Simulated climate vegetation interaction in semi-arid regions affected by plant diversity

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1 SULMNTARY INFORMATION DOI: 0.038/NGO96 Simulted climte vegettion interction in semi-rid regions ffected y plnt diversity M. Clussen,,*, S. Bthiny, V. Brovkin nd T. Kleinen []{Mx lnck Institute for Meteorology, Hmurg, Germny} []{Meteorologicl Institute, University of Hmurg, Germny} *Correspondence to: M. Clussen (mrtin.clussen@zmw.de NATUR GOSCINC 03 Mcmilln ulishers Limited. All rights reserved.

2 SULMNTARY INFORMATION DOI: 0.038/NGO96 A. Two relistions with the sme deterministic system. Since the precipittion is stochstic vrile, ( V, t mx( ( ( V, t ( t,0 =, where (t is rndom numer, + individul simultions with the sme set of plnt type differ. Fig. S depicts two such individul simultions where Fig. S,, c is copy of Fig,, c in the min text. In the second relistion (Fig. S e, f, some rupt chnges in vegettion coverge nd precipittion for plnt type (green lines re found in this relistion round 4000 y B. This figure demonstrtes tht just y chnce, seemingly stle system with wek feedck my look like n unstle system with strong feedck nd unstle collpse. N N V V e V V V V (V c (V f (V (V Figure S Two relistions with the sme deterministic set up.,, c, Copies of Figure C,, c in the min text. lnt type (red lines hs lower precipittion threshold of = 70 mm/y nd n upper precipittion threshold of = 370 mm/y, plnt type (green lines, C = 50 mm/y nd = =370 mm/y., Simultions without ny rndom precipittion fluctutions, N (t = 0, ut slowly evolving ckground precipittion forcing revel strong climte vegettion feedck for plnt type in which of multiple solutions develop, i.e. simultions forwrd in time (full line nd ckwrd in time (dshed line show hysteresis. lnt type hs only one solution in interction with precipittion. In simultions with rndom precipittion, plnt type yields rupt chnges in vegettion coverge in nd precipittion chnge (in mm/y in c. With plnt type lrge fluctutions, ut not distinct rupt chnge cn e seen. e, f, depict the sme cses, ut just different (rndom reliztion. In this reliztion, n rupt chnge in vegettion coverge of plnt type nd in precipittion occurs y chnce. NATUR GOSCINC 03 Mcmilln ulishers Limited. All rights reserved.

3 DOI: 0.038/NGO96 SULMNTARY INFORMATION B. Niche pproch versus potentil vegettion coverge pproch. Fig. S, is the stility digrm ( V (, ( V; t i for two plnt types nd with lower precipittion threshold of C = 70 mm/y nd n upper precipittion threshold of = 370 mm/y (green line, nd C = 50 mm/y nd = =370 mm/y (red line. Full lines depict the equilirium vegettion curves V i, i=,, (q. in the min text nd the dshed lue lines depict the equilirium precipittion curves ( V; t (q. 4, for t = 4500 y B (yers efore present, 4900 y B, 5300 y B, 5700 y B, 600 yb, 6500 y B, respectively, from right to left. The lck curve in Fig. S is the verge vegettion coverge sed on the N niche pproch (q. 3 V S =. In Fig. S, the lck line is the totl vegettion N i= N coverge computed from q. 3 V S =, where the vegettion coverge y plnt type i is interpreted s potentil vegettion coverge of plnt type i. i= Figure S Niche pproch nd potentil vegettion coverge pproch: Stility digrms. Dshed lue lines depict the equilirium precipittion curves ( V; t (q. 4, in the min text for t = 4500 y B (yers efore present, 4900 y B, 5300 y B, 5700 y B, 600 yb, 6500 y B, respectively, from left to right. The sensitivity of plnt type nd of plnt type to chnges in precipittion, i.e., V i, i =,, (q. in the min text, re shown C s red lines nd green lines, respectively. The lower precipittion threshold = 70 mm/y C nd the upper precipittion threshold = 370 mm/y for plnt type, nd = 50 mm/y nd = =370 mm/y, for plnt type. The lck is the verge vegettion coverge sed on the niche pproch (q. 3 in the min text in nd on the potentil vegettion coverge pproch (q. 3 in the min text in. NATUR GOSCINC Mcmilln ulishers Limited. All rights reserved.

