WWF ecoregions of the North American boreal forest. 

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... as forest. We conducted the ecoregion-level calculations using three different threshold values, i.e., 25%, 50%, and 75%. We selected the 75% threshold for estimating k NN-based mean AGB density because this threshold provided us with a large number of mostly pure forest pixels and resulted in the closest agreement with GLAS estimates of AGB density. For the GLAS analysis, ecoregion areas were based simply on the number of 25 m resolution (i.e., 0.0625 ha) EOSD forest classes falling within an ecoregion. The 1000 forest inventory plots that were sampled by PALS in this study were distributed across 11 of the 22 (50%) WWF boreal forest ecoregions of North America (Table 1; Figs. 1 and 2). Although the plots were largely concentrated in the managed com- mercial forests of Canada and Alaska, there were also plots in the boreal taiga of northern Quebec and in some fairly remote areas of Alaska (Fig. 2). The plots spanned a large range of AGB densities (range = 0 to 361 Mg·ha −1 , mean = 76.3 Mg·ha −1 , SD = 58.8; n = 1000) and fell into all four of the major boreal land cover classes (32% conifer, 25% hardwood, 38% mixedwood, and 6% treed wetland). Because this study used a lidar-assisted, model-based sampling approach, we make the assumption that these 1000 plots are representative of our area of interest and therefore meet an important statistical criterion needed to produce an accurate forest inventory. In Alaska, the most robust regressions for relating PALS metrics to the AGB density of the ground plots were found when we developed equations for specific ecoregions across all forest cover types, with R 2 values ranging from 0.58 to 0.80 (Table 2). In all cases, more than one height metric was selected by the best possible subset regression procedure, typically one variable related to the height of the upper canopy and one or more variables related to the height distribution of laser returns from the lower canopy (Table 2). Throughout the analyses, variance inflation factors (VIF) were monitored and variable selection adjustments were made to keep VIFs well below 10. In Canada, the most robust ground plot – PALS regressions were found when we developed generic equations for each forest land cover class with all ecoregions pooled, yielding R 2 values ranging from 0.50 to 0.84 (Table 3 a ). For the conifer and treed wetland equations, measurements of both upper and lower canopy heights were selected as independent variables, whereas for the hardwood and mixedwood forests, mid- to upper-canopy height measurements paired with canopy density metrics were selected. We were also able to develop robust equations for the major regions of Canada (eastern versus western) and for specific land cover types within some regions and ecoregions (Table 3 b ). These equations had a similar range of R 2 values as the generic equations but slightly lower root mean squared error (RMSE). Therefore, when available, we applied the more specific equations to gener- ate PALS biomass values along the PALS–GLAS flight lines; otherwise, we applied the generic equations for each land cover type. Our decision to use ecoregion-specific equations across all cover types in Alaska and generic equations for each land cover class across all ecoregions in Canada allowed us to use the equations that yielded the highest R 2 and (or) lowest RMSE values in the different regions and thus should have increased the precision of our estimates. We compared the estimates from these two different stratification approaches across the three main geographic regions and found that the impacts on mean biomass density were on the order of 3% to 5% with no consistent trends, i.e., stratified equations yielded both higher and lower mean AGB density than the nonstratified equations depending on the region. As well, standard errors were similar. The GLAS 3c and 3f lines that we flew with PALS spanned a large portion of the North American boreal forest in the western and central portions of the biome but did not include much sampling in the eastern portion of eastern Canada (Fig. 2). See the Materials and methods section for reasons why GLAS 2a data from Quebec were not included. For Alaska, the R 2 values for the regressions relating GLAS metrics to PALS-calculated AGB for each of the five cover types across all ecoregions were very similar and ranged from 0.53 to 0.57 (Table 2). RMSE values were lower than for the ground plot – PALS equations. The conifer and hardwood equations both included a GLAS-derived measurement of upper and lower canopy heights, as well as the GLAS acquisition as a dummy variable (Table 2). For the treed wetlands and burned areas, the GLAS-derived fslope measurement that is related to canopy closure was selected as an independent variable in addition to the height metrics. The fslope variable describes the angle formed between a vertical base line and the leading edge of the waveform; larger