Forestry An International Journal of Forest Researc Forestry 2014; 87, 249 255, doi:10.1093/forestry/cpt061 Advance Access publication 15 January 2014 Comparing te efficiency of intensity-based forest inventories wit sampling-error-based forest inventories Bogdan M. Strimbu 1,2 * 1 Scool of Forestry, Louisiana Tec University, 201-1501 Reese Dr., Ruston, LA 71272, USA 2 Forest Researc and Management Institute, Bulevardul Eroilor nr. 128, Voluntari, Ilfov, Romania *Corresponding autor. Tel.: +1 3182572168; E-mail: strimbu@latec.edu Received 17 August 2013 Forest resources can be assessed using two ground measurements approaces: one centred on preset intensity and te oter centred on sampling error. Te objective of te present researc is to evaluate te efficiency of te two sampling approaces using a factorial design, te factors being intensity, area, sampling error and coefficient of variation. Overall, an inventory executed using sampling error is likely more efficient tan using a preset intensity (i.e. 89 per cent of te investigated cases). For small tracts (i.e. 5 a) or tracts wit one stratum, forest inventories using preset intensities are more efficient, but mainly for reduced intensities (i.e. 5 per cent). For larger tracts and moderate variability (i.e. coefficient of variation 30 per cent), resource estimation based on sampling error is more efficient tan te intensity-based, especially wen te tract is stratified. Stratified random sampling inventories are almost always more efficient tan 10 percent intensity cruises, and, in 90 percent of te cases, 5 per cent cruises. For balanced strata, te efficiency is so large tat tracts wit same size but different variability are indistinguisable, from sampling efficiency perspective. Terefore, a preliminary cruise can focus on attributes tat are not te objective of te inventory but are related to te attributes of interest, easy, fast and accurate to measure, suc as diameter at breast eigt, basal area or tree eigt. Introduction A key information used as input in forest management is te spatial and temporal availability of resources (Davis et al., 2001). Tecnological developments, especially te advancements in remote sensing tecniques, switced te assessment of forest resources from an activity almost entirely ground based, to a mixture of software manipulation, wic supplied te estimates of te resource of interest, wit field verifications of te respective estimates. Te sift of te effort involved in te identification of te available resources did not affect te accuracy and precision of te estimates (Zarnoc and Feduccia, 1984; Popescu, 2007), but significantly reduced te amount of ground work. In te context of te new tecnological settings, one can question te efficiency of te forest inventory procedures based on preset intensities (Avery and Burkart, 2001), wic is te traditional approac used to evaluate forest resources. Moreover, te tecnological advancements are not alone in questioning te efficiency of forest inventories based on preset intensities, but also te users of te forest resources, as te connection between te users and te suppliers of te respective resource needs to be fast and accurately assessed. Several national and state entities (suc as US Forest Service or Departments of Forests and of Environmental protection for State of Florida) related te level of accuracy as a function of value (i.e. US Forest Service (Robertson, 2000)) or quality (i.e. State of Florida (Wallace et al., 2004)), and provided te teoretical framework ensuring te fulfilment of te respective regulations. Te main critique of te inventory based on preset intensities is te lack of a priori knowledge of te accuracy of te estimates. Tis lack of knowledge can lead to field efforts tat eiter do not meet te regulatory tresolds or exceed te optimal travail. Te objective of tis study is to assess te practical efficiency of te forest inventory based on preset intensities witin regulatory frameworks tat consider te accuracy of te estimates in designing te field effort. Metods Selection of an estimator for efficiency An unbiased estimator of a parameter is said to be efficient if its variance attains te Rao Cramer lower bound (Hogg et al., 2012). Te efficiency of an estimator is consequently defined as te ratio of te Rao Cramer lower bound to te actual variance of te unbiased estimator of te parameter. For probability density functions tat fulfil te regularity conditions, in te sense of Hogg et al. (2012), and are twice differentiable, te efficiency is e = 1/I(m), s 2 x # Institute of Cartered Foresters, 2014. All rigts reserved. For Permissions, please e-mail: journals.permissions@oup.com. Tis is an Open Access article distributed under te terms of te Creative Commons Attribution License (ttp://creativecommons.org/licenses/by/ 3.0/), wic permits unrestricted reuse, distribution, and reproduction in any medium, provided te original work is properly cited. 249
