Relative efficiency of ALS and InSAR for biomass estimation in a Tanzanian rainforest

Remo e Sens. 2015, 7, 9865-9885; doi:10.3390/ s70809865 emo e sensing ISSN 2072-4292 www.mdpi.com/jou nal/ emo esensing A icle Rela i e E iciency o ALS and InSAR o Biomass Es ima ion in a Tanzanian Rain o es End e Ho s ad Hansen 1,*, Te je Gobakken 1, S ein Solbe g 2, Annika Kangas 1, Li iu Ene 1, E nes Mauya 1 and E ik Næsse 1 1 Depa men o Ecology and Na u al Resou ce Managemen , No wegian Uni e si y o Li e Sciences, P.O. Box 5003, NO-1432 Ås, No way; E-Mails: e [email protected] (T.G.); [email p o ec ed] (A.K.); [email p o ec ed] (L.E.); e nes [email protected] (E.M.); [email p o ec ed] (E.N.) 2 No wegian Fo es and Landscape Ins i u e, P.O. Box 115, NO-1431 Ås, No way; E-Mail: [email p o ec ed] * Au ho o whom co espondence should be add essed; E-Mail: [email p o ec ed]; Tel.: +47-6496-5756. Academic Edi o s: Pa h Sa a hi Roy and P asad S. Thenkabail Recei ed: 22 Ap il 2015 / Accep ed: 27 July 2015 / Published: 4 Augus 2015 Abs ac : Fo es in en o ies based on ield sample su eys, suppo ed by auxilia y emo ely sensed da a, ha e he po en ial o p o ide anspa en and con iden es ima es o o es ca bon s ocks equi ed in clima e change mi iga ion schemes such as he REDD+ mechanism. The ield plo size is o impo ance o he p ecision o ca bon s ock es ima es, and be e in o ma ion o he ela ionship be ween plo size and p ecision can be use ul in designing u u e in en o ies. P ecision es ima es o o es biomass es ima es de eloped om 30 concen ic ield plo s wi h sizes o 700, 900, …, 1900 m2, sampled in a Tanzanian ain o es , we e assessed in a model-based in e ence amewo k. Remo ely sensed da a om ai bo ne lase scanning (ALS) and in e e ome ic syn he ic ape u e adio de ec ion and anging (InSAR) we e used as auxilia y in o ma ion. The indings indica e ha la ge ield plo s a e ela i ely mo e e icien o in en o ies suppo ed by emo ely sensed ALS and InSAR da a. A simula ion showed ha a pu e ield-based in en o y would ha e o comp ise 3.5–6.0 imes as many obse a ions o plo sizes o 700–1900 m2 o achie e he same p ecision as an in en o y suppo ed by ALS da a. OPEN ACCESS Remo e Sens. 2015, 7 9866 Keywo ds: ALS; ai bo ne lase scanning; LiDAR; ela i e e iciency; opical ain o es 1. In oduc ion Fo es in en o ies p o ide in o ma ion o managemen o o es esou ces on na ional, dis ic , and local le els. P ecise in o ma ion abou he quan i y and quali y o o es esou ces p o ides a solid basis o o es planning, managemen , and policies. O e he pas decade he ole o o es s has shi ed om a sou ce o imbe and non- imbe p oduc s, o a sou ce o a wide a ay o ecosys em se ices. One such se ice is he o es s’ ole in global clima e change mi iga ion, and he de elopmen o a ma ked-based mechanism o alue his se ice has esul ed in wha is known as he REDD+ mechanism. REDD+ ( educing emissions om de o es a ion and o es deg ada ion, conse a ion and enhancemen o o es ca bon s ocks, and sus ainable managemen o o es s in de eloping coun ies), desc ibed in he 16 h session o he Con e ence o Pa ies o he Uni ed Na ions F amewo k Con en ion on Clima e Change [1], gi es de eloping coun ies he oppo uni y o mone ize he se ice o seques e ing ca bon p o ided o he global clima e. Fu u e paymen s o pe o mance-based bene i s, such as enhanced o es ca bon s ocks, will equi e us wo hy sys ems o measu ing, epo ing, and e i ying (MRV) he ca bon s ock changes in o es s [2]. Fo es in en o ies ha e he po en ial o p o ide anspa en and con iden es ima es o o es ca bon s ocks needed in such sys ems. Fo es in en o ies a e usually based on a ield sample su ey suppo ed by one o se e al ypes o emo ely sensed da a. In o ma ion de i ed om emo ely sensed da