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Lifeng Guo; Xiaoye Zhang; Junting Zhong; Deying Wang; Changhong Miao; Licheng Zhao; Zijiang Zhou; Jie Liao; Bo Hu; Lingyun Zhu; Yan Chen

doi:10.1016/j.eng.2023.02.017

Engineering ›› 2024, Vol. 33 ›› Issue (2) :285 -297. DOI: 10.1016/j.eng.2023.02.017

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Abstract

CO₂ is one of the most important greenhouse gases (GHGs) in the earth’s atmosphere. Since the industrial era, anthropogenic activities have emitted excessive quantities of GHGs into the atmosphere, resulting in climate warming since the 1950s and leading to an increased frequency of extreme weather and climate events. In 2020, China committed to striving for carbon neutrality by 2060. This commitment and China’s consequent actions will result in significant changes in global and regional anthropogenic carbon emissions and therefore require timely, comprehensive, and objective monitoring and verification support (MVS) systems. The MVS approach relies on the top-down assimilation and inversion of atmospheric CO₂ concentrations, as recommended by the Intergovernmental Panel on Climate Change (IPCC) Inventory Guidelines in 2019. However, the regional high-resolution assimilation and inversion method is still in its initial stage of development. Here, we have constructed an inverse system for carbon sources and sinks at the kilometer level by coupling proper orthogonal decomposition (POD) with four-dimensional variational (4DVar) data assimilation based on the weather research and forecasting-greenhouse gas (WRF-GHG) model. Our China Carbon Monitoring and Verification Support at the Regional level (CCMVS-R) system can continuously assimilate information on atmospheric CO₂ and other related information and realize the inversion of regional and local anthropogenic carbon emissions and natural terrestrial ecosystem carbon exchange. Atmospheric CO₂ data were collected from six ground-based monitoring sites in Shanxi Province, China to verify the inversion effect of regional anthropogenic carbon emissions by setting ideal and real experiments using a two-layer nesting method (at 27 and 9 km). The uncertainty of the simulated atmospheric CO₂ decreased significantly, with a root-mean-square error of CO₂ concentration values between the ideal value and the simulated after assimilation was close to 0. The total anthropogenic carbon emissions in Shanxi Province in 2019 from the assimilated inversions were approximately 28.6% (17%-38%) higher than the mean of five emission inventories using the bottom-up method, showing that the top-down CCMVS-R system can obtain more comprehensive information on anthropogenic carbon emissions.

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CCMVS-R / Regional carbon assimilation system / Anthropogenic carbon emissions / CO₂ / POD 4DVar

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Lifeng Guo, Xiaoye Zhang, Junting Zhong, Deying Wang, Changhong Miao, Licheng Zhao, Zijiang Zhou, Jie Liao, Bo Hu, Lingyun Zhu, Yan Chen. Engineering. Engineering, 2024, 33(2): 285-297 DOI:10.1016/j.eng.2023.02.017