Forestry were I(m) = 1 ( 2 log f (x; m)/ m 2 )f (x; m)dx is te Fiser information 1 of te sample, f(x;m) is te probability density function of te random variable X tat as mean m, s2 x is te variance of te estimator. For independent and identical distributed random variables wit common probability density function f(x;m), te efficiency, as defined above, is equivalent to te asymptotic efficiency (Hogg et al., 2012). Wen two estimators are compared, te asymptotic efficiency becomes te asymptotic relative efficiency, and assesses te estimators on te basis of teir variance: terefore, e( x 1, x 2 )=s 2 x2 /s2 x1, were x 1, x 2 are te two estimators for te mean. Te more efficient estimator is te estimator wit smaller variance (Gujarati, 1995; Zar, 1996). Te estimators determined using preset intensities ave null variance, as te measurements are focussed on te size of te population and not on te attribute of interest; terefore te definition of efficiency as to be adjusted to accommodate computational metods leading to zero variance. Zar (1996) argued tat sample size can be used as an alternative to te definition of efficiency, as defined by Hogg et al. (2012). Zar s expression of efficiency is related to tat of Hogg et al. (2012), but rater tan investigating te magnitude of te variance obtained using equal sample sizes, it examines te magnitude of te sample size needed to acieve te same variance. Te efficiency articulated in terms of sample size, as advocated by Zar (1996), is commonly used in ypotesis testing (Nikitin, 2002). Furtermore, in ypotesis testing, te relative efficiency assesses te performances of one estimator against te performance of anoterestimator, and is commonly computed as te ratio of te sample sizes required by eac estimator to acieve te same power (i.e. te probability of rejecting te null ypotesis wen it is false). Consequently, te present study computes te efficiency using te formula proposed by Nikitin (2002): e = n intensity /n sampling error (1) were n intensity ¼ i A tract /A plot is te sample size computed using preset intensity i on a tract of area A tract using fixed area plots of size A plot and n sampling error is te sample size computed using sampling error and confidence level. Te sample size based on sampling error requires a priori knowledge of te coefficient of variation, or te standard deviation, wic commonly is determined using a dedicated sample called preliminary cruise/sample or pre-cruise/sample. Terefore, te n sampling error includes not only te size of te sample but also of te pre-sample: n sampling error ¼ n sampling error for actual cruise + n pre-cruise. Te magnitude of te preliminary cruise varies depending on te autor; at least five per stratum, according to te US Forest Service guidelines (Robertson, 2000), or minimum 10, according to Avery and Burkart (2001). Determination of sample size In te present study, te values determining te sample size (namely te sampling error and te confidence level) were obtained using te recommendations of te US Forest Service specified in te Timber Cruising Handbook (Robertson, 2000). Te Handbook suggests stratified random sampling witout replacement as main approac for computing sample size. Stratification wit more tan one stratum is recommended only in cases wen variability of te inventoried tract is large (e.g. te coefficient of variation is.35 per cent). Several allocation procedures can be selected to compute te sample size wen stratification is implemented (Cocran, 1977). For tis study, te Neyman allocation was selected, as being a procedure suitable for most forest inventories (i.e. it can be constrained to proportional or equal allocation), wen sampling costs are not considered (Tompson, 2012). Te sample size, n, determined using Neyman allocation among strata is (LeMay and Marsall, 1990; Cocran, 1977): ( t 2 n 1,a/2 w ) 2 s SE 2 + t 2 n 1,a/2/N w, (2) s 2 wen sampling error is represented in actual units, or ( t 2 n 1,a/2 w ) 2 k CV SE 2 + t 2 n 1,a/2/N w, (3) k 2 CV2 wen sampling error is represented in relative units wit respect to mean (%); were SE is te sampling error; k = y / y is te ratio between tract mean, y, and stratum mean, y, were represents te number of strata, between 1 and l; N ¼ A tract /A plot is te maximum number of plots of size A plot tat can