Comparison of Different Kriging Methods to Estimate the Tree Density. A Case Study: West of Karkheh in Southwest of Iran

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1 Avalable onlne at ProEnvronment ProEnvronment 7 (2014) Orgnal Artcle Comparson of Dfferent Krgng Methods to Estmate the Tree Densty. A Case Study: West of Karkheh n Southwest of Iran FAKHIRE Akbar 1, Mahmood NAJAFI ZILAIE 2 1 Assstant professor, Unversty of Gonbad-e kavoos, Faculty of Natural Resources, Gonbad-e kavoos, Iran 2 Unversty of Zabol, Zabol, , Iran Receved 5 May 2014; receved and revsed form 29 September 2 014; accepted 19 November 2014 Avalable onlne 10 December 2014 Abstract Krgng the geostatstcal methods used to create contnuous maps of spatally auto correlated characterstc, the ablty to estmate values at unsampled locatons wth regard to ther spatal correlaton values. The attrbutes and locaton (spatal coordnates) of trees s mportant because these factors lead to spatal heterogenety. Therefore, ths varous modelng technques have been appled to dscovery of spatal heterogenety n envronmental and forest studes. In ths study, geostatstcal methods of Smple Krgng and Cokrgng to nterpolate the tree densty n the forest of Beyt - Qasham n 4350 ha n the margn of Karkheh rver of Khuzestan provnce were comparson and evaluated. Feld samplng was performed based on a systematc random samplng a crcular plot wth ntensty of each 100 hectare n the 1000 m 2 area, tree densty nformaton and geographc coordnates of each plot center were recorded. The performance assessment of the above mentoned was carred out usng cross-valdaton technques and crtera for the comparson between ther ME, RMSE, ASE, MSE, RMSSE were used. The results showed that the tree densty have been hgh spatal correlaton n ths regon. The cross valdaton results also showed that among the used methods, the Cokrgng method s superor accuracy wth mnmum of ME, RMSE, ASE, MSE and RMSSE. Keywords: tree densty, krgng, geostatstcal methods, plantaton forest, Khuzestan. 1. Introducton Contnuous spatally varaton s one of common propertes and characterstcs of envronmental factors. Therefore, the geographc locaton of observatons must be specfed to be consdered smultaneously n addton property value to descrbe patterns of quanttatve dstrbuton of such envronmental varables [3]. Geostatstcal s sutable technques to local varatons analyze and varable estmated that are spatally dependent. Correspondng author. Tel: Fax: E-mal: Mahmoodnajaf1364@gmal.com Spatally nterpolaton technques are procedures that forecast the value at a gven locaton by usng values from sample ponts. For each calculaton the values of sampled ponts are weghted dependng on ther locatons. A basc prncple n geostatstcs s that observaton samples closer together are more smlar than samples of apart, or n other words, they are more contnuous. The most common geostatstcal method s krgng, whch was presented by Matheron n These methods has been used proftably n other felds, such as mnng, meteorology, and sol scence [22], however, ther applcatons has been lmted for forestry [10]. The attrbutes (such as heght), competton and poston (spatal coordnates) of trees are all of 204