a, in he o m o ae ial images, has been an impo an ool in o es in en o y since he 1940s [3], and he a ailabili y o op ical sa elli e images since he 1970s has esul ed in global o es co e s a is ics [4]. While high cos s ha e p e en ed he use o ae ial images, he use o low-cos op ical sa elli e images ha e been hampe ed by low spa ial esolu ion and pe sis en cloud co e in opical a eas. Fu he mo e, bo h echnologies ha e adi ionally only p o ided wo-dimensional in o ma ion, al hough ecen de elopmen s ha e esul ed in h ee-dimensional da a om ae ial and sa elli e images wi h he use o digi al pho og amme y and image ma ching (e.g., [5,6–8]). Modelling o biomass using image ma ching equi es a high quali y digi al e ain model (DTM) as e e ence su ace, usually de i ed om ai bo ne lase scanning (ALS). ALS is i sel a emo e sensing echnology ha p o ides h ee-dimensional da a o he o es ege a ion and has been used success ully o biomass es ima ion, e en in opical a eas [9,10]. Ano he echnology ha p o ides h ee-dimensional da a is syn he ic ape u e adio de ec ion and anging (SAR). Using a kind o s e eo imaging known as in e e ome y, h ee-dimensional su ace in o ma ion abou he ege a ion can be p oduced om SAR image pai s. Bo h ALS and SAR senso s a e ac i e senso s, emi ing pulses o elec omagne ic adia ion. Being ai bo ne, ALS has he ad an age o p o iding high esolu ion da a and heigh s o bo h he e ain and he canopy su ace. Sa elli e-based SAR has, in compa ison, lowe spa ial esolu ion, and i can only p o ide heigh s o he canopy su ace. I has, howe e , a highe a eal capaci y and lowe cos s. Wi h he abili y o p o iding ege a ion heigh in o ma ion, da a om ALS and SAR senso s ha e been used as auxilia y in o ma ion o biomass es ima ion in all majo o es ecosys ems [11]. Li e a u e e iews ha e a emp ed o assess he impac o di e en senso s, s a is ical modelling me hods, in en o y Remo e Sens. 2015, 7 9867 sample sizes, and in en o y plo sizes in di e en o es ypes [9,11]. Resul s om hese s udies seem o be conclusi e on wo issues: (1) Use o ALS-senso s gi es he bes esul s compa ed o all o he senso s o modelling biomass in e ms o oo mean squa e e o (RMSE); and (2) ha RMSE, as an exp ession o model p ecision, a ies wi h o es ype. A discussion on he impac o he size o in en o y plo s is included in bo h a o emen ioned s udies bu does no d aw conclusions on he impac o plo size on model p ecision, o gi e p ac ical ad ice on plo size. La ge plo s will ine i ably inc ease he es ima ed p ecision o biomass models in sample su eys due o he ac ha a iance be ween plo s is educed o la ge plo sizes since mo e o he o al a iance is cap u ed by he plo s, an e ec e e ed o as spa ial a e aging [9]. In sample su eys, suppo ed by emo ely sensed in o ma ion, addi ional sou ces o e o ha e been in es iga ed. Fi s ly, a misma ch be ween he emo ely sensed da a and he ield measu emen s in oduce noise in o he models [12]. This e ec , o en e e ed o as co- egis a ion e o , is educed wi h inc eased plo size. Secondly, a disc epancy o measu ing ees based on he loca ion o he s em, and he emo ely sensed da a which a e con ined by he e ical ex en o he ield plo bounda ies, is a sou ce o model noise [13,14]. This la e sou ce o e o s is e e ed o as bounda y e ec s. Bo h co- egis a ion e o s and bounda y e ec s a e educed wi h educing he a io o ield plo pe iphe y o plo a ea. Acco dingly, se e al s udies on modelling o o es biomass using emo ely sensed da a ha e documen ed ha inc eased plo size inc eased he model p ecision [13–16]. A common app oach o es ima ion o o es pa ame e s using ALS is known as he a ea-based app oach and was i s ou lined in Næsse [17,18]. Following his app oach, a ela ionship be ween biomass