Comment on Tompalski et al. Combining Multi-Date Airborne Laser Scanning and Digital Aerial Photogrammetric Data for Forest Growth and Yield Modelling. Remote Sens. 2018, 10, 347

emo e sensing Commen Commen on Tompalski e al. Combining Mul i-Da e Ai bo ne Lase Scanning and Digi al Ae ial Pho og amme ic Da a o Fo es G ow h and Yield Modelling. Remo e Sens. 2018, 10, 347 Ja i Vauhkonen Na u al Resou ces Ins i u e Finland (Luke), Bioeconomy and En i onmen Uni , Yliopis oka u 6, FI-80100 Joensuu, Finland; [email p o ec ed]; Tel.: +358-295328295 Recei ed: 4 July 2018; Accep ed: 24 Augus 2018; Published: 5 Sep embe 2018   Abs ac : Tompalski e al. (2018) p opose “ empla e ma ching” as a ( equi ed) in e media e s ep o use emo e sensing-based p edic ions o o es a ibu es as inpu s o he G ow h and Yield P ojec ion Sys em (GYPSY) o he simula ions o o es s and dynamics in Albe a, Canada. Ye , he easibili y o he app oach can be c i icized o many poin s ha call o expe imen al e i ica ion. The app oach canno be ully eplica ed based on he desc ip ion o he pape . Ne e heless, an expe imen al implemen a ion wi h syn he ic da a indica es ha he quali y o he p ojec ions may a y conside ably depending on pa ame e assump ions o he empla es, and he p ojec ions may include discon inui ies be ween he obse ed and p ojec ed o es a ibu es. The app oach is poo ly mo i a ed gi en ha he e ec s desc ibed abo e a e la gely a oidable, i he unde lying GYPSY models a e un wi hou he empla e ma ching s ep. The R-codes used o he analyses a e p o ided as supplemen a y da a o an in e es ed eade wishing o e alua e he conclusions made abo e. A seman ic analysis indica es u he p oblems wi h mul i-da e da a on a wall- o-wall g id. The p ojec ions ob ained by empla e ma ching should be exposed o c i icism o hei ealism and benchma ked agains o he app oaches p io o using empla e ma ching as p oposed by Tompalski e al. Keywo ds: o es in en o y; g ow h; unce ain y; e o ; model c i icism; e alua ion; alida ion 1. In oduc ion Tompalski e al. [ 1 ] p opose “ empla e ma ching” as an in e media e s ep om emo e sensing-based p edic ions o o es g ow h and yield p ojec ions. In he p oposed app oach, a se o o es a ibu es ( op heigh , densi y, basal a ea, o al olume in [ 1 ]) a e p edic ed o selec ed spa ial uni s (sample plo s o 20 × 20 m 2 g id cells in [ 1 ]) based on emo ely sensed da a (ai bo ne lase scanning and digi al ae ial pho og amme ic da a in [ 1 ]). The subjec s ands a e assumed o be co e ed by exis ing in en o y da a including age and species in o ma ion. In he empla e ma ching, exis ing g ow h models a e i s un wi h all possible combina ions o hei inpu pa ame e s o gene a e a da abase o g ow h ajec o ies (= empla es). Among he empla es, he ones ha bes ag ee wi h he a o emen ioned o es a ibu e p edic ions o he gi en age and species a e selec ed as he ajec o ies used o g ow h and yield p ojec ions (=ma ching). The idea o he empla e ma ching app oach is condensed o Figu e 1a om he o iginal, mo e de ailed illus a ion [1] (Figu e 4). Tompalski e al. aguely mo i a e he need o use he empla e ma ching app oach by disc epancy be ween emo ely sensed ou pu s and g ow h model inpu s, especially in he case o g id cells [ 1 ] (Sec ion 1). Howe e , easoning he app oach on such a basis can be ques ioned, because no e en con en ional in en o ies p o ide a o es a ibu e combina ion ha is exac ly he same as equi ed by Remo e Sens. 2018,10, 1411; doi:10.3390/ s10091411 www.mdpi.com/jou nal/ emo esensing Remo e Sens. 2018,10, 1411 2 o 13 g ow h and yield models. Ins ead, decades-old g ow h and yield modeling sys ems a e composed o model chains o de i e he equi ed inpu s om he limi ed measu emen s [ 2 – 4 ], and he same model chains can be eadily applied o g id-based in en o y da a wi hou speci ic a en ion on he g ow h and yield modeling me hodology, as demons a ed in plan a ions [5] and semi-na u al o es s [6,7]. Remo eSens.2018,10,xFORPEERREVIEW 2o 13  Figu e1.In he empla ema ching[1], he u u eg ow h ajec o y( edline)isde e minedas he weigh edmeano  hemos sui able empla e ajec o ies(blacklines)selec edbyma chingwi h obse a ions(blackdo s);(a)shows hecandida e empla esasg aycu esand hespacebounded by hemwi hligh g ay illing ha  ecu sin hesub‐ igu es.Theda ke g ay illingsindica e hesub‐ space omwhich he inal empla eisselec ed.No e ha  he o alsub‐spacea eaand he inal, a e agedg ow h ajec o yselec edacco ding oTompalskie al.