaplanets to understand the robust responses of comprehensive climate models to forcing 11

Fig. 5: Hadley circulation width (top) and strength (bottom) for each model and the multi-model mean (farright). Triangles denote the AMIP simulations (upward and downward pointing for northern and southernhemisphere, respectively) and circles the AQUA simulations. Gray markers show the control simulations, redthe SST+4K, and blue the 4⇥CO2. The diagnostics are calculated using the meridional mass stream functionvertically integrated between 700 and 300 hPa, y . The width is determined as the most equatorward latitudewhere y = 0 in each hemisphere, conditioned on being poleward of the absolute hemispheric maximum,yMAX , which defines the Hadley cell strength.

ities extend beyond the tropics, but the differences in the circulation make the comparison315

less clear. Keeping such similarities in the large-scale circulation in mind, we next turn to316

cloud changes.317

4 CRE response318

Figure 8 shows the dynamical regimes decomposition for all the models and the ensem-319

ble mean. There is substantial spread among the models, somewhat more so for convective320

regimes (w500 < 0). For most models, and the ensemble mean, the CRE increases moder-321

ately with w500, implying that the dynamic term must be small. The intermodel spread in322

CRE for a given w500, however, is as large as the variation of CRE across w500 for a given323

model. The spread in the DCRE is similarly large. On average, DCRE depends more on324

dynamical regime in the AMIP experiment (decreasing in magnitude with increasing w500)325

than in the AQUA experiment. The thermodynamic and dynamic contributions account for326

the area covered by each w500 interval and show that the weak vertical motion regimes con-327

tain much of the signal, and likewise the spread, by virtue of their prevalence (Fig. 4, middle328

panels). The AQUA experiments show a similar magnitude of spread in T , also predomi-329

nantly in regions of weak subsidence, but the magnitude of this term is somewhat less than330

in the AMIP experiments. In AMIP and AQUA experiments the dynamical contribution, D ,331

is confined to a narrow range near the peak of the subsidence distribution where CRE is332

relatively flat, so these terms have relatively little net effect.333

An indication of the difficulty in distinguishing cloud types using only w500 is provided334

by comparing the ensemble mean CRE with the w500–LTS joint distribution (Fig. 4). The335

Some recently published figures from the Earth and Planetary Science literature

Shirley et al, Icarus, 2019

maximum solar irradiance that occur at perihelion. A coincidence of thepeaks of the two waveforms would yield a phase identification for theyear in question of precisely 90°. Accordingly, the phase values de-termined for MY 33 and MY 34 (Fig. 2) are 107° and 67° respectively.Additional details of this procedure are provided in [SM17].

For purposes of the present study, it is important to recognize thatthe zero-crossing times of the dL/dt waveform of Fig. 2 are times whenthe acceleration field of Fig. 1 diminishes and disappears, re-emerging,thereafter, with reversed sign. The perihelion period of MY 32 (Fig. 2)exemplifies this condition. “Transitional years” such as MY 32 havelittle or no added forcing due to CTA during the southern summer duststorm season. Prior work has shown that the transitional phasing isunfavorable for the occurrence of GDS [SM17; MS17]. We will takeadvantage of this aspect (i.e., the cyclic disappearance of the putativeexternal forcing) in the analyses of Sections 4 and 5, below.

In the nomenclature of the prior studies [MS17; SM17], intervalswhen Mars is gaining orbital angular momentum are termed “positivepolarity intervals.” Positive polarity intervals for MY 33 and 34 areindicated in Fig. 2 by plus symbols near the zero line. Intervals whenMars is yielding up orbital angular momentum to other members of thesolar system family are termed “negative polarity intervals.” These arelikewise indicated on Fig. 2, by minus signs. MY 31 of Fig. 2 provides agood example of a “negative polarity year,” as the phase of the dL/dtwaveform at perihelion is near 270°. We will see evidence of markeddifferences in the response of the Mars atmosphere as a function of thepolarity of the waveform during the dust storm season in Sections 4 and6 below and in the companion study [N18].

