Polygon 1.5 user manual (18/Oct./2008) - 1
Contents
1. m Taxa fees Manual change Sisal Reset envelope Bi C Sequential 01 r Hide Tight Loose r Reference sites import fossil data Diagram Show all H Envelope analysis Sequential Hide Reset envelope 04 r Fossil data _ SSS C Show all ant wate C Sequential Diagram Hide Reconstruction Fig 11 Both pollen diagram and trajectory in the EOF space are showing essentially the same things in two different ways Those two windows as well as every other window are synchronized i e if you change selection of horizon in one window the display in the other window automatically follows it A Outliers detected by envelope analysis OLIN open red circle in the main window and red line in the diagram File E Edit E About Polygon A Import reference data r EOF analysis Axis settings M 22327 3 C Automatic change Interval sec m Manual change Prev r Envelope analysis Reset envelope T Fossil data oana C Showall Tight Loose Sequential 22327 3 X Diagram C Hide Reconstruction No of Axes 5 includ Curve Style S Tools T ACER AESCULUS ALNUS CAMELLIA CARPINUS CASTANOP CORYLUS CRYPTOMER gt EOFNo 1 E Quit B Manually selected horizon closed red circle in the main window2. Tarasov P Bezrukova E Karabanov Nakagawa T Wagner M Kulagina N Letunova P Abzaeva A Granoszewski W Riedel F Submitted Late glacial and Holocene vegetation and climate dynamics derived from the Buguldeika pollen record from Lake Baikal Russia Palaeogeography Palaeoclimatology Palaeoecology 12 Fig 1 Simplified flowchart of Polygon 1 5 Perform modern analogues technique Display results Calibrate results Input reference dataset Data pre treatment EOF analysis of reference dataset Return results to Polygon 1 5 Display results 2D or 3D Accuracy test by Leave one out method Display results Launch PolCalib 2 0 Launch PolHist 2 0 Input fossil dataset Envelop analysis detecting outlying fossil data Display results probability distribution or Display results 2 D or 3 D Input climate interpolation error model Input climate dataset End Generate calibration model Display results Perform calibration confidence regions Fig 2 Formatting of datasheets for Polygon 1 5 21 737 22 3678 Site names must be consistent between surface pollen and interpolated climate datasheets Eg SS Sse aS E Taxa names must be cena ABIES ACER ULMUSZEL VIBURNUM consistent betwee
3. Smoothing level 3 PalCalib PolHist pulkai m Define chord distance by Taxa proportions C EOF values Axis settings m Options No of analogs 8 2 Z enhancement Threshold 0 2 C Probability Confidence IV Inversed weighting Vv 22327 3 x Squared distance Distance IV Show Mode M Show Average I Enhancing minor taxa ms Square root Log
4. The calibration model generated by PolCalib 3 0 can be returned to Polygon 1 5 by clicking Return button of 10 Polygon 1 5 user manual 18 Oct 2008 PolCalib 3 0 D in Fig 17 The final step of the whole package of Polygon 1 5 which is calibration can be done by a single action of clicking the PolHist button A in Fig 19 Result can be saved both graphically and numerically in the same way as the other diagrams generated by Polygon 1 5 Results can be expressed in both probability density distribution and confidence regions Fig 20 Users can also choose between whether or not to show lines indicating mode and average of the probability density distribution 6 2 Calibration target important Calibration is not done on the original curve blue curve but on the smoothed curve of the running average red curve If you need to calibrate the original curve cancel the function of smoothing by moving the slider to the value of 1 running average of only 1 sample no smoothing 6 3 Resizing Resizing the diagrams can be easily done by moving a slider resizing vertical scale A in Fig 21 and stretching the window using mouse resizing horizontal scale B in Fig 21 You can copy resized images into your Windows clipboard by clicking the right button of your mouse on the target window 7 Questions and bug reports Queries and bug reports should be sent directly to the author E mail
5. and blue line in the diagram O x Fig 12 New window for climate reconstruction W Reconstruction Fig 13 Result of the climate reconstruction in default setting O Reconstruction Fie E Edt E Import climate data m Define chord distance by D gt Ss Taxa proportions EOF values Axis settings Smoothing level 3 m Options No of analogs 8 F a Threshold 0 2 G P M inversea weighting Squared distance Distance H T Enhancing minor taxa Square root f Log 5 xl Generate error model Fig 14 Result of the climate reconstruction and the error model generated by leave one out method A O Reconstruction 10 x File E Edit E Import climate data Smoothing level 3 PolHist p m Define chord distance by Taxa proportions C EOF values Axis settings r Options No of analogs 8 Zenhancement lt Vv 22327 3 x Probability C Confidence Threshold 0 2 Inversed weighting Squared distance C Distance V Show Mode IV Show Average Enhancing minor taxa z Square root Log Fig 15 New window of PolCalib 3 0 VPolcalib 3 0 Torx F Show fitting line R Showmode M Show ave Fig 16 PolCalib 3 0 showing climate reconstruction error scatter diagram in the first window and the error in climate estimation at