[1]wouldbeequalbe weensub‐ igu es(b,c),showingexampleso (b)e oneous(single‐da e)obse a ionsand(c)e o ‐ ee,mul i‐ da eda a. Tompalskie al. aguelymo i a e heneed ouse he empla ema chingapp oachby disc epancybe ween emo elysensedou pu sandg ow hmodelinpu s,especiallyin hecaseo g id cells[1](Sec ion1).Howe e , easoning heapp oachonsuchabasiscanbeques ioned,becauseno  e encon en ionalin en o iesp o idea o es a ibu ecombina ion ha isexac ly hesameas equi edbyg ow handyieldmodels.Ins ead,decades‐oldg ow handyieldmodelingsys emsa e composedo modelchains ode i e he equi edinpu s om helimi edmeasu emen s[2–4],and hesamemodelchainscanbe eadilyapplied og id‐basedin en o yda awi hou speci ica en ion on heg ow handyieldmodelingme hodology,asdemons a edinplan a ions[5]andsemi‐na u al o es s[6,7]. Ins eado clea lyiden i iablebene i so including empla ema chingasanin e media es ep o  emo esensingbased u u ep ojec ions,acu so yglancea  hep oposedapp oachdoes aisea ewca ea s.Toapply he empla ema chingo e awall‐ o‐wall o es in en o yg idandmul iple imepoin s,Tompalskie al.p esen p edic ionmodels[1](Table4) ha we e i independen ly o  eachconside ed o es a ibu eand imepoin sT1andT2.I iswo hwhile ono e ha  he aining da aco e ingbo hT1andT2we e epea edmeasu emen so  hesameplo s.Consequen ly, he esiduale o sbe ween hes anda ibu esand imepoin scanno beconside edindependen o  eacho he ,whichisagains  heassump ionso o dina yleas squa es eg essionapplied o model i ing[1].The ollowingp ac icalconside a ionso combining hep oposed empla ema ching app oachwi h heindependen modellingo  hedi e en  o es a ibu esa  hedi e en  imepoin s shouldsubsequen lybemade:  Assume ha Figu e1a ep esen sanidealcasewi he o ‐ eeobse a ions,whe easp edic ing hea ibu eso in e es independen lyo eacho he  o ag idcellhinde s hecu ema ching asillus a edinFigu e1b.Tompalskie al.[1]doconclude ha “ heaccu acyo cu ema ching wasdependen on heABA(a ea‐basedapp oach)p edic ione o ”.Howe e ,wha a e he implica ionso alowe “accu acyo cu ema ching”?Wha is hesensi i i yo  heapp oach o p oducesuchase e eincompa ibili y(e.g.,[2](Chap e 15))be weens anda ibu eso  hei  u u ep ojec ions ha causesp oblems o  he u he useo  hisin o ma ion?A e he e in e ac ionsin hissensebe ween hecomposi iono  heobse a ionsand he empla eda abase Figu e 1. In he empla e ma ching [ 1 ], he u u e g ow h ajec o y ( ed line) is de e mined as he weigh ed mean o he mos sui able empla e ajec o ies (black lines) selec ed by ma ching wi h obse a ions (black do s); ( a ) shows he candida e empla es as g ay cu es and he space bounded by hem wi h ligh g ay illing ha ecu s in he sub- igu es. The da ke g ay illings indica e he sub-space om which he inal empla e is selec ed. No e ha he o al sub-space a ea and he inal, a e aged g ow h ajec o y selec ed acco ding o Tompalski e al. [ 1 ] would be equal be ween sub- igu es ( b , c ), showing examples o (b) e oneous (single-da e) obse a ions and (c) e o - ee, mul i-da e da a. Ins ead o clea ly iden i iable bene i s o including empla e ma ching as an in e media e s ep o emo e sensing based u u e p ojec ions, a cu so y glance a he p oposed app oach does aise a ew ca ea s. To apply he empla e ma ching o e a wall- o-wall o es in en o y g id and mul iple ime poin s, Tompalski e al. p esen p edic ion models [ 1 ] (Table 4) ha we e i independen ly o each conside ed o es a ibu e and ime poin s T1 and T2. I is wo hwhile o no e ha he aining da a co e ing bo h T1 and T2 we e epea ed measu emen s o he same plo s. Consequen ly, he esidual e o s be ween he s and a ibu es and ime poin s canno be conside ed independen o each o he , which is agains he assump ions o o dina y leas squa es eg ession applied o model i ing [ 1 ]. The ollowing p ac ical conside a ions o combining he p oposed empla e ma ching app oach wi h he independen modelling o he di e en o es a ibu es a he di e en ime poin s should subsequen ly be made: • Assume ha Figu e 1a ep esen s an ideal case wi h e o - ee obse a ions, whe eas p edic ing he a ibu es o in e es independen ly o each o he o a g id cell hinde s he cu e ma ching as illus a ed in Figu e 1b. Tompalski e al. [ 1 ] do conclude ha “ he accu acy o cu e ma ching was dependen on he ABA (a ea-based app oach) p edic ion e o ”. Howe e , wha a e he implica ions o a lowe “accu acy o cu e ma ching”? Wha is he sensi i i y o he app oach o p oduce such a se e e incompa ibili y (e.g., [ 