calcula ed om ield measu emen s on in en o y plo s and emo ely sensed da a is modelled using s a is ical me hods such as eg ession analysis, nea es neighbou s, neu al-ne wo ks, o ensemble lea ning (e.g., [11,19,20]). The models a e subsequen ly used o p edic biomass o popula ion elemen s o he same size as he in en o y plo s. Biomass p edic ions a e pe o med o all popula ion elemen s co e ing he s udy a ea, gi en ha emo ely sensed da a a e a ailable. The biomass p edic ions o he popula ion elemen s a e subsequen ly used o de i e an es ima e o he popula ion, ei he as a mean o o al biomass es ima e. Accompanying he es ima e, a a iance es ima e is calcula ed o s a e he p ecision o he es ima e. Two main app oaches o a iance es ima ion ha e been used in o es in en o ies: design-based and model-based a iance es ima ion. In he design-based app oach he popula ion, om which samples a e aken, is ega ded as ixed. The only sou ce o sampling e o is he andom selec ion o elemen s included in he sample. Thus, he es ima ed sample e o is de i ed om he in en o y sample and he p obabili y o each popula ion elemen o be included in he sample, e e ed o as he inclusion p obabili y. This inclusion p obabili y is assumed o be posi i e and known o all popula ion elemen s. Such samples a e o en e e ed o as p obabili y samples. I is o en he case, howe e , ha he sample has been acqui ed in a non-p obabilis ic manne [21], esul ing in ze o- o unknown inclusion p obabili ies. The ze o- o unknown inclusion p obabili y can be he esul o oppo unis ic sampling, i.e., sampling close o oads o economic and/o p ac ical easons. Simila ly, pu posi e sampling, es ablished o in es iga e a speci ic subjec , o en esul in samples acqui ed in a non-p obabilis ic manne . Fu he mo e, he inclusion p obabili y can be a ec ed by he accessibili y o he a ea ([22], p. 76). In he case whe e he sample da a does no mee he equi emen s o a design-based app oach o a iance es ima ion, a model-based app oach may be a iable al e na i e. Model-based in e ence does no , as opposed o design-based in e ence, ely on a p obabilis ic sample ha ep esen s he popula ion. Ins ead he s a is ical in e ence elies on he model Remo e Sens. 2015, 7 9868 i sel as a alid model o he dis ibu ion o possible obse a ions o each popula ion elemen . The popula ion is no iewed as ixed, bu a he as a esul o a andom p ocess, e e ed o as a “supe popula ion” model. This supe popula ion model canno be obse ed, bu he pa ame e s o he model can be es ima ed om he in en o y sample. The in en o ied popula ion is iewed as only one andom ealiza ion o his supe popula ion. An ex ensi e e iew o design-based and model-based in e ence o o es su ey is gi en by G egoi e [23]. To examine he e ec s o co- egis a ion- and bounda y-e ec s on he p ecision o ALS-suppo ed biomass es ima es, Mauya e al. [16] compa ed he a iance o ield-based biomass es ima es o he co esponding a iance o he biomass es ima es suppo ed by ALS a di e en plo sizes. This a io o a iance es ima es is e e ed o as ela i e e iciency, and has been used o compa e di e en sample designs, es ima o s, and in e en ial amewo ks, e.g., Payandeh [24], Ene e al. [25]. The objec i e o calcula ing he ela i e e iciencies in Mauya e al. [16] was o assess he e ec o plo size on he p ecision o ALS-de i ed biomass models. Fo his pu pose he a iance was es ima ed in a design-based amewo k. Mauya e al. [16] concluded ha educed model noise om co- egis a ion e o s and bounda y e ec s mean ha la ge plo size was p e e able o ALS-suppo ed biomass es ima es. In o de o plan o cos -e ec i e in en o ies o o es biomass using sample su eys suppo ed by emo ely sensed da a, he e is a need o be e in o ma ion on how he ield plo size