Model for Isotopic Composition of Tropical Tree Cellulose ----------------------------------------------------------------------- World Data Center for Paleoclimatology, Boulder and NOAA Paleoclimatology Program ----------------------------------------------------------------------- NOTE: PLEASE CITE CONTRIBUTORS WHEN USING THIS DATA!!!!! NAME OF DATA SET: Model for Isotopic Composition of Tropical Tree Cellulose LAST UPDATE: 10/2007 (Original receipt by WDC Paleo) CONTRIBUTOR: Michael N. Evans (University of Arizona) IGBP PAGES/WDCA CONTRIBUTION SERIES NUMBER: 2007-094 SUGGESTED DATA CITATION: Evans, M.N. 2007. Model for Isotopic Composition of Tropical Tree Cellulose. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-094. NOAA/NCDC Paleoclimatology Program, Boulder CO, USA. ORIGINAL REFERENCES: Evans, M.N. 2007. Toward forward modeling for paleoclimatic proxy signal calibration: A case study with oxygen isotopic composition of tropical woods. Geochemistry, Geophysics, Geosystems, Vol. 8, No. 7, July 2007. DOI:10.1029/2006GC001406. Barbour, M.M., J.S. Roden, G.D. Farquhar and J.R. Ehleringer. 2004. Expressing leaf water and cellulose oxygen isotope ratios as enrichment above source water reveals evidence of a Peclet effect. Oecologia, vol. 138, pp. 426-435, DOI: 10.1007/s00442-003--1449-3. New, M., M. Hulme and P. Jones. 2000. Representing Twentieth-Century Space-Time Climate Variability, Part II: Development of 1901-1996 Monthly Grids of Terrestrial Surface Climate. Journal of Climate, Vol. 13, Issue 13, pp. 2217-2238, July 2000. ABSTRACT (Evans 2007): A forward model of the oxygen isotopic composition (d18O) of wood cellulose is parameterized for time series prediction in tropical environments and driven with meteorological data observed at La Selva Biological Research Station, Costa Rica, for 1985–2001. Monthly-resolution model results correlate modestly (r = 0.34, p < 0.05) with observed isotopic data, with higher correlation (r = 0.45, p < 0.01) over the earliest 10 years of comparison and nonsignificant correlation over the most recent 6 years of record. Analysis of model output for La Selva suggests that isotopic variations are strongly controlled by rainfall amount. The model simulates an analogous but stronger than observed negative isotopic anomaly associated with positive July-September rainfall anomalies during El Nino-Southern Oscillation (ENSO) warm phase event years. Simulated tree isotope data for the global tropics suggest that a network of well-replicated data series from selected locations may resolve the large-scale precipitation anomaly pattern associated with ENSO. GEOGRAPHIC REGION: Northwestern Costa Rica PERIOD OF RECORD: La Selva isotope modeling is 1985-2001; global modeling exercise 1901-2002. FUNDING SOURCE: National Science Foundation, USA grant ATM-0349356. DESCRIPTION: Matlab tree cellulose isotope modelling programs and sample input data imc.m: main program reading meteorological data and parameters; with Monte-Carlo routine for parameter sensitivity estimation ims.m: isotope model core, called by imc.m. rimco.m: script for loading meteorological forcing data, running imc.m, plotting results (matlab only). mc.dat: input data, described in Evans (2007). Please see commenting within model and the references for additional information on the model coding. The code is released under Gnu Public License: you are free to