2 ] (Chap e 15)) be ween s and a ibu es o hei u u e p ojec ions ha causes p oblems o he u he use o his in o ma ion? A e he e in e ac ions in his sense be ween he composi ion o he obse a ions and he empla e da abase ( o example, wha i obse a ions o p edic ions a e loca ed on bo de s o sligh ly ou side o he empla e space such as he lowes obse a ion o Figu e 1b)? • Assume ha mul i-da e da a a e a ailable (Figu e 1c) and obse a ions o p edic ions o T2 sys ema ically sugges a slowe u u e de elopmen o he s and, compa ed o single-da e Remo e Sens. 2018,10, 1411 3 o 13 obse a ions o p edic ions o T1. No e ha e en i he aining da a o model i ing we e il e ed o eco ded dis u bances be ween he wo ime s eps (as in Tompalski e al. [ 1 ]), si ua ions co esponding o Figu e 1c could occu due o a i ac s in he emo ely sensed da a and igno ing he dependencies be ween T1 and T2 in he p edic ion models. Applying he wo k low o Tompalski e al. [ 1 ] o wall- o-wall o es in en o y g id da a om mul iple da es would hus p oduce si ua ions ha esemble eal-wo ld dis u bances in he o es (c . Figu e 1c), bu i is unclea i and how he unde lying g ow h and yield modelling sys em logic can manage such si ua ions. • O e all, how well- easoned is ha wi h mul i-da e da a, “ he weigh ed means we e calcula ed sepa a ely o each da a se , and hen a e aged” [ 1 ] (Sec ion 3.3), i.e., he obse a ions o T1 and T2 we e conside ed wi h an equal weigh , e en i he la e ep esen da a acqui ed la e and should he e o e ha e a close empo al ma ch wi h he p esen o es s a e? The ex abo e sugges s ha e en i he empla e ma ching app oach is based on exis ing g ow h models, he selec ing and a e aging p ocess in ol ed p obably yields inal g ow h ajec o ies ha may ha e conside ably di e en p ope ies om hose included in he da abase. The e o e, e en i he unde lying g ow h models we e adequa ely e alua ed o hei ealism (c . [ 2 ] (Chap e 15); [ 3 ] (Chap e 18); [ 8 , 9 ]), a simila model c i icism should be applied o he ou pu s o he empla e ma ching. The e alua ion should p obably accoun o po en ial in e ac ions be ween he pa ame e s o he unde lying g ow h models and andom p edic ion e o s in he o es a ibu es used as inpu s o he empla e ma ching. To e i y and quan i y he poin s lis ed abo e, I simula ed he empla e ma ching app oach [ 1 ] wi h syn he ic da a. In he commen below, I pa icula ly ocus on e ec s o pa ame e choices on he subsequen empla e gene a ion and ma ching. Since a numbe o assump ions was made, he expe imen al implemen a ion is desc ibed in de ail and p o ided as R-code [ 10 ] in iles men ioned in he sub- i les o Sec ion 2. I discuss he esul s om model c i icism and benchma king poin s o iew. 2. Expe imen al Implemen a ion 2.1. The G ow h and Yield P ojec ion Sys em (GYPSY) Models (gypsy_models.R) The G ow h and Yield P ojec ion Sys em (GYPSY) unde lying he empla e ma ching app oach was implemen ed as closely as possible o co espond wi h Tompalski e al. [ 1 ] ollowing he model documen a ion [ 11 ]. Howe e , nei he Tompalski e al. [ 1 ] no he model documen a ion p o ide guidance on many choices ega ding possible pa ame e iza ions. Fi s , bo h non-spa ial and spa ial e sions o he GYPSY models a e a ailable [ 11 ], bu Tompalski e al. [ 1 ] do no indica e which one hey used. The choice be ween a spa ial o non-spa ial amewo k could be expec ed o esul in undamen al di e ences in he equi ed pa ame e iza ion, because “spa ial” models no mally in ol e spa ially explici compe i ion indices based on ee- o- ee dis ances o simila measu es ( o hin s on equi ed compu a ions, see e.g., [ 12 , 13 ] o [ 3 ] (Chap e 9)). Howe e , a mo e ho ough look a he models [ 11 ] indica es ha his is no he case wi h GYPSY. Compa ed o he non-spa ial e sion, he “spa ial” GYPSY only includes an addi ional pe cen s ocking componen , which is p edic ed om ee densi y using addi ional models p o ided [ 11 ]. One canno he e o e expec ha he non-spa ial and spa ial GYPSY p ojec ions would undamen ally di e . Howe e , because he non-spa ial models had conside able simple o ms, he non-spa ial e sion o GYPSY [ 11 ] was selec ed o he analyses below. GYPSY is implemen ed as a collec ion o sub-models o he di e en a ibu es [ 11 ]. The sub-models di e by pa ame e s and e en model o ms depending on species (g oup). I de i ed he p ojec ions sepa a ely o species g oups o Aspen, Pine, Black sp uce and Whi e sp uce, which co espond o hose