Effect of permanent plots on the relative efficiency of spatially balanced sampling in a national forest inventory

RESEARCH PAPER E ec o pe manen plo s on he ela i e e iciency o spa ially balanced sampling in a na ional o es in en o y Minna Rä y 1 &Annika Susanna Kangas 2 Recei ed: 18 July 2018 /Accep ed: 18 Janua y 2019 #The Au ho (s) 2019 Abs ac &Key message Using spa ially balanced sampling u ilizing auxilia y in o ma ion in he design phase can enhance he design e iciency o na ional o es in en o y. These gains dec eased wi h inc easing p opo ion o pe manen plo s in he sample. Using semi-pe manen plo s, changing e e y n h in en o y ound, ins ead o pe manen plo s, educed his phenomenon. Fu he s udies o accoun ing he pe manen sample when selec ing empo a y sample a e needed. &Con ex Na ional o es in en o ies (NFIs) p oduce na ional- and egional-le el s a is ics o sus ainabili y assessmen and decision-making. Using an in e p e ed sa elli e image as auxilia y in o ma ion in he design phase imp o ed he ela i e e i- ciency (RE). Spa ially balanced sampling h ough local pi o al me hod (LPM) used o selec ion o clus e s o sample plo s is designed o empo a y sample; hus, he me hod was es ed in a NFI design wi h bo h pe manen and empo a y clus e s. &Aims We es ima ed LPM me hod and s a i ied sampling o a NFI designed o successi e occasions, whe e he clus e s a e pe manen , semi-pe manen , o empo a y being eplaced: ne e , e e y n h, and e e y in en o y ound, espec i ely. &Me hods REs o sampling designs agains sys ema ic sampling we e s udied wi h simula ions o in en o y sampling. &Resul s The la ge he p opo ion o pe manen clus e s he smalle bene i s gained wi h LPM. REs o s a i ied sampling we e no depending on he p opo ion o pe manen clus e s. The semi-pe manen sampling wi h LPM emo ed he p e iously desc ibed dec ease and esul ed in he la ges REs. &Conclusion Sampling s a egies wi h semi-pe manen clus e s we e he mos e icien , ye no necessa ily op imal o all in en o y a iables. Fu he de elopmen o me hod o simul aneously ake in o accoun he dis ibu ion o pe manen sample when selec ing empo a y o semi- empo a y sample is desi ed since i could inc ease he design e iciency. Keywo ds Auxilia y in o ma ion .Local pi o al me hod .Pe manen clus e .Rela i e e iciency .Sampling design . Semi-pe manen clus e 1 In oduc ion Na ional o es in en o ies (NFIs) a e he main sou ce o in- o ma ion o cha ac e izing he s a e o he o es esou ces (Vidal e al. 2016, p. 8). The mos common in en o y a i- ables a e o es a ea, mean g owing s ock olume, and dis i- bu ion o g owing s ock olume in o ee species and imbe asso men s (Tomppo e al. 2010; Vidal e al. 2016). In addi- ion o he cu en g owing s ock, es ima ing he changes in he o es s o e ime is impo an . The plo s can be pe manen , meaning hey a e emeasu ed in all consecu i e in en o y ounds, o empo a y, meaning hey a e disca ded a e he i s measu emen s. Tempo a y plo s a e mainly in ended o cap u e he cu en s a e o he o es , whe eas pe manen plo s in addi ion o he cu en s a e aim a cap u ing he changes (Sco 1998; Tomppo e al. 2010). E en hough he inc emen s o g owing s ock can be accu a ely measu ed ia inc emen co es om empo a y plo s, es ima ing he changes such as na u al mo ali y and ha es s is much mo e p ecise om pe - manen han om empo a y plo s (e.g., Päi inen and Yli- Kojola 1989). NFIs can be solely on empo a y plo s (e.g., Handling Edi o : John M. Lho ka Con ibu ion o he co-au ho s MR did he analysis and w o e he o iginal d a . ASK supe ised and coo dina ed he esea ch, and e iewed and edi ed he o iginal d a . *Minna Rä y minna. a y@luke. i 1 Na u al Resou ces Ins i u e Finland (Luke), PO Box 2, FI-00791 Helsinki, Finland 2 Na u al Resou ces Ins i u e Finland (Luke), Yliopis oka u 6, FI-80100 Joensuu, Finland Annals o Fo es Science (2019) 76:20 h ps://doi.o g/10.1007/s13595-019-0802-6 Poland, Po ugal, F ance, and Spain), solely on pe manen plo s (e.g., Aus ia, Iceland, China, and Canada), o a combi- na ion o hese wo plo ypes (e.g., Finland, Sweden, Ne he lands, Es onia, New Zealand; see Tomppo e al. 2010). The designs also change cons an ly in ime, o in- s ance in F ance, plans o