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Model-based estimation of above-ground biomass in the miombo ecoregion of Zambia Halperin, James; LeMay, Valerie; Chidumayo, Emmanuel; Verchot, Louis; Marshall, Peter Jul 23, 2016

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RESEARCH Open AccessModel-based estimation of above-groundbiomass in the miombo ecoregion ofZambiaJames Halperin1* , Valerie LeMay1, Emmanuel Chidumayo2, Louis Verchot3 and Peter Marshall1AbstractBackground: Information on above-ground biomass (AGB) is important for managing forest resource use at local levels,land management planning at regional levels, and carbon emissions reporting at national and international levels. Inmany tropical developing countries, this information may be unreliable or at a scale too coarse for use at local levels.There is a vital need to provide estimates of AGB with quantifiable uncertainty that can facilitate land use managementand policy development improvements. Model-based methods provide an efficient framework to estimate AGB.Methods: Using National Forest Inventory (NFI) data for a ~1,000,000 ha study area in the miombo ecoregion, Zambia,we estimated AGB using predicted canopy cover, environmental data, disturbance data, and Landsat 8 OLI satelliteimagery. We assessed different combinations of these datasets using three models, a semiparametric generalized additivemodel (GAM) and two nonlinear models (sigmoidal and exponential), employing a genetic algorithm for variableselection that minimized root mean square prediction error (RMSPE), calculated through cross-validation. We comparedmodel fit statistics to a null model as a baseline estimation method. Using bootstrap resampling methods, we calculated95 % confidence intervals for each model and compared results to a simple estimate of mean AGB from the NFI groundplot data.Results: Canopy cover, soil moisture, and vegetation indices were consistently selected as predictor variables. Thesigmoidal model and the GAM performed similarly; for both models the RMSPE was ~36.8 tonnes per hectare (i.e., 57 %of the mean). However, the sigmoidal model was approximately 30 % more efficient than the GAM, assessed usingbootstrapped variance estimates relative to a null model. After selecting the sigmoidal model, we estimated total AGB forthe study area at 64,526,209 tonnes (+/− 477,730), with a confidence interval 20 times more precise than a simple design-based estimate.Conclusions: Our findings demonstrate that NFI data may be combined with freely available satellite imagery and soilsdata to estimate total AGB with quantifiable uncertainty, while also providing spatially explicit AGB maps useful formanagement, planning, and reporting purposes.Keywords: National Forest Inventory, Above-ground biomass, Miombo, REDD+, Generalized additive model, Nonlinearmodel, Landsat 8 OLI* Correspondence: j.halperin@alumni.ubc.ca1Department of Forest Resources Management, The University of BritishColumbia, 2424 Main Mall, Vancouver, BC V6T 1Z4, CanadaFull list of author information is available at the end of the article© 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.Halperin et al. Forest Ecosystems  (2016) 3:14 DOI 10.1186/s40663-016-0077-4BackgroundInformation on forest resources in tropical developingcountries is challenging to acquire due to financial andlogistical constraints (Holmgren and Marklund 2007;Skutsch and Ba 2010; Stringer et al. 2012). However,tropical forest resources are being exploited and con-verted to other uses at rates that seem to outpace thecapacity for regrowth (Shearman et al. 2012; Brink et al.2014; Sawe et al. 2014; Suberu et al. 2014). This is espe-cially true in the miombo ecoregion of southern Africa(Cabral et al. 2010; Mayes et al. 2015), where forestproductivity is marginal (Frost 1996). In this context,forest monitoring programs are required to provide in-formation on forest resources for: i) planning use andmanagement activities at local levels (Stringer et al.2012); and ii) designing effective policies and measuresat national levels. Above-ground biomass (AGB) is a keyvariable of interest in forest monitoring programs, whereestimates of AGB are necessary for assessing fuel woodand timber availability, as well as for monitoring forestcarbon stocks. Integrating ground plot data from a forestinventory with environmental and/or remotely-sensedpredictor variables to predict AGB has shown increasingutility for estimating AGB (Moisen et al. 2006; McRobertset al. 2010; Lu et al. 2016; GOFC-GOLD 2015).Optical remotely-sensed data alone have been used toestimate miombo AGB with varying success (Samimiand Kraus 2004; Kashindye et al. 2013; Næsset et al.2016). The use of these data is complicated by complex,nonlinear relationships between AGB and vegetation in-dices (Lu et al. 2016). Active sensor remotely-senseddata such as Airbone Laser Scanning (ALS) or radarmay provide improved accuracy of AGB models (Ryan etal. 2012; Mitchard et al. 2013; Mauya et al. 2015; Næssetet al. 2016), although this is not guaranteed (Solberg etal. 2015). Another way to improve AGB estimation is toincorporate percent canopy cover (CC) as a predictorvariable (Tiwari and Singh 1984; Lefsky et al. 2002; Hallet al. 2006; González-Roglich et al. 2014; GOFC-GOLD2015), particularly since percent canopy cover is morereadily estimated by optical remotely-sensed data (Lefskyand Cohen 2003; Lu et al. 2016).González-Roglich and Swenson (2016) capitalized onthe relationship between AGB and CC for modeling for-est carbon in temperate savannahs of South America.They first developed a model to estimate CC usingLandsat 5 Thematic Mapper along with topographic andclimatic variables, and then used the estimated CC asthe sole predictor to estimate forest carbon. Using thisprocess, the percent root mean square error (RMSE) forprediction of forest carbon was 35 %. Similar studies inarid woodlands of Australia (Suganuma et al. 2006) andSudan (Wu et al. 2013) also reported favorable resultsusing estimated CC to estimate AGB. One complicationis that the definition of CC varies (Jennings et al. 1999).In some cases, CC was defined as the percentage of thesky blocked by tree crowns over a hemispherical view(Jennings et al. 1999), often measured using a sphericaldensiometer. Alternatively, the vertical projection of treecrowns onto the ground is currently used in many coun-tries as the basis for minimum forest area definition (FAO2014). González-Roglich and Swenson (2016) used theformer definition, while Suganuma et al. (2006) and Wu etal. (2013) used the latter. Therefore, it is an open questionas to which measure of CC may better relate to AGB.Models to estimate AGB that also incorporate informa-tion on topography, soils, and disturbances may furtherimprove the accuracy (Moisen and Frescino 2002; Powellet al. 2010; Pflugmacher et al. 2014; GOFC-GOLD 2015).In the miombo ecoregion, as in other ecosystems, eco-logical and physiological factors limit vegetation establish-ment and survival, while disturbances result in changes tovegetation structure and composition (Frost 1996;Chidumayo et al. 1996; Sankaran et al. 2008). Soil charac-teristics, fire regimes, and anthropogenic use have all beenidentified as principal determinants of vegetation struc-ture (Timberlake and Chidumayo 2011; Ryan andWilliams 2011). Investigations of these and other variablesfor estimating miombo AGB appear to be sparse, and fur-ther exploration is warranted.The main goal of this research is to investigatemethods for estimating total AGB for a study areawithin the miombo ecoregion by using ecologically rele-vant predictor variables. For this purpose, we comparedmodels established within a model-based framework,where inference is derived from the assumption that theyi observations of AGB are considered realizations of therandom variable Yi, which in turn are realizations of arandom process termed a superpopulation (Gregoire1998; Ståhl et al. 2016). To assess these models, we com-pared outcomes to a simple design-based estimate com-monly used in forest inventories. The design-basedestimate assumes that the population of Yi is fixed, notrandom, while the sample of yi observations is therealization of a random process, and inference is inde-pendent from assumptions regarding the probability dis-tribution of Yi in the population (Gregoire 1998; Ståhl etal. 2016). In this framework, we then addressed the fol-lowing specific questions: 1) Which definition of CC ismore useful as a single predictor variable to estimateAGB, the hemispherical view or the vertical projectionview? 