impac s he p ecision o he subsequen biomass es ima es [26]. On his basis, he objec i es o he p esen s udy we e o (1) assess he impac o plo size on he ela i e e iciency o biomass es ima ion in a Tanzanian ain o es using wo di e en sou ces o emo ely sensed da a; and (2) quan i y he numbe o addi ional ield plo s needed o compensa e, in e ms o sampling e o , o a lack o emo ely sensed da a. To compa e he wo sou ces o emo ely sensed da a o a si ua ion wi hou such in o ma ion, simple models using e ain ele a ion (TE) as explana o y a iable we e de eloped. We made use o a ield da a se consis ing o 30 concen ic ci cula plo s o 700 m2 up o 1900 m2, and da a om ALS and in e e ome ic syn he ic ape u e adio de ec ion and anging (InSAR) senso s. Because he ield in en o y obse a ions had unknown inclusion p obabili ies a model-based app oach o es ima ion and in e ence was used. 2. Ma e ials and Me hods 2.1. S udy A ea The p esen s udy was conduc ed in he Amani Na u e Rese e (ANR) (5°08’S, 38°37’E, 200–1200 m abo e sea le el). The s udy a ea co e s a ound 88 km2 o opical submon ane ain o es and is loca ed in no h-eas e n Tanzania and is pa o he Eas Usamba a Moun ains. The a ea ecei es a ound 2000 mm ain all pe yea , and mos o he ain alls in he wo we seasons, Ap il–May and Oc obe –No embe . Daily mean empe a u es a y om abou 16–25 °C. Be o e he es ablishmen o he ANR in 1997, he a ea was comp ised o six o es ese es and abou hal o he a ea was classi ied as logged o co e ed wi h non-na i e species [27]. A e he logging was s opped in he la e 1980s mos o he logged a ea eco e ed and is now seconda y o es . Due o inaccessibili y he o he hal o he a ea had a limi ed human impac and is conside ed p ima y o es . Remo e Sens. 2015, 7 9869 2.2. Field Da a In he p esen s udy we u ilized ield da a (Figu e 1) om a sample su ey consis ing o 30 ci cula plo s collec ed du ing No embe 2011 in p e-de e mined loca ions. The plo loca ions we e chosen o cap u e he a ia ion in biomass by dis ibu ing hem in di e en al i udinal zones [16]. To e alua e he ep esen a i eness o he 30 ci cula plo s Mauya e al. [16] compa ed he p ope ies o he sample o a second sample o 153 sys ema ically dis ibu ed plo s co e ing he s udy a ea. Based on his e alua ion Mauya e al. [16] concluded ha , al hough being sampled in an oppo unis ic manne , he dis ibu ion in di e en al i udinal zones esul ed in a sample which closely esembled p ope ies o he sys ema ic sample. The ele a ion o he 30 ci cula plo s anged om 223 o 1018 m abo e sea le el wi h a mean o 552 m. Figu e 1. Le : S udy a ea (ma ked by s a ). Righ : Field plo loca ions (ma ked by do s) inside he Amani Na u e Rese e. The cen e coo dina es o he plo s we e es ablished by means o di e en ial global posi ioning sys em (GPS) and global na iga ion sa elli e sys em (GLONASS) using su ey-g ade ecei e s. All ees wi h diame e a b eas heigh (DBH) ≥5 cm we e callipe ed, ma ked, and species iden i ied. The ho izon al dis ance om he plo cen e o he on o each ee was measu ed using a Ve ex IV hypsome e [28]. Because he dis ance was measu ed o he on o he ees, hal o he ee DBH was added du ing da a p ocessing o ge he o al ho izon al dis ance o he ees om he plo cen e. The heigh s o h ee ees pe plo ( he la ges , medium, and smalles ee in e ms o DBH) we e measu ed using he hypsome e . Concen ic ci cula plo s o 700, 900, …, 1900 m2 we e cons uc ed o each o he 30 ield plo s cen ed on he posi ions de e mined in ield. The plo size o 700 m2 was chosen because i co esponds Remo e Sens. 2015, 7 9870 o he plo size used in he ecen ly es ablished na ional o es in en o y o Tanzania [29]. The maximum plo size on each loca ion was de e mined by he each o he hypsome e , and unde he mos challenging