in oduce pe manen plo s ha e been epo ed (Vidal e al. 2016). An in en o y wi h pu ely pe manen plo s is called con in- uous o es in en o y (CFI). Some imes, he pe manen plo s es ablished may lose hei impo ance as an indica o o change. Fo example, ea men bias can be impa ed when pe manen plo s a e managed di e en ly han he su ounding o es s and a ec CFI es ima es (Köhl e al. 2015). In such occasion, he possibili y o edis ibu e also he pe manen plo s would be bene icial. Ano he op ion is a sampling design whe e he pe manen plo s a e only used o a limi ed ime, i.e., hey a e semi-pe - manen . Such designs a e lexible since he p io i ies in su ey may be changed om a ound o ano he by alloca ion o di e en numbe s o empo a y plo s (Sco and Köhl 1994). A semi-pe manen plo is su eyed in a leas wo consecu i e in en o y ounds bu hen eloca ed like a empo a y plo . The e o e, i is capable o cap u ing change and, in addi ion, wi h an e icien ealloca ion, is no suscep ible o he ea - men bias in he same way as pe manen plo s. An example o his is sampling wi h pa ial eplacemen (e.g., Pa e son 1950; Ma is e al. 1984;Köhle al.1995). The measu emen cos s o pe manen plo s ha e been highe han hose o empo a y plo s, due o necessi y o mak- ing su e he plo is ound o emeasu emen s. Howe e , wi h mode n GPS, he ees in empo a y plo s may be loca ed as accu a ely as he ees in pe manen plo s, and he e o e, he measu emen cos s do no di e ma kedly any mo e (e.g., Tomppo e al. 2014). This makes i possible o in oduce new pe manen plo s wi hou addi ional cos s. In Sweden, he empo a y clus e s in he cu en NFI ound, which began in summe 2018, we e chosen wi h spa ially balanced sampling using local pi o al me hod (LPM) in he sample selec ion (G a s öm e al. 2017b). This has mo i a ed us o es he same me hod in he Finnish NFI se ing. In a spa ially balanced sampling, he dis ibu ion o he auxilia y a iables in he sample is ma ched as closely as possible o he dis ibu ion in he en i e popula ion (G a s öm e al. 2012). Auxilia y da a may be any da a a ailable o all uni s o he popula ion wi h no uppe limi o he numbe o auxilia y a iables used. Typically, auxilia y a iables a e spa ial loca- ion, o he geog aphic da a such as al i ude, and emo ely sensed da a (e.g., G a s öm and Ring all 2013; G a s öm e al. 2014). The unde lying assump ion is ha auxilia y in- o ma ion and in en o y a iables should be co ela ed (G a s öm e al. 2012). LPM is a sample selec ion me hod esul ing in app oxima ely spa ially balanced sample (G a s öm and Lunds öm 2013). The LPM was assessed in a simula ion s udy wi h independen auxilia y in o ma ion and eal NFI ield da a, whe e all sampling uni s belonged o one and he same popula ion a ailable o sampling (Rä y e al. 2018). In o he wo ds, he se ing in he s udy co esponded o an in en o y wi h empo a y in en o y plo s solely. The LPM can also be connec ed wi h o he sampling me hods such as s a i ica ion: in such a case, he LPM would be ca ied ou sepa a ely wi hin each s a um. So a , he e is no app oach accoun ing o he dis ibu ion o exis ing pe manen sample when selec ing a empo a y sample wi h he LPM. Such an app oach should no comp omise he equi emen ha each uni in he popula ion has la ge han ze o p obabili y o be included in he sample. To da e wi h LPM, i has been only possible o ma ch he dis ibu ion o he empo- a y sample i espec i e o he exis ing pe manen sample. The e o e, in he case o pe manen sample, s a i ica ion wi h sys ema ic o andom sample selec ion may be mo e e icien han s a i ica ion wi h LPM o pu e LPM. In s a i ied sam- pling, he sample wi hin a s a um is popula ed i s wi h he pe manen sample belonging o ha s a um. Then, he emain- ing sample wi hin a gi en s a um is illed using sys ema ic o andom selec ion. Thus, while s a i ied sampling (wi h o wi h- ou LPM) was shown o be less obus han pu e LPM in ou p e ious s udy (Rä y e al. 2018), i may be mo e obus han LPM in a design in ol ing pe manen plo s. The main su ey p inciples in he NFIs in hese wo coun- ies, Finland and Sweden, a e alike (Tomppo e al. 2010). The sample plo s a e a anged in clus e s, he loca ion o which e e s o a co ne poin (Fig. 1). The empo a y