On the NASA GEDI and ESA CCI biomass maps: aligning for uptake in the UNFCCC global stocktake

The two products compared in this study, i.e. GEDI and CCI estimates of AGBD, are produced independently using different approaches. Fundamentally, the GEDI approach is based on regression models and in situ reference data, and the CCI on both regression and simplified semi-empirical models, and various national/sub-national reports of AGBD (see table 1). Below, we state some of the common challenges relevant to AGBD estimation.

• 1.  
  The GEDI products are estimates derived at the footprint-level from waveform light detection and ranging (LiDAR), covering tropical and temperate forests between 51.6^∘ latitude N & S, which are used to extract information on canopy height and 3D structure (Dubayah et al 2020). GEDI relative height (RH) metrics have shown high consistency with forest structure (e.g. Adrah et al 2021, Liu et al 2021, Li et al 2023), although the over/under-estimation of ground elevation over seasonally flooded waters, or in complex topography, can hinder the extraction of these metrics (Urbazaev et al 2022, Bruening et al 2023). The GEDI L4B version 2, which is an AGBD estimate over 1 km × 1 km grid cells, has gaps owing to limited spatial coverage up until 2021.
• 2.  
  The CCI product is at a wall-to-wall global scale, produced using a variety of sensors, particularly imaging sensors of SAR. It relies primarily on the inversion of the semi-empirical water cloud model (WCM) (Askne et al 1997), relating AGBD (as a covariate) to SAR backscatter (as a response variable) (Santoro et al 2023a). Backscatter is known to be sensitive to surface moisture and prone to signal attenuation (Joshi et al 2017). To prevent the prediction of unrealistic AGBD values, multiple steps are taken; these involve (1) weighting stacks of multi-temporal SAR images (Santoro et al 2021), (2) constraining model parameters to a theoretical model of signal attenuation, number of observations and topography (Santoro et al 2021), and (3) constraining spaceborne-LiDAR height estimates, and AGBD estimates, to maxima based on height distributions and various literature across global regions (Santoro et al 2022).

Table 1. Summary of the NASA Global Ecosystem Dynamics Investigation (GEDI) and ESA Climate Change Initiative (CCI) 2020 Biomass map products. Product Algorithm Theoretical Basis Documents are available at Healey et al (2022) and Santoro et al (2023a).

	GEDI hybrid product	CCI 2020 version 4
Input type	LiDAR	LiDAR and SAR
Mission	GEDI	ALOS-2, Sentinel-1, ICESat and ICESat-2
Years	2019–2021	2020
Area or pixel size	Arbitrary or gridded (e.g. 1 km × 1 km)	∼100 m × 100 m at equator
Domain	$\pm\sim$51.6∘ lat	Global
Source of AGBD reference data	Compilation of globally distributed in situ plots with coincident airborne LiDAR (Duncanson et al 2022)	National/sub-national AGBD estimates, acquired from published NFI reports or FAO Forest Resource Assessments (FAO 2020).
Method	First, simulated GEDI waveforms are used to relate relative height (RH) metrics and the training AGBD estimates in 13 allometric models across broad global strata; four plant functional types (PFTs) and six geographic regions (Kellner et al 2023). Second, the models are applied to predict AGBD from GEDI RH metrics at 25 m footprint-level in regions with different combinations of the global strata, producing the L4A product (Dubayah et al 2022a). AGBD training data is not used in this step. Third, mean AGBD and variance is estimated from the L4A product, over either arbitrary irregularly-shaped regions (e.g. countries) or grid cells (e.g. the 1 km L4B product) in the GEDI gridded AGBD product (Dubayah et al 2022b).	First, spaceborne LiDAR data are used to relate mean canopy height and density metrics to reference AGBD estimates (compiled from the various reports) in two allometric models for each of 20 broad global strata. Second, only the parameters estimated in the allometric models are used to formulate a semi-empirical water cloud model (WCM), relating SAR backscatter (response variable) to AGBD and vegetation- and ground-components of scattering (as covariates) over the global strata. AGBD training data is not used in this step. Third, the WCM is inverted to estimate AGBD for each of N SAR images in a year, which are linearly weighted to obtain a single AGBD estimate. The procedure is applied separately to C- and L-band scenes, with outputs linearly weighted to derive a final AGBD estimate.
Data masks	Urban areas, open water-bodies and vegetation phenology from a set of external land cover data sources.	Cropland, urban areas, bare soil, permanent snow and ice, and water bodies from a set of external land cover data sources.
Precision of estimated AGBD	The standard error (SE) is reported per arbitrary region or per grid cell. Estimation is based on statistical sampling theory; the algorithm uses hybrid inference accounting for model parameter variability (i.e. in the covariance of the field-to-LiDAR L4A models) and sampling variability (e.g. the variation of AGBD means in GEDI tracks). Model residual errors are considered comparatively negligible at scales of 1 km grid-cells or larger (Patterson et al 2019).	The standard deviation (SD) is reported per 100 m pixel, or spatially aggregated to coarser resolutions. Estimation is based on the variance in numerous inputs to the many sequential regression or semi-empirical models in the algorithm. Specifically, the variance in model parameters and covariates, and residual errors, are accounted for. The variance in input AGBD training values from the public reports, however, is not accounted for Santoro et al (2023b).