condi ions, dis ance measu emen s a ed o ail a 25 m. Thus, he maximum plo size used in he cu en s udy was 1900 m2. Based on he dis ance om he plo cen e o he cen e o he s em, each ee was alloca ed o hei espec i e concen ic plo . Biomass o each ee was compu ed using an allome ic model [30] and a diame e o heigh model de eloped om he diame e s and he co esponding ee heigh s, see Mauya e al. [16] o u he de ails. The biomass o each ee was hen summed a plo le el and agg ega ed biomass was scaled o pe -hec a e alues (Table 1). Al hough his biomass is e e ed o as “obse ed biomass”, he compu ed alues a e subjec o e o s ela ed o he applied allome ic model, and he subsampling and measu emen o ee DBH and heigh . Table 1. Mean biomass and s anda d de ia ion (SD) o he 30 ield plo s wi h plo sizes o 700, 900, …, 1900 m2. Plo Size(m2) Mean Biomass(Mg∙ha−1) SD(Mg∙ha−1) 700 371.8 221.5 900 366.1 216.3 1100 365.6 203.0 1300 361.0 190.5 1500 354.2 180.4 1700 355.0 170.2 1900 351.1 159.6 2.3. ALS Da a Collec ion o ALS da a wi h wall- o-wall co e age was ca ied ou om 19 Janua y o 18 Feb ua y 2012 using a Leica ALS70 senso moun ed on a ixed wing ai c a . The acquisi ion pa ame e s a e summa ized in Table 2. Pos ligh p ocessing o he ALS da a was pe o med by he con ac o (Te a ec AS, No way) using Te aScan so wa e [31]. A e ain model was c ea ed by classi ying ALS echoes as g ound echoes using a p og essi e iangula ed i egula ne wo k (TIN) densi ica ion algo i hm [32]. The TIN model was used o calcula e he ele a ion abo e he g ound o all echoes. F om he TIN model a as e -based digi al e ain model (DTM) wi h a 10 m × 10 m cell size was c ea ed o he en i e s udy a ea. Table 2. ALS acquisi ion pa ame e s. Pa ame e s Value Fligh speed (m∙s−1) 70 Flying al i ude (m a.g.l.) 800 Scanne equency (kHz) 339 Foo p in size (cm) 22 Beam di e gence (m ad) 0.28 Hal scan angle (deg.) 16 Remo e Sens. 2015, 7 9871 2.4. InSAR Da a InSAR da a we e acqui ed by he Tandem-X sa elli e mission on 6 h Augus 2011. The Tandem-X sa elli e mission consis s o wo X-band SAR sa elli es ope a ing in a pai and p o ides in e e ome ic images in a single-pass mode. The acquisi ion had an incidence angle o 46°, was ope a ed in s ipmap mode, and he pola iza ion was ho izon al ansmi and ho izon al ecei e. The no mal baseline was 210 m, which co esponded o a 2π heigh o ambigui y o 38 m. The o iginal spa ial esolu ion o he InSAR da a was sligh ly less han 3 m. 2.5. ALS-De i ed Explana o y Va iables ALS echoes we e ex ac ed o he concen ic ci cula plo s o 700, 900, …, 1900 m2 o each o he 30 loca ions. F om a maximum o i e echoes egis e ed pe ALS pulse, echoes we e ca ego ized as “single”, “ i s o many”, and “las o many”. “Single” and “ i s o many” we e me ged in o one da ase and deno ed as “ i s ” while “single” and “las o many” we e me ged in o ano he da ase and deno ed as “las ”. F om he ALS echoes in each o he wo ca ego ies (“ i s ”, “las ”), a iables desc ibing he heigh and densi y o he ege a ion we e de i ed. Canopy heigh a iables included pe cen iles a 10% in e als (H10, H20, …, H90) de i ed om he lase echoes abo e a h eshold o 2 m abo e g ound. Canopy densi y a iables we e compu ed by i s di iding he ange be ween a 95% pe cen ile heigh and he 2 m h eshold in o 10 e ical laye s o equal heigh . Fu he , he p opo ion o echoes abo e each laye o he o al numbe o echoes we e compu ed esul ing in 10 canopy densi y a iables (D0, D1, …, D9). The a iables we e compu ed sepa a ely o each echo ca ego y (“ i s ”, “las ”) and a subsc ip L o F was used as no a ion. The a iables we e used o cons uc linea leas -squa e models (Sec ion 2.9) o each o he concen ic plo sizes. In o de o ge compa able esul s be ween models om di e en