clus e s com- p ise one hi d ≈33% o he clus e s in Sweden and 60% in Finland (Kangas e al. 2018). One in en o y ound las s o 5 yea s, and each yea , he sample o he sys ema ically posi- ioned clus e s co e s he en i e coun y. The excep ions in Finland a e he mos no he n pa and sou hwes e n a chipel- ago which bo h a e su eyed in one summe . The numbe o sample plo s measu ed annually is app oxima ely 10,000 and 15,000 in Sweden and Finland, espec i ely (Kangas e al. 2018). Thus, imp o ing he cos e iciency is impo an . We assess in his s udy he e iciency o sampling designs by simula ing he second phase o in en o y sampling wi h di e en p opo ions o pe manen clus e s in he sample. Ou i s hypo hesis is ha as he p opo ion o pe manen clus e s in he sample inc eases, he ela i e e iciency (RE) o sam- pling design using LPM o empo a y plo selec ion de- c eases, because a la ge p opo ion o sample is chosen wi h- ou u ilizing he auxilia y in o ma ion. In o he wo ds, wi h a la ge p opo ion o pe manen clus e s, i is mo e di icul o ma ch he dis ibu ion o a o al sample including bo h empo- a y and pe manen clus e s o he dis ibu ion o auxilia y a iables o e he s udy egion. As ou second hypo hesis, we assume ha as he p opo ion o pe manen clus e s in he sample inc eases, he pe o mance o s a i ied sampling designs wi h sys ema ic plo selec ion compa ed wi h ha o 20 Page 2 o 14 Annals o Fo es Science (2019) 76:20 he LPM sampling imp o es. This is because he sampling uni s in he s a i ied sampling a e selec ed independen ly o each o he , wi hou any need o accoun o he dis ibu ion o he pe manen clus e s in he same way as in LPM. In he las assessmen , he pe manen clus e s a e ea ed as semi-pe ma- nen , meaning all he semi-pe manen clus e s a e esampled and allowed o change hei posi ion a he same ime. In ha case, bo h he en i e empo a y clus e popula ion and semi- pe manen clus e popula ion a e sampled wi h LPM using auxilia y a iables. The se up could be hough as a maximal po en ial achie able wi h semi-pe manen clus e s. We as- sume ha his semi-pe manen / empo a y sampling design would be mo e e icien han he design wi h pe manen and empo a y plo s bu no as e icien as he design whe e all clus e s a e empo a y. 2 Ma e ial and me hods 2.1 S udy egion and p ima y da a The s udy egion is he sou he n pa o Finland excluding he sou hwes e n a chipelago ha co e s abou 153,000 km 2 land a ea and wo sampling egions (Fig. 1a). P ima y da a in his s udy a e he ield da a om he 11 h Finnish NFI (NFI11) which was ca ied ou in yea s 2009–2013. The sample plo s a e a - anged in he clus e s wi h sligh ly di e en clus e designs o he sampling egions (Fig. 1b, c). Da a comp ise al oge he 46,914 ield sample plo s in N= 5408 clus e s o which 1082 clus e s we e pe manen and he es 4326 we e empo a y. P ima y da a in ou s udy ep esen s he popula ion Ρ om which he samples a e chosen and popula ion pa ame e s a e es ima ed. Ou s udy is based on he main esul s o he Finnish NFI: o al g owing s ock olume on he o es ed land (m 3 ), o es ed land a ea p opo ion, and mean g owing s ock olumes by ee species g oups (m 3 /ha) (Table 1). The o es - ed land in his s udy is de ined o include he wo na ional o es y land classes: B o es land^and Bpoo ly p oduc i e o es land^(Tomppo e al. 2011), esul ing in an es ima e close o he o es land as de ined by he Uni ed Na ions Food and Ag icul u e O ganiza ion (FAO 2012). The ee species–speci ic g oups comp ising all he g owing s ock ol- ume a e as ollows: pine (Pinus syl es is L.) including all coni e s excep sp uce, sp uce (Picea abies L.), and b oad- lea es, which mos ly a e bi ches (Be ula pendula L. and Be ula pubescens L.) (Ko honen e al. 2017). 