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1. Introduction

Climate change, which is currently being discussed on an international scale, refers mainly to climate warming due to increased greenhouse gases (GHGs). Climate change, global warming, and the anthropogenic greenhouse effect are of great concern at home and abroad. The report by Working Group I of the Intergovernmental Panel on Climate Change (IPCC) known as the Fifth Assessment Report clearly states that the increase in GHGs (including carbon dioxide (CO₂), methane (CH₄), and nitrous oxide (N₂O)) and changes in land use will cause a series of effects, including an increase in average temperature, a change in extreme temperature, increased frequency of catastrophic weather, an increase in precipitation at the latitude of 30°N, and a decrease in rainfall in the tropics, which have been occurring since the 1970s [1]. In addition, the melting of glaciers due to global warming has led to a rise in sea level, with a global average sea level rise of 0.19 m between 1901 and 2010 and an average growth rate of 1.7 mm·a⁻¹. CO₂ is the most important anthropogenic GHG in the earth’s atmosphere. Due to the impact of human activities (e.g., fossil fuel consumption and cement production), the concentration of atmospheric CO₂ has increased from (289.9 ± 3.3) parts per million (ppm) in 1900 to (398.8 ± 7.3) ppm in 2010–2019—an increase of 38%, with rapid growth occurring in the last 50 years [2], [3]. According to the Paris Agreement, in order to limit global warming to below 1.5 °C by 2100 [4], the IPCC’s Sixth Assessment Report (AR6) recommends substantial and sustained reductions in anthropogenic CO₂ emissions. To limit global warming to 1.5, 1.7, or 2.0 °C, the IPCC’s 6th Assessment Panel Working Group I estimates remaining carbon budgets of 140, 230, and 370 petagrams of carbon (PgC) from 1 January 2020, respectively. However, CO₂ emissions from human activities are still increasing rapidly, with emissions from human activities such as fossil fuel use, cement production, and land-use change reaching 10.30 PgC·a⁻¹ from 2006 to 2015 [5], [6]; moreover, anthropogenic emissions of CO₂ were (10.90 ± 0.90) PgC·a⁻¹ from 2010 to 2019. The remaining carbon budget will be consumed within a few decades based on current estimates of anthropogenic emissions of approximately 10.00 PgC·a⁻¹ [7]. These anthropogenic carbon emissions are distributed among the three components of the earth system, with 46% being trapped in the atmosphere ((5.10 ± 0.02) PgC·a⁻¹), 23% absorbed by the oceans ((2.50 ± 0.60) PgC·a⁻¹), and 31% absorbed by vegetation in terrestrial ecosystems ((3.40 ± 0.90) PgC·a⁻¹) [2].

In September 2020, the Chinese government announced that “China will increase its autonomous national contribution, adopt more vigorous policies and measures, strive to peak CO₂ emissions by 2030, and achieve carbon neutrality by 2060” [8], [9], [10]. This solemn commitment shows the world that China is determined to follow a green, low-carbon, high-quality development path. China’s commitment to achieving carbon neutrality by 2060 is consistent with the Paris Agreement’s 2 °C targets for achieving zero emissions [11]. The core of the IPCC’s emissions inventory guidelines is the governance mechanism of monitoring, reporting, and verification (MRV)—an essential element of establishing an evaluation system for implementing policies and programs. One of these critical elements is verifying each country’s carbon emissions every five years, starting in 2023. The two main methods for estimating anthropogenic carbon emissions are known as the “bottom-up” and “top-down” methods. For example, global and national-scale CO₂ emission data are estimated by the Carbon Dioxide Information Analysis Center (CDIAC) under the US Department of Energy (1751–2006). Global CO₂ emission data are also collected by the International Energy Agency (IEA), whose database covers global CO₂ emissions from fossil fuels in more than 140 countries and regions (1971–2005), disaggregated by industry and fuel type.

However, the inventory survey method can generally be used to estimate only relatively static carbon emissions (usually on an annual scale). The statistical data on which this method is based are often incomplete or even erroneous, and there are significant differences and errors in the emission factors. Due to these limitations and errors, the emission fluxes estimated via the inventory survey method are subject to large uncertainties [2], [6], [7], [12], [13], [14], [15], [16]. The availability of multisource CO₂ concentration observations—including high-precision ground-based observations and observations from the GHGs observing satellites (GOSAT [17] and GOSAT-2 [18]), the orbiting carbon observatories (OCO-2 [19], [20] and OCO-3 [21]), and TanSat [22], [23]—provides data support for studying global/regional carbon assimilation systems [24]. Therefore, top-down anthropogenic carbon flux estimation methods are increasingly favored by researchers [25], [26], [27], [28], [29], [30]. CO₂ satellite observation assimilation will play an important role in global and regional carbon cycle studies and anthropogenic CO₂ accounting [31]. The European Space Agency (ESA) plans to use the same approach to estimate anthropogenic CO₂ emissions and to support a global inventory study in 2028 [32].

China has proposed reaching its carbon peak by 2030 and becoming carbon neutral by 2060 [8], [9], [10]. However, there is an urgent need to accurately calculate anthropogenic emissions from different regions in order to implement emission-reduction measures and assess whether the actions taken are appropriate and effective. To respond to the national carbon-neutral strategy, this paper develops a regional high-precision carbon assimilation system called the China Carbon Monitoring and Verification Support at the Regional level (CCMVS-R). In future research, we will introduce additional high-precision ground-based CO₂ concentration observation network data and multisource satellite observation data, which are expected to invert anthropogenic carbon emissions at the provincial/urban scale with high spatial and temporal resolutions. The structure of this paper is as follows: Section 1 provides an introduction; Section 2 introduces the materials and methods; Section 3 gives an analysis of the CCMVS-R ideal experiment and Shanxi inversion results; and Section 4 is the conclusion.