used by Tompalski e al. [1]. Rega dless o species, he models o in e es o his exe cise ake he ollowing a gumen s: Remo e Sens. 2018,10, 1411 4 o 13 H op = (SI, age), (1) N = (SDFsp, SI), (2) BAINC = (age, SI, Nini, SC, BA), and (3) T ol = (BA, H op), (4) whe e H op is he a e age heigh o he 100 la ges DBH ees pe ha (m), SI is he si e index (m), age is he s and age, N is he densi y (s ems/ha) o he subjec species, SDF is a species-speci ic s and-densi y ac o de ined as N a 50 yea s o age, BAINC is he annual basal a ea inc emen o he subjec species (m 2 /ha/yea ), N ini is he ini ial densi y a he age o ze o, SC is he cu en species composi ion (N species /N all ), BA is he cu en basal a ea (m 2 /ha) o he subjec species, and T ol is he g oss o al olume (m 3 /ha) “o he subjec species a he 0/0 u iliza ion s anda d” [ 11 ]. The models p esen ed in Equa ions (1)–(4) co espond o hose numbe ed by 4, 5, 6 and 10, espec i ely, in he GYPSY documen a ion [ 11 ], wi h naming con en ions o he a iables somewha simpli ied o he p esen pu pose. In addi ion, I ha e made he ollowing simpli ica ions when implemen ing he models: • Abo e, he de ini ion o “age” a ies be ween models and ee species (g oups): i is ei he o al age (yea s since he poin o ge mina ion) o b eas heigh age (age a he heigh o 1.3 m abo e g ound). Consequen ly, SI is he op heigh co esponding o he age de ini ion ha a ies be ween he models and species. Fo my exe cises, I assumed ha all age and SI alues inpu ed co esponded o he b eas heigh age. Whe e necessa y, I con e ed he b eas heigh age o o al age using a e age con e sion ac o s [ 11 ] (p. 5). Howe e , I did no con e SI, i.e., SI alues be ween Equa ion (1) and he o he models a e no consis en ega ding he de ini ion, which causes a le eling di e ence wi h a magni ude ha p obably could be assessed by applying exac con e sions [11] (Appendix A). This is u he explo ed below. • GYPSY p o ides a possibili y o simula e g ow h and yield o bo h pu e and mixed s ands [ 11 ]. Tompalski e al. [ 1 ] do no indica e whe he hei s ands we e conside ed o be pu e o mix u es o species. Fo he simula ions below, I assumed pu e s ands. This choice a ec ed he pa ame e iza ion o Equa ions (1)–(4) as ollows: The SC componen o he BAINC model (Equa ion (3)) was always ixed o 1. The GYPSY models o BAINC addi ionally include e m k, which is compu ed o he Aspen and Pine species as a ans o ma ion o he o he model pa ame e s. Howe e , o he wo Sp uce species, he e m kincluded he SDFs o each o he o he h ee species. In he s ands simula ed he e, whe e no o he species occu ed, he e m ko he Sp uce species ecei ed a alue o ze o. Due o he missing de ails, i was addi ionally ound impossible o guess he equi ed pa ame e iza ion o N (Equa ion (2)). The model equi ed he species-speci ic SDF as a key inpu pa ame e and nei he he model documen a ion [ 11 ] no Tompalski e al. [ 1 ] p o ide any in o ma ion on an allowable ange o his pa ame e . Fo his eason, implemen ing Equa ion (2) was en i ely omi ed, i.e., he empla e ma ching below was based on h ee models (H op , BAINC, and T ol o p oduce he op heigh , basal a ea and o al olume, espec i ely), which should ease he ma ching ask (c . Sec ion 2.3) compa ed o Tompalski e al. [ 1 ] who used all ou a ibu es. Howe e , none o he abo e simpli ica ions is expec ed o a ec gene al conclusions made based on he simula ions, a leas when he g ow h ajec o ies a e examined species a a ime and no be ween-species compa isons a e made. 2.2. Templa e Da abase (gene a e_ empla es.R) The ollowing ins uc ions [ 1 ] (Sec ion 3.2) we e ollowed o gene a e he empla e da abase (g ey lines o he schema ic Figu e 1a): “Following he app oach o Tompalski e al. [21], we used he simula o o c ea e a da abase o yield cu e empla es based on all possible inpu combina ions (e.g., e e y combina ion o species g oups, Remo e Sens. 2018,10, 1411 5 o 13 op heigh , o al age, densi y, and basal a ea). The da abase ep esen ed all possible s and condi ions in he s udy a ea and was based on he ange o s and a ibu es in he exis ing o es in en o y. The yield cu es we e gene a ed o he ou speci ied species g oups, om 1 o 200 yea s, by 1 yea inc emen s. An indi idual yield cu e empla e consis ed o ou sequences o alues ep esen ing op heigh , basal a ea, olume, and s em densi y, be ween 1 and 200 yea s, and being es ima ed by he simula o based on species g oup, op heigh , o al age, and basal a ea.” Jux