Before inter-comparing the products, a clarification of the terminology used for products' uncertainties (i.e. their precision and systematic errors) is warranted; precision is the 'variability around an estimated value' (i.e. the spread of its confidence interval (CI)), systematic error is the 'degree to which the estimated value deviates from the true population value', and negligible or non-existent systematic errors are an indication of accurate estimates Duncanson et al (2021), ch 4.

Crucially, the two products use different analytical frameworks to describe and estimate precision (table 1). As a product based solely on discrete samples, hybrid inference is used to estimate the SE of AGBD in each 1 km × 1 km grid cell of the GEDI L4B product, and over larger arbitrary-sized regions. The hybrid estimate combines (1) sampling variability (i.e. the variability among the GEDI tracks, each consisting of shots with predicted AGBD) and (2) model parameter variability (i.e. the uncertainty in the parameter estimates used to predict AGBD in the 25 m footprint-level L4A models). Residuals of the models (i.e. differences between observed and predicted AGBD) are comparatively negligible (relative to the sampling and model components) when aggregated over 1 km or larger cells/areas, and hence are not included in variance estimates (Patterson et al 2019, Dubayah et al 2022b). In contrast, the CCI product, on account of the suite of input data, is described by a number of regression and semi-empirical models that sequentially include estimates, whose errors arise from preceding models and propagate to subsequent models (Santoro et al 2021, 2023b). The variance of final AGBD predictions incorporates (1) the variance in all models' parameter estimates and in some covariates and response variables, and (2) model residual errors. However, the challenge in a comprehensive one-to-one comparison with GEDI products arises from differing statistical terminology with a lack of explicitly reported model results. The sampling variance, i.e. the variance associated with national/sub-national AGBD estimates in the various reports contributing to the compiled reference dataset (see table 1), is not rigorously assessed, primarily due differences in reporting protocols and incomplete information in the source documents. Hence, overall, the same components of variance in the final estimated AGBD, as those of the GEDI product, are not captured in the CCI product.

The above-mentioned differences imply that the products' reported precisions are not directly comparable. At the very best, the products can be compared to in situ data and the overlap of their prediction CIs, insofar as they are rigorously estimated and reported, can be investigated. To avoid erroneous inference in this study, the CCI product is treated as point estimates at pixel-level with unknown CIs, and the need for aligned analytical frameworks discussed in section 4.

For the purpose of map inter-comparison, the WWF Terrestrial Ecoregions of the World (TEOW), which defines lands 'containing distinct assemblages of natural communities and species' (Olson et al 2001), is used to delineate the 688 ecoregions grouped in 13 biomes across the GEDI range of observation. For these ecoregions, the CCI and GEDI L4B product (i.e. the 1 km gridded hybrid estimate), with GEDI's reported precision, are compared as follows:

• 1.  
  At the ecoregion-level, the mean estimated AGBD from each product is compared to identify if, where, and by how much the products differ. The values are also aggregated by continent and TEOW biomes (each containing a variety of ecoregions), to test whether systematic differences (if any) are driven by geographical location or climate zones.
• 2.  
  At the 1 km grid level, the 95% CI (i.e. $\pm 1.96\,\times$ SE) for each cell is estimated in the GEDI product to test if the mean CCI AGBD is contained within its range. Then, for each ecoregion, the fraction of pixels where this difference is non-significant, i.e. CCI falls within the GEDI 95% CI, is recorded. This exercise is not a validation of either product and the assumptions made here are important to note - (1) for GEDI, the hybrid estimator of mean AGBD and variance is unbiased (Patterson et al 2019), and violations of the assumptions of the estimator can be identified by systematic deviations to ground-truth data (Dubayah et al 2022b), and (2) for CCI, we assume the estimator of the mean is unbiased, until the contrary is proven with ground-truth data.