2. Materials and methods

2.1. Data information

2.1.1. Meteorological inputs

The boundary field weather-driven data used by the CCMVS-R system include National Centers for Environmental Prediction (NCEP) Final Operational Global (FNL) analysis data,^†(^† https://rda.ucar.edu/datasets/ds083.2/) with a resolution of 1° × 1° and containing information on 26 standard isobars (10–1000 hPa) in the troposphere and the surface layer. Global data analysis is performed every 6 h at 00:00, 06:00, 12:00, and 18:00 Coordinated Universal Time (UTC).

2.1.2. Anthropogenic carbon flux data

Anthropogenic carbon flux data mainly include carbon emissions due to fossil fuel combustion and fire carbon flux, where fossil fuel combustion emissions are a direct human influence on the global carbon cycle. The anthropogenic carbon emissions selected for this paper are shown in Table 1 [6], [7], [12], [33], [34], [35], [36].

2.1.3. VPRM model-driven data

The Vegetation photosynthesis respiration model (VPRM) is a carbon flux estimation model based on remote-sensing data. The spatial information and meteorological field information (2 m temperature and downward shortwave radiation data) within the target area required for driving the model are provided by the mesoscale atmospheric transport model (weather research and forecasting (WRF)) [37]; the surface cover data required for model input are provided by high-precision, vegetation-type data (SYNMAP with 1 km resolution); and the enhanced vegetation index (EVI) and land surface water index (LSWI) required for model input are extracted from high-resolution remote-sensing data (MOD09A1)^‡(^‡ https://ladsweb.modaps.eosdis.nasa.gov/missions-and-measurements/products/MOD09A1.). The EVI, LSWI, and other parameter data correspond to the target area grid through the application of spatial interpolation methods.

2.1.4. Initial and boundary CO₂ concentrations

The initial and boundary conditions for each type of CO₂ emission and concentration field (i.e., anthropogenic sources and background fields) are obtained from the global output product of the CarbonTracker system [38], [39]. The CarbonTracker system data product has a spatial resolution of 1° × 1° in China, a 34-layer vertical division, and a temporal resolution of 3 h. The CO₂ concentration fields included in this product include CO₂ total concentrations, biogenic combustion sources, and fossil fuel source concentrations.

2.1.5. CO₂ concentration observation data

The observation data in this paper comprise pseudo-observation data and actual observation data. Among these, the pseudo-observations are the CO₂ concentrations simulated by the WRF-GHG model [40], based on the ideal anthropogenic carbon emissions and then extracted as the observed values to participate in the assimilation. The actual observation data are from six high-precision ground stations in Shanxi Province (Table S1 in Appendix A), which are used for the assimilation inversion and analysis of anthropogenic carbon emissions in Shanxi. Strict quality control of CO₂ observations is required before they enter the assimilation system. The current trace-gas analyzer is based on Picarro, which can theoretically achieve an observation accuracy of 0.1 ppm using the calibration of multiple known concentrations of a standard gas; however, there are various problems in actual observations, such as missing standard gas concentration offset, abnormal sample gas offset, and inappropriate water vapor removal, which affect the observation quality. Thus, strict and uniform data quality control is needed to ensure reliable and accurate observation data. This study uses an integrated quality control, screening, and fitting system to process CO₂ observations from six ground-based stations in Shanxi. Finally, we produced a global ground-based high-precision CO₂ concentration dataset with complete quality control and uniform standards.