2 FAKHIRE Akbar et al./proenvronment 7(2014) mportant [13], so that these all factors lead to spatal heterogenety crosswse space [9]. Consequently, dfferent spatal methods have been appled to dscover the effect of spatal heterogenety n forest and ecologcal studes [5]. Generally, tree densty nformaton were collected from feldwork, that ths type of data collecton, requres spendng tme and expenses are exorbtant [19]. Few studes have been conducted on estmatons of contnuous forestry varables usng spatal models, although, a large number of geostatstcal and predcton models are obtanable n the lterature [17]. For tree densty estmate applcatons, a few studes have been conducted usng the geostatstcal approach and most of these studes focus on forest parameters estmate, such as leaf area ndex, bomass, heght and producton. For example, Berterretche et al. [2] and Zhang et al. [24] appled geostatstcal methods for estmaton forest varables, leaf area ndex, and categorze forest lands based on remote sensng data. They also concluded that Multvarable krgng methods showed better results. Gunnarsson et al. [8] n Sweden appled to revew Krgng effcency the level of the mass plantng of forests that were classfed by age. Results showed that nventory forest estmate was approprated wth Krgng n coeval mass needleleaf, but coeval masses broadleaf, where was not a good correlaton nventory forest and usng geostatstcal methods. Tuomnen et al. [20] used mprove to the accuracy of estmate nventory forest by geostatstcal nterpolaton and krgng n Fnland. They concluded that obtaned poor estmates and usng Krgng wll help not to ncrease accuracy. Freeman and Mosen [6] to mappng forest bomass n Amerca usng geostatstcal methods. They suggested that Krgng couldn t help to precse maps due to large nugget effect and poor spatal structure. Nanos et al. [16] appled both Cokrgng and the Krgng method to Heght/dameter models and stand densty n Span. They concluded that Cokrgng wll probably not mprove over krgng. They also expressed that Cokrgng can be used for predctng random stand effects at future stages of the stand development. Kng et al. [15] compared Krgng and Cokrgng methods for mappng forest volume n New York Cty. RMSE, overall accuracy and Kappa coeffcent were selected for compare krgng wth the Cokrgng method and concluded that Cokrgng gave the best results than Krgng n all case. Lus and Dupuy [14] mappng speces densty of trees, shrubs and vnes n a tropcal forest of Mexco was performed usng Unversal krgng. They concluded that a smlar dstrbuton pattern based on the number of plant speces densty for data estmated by Unversal krgng. Also expressed that sgnfcant dfferences between denstes of speces measured n the feld and estmated by Unversal krgng. Nevertheless, the dversty of envronmental stuatons and management has led n most cases to consderable spatal varatons n the stuatons of forest regons [11]. In ths context, the purpose of the study s usng geostatstcal methods for estmate the tree densty varable and compare of ths t to were created map and subtle estmatons n order to mprove, schematzaton and conservaton the objectves of plantaton forest management plannng and use of prncpled of study areas n known samplng and new parts sample to desgned a network wth possble mnmal samplng error. The nformaton obtaned from ths method make t possble to replace expensve methods n order to estmates of factors such as tree densty. 2. Materal and Method Study Area. The area pertans to to and to longtude and lattude respectvely. It covers about 4350 hectares and s located n dstance 40Km north of Ahvaz cty and n the margn of Karkhe rver, the captal of the Khuzestan provnce of Iran (Fg. 1). The mean annual temperature s 33/1 C; the amount of annual ranfall s 251/4 mm. Meanwhle, the mean annual relatve humdty s 54 percent. Gently slopng area between 0-2% overall slope and accounted the very flat areas. Most of the area s covered wth forests plantaton. The study area was hazards center for ths rver untl Because, the wnd eroson process transported partcles n form slp from other regons nto regon, and therewth t threatened all facltes, farms and suburb vllages. Hence, fxaton shftng sand appled duraton 6 year by mulch n order to combatng actve and moble sand dune and control eroson. To permanent fxaton almost every year 700 ha Prosops julflora seedlng to strp system dstance 4 m 4 m and depth 30 cm and 50 cm n pt dameter and densty 625 trees per hectare (about 2/5 mllon trees seedlngs) [1]. 205