aposing he abo e ins uc ions wi h he GYPSY models (Equa ions (1)–(4)) p o ides a clea idea o how he models should be pa ame e ized o age (a sequence o alues om 1 o 200 wi h an in e al o 1). The abo e ins uc ions p o ide no ideas on allowable anges o any o he equi ed inpu pa ame e s o Equa ions (1)–(4) and his in o ma ion canno be ound om ei he Tompalski e al. [1] o he model documen a ion [ 11 ]. The e o e, he anges o he emaining pa ame e alues we e ob ained om a ious di e en sou ces as desc ibed below: • Si e index (SI) as a sequence o alues om 5 o 30 m wi h an in e al o 1 m. The ange was ob ained as he one ha included all obse a ions o he species conside ed he e, acco ding o a g aphical in e p e a ion o he GYPSY Valida ion Summa y epo [14] (Figu es 1 and 6). • The ini ial densi y a he age o ze o (N ini ) as wo al e na i e sequences: (1) om 700 o 2700 s ems/ha wi h an in e al o 100 s ems/ha o (2) om 700 o 6700 s ems/ha wi h an in e al o 1000 s ems/ha. The alues abo e a e de i ed om common ee spacing used o a i icial egene a ion in Albe a [ 15 ]. E en hough a ixed densi y such as 2400 s ems/ha could be assumed as he mos ypical ee plan ing densi y, he e e ence ci ed abo e also men ions na u al egene a ion as a possible me hod o Albe a [ 15 ], which p obably esul s o mo e a ia ions o N ini ob iously impac ing he GYPSY p ojec ions [ 11 ]. When nei he egene a ion ype could be assumed, wo al e na i e sequences o N ini alues we e used o de i e wo dis inc empla e da abases. The mo i a ion was o assess how he al e na i e pa ame e anges a ec he g ow h ajec o ies and, subsequen ly, how hey po en ially p opaga e he empla e gene a ion and ma ching. • The GYPSY model documen a ion indica es ha he BAINC model (Equa ion (3)) could be un wi h o wi hou knowledge on he cu en basal a ea [ 11 ]. How o do i is, howe e , no i ial based on he model documen a ion [ 11 ] and Tompalski e al. [ 1 ] do no men ion i he basal a ea p edic ions we e explici ly used as he cu en basal a ea in he models. In he analyses below, a single basal a ea sequence co esponding o he age sequence was gene a ed by unning he BAINC model (Equa ion (3)) as ollows. Fi s , he BAINC model was un wi h age = 1, cu en basal a ea se o 0, and o he pa ame e s as each o he possible combina ions o he sequences desc ibed abo e. Then, he ob ained BAINC was added o he p e ious basal a ea and, inc emen ing he basal a ea simila ly o each age alue, he i e a ion was con inued un il a single basal a ea sequence was ob ained o each o he pa ame e combina ions abo e. The sequences gene a ed his way a e abb e ia ed as G o di e en ia e om BA used in Equa ions (3) and (4) . To ob ain T ol (Equa ion (4)), G was used oge he wi h H op ob ained om Equa ion (1) as pa ame e s o Equa ion (4). 2.3. Templa e Ma ching (ma ching.R) The wo key s a emen s [ 1 ] (Sec ion 3.3) we e used as ins uc ions o implemen he empla e ma ching o p ojec he a ibu es based on obse a ions o a single poin in ime: “Fi s , candida e cu es we e selec ed om he da abase, based on s and age, species g oup and he minimal di e ence be ween he s and a ibu e and a alue o a yield cu e.” and “ he inal yield cu e was de i ed by calcula ing a weigh ed mean o he candida e cu es, wi h he pe cen o explained a iance in he ABA model used as a weigh .” Remo e Sens. 2018,10, 1411 6 o 13 Tes da a a e hus equi ed o es he empla e ma ching acco ding o he i s s a emen . A es da a se was gene a ed by aking he mean species-speci ic s and age [ 1 ] (Table 1) and mean op heigh , basal a ea, and o al olume o he p edic ions a T1 [ 1 ] (Table 2) and combining hese a ibu es as one obse a ion pe species (Table 1). I should be no ed ha a ibu e combina ions shown in Table 1 migh no occu in eal o es s. Howe e , because hese alues a e he means o he da a used o i he p edic ion models [ 1 ] (Table 4) and he di e en a ibu es we e modeled independen ly by Tompalski e al. [1] , i is easonable o assume ha combina ions p esen ed by Table 1could occu among hei p edic ed o es a ibu es. Table 1. Tes da a se gene a ed om he species-speci ic mean alues o ime T1 [ 1 ] (Tables 1 and 2). Species G oup Age, Yea s H op, m BA, m2/ha T ol, m3/ha Aspen 81 19.6 32.3 269.3 Pine 112 12.9 22.8 162.5 Black sp uce 117 15.4 30.6 190.4 Whi e sp uce 120 21.8 36.1 304.4 The es da a (Table 1) we e ma ched wi h he empla e da abases gene a ed abo e. Acco ding o he second s a emen , I conside ed weigh ing he model p