be placed in a tract wit area A tract ; w ¼ A /A tract is te weigt associated wit stratum ; s is te standard error of stratum ;CV is te coefficient of variation of stratum, CV = s / y, and t n21,a/2 is te t value for n 1 degrees of freedom and significance level a. Considering tat and i y = y i N = l nl =1 i=1 y l i =1 = N y = l w y N N =1 y = k y, te relationsip between strata weigts and ratios of strata means to tract mean is w k = 1. (4) In te case wen te tract is omogeneous and only one stratum can be used, te sample size simplifies to te known formula: or 1 1/N + SE 2 /(t 2 n 1,a/2 s 2 ) (5) 1 1/N + SE 2 /(t 2 n 1,a/2 CV 2 ), (6) depending on weter sampling error is expressed in actual unit (te former) or as a proportion of tract mean (te latter). Te relative efficiency of te estimators obtained using te two sampling approaces (i.e. intensity-based and sampling-error-based) is consequently n intensity e = n pre cruise + n sampling error i A tract /A plot = t 2 n 1,a/2 ( w k CV ) 2 n pre cruise + SE 2 + t 2 n 1,a/2 A plot /A tract w k 2 CV2 for te case wen sampling error is represented in relative units. Te parameters needed to determine te sample size (equations 2, 3, 5, 6) are identified by te US Forest Service guidelines as being 0.05 (for significance level), and sampling error between 10 per cent (for estimated sale value of more tan $95 000) and 20 per cent (for estimated sale value between $5000 and $15 000). Te present investigation uses a minimum sample size for te preliminary cruise of ten, n pre-sample ¼ 10, wic fulfils te US Forest Service guidelines, and most likely will provide at least 50 trees witin te sample, wic is anoter limiting condition in sampling establisment (Avery and Burkart, 2001; Kangas, 2006). (7) 250
Intensity-based versus sampling-error-based forest inventories To accommodate te large palette of forest inventory conditions, te present researc is focussed only on tracts wit at most two strata, eac wit coefficient of variation 90 per cent, and te stratum size, in respect of te tract, eiter balanced (i.e. w ¼ 1/number of strata ¼ 0.5) or unbalanced (e.g. w is 0.8 and 0.2). Te range for coefficient of variation was selected to cover te most likely values encountered in forest inventory. Considering tat uneven-aged stands ave volume or biomass spatially more variable tan even-age stands, te maximum coefficient of variation consider in te study will be associated wit stands aving tree or more age classes (Smit, 1997). Tree distribution of uneven-aged stands is commonly described by te exponential distribution, wic as a coefficient of variation of 100 per cent. However, plot-level distribution does not ave a coefficient of distribution as large as tree distribution does, as it group te trees, wic reduces te variability (Brockwell and Davis, 1996). Terefore, te maximum coefficient of variation considered in tis study was 90 per cent. According to equation (4), in te case of balanced strata, te relationsip between te stratum mean and te tract mean become k 1 + k 2 ¼ 2. One possible solution to tis non-singular equation, in te sense of Poole (2005),isk 1 ¼ 1.5 and k 2 ¼ 0.5, wic indicatestat one stratum is probably older tan te average tract, wile te oter stratum is likely younger. An additional solution to te equation k 1 + k 2 ¼ 2isk 1 ¼ k 2 ¼ 1, wic could identify te strata based on te species rater tan on te magnitude of te dendrometic attributes. Based on equation (4), for te unbalanced strata, a possible solution of te non-singular equation 0.8 k 1 + 0.2 k 2 ¼ 1isk 1 ¼ 0.75 and k 2 ¼ 2. Te selection of te sizes of te strata wit respect to te tract was made not to describe a general case but to represent possible situations encountered in te planning pase of a forest inventory. Furtermore, inference for oter inventories using two strata can be drawnbyassessingte departure fromte balanced case in te direction of te unbalanced case. Te generalization of te results based on te selected cases is ensured by te Caucy Bunyakovsky Scwarz inequality (Poole, 2005), wic proves tat te findings derived from te selected values are just increased or decreased depending on te relationsip between te variability and magnitude of eac strata. However, Caucy Bunyakovsky Scwarz inequality is nonlinear, wic indicates tat additional computations, likely in an iterative sceme, sould be executed if one needs precise inference derived from te two proposed values. Te coefficient of variation of te two strata tat were used in sample size computations was determined based on two facts. First, older stands (i.e. larger dendrometic values) ave larger coefficient