3. Methodology and model calibration

3.1. Overview

The orbit-spin coupling hypothesis remains controversial, as onlyone prior study (i.e., [MS17]) has directly evaluated the response of a

planetary atmosphere to forcing by the CTA as outlined in Figs. 1 and 2.Thus our test procedure must allow us to clearly differentiate betweensingle-year model outcomes that are attributable to CTA forcing, versusoutcomes that might arise due to intrinsic variability within theMarsWRF GCM. This issue is addressed through the use of control runsof the GCM without CTA forcing, whose outcomes may be compareddirectly with those obtained with CTA forcing included. In addition, forthe present study, we wish to determine whether or not the degree ofsuccess achieved in simulating the historic record differs significantlyfrom what may be obtained by chance.

In order to achieve these goals, we must first define our criteria fordetection and identification of simulated GDS events. We are likewiserequired to show that the parameters supplied to the GCM employed inobtaining the control simulations yield reasonable results. These topicsare addressed in Sections 3.3 and 3.4 below, following a brief overviewof the MarsWRF GCM in Section 3.2.

Finally, in Section 3.5, we describe the steps taken to validate thechoice of the obit-spin coupling efficiency coefficient, c. Our controlruns, by definition, incorporate a value of zero for c. A nonzero value ofc, if found, may provide new insights and constraints bearing on themagnitude and nature of the coupling mechanism(s) and the response.We will return to this question in Section 6 below.

3.2. MarsWRF

The MarsWRF model and the model output used in this study aredescribed in [N18]. The model includes radiative heating due to dust inthe atmosphere that is mixed by resolved and parameterized processes,and sediments under the influence of gravity. Dust is lifted from thesurface via two parameterized processes representing “dust devil”convection and resolved wind stresses (see [NR15] and N18]). Themodel also includes a full CO2 cycle in the model version employedhere. Although the atmospheric water cycle and constraints due to fi-nite surface dust availability may be important in the real dust cycle,

Fig. 2. Phasing of the annual cycle of solar irradiance (orange curve, shown as the variation about the mean) with respect to the waveform of the orbit-spin couplingforcing function, dL/dt, over 7 Mars years (as labeled in blue). The polarity (positive or negative) of the forcing function is shown explicitly at right for MY 33 and 34.Positive polarity intervals correspond to times when Mars is gaining orbital angular momentum (from other members of the solar system family) due to gravitationalinteractions. During negative polarity intervals, Mars is correspondingly yielding up orbital angular momentum. Responses of the geophysical systems of Mars(including the Mars atmosphere) may differ significantly as a function of the polarity of the dL/dt waveform. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

J.H. Shirley et al. ,FDUXV���������������²���

���

Fig. 2. Phasing of the annual cycle of solar irradiance (orange curve, shown as the variation about the mean) with respect to the waveform of the orbit-spin coupling forcing function, dL/dt, over 7 Mars years (as labeled in blue). The polarity (positive or negative) of the forcing function is shown explicitly at right for MY 33 and 34. Positive polarity intervals correspond to times when Mars is gaining orbital angular momentum (from other members of the solar system family) due to gravitational interactions. During negative polarity intervals, Mars is correspondingly yielding up orbital angular momentum. Responses of the geophysical systems of Mars (including the Mars atmosphere) may differ significantly as a function of the polarity of the dL/dt waveform. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Shirley et al, Icarus, 2019

samples of any size in which the frequency of occurrence of our proxyfor GDS years approximately matches that of the available historic re-cord.

The historic record of GDS occurrence defines our reference timeseries for comparisons. For convenience we represent GDS years withthe number 1 in this case, while GDS-free years are denoted with thenumber zero. In this way we obtain an observations-based referenceseries (with n=22) consisting entirely of a sequence of zeros and ones,suitable for making automated comparisons, as illustrated in the thirdand fourth rows of Table 2 below.

Table 2 illustrates the operation of the above algorithm for com-parisons. Random numbers within the synthetic series with values <=0.409 (shaded in brown) represent GDS years. When a synthetic GDSevent corresponds to a real GDS year in the ordered reference sequence(third row, also shaded in brown), a “success” is claimed. Likewise,when rows 1 and 3 each contain blue shading, corresponding to a GDS-free year, a second type of successful comparison is identified. Greenshading in the third row of the figure indicates all cases of agreementbetween the two series, which are here termed “successes.” We observe10 cases of agreement (“successes” ) among the 22 comparisons illu-strated in Table 2.