Neither of the two approaches informs on products' accuracies. The first reveals if, by how much, and where the products differ most. The second reveals if the AGBD estimates reported in one have CIs that contain the AGBD estimates of the other; areas with very precise GEDI hybrid estimates (narrow CIs), but large differences between the maps, are likely to most require independent reference data to assess accuracy. Further, areas with imprecise estimates (wide CIs) and large differences between the maps are likely to most benefit from reference plots to improve model calibration. Statistical inference for the above is based on generalized linear models (GLMs).

Across four countries—Mexico, Peru, Lao People's Democratic Republic (Lao PDR) and Spain—NFIs were compiled to compare against the AGBD map estimates (table 2). The developing countries, where reporting to UNFCCC is infrequent or incomplete (Grassi et al 2022, Melo et al 2023), could benefit from regular biomass assessments while transitioning to more stringent requirements of the Paris Agreement (UNFCCC 2019). Spain was chosen for two reasons: (1) Spain's NFI covers diverse ecosystems from Atlantic forests and fast-growing plantations in the North, to the Pyrenees mountains and sparse vegetation in Central Spain and the Canary Islands, and (2) it is a country where there are few differences between the CCI and GEDI estimates of AGBD, and where an advanced, systematically-designed, and dense NFI plot network allows sub-national comparisons. These exercises serve only as a means to comparatively assess the performance of products; the use of NFI reports to calibrate the CCI models (see table 1), although without plot-level data, precludes independent product validation with NFIs.

Table 2. Summary of the national forest inventory (NFI) data analyzed. The sample size indicates the number of plots/sub-plots visited on the field, based on each country's sampling design. The designs, and the equations of the statistical estimators, are detailed in supplementary information, section 2.

Country	Sample size	NFI cycle (years)	No. of forest strata	Sampling design	Statistical estimator
Mexico	9955	3$^\mathrm{rd}$ cycle (2015 to 2019)	11	Systematic grids of $5\times5$ km for temperate/tropical forests, $10\times10$ km for semi-arid, and $20\times20$ km for arid areas, with 1-ha plots consisting of four sub-plots of ∼11 m radius (CONAFOR 2017)	Simple expansion estimator
Peru	358	Ongoing (2011 to date)	5	Non-aligned systematic sampling, with plots located randomly within grid-cells of varying sizes (SERFOR 2019)	Nationally-defined estimators
30 Spanish regions/ provinces	39 534	4th cycle (2008 to 2019)	2	Systematic 1 km grid, with sample units of four circular concentric plots of radius 5, 10, 15, and 25 m (Álvarez-González et al 2014)	Simple expansion estimator
Lao PDR	1394 secondary sampling units (SSUs)	3$^\mathrm{rd}$ cycle (2019)	5	Two-stage stratified random sampling; primary sampling units (PSUs) were 3 km wide squares, and 4 circular plots (SSUs) of 20 m radius were chosen within selected PSUs (DOF 2019)	Two-stage estimator for unequal areas of strata within PSUs

Comparisons to NFIs follow the CEOS Biomass Validation Protocol (Duncanson et al 2021), wherein the mean, SE and 95% CI of AGBD are estimated over each nationally-defined forest stratum, with forest/non-forest masks. The estimates are compared to the mean estimated CCI AGBD or GEDI hybrid AGBD (i.e. a single AGBD and variance estimate for each arbitrary-sized forest stratum). Since GEDI's hybrid inference framework provides the precision of AGBD estimates, deviations from reference data can be assessed in a fully probabilistic manner. The CCI product does not have a comparable framework for large-area assessments, and only the mean stratum-wise AGBD estimate is examined.