of variation tan younger stands (Husc et al., 2002), and second, variance of te tract is te sum of te variance of te two strata (Hogg et al., 2012). Assuming independence of strata, CV 2 tract = s2 tract y 2 = s2 stratum1 + s 2 stratum2 tract y 2 tract = s2 stratum1 y 2 stratum1 y2 stratum1 y 2 + s2 stratum2 tract y 2 y2 stratum2 stratum2 y 2 tract tat leads to CV 2 tract = k 2 1 CV 2 stratum 1 + k 2 2 CV 2 stratum 2. (8) Consequently, te coefficient of variations tat were used as representing possible candidates for te balanced size case encountered in forest inventories were CV 1 = CV 2 = CV tract / 2, wen strata were probably similar (i.e. k 1 ¼ k 2 ¼ 1), and 0.65 CV tract (for te stratum wit possible larger dendrometric attributes) and 0.44 CV tract (for stratum wit possible smaller dendrometic attributes), wen strata were different (i.e. k 1 ¼ 1.5 and k 2 ¼ 0.5). For te unbalanced strata sizes, possible candidates for te coefficient of variations are 0.5 CV tract and 0.7 CV tract, former for te stratum wit smaller dendrometric attributes, and latter for te larger stratum. Te values for te latter case (i.e. different strata) were selected based on te Hendricks and Robey (1936) and McKay (1932) results, wo proved tat coefficient of variation as a sampling distribution wit a probability density function determined numerically. Te sample size depends on te magnitude of te tract; terefore, variation of te relative efficiency was determined for tracts wit areas between 5 and 50 a, a range covering te size of te common units used in forest management (Davis et al., 2001). Te sample unit for wic te relative efficiency was computed ad a fixed area of 0.05 a (i.e. a sampling tecniques tat as te probability of selection proportional to frequency of occurrence), a widespread size used in forest inventories (van Laar and Akca, 1997; Avery and Burkart, 2001; Husc et al., 2002; Pretzsc, 2009). Te values for wic efficiency will be assessed were selected to cover an array of likely situations (Table 1), allowing generalizations witout a significant loss of accuracy. Te factorial layout of te investigation presented in Table 1 leads to 432 sample sizes (i.e. 6 tract sizes 2 sampling errors 9 coefficients of variation (1 one stratum + 1 two strata unbalanced + 2 two strata balanced). Results For tracts,5 a, te preset intensity cruise as eiter te same efficiency or is twice as efficient as sampling-error-based cruise, depending on intensity (i.e. 10 or 5 per cent, respectively), regardless te variability of te tract, as te preliminary cruise as 10 plots (i.e. te same wit 10 per cent intensity cruise or double te number of plots compared wit 5 per cent intensity cruise). Terefore, for small tracts, it is recommended to cruise using eiter preset intensity or te recommended 10 plots. However, if only five plots are measured (i.e. 5 per cent cruise), likely te confidence intervals would be too large to provide meaningful results (i.e. standard error of te mean would be large and t-value for a 0.05 significance level is 2.776). Te standard error of te mean of a random variable X decreases yperbolically wit sample size, as expectation of its variance, E[s 2 X] =s 2 /n, converges to 0 wen n increases. Table 1 Te cases for wic te sample size was computed using sampling error Tract area (a) Sampling error (%) Coefficient of variation (%) Number of strata Strata weigts Possible strata dendrometric attributes 5, 10, 20, 30, 40, 50 10, 20 5, 10, 15, 20, 25, 30, 50, 70, 90 One Two Equal Different Similar Unequal Different 251
Forestry Figure 1 Efficiency of sampling-error-based inventory compared wit 5% intensity-based inventory: (a) one stratum and SE ¼ 10%, (b) one stratum and SE ¼ 20%, (c) balanced equal strata and SE ¼ 10%, (d) balanced equal strata and SE ¼ 20%, (e) balanced unequal strata and SE ¼ 10%, (f) balanced unequal strata and SE ¼ 20%, (g) unbalanced strata and SE ¼ 10%, () unbalanced strata and SE ¼ 20%. 252