6. format that can be immediately imported to Polygon 1 5 PolCalib 2 0 normalises the probability density distribution only once along the vertical axis A in Fig 17 Before this step PolCalib 3 0 is able to insert another step of normalisation along the horizontal axis by clicking a check box B in Fig 17 and Fig 18 Insertion of this step helps to reduce the effect of uneven distribution of the surface pollen dataset However distortion of the calibration model towards the marginal parts end effect tends to become larger In other words if your reference dataset covers a large climatic range but has considerably uneven site distribution it is recommended to insert this step If by contrast your dataset is not so extensive but has more or less even coverage for the whole range of climate it is recommended to skip this step In order to reduce the end effect it is possible by PolCalib 3 0 to reject areas represented by too small number of sites Users can define threshold by sliders C in Fig 17 In the final calibration model expressed in probability density distribution A in Fig 17 PolCalib 2 0 leaves some areas blank when the probability density value is below arbitrary threshold In PolCalib 3 0 blank means that the area is not within the confidence regions which is statistically more meaningful This difference also applies to the all following steps 6 Calibration of reconstructed curve 6 1 Outline
7. it in both EOF projection and the conventional pollen diagram Either sliding the blue line in the diagram window or clicking Next or Prev buttons of the fossil data in the main window can do this selection The diagram window is resizable Both height and width of the pollen diagram change following the window size The window also shows EOF scores orthogonal projection of fossil data onto the EOFs of the surface dataset which is potentially useful to identify the vegetation types represented by the EOF axis However authors do not suggest using the EOF scores as proxies of any climatic parameters because theoretically it does not make sense 4 Climate reconstruction by modern analogues technique using Polygon 1 5 4 1 Reconstruction by default setting Once the envelope analysis has been done the climate reconstruction by modern analogues technique is ready A new window will open if you click on the Reconstruction button D in Fig 7 and you will be requested to import the dataset of climate estimated at surface pollen sites 3_climate_data scv file in the sample data collection please refer to Nakagawa et al 2002 for details by the highlighted Import climate data button If you do not have the datasheet of climate already estimated at each surface pollen site but only have a raw climate dataset at meteorological observatories and coordinates of surface pollen site use Polation 1 0 software w
8. potentially useful to exclude human influence from your analyses if Polygon 1 5 user manual 18 Oct 2008 you can identify an EOF that is showing a degree of anthropogenic disturbance on the forest To perform envelope analysis click the Envelope button B in Fig 8 Open red circles on the trajectory indicate fossil assemblages that are not included in the envelope The surface sites that constitute corner points are shown in blue colour Obviously the more axes you include for the analysis the more horizons tend to come out of the envelope Fig 10 If you include all EOFs as an extreme case presence absence of only one minor taxon may cause otherwise quite normal assemblages be recognised as an outlier This is not scientifically meaningful Realistically choosing only major EOF axes whose cumulative contribution to the total variability exceeds 70 or 80 will be a good compromise The contribution of each EOF and the cumulative contribution of chosen EOFs are both given on the control panel Fig 9 3 7 Pollen diagram If one or more horizons were recognised as outliers by the envelope analysis it is also possible to check these horizons in conventional pollen diagram If you click on the Diagram button C in Fig 7 a new window opens and shows the pollen diagram red lines represent the outliers A in Fig 11 It is also possible to select any horizon from the fossil pollen dataset and visualise