edic ions o he empla e ma ching by he a iance he models explained. Howe e , because o he small di e ences in he adjus ed coe icien s o de e mina ion o he a ibu es conside ed ( he R 2 alues o he T1 models in [ 1 ] (Table 4) we e 0.76, 0.71, and 0.78 o he op heigh , basal a ea, and o al olume, espec i ely), I ound mo e s aigh o wa d o his exe cise no o weigh he a ibu es. 2.4. E alua ion (d aw_ ig2.R & d aw_ ig3.R) The esul s o he expe imen al implemen a ion a e p esen ed below o Aspen, which was he mos common species in he plo da a o Tompalski e al. [ 1 ] (Table 2). The emphasis below is on a g aphical in e p e a ion o Figu es 2and 3, which can be ep oduced wi h a ying assump ions by unning he ea lie R sc ip s sequen ially be o e hose men ioned in he sub- i le. Figu e 2p esen s he candida e empla es and he ma ching esul based on using he N ini pa ame e alues (Sec ion 2.2) o ei he 700 o 2700 s ems/ha wi h an in e al o 100 s ems/ha (Figu e 2a–c) o 700 o 6700 s ems/ha wi h an in e al o 1000 s ems/ha (Figu e 2d– ). A glance a he Figu e 2sugges s ha he spa si y o he empla e da abase a ies conside ably depending on his choice. The heigh empla es a e he same in bo h Figu e 2a,d, because no o he pa ame e s han age and SI we e included in he espec i e model (Equa ion (1)). Ye , he di e ence be ween he numbe o possible empla es o his a ibu e s basal a ea and o al olume can clea ly be obse ed. Fu he , he numbe o empla es and hei sp ead and densi y a y o he la e a ibu es depending on he Nini pa ame e ange applied (compa e Figu e 2b–c o Figu e 2e– ). The cu es ma ched wi h he ield obse a ions and he a e aged cu es a e shown in Figu e 2, bu Figu e 3can be used o an easie compa ison be ween he de elopmen ajec o ies, which a e clea ly di e en o he wo dis inc empla e da abases. The de elopmen ajec o ies o each a ibu e a e speci ically no ed o include a discon inui y be ween he obse a ion and he g ow h cu e, which o igina es om he a e aging be ween he ini ial candida e cu es and a ies be ween a ibu es depending on he ma ch o he obse a ions and he empla e cu es. A nume ic cha ac e iza ion and compa ison o he de elopmen ajec o ies is omi ed due o known inconsis ency o he si e index de ini ion be ween Equa ions (1), (3) and (4) (Sec ion 2.1), o example. Remo e Sens. 2018,10, 1411 7 o 13 Remo eSens.2018,10,xFORPEERREVIEW 7o 13  Figu e2.The esul o  empla ema ching o  he opheigh ,basala ea,and o al olume, espec i ely; heg aycu esshow he empla esob ainedusingNinipa ame e sequences(a–c) om700 o2700 s ems/hawi hanin e alo 100s ems/ha;o (d– ) om700 o6700s ems/hawi hanin e alo 1000 s ems/ha(Sec ion2.2).Thecu esma ched o  hesea ibu eswi hobse a ionso Table1a eshown byb okenblacklines,while he edcu esshow he inal,a e agedg ow h ajec o iesob ained using heme hodologyexplainedinSec ion2.3.Theb oken e icallinesa ed awn ohighligh  he Figu e 2. The esul o empla e ma ching o he op heigh , basal a ea, and o al olume, espec i ely; he g ay cu es show he empla es ob ained using N ini pa ame e sequences ( a – c ) om 700 o 2700 s ems/ha wi h an in e al o 100 s ems/ha; o ( d – ) om 700 o 6700 s ems/ha wi h an in e al o 1000 s ems/ha (Sec ion 2.2). The cu es ma ched o hese a ibu es wi h obse a ions o Table 1a e shown by b oken black lines, while he ed cu es show he inal, a e aged g ow h ajec o ies ob ained using he me hodology explained in Sec ion 2.3. The b oken e ical lines a e d awn o highligh he di e ence be ween he obse a ions (black do s) and he cu es selec ed o he p ojec ions a he age o he obse a ions. Remo e Sens. 2018,10, 1411 8 o 13 Remo eSens.2018,10,xFORPEERREVIEW 8o 13 di e encebe ween heobse a ions(blackdo s)and hecu esselec ed o  hep ojec ionsa  heage o  heobse a ions.  Figu e3.Ag aphicalcompa isono g ow hp ojec ionsassumingdi e en inpu sandei he  he empla ema chingo adi ec useo  heGYPSYmodels;(a) opheigh ;(b)basala ea;and(c) o al olume.AsinFigu e2, heblackand edlinesindica e hea ibu e‐speci iccandida ecu esand inal cu eso  he empla ema ching, espec i ely.Bluelinesindica e hep ojec ionsob ainedbyinse ing heinpu so  empla ema chingdi ec ly o heunde lyingGYPSYmodels( hebluelineisp ecisely o e lapping heblackonein(a)).Twolineso  hesamecolo depic  hedi e ence esul ing om assuming he woNinipa ame e sequences,whenapplicable(dis inguishingbe ween he wocu esis no seennecessa y).AsinFigu e2, heb oken e icallinesshow hedi e encebe ween he obse a ions(blackdo s)andp ojec ionsa  