Intensity-based versus sampling-error-based forest inventories To ensure tat confidence intervals will be significantly smaller compared wit te estimates, several autors recommended te measurements of at least two plot per ectare for areas,5 a(avery and Burkart, 2001; Husc et al., 2002). Depending on stand structure, for areas equal or larger tan 10 a, te sampling error cruise is predominantly more efficient, and requires less plots tan intensity-based cruise (Supplementary data). For 20 per cent sampling error (i.e. less valuable tracts), te efficiency of sampling-error-based cruise constantly increases up to 4.5 times compared wit 5 per cent intensity cruise (Figure 1d, f and ), except for tracts wit one stratum (Figure 1b) and larger coefficient of variation (i.e. 30 per cent). Even for more valuable stands, wen te sampling error was 10 percent, sampling errorcruise was more efficient tan 5 per cent intensity cruise but for larger areas (e.g. 30 a) and smaller variability (e.g. coefficient of variation 20 per cent; Figure 1c, e and g), except wen only one stratum is present, wen coefficient of variation was,15 per cent (Figure 1a). Overall, out of te 864 sample sizes (i.e. 432 cases from Table 1 2 cruise intensities (i.e. 5 and 10 per cent )), only for 21.4 per cent (i.e. 185 cases) te intensity-based cruise was more efficient tan te sampling-error-based cruise (Supplementary data). Wile a 5 per cent intensity cruise ensures a more efficient sampling in 34.5 per cent of te situations (i.e. 149 cases out of 432), a 10 per cent intensity cruise is only 8 per cent more efficient tan a sampling-error-based cruise (i.e. 36 cases out of 432), mainly wen stand as a pronounced variability (i.e. CV 50 per cent). Te results are aligned wit te teorems proving te superior efficiency of te stratified random sampling over simple random sampling (Figure 1a and b vs c ). Te findings are obvious for te case wen strata are similar (i.e. same surface area and equivalent attributes of interest), wen te relative efficiency was always.1 (Figure 1c and d). Neverteless, stratification increases te efficiency even wen strata are different (Figure 1e ), but for larger tracts (i.e. 30 a) or resources tat are less valuable (e.g. pulpwood or cip-and-saw). A 10 per cent intensity cruise was less efficient tan a stratified sampling-error-based cruise, almost for all sizes and variability, te exception being situations resembling natural, unmanaged or uneven-aged stands. A similar conclusion olds for a 5 per cent intensity cruise, wen stratification increased efficiency in 74 per cent of te cases, compared wit non-stratified approac, wic was more efficient in 39 per cent of te cases (Supplementary data). Discussion Te sample size determined using equation (3) is larger for eterogeneous tracts tan for omogeneous tracts, recommending te separation into several omogeneous strata. Te increase in number of strata does reduce te overall number of plots, but if precise estimates are needed at stratum level, te confidence intervals are larger as t-values increase. Neverteless, te tract-level estimates will ave te desired precision. Plantations intensively managed for arvesting ave low variability, wic recommends tat resource assessment sould be executed using sampling error, irrespective te size. For natural forests, were variability is larger, te inventory sould be still carried using sampling error, but stratification is recommended to reduce te field effort. Te size of te sample does not depend only on te omogeneity of te tract, but also on te relationsip between te strata. Tis is a direct result of te Caucy Bunyakovsky Scwarz inequality (Poole, 2005), wic reaces a local extreme wen all te variables ave te same value; in sampling case, te variables being strata tat ave equal size and equal coefficient of variation. Wen a local extreme is reaced, stratification of a cruise based on sampling error seems to diminis te impact of stratum variability regardless te tract value (i.e. sampling error), as coefficient of variations of 10 and 15 per cent lead to same sample sizes (Figure 1e). Furtermore, inventory of less valuable tracts do not distinguis between 25 and 30 per cent coefficient of variation, wic allows inclusion of errors in estimating te coefficient of variation. Te relaxation of precise estimation of te coefficient of variation support its derivation using not necessarily te attribute of interest (i.e. volume or mass), but oter attributes tat can replace it and are easy, fast or not expensive to measure, suc as diameter at breast eigt, basal area or even eigt, wen LIDAR data are available. For largeand less valuable tracts (i.e. 30 a), tere iste possibility tat even unbalanced strata could be inventoried witout loss of precision wen te estimation of coefficient of variation is determined using not te attribute of interest, but an attribute strongly related but more convenient to measure (Figure 1). Te objective of te preliminary cruise is estimation of te coefficient of variation. Te usage of single entry equations could reduce significantly te field effort needed to determine te coefficient of variation. Let us assume te existence of a linear relationsip between te attribute of interest and one variable, possible from a single entry