Hollmén, Jaakko

Mäkinen, Harri

Nöjd, Pekka

Sulkava, Mika

Jukuri

Automatic detection of onset and cessation oftree stem radius increase using dendrometerdata and CUSUM chartsMika Sulkava1, Harri Ma¨kinen2, Pekka No¨jd2, and Jaakko Hollme´n1 ∗1- Helsinki University of TechnologyDepartment of Information and Computer ScienceP.O. Box 5400, FI-02015 TKK - Finland2- Finnish Forest Research Institute - Vantaa Research UnitP.O. Box 18, FI-01301 Vantaa - FinlandAbstract. Dendrometers are devices, which measure continuously thestem radius of a tree. In this work, we studied the use of cumulative sum(CUSUM) charts for automatically and, thus, objectively determining theonset and cessation dates of radial increase based on dendrometer data.We used data measured in two forest stands in southern Finland to demon-strate the idea and to test the performance of the CUSUM chart. In orderto produce reliable results, one has to choose suitable parameter values forthe chart. Once configured properly, the method produced results similarto those determined by an expert.1 IntroductionFormation of wood depends on various endogenic and exogenic factors and it isrestricted to a certain period in the year, e.g. [1]. Wood formation is regulatedby several factors including genotype, site, silviculture, and climatic variation.In spite of the basic nature of the underlying process, our present knowledgeconcerning the timing of the various phases and the rate of increment during agrowing season is still far from complete. This lack of knowledge is largely due todifficulties in measuring wood formation at short intervals. Dendrometers havetraditionally been used for measuring the intra-annual wood formation of treeswith high precision, e.g. [2, 3].Changes in stem dimensions are not solely a result of wood formation; theyare often caused by other processes, especially changes in stem hydration, e.g. [4].Because of the large and frequent changes in stem radius associated with fluctu-ations in stem water potential, it is difficult to use dendrometer measurements todetermine the onset, cessation, and rate of wood formation, i.e., radial incrementdue to formation of new cells, e.g. [5, 6, 7].In recent years, few studies have been published describing the timing of ra-dial increase or weather-growth relationship based on dendrometer data, e.g. [7,8, 9]. However, the definitions and approaches for identifying the onset and ces-sation of radial increase have been different between the studies. Thus, criteria∗M. S. and J. H. were supported by Academy of Finland, research project: analysis ofdependencies in environmental time-series data (AD/ED) (grant number 116853).and methods for determining onset and cessation dates are not yet generallyaccepted.The problem in this study is to objectively and automatically detect the onsetand cessation of radial increase period based on dendrometer data. We testedthe suitability of the cumulative sum (CUSUM) charts [10, 11] for performingthis determination automatically solely based on the data, cf. [12].2 Dendrometer dataDendrometer data was collected from two sites located 300 m from each otherin southern Finland (Ruotsinkyla¨, 60◦ 21’ N, 25◦ 00’ E). In both stands, sampletrees without visible damage were selected from the dominant tree layer. Inthe first stand (altitude 45 m a.s.l.), the Norway spruce trees were growing ina pure spruce stand on fertile mineral soil (H100 = 30 m, dominant heightat age 100 years) classified as Oxalis-Myrtillus forest type [13]. Mean stemdiameter of the sample trees at breast height was 27 cm and relative crownlength was 68%. The sample trees were monitored during the growing seasonsof 2001–2005. In the second stand (altitude 60 m a.s.l.), four Norway spruceand four Scots pine trees were monitored during the growing seasons of 2002–2003, and another four spruce and four pine trees during the growing seasonsof 2004–2005. They were growing in a mixed spruce-pine stand on a relativelyfertile mineral soil classified as Myrtillus forest type (H100 = 27 m) [13]. Thetotal number of observations (year × tree combinations) was, thus, 57. Meandaily temperatures and precipitation sums were obtained from a meteorologicalstation of the Finnish Meteorological Institute located about 5 km from thestudy stands.Stainless-steel band-dendrometers were installed on each tree at a heightof about 2 m. Before installing the band, the outer bark under the band waslightly brushed to ensure smooth contact with