2.2 Auxilia y in o ma ion Auxilia y in o ma ion in his s udy was om he en h mul i- sou ce NFI (MS-NFI10) (Tomppo e al. 2008), which was a ailable as geo e e enced as e laye s o 20 × 20 m pixel size. These o es esou ce maps we e based on he ield mea- su emen s (NFI10 in yea s 2003–2008) and Landsa 5 TM images om yea 2007 (Tomppo e al. 2012). Fig. 1 aLoca ions o NFI11 sample plo clus e s wi hin he s udy egion ( ed: pe manen clus e s, o ange: empo a y clus e s). b,cClus e design in Cen al Finland and Sou he nmos Finland (digi al map da a: © Na ional Land Su ey o Finland MML/VIR/MYY/328/08) Annals o Fo es Science (2019) 76:20 Page 3 o 14 20 To calcula e he auxilia y a iables o sampling uni s, i.e., clus e s, a i e-pixel window o each sample plo in a clus e was ex ac ed om he o es esou ce map as e s: a cen e pixel whe e he plo cen e loca ed and one adjacen pixel o all main ca dinal di ec ions, i.e., he so called Rook’s case con igui y (e.g., Lloyd 2009). The clus e -le el auxilia y a - iables we e es ima ed as sums, means, o a iances using equal weigh o all ex ac ed pixels belonging o any sample plo in he clus e . Fo he o es ed land p opo ion, o all pixels classi ied as land, and o g owing s ock olume– based mean and a iance es ima es, he pixels classi ied as o es ed land we e u ilized. Six o es esou ce hema ic maps we e u ilized o p oduce he ollowing six auxilia y a iables o he clus e s: (1) mean g owing s ock olume o all ee species, (2) mean g owing s ock olume o pine including o he coni e s han sp uce, (3) mean g owing s ock olume o sp uce, (4) mean g owing s ock olume o b oadlea es, (5) a iance o g owing s ock olume o all ee species wi hin he clus e , and (6) o es ed land p opo ion (Table 2). 2.3 LPM LPM u ilizes auxilia y in o ma ion in sample selec ion. In his s udy, he used combina ions o clus e -le el auxilia y a i- ables a e he ones ha p o ed o be e icien in he p e ious s udy (Rä y e al. 2018). LPM aims a selec ing a sample om a popula ion whose dis ibu ion in auxilia y space is as close as possible o i s dis ibu ion in popula ion (G a s öm e al. 2012). Consequen ly, he sample is i egula i auxilia y a i- ables include o he a iables besides spa ial coo dina es. Each sampling uni iin he popula ion Ρo size N ecei es an (equal o unequal) ini ial inclusion p obabili y, π i , which sum up o hesamplesize,n: n¼∑ N i¼1 πiand 0 <πi<1ð1Þ In he selec ion p ocess, he ini ial inclusion p obabili ies a e u ned in o inclusion indica o s, which a e upda ed wi h an algo i hm. Howe e , while hese indica o s change du ing he p ocess, he ac ual inclusion p obabili ies emain a he ini ial le el. The upda ing is ca ied ou using pai wise compa isons. Fu he , while he LPM algo i hm is selec ing a sample, he popula ion di ides in o wo: a ailable and decided popula ion. In he beginning, he en i e popula ion is a ailable, i.e., all inclusion indica o s di e om alues 1 and 0. I he upda ed indica o alue is 0, ha uni will no be included in he sample and i is mo ed om he a ailable popula ion o he decided popula ion. Simila ly, a uni chosen o he sample and ha ing an inclusion indica o alue o 1 will also be mo ed o he decided popula ion. As he selec ion p oceeds, in e e y algo i hm ound, a leas one uni is ei he chosen o he sample o loses i s possibili y o be included in he sample and hus is mo ed o he decided popula ion. So, when LPM algo i hm is unning, he a ailable popula ion is diminishing and decided popula ion consis ing o included and excluded uni s is inc easing. Fo mo e de ails o LPM, see, e.g., G a s öm e al. (2012)andFig.2inRä ye al.(2018). The dis ance be ween he clus e s is a Euclidian dis ance in he space o he auxilia y a iables: di;jðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ q k¼1 x; ik−x; jk  2 sð2Þ whe e x; i1;x; i2;…;x; iq  a e he s anda dized alues o auxil- ia y a iables associa ed o all pai s (i,j) o sampled clus e s. S anda diza ion o auxilia y a iables gua an ees an equal im- po ance in dis ance calcula ion (G a s öm and Ring all 2013). Table 1 Re e ence le els in he s udy: he popula ion-le el alues o chosen popula ion pa ame e s ( i s ow) and he mean squa ed e o s (MSEs) o local pi o al me hod wi h spa ial coo dina es (=geospa ial sp ead) by inc easing p opo ion o pe manen clus e s (p) wi h he sam- ple size o n= 400. Uni o MSE is he squa ed uni o ha a iable P opo ion o o es ed land (%) To al olume (Mill. m 3 ) Mean olume (m 3 /ha) Coni e ous B oadlea All ee species Pine Sp uce Popula ion 74.8 1553 59.6 48.1 28.3 136.0 MSE, p= 0.1 1.28 1.20E+15 2.80 3.76 1.24 5.80 MSE, p= 0.2 1.29 1.16E+15 2.73 3.71 1.15 5.78 MSE, p= 0.3 1.35 1.18E+15 2.78 3.54 1.13 5.59 MSE, p= 0.4 1.35 