equation Y = b 0 + b 1 X + e, (9) were Y is te attribute of interest, X is te auxiliary variable, likely from single entry equation, b 0 and b 1 are coefficients relating te two attributes, and e is te error. Considering tat s 2 Y = s2 b 0 +b 1 X+e = b2 1 s2 X + s2 e, Y = b 0 + b 1 X = b 0 + b 1 X (Ross, 2001), and assuming tat standard deviation of te error term is significantly smaller tan Y variation (i.e. magnitude of b 1 X is equal or larger tan variation of Y), te CV Y = s Y Y = b 2 1 s2 X + s2 e = b 0 + b 1 X s 2 X / X 2 + s 2 e /(b 1 X) 2 b 0 + b 1 X CV X. 1 + b 0 /(b 1 X) (10) Terefore, te objective would be to determine te expected value of te coefficient of variation and te mean for te attribute used as a replacement for volume, or biomass. Te most likely attributes used in single entry equations tat can be used as substitute for volume (or biomass) are diameter at breast eigt (db), basal area or eigt (Avery and Burkart, 2001; Husc et al., 2002; Algeria, 2011). In eventuality tat equation (9) as no intercept, te attributes ave te same coefficient of variation, as anticipated considering tat te random variables representing te attributes are linearly related. Wen remote sensing data are available (suc as LIDAR or stereo potos), te attribute selected as replacement for volume or biomass is likely eigt; te replacement is suggested 253
Forestry by Eicorn (1904) and supported by Zeide (2004) and Pretzsc (2009). In tis situation, coefficient of variation for tree eigt is computed at te office, te field effort being entirely concentrated on te actual cruise. Terefore, te efficiency of te samplingerror-based inventory is even larger tan five times (sometimes more tan nine times wen coefficient of variation 10 per cent), as te preliminary cruise plots (i.e. 10 plots) are not measured in te field anymore, only at te office, were productivity is significantly larger (i.e. faster and more accurate). Wen remote sensing data are not available, db or basal area are widely used as predictors for volume or biomass. Terefore, te preliminary cruise will measure only db or basal area. Te estimated coefficient of variation for db or basal area is more accurate tan te coefficient of variation of volume (or biomass) as it uses less measurements, wic are more accurate tan ground measured eigts, te attribute needed in volume computations (e.g. commonly, te tolerance is double for eigt tan for db: 10 per cent for eigt and 5 per cent for db (Robertson, 2000)). In eventuality tat instead of fixed area plots, variable radius plots are used, specifically orizontal point sampling (Husc et al., 2002), te basal area, wic is te fastest measured attribute for tis type of sampling (i.e. basically counting trees inside te plot), sould supply te CV. Furtermore, variable radius plots samplings ave a smaller number of plots compared wit fixed area plots; all oter parameters kept te same, as no finite population correction factor is included in sample size computations. Tis suggests tat stands presenting pronounced dendrometric variability (i.e. CV 50 per cent), suc as uneven-aged stands or wit two coorts, sould be inventoried, if possible, wit variables radius plots. Neverteless, te accuracy gained in db or basal area will not necessarily be translated to volume (or biomass), as equation (9) lacks compreensiveness (i.e. population aspect). However, forest inventories designed using stratified random sampling and sampling error not only will be more efficient tan intensity-based cruises, but can be executed faster in te field wen te attribute of interest is replaced in te preliminary cruise by an alternate attribute faster, more accurate and less expensive to measure. Conclusion To assess forest resources based on ground measurements, two approaces can be used: one centred on preset intensity and te oter centred on sampling error. To evaluate te efficiency of te two sampling approaces, a factorial design was implemented, wic ad te following as factors: intensity (wit two levels: 5 and 10 per cent), tract area (wit six levels: 5, 10, 20, 30, 40 and 50 a), sampling error (wit two levels: 10 and 20 per cent) and coefficient of variation (wit nine levels: 5 90 per cent). Te efficiency of a sampling error cruise wit respect to intensity cruise ranges from 0.07 to 9.1, larger for 20 per cent sampling error and smaller for 10 per cent. Overall, an inventory executed using sampling error is likely more efficient tan tat using a preset intensity (i.e. 78.6 per cent of te investigated cases). For small tracts (i.e. 5 a) or tracts wit one stratum, forest inventories using preset intensities are more