heageo  heobse a ions.Anopenci cleisd awn o indica e he olumees ima e(c)ob ainedbyusing hesequenceso (a,b)as heinpu so Equa ion(4). Fo benchma kingpu poses,Figu e3alsop esen sp ojec ions ha canbedi ec lyob ained om heGYPSYmodels,i.e.,pa ame e izingEqua ions(1),(3)and(4)by hesameinpu sasabo e, bu wi hou  he empla ema chings ep.Toob ain he opheigh p ojec ion(Figu e3a),Equa ion(1) wasusedwi h hesameSI alueasabo e.Toob ain hebasala eap ojec ion(s)(Figu e3b),Equa ion (3)wasusedwi h hesameSIasabo e,basala eao 32.3m2/ha o  heini ialageo 81yea s(Table 1),andNinio 700and6700s ems/ha,i.e., he ange o  hese aluesassumedabo e.Toob ain he o al olumep ojec ion(Figu e3c),Equa ion(4)wasusedwi h he opheigh andbasala ea sequencesob ained om hep e iouss eps.No ably,assumingsimila inpu saswe ea ailable o  he empla ema ching, hedi ec useo  heGYPSYmodelsp o idedp ojec ions ha we eless a ec edby he angeo  heNini alues,includednosimila discon inui iesand,o e all, esembled hea ibu e‐speci iccandida ecu eso  he empla ema chingmo e han hea e agedones.One couldconside  hes a ingpoin o  he olumep ojec ion obedisconnec ed om he olume obse a ion.Howe e , heuseo  helowe  aluecanbemo i a edbyconsis ency om hepoin o  iewo  heappliedg ow handyieldmodelingsys em: he olumees ima eisp oducedbyEqua ion (4)andi is he e o ecompa iblewi ho he a ibu eso  hesys em. 3.Discussion 3.1.Implica ionso  heResul s om heExpe imen alImplemen a ion I isacknowledged ha  hesimula iondesc ibedabo emaysu e  om henumbe o  simpli ica ions ha had obemadewhenimplemen ing heGYPSYmodelsand hesubsequen  empla ema chingdue o helacko essen ialde ailson he equi edpa ame e s(c .Sec ion2).Gi en ha R‐codesused o de i ing he esul sa eincludedassupplemen a yda a,anin e es ed eade  Figu e 3. A g aphical compa ison o g ow h p ojec ions assuming di e en inpu s and ei he he empla e ma ching o a di ec use o he GYPSY models; ( a ) op heigh ; ( b ) basal a ea; and ( c ) o al olume. As in Figu e 2, he black and ed lines indica e he a ibu e-speci ic candida e cu es and inal cu es o he empla e ma ching, espec i ely. Blue lines indica e he p ojec ions ob ained by inse ing he inpu s o empla e ma ching di ec ly o he unde lying GYPSY models ( he blue line is p ecisely o e lapping he black one in ( a )). Two lines o he same colo depic he di e ence esul ing om assuming he wo N ini pa ame e sequences, when applicable (dis inguishing be ween he wo cu es is no seen necessa y). As in Figu e 2, he b oken e ical lines show he di e ence be ween he obse a ions (black do s) and p ojec ions a he age o he obse a ions. An open ci cle is d awn o indica e he olume es ima e ( c ) ob ained by using he sequences o ( a , b ) as he inpu s o Equa ion (4). Fo benchma king pu poses, Figu e 3also p esen s p ojec ions ha can be di ec ly ob ained om he GYPSY models, i.e., pa ame e izing Equa ions (1), (3) and (4) by he same inpu s as abo e, bu wi hou he empla e ma ching s ep. To ob ain he op heigh p ojec ion (Figu e 3a), Equa ion (1) was used wi h he same SI alue as abo e. To ob ain he basal a ea p ojec ion(s) (Figu e 3b), Equa ion (3) was used wi h he same SI as abo e, basal a ea o 32.3 m 2 /ha o he ini ial age o 81 yea s (Table 1), and N ini o 700 and 6700 s ems/ha, i.e., he ange o hese alues assumed abo e. To ob ain he o al olume p ojec ion (Figu e 3c), Equa ion (4) was used wi h he op heigh and basal a ea sequences ob ained om he p e ious s eps. No ably, assuming simila inpu s as we e a ailable o he empla e ma ching, he di ec use o he GYPSY models p o ided p ojec ions ha we e less a ec ed by he ange o he N ini alues, included no simila discon inui ies and, o e all, esembled he a ibu e-speci ic candida e cu es o he empla e ma ching mo e han he a e aged ones. One could conside he s a ing poin o he olume p ojec ion o be disconnec ed om he olume obse a ion. Howe e , he use o he lowe alue can be mo i a ed by consis ency om he poin o iew o he applied g ow h and yield modeling sys em: he olume es ima e is p oduced by Equa ion (4) and i is he e o e compa ible wi h o he a ibu es o he sys em. 3. Discussion 3.1. Implica ions o he Resul s om he Expe imen al Implemen a ion I is acknowledged ha he simula ion desc ibed abo e may su e om he numbe o simpli ica ions ha had o be made when implemen ing he GYPSY models and he subsequen empla e ma ching due o he lack o essen ial de ails on he equi ed pa ame e s (c . Sec ion 2). Gi en ha R-codes used o de i ing he esul