1.19E+15 2.86 3.62 1.13 5.57 MSE, p= 0.5 1.30 1.14E+15 2.84 3.64 1.08 5.48 MSE, p= 0.6 1.34 1.13E+15 2.71 3.46 1.07 5.39 MSE, p= 0.7 1.32 1.14E+15 2.70 3.60 1.06 5.39 20 Page 4 o 14 Annals o Fo es Science (2019) 76:20 2.4 S a i ied sampling In s a i ied sampling, he popula ion is di ided in o as ho- mogenous s a a as possible using he auxilia y a iables. We used equal-dis anced limi s along he cumula i e dis ibu- ion o he squa e oo o he densi y unc ion o auxilia y a iable o de ine he s a a (see Coch an 1977; sec ion 5A.7). The sample size wi hin each s a um was de ined wi h op imal alloca ion whe e he wi hin-s a um a iance o aux- ilia y a iable was weigh ed wi h he size o he s a um (Coch an 1977). In his s udy, we u ilized he s a i ica ions ha p o ed o be mos e icien and obus in ou p e ious s udy (Rä y e al. 2018). The s a um o clus e s was de ined p io o he sampling simula ion (Table 3). No sepa a ion was made be ween he pe manen and empo a y clus e s in he popula ion when i was s a i ied, bu in he sample selec ion, he pe manen clus- e s we e chosen i s using LPM wi h spa ial coo dina es wi h equal inclusion p obabili y, called geospa ial sp ead om his poin onwa ds in his pape . Then, he empo a y clus e s we e selec ed wi h LPM wi h geospa ial sp ead based on he si ua- ion a e he alloca ion o chosen pe manen clus e s in o s a a o ul ill he sample sizes in each o hem (Table 4). I he numbe o sample clus e s in any s a um exceeded he p ede ined sample size(s) al eady a e alloca ion o pe ma- nen clus e s, s a a we e combined. As a esul was a sample whe e he pe manen plo s we e spa ially as sp ead as possible in he whole es a ea and he empo a y plo s wi hin each s a um. S anda d s a i ied es i- ma o s we e used o compu e he es ima es o popula ion pa ame e s om each s a i ied sample. 2.5 Design e iciency and sampling simula ions The hypo heses we e es ed in sampling simula ions wi h he eal NFI ield clus e s. In he simula ions, he pe manen and empo a y NFI ield clus e s we e pu in one and he same popula ion, i.e., he sampling popula ion was N= 5408 clus e s and sample size n= 400. Fu he , he clus e s chosen o ei he se we e no excluded om he selec ion o he o he se . This co esponds o he si ua ion whe e he wo di e en clus e se s a e sp ead independen ly om each o he . The sample selec ion me hod was LPM wi h geospa ial sp ead o pe manen clus e s. Fo empo a y and semi- pe manen clus e s, LPM wi h auxilia y da a was used. In he case o s a i ica ion, i s pe manen and hen empo a y clus e s we e selec ed using geospa ial sp ead. Fu he , p o- po ion o pe manen clus e s in he sample was changed o show i s impac on he pe o mance o he sampling design. Thus, he changing elemen s in he sampling simula ion we e he sample selec ion me hod, auxilia y a iables (Tables 3,4, and 5) in he selec ion me hod, and p opo ion o pe manen clus e s esul ing in se e al sampling designs. Pe o mance o each sampling design was measu ed by he mean squa ed e o (MSE): MSE2¼1 T∑ T ¼1 ^ y^ −yðÞ 2ð3Þ whe e yis he ue alue o he a ge pa ame e ( om Table 1), ^ y he es ima e ob ained om he h eplica ion o he design, and T= 5000 is he numbe o eplica ions. Compa ison o sampling designs was based on RE which is a a io be ween he MSEs o e e ence and me hod (m=LPM o s a i ica ion): REm;p¼MSE e ;p MSEm;p ð4Þ whe e pis he p opo ion o pe manen clus e s o he sample size, p=0.1–0.7. The e e ence is a design whe e bo h pe ma- nen and empo a y clus e s a e chosen wi h LPM wi h geospa ial sp ead. I can be in e p e ed as a sys ema ic sam- pling design which is close o he cu en sampling design o Finnish NFI. The e e ence was es ima ed sepa a ely o each le el o p opo ion p. Values RE > 1 mean ha he me hod unde in es iga ion is mo e e ec i e han he e e ence. Table 2 Thema ic maps u ilized in he s udy, clus e -le el auxilia- y a iable desc ip ion, and co - ela ion be ween he auxilia y and p ima y da a Va iable Thema ic map (s) Desc ip ion Co ela ion 4 x 1 Mean olume o all ee species 1 (m 3 /ha) Mean 0.56 x 2 Mean pine olume 1 (m 3 /ha) Mean 0.54 x 3 Mean sp uce olume 1 (m 3 /ha) Mean 0.64 x 4 Mean b oadlea olume 1,2 (m 3 /ha) Mean 0.49 x 5 Mean olume o all ee species 1 (m 3 /ha) Va iance 0.37 x 6 Land class 2 P opo ion o o es ed land 0.67 1 De ined only o pixels classi ied as o es ed land 2 U ilized hema ic maps Bmean olume o bi ch^and Bmean olume o o he b oadlea species^ 3 The heme was agg ega ed o wo classes: o es ed land and o he lands. Pixels classi ied as wa e we e disca ded 4 Co ela ion be ween he auxilia y and co esponding p ima y da a in he na ional o es in en o y ield mea- su emen da a Annals o Fo es Science (2019) 76:20 Page 5 o 14 20 All simula ions, analyses, and isualiza ions we e made wi h R (R Co e Team 2018). The LPM was pe o med wi h lpm1 unc ion a ailable in R package BalancedSampling (G a s öm and Lisic 2018). 3 Resul s In he e e ence me hod, no o he auxilia y in o ma ion was u ilized besides spa ial coo dina es in sample selec ion. Fu he , he popula ion om which he sample was chosen was always he same o bo h se s o clus e s comp ising all NFI clus e s. The e e ence MSEs o a ge a iables de i ed wi h simula ion as well as he eal alues o popula ion pa- ame e s a e shown in Table 1. The simula ion was eplica ed T= 5000 imes which was a su icien la ge numbe o le he es ima es o mean o se le (Fig. 2). When he p opo ion o pe manen clus e s in he sample inc eased, he RE o LPM dec eases as expec ed (Fig. 3). Pa icula ly, he RE o he o es ed land p opo ion dec eased. I changed om he le el o 1.80 o 1.16 as he p opo ion o empo a y clus e s changed om 90 o 30%. In he REs o mean g owing s ock olume and o al g owing s ock olume, he dec eases we e 0.20 and 0.34 uni s, espec i ely (Table 5). Fo he ee species–speci ic mean g owing s ock olumes, we we e able o obse e h ee phenomena: Fi s , he dec easing end as a unc ion o inc easing p opo ion o pe manen clus- e s was no as ob ious as o he o he pa ame e s. Second, o all ee species–speci ic mean g owing s ock olumes, he RE was la ge i he auxilia y in o ma ion included he ee-speci ic a iables. Thi d, he clea di e ences in he REs be ween he cases using di e en auxilia y a iables wi h small p opo ions o pe manen clus e s anished as he p opo ion o pe manen clus e s inc eased. In he end, he REs we e he same despi e he auxilia y a iables included in he sample selec ion. Fo he s a i ied sampling, he changes depended bo h on he s a i ica ion and on es ima ed popula ion pa ame e . Fo exam- ple, in b oadlea mean g owing s ock olume es ima ion, he REs had somewha dec easing end whe eas in o al g owing s ock olume es ima ion, he REs o mos o he s a i ica ions we e luc ua ing a he same le el (Fig. 4). When s a i ica ion included o es ed land p opo ion, i s es ima ion was e icien , o he wise no (Fig. 4, op le ). The same applied o he ee species–speci ic g owing s ock olumes. I he s a i ica ion in- cluded in o ma ion on a gi en ee species, he RE o ha spe- cies was la ge han ha o he o he s a i ica ions. When sampling wi h LPM u ilizing he same se o auxil- ia y in o ma ion in bo h empo a y and pe manen clus e Table 3 Limi s o s a a in s a i ica ions based on clus e -le el auxilia y a iables (see Table 2 o de ini ions) Name S a um/limi s 12 3 4 5 6 Vol4 x 1 < 87.4 87.4 ≤x 1 < 120.8 120.8 ≤x 1 <159.4 x 1 ≥159.4 –– Vol5 x 1 < 79.6 79.6 ≤x 1 < 107.7 107.7 ≤x 1 < 135.2 135.2 ≤x 1 <169.8 x 1 ≥169.8 – SPVol2 x 4 <x 2 +x 3 (coni e -domina ed) x 4 ≥x 2 +x 3 (o he s) x 1 < 89.1 89.1 ≤x 1 < 122.2 122.2 ≤x 1 <160.5 x 1 ≥160.5 x 1 <78.5 x 1 ≥78.5 SPVol1 x 4 <x 2 +x 3 (coni e -domina ed) x 4 ≥x 2 +x 3 (o he s) – x 1 < 89.1 89.1 ≤x 1 < 122.2 122.2 ≤x 1 <160.5 x 1 ≥160.5 x 5 < 3952.2 x 5 ≥3952.2 x 5 < 6001.8 x 5 ≥6001.8 VolSp x 1 < 99.2 99.2 ≤x 1 <145.0 x 1 ≥145.0 x 3 <19.7 x 3 ≥19.7 x 3 <42.7 x 3 ≥42.7 x 3 <271.4 x 3 ≥271.4 FL%Vol x 6 < 0.36 0.36 ≤x 6 < 0.64 0.64 ≤x 6 < 0.86 0.86 ≤x 6 ≤1.00 x 1 <121.0 x 1 ≥121.0 x 1 < 119.5 x 1 ≥119.5 FL%Pi x 6 < 0.36 0.36 ≤x 6 < 0.64 0.64 ≤x 6 < 0.86 0.86 ≤x 6 <1.00 x 3 <53.1 x 3 ≥53.1 x 3 <56.1 x 3 ≥56.1 Con5 x 2 +x 3 < 59.3 59.3 ≤x 2 +x 3 < 85.3 85.3 ≤x 2 +x 3 < 110.6 110.6 ≤x 2 +x 3 <144.9 x 2 +x 3 ≥144.9 – Con6 x 2 +x 3 < 53.3 53.3 ≤x 2 +x 3 < 77.4 77.4 ≤x 2 +x 3 < 97.3 97.3 ≤x 2 +x 3 < 120.2 120.2 ≤x 2 +x 3 <152.2 x 2 +x 3 ≥152.2 Con3BL2 x 2 +x 3 < 77.4 77.4 ≤x 2 +x 3 <120.2 x 2 +x 3 ≥120.2 x 4 <25.8 x 4 ≥25.8 x 4 <25.3 