angles connote a denser upper canopy layer (see fig. 1 in Boudreau et al. 2008). The mixedwood and burned area equations had higher co-linearity but were still within acceptable ranges (Table 2). We had no coincident measurements of PALS and GLAS for burned areas in Alaska, but we did have 179 data points where PALS flew over GLAS pulses classified as shrubland or grassland (Table 2). Consequently, we applied these shrub–grassland equations to the burned areas in Alaska and used the resulting equation for scaling GLAS to the region for the burned area land cover type (see next section). This is not the ideal method for estimating burned area biomass as GLAS has low sensitivity for detecting vegetation heights less than 5 m (Nelson 2010); however, it does at least provide a quantitative estimate for comparison with future estimates derived using other methods. For Canada, we developed another set of generic regressions between GLAS metrics and PALS-derived AGB for each forest cover type by region, i.e., western versus eastern Canada (Table 4). However, we did not have a sufficient number of coincident PALS– GLAS observations in burned areas in eastern Canada, so we used the 31 observations available in western Canada to develop an equation that could be applied to burned areas across the country. RMSE values were generally similar to those for the Alaska equations for the three most common forest cover types (conifer, hardwood, mixedwood), ranging from 21.3 to 27.6 Mg·ha −1 (Tables 2 and 4). Both R 2 values and sample sizes were higher for the Canadian equations than for Alaska equations, with the exception of treed wetlands in western Canada (Tables 2 and 4). The highest R 2 (0.79) was obtained for hardwood forests in eastern Canada. The GLAS-14 standard height product was selected as an independent variable for six of the nine equations. As found for Alaska, GLAS- derived measurements of both upper and lower canopy heights were included in the equations. The fslope variable describing the density of the upper canopy was selected as an independent variable for treed wetlands in eastern Canada, as it was in Alaska. Co-linearity between independent variables was again at acceptable levels for all PALS–GLAS equations in Canada. We present our AGB estimates for each of the three main boreal regions, i.e., Alaska, western Canada, and eastern Canada, and then report our totals for all of North America. Note that we report average biomass densities for the forest areas of the different ecoregions. On the other hand, Neigh et al. (2013) reported biomass densities averaged across forested and nonforested areas of an ecoregion assuming zero biomass for nonforested areas. An individual GLAS orbit is the sampling unit used for estimating AGB at the ecoregion level. In Alaska, there were 57 GLAS 3c and 3f orbits available, which included 22 682 GLAS pulses (Table 5). The number of GLAS orbits available per ecoregion varied from 7 to 55, and the number of GLAS pulses per ecoregion ranged from 29 to 17 025 (Table 5). The Interior Alaska–Yukon Lowland Taiga ecoregion was intercepted by the largest number of orbits (i.e., 55), due in large measure to the very large east–west extent of the ecoregion. The three ecoregions for Alaska with the lowest sampling intensity had only 7 to 8 GLAS orbits each. These three ecoregions also tended to have only small areas occupied by forest. The Alaska–St. Elias Range Tundra ecoregion also supports limited forested areas, but because it is oriented largely in an east–west direction, it was sampled more intensively (29 orbits). Total AGB for Alaska forests was estimated at 2110 ± 45 Mt (Table 5). The forests of the Interior Alaska–Yukon Lowland Taiga ecoregion contained nearly two-thirds (1386 ± 28 Mt) of the AGB. However, this was due to its large surface area and not to a particularly high AGB density. The forests within the Interior Yukon– Alaska Alpine Tundra ecoregion had the second greatest amount of AGB (15.2%; 320.5 ± 7.4 Mt). These two ecoregions, which accounted for >80% of the total AGB in Alaska, had similar AGB densities (56.3 and 56.9 Mg·ha −1 ), and these densities were very close to the average for all ecoregions (57.0 ± 1.2 Mg·ha −1 ). Model error was a large component of the overall error for all ecoregions (Table 5). The two ecoregions with the greatest number of GLAS orbits also had the highest percent model error (54.4% and 51.0%). The general empirical relationship between the number of orbits, percent model error, and percent sampling error is addressed later. Conifers were the most intensively sampled stratum (12 547 GLAS pulses), had the largest forest area, and were estimated to contain 54.9% (1159 ± 27.4 Mt) of Alaska's boreal forest AGB. The high sampling intensity for conifers was associated with low sampling error and higher percent model error (80.8%; Table 6). Hardwoods and mixedwoods accounted for similar percentages of the AGB in Alaska (20.5% and 16.4%, respectively), whereas treed wetlands and ...