Statistical inference is based on Fay–Herriot small area estimation (FH-SAE) models (Fay III and Herriot 1979, Rao and Molina 2015). FH-SAE models account for sampling error in the response variable, the stratum population estimates, and infer the relationships between the true (but unknown) population means and model covariates. Here, 'sampling error' refers to random variation in the NFI estimates due to finite within-stratum samples, and for the map-products, finite AGBD training data. Accounting for such variation allows inference on underlying systematic deviations, while filtering random deviations occurring simply due to finite sampling. Specifically, we assume

$$\begin{equation} \hat{y} = y + \delta, \end{equation} \tag{ 1 }$$

where $\hat{y}$ is the given stratum population estimate, y is the unknown expected value of this estimate, and δ is the sampling error. Error δ is assumed to have zero mean and known variance, where the variances are inherited from the associated product- or NFI-estimated AGBD (note, CCI's contribution to δ is omitted by necessity). The difference in the product and NFI estimates is set to $\hat{y}$, and y is the expected value of this difference upon infinite re-sampling. We further assume the regression model

$$\begin{equation} y = \alpha + x\beta + \epsilon, \end{equation} \tag{ 2 }$$

where x is a model covariate, $\alpha,~\beta$ are regression coefficients, and ε is model prediction error, giving the remaining variation between the unknown expected value, y, and the regression line. We can also entirely omit covariate effect $x\beta$, leaving only the intercept α and model prediction error, creating a null model where α represents the expected difference in estimates across all forest strata (supplementary information, section 1). Code for the FH-SAE models is available at Hunka et al (2023).

The estimation of mean AGBD and associated variance from NFIs (inputs to the FH-SAE models) required different approaches in the four countries. For Peru, estimates were provided directly by the Servicio Nacional Forestal y de Fauna Silvestre (SERFOR 2023) for five strata from the Amazonian lowlands to coastal areas. For the other countries, estimators were developed taking into consideration their NFI sample designs. Plot/sub-plot AGBD estimates were acquired in Mexico and Spain, where one can assume equal probability systematic sampling designs, and use simple expansion estimators (supplementary information, section 2a). In the Lao PDR, tree-level information and a land strata map were provided by the Department of Forestry (DOF 2019). The mean AGBD and variance estimates required consideration of two-stage sampling accounting for the occurrence of various forest types (e.g. mixed broadleaves, conifers, dry deciduous forests etc) in each map-delineated stratum. A two-stage estimator of Lohr (2010), equations (5.26) and (5.28) was applied (supplementary information, section 2b). Hence, stratum-wise mean AGBD and variance are not to be compared with nationally-reported forest-type estimates in the Lao PDR.

Globally, averaged over ecoregions, the differences in estimated means of AGBD from the CCI and GEDI products range largely between −50 and +25 Mg ha⁻¹ (the 10th to 90th percentile) and show a geographic pattern (figure 2(a)); they are largest in the tropical-subtropical moist broadleaf biomes, where CCI predicts greater AGBD than the GEDI product, and in tropical-subtropical conifers, where CCI predicts less than GEDI. By continent, systematic and significant differences are found, e.g. the CCI product is found to systematically predict more AGBD in nearly all biomes in South America (GLM, p $\lt$ 0.05, supplementary information, section 3). In contrast, large parts of east Asia (e.g. southern China) and southeast Asia show systematically less AGBD across biomes including temperate and tropical forests, in the CCI product (GLM, p $\lt$ 0.05).

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Despite the differences in the products across the tropical belt, the CCI product's estimates fall within the reported 95% CI of GEDI's hybrid estimates across many tropical ecoregions. This is true in the tropics of South America and Southeast Asia, where in some ecoregions up to 50% of cells have an overlap of AGBD estimates (figure 2(b)). In contrast, AGBD differences over the Congolese moist broadleaves in Africa are large, GEDI 95% CIs are relatively narrow, and the estimates overlap in only ∼20$\%$ of cells. Disagreements are also observed in temperate biomes of South America and Indochina (i.e. the continental region of southeast Asia), highlighting particularly mismatched ecoregions. Finally, the low fraction of overlap of CCI estimates with GEDI 95% CIs in the African woodlands/savanna/grasslands, central Asia and northern Australia are noted, although these areas generally have low absolute differences in estimated AGBD (∼20 Mg ha⁻¹) between the two products (figure 2(a)).