plo sizes we chose o use he same ALS a iables in all models. S udies ha e shown ha a model consis ing o one canopy heigh a iable and one canopy densi y a iable is o en su icien o modelling o es biomass [33,34]. In a p e ious s udy using he same ield and ALS da a, Mauya e al. [16] ound ha he 60 h pe cen ile heigh om he “ i s ” echo ca ego y (H60.F) and he p opo ion o echoes abo e he second o he 10 e ical laye s o he o al numbe o echoes om he “las ” echo ca ego y (D1.L) we e he mos equen ly selec ed a iables in modelling biomass using plo sizes om 700 o 1900 m2. We he e o e a p io i selec ed H60.F and D1.L o cons uc ion o biomass models. 2.6. InSAR-De i ed Explana o y Va iable The Sa scape module o he ENVI 5.0 so wa e was used o p ocess Tandem-X image pai s esul ing in a digi al su ace model (DSM). An in e e og am was gene a ed om each image pai , and his was u he p ocessed in o a di e en ial in e e og am by using he ALS DTM as inpu . Phase noise was emo ed om he in e e og am wi h a Golds ein il e . Phase o se and phase amp e o s we e also emo ed using 30 g ound con ol poin s, placed in non- ege a ed loca ions, sp ead o e he s udy a ea. Phase unw apping was ca ied ou using he minimum cos low me hod, and he DSM was geocoded o a g ound esolu ion o 10 m × 10 m. Following he cons uc ion o he DSM, he DTM de i ed om he ALS TIN was sub ac ed om he DSM, esul ing in ob ained InSAR heigh s, i.e., heigh s o he cen e Remo e Sens. 2015, 7 9872 o he ada echo abo e g ound. Mean InSAR heigh was hen de i ed o each ield plo by weigh ing he heigh o each 10 m × 10 m cell o he no malized InSAR DSM by he a ea o he cells in e sec ing he a ea o he ield plo . This mean InSAR heigh was de i ed o each concen ic ield plo a ea. 2.7. DTM-De i ed Explana o y Va iable In a s udy o o es biomass in wo moun ain loca ions in Tanzania, including ANR, Ma shall e al. [35] ound TE o be posi i ely ela ed o biomass. The e o e, o compa e a iance es ima es ob ained using ALS and InSAR, a simple model wi h TE as he explana o y a iable we e cons uc ed o each plo size. The DTM de i ed om he ALS TIN was used o calcula e he mean TE o each concen ic plo size, 700, 900, …, 1900 m2, by weigh ing he alue o each 10 m × 10 m cell o he DTM by he cell a ea in e sec ed by he plo . The mean TE was subsequen ly used as an auxilia y a iable. 2.8. Tessella ing he S udy A ea and he Remo ely Sensed Da a The s udy a ea was essella ed in o egula g ids wi h hexagonal iles o 700, 900, …, 1900 m2 co esponding o he di e en plo sizes. To a oid spli ing he iles along he bounda y o he s udy a ea only iles wi h he cen oid alling inside o he s udy a ea we e e ained. Remo ely sensed a iables om ALS and InSAR, along wi h he TE in o ma ion we e calcula ed o all hexagonal iles in he s udy a ea. 2.9. Model Cons uc ion Fo each plo size, sepa a e linea leas -squa e models we e cons uc ed wi h he biomass es ima ed on he g ound plo s as esponse a iable and he co esponding emo ely sensed a iables, om ei he ALS o InSAR, as explana o y a iables. Simila ly, simple models we e cons uc ed using he TE as explana o y a iable. This esul ed in a model o each o he h ee sou ces o auxilia y da a: (1) ALS; (2) InSAR; and (3) TE o each plo size. The gene al model o ms a e shown in Table 3. To imp o e he linea ela ionship be ween he explana o y a iables and he esponse, a na u al-log ans o ma ion o bo h esponse and explana o y a iable was pe o med o all models. Such log-log models ha e been ound o be sui able o es ima ing o es p ope ies using emo ely sensed da a [33,36–38]. This ans o ma ion will in oduce a bias by back- ans o ma ion o a i hme ic scale, and a a io o he mean obse ed biomass o he mean o he back- ans o med es ima ed biomass p oposed by