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... measured geolocated ground plots and were also collected along all of the GLAS 3c and 3f orbital ground tracks used in this study (Fig. 2). Following quality filtering of the GLAS pulses for implausible (e.g., >50 m) height metrics, we had 10 421 coincident PALS–GLAS observations that we used to relate PALS-based estimates of biomass to GLAS measurements. Once these AGB models were in place, we could use GLAS as our regional sampling tool to inventory the North American boreal forest. The Canadian Forest Service (CFS) worked with various provincial and territorial natural resource management agencies to provide us access to geolocated ground plots within Canada's boreal ecoregions. The inventory plot measurements used in this study were collected in the Northwest Territories (2006–2008), Saskatchewan (2004–2006), Ontario (2006–2007), and Quebec (2001–2004) (Table 1). Consequently, these plot data originated from a number of different jurisdictions (Table 1). The CFS has developed species-specific, national-level equations (Lambert et al. 2005) that we used in this study to convert ground plot measurements of tree height and diameter to AGB. In Alaska, ground plot information was provided by the Forest Inventory and Assessment (FIA) Program of the USDA Forest Service (Woudenberg et al. 2010). We successfully sampled precisely 1000 geolocated forest inventory sample plots across eastern Canada, western Canada, and Alaska (Table 1) of which 303 were located in Quebec, 196 in Ontario, 80 in Saskatchewan, 57 in the Northwest Territories, and 364 in Alaska (Table 1). Land cover classifications derived from Landsat data were used for stratification and reporting of AGB by forest stratum. In Canada, we used the 25 m resolution, 23-class EOSD (Earth Observation for Sustainable Development) land cover map of Canada (Wulder et al. 2003, 2013 b ). For Alaska, we used the NLCD-2001 version 1.0 land cover product developed for Alaska at 30 m spatial resolution ( This NLCD product uses 20 land cover classes, but only four of these are forest classes (deciduous forest, conifer forest, mixed forest, treed wetland). We condensed and harmonized the two land cover classifications into the four NLCD forest classes (trees > 5 m) to obtain a uniform land cover stratification for all of boreal North America. More specifically, dense, open, and sparse covers in EOSD were harmonized with NLCD covers, respectively, for conifers, hardwoods, mixedwoods, and treed – woody wetland forest covers. Recently burned areas were overlaid onto the land cover map to provide a unique stratification for this category. Fire polygons from the Canadian Forest Service and the Alaskan Department of Natural Resources were used to define the areas burned between 2001 and 2006, the final year of GLAS acquisitions. Information from the MODIS MCD45 burned area product (Roy et al. 2006) was also used to supplement the fire polygon information when required. Fire is a very common disturbance in the boreal forests of North America, with historical annual burn rates varying from 0.2% to 2.0% across different ecoregions (Bergeron et al. 2004). The burned area biomass values reported in the current article refer only to a subset of the total burned area, i.e., surviving or regen- erating forests on areas burned between 2000 and 2006. Furthermore, harvested areas are only included in our analysis if they fell into one of our EOSD or NLCD forest cover classes, e.g., conifer, mixedwood, hardwood, or treed – woody wetland. For topographic information at the scale of individual GLAS pulses, we used version 1 of the ASTER Global Digital Elevation Model (GDEM) ( At a spatial resolution of 30 m, the ASTER GDEM has a finer resolution and more northern coverage (83°N) than the Shuttle Radar Topography Mission (SRTM) topographic product that was used for the previous PALS–GLAS analysis in Quebec (60°N, 90 m) (Boudreau et al 2008). We mosaicked the ASTER tiles for each of our three regions (Alaska, western Canada, eastern Canada), masking out data less than 3 m and more than 6195 m in elevation, the elevation of the highest mountain peak in North America. We then calculated 3 × 3 pixel slopes using the topographic modeling feature in the ENVI 4.1 image process software. For obtaining a general quantification of slopes for different ecoregions to char- acterize the overall ecoregion topography (e.g., mountainous versus flat, average slope, percentage of forested area per ecoregion above 20° slope), we used a SRTM DEM version at 250 m resolution available from Beaudoin et al. (2014). To provide a pan-biome ecosystem-oriented context, we used the WWF map of global terrestrial ecoregions (Olson et al. 2001), which we rasterized to a 1 km resolution. We used this classi- fication to stratify the North American boreal forest into bio- geographic reporting units for our AGB estimates. Of the 867 ecoregions identified globally, 22 were located in the