There are 10 GDS years and 12 GDS-free years in the tested randomsample; these frequencies are close to the frequencies actually observed(9 historic GDS years versus 13 GDS-free years).

We repeat the above comparison many times, employing differentrandom samples in each trial, in order to identify the possible range ofoutcomes and characterize the macroscopic statistical properties of thedistributions that emerge in this specific problem. We employ a best-practices random number generator (as implemented in the IDL pro-gramming language) to obtain a 1-dimensional array of random num-bers of a specified length. The length of the array corresponds to theproduct of the number of samples compared (n=22) with the numberof separate trials requested. Comparable and consistent results wereobtained in experiments involving 10, 100, 1000, 10,000, and 100,000comparisons. 106 trials were performed in our most extended com-parison.

Fig. 5 illustrates a typical distribution of success rates resulting fromthe Monte Carlo modeling. In this case, 10,000 trials were performed.The horizontal axis of the histogram indicates the full range of possibleoutcomes (i.e., from 0 successes to 22 successes). The values are ap-proximately normally distributed about a mean of 11.36 successes, withstandard deviation σ=2.32. The number of successes obtained (17) inthe comparison of numerical modeling outcomes with the historic re-cord of the present study is indicated by the black arrow. This lies at adistance of more than 2.4 σ from the mean of the distribution. Fromstandard tables we obtain a significance level of 0.9925 for this out-come. Success rates of 17/22 or higher were recorded in ∼1% of the10,000 random samples that were evaluated to produce Fig. 5.

A limited number of comparison tests were performed with differentsets of frequencies. In particular, a GDS frequency of ∼0.333 yr-1 isoften cited, following the work of Zurek and Martin (1993). In this case,for 10,000 trials, the mean success rate was increased slightly (to 11.63,from 11.36) but the significance level obtained for the case with 17successes was unchanged. The test procedure is insensitive to the choice

of event frequency within our range of interest. Monte Carlo modelingthus confirms our initial impression that the rate of successful com-parisons obtained in the present investigation is unlikely to arise bychance. The results of our tests clearly favor the hypothesis of a de-terministic forcing of GDS occurrence (by orbit-spin coupling), over onerelying exclusively on stochastic processes.

6. Discussion

The annual-time-scale resolution of the above analysis represents asignificant limitation of the present paper, particularly with respect toquestions such as intra-seasonal GDS inception dates and the spatial andtemporal patterns of storm development and evolution. These topicswill be addressed in [N18] and in subsequent papers.

Statistically significant relationships linking solar system dynamicalquantities with GDS occurrence were previously reported inShirley (2015) and in [SM17]. The use of a GCM with a fully interactivedust cycle provides greater realism and fidelity to atmospheric condi-tions than was possible in prior studies [SM17, MS17]. The statisticalsignificance obtained in the present study thus carries greater weightthan was the case for prior investigations.

The cases in which model outcomes fail to correspond with thehistoric record of dust storm occurrence on Mars can provide us with

Table 2A synthetic series of random numbers (top row) is compared with the time series of observed GDS years and GDS-free years of Table 1 (third row). GDS “events”(brown shading) are identified in the random number series whenever the value listed is< =0.409 (see explanation in text). GDS-free years in both series haveblue shading. A successful match (denoted by green shading in the second row, between the two series) occurs when the condition in the synthetic time series (toprow) is identical to that in the reference sequence (third row). Mars year designations for the reference sequence are provided in the fourth row.

Fig. 5. Distribution of counts of successes obtained through 10,000 trials withrandom samples (see discussion in text). The black arrow indicates the successrate obtained in our comparison of MarsWRF GCM modeling outcomes with thehistoric record of global dust storm occurrence. The probability of obtaining 17or more successes in this type of comparison employing sequences of randomnumbers is about 1%.