copy, modify and distribute it, with the entire contents of the .tar.gz file. Please contact author with bug reports and improvements. The isotopic model has been tested in the following programming environments, x86_64 cpu architecture, linux operating system: -- Matlab v. 2007a (commercial: www.mathworks.com) -- Octave v. 2.9.9 (freeware: www.octave.org) A database of model output for the tropics (30N-30S), based on the CRU [T,P,Td] dataset (New et al., 2000) version TS2.1, default model parameters, as from Evans (2007), and with random 0.3 permil observational error, is at: http://kalman.ldeo.columbia.edu:81/expert/(/home/mevans/im7/im7.in)/readfile/.o18c/. DATA: 1. Program file imc.m: function [o18e,o18l,o18s,o18c,o18cc,mcerr,o18ccp]=imc(pr,ta,rh,dfs,dfb,efc,blc,c10,c11,pl,feo,fwxm,c1,c2,c3,c4,c5,c6,c7,c8,c9) % function [o18e,o18l,o18s,o18c,o18cc,mcerr]=imc(pr,ta,rh,dfs,dfb,efc,blc,c10,c11,pl,feo,fwxm,c1,c2,c3,c4,c5,c6,c7,c8,c9) % Barbour-modified Roden model % for use in constructing synthetic % oxygen isotope series % for comparison with collected data % after Barbour et al. (2004) % (hereafter referred to as BRFE2004) % See end of script for full references cited % % % % default values for BRFE2004 model parameters are: % % dfs=32; % diffusive fractionation through stomata (per mil) % dfb=21; % diffusive fractionation through boundary layer (per mil) % efc=27; % equilibrium fractionation between C=O and water (per mil) % blc=2100; % boundary layer conductance (mmol m-2 s-1) % pl=0.018; % effective length for the Peclet effect (m) % feo=0.42; % proportion of exchangeable oxygen in cellulose % fwxm= 1.0; % proportion of xylem water in meristem % % parameters for timeseries model extension are: % % ta = air temperature(degC) % pr = precipitation(mm/mo) % rh = relative humidity(%) % c1 = y-intercept of o18sw vs. precipitation amount relationship % c2 = slope of o18sw vs. precipitation amount relationship % c3 = y-intercept of leaf T vs. air T relationship % c4 = slope of leaf T vs. air T relationship % c5 = height(Km) at which precip reaching ground is condensing % c6 = moist adiabatic lapse rate (K/Km) % c7 = mean observed o18 of cellulose (for baseline correction) % c8 = fraction RMS variance due to environmental forcing % c9 = percent uncertainty in model parameters for Monte Carlo % error estimation % c10 = first constant for stomatal conductance function of air vapor pressure deficit % (mb mmol m-2 s-1 ) % c11 = second constant for stomatal conductance function of air vapor pressure deficit % (mmol m-2 s-1) % % default values of timeseries model extension parameters are: % % c1 = 0.74 permil; % [Lachniet and Patterson, 2004 (submitted)] % c2 = -0.0285 permil/(mm/mo); % [Lachniet and Patterson, 2004] % c3 = 10 degC; % [Linacre, 1964] % c4 = 23/33 degC/degC; % [Linacre, 1964] % c5 = 3 Km; % [after Lawrence and Gedzelman (2003); Lawrence et al. (2004)] % c6 = 6 K/Km; % [e.g. Wallace and Hobbs, 1977] % c7 = 27 permil; % [reasonable values are 24-35 permil] % c8 = 0.45; % free parameter chosen to match variance in simulated % vs. observed data % c9 = 20; % percent uncertainty in model parameters for Monte Carlo % error estimation %error(nargchk(1,21,nargin)); if nargin <= 21, dfs=32; dfb=21; efc=27; blc=2100; pl=0.018; feo=0.42; fwxm= 1.0; c1 = 0.74; c2 = -0.0285; c3 = 10; c4 = 23/33; c5 = 3; c6 = 6; c7 = 27.17; c8 = 0.45; c9 = 20; c10= 4290; c11=-43; end