3 FAKHIRE Akbar et al./proenvronment 7(2014) Fgure 1. Locaton of study area The am of the study s to nvestgate dfferent krgng methods regardng the calculaton of the spatal dstrbuton of tree densty on area the adjacent of Karkhe rver of Khuzestan provnce. The applcaton of stochastc nterpolaton technques such as Smple krgng and Cokrgng needs the characterstc of a certan procedure as well as several parameters. For ths am t s mmedate to elucdate several aspects of the data, n specfc they whch wll nfluence the selecton of parameters. Dfferent dscovery technques were used to analyss the spatal varablty of the dependent and avalable nput varables. Spatal components of the dstrbuton of tree densty and canopy percent data of the sample ponts were analyzed, usng the exploraton tools provded n the ArcGIS software. Feld samplng was performed based on a systematc random samplng a crcular plot wth ntensty of each 100 hectare n the 1000 m 2 area, In every plot computed the total number of trees and geographc coordnates nformaton. A set of 40 sample plots were collected a grd of vegetaton h 1 2N h h 2 1 Z x Zx h h s the semvarance estmate; x s a data where locaton, Z(x) and Z(x +h) s the data value of one knd of attrbute at locaton x and x +h respectvely, N cover nto 8 lnes. The major tree speces was Prosops julflora (plantaton speces) n each sampled plots, other attrbutes such as canopy percent were estmated, Because of that canopy percent nformaton as a source of secondary data has been used for ancllary varables. In estmate geostatstcs operatons spatal contnuty s determned by the semvarogram, whch s a statstcal model of structural spatal dependence. Afterwards, usng nterpolaton selectve methods obtaned estmate tree densty maps n study area. Stages of study are descrbed below: Semvarogram. One of the man steps n geostatstcal modelng s the semvarogram. The semvarogram show that n general greater spatal dstance between ponts causes to a greater degree of dssmlarty n values. In other words, A functon that descrbng the spatal correlaton of the spatal varable. The expermental semvarogram generally s computed from the formula as follows [7]: (1) h s a vector of dstance, N(h) s the number of pars for a certan dstance and drecton of h unts. 206

4 FAKHIRE Akbar et al./proenvronment 7(2014) The expermental semvarance provdes a measure of spatal dependence of the studed attrbute. Typcally, the semvarance values dsplay an ascendng behavor close the orgn of the semvarance and they usually level off at larger dstances (the sll of the semvaran ce). The semvarance value at dstances near to zero s called the nugget effect. The maxmum varogram value on the vertcal axs for ths asymptote s called the sll. The dstance at whch the semvarogram reaches ts sll and flattens out s called rang that equal to sum of total varaton descrbed by the spatal structure and nugget effect (Fg. 2). In fact, the varable value s ndependent n outsde ths dstance. Also, proporton of spatal structure determned the samples varance. The hgher Spatal Structure contaned when that closer to one. C PSS C C 0 where: PSS - Proporton of spatal structure C - Spatal structure C 0 - Nugget effect (2) Fgure 2. A common semvarogram form Interpolaton methods. The geostatcal methods used n ths study are Smple Krgng and Cokrgng for tree densty estmate. The man dfference these methods, s the crteron whch s used to wegh the values of the observaton ponts that calculated based on ther dstance to the pont of nterest. They are not really based on an assessment of the unsampled value as a functon of the dstance. In addton to that they perform the functon of unsampled spatal autocorrelaton between the values of the observaton ponts. Generally geostatcal methods requred the locaton and parameters value. The methods used n bref as follows: 1. Smple Krgng: ths s a method for estmatng or nterpolatng values of contnuous spatal varables from data wthout bas and wth mnmum varance. All supposton n Smple krgng are the same as for Ordnary krgng except that the average of the varable value n observaton samples, m, s assumed to be known and s equvalent to the mean of them. In ths technque the varable z(x 0) located n x 0 s nterpolated wth the followng equaton: n σ Z( x0 ) m Z ( x ) m 1 (3) 2. Cokrgng: Cokrgng s a multvarate extenson of krgng that one or more ancllary varables to be appled n the technque and supposng that the prmary and ancllary varables was moderately correlated. The crosscorrelaton also between the prmary varable and an ancllary varable [11, 12]. Cross-valdaton used to Cokrgng model. In Cokrgng, a crossvargram, γ 12, as a functon of dstance between the two varables, h, s determned for both prmary and ancllary varables. Cokrgng performed by the followng equaton: 207