North American boreal forest (Fig. 1). We used a model-based procedure for estimating AGB density from the ground-plot, PALS, and GLAS data (Nelson et al. 2012; Ståhl et al. 2011). In this procedure, we do not rely on a probability- based forest inventory, rather we use the ground plots that were available and that were as representative as possible of our area of interest, i.e., the plots spanned a wide east to west swath across the North American boreal forest and included plots from both southern and northern portions of the biome (Table 1). In the current case, we applied a three-phase sampling design that linked the three sampling phases (ground plots, airborne profiling lidar, and satellite lidar) via two sets of equations, i.e., a two- phase estimator. The first set of equations estimates ground plot biomass density as a function of the PALS lidar metrics. The second set of predictive equations links the PALS-derived estimates of biomass density, calculated from the first set of equations, to the GLAS metrics. We then used all of the 311 981 quality-filtered GLAS 3c and 3f pulses available in the entire study region (Fig. 3) to obtain AGB estimates for only the forest strata, i.e., conifers, hardwoods, mixedwood, and treed wetlands, where the strata types were determined by the land cover maps. Of the 311 981 quality- filtered GLAS shots, 73.4% of the pulses (229 096 pulses) were identified as measuring one of the four forest strata. Strata identified as nonforest strata, e.g., shrubs, grassland, barren, and urban, were consequently assumed to have zero AGB regardless of the GLAS measurement. Finally, these strata were condensed into the three major regions, i.e., Alaska, western Canada, and eastern Canada. The estimates of the AGB for a given stratum (land cover, ecoregion, region) from all available GLAS pulses were obtained using eqs. 1 through 4 presented in table 4 of Neigh et al. (2013). Here, we provide a brief summary of the approach. (1) An estimated mean stratum AGB density (in Mg·ha −1 ) for a single ascending or descending ICESat orbit was calculated by averaging the GLAS-based biomass estimates for all pulses intercepting that stratum along an orbit. If a particular stratum was not intercepted along a given orbit, then the stratum mean was taken to be zero. (2) The mean AGB density for a given stratum can then be multiplied by a weighting factor proportional to the area of that stratum within a region or an ecoregion or using eq. 2 from Neigh et al. (2013). (3) The variance of this mean AGB estimate across all strata is provided by eq. 3 in Neigh et al. (2013), and the variance of the individual stratum for AGB density is given in eq. 4 of Neigh et al. (2013). These variance calculations include both sampling error and model error, with the latter term quantifing the variance of the coefficient estimates of the predictive model, i.e., how much the predictive model would change with repeated samples. In the current context, there is no assumption of randomness in the selection of ground plots. However, there are three other basic assumptions for this model approach. (1) The coincident PALS– GLAS observations are characteristic of the area of interest (AOI, e.g., stratum, ecoregion, or region) and they represent the full range of conditions within the AOI. We note that our decision to exclude GLAS data on >20° slopes violates this assumption to some extent, but we explain why this should not be a major con- straint in the Discussion. (2) There is an assumption that the GLAS orbits are randomly acquired. (3) The models to predict biomass for different strata are developed independently. We compiled data from two other sources of North American boreal forest AGB to compare with the estimates obtained in our GLAS study. First, we calculated mean AGB density from Canada's National Forest Inventory (NFI) database across the Canadian terrestrial ecozones (Ecological Stratification Working Group 1996) used by NFI for reporting purposes (https://nfi.nfis.org/standardreports. php?lang=en). These calculations use NFI total AGB estimates by forest type, age class, and terrestrial ecozone. The wood volume estimates from the NFI photo plots were then converted by NFI into AGB density using allometric equations and expansion factors (Boudewyn et al. 2007; Stinson et al. 2011). Unfortunately, standard errors were not tractable at the required forest strata level, so we only had access to mean values. We weighted the respective areas of the WWF ecoregions that fell into each Canadian NFI ecozone. Next, we applied this weighting to the GLAS estimates for each WWF ecoregion to obtain an equiv- alent GLAS estimate of AGB density for a given Canadian NFI ecozone. In three of the seven cases, the two systems aligned very closely; for the other four cases, there were significant spatial differences between the two systems. In the second approach, we used 2001 AGB density maps developed at 250 m resolution (i.e., 6.25 ha) using the k ...