c=[dfs dfb efc blc c10 c11 pl feo fwxm c1 c2 c3 c4 c5 c6 c7 c8 c9]; % simulation with selected parameter values: [o18e,o18l,o18s,o18c,o18cc]=ims(pr,ta,rh,dfs,dfb,efc,blc,c10,c11,pl,feo,fwxm,c1,c2,c3,c4,c5,c6,c7,c8); % apply Monte Carlo parameter error estimation to get error bars: o18ep=zeros(1,length(pr)); o18lp=zeros(1,length(pr)); o18sp=zeros(1,length(pr)); o18cp=zeros(1,length(pr)); o18ccp=zeros(1,length(pr)); a=0; v=[(100-c(18))/100:2*c(18)/(100*(length(c)-1)):(100+c(18))/100]; cm=zeros(1,length(v)); mcerr=zeros(length(pr),2*5); if c(18)==0, cm=c; [o18emc,o18lmc,o18smc,o18cmc,o18ccmc]=ims(pr,ta,rh,cm(1),cm(2),cm(3),cm(4),cm(5),cm(6),cm(7),cm(8),cm(9),cm(10),cm(11),cm(12),cm(13),cm(14),cm(15),c(16),cm(17)); o18ep=o18emc'; o18lp=o18lmc'; o18sp=o18smc'; o18cp=o18cmc'; o18ccp=o18ccmc'; cmp=cm; elseif c(18) ~=0, for i=1:1000 m=randperm(length(v)); cm=c.*v(m); [o18emc,o18lmc,o18smc,o18cmc,o18ccmc]=ims(pr,ta,rh,cm(1),cm(2),cm(3),cm(4),cm(5),cm(6),cm(7),cm(8),cm(9),cm(10),cm(11),cm(12),cm(13),cm(14),cm(15),c(16),cm(17)); o18ep(i,:)=o18emc'; o18lp(i,:)=o18lmc'; o18sp(i,:)=o18smc'; o18cp(i,:)=o18cmc'; o18ccp(i,:)=o18ccmc'; cmp(i,:)=cm; end end if c(18)~=0, o18eps=sort(o18ep); o18lps=sort(o18lp); o18sps=sort(o18sp); o18cps=sort(o18cp); o18ccps=sort(o18ccp); mcerr=[o18eps(50,:)' o18eps(950,:)' o18lps(50,:)' o18lps(950,:)' o18sps(50,:)' o18sps(950,:)' o18cps(50,:)' o18cps(950,:)' o18ccps(50,:)' o18ccps(950,:)']; end return 2. Program file ims.m: %-------- subroutine ims.m------------% function [o18e,o18l,o18s,o18c,o18cc]=ims(pr,ta,rh,dfs,dfb,efc,blc,c10,c11,pl,feo,fwxm,c1,c2,c3,c4,c5,c6,c7,c8) % Parameterized variable calculations o18sw = c1 + c2*pr; lt= c3 + c4.*ta; tc=-c6*c5+273.15+ta; alv=exp(1137./tc.^2 -0.4156./tc -0.00207); o18wva=1000*(1./alv-1)+o18sw; % Majoube, 1971; referenced in % Gonfiantini et al., 2001: % equilibrium fraction between water % liquid and vapor %o18wva = o18sw - 8; % Constants rsmow=0.0020052; % 18/16 ratio for intl working std cw=55500; % concentration of water (mol/m^3) dw=0.00000000266; % diffusivity of H218O in water (m^2/s) % calculated parameters % environmental conditions svpa=(6.13753.*exp(ta.*((18.564-(ta./254.4)))./(ta+255.57))); % saturated vapour pressure of the air (mbar) avpa=(rh./100).*svpa; % actual vapour pressure of the air (mbar) rsw=((o18sw./1000)+1)*rsmow; % 18O/16O of source water rwv=((o18wva./1000)+1)*rsmow; % 18O/16O of water vapour do18wvs=((rwv./rsw)-1)*1000; % delta 18O of water vapour (per mil, wrt source water) % leaf evaporative conditions vpl=(6.13753.*exp(lt.*((18.564-(lt./254.4)))./(lt+255.57))); % leaf internal vapour pressure (mbar) vpd=vpl-avpa; % leaf - air saturation vapor pressure deficit (mbar) sc=c10./vpd + c11; % Lohammar function for sc=f(vpd); vpd units in mb; sc units in mmol/m^2/sec tr=sc.*vpd./1013; % tr = sc*vpd/Patm (mb); % Note for tr calculation, atmospheric pressure is assumed constant at sea level value; % this should be adjusted for sites at appreciable elevation, or input as monthly timeseries p=((tr./1000)*pl)./(cw*dw); % Peclet number % fractionation factors tdf=(((1./sc).*dfs)+((1/blc)*dfb))./((1/blc)+(1./sc)); % total diffusive fractionation (per mil) evpf=((exp((1137./((lt+273.16).^2))-(0.4156./(lt+273.16))-0.0020667))-1)*1000; % equilibrium vapour pressure fractionation (per mil) % outputs do18e=(((1+(evpf./1000)).*(1+(tdf./1000)+(((do18wvs./1000)-(tdf./1000)).