J.H. Shirley et al. ,FDUXV���������������²���

���

Shirley et al, Icarus, 2019

existing record. Thus, with GDS occurring in 9 of the 22 years of thehistoric record (Table 1), our nominal frequency of GDS events is in-itially taken to be 0.409 yr-1, while that for GDS-free Mars years is0.591 yr-1. (Other sets of frequencies will be considered below). Given a

series of random numbers distributed between 0 and 1, we adopt asimple scheme in which all random numbers<= 0.409 are consideredto represent GDS years, while numbers with values> 0.409 are takento represent GDS-free Mars years. By so doing, we may obtain random

Fig. 4. T15 curves for the 56 Mars years of simulation CTA1. Dashed lines indicate modeled temperatures for control simulations when wind stress dust lifting is notenabled.

J.H. Shirley et al. ,FDUXV���������������²���

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Fig. 4. T15 curves for the 56 Mars years of simulation CTA1. Dashed lines indicate modeled temperatures for control simulations when wind stress dust lifting is not enabled.

McMonigal et al, GRL, 2018

Geophysical Research Letters 10.1029/2018GL078420

Month

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90b Agulhas

Mass balanceGyre

Figure 2. (a) Seasonal cycle of gyre strength, defined as the transport between 35∘ and 110∘E, following Palmer et al.(2004). Dashed lines show the combined sampling and statistical error. Blue and green boxes show gyre strengthestimates from Palmer et al. (2004), including their error estimates. (b) Seasonal cycles based on monthly averagesof the upper 2,000-m Agulhas Current transport from an SSH-based proxy (red line) and upper 2,000-m interiortransport from Argo/SSH (black line). The Agulhas Current transport is shown as positive southward, while the interiortransport is positive northward. Dashed lines show combined statistical and sampling error. The blue line shows theseasonal cycle of the gyre as predicted by mass balance in the basin, considering the Agulhas Current as the southwardflow out of the basin and the Indonesian Throughflow as the input. The interior transport is defined as the transportfrom just offshore of the Agulhas Current to the 2,000-m isobath offshore of the Australian coastline.

conducted in fall (March–April). To investigate how much of the change could be due to seasonal aliasing, wecalculate gyre strength using the same definition as Palmer et al. (2004): the maximum transport cumulatedbetween 35∘E and 110∘E across 32∘S (Figure 2a). This does not include the Agulhas Current, and thus, the gyrestrength is only dependent on the Argo/SSH product. We calculate monthly values for 2007 through 2016and take monthly means over the 10-year period. The seasonal cycle has a minimum in austral winter anda maximum in austral summer, with peak-to-peak amplitude of 10.0 ± 3.1 Sv. Although the seasonal cycleamplitude is larger than the estimated error, there is only a 2-Sv difference between the November–Decemberand March–April gyre strengths. Assuming that the seasonal cycle has not changed since 1987, this impliesthat the gyre changes estimated by Palmer et al. (2004) are not aliased by the seasonal cycle and are likelyevidence of a longer-term change to the gyre circulation as they interpreted. There is not yet enough Argodata to address a possible change to the seasonal cycle over time.

By varying the longitudes of the boundaries of the gyre, we find that the gyre seasonal cycle is sensitive to theend points chosen. The endpoints used by Palmer et al. (2004) do not extend all the way to the offshore edgeof the Agulhas Current nor to the eastern boundary. We define a gyre strength which spans the full basin,connecting with the Agulhas Current transport array in the west and excepting the Leeuwin Current shallowerthan 2,000 m in the east. More precisely, we define the gyre transport as the transport between the first gridpoint offshore of the Agulhas Current time-series array (28.75∘E and 35.75∘S) and the last grid point beforethe 2,000-m isobath offshore of the Australian coastline (114∘E and 34.75∘S). This full basin definition allowsus to test mass balance on seasonal time scales, by comparing the Argo/SSH-derived cycle to that predictedby the inflows and outflows of the basin.

MCMONIGAL ET AL. 9038

McMonigal et al, GRL, 2018

Geophysical Research Letters 10.1029/2018GL078420

Figure 3. Colors show dynamic height anomaly of the surface relative to2,000 m, in meters, derived from Argo/SSH. Each is an anomaly of a 3-monthperiod relative to the time mean (top is January, February, and March;second is April, May, and June; third is July, August, and September; bottomis October, November, and December). Black line shows the interior line usedin calculating the seasonal cycle of integrated transport across the basin.