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... and carbon stocks in the boreal forest of North America involves combining forest inventory ground plots with growth and yield curves for different land cover types and disturbance frequencies (Stinson et al. 2011). Laser-ranging airborne lidar has the potential to provide supplemental information on aboveground biomass (AGB) density of forests and has been used in- creasingly as a sampling tool at local to regional scales (Wulder et al. 2012 a , 2012 b ). This airborne technology is particularly useful in extending AGB measurements into areas where few, if any, ground plots exist, e.g., unmanaged forest regions. Airborne lidars provide direct measurements of distances between the aircraft and various ground targets. Data processing algorithms calculate both the distance to the ground and the height above the ground of different components of the forest. From these measurements, a number of lidar metrics related to forest height and canopy structure can be derived, which can then be converted into AGB (Nelson et al. 1988). Both profiling and scanning lidars have been used as sampling tools (e.g., Nelson et al. 2012; Gobakken et al. 2012), and various statistical approaches have been developed to estimate both AGB and carbon stocks, as well as their statistical uncertainties (Gregoire et al. 2011; Ståhl et al. 2011). For example, in lidar-assisted model-based sampling, ground plots representative of the entire area of interest are selected. Models are constructed that predict ground- measured biomass as a function of lidar height and canopy density metrics, and then these models are applied to the entire area (Nelson et al. 2012). The error calculations account for the nonrandom, spatially dependent transect data obtained by the lidar (Ene et al. 2013), which is accomplished partially by using the transect as the sampling unit. Reliable measurements of forest AGB from a spaceborne lidar would be useful because such an instrument could provide repeated global-scale sampling of variables related to forest height from which regional and global biomass could be derived. The first opportunity to explore the utility of a global sample of satellite-based lidar measurements occurred in 2003 when ICESat-1 (Ice Cloud and land Elevation SATellite) was launched with the Geosciences Lidar Altimetry System (GLAS) aboard. Using the GLAS waveform lidar, the ICESat mission's main objective was to measure changes in the mass balance of the polar ice sheets, and it collected ice elevation data from 2003 to 2009. However, GLAS also offered the scientific community the possibility of estimating forest height and AGB, although the sensor was not ex- plicitly designed for this objective. Global tree height maps have been developed (Simard et al. 2011) and Bolton et al. (2013) compared this information with tree height data in Canada and found that discarding GLAS waveforms from steep terrain reduced errors in height estimates. Boudreau et al. (2008) and Nelson et al. (2009 a ) applied a sampling approach for 1.3 million km 2 of forest in the province of Quebec that involved three different sampling phases, i.e., ground, airborne, and satellite. The basic approach involved ( i ) building an initial statistical model to link PALS (Portable Airborne Laser System) height measurements to ground plot biomass, ( ii ) building a second model to relate the estimated biomass from the airborne lidar to the height metrics obtained by GLAS for the 1325 GLAS pulses that were flown by the aircraft, and ( iii ) using the GLAS height metrics, slope, and land cover for the ϳ 104 000 quality-filtered GLAS pulses available across the province of Quebec to calculate the AGB and carbon stocks for the province by land cover type. In 2008 and 2009, we extended the PALS lidar measurements of ground plots and GLAS ground tracks to the rest of Canada and Alaska. Neigh et al. (2013) used these data in an analysis of the aboveground carbon stocks of the entire circumpolar boreal forest by combining the North American data with similar data in Scandinavia (Næsset et al. 2011) and only ground plot and GLAS data in Siberia (Nelson et al. 2009 b ). They were thus able to compare aboveground carbon stocks between the different regions of the circumpolar boreal. The goal of the current study is to report for the first time on the detailed results for the three-phase sampling of the 3.7 million km 2 of the North American boreal forest. We extend the work of Neigh et al. (2013) by reporting detailed estimates of the amount, distribution, and uncertainty of the AGB of the different ecoregions and land cover classes within the boreal forest of North America, analyze some of the factors driving the error estimates, compare our AGB estimates with other available estimates in Canada, and offer our perspectives on the future of lidar sample-based approaches for forest biomass estimation. The study area encompasses the boreal forest biome