9. takeshi nakagawa newcastle ac uk Acknowledgements The author thanks Pavel E Tarasov for introducing me to the world of numerical approaches of palaeoecology Yoshiharu Akahane for introducing me to the world of programming Kotoba Nishida for helping me in mathematics and anonymous Yahoo Japan community members for assisting me for coding grammar References Guiot J 1990 Methodology of the last climatic cycle reconstruction in France from pollen data Palaeogeography Palaeoclimatology Palaeoecology 80 49 69 Gotanda K Nakagawa T Tarasov P E Kitagawa J Inoue Y Yasuda Y 2002 Biome classification from Japanese pollen data application to modern day and Late Quaternary samples Quaternary Science Reviews 21 647 657 Nakagawa T Tarasov P E Nishida K Gotanda K Yasuda Y 2002 Quantitative pollen based climate reconstruction in central Japan application to surface and Late Quaternary spectra Quaternary Science Reviews 21 2099 2113 Polygon 1 5 user manual 18 Oct 2008 Nakagawa T Kitagawa H Yasuda Y Tarasov P E Nishida K Gotanda K Sawai Y Yangtze River Civilization Program Members 2003 Asynchronous Climate Changes in the North Atlantic and Japan During the Last Termination Science 299 688 691 Nakagawa T Tarasov P Kitagawa H Yasuda Y Gotanda K 206 Seasonally specific responses of the East Asian monsoon to deglacial climate changes Geology 34 521 524
10. the surface pollen sites second window Special attention must be paid to use proper estimation error model according to the climate parameter of the curve that you are going to calibrate B in Fig 14 A 5 x ARE E Import Vest Vobs file File E Edit E About A I Show fitting line I Generate model Threshold 2 sample s Smoothing level 10 Skip Basal width of range N1 285 N2 147 R1 0 8431611 R2 0 9860364 Fitting line y 0 989 x 0 181 Std Dev 0 66087 j Retin Threshold 1 sample s Se ee Confidence coefficients _ _clese___ M Showmode M Show ave Fig 17 End product of PolCalib 3 0 J PolCalib 3 0 File F Edit E About A I Show fitting line J Generate model hreshold 2 sample s Smoothing level 10 F Skip B Basal width of N1 285 N2 147 R1 0 8431611 F R2 Fitting line Std Dev ETEA i D Threshold 1 sample s emmy ral ayy Confidence coefficients V Showmode V Show ave Fig 18 Artificially generated climate estimation error model top right corner YPolcalib 3 0 Dox F Show fitting line R Showmode M Show ave Fig 19 Reconstructed climate curve and the calibration model generated by PolCalib 3 0 just one step ahead from Fig 14 O Reconstruction Fie F Edit E Impor climate data m Define chord distance by T
11. N No PN eee e i z 2 z 3 z 2 14 961 51 87 3 11 223 63 093 EOFs for emvelope analysis 4 9 908 73 001 5 6 082 79 084 lM Set more axes 6 5 882 84 966 7 5 217 90 183 1 1 8 3 342 93 525 2 2 g 1 577 95 102 3 3 10 1 277 96 38 4 Addie 4 1 0 851 97 231 5 5 12 0 697 97 928 6 E 13 0 287 98 215 7 ae 14 0 275 98 49 8 15 0 215 98 704 g 16 0 191 98 895 1 17 0 152 39 047 v Total 79 084 Total 100 No of selected EOFs 5 No of parameters 32 Reflect Fig 10 Two different results of envelop analyses using EOFs 1 3 left and EOFs 1 5 right EOFs 1 4 and 5 are being used for the display of the 5 D image All fossil data are included in the envelope tightness 0 1 in case of 3 axes whereas one horizon A becomes outlier when 5 axes are used sox File E Edit E About Polygon A m Display mode gt Import reference data EOF 2 p 4 2D Role k r EOF analysis 3D Wl mee Velocity k Axis settings 4 4 TO IIx ayaa etoRhenee a rm File E Edt E About Polygon a 4 L r Display mode Interval sec EOF 3 F Import reference deta Manual change D Ota ee See 3D m e Velocity I Stereo V Pause Reverse Tick Label r EOF analysis 4 Axis settings No of Axes 3 all visible Prey Next 2 C Automatic change import fogeil data Interval sec
12. Polygon 1 5 user manual 18 Oct 2008 Polygon 1 5 a user friendly Windows programme for climate reconstruction using palaeoecological data seamlessly bundled with PolCalib 3 0 and PolHist 2 5 programs for calibration of reconstruction results Takeshi NAKAGAWA Department of Geography University of Newcastle Newcastle upon Tyne NE 7RU UK takeshi nakagawa newcastle ac uk Abstract This paper is a brief instruction of Polygon 1 5 the newly developed free PC software that principally performs quantitative climate reconstruction by modern analogue technique using palaeoecological datasets pollen diatom etc The reconstruction can be done using either percentage values of all taxa or selected EOF axes The program package also provides some other useful features including i visualisation of the distribution pattern of the reference dataset using 2 D or 3 D graphics of the space defined by EOFs ii visualisation of the fossil dataset as the trajectory in the same EOF space iii identification of outliers among the fossil dataset envelope analysis iv drawing temporary pollen diagram v generation of error models specific to the reconstruction method and datasets vi calibration of the reconstruction results using the error model and vii the ability to export result figures to the clipboard Polygon 1 5 has a very user friendly graphical interface that helps users adapt to the software easily An installer package of the so