the trunk. The girth band consistsof three basic elements: 1) a stainless-steel band encircling a tree, 2) a sensor(rotating potentiometer) reacting to movements of the stainless-steel band and 3)an aluminium-body and fastening mechanism (Fig. 1). The fastening mechanismconsists of three parts: 1) a constant force spring, 2) a fastening arm, and 3) anadjustable foot (Fig. 2). The spring stretches the steel band around the tree witha force of about 3 N, making the band capable of reacting to small variations ingirth but without damaging the tree.Changes in tree girth were measured at a resolution of 0.1 mm, correspondingto diameter change of about 0.03 mm. The output of the dendrometers wasstored as hourly averages. Examples of dendrometer data showing the change inthe stem radius during one year are shown in Fig. 3. From these measurements,the daily values of stem circumference were calculated as the mean of hourlyvalues and the circumference changes were converted to radial changes assuminga circular stem cross-section. The dendrometer has been described in more detailin [3].Fig. 1: The girth band mounted on a tree.Fig. 2: Structure of the girth band: A = stainless-steel band; B = rotatingpotentiometer; C = fastening arm; D = adjustable foot; E = cable; F = spring.0 100 200 30000.51Julian dayradius (mm)20020 100 200 30000.51Julian dayradius (mm)2003Fig. 3: Examples of the dendrometer data; a Norway spruce tree in Ruotsinkyla¨measured in 2002 and 2003. The zero level is the first observation of the year.The resolution the measurements is one hour.0 100 200 30000.20.40.60.8Julian dayradius (mm)2003Fig. 4: Example of a difficult growth pattern. It is difficult to distinguish whenthe actual radial increase starts: on around day 115 or around day 150. Also,only based on the curve it is difficult to tell whether the increase ceases on aroundday 190, 235, or 340.We visually evaluated the methods used in the previous studies (cited in theintroduction) for determining the onset and cessation dates of radial increasefrom dendrometer data. All the methods had difficulties in identifying the onsetand cessation dates because of stem hydration changes, i.e., they were not suffi-cient for identification of the crucial dates for all trees and years. It may happen,for example, that during spring stem radius starts to increase at a certain timepoint, but then stays constant for a rather long time, before the increasing trendreappears (Fig. 4). It is difficult to say, whether new xylem has actually beenformed or whether the stem has just swollen.We ended up, therefore, determining the onset and cessation dates visuallyfrom the dendrometer data to obtain labeling for training purposes. It should beemphasized that manual determination of the crucial dates is laborious and islikely to result in observer-related subjective differences and human errors. Thedates identified visually are called below as the ‘expert choice’.The tests can be done with all the data. Alternatively, difficult cases (Fig. 4)can be left outside the data in order to get more reliable results. We labeled anonset or cessation date of radial increase as a difficult case if there was a clearjump-like increase of at least about 0.07 mm in stem radius before the onset dateor after the cessation date or if the minimum achievable difference between thepredicted date and the ‘expert choice’ was at least 10 days. Altogether, therewere 22 and 16 difficult cases for onset and cessation, respectively.3 Cumulative sum chartThe cumulative sum (CUSUM) chart is a statistical process control tool, whichdetects small changes in the mean µ of a signal. It monitors the cumulative sumdkFig. 5: Parameters d and k of the CUSUM chart define the shape of the V-mask.The shape affects how soon and how large changes are detected.of previous observations x.X ∼ N(µ,σ2) (1)Sm =m∑i=1(xi − µ) (2)The cumulative sum Sm at time step m is the sum of the differences between theprevious observations and µ. The CUSUM chart detects up or down drifts andabrupt changes in µ, which is assumed to be known. The chart has 2 parameters:d and k, which depend on standard deviation σ, size of detectable change ∆X,and probabilities of type I (α) and type II (β) errors. The parameters define theshape of a so-called V-mask (Fig. 5), which is used to detect the changes in themean. In case a previous value of Sm is outside the mask, it is concluded thatthe mean has changed (see Fig. 6).We studied how to set the parameters