2) Does AGB estimation accuracy improve if CCis combined with other predictor variables? 3) Whatmodel-based AGB estimation method performs best interms of fit and validation statistics? and 4) How domodel-based methods compare to a simple design-basedestimate of the sample mean? This research is intendedas a case study to help inform development of forestHalperin et al. Forest Ecosystems  (2016) 3:14 Page 2 of 17monitoring programs which apply National Forest In-ventory (NFI) data to estimation of AGB at sub-nationalor national scales.MethodsStudy areaThis study was carried out in Nyimba District (14°-15°S,30°-31°E, ~1,000,000 ha), Eastern Province, Zambia(Fig. 1). Nyimba lies in the center of the miombo eco-region, a biome of diverse vegetation types dominatedby tree species from the Caesalpinioideade sub-family ofleguminous plants (Timberlake and Chidumayo 2011).Across the ecoregion, vegetation composition and struc-ture varies depending on climate, soil, landscape pos-ition, and level of disturbance (Frost 1996; Timberlakeand Chidumayo 2011). Nyimba is found within the drymiombo ecozone and is dominated by four vegetationtypes (Table 1; GRZ 1976; Timberlake and Chidumayo2011). Approximately 75 % of the district can be charac-terized as forest land, based on canopy cover ≥ 10 % per0.5 ha area (Halperin et al. 2016). Nonforest land usesare dominated by small-scale agriculture (Gumbo et al.2016). Fire is a frequent disturbance, with an estimatedreturn interval of one to three years (Frost 1996;Timberlake and Chidumayo 2011). Fires generally resultfrom people engaged in agricultural land clearing, char-coal making, and hunting, with early dry-season firesexhibiting less intensity than late dry-season fires (Frost1996). Average rainfall is approximately 600–900 mmper year (GRZ 1968); most rain falls in the December toFebruary period, with a distinct dry season from May toNovember. Soils are generally characterized as Lithosol-Cambisols on the hills and plateaus, and Fluvisol-Vertisols in the valleys (GRZ 1986). Elevation rangesfrom 450 m along the Luangwa River valley bottom to1000 m on the plateau area around Nyimba district cap-ital, and higher on the mountain tops in the western halfof the district.Ground plot measurementsGround plot measurements were collected at 64, 0.1 hapermanent plots from May – December 2013 (Fig. 1). Theground plots were located on a systematic 10 km× 10 kmgrid corresponding to the Zambian Integrated Land UseAssessment 2 (ILUA2), an NFI program implemented bythe Zambian Forest Department in collaboration with theFAO (GRZ 2014). Nationally, the Zambian Forest Depart-ment collects field data at approximately 20 % of the gridintersections using a cluster plot design. Each cluster plothas four 20 m× 50 m rectangular subplots, and each sub-plot has a nested 10 m× 20 m microplot starting at thesame origin as the subplot. In this study, we collected dataonly for the first ground subplot of a cluster to increase thenumber of locations within time constraints, thereby cap-turing variations in conditions and land uses across thelandscape. As such, we refer to the 20 m× 50 m area wherewe collected ground measurements as the plot, and the10 m× 20 m area as the subplot.Measurements within each ground plot followed theILUA2 protocol (GRZ 2014). Species, total height, anddiameter at breast height (DBH; outside bark diameter at1.3 m above ground) were measured and recorded for eachlive tree with DBH ≥ 10 cm at the plot level and each livetree ≥ 5 cm and < 10 cm DBH at the subplot level. Thesetree attributes were used to calculate tree-level AGB, usingspecies-specific allometric models developed by Chidumayo(2012) and utilized by the Zambian Forest Department(GRZ 2014). In some cases, species-specific models wereFig. 1 Location of Nyimba District, Zambia within the miombo ecoregion. Inset: National Forest Inventory grid within Nyimba DistrictHalperin et al. Forest Ecosystems  (2016) 3:14 Page 3 of 17not available and forest type models were used (Chidumayo2012). We summarized tree-level AGB in plots and sub-plots to obtain plot-level AGB in tonnes per hectare (t∙ha−1).We also measured percent CC for each ground plotusing a spherical densiometer and recorded the dom-inant vegetation type (i.e., miombo woodland, mopanewoodland, munga woodland, or riparian forest, GRZ2014). We recorded ‘nonforest’ if the ground plot wasdominated by nonforest land use with none of thevegetation types present. Ground plot coordinateswere determined using a Trimble GeoXT, which weredifferentially corrected (+/− 1 m). Lastly, we gatheredGPS line data for roads and point data for villagelocations. Most of the ground plots (49) were visitedbetween 5 May and 30 July 2013, while the remainingplots (15) were visited between 27 Oct and 6 Dec2013.Predictor variablesWe employed two types of estimated CC as a single pre-dictor variable in separate models to estimate AGB.First, CC was estimated as the vertical projection of treecrowns onto the ground using a binomial generalizedadditive model (GAM) model developed for the samestudy area (Halperin et al. 2016), referred to as CC^VERT.Second, CC was estimated as the percentage of the skyblocked by tree crowns over a hemispherical view byusing the densiometer. For this purpose, we built a bino-mial GAM to estimate percent CC using the same pre-dictor variable selection methods described in Halperinet al. (2016), and refer to its estimates as CC^HEMI . Wecompared the results of estimating AGB using eitherCC^VERT or CC^HEMI , and used the better performingmodel as the base upon which to add other predictorvariables.Disturbance factors, such as small scale conversionto agriculture, unmanaged harvesting for charcoaland timber, and fire are known to affect miomboAGB (Chidumayo 1988; Frost 1996; Timberlake andChidumayo 2011). Proximity to roads and villageshas been shown to be related to increasing levels ofanthropogenic disturbance and decreased AGB(Helmer et al. 2008; Ahrends et al. 2010). We calcu-lated Euclidean distance from each ground plot cen-ter to roads and to villages, based on the GPS lineand point data collected during field surveys(Table 2). Fire frequency and intensity both impactmiombo AGB, where low intensity burns are morecharacteristic of the early dry season when grass isstill curing, and higher intensity burns are more likely tooccur in the late dry season (Ryan and Williams 2011).We included monthly fire history data for 500 m pixelsfor 