x 4 ≥25.3 x 4 <25.5 x 4 ≥25.5 Con3FL%2 x 2 +x 3 < 77.4 77.4 ≤x 2 +x 3 <120.2 x 2 +x 3 ≥120.2 x 6 <0.61 x 6 ≥0.61 x 6 <0.68 x 6 ≥0.68FLC2 x 6 <0.59 x 6 ≥0.59 Pi3Sp 2 x 2 < 40.6 40.6 ≤x 2 <66.2 x 2 ≥66.2 x 3 <53.5 x 3 ≥53.5 x 3 <51.7 x 3 ≥51.7 x 3 <49.6 x 3 ≥49.6 Sp 3Pi2 x 3 < 32.4 32.4 ≤x 3 <71.2 x 3 ≥71.2 x 2 <54.6 x 2 ≥54.6 x 2 <54.3 x 2 ≥54.3 x 2 <53.1 x 2 ≥53.1 20 Page 6 o 14 Annals o Fo es Science (2019) 76:20 popula ions, he e ec o inc easing p opo ion o hese semi- pe manen clus e s was no anymo e e iden o all popula ion pa ame e es ima ions (Fig. 5). The RE o o es ed land p o- po ion and mean g owing s ock olume o pine did no ha e any de ec able end. Fo he o he pa ame e s, he e was a sligh dec ease which seemed o u n o inc ease be o e he las simula ed p opo ion, 70%. On he a iable le el, he RE o ee species–speci ic mean g owing s ock olumes depended on he chosen se o auxilia y a iables simila ly o he p e ious LPM case (Fig. 3). 4 Discussion The aim o his s udy was o es ima e he e iciency o spa ial- ly balanced and s a i ied sampling designs in a ealis ic NFI si ua ion. Spa ially balanced sampling used LPM in sample selec ion, and i was applied in wo di e en se ups: In he i s se up, he ield clus e s we e di ided in o pe manen clus e s being su eyed in he consecu i e in en o ies and empo a y clus e s, which we e measu ed only once. The loca ion o pe manen clus e s was ixed and a anged spa ially sys ema - ically in consecu i e in en o ies, bu he empo a y clus e s we e ealloca ed inside he s udy egion each simula ion ound wi h LPM u ilizing emo e sensing da a om p e ious in en- o y. In he second se up, he clus e g oups we e semi- pe manen and empo a y; hus, bo h clus e popula ions we e ealloca ed each simula ion ound wi h LPM u ilizing simila auxilia y emo e sensing da a. In he i s se up abo e, also he s a i ied sampling me hod was assessed. In all simula ions, he sample size was ixed bu di e en p opo ions o samples we e alloca ed in o he wo clus e popula ions. Table 4 The s a i ica ions pe o med and bo h he sizes, N s , and sample sizes, n s , o s a a. Fo a mo e de ailed de ini ion o auxilia y a iables, see Table 3 Name S a i ying a iable(s) Numbe o s a a N 1 N 2 N 3 N 4 N 5 N 6 n 1 n 2 n 3 n 4 n 5 n 6 Vol4 Volume x 1 4 1027 1888 1718 775 –– 93 103 108 96 Vol5 Volume x 1 5 680 1458 1566 1192 512 – 71 82 88 83 76 SPVol2 Species g oup dominance 1 / olume x 1 6 (2/4,2) 2 990 1869 1660 740 98 51 83 101 104 92 11 9 SPVol1 Species g oup dominance/ olume x 1 5 (2/4,1) 3 990 1869 1660 740 149 – 80 98 100 89 33 VolSp Volume x 1 /sp uce olume x 3 6 (3/2) 978 671 1364 1125 746 524 95 34 82 67 52 70 FL%Vol % o es ed x 6 / olume x 1 6 (4/1,1,2,2) 4 813 1431 1183 825 733 423 121 120 39 40 40 40 FL%Pi % o es ed x 6 /pine olume x 2 6 (4/1,1,2,2) 881 1258 864 726 894 785 115 124 39 41 40 41 Con5 Volume o coni e s x 2 +x 3 5 754 1437 1577 1164 476 – 72 93 102 80 53 Con6 Volume o coni e s x 2 +x 3 6 558 1118 1323 1221 843 345 56 78 88 78 58 42 Con3BL2 Volume o coni e s x 2 +x 3 / olume o b oadlea es x 4 6 (3/2) 1061 615 1569 975 691 497 81 47 92 62 72 46 Con3FL%2 Volume o coni e s x 2 +x 3 /% o es ed x 6 6 (3/2) 721 955 931 1613 532 656 71 57 66 99 58 49 Pi3Sp 2 Pine olume x 2 /sp uce olume x 3 6 (3/2) 842 840 1625 833 940 328 62 80 102 66 66 24 Sp 3Pi2 Sp uce olume x 3 /pine olume x 2 6 (3/2) 448 570 2375 1108 705 202 32 60 157 86 51 14 1 Clus e s we e di ided in o coni e -domina ed o es s, x 2 +x 3 >x 4 , and o he s 2 Fou s a a o coni e -domina ed o es s, wo o he o he s 3 As abo e, bu Bo he s^s a um was no u he di ided 4 The wo s a a wi h la ges p opo ion o o es ed land we e u he di ided acco ding o he olume o all ee species Annals o Fo es Science (2019) 76:20 Page 7 o 14 20 We es ima ed he sampling e iciencies using he ixed po- si ions and designs o sample clus e s om he p e ious in- en o ies wi h o al sampling in ensi y o 400/5408 ≈7.4%. A sampling design ha is sys ema ically placed should cap u e all he a ia ion in he popula ion, and he small sampling in ensi y gua an ees ha di e ences in design e iciency esul om ac ual pe o mance o he me hods. E iciencies o di - e en sampling designs we e s udied in espec o he