Defined in this way, the gyre has a weak seasonal cycle dominated by semi-annual variability (Figure 2b; black line). The minimum transport occurs inAugust and the maximum occurs in May, with peak-to-peak amplitude of6.4 Sv ± 3.1 Sv. The semiannual cycle does not change qualitatively if thewestern boundary is moved up to 100 km farther offshore of the Africancoastline. However, moving the western boundary to 35∘E, as done byPalmer et al. (2004), yields a cycle with a more annual structure. Alteringthe eastern boundary also yields a cycle that is more annual in structure.

To investigate if mass balance can account for the observed semiannualcycle of the gyre interior, we compare the Argo/SSH-derived cycle to theseasonal cycle implied by mass balance of the Agulhas Current and theIndonesian Throughflow. A 1-Sv mass imbalance over 1 month wouldcause more than 3.5 cm of sea level rise over the basin, and thus, mass mustbalance in the basin. However, we are only considering the upper 2,000-mbaroclinic transport, while mass balance requires a full depth, absolutevelocity field, and so we may miss significant flow compensation at depth.The upper 2,000-m Agulhas Current transport proxy (Beal & Elipot, 2016;Figure 2b; red line) has a minimum southward transport in August anda maximum southward transport in April, with peak-to-peak amplitudeof 7.6 ± 1.6 Sv (uncertainty is the standard error from monthly meansof the 23-year time series). The observed Indonesian Throughflow has asemiannual cycle with maximum transport into the Indian Ocean in Jan-uary and July and minimum transport into the Indian Ocean in April andOctober Sprintall et al. (2009). Based on monthly means, the peak-to-peakamplitude of the seasonal cycle is 6.4 Sv, although the amplitudes of theannual and semiannual harmonics as computed by Sprintall et al. (2009)are smaller, 1.23 and 2.67 Sv, respectively. We estimate an interior gyreseasonal cycle based solely on mass balance between the upper 2,000-mAgulhas Current proxy and observed monthly Indonesian Throughflowtransports, smoothing this cycle with a 90-day running mean filter similarto the smoothing used on the Argo/SSH data product (Figure 2; blue line).

This simple balance between inflows and outflows above 2,000 m agrees well with the seasonal cycle fromArgo/SSH. Both seasonal cycles are strongly semiannual, with a similar amplitude of 6–7 Sv and similar phas-ing. In most months, the mass balance-predicted cycle falls within the Argo/SSH gyre seasonal cycle error bars.We hypothesize that the agreement between the Argo/SSH seasonal cycle and the mass balance-predictedseasonal cycle may be due to the relatively small amplitude of the full, cross basin seasonal transport (Agul-has + gyre), causing only a small barotropic signal at seasonal time scales. This unresolved barotropic signalis within our error bars.

Dynamic height anomalies near the eastern boundary of the North Atlantic dominate the seasonal cycleof the Atlantic meridional overturning circulation (Chidichimo et al., 2010), and we wonder if a similar con-clusion can be drawn about the South Indian subtropical gyre. To investigate this, we compute seasonalanomalies of 0/2,000-m dynamic height from our Argo/SSH product (Figure 3). We make the same dynamicheight calculations using the CSIRO Atlas of Regional Seas 2009, a climatology constructed from hydro-graphic and Argo data from 1950 to 2009 using locally weighted least squares fitting (Ridgway & Dunn, 2007;http://www.marine.csiro.au/˜dunn/cars2009/). We find similar patterns in seasonal dynamic height from ourproduct and from the CSIRO Atlas of Regional Seas. Although the CSIRO Atlas of Regional Seas is not inde-pendent from our product, as both use Argo data, the good agreement between the two data products givesus confidence that our results are not overly sensitive to the time period considered or the method of datamapping used.