Snowdon [39] was he e o e used as a co ec ion ac o o he model p edic ions. Table 3. Gene al model o ms o models using TE, ALS, and InSAR da a. Model Model Fo m a TE ln(biomass) = ln( e ain ele a ion) ALS ln(biomass) = ln(H60.F) + ln(D1.L) InSAR ln(biomass) = ln(InSAR heigh ) a Va iables explained in Sec ions 2.5–2.7. Unlike design-based es ima o s, which o en a e unbiased o nea ly unbiased, he unbiasedness o model-based es ima o s depends on he model being co ec ly speci ied. I was he e o e pa amoun o assess how well he model i he ield plo obse a ions. Assessmen o he i o he models ollowed Remo e Sens. 2015, 7 9873 he app oach used by McRobe s e al. [40]. Sca e plo s o obse ed s. p edic ed biomass we e p oduced o each plo size. Co ec ly speci ied models should esul in poin s alling closely along a 1:1 line wi h in e cep 0 and slope 1. Fu he , pai s o obse a ions and p edic ions we e o de ed wi h espec o he p edic ed alues and g ouped in o h ee classes o 10 pai s. The mean o he obse ed e sus p edic ed biomass was plo ed o each g oup. A co ec ly speci ied model should again esul in poin s alling along a 1:1 line. 2.10. Model-Based In e ence Model-based in e ence does no , as opposed o design-based in e ence, ely on a p obabilis ic sample ha ep esen s he popula ion. Ins ead, as s a ed abo e, he in e ence elies on he model i sel as a alid model o a supe popula ion. Following he no a ion in S åhl e al. [41] an elemen o he supe popula ion was exp essed as yi= g(xi,α,εi) (1) whe e y is a ec o o he obse ed plo biomass on plo i, x is a ec o o a iables de i ed om he auxilia y da a, α is a ec o o model pa ame e s and ε is a ec o o e o s, and g is a unc ion desc ibing he supe popula ion. I is assumed ha he e o s a e independen , no mally dis ibu ed, wi h a cons an a iance, and wi hou spa ial au o-co ela ion. The pa ame e s α we e es ima ed wi h α using leas squa e eg ession, and used o es ima e he popula ion mean by μ = 1 N∑g(xi,α) N i=1 (2) whe e i indexes he popula ion elemen s and N is he numbe o elemen s, i.e., i=1, 2, …, N. Assuming ha he es ima ed α is accu a e, he g unc ion was linea ized in he neighbou hood o he ue unc ion using i s o de Taylo se ies expansion. De ails o he de i a ion o he unc ion is gi en in Appendix A o S åhl e al. [41]. The a iance o he popula ion mean was hen es ima ed by a (μ)=∑ ∑ Co  p k=1 p j=1 (αj,αk)g j ′g k ′ (3) whe e g j ′ and g k ′ a e he es ima ed mean alues o he i s o de de i a i es o he g unc ion o pa ame e s j and k (j = 1, 2, …, k, …,), espec i ely (c . [41]). S anda d e o s (SE) o he mean es ima es, i.e., he squa e oo o he a iance es ima e (√ a (μ)), we e epo ed along wi h SE ela i e o he mean es ima es. 2.11. Rela i e E iciency To assess he gain in p ecision o using emo ely sensed da a o enhance he es ima es, ela i e e iciency was calcula ed o bo h ALS (RETE:ALS) and InSAR (RETE:InSAR). The ela i e e iciencies we e calcula ed as a ios o he es ima ed a iance o he mean biomass es ima e (μ) o each plo size using he TE models di ided by he a iance es ima es o each plo size using he ALS models: RETE:ALSs= a (μTE)s a (μALS)s ⁄ (4) whe e s is an indica o o he plo sizes 700, 900, …, 1900 m2. Simila ly, ela i e e iciency o InSAR was compu ed as: Remo e Sens. 2015, 7 9880 map se ies o Tanzania, would mos likely ha e esul ed in subs an ially inc eased SE o he InSAR and TE es ima es. In a s udy using InSAR heigh o es ima e o es biomass in No way Næsse e al. [34] i was ound ha ela i e RMSE was app oxima ely se en pe cen age poin s highe using a DTM om opog aphic maps wi h a con ou in e al o 20 m, compa ed o using an ALS-de i ed DTM. P-band SAR, used wi h good esul s in Nee e al. [51], is cu en ly only a ailable om ai bo ne pla o