*(avpa./vpl))))-1).*1000; % Craig-Gordon evaporation-site water (D\18Oe) (per mil wrt source water ) do18l=(do18e.*(1-(exp(-p))))./p; % Bulk leaf water (D18OL) (per mil wrt source water) do18s=do18l+efc; % Sucrose D18O (per mil wrt source water) do18c=do18l.*(1-(fwxm*feo))+efc; % Cellulose D18O (per mil wrt source water) % [do18e; do18l; do18s; do18c]; %convert back into ratios wrt SMOW: M=1000; o18e=(((do18e./M+1).*rsw)./rsmow-1).*M; o18l=(((do18l./M+1).*rsw)./rsmow-1).*M; o18s=(((do18s./M+1).*rsw)./rsmow-1).*M; o18c=(((do18c./M+1).*rsw)./rsmow-1).*M; % correct to observed o18 given observed mean (c7) % and fraction (c8) water from meteoric sources j=find(~isnan(o18c)); o18cc=o18c; o18cc(j)=c8.*(o18c(j)-(mean(o18c(j))-c7))+(1-c8).*c7; return %------------------ % References cited: % % M.M. Barbour, J.S. Roden, G.D. Farquhar, J.R. Ehleringer, 2004, % Expressing leaf water and cellulose oxygen isotope ratios as % enrichment above source water reveals evidence of a Peclet effect, % Oecologia 138:426-435, doi 10.1007/s00442-003-1449-3 excel model % from ftp://ecophys.biology.utah.edu/tree_ring/ % % Lachniet, M.S. and W.P. Patterson, 2006: Use of correlation and % stepwise regression to evaluate physical controls on the stable % isotope values of Panamanian surface waters, J. Hydrology, 324(1-4), % 115-140. % % Lawrence, J.R. and S.D. Gedzelman, 2003: Tropical ice cores: Do they % reflect changes in storm activity?, Geophys. Res. Lett., 30(2), 1072, % DOI:10.1029/2002GL015906. % % Lawrence, J.R. and S.D. Gedzelman, D. Dexheimer, H.-K. Cho, G.D. Carrie, % R. Gasparini, C.R. Anderson, K.P. Bowman and M.I. Biggerstaff, 2004: % Stable isotopic composition of water vapor in the tropics, J. Geophys. % Res., 109, D06115, DOI:10.1029/2003JD004046. % % Linacre, E.T., 1964: A note on a feature of leaf and air % temperatures, Agr. Meteorol. 1:66-72. % % Wallace, J.M. and P.V. Hobbs, 1977: Atmospheric Science: An Intro- % ductory Survey, New York: Academic Press, 467 pp. 3. Program file rimco.m: % test imc.m and ims.m for compatibility with matlab and octave clear load mc.dat % data from La Selva meteorological station %lsm=mc(34:34+193,:);t=lsm(:,1); lsm=mc;t=lsm(:,1); pr=lsm(:,2);ta=lsm(:,3);rh=lsm(:,4); % Set parameters and variables as in Evans (2007) c1 = 0.74; c2 = -0.0285; c3 = 10; c4 = 23/33; c5 = 3; c6 = 6; c7 = 27.17; c8 = 0.45; c9 = 20; c10=4290; % first constant for stomatal conductance calc (mb mol m-2 s-1) c11=-43; % second constant for stomatal conductance (mmol m-2 s-1) dfs=32; % diffusive fractionation through stomata (per mil) dfb=21; % diffusive fractionation through boundary layer (per mil) efc=27; % equilibrium fractionation between C=O and water (per mil) blc=2100; % boundary layer conductance (mmol m-2 s-1) [Reich et al., 2004] pl=0.018; % effective length for the Peclet effect (m) feo=0.42; % proportion of exchangeable oxygen in cellulose [Roden et al. 2000] fwxm= 1.0; % proportion of xylem water in meristem [Barbour et al. 2002] c=[dfs dfb efc blc c10 c11 pl feo fwxm c1 c2 c3 c4 c5 c6 c7 c8 c9 ]; tic [o18e,o18l,o18s,o18c,o18cc,mcerr,o18ccp]=imc(lsm(:,2),lsm(:,3),lsm(:,4),c(1),c(2),c(3),c(4),c(5),c(6),c(7),c(8),c(9),c(10),c(11),c(12),c(13),c(14),c(15),c(16),c(17),c(18)); toc %% plotting will only work in matlab figure(1) subplot(211) % o18cc plot(t,o18cc,'k',t,mcerr(:,9),'y'); % legend('default params','MC +/-20% values 95% conf int') % legend boxoff