13. a files Choice of taxa is not essential for the software Users can include any number of taxa in any order as far as they are consistent between surface and fossil pollen data files There is no limitation for either the taxa or pollen site name lengths Users can also include as many climatic parameters as they want but again the site names and their order need to be consistent between the surface pollen dataset and the dataset of climatic values estimated interpolated to each surface pollen site Fig 2 All datasheets must be saved in csv format Polygon has a function to re calculate percentage values for the surface pollen values i e you do not necessarily need to type in percentage values instead of raw counts to the surface pollen dataset However fossil dataset must be expressed in percentage values taking the sum of all pollen taxa included in the datasheet as 100 If you put additional lines at the top and the bottom of the fossil data series and input zero value for all taxa the depths or ages of those void horizons will be used as the top and bottom of the range of time series diagrams If Polygon 1 5 user manual 18 Oct 2008 you insert such void horizon with zero values in the middle of the data series Polygon 1 5 will consider it as the discontinuity of curves at that horizon 3 Envelope analysis by Polygon 1 5 3 1 Outline Before reconstructing climate Polygon 1 5 is required to perform envel
14. any users across the world However the author has received a lot of requests from users to provide written instruction which did not previously exist The aim of this paper is to meet these requests and provide the first complete instruction of Polygon 1 5 Hereafter the instructions will be written assuming that the user is reconstructing climate in Japan using fossil and surface pollen datasets just for clarity However this choice is essentially arbitrary and precisely the same approach can be applied to any other region for any environmental parameter 0 Framework of Polygon 1 5 Fig 1 is a simplified flowchart showing only the main stream of climate reconstruction and results calibration by Polygon 1 5 Almost all the steps are performed either automatically or by clicking a single button Normally the next action that needs to be made is indicated by usually one highlighted button Polygon 1 5 user manual 18 Oct 2008 1 Installation of Polygon 1 5 An installer package of Polygon 15 can be downloaded from the web page lt http dendro naruto u ac jp nakagawa gt The download has no limitation and is free of charge Extract the downloaded zip file and double click SetUp exe file Next simply follow the ordinary procedures of installing Windows software If successfully installed you will find a shortcut to the Polygon software in your Start menu Start gt Programs gt Polygon gt Polygon 1 5 You do not need to restart y
15. axa proportions C EOF values Axis settings r Options No of analogs 8 Threshold 0 2 Inversed weighting Squared distance C Distance I Enhancing minor taxa Square root Log Smoothing level 3 PolCalib Zenhancement Probability C Confidence IV Show Mode NM Show Average Vv 22327 3 x Fig 20 End product of Polygon 1 5 expressed in probability density distribution upper and confidence regions lower modes Reconstruction E la x File F Edit E Import climate data Smoothing level 3 PolCalib PolHist m Define chord distance by Taxa proportions C EOF values Axis settings m Options No of analogs 8 Threshold w Zenhancement m 223237 3 gt I Inversed weighting Probability C Confidence Squared dictanre C Dist Gin File E Edit E I Enhan Squ Import climate data Smoothing level 3 PolCalib PalHist Los _ Define chord distance by 5 Taxa proportions C EOF values Axis settings r Options No of analogs 8 Threshold 0 2 Zenhancement Vv 22327 3 x _ _ C Probability Confidence Inversed weighting Squared distance C Distance Enhancing minor taxa Square root Log Fig 21 Resizing the diagrams Reconstruction O x File E Edit E Import climate data
16. en site The results can be expressed in 2 D space defined by two EOFs default EOF 1 and 2 or in 3 D space defined by three EOFs default EOFs 1 3 Fig 5 3 4 How to save results Results of every analysis i e not only the PCA performed by Polygon 1 5 can be saved both graphically and numerically The easiest way is to put your cursor on the graphic window and click the right button of mouse If the window is showing results of analyses a popup menu will appear and options of Copy and Save matrix will be given Fig 6 Copy means to copy the image into the Windows clipboard in bitmap format This allows the figure to be exported to any graphical software such as Photoshop Illustrator PowerPoint etc Save matrix allows the results to be saved in a spreadsheet in csv format 3 5 Projecting fossil data in the EOF space The next step of the envelope analysis is to project the fossil dataset as a trajectory in the space defined by EOFs of the reference dataset To do this import the fossil dataset 2_fossil_data csv file in the sample data collection using the Import fossil data button A in Fig 5 Polygon 1 5 automatically converts the fossil dataset using the settings of data pre treatment percentage conversion and minor taxa enhancement that are precisely the same as those chosen for the surface dataset and projects fossil data in the EOF space At this step Polygon 1 5