2003–2013, derived from the MODIS Burned AreaProduct (Boschetti et al. 2013). We processed the fire his-tory data and determined the number of low intensity,early season fires and high intensity, late season fires perpixel (Table 2).Underlying factors that affect miombo AGB in-clude topography and soils (Frost 1996; Timberlakeand Chidumayo 2011). We assessed landscape pos-ition using the compound topographic index (CTI),distance to perennial rivers, and slope percent. Thesevariables were calculated based on 30 m ShuttleRadar Topography Mission Digital Elevation ModelTable 1 Characteristics of the four dominant vegetation types found in Nyimba District, Eastern Province, ZambiaVegetation type Dominant species Structure Phenology Fire susceptibilityof dominant speciesSoils and topography SourceDry miombowoodlandBrachystegia spiciformis, B.boehmii and JulbernardiaglobifloraOpen to closedtwo layer canopy,with meanheight≤ 15 m;dense grass layerdeciduous orsemi-deciduousfire-tolerant Nutrient-poor,plateaus and hillsTimberlake andChidumayo (2011);GRZ (2014)MopanewoodlandColophospermum mopane(generally monospecific)Open one layercanopy, withheight rangingfrom 6 to 18 m;sparse grass layerdeciduous fire-intolerant Clay dominated,on wide valley bottomsTimberlake (1995);Makhado et al.(2014); GRZ (2014)MungawoodlandVechellia sp., Senegaliasp., Combretum sp., andtrees associated with thePapilionoideae subfamilyOpen one or twolayer canopy,emergents up to18 m; dense grasslayerdeciduous fire-tolerant Nutrient-rich andwell-drained, plateausTimberlake andChidumayo (2011);GRZ (2014)Riparian forest Mixed Closed three layercanopy, up to25 m; vinescommonlyoccurringevergreen fire-intolerant Restricted to bufferzones aroundsignificant riversGRZ (2014)Halperin et al. Forest Ecosystems  (2016) 3:14 Page 4 of 17(USGS 2004) (Table 2). ISRIC – World Soil Informa-tion has produced a consistent and comprehensivedata source for soils information at 250 m pixel size,covering the continent of Africa (Hengl et al. 2015).The data is provided as estimates at six depths (2.5,10, 22.5, 45, 80, and 150 cm). We downloaded thesedata, clipped each dataset to the study area bound-ary, and calculated the mean across all depths foreach variable (Table 2).The use of predictor variables developed from op-tical satellite imagery in models to estimate AGB hasa long history. However, the utility of various bands,indices, or texture values to use as predictor variablesstill remains an area of active research (Banskota etal. 2014; Lu et al. 2016). We downloaded Landsat 8OLI data from the Landsat Ecosystem DisturbanceAdaptive Process (LEDAPS) archive that spatially andtemporally corresponded to the study area and theground measurements (Path 170, Row 70; Path 171,Row 70). LEDAPS data are processed to surface re-flectance (Masek et al. 2006); therefore, we did notperform atmospheric correction or radiometricnormalization. We created one mosaic from the twoscenes that were found to be in acceptable agreementwith the GPS line data for roads based on visual as-sessment. We derived 24 predictor variables fromLandsat 8 OLI satellite imagery in order to assess theuse of a wide range of spectral and textural attributesfor predicting AGB (Table 3).Before selecting pixels to match with ground plotsfor all predictor datasets, we masked out major riversand paved roads by on-screen digitizing using Landsatdata at 1:10,000. All spatial data were clipped to thestudy area boundary. To account for spatial extentmismatches between ground plot size and predictorvariables, we resampled all predictor variable spatialdata to a 20 m × 50 m pixel size using a nearestneighbor method which maintained the actual pixelvalues. The values for each predictor variable wereassigned to ground plots, based on proximity of theground plot center to the nearest pixel center foreach predictor variable. Preparation of spatial pre-dictor variables was conducted using the R rasterpackage v.2.3-41 (Hijmans et al. 2015) and ArcGIS v.10.1 (ESRI 2012).AGB ModelsModels using CC onlyAs noted, we estimated AGB first using either CC^VERTor CC^HEMI as a single predictor variable using threemodels. A semiparametric GAM was used since it iswell-suited to modeling complex relationships where anunderlying nonlinear relationship is not known a prioriTable 2 Description of disturbance and environmental predictor variables for estimating above-ground biomass at the ground plot levelPredictor variable Description Minimum Maximum MeanAvailable soil water capacity (AWC) Volumetric fraction 12.1 15.2 14.0Bulk density (Bulk) kg∙m−3 1299.6 1501.2 1378.9Carbon Organic soil carbon content (g∙kg−1) 4.3 11.5 7.0Cation Exchange Capacity (CEC) cmolc∙kg−1 7.7 21.8 12.3Clay Percent volume 21.5 35.1 28.7Coarse fragments (Crs.frg) Percent volume 2.2 17.0 9.5Compound Topographic Index (CTI)Unitless. High values indicate higherpotential soil moisture.5.8 39.6 8.2Distance from ground plot to district capital (D2cap) Euclidean distance (m) 5704 90,146 40,635Distance from ground plot to nearest perennial river/stream (D2hydro) Euclidean distance (m) 91 26,194 7203Distance from ground plot to nearest village or settlement (D2vill) Euclidean distance (m) 542 42,902 8948Distance from ground plot to nearest improved road (D2road) Euclidean distance (m) 192 59,363 12,042Fire history – early season (Fire.early)Total number of fires per pixel,Apr. 1 – Jul. 310.0 6.0 0.6Fire history – late season (Fire.late)Total number of fires per pixel,Aug. 1 – Nov. 300.0 8.0 1.8pH Unitless 59.0 67.8 62.6Sand Percent volume 43.4 66.2 54.3Silt Percent volume 9.9 22.8 17.0Slope Percent 0.0 43.8 8.4Minimum, maximum, and mean values calculated from n = 64Halperin et al. Forest Ecosystems  (2016) 3:14 Page 5 of 17(Wood 2006). Because of their flexibility, GAMs havebeen used to estimate forest attributes from remotely-sensed data (Moisen and Frescino 2002; Kattenborn etal. 2015). The form of the GAM is:log AGB^i ¼ β0 þXJj¼1f j xij  þ εi; ð1Þwhere i is the ground plot, AGBi is in t∙ha−1, β0 is theintercept, εi is the residual error, and fj is the smoothingfunction for a predictor variable xj created via a regressionspline (Wood 2006). The GAM was fit with a normal dis-tribution, the log link, and the default variance function.Using the log link avoids negative AGB estimates. A valueof 0.1 was added to the AGB for two ground plots with notrees. We found that setting the maximum smoothingparameter at 2 was sufficiently flexible to account for po-tential nonlinearity in the model, yet reduce the possibilityof overfitting that may occur in GAM’s (Moisen et al.2006; Halperin et al. 2016). The GAM was fit with themgcv package v. 1.8-9 in R v. 3.2.2 (Wood 2015; R Devel-opment Core Team 2015).We also fit two nonlinear models that restricted theAGB estimate to be positive with an upper limit. First,we used a sigmoidal model (e.g., McRoberts et al. 2015):AGB^i ¼ α1þ exp β0 þXj¼1Jβjxij þ εi; ð2Þwhere parameters are α and the β’s, and the other termsare as in Eq. 1. Second, we used an exponential model,also used for estimating AGB (e.g., Anaya et al. 2009):AGB^i ¼ α x expXJj¼1βjxij !