hold on fill([t;flipud(t)],[mcerr(:,9);flipud(mcerr(:,10))],'y','edgecolor','y'); axis([1985 2001 18 34]) plot(t,o18cc,'k') hold off grid set(gca,'FontName','Times','Fontsize',16) set(gca,'YTick',[18:2:34]); set(gca,'XTick',[1985:2:2001]) title('sensitivity of model to parameters and variables') ylabel('modeled \delta^{18}O') text(1985.24,33,'a','Fontname','Times','Fontsize',16); 4. Sample data file mc.dat 1.9822917e+03 8.0600000e+01 2.5820000e+01 8.6440200e+01 1.9823750e+03 1.1930000e+02 2.6933050e+01 8.6059196e+01 1.9824583e+03 5.6860000e+02 2.6508935e+01 9.0844835e+01 1.9825417e+03 8.5100000e+02 2.4665517e+01 9.4940794e+01 1.9826250e+03 6.7140000e+02 2.6107968e+01 9.2149502e+01 1.9827083e+03 5.5390000e+02 2.6211855e+01 9.0902820e+01 1.9827917e+03 7.9360000e+02 2.5821883e+01 9.3568900e+01 1.9828750e+03 4.5470000e+02 2.5342484e+01 9.0510686e+01 1.9829583e+03 4.5220000e+02 2.4786050e+01 9.0869626e+01 1.9830417e+03 2.9220000e+02 2.4950629e+01 8.9156066e+01 1.9831250e+03 1.5080000e+02 2.5782983e+01 8.7167742e+01 1.9832083e+03 1.3430000e+02 2.6503650e+01 8.6505482e+01 1.9832917e+03 1.6100000e+01 2.6476129e+01 8.5342471e+01 1.9833750e+03 4.8830000e+02 2.6541317e+01 9.0019492e+01 1.9834583e+03 3.3090000e+02 2.7491306e+01 8.7789999e+01 1.9835417e+03 6.5370000e+02 2.6861483e+01 9.1452577e+01 1.9836250e+03 3.2120000e+02 2.6696661e+01 8.8241304e+01 1.9837083e+03 3.6840000e+02 2.6844290e+01 8.8611440e+01 1.9837917e+03 4.9780000e+02 2.6317200e+01 9.0269132e+01 1.9838750e+03 1.6430000e+02 2.6076984e+01 8.7099881e+01 1.9839583e+03 1.2120000e+02 2.5238050e+01 8.7247746e+01 1.9840417e+03 2.7880000e+02 2.4196081e+01 8.9542704e+01 1.9841250e+03 2.1500000e+02 2.5396250e+01 8.8076588e+01 1.9842083e+03 1.4800000e+02 2.5539383e+01 8.7307826e+01 1.9842917e+03 7.2100000e+01 2.6806016e+01 8.5674849e+01 1.9843750e+03 3.4280000e+02 2.6471633e+01 8.8612573e+01 1.9844583e+03 3.3650000e+02 2.6357661e+01 8.8628214e+01 1.9845417e+03 2.7880000e+02 2.6172183e+01 8.8179193e+01 1.9846250e+03 4.2960000e+02 2.5891081e+01 8.9881154e+01 1.9847083e+03 2.4270000e+02 2.6326677e+01 8.7711593e+01 1.9847917e+03 4.7350000e+02 2.5718300e+01 9.0439373e+01 1.9848750e+03 4.2660000e+02 2.5096435e+01 9.0399460e+01 1.9849583e+03 3.0130000e+02 2.4614667e+01 8.9478880e+01 1.9850417e+03 1.2370000e+02 2.3995597e+01 8.8130038e+01 1.9851250e+03 2.3270000e+02 2.4475690e+01 8.8888774e+01 1.9852083e+03 8.3300000e+01 2.4718250e+01 8.7227407e+01 1.9852917e+03 7.1800000e+01 2.5905661e+01 8.6293094e+01 1.9853750e+03 1.8900000e+02 2.6435850e+01 8.7099264e+01 1.9854583e+03 6.1570000e+02 2.6047823e+01 9.1634002e+01 1.9855417e+03 3.1800000e+02 2.5560100e+01 8.8993531e+01 1.9856250e+03 4.6270000e+02 2.5510161e+01 9.0474989e+01 1.9857083e+03 3.6390000e+02 2.7004677e+01 8.8455773e+01 1.9857917e+03 2.2400000e+02 2.6650550e+01 8.7301120e+01 1.9858750e+03 3.1270000e+02 2.6184516e+01 8.8509684e+01 1.9859583e+03 1.6940000e+02 2.4586417e+01 8.8179372e+01 1.9860417e+03 1.9690000e+02 2.3556355e+01 8.9165115e+01 1.9861250e+03 1.0020000e+02 2.4863397e+01 8.7296256e+01 1.9862083e+03 2.1180000e+02 2.4823717e+01 8.8439636e+01 1.9862917e+03 2.3560000e+02 2.6016839e+01 8.7854381e+01 1.9863750e+03 1.7590000e+02 2.6268233e+01 8.7083919e+01 1.9864583e+03 5.1890000e+02 2.6660210e+01 9.0243455e+01 1.9865417e+03 4.4320000e+02 2.6166533e+01 8.9827092e+01 1.9866250e+03 5.8920000e+02 2.6592774e+01 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