s a e included as supplemen a y da a, an in e es ed eade may e-pa ame e ize he empla e ma ching by be e knowledge on applicable pa ame e Remo e Sens. 2018,10, 1411 9 o 13 anges o es he sensi i i y o he assump ions made. Ye , I belie e ha he conclusions made below a e alid i espec i e o nuances o he pa ame e iza ion and a he ela e o he easibili y o he empla e ma ching app oach i sel . The lack o de ails gi en by Tompalski e al. [ 1 ] o he model pa ame e iza ion could o igina e om he use o in e aces wi h ixed pa ame e alues o gene a e cu e empla es. Wha e e he eason, he implemen a ions o Tompalski e al. [ 1 ] a e unlikely based on a ull unde s anding o he unde lying models, which is unde lined by ew ins ances in he pape : Fi s , i he au ho s had ca ied ou simila explo a o y analysis as abo e, hey would unlikely assume “ ha e o s in oduced by GYPSY’s in e nal sub-models a e equal o each p ojec ion and consequen ly we did no accoun o hem in ou s udy” [1] (Sec ion 3.2). On his poin , look a Equa ions (1)–(4) and especially Equa ion (4): using he ou pu s o ea lie models as inpu s o ollowing ones canno esul bu a signi ican co ela ion o he e o s be ween he sub-models. Second, i is unclea i he au ho s ca ied ou he empla e ma ching s ep using he cu en basal a ea as a pa ame e o Equa ion (3) and he op heigh and basal a ea om he GYPSY’s in e nal sub-models as pa ame e s o Equa ion (4), which would bo h ha e imp o ed he consis ency o he ma ched a ibu es and he empla es om he g ow h and yield sys em poin o iew. Thi d, based on he s a emen “Following he app oach o Tompalski e al. [21]...” [ 1 ] (Sec ion 3.2), a eade could expec he ea lie publica ions o p o ide hin s o he mul iple pa ame e choices yea ned o abo e (Sec ion 2). The same eade migh be disappoin ed, howe e , o ind ou ha he unde lying g ow h model o ha pape was di e en and he desc ip ion was hus no help ul o implemen a ions whe e GYPSY was used as he unde lying g ow h and yield p ojec ion sys em. Tompalski e al. [ 1 ] alida ed hei u u e p ojec ions essen ially by compa ing bo h he obse ed and p edic ed o es a ibu es p ojec ed o 80 yea s o age. Such a choice can be c i icized: i he p edic ions and alida ion da a a e blindly un h ough he same (he e, empla e ma ching) p ocess and only he esul ing numbe s a e compa ed, he e is a ai chance o miss seman ic o logical p oblems po en ially a ec ing he p ojec ions based on di e en inpu da a he same way. Also, gi en ha no alida ion da a wi h a longe ime lag be ween he obse a ions and p ojec ions exis ed, he assessmen o he empla e ma ching me hod would clea ly ha e bene i ed om a quali a i e analysis o he p ojec ions ela i e o he p ope ies o he unde lying models and da a. Acco ding o such an analysis wi h a i icial da a as abo e, he esul s and discussion o Tompalski e al. [ 1 ] lack o he ollowing ema ks, in addi ion o hose poin ed ou in Sec ion 1o his commen : • The esul s o he empla e ma ching a e e y sensi i e o he assump ions made when gene a ing he empla e da abase, o which eason he esul s should be p esen ed as a unc ion o he applied pa ame e s. Wi h he GYPSY models, especially assump ions on he ini ial ee plan ing densi ies (N ini ) had a conside able e ec on he inal de elopmen ajec o ies ob ained. The empla e ma ching could e en p oduce ajec o ies wi h di e en si e indices, when ca ied ou wi h empla e da abases based on di e en assump ions on N ini . Whe he he d i e o he u u e de elopmen is ei he di e en plan ing densi y o p oduc i i y (si e index) a ec s he u u e g ow h and yield es ima es d as ically, especially i he simula ions a e con inued beyond he cu en o a ion. • Templa e ma ching may inhe en ly p oduce discon inui ies be ween he cu en s a e o he o es and i s p ojec ed u u e s a e. No e ha in Figu es 2and 3, he discon inui ies a e p obably magni ied, because he si e index di e ing be ween Equa ions (1) and (2) by i s de ini ion was no s anda dized (Sec ion 2.1). Ne e heless, i is di icul o a gue agains he isk o he discon inui ies, conside ing ha obse a ions o p edic ions a e ma ched wi h he empla es independen ly (c . Figu e 1). Tompalski e al. [1] do no seem o iden i y his p oblem, bu o con i m he usabili y o he p ojec ions, hose should be exposed o “model c i icism and benchma king” [ 2 ] (Chap e 15), wi h emphases on e i ying he biological ealism and compa ibili y o he esul ing a ibu es (see also [3,8,9] (Chap e 18)) wi h espec o abo e.