of the chart to produce results assimilar as possible to the ‘expert choice’. One has to choose suitable values for∆X, σ, α, and β. In addition the onset or cessation levels µ for radial increasehave to determined. Cessation of radial increase can be detected by running thechart in reverse time.The correct values of suitable detectable size of change and magnitude ofnoise were not known in advance. Therefore, parameters d and k were varied ina wide range: d between 1 and 50 and k between 0.01 and 0.1. The accuracyof the predicted dates was verified by 10-fold cross-validation [14]. In 10-foldcross-validation, the data set is divided into 10 disjoint sets of equal size. Theparameters of the chart yielding the minimum error are selected 10 times andeach time one of the sets is held out as a validation data set. Parameter values,which yielded the minimum mean absolute deviation e in days (Equation 3) fora training data set, were chosen. The performance of the model is estimated asthe mean of the 10 errors obtained using the validation data sets.e =1nn∑i=1|ae − ac| (3)0 20 40246810121416data0 20 40!40!2002040CUSUM0 20 40246810121416data0 20 40!40!2002040CUSUM0 20 40246810121416data0 20 40!40!2002040CUSUMFig. 6: Artificial data with constant mean (left column) and abrupt (middlecolumn) and gradual change in mean (right column) and the respective CUSUMcharts (bottom row). When µ stays the same, the values of cumulative sum Smstay inside the V-mask. A change in µ is detected, when a previous value ofcumulative sum is outside the V-mask.Above, n is the number of onset or cessation dates in the training or validationset, ae is the ‘expert choice’ and ac is the date predicted by the CUSUM chart.Performance of the CUSUM chart can be improved by focusing on only up-ward (onset) or downward (cessation) shifts in mean, i.e., using only one half ofthe V-mask for detecting the changes. This reduces the number of false alarms.This procedure was used to produce the presented results.4 ResultsIt was found that the average stem radius during spring or fall is a better valuefor µ than the average of whole winter due to, e.g., swelling and shrinkage of thestem. The spring was defined as the two week period before the first day withaverage temperature > 3 ◦C. Similarly, fall was defined as the two week periodafter the first day with average temperature < 3 ◦C after summer.Lowest average errors obtained with separate parameter values k and d foreach tree and year were 1.6 days for onset and 2.9 days for cessation, respectively.The onset and cessation dates of other trees cannot, however, be detected withthe same accuracy using these parameter values, because the optimal parametersdiffered between the trees and years. Same parameter values were, therefore,used for all the trees and years. The average training errors were 8.6 and 9.8days for onset and cessation, respectively. The average errors in the validationdata set were 8.9 and 11.0 days for onset and cessation, respectively.The relatively high errors were mainly caused by some difficult cases. Thedifficulty was caused by increasing stem radius related to stem hydration beforethe actual radial increase begins and during fall after the radial increase hasceased (Fig. 4). These kinds of curves were also difficult for the CUSUM chart,i.e., it detected the onset date too early and cessation date too late. When thedifficult cases were left out, the average errors clearly decreased. The averageerrors in the training data set were 2.5 days and 7.3 days for the onset andcessation, respectively. The average errors in the validation data set were 3.1days and 8.2 days for the onset and cessation, respectively.5 DiscussionThe development of stem radius or circumference can be monitored with a hightime resolution and summed up to long-term results using modern automaticdendrometers. Durability, automated measurement, and low price make den-drometers suitable to be used in a growth monitoring network covering largeregions.Much of the variation in stem radius is, however, independent of xylem for-mation. In late winter and early spring, rising temperature may increase evap-otranspiration, whereby this water loss cannot be replaced by water uptake dueto soil frost and it consequently causes a reduced stem radius, e.g. [7]. Later inspring, water uptake will result in an increase of stem radius not related to theformation of new tracheids, e.g. [15, 16, 8, 17]. Onset of wood formation may,thus, be masked