17. ence data EOF analysis Axis settings Automatic change Palsi 3 m Displa mode C 2 D Rotale 3D lt Meeran locity a Pause Reverse Several display modes can be chosen 4 e BETULA I Stereo I Tick Label Interval sec ae C Manual change Showall Prey Next Sequential Prev Next 4 BETULA X z C Hide ible r Reference sites C Show all Prev Next Jss 009 Sequential C Hide Envelope analysis Envelop r Fossil data Show all Tight Loose Diagram Reconstruction Sequentig Hide EOF scores Selected site is highlighted in red Fig 6 Saving results by right clicking graphics Copy in the popup menu means to copy the figure into the clipboard Save matrix means to save results as numerical spreadsheet in csv format which can be opened by Excel mi File Edit E About Polygon A m Display mode C 2D Rotale i 3D eS Velocity Stereo W Pause Reverse I Tick Label Import reference data r EOF analysis Axis settings Automatic change Interval sec r Taxa C Show all Manual change Prev Next Sequential BETULA X C Hide 4 ible r Reference sites C Show all r Envelope analysis Envelop 0 5 Tight Loose Diagram Reconstruct
18. er F in Fig 13 For the reason of consistency with existing pioneer studies the threshold is defined by squared chord distance that is defined as 2 AP co gt w 100 where Cc denotes squared chord distance AP denotes difference in percentage values of taxa number i and n denotes the number of taxa used for the reconstruction 4 3 Number of analogues The number of analogues is changed by a different slider E in Fig 13 The default setting of Polygon 1 5 is 8 which means Polygon 1 5 chooses from 1 to maximum 8 analogues from the reference dataset unless the chord distance exceeds the threshold value 4 4 Reconstruction using EOF scores Determination of the modern analogues is normally performed in the multi dimension space defined by all taxa percentage values However Polygon 1 5 is also capable of finding modern analogues in the space defined by selected EOF axes The choice can be instantly made by clicking a radio button D in Fig 13 Because the EOF scores are normalized to the average and standard deviation the latter of which is proportionally equivalent to the contribution of EOF to the total variability here the squared chord distance needs to be calculated with weighting by contribution of each EOF to the total variability i e Polygon 1 5 user manual 18 Oct 2008 k 2 w AS Caya 2 100 where C denotes squared chord distance k denotes numbers of selec
19. ftware can be downloaded free of charge from the website lt http dendro naruto u ac jp nakagawa gt Key words Polygon PolCalib PolHist quantitative climate reconstruction modern analogues technique Palynology Introduction Quantitative climate reconstruction using multivariate palaeoecological data i e pollen diatom etc has increasingly become common and important in the field of Quaternary science since the early to mid 1990 s e g Guiot 1990 Nakagawa et al 2002 Modern analogues technique MAT is one of the most commonly used methods among tens of proposed reconstruction methods because of its relatively straightforward logical background and ability of handling datasets without any regression by applying simplified models e g Nakagawa et al 2006 Tarasov et al Submitted However when one intends to apply the method to his her fossil dataset it is normally inevitable to encounter a series of difficulties due to the following reasons Polygon 1 5 user manual 18 Oct 2008 1 Most of the existing computer programs were not user friendly and were virtually impossible to use by people other than the developers and their colleagues an exception to this rule is C2 developed by Juggins http www campus ncl ac uk staff Stephen Juggins software htm 2 Reference datasets i e surface pollen datasets in the case of palynology were exclusively possessed by limited community members and were not read
20. hich is also available free of charge at the same download site as Polygon 1 5 http dendro naruto u ac jp nakagawa You will easily obtain the csv spreadsheet of climate estimated at pollen sites which can be readily imported to Polygon 1 5 Once Polygon 1 5 user manual 18 Oct 2008 the climate dataset is imported Polygon 1 5 automatically performs modern analogues technique and displays the results Fig 13 The blue curve is the raw reconstruction and the red curve is the running average Both age depth and climate indices are averaged for the number of nearby horizons defined by the slider at the top of the diagram Graph range and the climatic parameter to display can be changed using text boxes at the bottom of the diagram The red horizontal thin lines in the diagram A in Fig 13 represent fossil horizons that were detected as being outliers by the envelope analysis These correspond to the open red circles in the EOF diagram A in Fig 11 The blue horizontal thin line B in Fig 13 is the manually selected horizon which corresponds to the closed red circle in the EOF diagram B in Fig 11 4 2 Threshold Interruptions in the reconstructed climate curve C in Fig 13 means that the fossil horizons did not have any close enough analogues no analogue situation and thus it was not appropriate to infer climate indices to those horizons The threshold value is changed by using the slid