Several features can be seen in the seasonal anomalies of dynamic height. A basin wide seasonal heating andcooling signal is evident, with higher dynamic heights in the summer months and lower in the winter months.This is not expected to have an impact on the gyre transport since transport is related to the difference indynamic height, and the heating and cooling seem largely uniform across the basin. A regional anomaly canbe seen approximately parallel to the African coastline, offshore of the Agulhas Current, with a maximum

MCMONIGAL ET AL. 9039

Buermann, Nature, 2018

LETTER RESEARCH

we performed a similar seasonal correlation analysis with satellite and modelled leaf area index (LAI) data (see Methods). The results reveal an even larger discrepancy between the areal proportions of positive and negative lagged responses of LAI to spring warming determined using observation-based and modelling approaches compared to those deter-mined using productivity metrics (Fig. 2c, d, Extended Data Fig. 4). The substantial overestimation of growing-season LAI in the models in response to spring warmth could cause too much new carbon to be allocated in plant tissue, which then enhances GPP.

Limited water availability may cause adverse lagged effects in response to spring warmth and could help to reconcile the differ-ences between observations and models. To further investigate this we performed a regional analysis for western USA and Siberia, for which observation-based and simulated lagged productivity responses show more converging and diverging patterns, respectively (see Fig. 2). For western USA, we find that seasonal trajectories in aggregated satellite-data-constrained and modelled LAI and evapotranspiration display positive anomalies during spring in years with warmer springs and corresponding negative anomalies later in the growing season (suggestive of negative lagged effects associated with a build-up of water stress) (Fig. 3a, b). However, for Siberia, the seasonal trajecto-ries in observation-constrained and modelled LAI for warm-spring years start to diverge substantially during summer and autumn, with the observations displaying more negative anomalies during summer and autumn (again suggestive of water stress) and the opposite pattern predicted by the models (Fig. 3c). Seasonal trajectories of observation- based and modelled evapotranspiration for years with anomalous

spring temperatures are more in agreement, although there is some indication that the models underestimate water stress in summer in warm-spring years (Fig. 3d). The consistency between the observed and modelled responses of LAI and evapotranspiration to spring warmth over western USA, a region that is known for its vulnerability to drought in response to spring warmth27–29, suggests that the hydrol-ogy and phenology schemes included in the models are generally fit for purpose. The strong divergence between observation-based and mod-elled responses of seasonal vegetation growth to spring warmth over Siberia (which is dominated by needleleaf deciduous forests) may be due to underestimation of the effects of water stress on seasonal canopy development and general omission of fixed leaf lifespans in the mod-els (Extended Data Table 1, Supplementary Information, section 3). We estimate that, owing to the difference between observation-based and modelled productivity responses to anomalous spring tempera-tures across Siberia, annual GPP for a warm-spring year may be up to four times higher in the TRENDYv6 ensemble (1.7 Pg C yr−1) than an observation-constrained estimate based on upscaled FLUXNET data (0.4 Pg C yr−1) (Extended Data Fig. 5).

Our analysis based on satellite vegetation records over multiple dec-ades provides evidence for widespread positive and negative lagged plant-productivity responses across northern ecosystems associated with warmer springs. The spatially extensive pattern of negative lagged effects that we identified implies substantially reduced benefits for ecosystem productivity and carbon sequestration from longer north-ern growing seasons under climate change. We have also shown that current terrestrial carbon-cycle models substantially underestimate

a

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Fig. 3 | Seasonal trajectories of regionally averaged LAI and evapotranspiration anomalies based on observation-constrained and modelling approaches for warm- and cold-spring years. a–d, Monthly anomalies in spatially averaged and maximum composited LAI (a, c) and evapotranspiration (b, d) based on satellite-data-constrained estimates (LAI3g, ET-GLEAM) and model simulations (TRENDYv6 multi-model mean) for western USA (a, b) and Siberia (c, d). Western USA encompasses the non-agricultural regions from 120° W to 105° W and 40° N to 50° N, whereas Siberia is defined to be

from 80° E to 125° E and 60° N to 70° N (see also Fig. 2). Anomalies are relative to the mean over the study period, 1982–2011. The monthly maximum composites shown are based on the mean LAI or evapotranspiration of the seven warmest- and coldest-spring years within the study period. The climatological seasons are indicated by the vertical grey dashed lines. Uncertainty bounds (shaded areas) reflect the spread in the monthly LAI or evapotranspiration anomalies within the compositing period (±1 s.d., n = 7).