ms, and was no collec ed in ANR. The analysis in he p esen s udy showed ha use o emo ely sensed da a om ALS and InSAR was able o inc ease he p ecision o he es ima es. Howe e , ALS da a a e expensi e compa ed o he ma ginal cos o es ablishing addi ional in en o y plo s (100–150 USD pe plo [52]). The e ec o inc eased numbe o ield plo s on he sampling e o o he TE models was simula ed using a Pólya-u n esampling scheme. To each simila le els o sampling e o as o he ALS models, he numbe o ield plo s would ha e o be inc eased by a ac o o 3.5–6 depending on plo size (Figu e 10). Figu e 10. S anda d e o o biomass es ima es (SE) using models wi h auxilia y da a o InSAR (dashed line), ALS (solid line), and TE. TE model SE is de i ed om 60 (do ed g ey line), 120 (dashed g ey line), and 180 (solid g ey line) simula ed obse a ions. Wi h he ela i ely low cos o inc easing he in ensi y o he ield in en o y (180 plo s × a cos o 125 USD = 22,500 USD), he inc eased p ecision o using ALS is no solely enough o de end he in es men o abou 100,000 USD o he ALS mission. Howe e , ALS does p o ide a good quali y DTM which can be used o u u e su eys suppo ed by o he sou ces o emo ely sensed da a equi ing such a DTM. The cos o ALS is la gely go e ned by he ligh ime. By lying highe , co e ing a la ge a ea wi h a single ligh s ip, he cos o acqui ing ALS can be educed. Findings om s udies o educed pulse densi y ei he by means o simula ions (e.g., [53]), o acquisi ions om di e en al i udes (e.g., [54]), ha e shown ha sa is ac o y esul s can be a ained a lowe pulse densi ies. A simula ion s udy conduc ed in ANR [55], con i med ha explana o y a iables de i ed om low pulse densi y is eliable down o abou 0.5 pulses·m−2, e en in dense opical o es s. Al hough he s udy [55] does no p esen esul s on RMSEs o a subsequen biomass model, he s anda d de ia ion o he digi al e ain model was s abile down o abou 0.5 pulses·m−2. Because a iance in he e ain model is ca ied o wa d in o he explana o y Remo e Sens. 2015, 7 9881 a iables in a biomass model, he RMSEs ob ained wi h lowe pulse densi ies would also be s abile down o abou 0.5 pulses·m−2. 4. Conclusions The esul s om he p esen s udy demons a ed, in acco dance wi h ea lie s udies, ha auxilia y emo ely sensed in o ma ion could be u ilized o inc ease he p ecision o biomass es ima es in opical o es s. Fu he , he esul s showed ha he ela i e e iciency o using emo ely sensed da a om bo h ALS and InSAR senso s inc eased wi h inc eased ield plo size. Thus, biomass es ima ion assis ed by emo ely sensed da a om ALS and InSAR will p o i ela i ely mo e in e ms o inc eased p ecision by inc easing plo size han es ima ion wi hou ALS and InSAR da a. The ela i e e iciency o bo h ALS and InSAR inc eased con inuously wi h inc eased plo sizes. To compensa e o a lack o ALS da a he pu e ield-based in en o y would ha e o con ain 3.5–6.0 imes as many obse a ions o plo sizes o 700–1900 m2 o achie e he same p ecision as an in en o y suppo ed by ALS da a. Many opical coun ies a e abou o es ablish hei i s na ion-wide o es sample su eys and plo size is a su ey design pa ame e ha mus be conside ed in ligh o u u e use o emo ely sensed da a o enhance es ima ion. Thus, i is impo an o quan i y he in luence o plo size on es ima ion e iciency o biomass in a ious o es ypes ound in opical coun ies o in o m design and in es men decisions in u u e su eys. Acknowledgmen s This wo k has been unded by he Royal No wegian Embassy in Tanzania as pa o he No wegian In e na ional Clima e and Fo es Ini ia i e. We wish o hank Te a ec AS, No way, o acqui ing and p ocessing he ALS da a and Deu sches Zen um ü Lu und Raum ah o p o iding he InSAR da a. 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