21. ily accessible though this is not really true most researchers were under this impression 3 Even if one managed to obtain a reference dataset and figure out how to operate the software it remained difficult to understand instinctively what the software was actually doing because the output was normally only in the text format Polygon 1 5 was developed in an attempt to solve all these problems A key effort was made to provide a graphical and user friendly interface The installer package also includes Japanese surface pollen dataset established by Gotanda et al 2002 The algorithms both for reconstruction and calibration are basically similar to Nakagawa et al 2002 unless otherwise stated in this paper The software is not protected by copy right and can be freely downloaded from our web site lt http dendro naruto u ac jp nakagawa gt A key strength of the method proposed by Nakagawa et al 2002 is that it provides a new technique of estimating error ranges to the reconstructed climatic indices The specific PC programs for this calibration PolCalib 3 0 and PolHist 2 5 are still available on the same website However they are seamlessly integrated in Polygon 1 5 and users can calibrate their reconstruction results using the same or slightly improved algorithms nearly without feeling that some modules of the Polygon 1 5 were originally independent programs Polygon 1 5 is already becoming the software of choice for m
22. ion Save Matrix Reference Save Matrix Fossil Fig 7 Projecting fossil data as a trajectory in the space defined by EOFs of the reference dataset Pet File E Edit E About Polygon A r Display mode Import reference da EOF 2 p 4 2D Rotale a m EOF analysis C 3D Whe gt MEE i velociy H s settings A I Stereo Pause f Reverse 4 te 4 Automatic change 1 IV Tick Label EOF 1 Interval sec t Taxa Manual change cashew C Sequential Prev Next z a Hide No of Axes 2 all visible r Reference sites EOF 2 p 4 C Showall Impor fossil data m Envelope analysis B Envelop Sequential Hide r Fossil data 0 1 4 4 at J EOF Show all Tight Loose Sequential Hide C _ gt Diagram D _ gt Reconstruction Selected horizon is highlighted in red Fig 8 Tight solid line and loose dotted line envelopes in 2 dimension space Tightness of the loose envelope is defined as the departure A form the tightest envelope unit EOF scores where 1 means one standard deviation Grey color of dots indicates that the dot constitutes corner points of the envelope Fig 9 Control panel for display and envelope analysis Five axes are being chosen in this example x m Selected EOFs for default display Axis Y Axis Z Axis FE
23. is not doing another EOF analysis of the fossil dataset Instead it is using the EOFs of the surface dataset and projecting fossil dataset in the same space In more mathematical words EOFs are defined as the normalised eigen vectors of variance covariance or correlation coefficient matrix of the surface dataset and the EOF scores of the fossil dataset are defined as the orthogonal projections of the fossil data values to the EOF axes 3 6 Envelope analysis Envelope is a user friendly word to replace convex hull which is mathematically defined as the minimal convex set containing set of points but can be better understood as a package wrapping by rubber film of a set of points Fig 8 Envelope analysis Polygon s unique feature enables you to check if a fossil pollen spectrum is in or out of the envelope defined by the reference dataset If it is out then the reference dataset is not suitable for climate reconstruction of the fossil dataset If it is in we cannot reject the hypothesis that the reconstruction is reliable Polygon 1 5 uses two EOF axes to define the envelope when it is in 2 D display mode or uses three or more axes when the display is in 3 D mode Axes to use for the envelope analysis and display can be freely chosen from a whole range of EOFs from the control panel Fig 9 which you can open by clicking the Axis setting button on the main window A in Fig 7 This function is also
24. mperature import 4_Tann EstObs csv file from the sample data collection A in Fig 15 and the scatter diagram showing relationships between Vest and Vobs in Polygon 1 5 user manual 18 Oct 2008 Nakagawa et al 2002 will be given on the second graphic window Now click the Start button A in Fig 16 and all the following steps will be completed automatically Fig 17 Warning Choose proper csv file of the estimation error model so that it is consistent to the climate parameter of the curve that you are going to calibrate B in Fig 14 For example the 4 _Tann EstObs csv file is only good for the mean annual temperature Tann If you care calibrating other parameters such as mean temperature of the warmest months MTWA you need to use other estimation error file such as 4_ MTWA EstObs csv accordingly Changes from PolCalib 2 0 There are some important changes between PolCalib 2 0 and 3 0 a 2 3 4 If you do not have the dataset of estimation error PolCalib 3 0 allows you to generate an artificial error model using a check box B in Fig 15 Another solution for such case is to use Polation 1 0 and estimate climate at surface pollen sites using an original meteorological dataset As a bi product of that estimation Polation 1 0 will also generate a scatter diagram of the estimation error calculated by the leave one out method and save the results in csv