Unlike the product inter-comparison, comparisons of map-estimated and NFI-estimated AGBD provide a basis to assess the relative performance of the products (note, since stratum-wise variance in CCI estimates are omitted, its results must be interpreted with caution). Overall, the relation between stratum-wise mean estimated AGBD of the maps and NFIs is found to be strong for both products (figure 3); the trend from high to low AGBD estimates is largely captured across all strata in the four countries combined, with no significant under- or over-prediction in either product (p $\gt$ 0.05, null FH-SAE models (1) and (3), table 3). In over half the forest strata (47 of 80), either one or both products are accurate, i.e. they overlap the 95% CIs of NFI-estimated AGBD (figure 4). Note, this fraction may have been larger if the 95% CIs of estimated AGBD were assessed for CCI. In the Peruvian Amazon, which is the AGBD-richest stratum with largest area, both products perform particularly well. Stratum-specific deviations, however, remain problematic for operational use of the products for national reporting. In the following, we examine their possible causes more closely.

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Table 3. Results of FH-SAE models (equation (2)) relating stratum-wise product- and NFI-estimated AGBD. The null models have a single response variable equal to the difference of the estimates, and no covariate effects. $\hat{R}^{2}$ values can be interpreted as the fraction of variation in this difference, omitting sampling error, explained by Slope90p (i.e. the 90th percentile of SRTM slopes mapped at a 1 km). Parameter $\hat{\sigma}^2$ is the estimated variance of the model prediction error and SE is the standard error the coefficient estimate.

	FH-SAE Model	Coefficient	Estimate	SE	t-value	p-value	$\hat{\sigma}^2$	$\hat{R}^{2}$
(1)	GEDI − NFI ∼ null	$\hat{\alpha}$ (Intercept)	0.36	5.81	0.06	0.95	396.77	NA
(2)	GEDI − NFI ∼ Slope90p	$\hat{\alpha}$ (Intercept)	−48.54	9.39	−5.17	2.00	20.28	0.95
		$\hat{\beta}$ (slope)	3.15	0.52	6.07	4.34$\times 10^{-08}$
(3)	CCI − NFI ∼ null	$\hat{\alpha}$ (Intercept)	9.33	5.2	1.79	0.08	247.27	NA
(4)	CCI − NFI ∼ Slope90p	$\hat{\alpha}$ (Intercept)	−23.36	10.02	−2.33	1.98	67.55	0.73
		$\hat{\beta}$ (slope)	2.34	0.57	4.09	1.06$\times 10^{-04}$

3.2.1. Estimates in mountainous forest strata

Over mountains (e.g. mesophytic and conifer forests of Mexico, and highlands in Peru and Lao PDR), AGBD is over-predicted in the GEDI hybrid product. Topographic slope (here, the within-stratum distribution of Shuttle Radar Topography Mission (SRTM, averaged to 1 km) slopes (NASA 2013)) was tested as a covariate to explain the differences in stratum-wise mean GEDI and NFI AGBD estimates. FH-SAE models reveal that the 90th percentile of slope distribution in each stratum can largely explain these differences, while filtering sampling error (p $\lt$ 0.01 on $\hat{\beta}$ -slope, FH-SAE model (2), table 3). This observation is a subject of ongoing research (e.g. Bruening et al 2023); signal processing errors caused by multi-modal LiDAR waveforms over complex terrain, or mis-identification of waveform noise as ground/canopy signal, can cause underestimation of ground elevation and/or overestimation of canopy height. This can lead to high values of RH metrics (e.g. RH98 in Mexico, figure 5(a), that in turn result in an over-estimation of L4A 25-m footprint AGBD and the subsequent over-estimation in the GEDI hybrid product. A significant (p $\lt$0.01 on $\hat{\beta}$ -slope, FH-SAE model (4), table 3) influence of topographic slope is also noted when relating the CCI to NFI estimates. However, constraining spaceborne LiDAR height metrics to maxima in the CCI algorithm challenges conclusive interpretations of the FH-SAE model results.