4 O C T O B E R 2 0 1 8 | V O L 5 6 2 | N A T U R E | 1 1 3© 2018 Springer Nature Limited. All rights reserved.

LETTER RESEARCH

we performed a similar seasonal correlation analysis with satellite and modelled leaf area index (LAI) data (see Methods). The results reveal an even larger discrepancy between the areal proportions of positive and negative lagged responses of LAI to spring warming determined using observation-based and modelling approaches compared to those deter-mined using productivity metrics (Fig. 2c, d, Extended Data Fig. 4). The substantial overestimation of growing-season LAI in the models in response to spring warmth could cause too much new carbon to be allocated in plant tissue, which then enhances GPP.

Limited water availability may cause adverse lagged effects in response to spring warmth and could help to reconcile the differ-ences between observations and models. To further investigate this we performed a regional analysis for western USA and Siberia, for which observation-based and simulated lagged productivity responses show more converging and diverging patterns, respectively (see Fig. 2). For western USA, we find that seasonal trajectories in aggregated satellite-data-constrained and modelled LAI and evapotranspiration display positive anomalies during spring in years with warmer springs and corresponding negative anomalies later in the growing season (suggestive of negative lagged effects associated with a build-up of water stress) (Fig. 3a, b). However, for Siberia, the seasonal trajecto-ries in observation-constrained and modelled LAI for warm-spring years start to diverge substantially during summer and autumn, with the observations displaying more negative anomalies during summer and autumn (again suggestive of water stress) and the opposite pattern predicted by the models (Fig. 3c). Seasonal trajectories of observation- based and modelled evapotranspiration for years with anomalous

spring temperatures are more in agreement, although there is some indication that the models underestimate water stress in summer in warm-spring years (Fig. 3d). The consistency between the observed and modelled responses of LAI and evapotranspiration to spring warmth over western USA, a region that is known for its vulnerability to drought in response to spring warmth27–29, suggests that the hydrol-ogy and phenology schemes included in the models are generally fit for purpose. The strong divergence between observation-based and mod-elled responses of seasonal vegetation growth to spring warmth over Siberia (which is dominated by needleleaf deciduous forests) may be due to underestimation of the effects of water stress on seasonal canopy development and general omission of fixed leaf lifespans in the mod-els (Extended Data Table 1, Supplementary Information, section 3). We estimate that, owing to the difference between observation-based and modelled productivity responses to anomalous spring tempera-tures across Siberia, annual GPP for a warm-spring year may be up to four times higher in the TRENDYv6 ensemble (1.7 Pg C yr−1) than an observation-constrained estimate based on upscaled FLUXNET data (0.4 Pg C yr−1) (Extended Data Fig. 5).

Our analysis based on satellite vegetation records over multiple dec-ades provides evidence for widespread positive and negative lagged plant-productivity responses across northern ecosystems associated with warmer springs. The spatially extensive pattern of negative lagged effects that we identified implies substantially reduced benefits for ecosystem productivity and carbon sequestration from longer north-ern growing seasons under climate change. We have also shown that current terrestrial carbon-cycle models substantially underestimate

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Fig. 3 | Seasonal trajectories of regionally averaged LAI and evapotranspiration anomalies based on observation-constrained and modelling approaches for warm- and cold-spring years. a–d, Monthly anomalies in spatially averaged and maximum composited LAI (a, c) and evapotranspiration (b, d) based on satellite-data-constrained estimates (LAI3g, ET-GLEAM) and model simulations (TRENDYv6 multi-model mean) for western USA (a, b) and Siberia (c, d). Western USA encompasses the non-agricultural regions from 120° W to 105° W and 40° N to 50° N, whereas Siberia is defined to be

from 80° E to 125° E and 60° N to 70° N (see also Fig. 2). Anomalies are relative to the mean over the study period, 1982–2011. The monthly maximum composites shown are based on the mean LAI or evapotranspiration of the seven warmest- and coldest-spring years within the study period. The climatological seasons are indicated by the vertical grey dashed lines. Uncertainty bounds (shaded areas) reflect the spread in the monthly LAI or evapotranspiration anomalies within the compositing period (±1 s.d., n = 7).