efficient, but mainly for reduced intensities (i.e. 5 per cent), oterwise sample sizes determined using sampling error are likely smaller, terefore more efficient. For large tracts, resources estimation based on sampling error is more efficient tan intensity-based, especially wen te tract is stratified. For stands presenting moderate variability (i.e. CV 30 per cent) stratified random sampling cruises are always more efficient tan 10 per cent intensity cruises, and in 90 per cent of te cases, tan 5 per cent cruises and. For balanced strata, te efficiency is so large tat inventories of tracts wit same size but different variability are undistinguisable from cruise efficiency perspective. Terefore, te preliminary cruise required in sampling-error-based cruise can focus on attributes tat are easy, fast and accurate to measure, suc as db, basal area or tree eigt. Wen remote sensing data are available, te coefficient of variation for tree eigt is determined at te office (i.e. no field work), and can be used as replacement for te coefficient of variation of volume or biomass. Wen field measurements are executed in a multi-strata forest inventory, only db or basal area can be measured in te preliminary cruise, as te coefficient of variation of volume (or biomass) would be replaced by te same statistics of te db or basal area. Stands wit two or more coorts sould be inventoried using orizontal point sampling, if possible, as te preliminary cruise could be focussed on basal area even tat te objective of te inventory is volume or biomass. Supplementary data Supplementary data are available at Forestry online. Conflict of interest statement None declared. Funding Tis work was supported by te USDA, NIFA, McIntire-Stennis Cooperative Forestry Researc Program project No. LAZ00071, and UEFSCDI project No. PN-II-PT-PCCA-2011-3.2-1710. Funding for Open Access carge: Bogdan Strimbu. References Algeria, C. 2011 Modelling mercantable volumes for uneven aged maritime pine (Pinus pinaster Aiton) stands establised by natural regeneration in te central Portugal. Ann. For. Res. 54, 197 214. Avery, T.E. and Burkart, H. 2001 Forest Measurements. Mcgraw-Hill Ryerson, pp. 1 480. Brockwell, P.J. and Davis, R.A. 1996 An Introduction to Time Series and Forecasting. Springer, pp. 1 420. Cocran, W.G. 1977 Sampling Tecniques. Jon Wiley and Sons, pp. 1 428. Davis, L.S., Jonson, K.N., Howard, T.E. and Bettinger, P. 2001 Forest Management. McGraw-Hill, pp. 1 804. Eicorn, F. 1904 Bezieungen zwiscen bestandsoe bestandsmasse. Allgemeine Forst und Jagdzeitung 80, 45 49. Gujarati, D.N. 1995 Basic Econometrics. McGraw-Hill Companies, pp. 1 350. Hendricks, W.A. and Robey, K.W. 1936 Te sampling distribution of te coefficient of variation. Ann. Mat. Stat. 7, 129 132. Hogg, R.V., McKean, J. and Craig, A.T. 2012 Introduction to Matematical Statistics. 7 edn. Pearson, p. 640. Husc, B., Beers, T.W. and Kersaw, J.A. 2002 Forest Mensuration. 4t edn. Wiley, p. 456. 254
Intensity-based versus sampling-error-based forest inventories Kangas, A. 2006 Mensurational aspects. In: Forest Inventory Metodology and Applications. Kangas, A. and Maltamo, M. (eds). Springer, pp. 53 63. LeMay, V.M. and Marsall, P.L. 1990 Forest Mensuration. Distance Education and tecnology, Continuing Studies, pp. 1 213. McKay, A.T. 1932 Distribution of te coefficient of variation and te extended t distribution. J. R. Stat. Soc. 95, 695 698. Nikitin, Y.Y. 2002 Efficiency, asymptotic. In: Encyclopedia of Matematics. Remann, U. (ed). Kluwer Academic Publisers. Poole, D. 2005 Linear Algebra. Tomson Brooks/Cole, pp. 1 712. Popescu, S. 2007 Estimating biomass of individual pine trees using airborne lidar. Biomass Bioenergy 31, 646 655. Pretzsc, H. 2009 Forest Dynamics, Growt and Yield. Springer, p. 664. Robertson, F.D. 2000 Timber Cruising Handbook. USDA Forest Service. Ross, S. 2001 A First Course in Probability. 6 edn. Prentice Hall, p. 528. Smit, D.M. 1997 Te Practice of Silviculture: Applied Forest Ecology. 9t edn. Wiley, pp. xvii, 537. Tompson, S.K. 2012 Sampling. Jon Wiley & Sons. van Laar, A. and Akca, A. 1997 Forest Mensuration. Cuvillier Verlag, pp. 1 418. Wallace, T., Candler, R., Curtis, D., Foster, A., debrauwere, J. and King, C. et al.. 2004 Timber Cruise Timber Appraisal Standards Department of Agriculture and Department of Environmental Protection, Tallaassee FL. Zar, J.H. 1996 Biostatistical Analysis. Prentice Hall, pp. 1 662. Zarnoc, S.J. and Feduccia, D.P. 1984 Slas pine plantation site index curves for te west gulf. Soutern J. Appl. For. 8, 223 225. Zeide, B. 2004 Intrinsic units in growt modeling. Ecol. Model. 175, 249 259. 255