Science-based approach for credible accounting of mitigation in managed forests

Background

The credibility and effectiveness of country climate targets under the Paris Agreement requires that, in all greenhouse gas (GHG) sectors, the accounted mitigation outcomes reflect genuine deviations from the type and magnitude of activities generating emissions in the base year or baseline. This is challenging for the forestry sector, as the future net emissions can change irrespective of actual management activities, because of age-related stand dynamics resulting from past management and natural disturbances. The solution implemented under the Kyoto Protocol (2013–2020) was accounting mitigation as deviation from a projected (forward-looking) “forest reference level”, which considered the age-related dynamics but also allowed including the assumed future implementation of approved policies. This caused controversies, as unverifiable counterfactual scenarios with inflated future harvest could lead to credits where no change in management has actually occurred, or conversely, failing to reflect in the accounts a policy-driven increase in net emissions. Instead, here we describe an approach to set reference levels based on the projected continuation of documented historical forest management practice, i.e. reflecting age-related dynamics but not the future impact of policies. We illustrate a possible method to implement this approach at the level of the European Union (EU) using the Carbon Budget Model.

Results

Using EU country data, we show that forest sinks between 2013 and 2016 were greater than that assumed in the 2013–2020 EU reference level under the Kyoto Protocol, which would lead to credits of 110–120 Mt CO₂/year (capped at 70–80 Mt CO₂/year, equivalent to 1.3% of 1990 EU total emissions). By modelling the continuation of management practice documented historically (2000–2009), we show that these credits are mostly due to the inclusion in the reference levels of policy-assumed harvest increases that never materialized. With our proposed approach, harvest is expected to increase (12% in 2030 at EU-level, relative to 2000–2009), but more slowly than in current forest reference levels, and only because of age-related dynamics, i.e. increased growing stocks in maturing forests.

Conclusions

Our science-based approach, compatible with the EU post-2020 climate legislation, helps to ensure that only genuine deviations from the continuation of historically documented forest management practices are accounted toward climate targets, therefore enhancing the consistency and comparability across GHG sectors. It provides flexibility for countries to increase harvest in future reference levels when justified by age-related dynamics. It offers a policy-neutral solution to the polarized debate on forest accounting (especially on bioenergy) and supports the credibility of forest sector mitigation under the Paris Agreement.

     

Estimating urban above ground biomass with multi-scale LiDAR

Background

Urban trees have long been valued for providing ecosystem services (mitigation of the “heat island” effect, suppression of air pollution, etc.); more recently the potential of urban forests to store significant above ground biomass (AGB) has also be recognised. However, urban areas pose particular challenges when assessing AGB due to plasticity of tree form, high species diversity as well as heterogeneous and complex land cover. Remote sensing, in particular light detection and ranging (LiDAR), provide a unique opportunity to assess urban AGB by directly measuring tree structure. In this study, terrestrial LiDAR measurements were used to derive new allometry for the London Borough of Camden, that incorporates the wide range of tree structures typical of an urban setting. Using a wall-to-wall airborne LiDAR dataset, individual trees were then identified across the Borough with a new individual tree detection (ITD) method. The new allometry was subsequently applied to the identified trees, generating a Borough-wide estimate of AGB.

Results

Camden has an estimated median AGB density of 51.6 Mg ha^–1 where maximum AGB density is found in pockets of woodland; terrestrial LiDAR-derived AGB estimates suggest these areas are comparable to temperate and tropical forest. Multiple linear regression of terrestrial LiDAR-derived maximum height and projected crown area explained 93% of variance in tree volume, highlighting the utility of these metrics to characterise diverse tree structure. Locally derived allometry provided accurate estimates of tree volume whereas a Borough-wide allometry tended to overestimate AGB in woodland areas. The new ITD method successfully identified individual trees; however, AGB was underestimated by ≤?25% when compared to terrestrial LiDAR, owing to the inability of ITD to resolve crown overlap. A Monte Carlo uncertainty analysis identified assigning wood density values as the largest source of uncertainty when estimating AGB.

Conclusion

Over the coming century global populations are predicted to become increasingly urbanised, leading to an unprecedented expansion of urban land cover. Urban areas will become more important as carbon sinks and effective tools to assess carbon densities in these areas are therefore required. Using multi-scale LiDAR presents an opportunity to achieve this, providing a spatially explicit map of urban forest structure and AGB.

     

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.     

Improving GOCE cross-track gravity gradients

The GOCE gravity gradiometer measured highly accurate gravity gradients along the orbit during GOCE’s mission lifetime from March 17, 2009, to November 11, 2013. These measurements contain unique information on the gravity field at a spatial resolution of 80 km half wavelength, which is not provided to the same accuracy level by any other satellite mission now and in the foreseeable future. Unfortunately, the gravity gradient in cross-track direction is heavily perturbed in the regions around the geomagnetic poles. We show in this paper that the perturbing effect can be modeled accurately as a quadratic function of the non-gravitational acceleration of the satellite in cross-track direction. Most importantly, we can remove the perturbation from the cross-track gravity gradient to a great extent, which significantly improves the accuracy of the latter and offers opportunities for better scientific exploitation of the GOCE gravity gradient data set.     

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.     

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.     

Three-frequency BDS precise point positioning ambiguity resolution based on raw observables

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers.     

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the \(4 \pi \) fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as \(2^{30}\,{\approx }\,10^9\). The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.     

An iteratively reweighted least-squares approach to adaptive robust adjustment of parameters in linear regression models with autoregressive and <Emphasis Type="Italic">t</Emphasis>-distributed deviations

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model.