þ εi: ð3ÞTo fit these nonlinear models, we used the Gauss-Newton method in the nls function in R v.3.2.2. StartingTable 3 Description of remotely-sensed predictor variables generated from Landsat 8 OLI, used for estimating above-ground biomass atthe ground plot levelPredictor variable Description Minimum Maximum Mean CitationAlbedo Sum of all bands 0.4156 1.1433 0.7103 Lu et al. (2016)Albedo.texturea 0.0112 0.6469 0.0661 Hansen et al. (2002)Atmospherically Resistant Vegetation Index (ARVI) NIR – 2 x Red – Blue/NIR + 2x Red – Blue−0.1329 0.1974 0.0494 Kaufman and Tanre (1992)ARVI.texture 0.0039 0.1675 0.0283Blue band 0.0115 0.0623 0.0324Blue.texture 0.0008 0.0556 0.0049Enhanced Vegetation Index (EVI) 2.5 x ((NIR – Red)/(NIR + (6 x Red)– (7.5 x Blue) + 1)0.9530 1.6688 1.4284 Justice et al. (1998)EVI.texture 0.0079 0.1875 0.0545Green band 0.0297 0.0966 0.0547Green.texture 0.0006 0.0786 0.0064Normalized Burn Ratio (NBR) NIR – SWIR2/NIR + SWIR2 −0.1119 0.5962 0.3084 Key and Benson (2006)NBR.texture 0.0054 0.3623 0.0561Normalized Difference Moisture Index (NDMI) NIR – SWIR1/NIR + SWIR1 −0.2136 0.3247 0.0475 Jin and Sader (2005)NDMI.texture 0.0047 0.2289 0.0419Normalized Difference Vegetation Index (NDVI) NIR - Red/NIR + Red 0.3133 0.8169 0.5398 Rouse et al. (1974)NDVI.texture 0.0091 0.3330 0.0482NIR band Near infrared 0.1187 0.2974 0.2263NIR.texture 0.0034 0.0455 0.0152Red band 0.0247 0.1368 0.0685Red.texture 0.0016 0.1150 0.0106SWIR1 band Shortwave infrared 1 0.1071 0.3333 0.2073SWIR1.texture 0.0028 0.1624 0.0205SWIR2 band Shortwave infrared 2 0.0497 0.2527 0.1212SWIR2.texture 0.0021 0.1910 0.0156Minimum, maximum, and mean values calculated from n = 64aAll variables denoted with .texture were calculated using the standard deviation for each band or index using a 3 × 3 pixel windowHalperin et al. Forest Ecosystems  (2016) 3:14 Page 6 of 17parameters were estimated using the linearized form ofeach nonlinear model (i.e., log (AGBi)). After experi-menting with a flexible or fixed asymptote α, we foundthat setting α = 500 produced realistic estimates. This isin line with Næsset et al. (2016), who truncated miomboAGB estimates from linear ordinary least squares modelsat twice the maximum observed value in their sampledata. For each fitted model (three models and CC^VERTor CC^HEMI), we used 20-fold cross-validation and calcu-lated the root mean square prediction error (RMSPE)and RMSPE as a percent of the mean (RMSPE%), de-fined as:RMSPE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1yiv− y^ivð Þ2nsð4Þwhere yiv is the AGB (t∙ha−1) of ground plot i not usedfor fitting in fold v, y^iv is its corresponding estimate, andn = the number of ground plots (64). RMSPE% was cal-culated as:RMSPE% ¼ RMSPEy 	 100; ð5Þwhere y is the mean AGB (t∙ha−1) calculated from theground plots. We then calculated and compared themean RMSPE and mean RMSPE% across the threemodels using CC^VERT or CC^HEMI . Based on these valid-ation statistics, we included either CC^VERT or CC^HEMI inmodels with multiple predictor variables.Models using multiple predictor variablesNext, we investigated whether expanding the modelswith increasingly diverse combinations of predictor vari-able sets could improve the accuracy of AGB estimates.For this purpose, we compared models using: CC^VERT orCC^HEMI alone; remotely-sensed (Landsat) variablesalone; environmental and disturbance (Env/Dist) vari-ables alone; and combinations of each predictor variableset (i.e., Landsat and Env/Dist, CC^VERT or CC^HEMI andLandsat, etc.). A genetic algorithm (GA) was used toperform predictor variable selection within each pre-dictor variable set. The GA has been demonstrated toprovide near optimality for predictor variable identifica-tion and subsetting when there are a large, diverse rangeof possible predictor variables (Tomppo and Halme2004; Garcia-Gutierrez et al. 2014); a description of thealgorithm is given in Scrucca (2013). We set the object-ive criteria (i.e., “fitness”) to minimize the RMSPE, andestablished the GA stopping criteria at 20 consecutivegenerations with no improvement in fitness, or a max-imum of 100 generations. We restricted the number ofvariables under consideration to a maximum of six ineach predictor variable set, in order to decrease the riskof near multicollinearity and overfitting. For each pre-dictor variable set (except CC^VERT or CC^HEMI alone), weimplemented the GA one time and recorded the lowestRMSPE. We then calculated and compared meanRMSPE and mean RMSPE% for each predictor variableset, and chose the predictor variable set that minimizedthese two fit statistics. The GA analysis was conductedusing the GA package v.2.2 in R (Scrucca 2013).Final variable selectionWe performed final predictor variable selection usingthe predictor variable set that minimized RMSPE inthe previous section. For this purpose, we imple-mented the GA 100 times for each model using thesame fitness and stopping criteria as before, and se-lected the subset of predictor variables that minimizedRMSPE across all 100 GA implementations. For thesigmoidal and exponential models, we also consideredcommonly used transformations (i.e., square, squareroot, inverse, etc.) for each predictor variable, once thepredictor variables were chosen through this process.Use of transformations for predictor variables has beenexamined in nonlinear models for improving modelperformance (Wang et al. 2007; Timilsina and Staud-hammer 2012). To compare performance among thethree models, we computed the following fit statistics:root mean square error (RMSE), RMSE as a percent ofthe mean (RMSE%), mean difference (MD), andPseudo-R2 as follows:RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1yi− y^ið Þ2ns; ð6ÞRMSE% ¼ RMSEy 	x 100; ð7ÞMD ¼Xni¼1yi − y^ið Þn; ð8ÞPseudo‐R2 ¼ 1−Xni¼1ðyi− y^iÞ2Xni¼1 yi− yð Þ2; ð9Þwhere yi and y^i are the observed and estimated AGB(t∙ha−1) for ground plot i, and n and y were defined inEq. 4 and Eq. 5, respectively. We also calculated 20-foldvalidation statistics, namely RMSPE (Eq. 4) and themean prediction difference (MPD) defined as:MPD ¼Xni¼1yiv − y^ivð Þn; ð10Þwhere yiv, y^iv, and n were defined for Eq. 4.Halperin et al. Forest Ecosystems  (2016) 3:14 Page 7 of 17Uncertainty assessment and model selectionAfter choosing the best performing predictor variablesubset for each model, we estimated the AGB total(tonnes), 95 % confidence interval (CI) for the total, andAGB (t∙ha−1) for the entire study area. We accomplishedthis using a bootstrap method involving resampling nsamples from the ground plot data with replacementusing equal probability sampling, following recommen-dations from McRoberts et al. (2011) and based on workby Efron and Tibshirani (1986). Using 500 bootstrapsamples, we refitted each model to the predictor variabledata covering the entire study area, and estimated AGBfor every 20 m × 50 m pixel. Because the GAM is notasymptotic, we limited the maximum estimated valuefor AGB (t∙ha−1) to the same value as the asymptote forthe sigmoidal and exponential models, as is commonlydone in non-asymptotic models (e.g., Næsset et al.2016). For each model, we estimated total AGB (Y^boot )using the following equation:Y^boot ¼Xnbootk¼1Y^bootknboot; ð11Þwhere Y^bootk is the estimated total AGB by summing allpixels (in tonnes) across the study area for bootstrap k, andnboot is 500. AGB/ha was calculated from dividing Y^boot bythe number of ha in the study area. We estimated the vari-ance for Y^boot using the following equation:Var^ðY^bootÞ ¼Xnbootk¼1ðYk^boot− Y^bootÞ2nboot−1: ð12ÞWe used this variance estimate to calculate a 95 % confi-dence interval (CI) for estimated total AGB based on thenormal distribution (Efron and Tibshirani 1986), and re-ported the half-width of the CI for each model. To estab-lish a baseline for comparing model performance, we fit anull model with no predictor variables. Using this nullmodel, we estimated the AGB total, 95 % CI for the total,and AGB (t∙ha−1) (Bater et al. 