5 FAKHIRE Akbar et al./proenvronment 7(2014) N h 2 n Z x Zx h Z x Z x h (4) To nterpolate the prmary varable z(x 0) located at x 0, the followng equaton must be used (5), where z 1(x ), z 2(x j) are the values of th man and jth auxlary varables located at x and xj, and λ 1 and λ 2j are the weght of the th prmary and jth ancllary varables, respectvely. The n and m are the number of the prmary and ancllary varables. n m x0 1 Z1x 2 j Z x j Z 2 1 j1 (5) Model evaluaton. In ths study to evaluate and select the nterpolaton technques, crossvaldaton method was used [7]. In such a system, each sample value from the data set are teratvely omtted, one at a tme and afterwards the value n return s nterpolated by performng the technque wth the remanng sample values. Fnally, for every tral, n terms of the valdaton ponts and the measured values at these locatons was calculated by the dfferent statstcal crtera [21]. The evaluaton crtera are defned n ths study based on the parameters such as ME, RMSE, ASE, MSE, RMSSE, sll, nugget, ranges. The Root Mean Squared Error (RMSE) value fttng of crtera to estmate evaluaton s most mportant and forecasts are ncreasngly accurate wth lower RMSE values [18]. ME s the mean of errors or the average of the dfference between the th predcted value (z ) and observed value ( Z ). The ME can be calculated by the followng equaton: ME E Z Z (6) RMSE (root-mean-square error) was appled as a measure of forecast accuracy and can be calculated by the followng equaton: RMSE Z Z 2 (7) n Where n s the number of observatons. ASE s the average standard error. Ths statstcal crteron can be calculated for Smple krgng accordng to the followng equatons: sk ( x0 ) C0 (1 ) C0 C (8) Where c s forecast covarance, and c 0 s the nugget effect [12]. MSE s the mean standardzed error that can be calculated by the followng equaton: MSE n-1 1 Z Z Standarderror n 1 (9) RMSSE s the root mean square standardzed error and can be calculated by the followng equaton [12]: RMSSE n 1 1 Z Z Standard error n 1 2 (10) Generally, the sutable method s the way that ME, MSE and ASE values close to zero and RMSE and PSS values close to one. In ths study, we used ArcGIS 9.2 software [4], to varographs analyss and Smple krgng and Cokrgng nterpolaton. 3. Results and Dscussons The applcaton of the krgng methods n order to the spatal nterpolaton of data supposes a based on the normal dstrbuton. The statstcal analyss of the tree densty and canopy percent data shows that the data are normally dstrbuted (Table 1). 208

6 FAKHIRE Akbar et al./proenvronment 7(2014) Table 1. Summary statstcal analyss of the data observed samples Coeffcent Standard Kurtoss Skewness Varance of varaton devaton Average Max Mn tree densty Canopy percent Table 2 shows the specfcaton of the nterpolaton methods the tree densty and canopy percent semvarogram values n order to apply Cokrgng Method. The tree densty of the sample plots n the regon was n the range of meter. The crossvaldaton results show that the best-ft model was the Cokrgng wth the values of ME, MSE and ASE close to 0, and RMSE and PSS close to 1. The results tree densty data show that n the regon there are hgh spatally structure. In addton, the hghest RMSE and lowest PSS value occurrences for Smple krgng. Therefore t method provde the lowest estmaton accuracy. The follow results show that the use of ancllary nformaton can consderably reduce the errors when the forecast model s good. The Cokrgng has been wdely range that Smple krgng. In other words, the smoothng vrtue was expected more for Cokrgng. Fg. 3 shows the estmaton map of tree densty for Smple Krgng and Cokrgng method. Table 2. Results of cross-valdaton comparson statstcs for krgng procedures appled n ths study. Smple krgng Cokrgng ME RMSE ASE MSE RMSSE Nugget Sll Range PSS In other words, the smoother predcted tree densty n Cokrgng relatve to other methods s further due to hgher ranges. Fg 3 shows that the hghest tree mass occurred n northern part of the study area (more dark areas) and the lowest tree mass obtaned n the southern to center part of the study area (more lght areas) n the all maps. Fgure 3. Maps of tree densty estmaton obtaned wth Smple krgng (A) and CoKrgng (B) 209

7 FAKHIRE Akbar et al./proenvronment 7(2014) Fgure 4. Maps of tree densty varance obtaned wth Smple krgng (A) and CoKrgng (B) The performance of Cokrgng, n ths study n terms of the assessment crtera was provded greater accuracy. Hence, dstrbuton maps of estmated versus the real values are dsplayed n Fg 5. The dfference between the measured n feld and estmate values are not sgnfcant n percent error levels 5. The Cokrgng method was suppled excellence accuracy by produce 82% correlaton coeffcents. 300 correlaton coeffcent = 0.82 estmated value estmaton Lnear (estmaton) real value Fgure 5. Dstrbuton maps of estmated versus the real values for Cokrgng The map of the estmaton varance for Smple krgng and Cokrgng are dsplayed n Fg 4, n order to reconnassance the most effectve model. Whatever the lower was estmated varance 210