design whe e bo h clus e sub-popula ions we e geospa ially sp ead wi h LPM, which means ha samples in sub-popula ions we e close o a cu en sys ema ic sampling design. Ou i s hypo hesis conce ning he RE o LPM held. The RE o sampling designs dec eased as he p opo ion o pe ma- nen clus e s in he sample inc eased he sampling simula ions (Fig. 3). In a p e ious s udy (Rä y e al. 2018), whe e all he clus e s we e chosen wi h LPM om one popula ion, he la g- es REs we e 1.77 and 2.15 o o al g owing s ock olume and o es ed land p opo ion es ima ion, espec i ely (Table 5). As he p opo ion o pe manen clus e s inc eased o 60% o he sample, he REs dec eased e en as much as 40% (Table 5). Ne e heless, as in he p e ious s udy (Rä y e al. 2018), LPM was p oducing simila esul s i espec i e o he Fig. 2 Illus a ion o sample means o di e en popula ion pa ame e s in di e en sampling designs as a unc ion o sample size 20 Page 8 o 14 Annals o Fo es Science (2019) 76:20 auxilia y a iables chosen, bu in s a i ica ion, he esul depended hea ily on he chosen s a i ica ion s a egy (Figs. 3and 4, Table 5). Thus, wi h LPM, he es ima ion o a gi en ee species–speci ic mean g owing s ock olume was en- hanced i he g owing s ock olume o ha species was in- cluded in he auxilia y in o ma ion gi en o LPM (Table 5). Also, he second hypo hesis, ha he s a i ied sampling would become mo e e icien in espec o LPM as he p o- po ion o pe manen clus e s inc eases in he sample, held o some s a i ica ions (Fig. 6). In ac , he s a i ied sampling was in a ian in espec o he p opo ions (Table 5). Howe e , he a ia ion in pe o mance be ween he di e en s a i ica ions was la ge, and enhancemen o RE o one o ew popula ion pa ame e s mean o en ine iciency in he o he popula ion pa ame e es ima ions. Con a ily, spa ially bal- anced sampling was eaching abou he same le el o RE ega dless o he se o auxilia y a iables chosen. This means ha he s a i ica ion should always be based on expe ience, conside a ion, and knowledge whe eas wi h LPM, he RE is a leas on he same le el wi h sys ema ic sampling (Fig. 3) (G a s öm e al. 2017b). The p opo ion o pe manen clus e s in he Finnish NFI is 60% (Kangas e al. 2018). Based on his s udy, sampling wi h LPM would enhance he es ima ion in espec o he cu en sys ema ic sampling design, bu he expec ed imp o emen s a e smalle han he p e ious s udies (G a s öm e al. 2017b; Rä y e al. 2018) an icipa ed, being a 5–25% o di e en popula ion pa ame e s when he p opo ion o pe manen plo s in he sample is 60%. The ques ion is whe he he imp o e- men s gained a design phase wi h LPM would con ibu e enough in con as o he o he exis ing me hods like pos - s a i ica ion o model-assis ed es ima ion me hods (Haakana e al. accep ed; Sä ndal e al. 1992;Kangase al.2016; Myllymäki e al. 2017) applied in he es ima ion phase o he esul s om sys ema ic sampling design. Possibly, he mos e icien app oach would hen be a combina ion o clus e - le el LPM and plo -le el pos -s a i ica ion. One possible way o mi iga e he dec ease in e iciency as he p opo ion o pe manen plo s in sample inc eases would be selec ing bo h he pe manen and empo a y plo s wi h LPM u ilizing auxilia y in o ma ion. E en hough changes happening in he pe manen plo s du ing he yea s would im- pac also on hei dis ibu ion, i would s ill p obably ma ch he dis ibu ion o auxilia y a iables be e han sys ema ical- ly chosen pe manen clus e s. I he pe manen plo s a e main- ly used o es ima ing sho - ange changes, semi-pe manen plo s ha a e measu ed, say wo o h ee imes, could be a use ul comp omise ha would imp o e he design e iciency (Table 6). Howe e , he s a egies o using pe manen and semi-pe manen sample plo s in NFI need o be s udied u - he , because pe manen plo s p oduce ime se ies da a ha a e aluable. Na u ally, aking in o accoun he dis ibu ion o Fig. 3 Rela i e e iciency o sampling designs when p opo ion o pe manen clus e s in a sample o n= 400 a ied om 10 up o 70%. The pe manen clus e s we e chosen wi h local pi o al me hod (LPM) using spa ial sp ead and empo a y clus e s wi h LPM u ilizing also o he auxilia y in o ma ion besides spa ial loca ion Annals o Fo es Science (2019) 76:20 Page 9 o 14 20