by the rehydration of the stem, cf. [18].Likewise, increases in stem radius in late summer may be caused by stemswelling rather than wood formation, making it difficult to determine the ces-sation of wood formation from dendrometer measurements. Especially in theslow-growing boreal forests, the daily swelling and shrinkage of the stem is rel-atively large compared to the radial stem increase caused by cell division andenlargement. In cold regions, such as Finland, wintertime ice formation in stemsdoes further complicate the interpretation of girth band data [19].In the experiments, the CUSUM chart proved to be a good starting pointfor detecting automatically the dates when the radial increase of trees beginsand ceases. Suitable parameters values for the CUSUM chart are needed to getaccurate results. Once configured properly, the CUSUM chart produced resultssimilar to the ‘expert choice’. In most cases, the results were accurate for theonset of radial growth. To detect the cessation date is more difficult, becauseduring fall the amount of stem radius increase is small compared to the reversiblechanges in stem radius, which cause false alarms.A relatively high number of cases (39% and 28% for the onset and cessation,respectively) were labeled as difficult. The changes in stem radius caused bywood formation and other factors can not always be distinguished using theCUSUM chart. It proved necessary to compare the dendrometer measurementwith direct measurements on tracheid formation on the stems. Thus, the resultsachieved by using the CUSUM chart should always be checked by an expertbefore using them in further analysis. The amount of manual work needed foridentifying the crucial dates can anyway be reduced by the CUSUM chart.The CUSUM chart is also a useful method for on-line detection of onset ofradial increase. In contrast, the cessation of radial increase can not be detectedon-line using the CUSUM chart. In retrospective analysis of onset and cessationof radial increase it is probably advantageous to use the observations on bothsides of the change point to improve the performance of the detection method.6 ConclusionsIn this study, using the CUSUM chart was studied for automatic detection of on-set and cessation dates of radial increase of stems based on automated dendrom-eter data. At their best, the results agreed rather well with dates determinedby an expert. Detecting the cessation of radial increase was a more challengingtask compared to the onset date.In the experiments, trees from two stands were analyzed. The method andthe estimated parameters can be used to assign preliminary onset and cessationlabels to trees in other stands.Other change detection methods may also be suitable for the problem. Ina future study, the CUSUM chart will be compared with, e.g., segmentationand regression methods and trend tests such as the Mann-Kendall test and F-test. We will also analyse the relationship between environmental factors andthe onset and cessation dates of radial increase.References[1] R. A. Savidge. Xylogenesis, genetic and environmental regulation (review). IAWA Jour-nal, 17:269–310, 1996.[2] K. Yoda, M. Suzuki, and H. Suzuki. Development and evaluation of a new type of opto-electronic dendrometer. IAWA Journal, 21:425–434, 2000.[3] Erkki Pesonen, Kari Mielika¨inen, and Harri Ma¨kinen. A new girth band for measuringstem diameter changes. Forestry, 77:431–439, 2004.[4] H. Abe and T. Nakai. Effect of the water status within a tree on tracheid morphogenesisin Cryptomeria japonica D. Don. Trees, 14:124–129, 1999.[5] Harri Ma¨kinen, Pekka No¨jd, and Pekka Saranpa¨a¨. Seasonal changes in stem radius andproduction of new tracheids in Norway spruce. Tree Physiology, 23:959–968, 2003.[6] Harri Ma¨kinen, Jeong-Wook Seo, Pekka No¨jd, Uwe Schmitt, and Risto Jalkanen. 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Link between diurnal stem radius changes and treewater relations. Tree Physiology, 21:869–877, 2001.[18] K. Kuroda and Y. Kiyono. Seasonal rhythms of xylem growth measured by the woundingmethod and with a band-dendrometer: an instance of Chamaecyparis obtusa. IAWAJournal, 18:291–299, 1997.[19] R. Zweifel and R. Ha¨sler. Frost-induced reversible shrinkage of bark of mature subalpineconifers. Agricultural and Forest Meteorology, 102:213–222, 2000.

Automatic detection of onset and cessation of tree stem radius increase using dendrometer data and CUSUM charts

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