8 FAKHIRE Akbar et al./proenvronment 7(2014) value s better because t estmaton more accurate and can be done more confdence. The Cokrgng technque based on expermental varogram model and sampled ponts s more accurate to gve lower bases and mnmum varance n the estmates of the unsampled ponts than the technques presented n ths paper. The varance values closer to the sampled ponts hgher than those that at a greater dstance. Ths means that large numbers of varance concentrate around observaton ponts, and n other parts ntensty of varance decreases gradually wth ncreasng sampled dstances. It s demonstrated that the estmaton varance these methods were ndependent of varable value. The map of varance can be consdered as an error or relablty map [23]. 4. Conclusons Predcton geostatstcal methods and error estmate maps are new technques were appled to spatally estmate of forest parameters, It technques has numerous applcatons n natural resource or forest management. The geostatstcal technques were used to analyze the spatal predctng of the tree densty varables n ths study. Also was analyzed to nvestgate on spatal structure and estmaton of tree densty varable n a forest plantaton of 18 years by dfferent krgng methods. Smple krgng, and cokrgng method are used. Interpolaton of these varables wll mprove the nterpolaton n dfferent aspects and assessment crtera. Investgatng of dfferent methods showed that the sphercal semvarogram model was obtaned as the best model for the geostatstcal methods used. Smple krgng due to of ther large nugget effect were created lower spatal structure, It methods s not been sutable for create the estmaton of the tree densty. The results agree wth [20, 6], they suggested that Krgng wll help not to ncrease accuracy and couldn t help to precse maps due to large nugget effect and poor spatal structure. The cross-valdatons results show that Cokrgng method are acheved acceptable accuracy for predcton of tree densty varable and can be better nterpolated by t (Table 2). Evaluaton of the accuracy of the model s estmates suggested that the Cokrgng method wth the lowest values for ME, MSE and ASE, Also RMSE and PSS are close to 1 were more accurate than another method. Ths result s also n agreement wth the results found by [15] that Cokrgng gave the best results than Krgng n all assessment crtera. At the same tme, ths result s not n agreement wth the results found by [16] Cokrgng wll probably not mprove over krgng. However, they suggested that Cokrgng can be used for predctng random stand effects at future stages of the stand development. In general, results tree densty varable show that n the regon were showed hgher spatal structure (Table 2). Compared to other studes, because of that the Cokrgng method consdered n multvarable geostatstcs technques category, t results s n agreement wth the results found by [2, 24]. The varograms range of the cokrgng meter for the tree densty sample plots of the basal area (Table 2), In other words, the tree densty varable are spatal correlaton and the dstance after whch spatal correlaton s no longer sampled value and are thus ndependent. The sample grds dmensons can were desgned based on statstc varance of socety, so that sample dstances are equal wth the range length nfluence. Comparng the estmated dstrbuton maps of these methods shows that, estmate of tree mass s generally great n the northern regon (more dark areas) and low n the southern and central regon. Because of t that northern area adjacent to the Karkheh Rver that provded the more sutable condtons whle trees plant and ther development stages than South and dstant regons, and another the effect of the senstve to wnd eroson regons (the most of central and southern Regons) that led to ncreased waste n the seed and young saplng towards the northern areas n the early plant. Ths study showed that these Geostatstcal technques can be used and are useful n the context of to predct of spatal dstrbuton of tree densty n smlar areas for local estmaton n Khuzestan provnce of Iran. Fnally, the use of the capabltes of geostatstcal tools and methods because of ts smplcty and robust predctons, lower cost rate and economy n tme and provde the quckly and acceptable results suggested the n order to estmate forest parameters. Acknowledgements The authors thank the colleagues of Natural Resources Department of Khuzestan Provnce who provded the data of the tree densty and canopy percent used n the research. Thereto, would lke to Mr. Rohmoghadam Assstant professor of Faculty of Natural Resource, Unversty of Zabol (Iran) thank for crtcal help wth desgn for ths study. 211

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