2009). Then, we calculatedthe relative efficiency for each model by dividing the nullmodel variance estimate by each model’s variance esti-mate, following Næsset et al. (2016). Finally, we comparedthe four model-based estimates of total AGB, AGB/ha,and CI to a simple design-based estimate of AGB total,95 % CI for the total, and AGB (t∙ha−1) using the NFI sys-tematic sample of ground plots, assuming equal probabil-ity sampling (Cochran 1977).Based on these statistics, along with observed versuspredicted AGB graphs, we chose one model and usedthis to estimate AGB for each 20 m × 50 m pixel in thestudy area. To assess the pixel-level variability of theAGB estimates, we calculated the Coefficient of Vari-ation (CV) in percent (i.e., standard deviation per pixelacross the 500 resamples divided by the correspondingmean pixel value, multiplied by 100, which was also usedby Carreiras et al. 2013; Faßnacht et al. 2014; Kattenbornet al. 2015), present a map of CV, and report the meanCV for the study area.ResultsModels using CC onlyObservations of AGB (t∙ha−1) and CCVERT (%) for themiombo woodland vegetation type follow a more regularpattern than the mopane woodland and riparian forestvegetation types, which exhibit a large range of observedAGB values at low observed values of CCVERT (Fig. 2). Ob-servations of CCHEMI greater than 50 % display a widerange of observed AGB values; however, observed AGBvalues corresponding to CCHEMI less than 50 % follow amore regular pattern. As expected, the six nonforestground plots which were measured have low observedAGB and low observed CC for both forms of CC. A bino-mial GAM was used to fit separate models for CCVERT andCCHEMI; the model to estimate CC^VERT had better fit andvalidation statistics than the model to estimate CC^HEMI(Table 4). However, in predicting AGB, clear differencesare apparent in the usefulness of CC as the percentage ofthe sky blocked by tree crowns over a hemispherical view( CC^HEMI ) versus CC as the vertical projection of treecrowns onto the ground (CC^VERT ). Across three modelforms, CC^HEMI had an average RMSPE% that was 18 %lower than for CC^VERT (Table 5). The exponential modelperformed poorly with RMSPE (72.1 t∙ha−1) larger thanthe mean estimate of AGB t∙ha−1 from the sample data(64.1 t∙ha−1). Considering only the GAM and sigmoidalmodels, the average difference in RMSPE betweenCC^VERT and CC^HEMI as a single predictor variable was5 t∙ha−1 in favor of CC^HEMI. Because of these statistics andrelationships, we chose CC^HEMI for estimating AGB inmodels with multiple predictor variables.Models using multiple predictor variablesA clear pattern in reduction of RMSPE can be seen byincluding more diverse combinations of predictor vari-able datasets (Table 5). Across models, CC^HEMI alone isa better predictor of AGB than models that use onlyLandsat 8 OLI predictor variables; however, the expo-nential model that uses Landsat 8 OLI has a slight edgeover CC^HEMI (RMSPE 45.9 vs. 46.6, respectively). Thepredictor variable combination of environmental anddisturbance data alone and CC^HEMI alone are compar-able with two of the three combinations that have twopredictor variable datasets (Landsat + Env/Dist andCC^HEMI + Landsat), with a difference in mean RMSPE%of only three percent. Noticeable improvements in AGBRMSPE% are seen when combining CC^HEMI with envir-onmental and disturbance data, as mean RMSPE% dropsHalperin et al. Forest Ecosystems  (2016) 3:14 Page 8 of 17seven percent. However, the greatest improvement iswhen performing variable selection using all three pre-dictor variable datasets combined, with a mean RMSPE%of 58 %. Therefore, we performed final variable selectionusing this combination.Final variable and model selectionOne influential observation, which likely resulted fromhaze in the remotely-sensed data, was evident across allmodels. As the influence could be considered uncom-mon given this dataset, we discarded the observationFig. 2 Top row: Scatterplot for two forms of observed canopy cover (CC) versus observed above-ground biomass (AGB), by vegetation type orland use. CCHEMI is the vertical projection of tree crowns onto the ground, derived from crown area-DBH models; CCHEMI is percentage of the skyblocked by tree crowns measured using a spherical densiometer. Bottom row: Scatterplot for two forms of predicted canopy cover (CC) versusobserved above-ground biomass (AGB), by vegetation type or land use, with three models to estimate AGB based on CC^ VERT or CC^ HEMITable 4 Goodness-of-fit and validation statistics for two binomial generalized additive models to estimate percent canopy coverbased on crown radius-DBH models (CC^ VERT) and measurements using a spherical densiometer (CC^ HEMI)Fit statistics Validation statisticsModel RMSE (6) MD (8) RMSPE (4) MPD (10)CC^ VERT ¼ −1:8747þ f NDVIð Þ þ f ARVI:textureð Þ þ f SWIR1:textureð Þ þ f D2capð Þ þ f AWCð Þ þ f slopeð Þ 8.5 % 0.0 % 8.4 % 1.5 %CC^ HEMI ¼ 0:6788þ Fire:lateþ D2capþ carbonþ f ðbulkÞ þ f ðcrs:frgÞ 13.4 % −0.7 % 17.2 % −0.5 %RMSE root mean square error, MD mean difference, RMSPE root mean square prediction error, MPD mean prediction differenceSee Tables 2 and 3 for descriptions of predictor variablesHalperin et al. Forest Ecosystems  (2016) 3:14 Page 9 of 17and continued with the analysis, following the recommen-dation of Kutner et al. (2005, p.438). Using the final selectedvariables, we explored use of predictor variable transforma-tions for the sigmoidal and exponential models. By incorp-orating squared terms in the sigmoidal model for twopredictor variables (CC^HEMI2and pH2), we found an im-provement of 4 % in terms of RMSE% and an overall betterfit in graphs of observed versus estimated values of AGB.The exponential model did not improve by incorporatingany transformed predictor variables. However, we foundthat the fit and validation statistics of the exponential modelremained the same after removing one variable (EVI.tex-ture); therefore, we used a subset of five predictor variablesfor this model. With the GAM, three variables were esti-mated with a smoothing parameter of 1 (NBR, CTI, bulkdensity); therefore we fit the model with these variables asparametric terms, as recommended by Wood (2006).For each of the three models, average RMSE% was lessthan 60 % and average RMSPE% was less than 65 %(Table 6). The mean prediction difference (MPD) for thesigmoidal model was the highest at 3.2 t∙ha−1; however,mean differences (MD) across all models were less than1 t∙ha−1. Despite the difference in MPD, the fit and valid-ation statistics for the GAM and the sigmoidal modelswere otherwise similar, while the exponential model hadthe worst fit (Fig. 3). Each model had a tendency tounder-estimate AGB at higher values, which was mostpronounced in the exponential model; however, observa-tions and estimations were relatively balanced along the1:1 line up to approximately 100 t∙ha−1.As expected, CC^HEMI was selected as a predictor vari-able in all three models. Vegetation indices were chosenmore consistently over raw band values or texture indi-ces among the Landsat 8 OLI predictor variables. TheNormalized Difference Moisture Index (NDMI) waschosen in both the GAM and the sigmoidal model, theNormalized Burn Ratio (NBR) was selected as anotherindex in the GAM, while the common Normalized Differ-ence Vegetation Index (NDVI) was selected as the onlyvegetation index in the exponential model. In the GAMand the sigmoidal model, NDMI was selected in conjunc-tion with topographic or soil variables related to soil mois-ture (AWC, CTI, D2hydro). Available soil water capacity(AWC) was selected in both the sigmoidal and exponentialmodels. Frequency of late season fire was the only disturb-ance variable selected, and only in the sigmoidal model.When each model was applied across the entire studyarea, AGB ranged from 61.9 to 67.3 t∙ha−1 and total AGBranged from 64.3 million tonnes to 69.9 million tonnes(Table 7). For comparison, the null model estimate and thesimple design-based estimate were both within this samerange. All of the model-based methods, including the nullmodel, exhibit confidence intervals that are more precisethan the design-based estimate by an order of magnitude.Interestingly, even though the sigmoidal model exhibitedthe highest mean prediction bias, it had the smallest confi-dence interval based on bootstrap resampling. Conversely,while the GAM demonstrated the best fit and validationstatistics across the three models where variable selectionwas performed, it had a confidence interval wider than theother models. The sigmoidal model and the exponentialmodel were both more efficient than the null model, whilethe GAM was less efficient. Since the sigmoidal model hadfit and validation statistics similar to the GAM, yet hadhigher relative efficiency than the GAM, we selected thesigmoidal model to estimate AGB and the correspondingCV for each 20 m× 50 m pixel in the study area.AGB estimations per pixel using the sigmoidal modelranged from 0 to 390 t∙ha−1, where lower values were morecommon around areas with higher population and highervalues were more common in remote areas in the LuangwaRiver valley (Fig. 4). Estimates of CV per pixel generallyTable 5 Above-ground biomass (AGB, t∙ha−1) root mean square prediction error (RMSPE) using different predictor variable datasetcombinations and models, ordered by mean RMSPE and mean RMSPE%Model CC^ VERT CC^HEMI Landsat Env/Dist Landsat + Env/Dist CC^HEMI + Landsat CC^HEMI + Env/Dist CC^HEMI + Env/Dist + LandsatGAM (1) 50.1 44.3 48.8 41.5 40.7 43.4 37.9 35.1Sigmoidal (2) 49.8 45.2 47.8 47.0 45.6 44.2 39.8 37.5Exponential (3) 72.1 46.3 45.9 46.6 44.3 42.8 40.5 39.4Mean RMSPE 57.3 45.3 47.5 45 43.5 43.5 39.4 37.3Mean RMSPE% 89 % 71 % 74 % 70 % 68 % 68 % 61 % 58 %Table 6 Fit and validation statistics for predicting miombo above-ground biomass (AGB, t∙ha−1) using three modelsModel RMSE (6) RMSE% (7) MD (8) Pseudo R2 (9) RMSPE (4) RMSPE% (5) MPD (10) VariablesaGAM (1) 29.2 45 % 0.8 0.65 36.8 57 % 0 CC^ HEMI, NBR, NDMI, Bulk, CTI, D2hydroSigmoidal (2)29.947 %0.9 0.63 36.958 % 3.2CC^ HEMI, CC^ HEMI2, NDMI, ARVI.texture,Fire.late, AWC, pH, pH2Exponential (3) 36.1 56 % 0.6 0.47 39.7 62 % 0.4 CC^ HEMI, NDVI, AWC, Sand, SiltaSee Tables 2 and 3 for descriptions of remotely-sensed, environmental and disturbance variablesHalperin et al. Forest Ecosystems  (2016) 3:14 Page 10 of 17were highest where AGB was the lowest, with a large area ofhigh CV on the eastern boundary and two small valleys inthe west half of the study area. The area of high CV on theeastern boundary is dominated by agricultural, nonforestland use; whereas the two small valleys appear to be domi-nated by grassland. The average CV per pixel across thewhole study area was 31 %, with a standard deviation of 14.DiscussionThis research provides encouraging results for using amodel-based approach to estimate miombo AGB withNational Forest Inventory data. The usefulness of canopycover as a predictor variable in estimating AGB wasclear. Similar results were found by Hall et al. (2006) forboreal forests, by Wu et al. (2013) for tropical wood-lands in Sudan, and by González-Roglich and Swenson(2016) for wooded savannas in Argentina. Hall et al.(2006) and González-Roglich and Swenson (2016) usedCC as the percentage of the sky blocked by tree crownsover a hemispherical view, whereas Wu et al. used CC asthe vertical projection of tree crowns onto the ground.In our case study, CCHEMI (i.e., the hemispherical viewof canopy cover) demonstrated a better relationship toAGB for two possible reasons. First, taller trees projectmore cover in a hemispherical measurement device suchas the spherical densiometer (Jennings et al. 1999), andtree height has been shown to be an important covariatein predicting tree-level biomass (Chave et al. 2014).Second, CCVERT (i.e., vertical projection) relies on DBH-crown radius models (Burrows and Strang 1964; Fuller etal. 1997; Isango 2007) to estimate canopy cover perground plot; these models are outdated and not localizedin our study (Halperin et al. 2016). Updating DBH-crownradius models may improve the usefulness of CCVERT as apredictor variable in AGB models for the miombo eco-region and should be an area of active research. This is es-pecially true for less common vegetation types such asmopane woodlands and riparian forests.Improvements in AGB estimates were observed whenincluding a diverse range of ecologically meaningful co-variates along with CC^HEMI. In this context, two aspectsof moisture stand out. First, soil moisture was character-ized by available soil water content (AWC, Hengl et al.2015) in the sigmoidal and exponential models, orthrough landscape position via the compound topo-graphic index (CTI) and distance to perennial water inthe GAM. Soil moisture has been identified as an under-lying factor contributing to miombo vegetation dynamics(Frost 1996; D’Odorico et al. 2007). For example, higherlevels of soil moisture have been found under closedcanopy miombo woodland compared with open canopymiombo woodland (Campbell et al. 1988).Second, vegetation moisture was captured through theNormalized Difference Moisture Index (NDMI), an im-portant variable in both the GAM and sigmoidal models.NDMI has been shown to be correlated with tree canopyFig. 3 Observed versus estimated above-ground biomass (AGB) using predicted canopy cover, environmental, disturbance, and remotely-sensedpredictor variables. The solid line indicates 1:1 correlation between observed and estimated valuesTable 7 Bootstrap results for mean and total above-ground biomass (AGB) with corresponding 95 % confidence intervals for fourmodel-based methods, compared to a design-based methodMethod Mean Total 95 % CI for total AGB Relative efficiencyAGB (t∙ha−1) AGB (t) (half-width)GAM (1) 67.3 69,961,134 694,260 0.82Sigmoidal (2) 62.1 64,526,209 477,730 1.20Exponential (3) 61.9 64,316,094 500,070 1.15Null model 62.8 65,244,018 573,365 –Design-based 63.0 65,472,297 13,055,331 –Halperin et al. Forest Ecosystems  (2016) 3:14 Page 11 of 17water content and is competitive with the more well-known Normalized Difference Vegetation Index (NDVI)for a variety of forest mapping purposes (Hunt and Rock1989; Jin and Sader 2005). This study targeted collectionof field and remotely-sensed data for the early dry season,which is considered a prime period for linking these ob-servations in the miombo ecoregion. In this timeframe,grass layers have generally senesced while the deciduoustree canopies have not yet fully shed their leaves (Fuller etal. 1997). As such, NDMI appears to be an importantvegetation index for characterizing vegetation moisture intree canopies, and higher canopy moisture could be re-lated to greater levels of AGB (D’Odorico et al. 2007).Our study area is in the dry miombo ecozone whererainfall averages less than 1000 mm∙yr−1 (Timberlakeand Chidumayo 2011). Comparing our results with simi-lar studies in the same ecozone, Næsset et al. (2016) es-timated mean AGB at 51.3 t∙ha−1, Mauya et al. (2015) at65.8 t∙ha−1, Ryan et al. (2011) at 59.4 t∙ha−1, and