within Canada and Alaska (Fig. 1) and ranges from a minimum latitude of 44.4°N to a maximum of 69.0°N and from longitudes 52.6°W to 165.0°W. Various definitions and maps of the North American boreal forest have appeared in the literature (e.g., Brandt 2009; Olson et al. 2001). The boundaries of the boreal forest used in the current study were based on those proposed by Brandt (2009, see his fig. 22) for Canada. The Brandt (2009) boundaries were estab- lished by digitizing and then harmonizing several existing maps. The northern extent of the boreal forest was defined as the northern tree limit, i.e., the taiga–tundra boundary. Consistent with the traditional approach used in North America for defining the boreal forest, we do not include eastern hardwood forests (e.g., areas in which cold-intolerant hardwoods begin to intermingle with cold-tolerant tree species). On the other hand, we decided to include the Canadian Aspen Forests and Parklands ecoregion in our boreal forest area as it is such an important transition zone that is highly vulnerable to climate change (Michaelian et al. 2011) and is generally considered to be in the boreal zone. For Alaska, we applied additional adjustments to the Brandt (2009) map to retain consistency with the World Wildlife Fund (WWF) ecoregions used as the spatial reporting units (see below). We truncated our boreal biome at the northern US – southern Canadian border, which allowed us to more readily report biomass for the boreal forest in Canada. Areal extents of the boreal forests of Canada and Alaska for our study were 3 326 658 km 2 (90%) and 370 074 km 2 (10%), respectively. Launched on 12 January 2003, the ICESat satellite carried three lasers packaged within the Geoscience Laser Altimetry System (GLAS). GLAS was the first spaceborne lidar instrument developed for continuous global observations of the Earth. The three lasers were deployed sequentially over the life of the satellite (January 2003 to October 2009). For the current study, we used GLAS data acquisitions 3c and 3f, both of which relied on the last of the three lasers. These collections were used because ( i ) they were the most recent acquisitions available when laser power was still high enough for forest applications and ( ii ) these acquisitions were collected during the growing season in June 2005 and 2006, respectively, and therefore avoided possible contamination of the data from either snow cover or leaf-off conditions. Previous forest inventory studies that used GLAS as a regional sampling tool in Quebec (Nelson et al. 2009 a ; Boudreau et al. 2008) and Siberia (Nelson et al. 2009 b ) used acquisition 2a. This acquisition, collected between 24 September and 17 November 2003, was used in these previous studies because, at the time that the results were compiled, it was the only acquisition available that was acquired under close to leaf-on conditions. In the current study, the more temporally suitable acquisitions 3c and 3f, collected from 8 to 13 June 2005 and from 8 to 26 June 2006, respectively, were used. However, the differences in the GLAS acquisitions used, combined with the differences in the spatial reporting units, prevent us from making useful quantitative comparisons of AGB between the two studies. In the current study, we only used GLAS pulses that were obtained from footprints that had slopes of <20 degrees as determined by the ASTER DEM (Advanced Spaceborne Thermal Emission and Reflection Radiometer Digital Elevation Model). This was based partially on our analyses of slope effects on bio- mass regressions from our earlier study (Boudreau et al. 2008). Below, we provide more information on the ASTER DEM. GLAS collected altimetry data using a 1064 nm laser sending pulses at 40 Hz with a ground footprint that varied in size and shape with laser power, although laser power decreased markedly over time. During acquisitions 3c and 3f, the size of the elliptical footprint of the GLAS pulse was nominally ϳ 60 m × ϳ 40 m, and the distance between pulses was 172 m (Neigh et al. 2013). The GLAS sensors collected waveform data on the intensity of the energy returned from a laser pulse, thus providing information on the vertical distribution of canopy structure (Boudreau et al. 2008). In this study, we made use of both a standard GLAS data product (GLA14) provided by the National Snow and Ice Data Center (NSIDC) and extracted our own structural metrics from the raw waveforms (GLA01) data product. GLA14 is the standard laser altimetry product that uses information from the waveforms recorded over vegetated land by fitting up to six Gaussian distributions to the waveform to describe different features of the vertical structure of the vegetation. The raw GLA01 waveforms were used to calculate additional forest canopy metrics related to forest height and canopy density such as median, mean, and quadratic-mean canopy height, height of different levels of energy return, descriptors of the waveform such as total waveform ...