25. n surface 2f 6 52 0 0 0 and fossil pollen datasheets 3l o o o 3 47 a 2 05 o 109 5 0 fa O ESE 6l 204 0 2 04 i SF een Ley 284 18 46 092 615 _1 Age ABIES ACER ULMUSZELVIBURNUM 284 39 77 o qt 2 Q o o 9 o 3298 o 213 3 939 5349 119 o 1 59 o 28d 54 o 1o02 4 1644 186 3 o 4 o 287 5 2348 837 1 97 0 39 2 36 0 288 6 2701 163 1 13 0 38 1 88 o M 4 gt Mh Reference data 88 43076 92 1 05 i RFA 6 28 0 Ot 44961 54 045 0 45 2 03 o 90 46846 15 0 27 0 27 4 55 o 91 50000 o o 0 o hamwe OUUU A B Cc G H I 1 Siteepame TANN PANN PWIN PSUM 2f 9 7684 3939 53 1553 221 2422 288 3 17 4434 2236 75 615 313 1621 437 17 3294 2236 75 615 31 ea 5 15 8174 2236 75 615 313 a z 6l 15 8234 2236 75 615 313 Tann Est Tann Obs 284 4 8216 815 34 348 701 5 5634 6 41 284 5 6468 1123 74 601 77 5 3626 5 54 289 64268 1123 74 601 77 7 4242 717 28e 6 4268 1123 74 601 77 5 932 5 32 287 7 0758 7 33 286 21 728 22 42 M 4 gt h3 Climate data 22552 21 86 22 3 22 87 These blank data optional defines e upper and lower limits of diagrams Fig 3 Initial window of Polygon 1 5 Polygon 1 0 change MEX fe Hide Reconstruction Fig 4 Data pre treatment prompt Data pre treatment for PCA fe square root f Log Fig 5 Results of PCA by Polygon 1 5 EOF loadings Selected taxa is highlighted in red OD 1 0 File E Edit E About Polygon A Import refer
26. ope analysis which is a newly proposed method to check if the surface pollen dataset has wide enough coverage to be used for the climate reconstruction of the given fossil dataset The envelope analysis starts from standard principal component analysis PCA also known as empirical orthogonal function EOF analysis of the reference surface pollen dataset This is then followed by projection of the fossil pollen dataset in the multi dimension space defined by the EOFs of the reference dataset If a fossil pollen spectrum is within the area covered by the surface pollen dataset then Polygon 1 5 considers that the fossil spectrum is safe to infer climate indices For the fossil spectra that are out of the area covered by the reference dataset Polygon 1 5 gives warning for those horizons as being presumably inappropriate to reconstruct climates using the reference dataset The only solution for the latter case is to include more sites in the reference dataset and enlarge both the geographical and climatic coverage 3 2 Data pre treatment Fig 3 shows the main window of Polygon 1 5 as viewed when you have just started the program Click the Import reference data button at the left upper corner A in Fig 3 choose the 1_Reference_data csv file from the sample data collection Another small window of data pre treatment for PCA will open Fig 4 If the surface dataset is already in percentage values or contains differen
27. our computer to activate the software 2 Formatting data files Polygon 1 5 requires at least three or preferably four if you intend to calibrate your reconstruction results datasheets i e i a surface reference pollen dataset ii a fossil pollen dataset iii a climate dataset estimated at or interpolated to each surface pollen site and iv an error model for climate estimation interpolation one datasheet for each climatic parameter As for the scientific meaning of those datasets please refer to our previous paper on the reconstruction calibration methods Nakagawa et al 2002 If you are doing pollen based climate reconstruction in Japan using the Gotanda et al 2002 datasets the files i iii and iv are all included in the installer package The file ii is your data which must be formatted according to the Polygon 1 5 protocol This chapter describes how the datasheets must be formatted It is crucial to keep your pollen taxa names and surface pollen site names as well as their order consistent across all datasheets Make sure that all cells out of the data field are blank having invisible space is one typical mistake in formatting datasheets The easiest way to avoid this mistake is to copy the data field into a new spreadsheet and save it in csv format The installer package contains sample datasheets for reference Check the format carefully and harmonise your own datasheets in the same way as the sample dat