Ribeiroet al. (2008) at 70 t∙ha−1, while Carreiras et al. (2013) es-timated AGB at 25.7 t∙ha−1. However, Carreiras et al.only studied areas with canopy cover < 50 %. The reviewby Frost (1996) provided an AGB estimate of 55 t∙ha−1for dry miombo of Zambia and Zimbabwe, and in themost recent FAO Forest Resources Assessment forZambia, the national estimate of AGB was 84 t∙ha−1 (FAO2014). Across models, our AGB estimates ranged from61.9 to 67.3 t∙ha−1, where the best performing model andthe null model estimated 62.1 and 62.8 t∙ha−1, respectively.Clearly, our estimates of AGB for a study area in the Zam-bian dry miombo ecozone are in line with other studies.Comparing accuracy statistics with other published re-sults is challenging, given the number of studies usingsimilar data sources in the same ecozone, as well as theuse of a wide variety of statistics. Therefore, a compari-son of similar studies estimating AGB in other miomboecozones or dry forest ecoregions is necessary. Some re-searchers presented model fit statistics such as R2 (Wuet al. 2013; Kashindye et al. 2013), while others empha-sized RMSE (Mitchard et al. 2013; Solberg et al. 2015).The latter two estimated RMSE at 12.8 t∙ha−1 (22 % CV) inMozambique and 40.3 t∙ha−1 (78 % CV) in Tanzania, re-spectively. However, fit statistics are known to be optimisticwhen concerning prediction (Guisan and Zimmermann2000; Packalén et al. 2012). Using resampling methods toestimate prediction error for AGB in Mozambique, Ryan etal. (2012) and Carreiras et al. (2013) reported RMSPE of19.6 t∙ha−1 and 5.0 t∙ha−1, respectively, where the latter re-ported a mean CV of 25 %. In a study site in Tanzania withsimilar vegetation and rainfall to our study area, Mauya etal. (2015) and Næsset et al. (2016) reported RMSPE% of 47and 62 %, respectively. These latter studies all employed ac-tive sensor (radar or ALS) imagery as the single source forpredictor variables.Research on the use of optical sensor satellite imageryfor estimating AGB in the miombo ecoregion is morelimited. Næsset et al. (2016) used a linear ordinary leastsquares model and a stepwise predictor variable selec-tion method. As potential predictor variables, these au-thors included canopy cover predictions and canopycover gain or loss from Hansen et al. (2013), raw bandvalues from Landsat 7 ETM+ and Landsat 8 OLI, NDVIcalculated from the Landsat data, and square and squareroot transformations for all of these predictor variables.Based on their stepwise predictor variable selection pro-cedure, squared canopy cover was the only predictorvariable chosen. While their finding helps to corroborateour result of canopy cover and squared canopy cover inFig. 4 Map of estimated above-ground biomass (AGB) per pixel (0.1 ha) and the Coefficient of Variation per pixel (CV). AGB estimates derivedfrom a sigmoidal modelHalperin et al. Forest Ecosystems  (2016) 3:14 Page 12 of 17the sigmoidal model, their model resulted in poor AGBprediction with an RMSPE% of 87 %. It is possible thattheir model using Landsat data was disadvantaged bytwo aspects. First, they did not include other commonlyused vegetation indices (i.e., NDMI, NBR) or texture var-iables (i.e. standard deviation in a 3 × 3 window aroundthe ground plot), which we found to be useful in ourstudy, as have others (e.g., Lu et al. 2014). Second, theLandsat data that Næsset et al. used differed by at least ayear from the time of their ground plot measurements.Two studies that estimated miombo tree volume(m3∙ha−1) using Landsat also provide a useful compari-son. Employing cross-validation to compute RMSPE%,Pereira (2006) reported 48 % in Mozambique usingLandsat and k-Nearest Neighbor imputation, while Garaet al. (2015) averaged 62 % using Landsat and nonlinearmodels. Our chosen model (sigmoidal) has estimates ofRMSE% at 47 and RMSPE% at 58 %, indicating that ourfit and validation statistics are comparable to similarstudies using large-scale inventories in the miombo eco-region using optical remotely-sensed data (Pereira 2006)and active remote sensing data such as ALS or radar(Solberg et al. 2015; Mauya et al. 2015; Næsset et al.2016). However, more research is needed to compareAGB confidence intervals to other studies because appli-cation of a model-based approach appears relatively un-common in the miombo ecoregion.The use of GAMs and nonlinear models, such as thesigmoidal and exponential models in this study, for pre-dicting AGB has shown promise in a number of studiesin different biomes (e.g., Moisen and Frescino 2002; Hallet al. 2006; Anaya et al. 2009; McRoberts et al. 2015;Kattenborn et al. 2015). However, it appears that mostapproaches to estimate and map AGB in the miomboecoregion used linear ordinary least squares (Ryan et al.2012; Kashindye et al. 2013; Mitchard et al. 2013;Solberg et al. 2015; Næsset et al. 2016), despite the non-linear relationships between forest attributes andremotely-sensed data (Sedano et al. 2008; Banskota et al.2014; Lu et al. 2016 ; Gara et al. 2015). We found GAM’sto perform as well as nonlinear models with respect tofit and validation statistics; however, when applied to thepopulation of predictor data the bootstrap confidenceinterval was less efficient than the null model.We protected against overfitting of the GAM by usingcross-validation in the variable selection process (Guisanand Zimmermann 2000; Hawkins 2004; Packalén et al.2012); however, the smoothing splines of GAM’s mayperform in an unpredictable manner when applied topopulation-level data which includes ranges of valuesnot within the observation data (Guisan et al. 2002;Venables and Dichmont 2004). Because of this, nonlin-ear models may be preferred for several reasons. First,the sigmoidal and exponential models in this study areasymptotic, thereby preventing both negative and unrea-sonably high estimations (McRoberts et al. 2015). Sec-ond, nonlinear models are able to achieve more stableextrapolation at the ends of, and beyond, the ranges ofthe values of the predictor variables (Venables and Dich-mont 2004). Third, judicious application of transforma-tions may improve performance if there appears to be alack of fit in nonlinear models.One issue with the nonlinear models we used in thisstudy is estimating the asymptote. We initially investigateda flexible asymptote (α), with α estimated in the model fit-ting process. For our dataset, α was often estimated at un-realistically high values or the nonlinear models would notconverge, both of which may indicate that the data doesnot support estimating a biologically meaningful asymp-tote. We further investigated estimating α as a function ofthe predictor variables in the models (i.e., α0 + α1xi); how-ever, no improvements in model fit or biologically mean-ingful values of α were noted. In this context, Burkhartand Tomé (2012 p. 123) stated that if an asymptote can-not be realistically fit with the data at hand, then expertjudgement may be employed to fix the asymptote at a rea-sonable value and continue with model fitting. AGB t∙ha−1for most vegetation types in the dry miombo ecozone tendto be less than 100 t∙ha−1 (Frost 1996), although upperlimits generally appear to be understudied. Mauya et al.