4 SULMNTARY INFORMATION DOI: 0.038/NGO96 When using this potentil vegettion cover pproch, the simultions in the cse of mixture of plnt type nd plnt type differ from the simultions when using the niche pproch. This is demonstrted in Fig. S3 where Fig. S3,, c re copies of Fig. d, e, f in the min text. As mentioned in the min text, the dynmic ehviour remins qulittively the sme, regrdless of which pproch (q. 3 or (q. 3 is chosen, with the exception tht the life spn of plnt types re more extended in the cse of the potentil vegettion coverge pproch thn in the cse of the nice pproch. V d V V V V e V V V (V,V c (V,V f Figure S3 Niche pproch versus potentil vegettion coverge pproch: Trnsient simultions with two plnt types intercting with precipittion. If plnt type nd, whose trnsient ehviour when intercting with precipittion s individul plnt types re shown in Fig. S, interct simultneously with precipittion, then stility of plnt type in terms of with nd mplitude of hysteresis ecomes weker nd plnt type develops hysteresis in. In the stochstic simultion, lrge fluctutions occur in vegettion coverge of ech type in, nd no discernile rupt chnge in precipittion cn e found in c. This ehviour is qulittively the sme when the potentil vegettion coverge pproch in d, e, f is chosen insted of the niche pproch in,, c. 4 NATUR GOSCINC 03 Mcmilln ulishers Limited. All rights reserved.

5 DOI: 0.038/NGO96 SULMNTARY INFORMATION C. Reltion of vegettion coverge to nnul men precipittion in Northern Afric. In Fig. S, the plnt type (green lines yields reltive vegettion coverge of up to 0.5 with n nnul precipittion of pproximtely 50 mm/y nd up to 0. with some 00 mm/y. Such reltively high vegettion coverge t reltively low vlues of nnul rinfll in semi-rid regions is not unrelistic. We hve plotted sctter digrm of vegettion response to precipittion in the Northern Afric region from 0 N to 30 N (Fig. S4. We hve ssumed tht the temperture is not n importnt fctor, which is correct for most of the re, except for the high elevtion regions. We hve used the -km vegettion continuous fields (VCF sed on MODIS dt from Hnsen et l. for the yer 00 upscled to sptil resolution the 0.5 deg. nd the nnul precipittion dt from the CRU dtse verged for the period (New et l. 3 on the sme 0.5 deg. resolution. One cn clerly see tht the vegettion response is very steep round threshold of mm/yr nd tht with the rinfll of 50 mm/yr, most of the grid cells revel vegettion frction in the rnge of 0.4 to 0.6. This is very pproximte estimte only s vegettion dt nd precipittion dt do not cover the sme time period. Figure S4 Vegettion coverge s function of nnul men precipittion in Northern Afric. Dt re tken from Hnsen et l. for vegettion coverge in 00 nd from New et l. 3 for nnul men precipittion in the yers NATUR GOSCINC Mcmilln ulishers Limited. All rights reserved.

6 SULMNTARY INFORMATION DOI: 0.038/NGO96 D. Mixture of three nd more sensitive plnt types. Fig. S5 depicts the stility digrm of the cse with mixture of three sensitive plnt types. The dshed lue curves show the equilirium precipittion ( V; t which re the sme s in Figure S,. The green, red nd lue curves refer to the equilirium vegettion curves for plnt types i =,,3. The precipittion thresholds re given in the figure cption. Figure S5 Stility digrms of three plnt types intercting with precipittion. Sme s C Figure S, ut for three plnt types with precipittion thresholds = 00mm/y, = 0 mm/y (green lines, C =80 mm/y, =300 mm/y (red lines, 3 = 360 mm/y, 3 = 380 mm/y (lue lines. The lck line is the verge vegettion coverge when using the niche pproch. The lck line is the verge vegettion coverge V S ( sed on the niche pproch. The steps in equilirium curve V S ( yields curves V S (t which develop smll hystereses in the deterministic simultion (see Fig. 3 d in the min text. In the stochstic simultions, these smll hystereses led to strong vritions in V S (t (see Fig. 3 e in the min text. Interestingly, our conceptul model with three plnt types (Fig. S5 resemles Fig. in Kleidon et l. 4, ut there re importnt differences. Kleidon et l. 4 rgued tht coupling of discrete (iome-like vegettion description with smll numer of plnt types to climte model lwys leds to multiple equiliri. This ehviour cn, indeed, e reproduced in our model, if the difference etween precipittion thresholds, referred to C D i, see Methods, q. 6 NATUR GOSCINC 03 Mcmilln ulishers Limited. All rights reserved. 6