28. rovides the stereo view 5 Error estimation and results calibration 5 1 Cross validation by leave one out method Estimation of reconstruction error by leave one out method can be automatically done by clicking Generate error model button T in Fig 13 The details of the method are described in full in Nakagawa et al 2002 The scatter diagram in the middle of Fig 14 shows the discrepancy between the reconstructed climates Vrec in Nakagawa et al 2002 and the climates estimated at the surface pollen sites Vest in Nakagawa et al 2002 It should be noted that the scatter diagram is specific to the setting of the reconstruction method and the reconstructed climatic parameter 5 2 Generating calibration model Nakagawa et al 2002 proposed an algorithm to generate calibration model by smoothing the scatter diagram of the reconstruction error as well as the software to perform the calculation PolCalib 2 0 Polygon 1 5 is seamlessly bundled with an updated version of the software PolCalib 3 0 Once the scatter diagram of reconstruction error has been drawn the Generate error model button changes its name into PolCalib A in Fig 14 Click this button and a new window of PolCalib 3 0 opens Fig 15 The original algorithm of PolCalib version 2 0 or earlier is described in full in Nakagawa et al 2002 First import dataset of climate estimation error in case of the mean annual te
29. sites which are determined as the modern analogues of the fossil horizon i see section 4 3 CE denotes climate indices estimated at the surface site j and m denotes the number of taxa used for the reconstruction The n value in the equation 5 and the g function of the equation 6 can be chosen by the users G and H in Fig 13 Important notice Polygon 1 5 user manual 18 Oct 2008 The mode of minor taxa enhancement for climate reconstruction is independent from minor taxa enhancement for EOF analysis i e for envelope analysis In other words Polygon 1 5 allows detecting outliers by envelope analysis with minor taxa enhancement and performing climate reconstruction without minor taxa enhancement or vice versa 4 6 Saving data Results of the climate reconstruction as well as every other result generated by Polygon 1 5 can be saved both graphically and numerically The diagram can be copied into the Windows clipboard or saved in csv format which can be read edited by Excel This is done by clicking the right button on the drawn diagram and choosing the appropriate option in the popup menu Please also refer to the Fig 6 4 7 Stereo image One weak point of the animated 3 D image is the fact that the animation cannot be printed on paper for publication in journals Ticking the Stereo check box generates the same figure in two windows at slightly different angle so that the combination of the two images p
30. t types of parameters it is not necessarily a rule to perform percentage conversion In that case however you need to be sure that the percentage values are calculated taking the sum of all taxa included in the reference dataset as 100 i e not the total pollen sum nor the AP arboreal pollen sum If you do not want to use certain taxa for the climate reconstruction you need to exclude those taxa from your reference dataset and create a new csv file Minor taxa enhancement can be done by square root or logarithmic conversion by clicking the check box and radio buttons You can also choose between two different types of PCA one using variance covariance matrix and the other using correlation coefficient matrix by clicking radio buttons In short variance covariance matrix reflects dominance of each taxon whereas correlation coefficient matrix treats all taxa equally For an ordinary pollen dataset variance covariance matrix is recommended Correlation coefficient matrix is suitable for cases of multidisciplinary datasets that contains variables expressed in different units 3 3 EOF analysis Polygon 1 5 user manual 18 Oct 2008 If you click on the OK button at the bottom of the data pre treatment form Polygon 1 5 automatically performs PCA EOF analysis and display results on two windows in the main form The upper window shows loadings of each taxon to the EOF axes whereas the lower one shows EOF scores of each reference poll
31. ted EOF axes w denotes contribution of EOF axis number i expressed in percentage and AS denotes difference in normalised EOF scores on the selected EOF number i If all EOF axes are taken into account theoretically it must give identical value as the chord distance defined using percentages C gt in equation 1 This function of EOF based modern analogues technique is potentially useful to exclude non climatic factor in the vegetation variability typically like human influences and or ecological succession For the EOF based reconstruction Polygon 1 5 uses the set of EOFs selected for envelope analysis i e the reconstruction window and envelop analysis window are synchronised Selection of EOFs can be changed using the control panel which opens by clicking the Axis setting button 4 5 Weighting and minor taxa enhancement Climatic indices are calculated as the weighted average of the climates interpolated to the selected modern analogues sites Nakagawa et al 2002 Weighting factor can be defined as either inverse or squared inverse of the chord distance between fossil pollen data and surface pollen data Minor taxa can be enhanced using square root or logarithmic conversions i e k fre cz CR z 3 ICD j l g p 8 p E amp P 8P fi 100 f x x n 1or 2 5 g x x or Jx or logo x 6 Where CR denotes reconstructed climate at fossil horizon i k denotes the numbers of surface
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