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3.2.2. Limitations of the underlying models

First, regardless of the use of the AGBD maps, they must move towards a consistent and common analytical framework for defining and reporting information on the precision of AGBD estimates. Conflicting statistical terminology is unappealing and has led to considerable confusion on the products' alignment with IPCC terminology and their applicability to national/sub-national assessments. The GEDI products provide a strong example of such a framework, breaking down reported precision into the categories of sampling, model prediction and residual variability (negligible over large areas). This holistic overview of the precision of AGBD predictions implies that meeting IPCC guidelines for large-area assessments (see below) is a likely prospective. For the CCI product, specifically, setting the many model results (including values of variance-covariance matrices of each model's estimated parameters and variance of each response variable), in a comparable analytical framework is recommended. If the error arising due to variance in the AGBD training dataset is estimated, the contributing sources of error in the predictive models of the two maps will be aligned. If addressed in future iterations, the information may not only enable direct comparisons to GEDI products, but also assessments of how changes in the CCI methods impact the precision of its estimates.

Second, primarily if the maps are the only source of data (e.g. for countries without NFIs), the development of transparent, well-documented and open-source code to estimate mean and total biomass stocks with associated uncertainties over arbitrarily large areas must be resourced and publicly released. This is crucial; users cannot estimate uncertainty at national or sub-national scales, nor validate the maps in any statistically rigorous way without input from the map producers, and often do not have the expertise to do so even if relevant data are available. Such open-source codes must incorporate processing the covariance amongst map-unit values, i.e. spatial correlations of uncertainties from pixel to pixel, when aggregating maps-units. Further, they should be flexible to allow users to mask map-units based on national definitions of forest strata. Finally, if they are designed to allow for the insertion of reference data, they must return the 'residual differences between map unit values and reference data' as well as 'the covariance among the residual differences' (GFOI 2020). It is only with such information can a comprehensive and statistically rigorous report of uncertainty be generated for policy purposes. As open-science developments at both ESA and NASA shift to high-computing cloud-based platforms, the operational launch and upkeep of such codes is already feasible. The NASA-ESA Multi-mission Analysis and Algorithm Development Platform (MAAP) is one such ideally-positioned platform; it is a collaborative open-source science tool being developed at both space agencies, it can host multiple global AGBD maps, and it can support fast computing for large-area AGBD estimation transparently and comprehensively for research and public use.

Third, in the context of nations with NFIs (whether preliminary or advanced), guidance on methods and open-source codes to enhance national-level biomass stock estimates are urgently required. For these nations, the map-based AGBD products will be used as a auxiliary source of data to facilitate compliance with the second IPCC good practice guideline to reduce uncertainties. Here, design-based estimators that underlie the integration of the two (i.e. the NFI data and AGBD maps) do not rely on an exhaustive breakdown of the sources of uncertainty (see examples in Næ sset et al (2020) and Málaga et al (2022)). Instead, the nations need practical guidance on how to relate plot-based to map-based AGBD estimates for their specific NFI sampling designs. For this, scientists should agree on rigorous statistical procedures to enhance national and sub-national estimates with AGBD maps. These exercises must be conducted with, and ideally co-led by, designated national experts to ensure adequate collaboration, knowledge transfer and trust in the products. They should also be open-source, transparent and flexible to allow for the inclusion of new AGBD maps, as they are publicly released. Active support and liaising with the Global Forest Observations Initiative's Methods and Guidance Documentation component (GFOI 2020) to provide unambiguous examples, for a range of data from countries with basic to advanced NFIs, is strongly advised.

Current documentation supporting space-based AGBD maps, including products beyond the two examined in this study, appeals primarily to scientific readership. While a number of recent CEOS initiatives have narrowed the science-communication gap (e.g. biomass harmonization portal (NASA 2021) and Online Biomass Inference using Waveforms and iNventory with GEDI (OBIWAN 2023)), considerable effort is needed to effectively support UNFCCC processes, i.e. NGHGI measurement and reporting, and the provision of independent estimates to inform the GST. For both of these processes, the products made available in public platforms need to be presented in a manner consistent with IPCC guidance. This may be achieved, for example, by clearly declaring if map-based AGBD estimates can be used in the equations recommended in IPCC Generic Methodologies to estimate carbon stock changes (ch 2 in IPCC 2006, with examples in supplementary information, section 4). The generation of map-based AGBD estimates as in the IPCC tables for Tier 1 approaches (i.e. tables 4.7 to 4.10 in ch 4, IPCC (2019)) is another such practical presentation of the maps. The release of such independently assessed and unambiguous information, particularly if accompanied with estimates of uncertainty, can also effectively support technical expert reviews of submissions to the UNFCCC.