7 DOI: 0.038/NGO96 (, is set to zero. If C Di SULMNTARY INFORMATION is lrger thn zero, then our conceptul model cn still produce multiple sttes, see red lines in Figures nd S. However, if C Di is sufficiently lrge, then it does not produce multiple equiliri, see green lines in Figures nd S. In this wy, our conceptul model is close ctully stepwise liner pproximtion - to the vegettion continuous description proposed y Brovkin et l. 5 nd depicted in Fig. in Kleidon et l. 4. In nture generlly more thn two or three different plnt types coexist. Hence we extend our nlysis to cses with more thn three plnt types. Figures S6, show the stility digrms of plnt types which hve the sme sensitivity to chnge in precipittion s in the cse depicted in Fig. S5 Figure S6 Stility digrms of five ( nd nine ( plnt types intercting with precipittion. Sme s Figure S, ut for five nd nine plnt types (here indicted y dshed red lines.the plnt types hve the sme sensitivity to chnge in precipittion s the plnt types shown in Fig. S5. Only the precipittion thresholds differ.. The precipittion thresholds in the cse with nine plnt types re chosen such tht the resulting verge vegettion coverge (lck line in Fig. S6 is not step function ny more, ut stright line. The slope of V S ( is smller thn /D B (the slope of the dshed lue precipittion curves in Fig. S6. Hence the ensemle of nine plnt types hs, on verge, stility chrcteristics which re very similr to those of plnt type in the cse of two different plnt types (Fig. S. NATUR GOSCINC Mcmilln ulishers Limited. All rights reserved.

8 SULMNTARY INFORMATION DOI: 0.038/NGO96 d e c f Figure S7 Trnsient dynmics of mixture of five nd nine sensitive plnt types intercting with climte. Sme s Fig. S,,c, ut for five (,, c nd nine (d, e, f plnt types. The trnsient ehviour of vegettion coverge of the individul plnt types re depicted s red lines. The precipittion thresholds nd stility chrcteristics of the individul plnt types for five plnt types nd nine plnt types re shown in Fig. S6,, respectively. The lck lines in, e show the verge vegettion coverge. The thin lck lines in c nd f re nnul men precipittion nd the thick lck lines, the 00-yer running men of precipittion. Fig. S7 shows tht, if more nd more plnt types re considered, the conclusions regrding ttenution of the climte vegettion interction still hold: the hystereses ecome nrrower, i.e., the interction etween plnt types nd precipittion ecomes more stle. In the stochstic simultions, ech plnt type revels rther grdul decline with strong fluctutions. So does the verge vegettion coverge nd the nnul men precipittion. By mere inspection of vegettion nd precipittion curves, one would dignose wek feedck of climte vegettion interction. In the cse with nine plnt types, the hystereses in V S ( cese to exist. However, due to the finite numer of types nd the fct tht ll curves ( re piecewise liner, V S (, nd the 8 NATUR GOSCINC 03 Mcmilln ulishers Limited. All rights reserved. 8

9 DOI: 0.038/NGO96 SULMNTARY INFORMATION deterministic cse of V S (t, still re non-differentile. In the limit of n infinite numer of types (N, V S ( will pproch sigmoidl shpe the piecewise liner shpe of the individul types is therefore smoothed out, especilly in cse of Gussin distriution of C 6,7. This fct seems resonle justifiction for the use of grdul V S ( with sigmoidl shpe in simple vegettion models 5,8. Such system would e completely undistinguishle from homogeneous cse of one plnt type only which follows the response function V S (. References. Bthiny, S., Clussen, M. & Fredrich, K. Implictions of climte vriility for the detection of multiple equiliri nd for rpid trnsitions in the tmosphere-vegettion system. Climte Dynm. 38, (0.. Hnsen, M., R. DeFries, J. R. Townshend, M. Crroll, C. Dimiceli, nd R. Sohlerg, 00 ercent Tree Cover, Collection 4, Vegettion Continuous Fields MOD44B, Univ. of Md., College rk ( New, M., Hulme, M. nd Jones,.D. Representing twentieth century spce-time climte vriility. rt : development of men monthly terrestril climtology. Journl of Climte, ( Kleidon, A., Fredrich, K. & Low, C. Multiple stedy-sttes in the terrestril tmosphereiosphere system: result of discrete vegettion clssifiction? Biogeosciences 4, ( Brovkin, V., Gnopolski, A. & Svirezhev, Y. A continuous climte-vegettion clssifiction for use in climte-iosphere studies. cologicl Modelling 0, 5-6 ( Sternerg, L. D. Svnn-forest hysteresis in the tropics. Glol cology nd Biogeogrphy 0, ( Scheffer, M., Holmgren, M., Brovkin, V. & Clussen, M. Synergy etween smll- nd lrge-scle feedcks of vegettion on the wter cycle. Glol Chnge Biology, ( Brovkin, V., Clussen, M., etoukhov, V. & Gnopolski, A. On the stility of the tmosphere-vegettion system in the Shr/Shel region. J. Geophys. Res. 03 (D4, (998. NATUR GOSCINC Mcmilln ulishers Limited. All rights reserved.