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Buermann, Nature, 2018

LETTERRESEARCH

positive lagged effects are more common in eastern Eurasia north of 50° N (except Siberia).

Carbon-cycle models must be able to simulate the responses of vegetation phenology and the corresponding effects on ecosystem productivity and net carbon uptake realistically to estimate climate–carbon feedbacks credibly25. We therefore assessed the ability of ten current-generation models that contribute to TRENDYv622,23 to repli-cate the observed lagged productivity responses to spring warming. The results reveal a substantially higher multi-model mean areal coverage of positive lagged effects on plant productivity (and much lower coverage of negative lagged effects) than for the satellite estimates (Fig. 2a, b). Although there are marked differences among the individual models (Extended Data Fig. 3), a notable pattern in the ensemble is the near absence of any negative lagged effects across Siberia and the overall abundance of positive lagged effects that extend over summer and autumn (Fig. 2a, b). Satellite greenness has been used extensively as a proxy for vegetation productivity3,26, but direct comparisons between greenness and GPP patterns are limited (see Methods). However,

a similar analysis using two satellite-data-constrained GPP datasets (based on upscaled FLUXNET data and a light-use-efficiency model; see Methods) reveals nearly identical lagged productivity patterns to those based on satellite greenness (Extended Data Fig. 4).

Grouping the lagged productivity responses more broadly, into pos-itive and negative lagged effects, yields an areal extent of regions with positive lags of 36% for the TRENDYv6 ensemble (9%–54% for the ten individual TRENDYv6 models) and 4%–6% for the estimates derived from satellite data and satellite-data-constrained approaches (Fig. 2c). The areal coverage of negative lagged effects predicted by the TRENDYv6 ensemble is only 2% (1%–14% for the ten models), whereas that estimated from the satellite-based approaches is 13%–16%. (The ranges for the satellite-based estimates encapsulate the spread among the three different estimates; see shading in Fig. 2c.)

It is not clear why these terrestrial carbon-cycle models cannot ade-quately replicate the observed spatial pattern of lagged productivity responses to warmer springs. One key factor could be how seasonal vegetation growth is represented in the models. To assess this,

Fig. 2 | Spatial pattern of lagged productivity responses based on satellite greenness observations and models. a, b, The maps summarize the direction of robust (P < 0.05) grid-cell correlations between annual spring temperature and spring, summer and autumn NDVI determined from satellite data (a) or spring, summer and autumn GPP determined from the TRENDYv6 multi-model mean (b). For example, the lagged productivity response denoted as ‘+−0’ represents positive correlations between spring temperature and spring NDVI or GPP, negative correlations between spring temperature and summer NDVI or GPP, and no correlations between spring temperature and autumn NDVI or GPP. The relationships between spring temperature and summer as well as autumn NDVI or GPP are estimated using partial correlations, whereby effects of covarying concurrent climate influences have been controlled for (see Fig. 1, Methods). The corresponding patterns for individual models are shown in Extended Data Fig. 3. Areas with no robust link between spring temperature and spring NDVI or GPP (dark grey) and areas that are cultivated or managed (light grey) are also shown. The two focal

regions in this study (western USA and Siberia) are indicated by black-dashed rectangles. c, Extent of areas with no, positive or negative lagged effects (see definition in a) within the study region for satellite NDVI data (brown) and GPP based on TRENDYv6 models (dark blue, multi-model mean; light blue, individual models). Corresponding results from a similar analysis for two satellite-data-constrained GPP datasets, based on upscaled FLUXNET data (FluxNetG; green) and a light-use-efficiency model (LUE-FPAR3g; magenta; see Methods), are also shown (see also Extended Data Fig. 4). The horizontal dashed lines are to aid comparison to the TRENDYv6 model results and the shaded regions encapsulate the spread among the three estimates derived from satellite-based approaches. d, Results from a complementary analysis for satellite-data-constrained and modelled LAI (see Methods). Results from the same analysis for detrended data show that the differences between observation- and model-based estimates of the areal fractions of positive and negative lagged effects are similar (Supplementary Information, section 1).

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