(2015) found an upper limit of 350 t∙ha−1 in dry miombowoodland vegetation type for a study site in southeastTanzania, while the riparian forest vegetation type may ap-proach 500 t∙ha−1 (Chidumayo personal communication2016). Future modeling efforts should assess practicalasymptotic limits for AGB in all miombo vegetation types.While this study made progress in terms of ecologic-ally meaningful variable selection and highlighted modeladvantages and disadvantages, improvements may be re-alized in several aspects. First, we found that canopycover as the percentage of the sky blocked by treecrowns over a hemispherical view (CC^HEMI) was a betterpredictor for AGB than canopy cover as the vertical pro-jection of tree crowns onto the ground (CC^VERT). How-ever, values of CCVERT, used to predict CC^VERT , werederived from DBH-crown radius models (Burrows andStrang 1964; Fuller et al. 1997; Isango 2007) that shouldbe updated for conditions in Zambia (Halperin et al.2016). Once updated, CC^VERT may prove to be as usefulas CC^HEMI as a predictor of AGB. Second, the highestpercent CV pixel values occurred where AGB was pre-dicted to be the lowest, likely because there were veryfew ground plots with no trees. To accommodate suchunder-sampled areas, off-grid ground plots could be in-cluded along with the NFI ground plots in implementa-tion of the model-based methods. Model-based methodsare not restricted to one single sample design as long asthe same variable of interest (i.e., AGB) is being sampledHalperin et al. Forest Ecosystems  (2016) 3:14 Page 13 of 17according to the same definitions; the main consider-ation is that sample selection is required to be unin-formative in terms of Y (Gregoire 1998).Third, active sensor remotely-sensed data allow treeheights to be estimated and height is known be corre-lated with tree-level (Chave et al. 2014) and plot-levelbiomass (Wulder et al. 2012). ALS data is a provensource of height estimates, yet remains operationallyout-of-reach for many countries (Ribeiro et al. 2012).Testing of this source of predictor variables for use inoperational monitoring programs is just now underwayin the miombo ecoregion (Mauya et al. 2015; Næsset etal. 2016). Additionally, significant challenges remain inusing more readily available radar data (Sinha et al.2015; Solberg et al. 2015). However, space borne laserscanning systems are under development (Moussavi etal. 2014; GOFC-GOLD 2015) and may prove useful infuture applications.Fourth, a model-assisted approach may lend itself touse of the GAM, balancing the variability in population-level estimation with more conservative inference thattakes advantage of the design-based properties of thesample (Opsomer et al. 2007; Næsset et al. 2016). Fifth,there is significant opportunity to explore model-assistedor model-based approaches in a small area estimationcontext for improving both estimates and inference atspatial scales where traditional design-based approachesare not possible (Magnussen et al. 2014). Lastly, if a mapof AGB is a requirement, then use of georeferenced pre-dictor variables is required. However, if a map of AGB isnot required, then our null model would provide a viablealternative that could also be applied within a small areaestimation framework.ConclusionEstimating the amount and distribution of AGB is cru-cial for improving land management planning and forengaging in international discussions on REDD+. Ourunderstanding of AGB is enhanced by including eco-logically meaningful predictor variables in a model-based approach to estimation. This study generated sev-eral insights for improving miombo AGB estimationusing NFI data. First, the biophysical relationship be-tween AGB and CC can be exploited to improve AGBestimation. Second, model-based methods improve pre-cision of AGB estimates by an order of magnitude oversimple design-based estimation. Third, if a map of AGBis not required, estimating the confidence interval oftotal AGB using bootstrap resampling for a null modelis a viable alternative to the traditional design-basedconfidence interval. Fourth, if a map is required, expen-sive predictor variables such as those derived from ALS,are not necessarily required as there is freely availablespatial data (i.e., Landsat, Digital Elevation Model, soils,etc.) which can be used as predictor variables in themodel-based framework. Fifth, a genetic algorithm pro-vides an efficient way to perform predictor variable se-lection. Lastly, future approaches to improve ourunderstanding of AGB distribution in the miombo eco-region should include small area estimation.AbbreviationsAGB, above-ground biomass; ALS, airborne laser scanning; CC, canopy cover;CV, Coefficient of Variation; GA, genetic algorithm; GAM, generalized additivemodel; NFI, National Forest Inventory; OLI, Operational Land Imager; REDD+,Reducing Emissions from Deforestation and forest Degradation; RMSE, rootmean square error; RMSPE, root mean square prediction error; t∙ha−1, tonnesper hectareAcknowledgementsThe authors wish to thank Dr. Nicholas Coops, Dr. Davison Gumbo, Mr. KaalaMoombe, Mr. Joel Lwambo, Mr. Martin Lyambai, Mr. Andrew Goods Nkoma,Chief Nyalugwe, Chief Ndake, Chieftaness Mwape, Chief Luembe, Mrs. BerthaKauseni, Ms. Rhoda Chiluba, Mr. Shadreck Ngoma, Mr. Sylvester Siame, Mr.Geoffrey Tebuho, Mr. Susiku Muyapekwa, Mr. Smart Lungu, Mr. Saule Lungu,Mr. Moses Ngulube, Dr. Julian Fox, Mr. Abel Siampale, and the residents ofNyimba District, Zambia. We also wish to thank two anonymous reviewersfor their helpful comments and suggestions.FundingFunding for the field work in this study was provided by the United StatesAgency for International Development under grant number BFS-G-11-00002to the Center for International Forestry Research, entitled the Nyimba ForestProject. Funding for the lead author to conduct analysis has been providedby The University of British Columbia.Authors’ contributionsJH designed the study, led the field work, analyzed the data, and wrote themanuscript. VL supervised the study design, analysis, and initial manuscriptdrafts. EN, LV, and PM provided essential suggestions and advice throughoutthe process. All authors read and approved the final manuscript.Competing interestsThe authors declare that they have no competing interests.Author details1Department of Forest Resources Management, The University of BritishColumbia, 2424 Main Mall, Vancouver, BC V6T 1Z4, Canada. 2Makeni SavannaResearch Project, P.O. Box 50323, Ridgeway, Lusaka, Zambia. 3InternationalCenter for Tropical Agriculture, Km 17 Recta Cali-Palmira, Apartado Aéreo6713, Cali 763537, Colombia.Received: 2 June 2016 Accepted: 10 July 2016ReferencesAhrends A, Burgess ND, Milledge SA, Bulling MT, Fisher B, Smart JC, Clarke G,Mhorok BE, Lewis SL (2010) Predictable waves of sequential forestdegradation and biodiversity loss spreading from an African city. Proc NatlAcad Sci 107(33):14556–14561Anaya JA, Chuvieco E, Palacios-Orueta A (2009) Above-ground biomassassessment in Colombia: a remote sensing approach. For Ecol Manage257(4):1237–1246Banskota A, Kayastha N, Falkowski MJ, Wulder MA, Froese RE, White JC (2014)Forest monitoring using Landsat time series data: a review. Can J RemoteSens 40(5):362–384Bater CW, Coops NC, Gergel SE, LeMay V, Collins D (2009) Estimation of standingdead tree class distributions in northwest coastal forests using lidar remotesensing. 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Remote Sens Environ 121:196–209Submit your manuscript to a journal and benefi t from:7 Convenient online submission7 Rigorous peer review7 Immediate publication on acceptance7 Open access: articles freely available online7 High visibility within the fi eld7 Retaining the copyright to your article    Submit your next manuscript at 7 springeropen.comHalperin et al. Forest Ecosystems  (2016) 3:14 Page 17 of 17


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