2.2. Introduction to the WRF-GHG model

The CCMVS-R was developed based on the WRF-GHG model (V3.9.1), which is based on the mesoscale weather forecasting model WRF and mainly simulates the GHGs of CO₂, carbon monoxide (CO), and CH₄. The WRF model was developed by the National Center for Atmospheric Research (NCAR) in the 1990s. The WRF-GHG model can simulate the exchange of GHGs between the atmosphere and terrestrial ecosystems, taking into account the effects of atmospheric dispersion and transport on GHGs, and can simulate and predict the distribution of GHGs in time and space. WRF-GHG was originally developed to simulate atmospheric GHGs (CO₂, CH₄, and CO) in the Amazon Basin in the Balanço Atmosférico Regional de Carbono na Amazônia (BARCA) project. For CO₂, it is a direct dynamic coupling of the WRF model and the VPRM model, while the VPRM is mainly used to simulate the high-resolution spatial and temporal distribution of natural carbon flux. Structurally, for the CO₂ module, WRF-GHG was developed based on the WRF model with chemistry (WRF-Chem) by adding the corresponding input and output variables (ebio_gee, ebio_res, e_co₂, co₂_ant, co₂_bio, co₂_oce, co₂_bck, etc.) to the registry.ghg registry and adding module_ghg_fluxes.F and other GHG modules.

The various source concentration variables CO₂_ANT, CO₂_BIO, CO₂_OCE, and CO₂_BCK are shown in Table 2 and represent CO₂ concentration variations from anthropogenic sources, CO₂ concentration variations from biological activities, CO₂ concentration variations from ocean fluxes, and atmospheric background concentration values, respectively. The CO₂ flux source in question can not only be obtained from an external file—that is, called offline (ext.)—but can also be calculated online in mode (int.). The time step can be set in half-hourly, daily, or WRF time steps, all of which can be controlled via the namelist.input file.

Due to space limitations, the CCMVS-R regional high-precision carbon assimilation system is optimized for natural carbon flux simulation by means of the VPRM ecological diagnostic model, which will be described in detail in other research results. The natural carbon flux is the result of the optimization; therefore, in this study, the natural carbon flux is considered to have no error, and only the anthropogenic carbon emissions are assimilated and inverted.

2.3. The CCMVS-R building process

The CCMVS-R was mainly developed using Fortran and Python in order to realize multicore parallel computing. Many researchers favor the Fortran language as a scientific computing language, while Python is an object-oriented interpreted computer programming language with powerful and rich computational libraries. The CCMVS-R building process consists of four main parts.

(1) Monte Carlo methods are run to generate ensemble perturbations, and then proper orthogonal decomposition (POD) and four-dimensional variational (4DVar) partitioning are applied to compute the eigenvalues and eigenvectors of the ensemble.

(2) The obtained basis vector (i.e., anthropogenic carbon emissions) and the mean state vector replace the initial anthropogenic carbon emissions of the WRF-GHG model, and the parallel pooling task is submitted to the Linux system.

(3) A scripting program to dynamically listen to the ensemble tasks is run. Once all tasks are completed, the simulation results for each ensemble and its mean value are resolved, and the POD 4DVar method is applied to construct a cost function in conjunction with the CO₂ concentration observations.

(4) The a posteriori anthropogenic carbon emission data obtained by the cost function solution are used to update the anthropogenic carbon emission input of the WRF-GHG model, and the model reruns this assimilation window. The resulting CO₂ concentration product is the simulated value of the CO₂ concentration after anthropogenic carbon emission inventory optimization.

The regional carbon assimilation system runs in a cycle according to the above operation until all assimilation is finished, which is schematically shown in Fig. 1.

2.4. Introduction of efficient assimilation methods for POD 4DVar

In this study, we applied POD to the 4DVar algorithm [41], [42]. The CCMVS-R was constructed based on the WRF-GHG model, which largely reduces the computer resources required for assimilation inversion and improves the computational efficiency and estimation accuracy with a spatial resolution up to the kilometer level. POD 4DVar is a straightforward method that uses the Monte Carlo method to generate a 4D sample ensemble similar to the ensemble Kalman filtering method (EnKF), where the distribution is Gaussian with a mean of 0 and 30% uncertainty. Since the POD orthogonal basis has optimality in the least-squares sense, the POD method is applied to extract the orthogonal basis from the forecast ensemble in four dimensions, which can capture more information of the forecast ensemble and better characterize the spatial structure and temporal evolution of the 4D variables. This method does not require an integral adjoint model and is straightforward in operation and maintenance.

Since the traditional 4DVar data assimilation method requires tangent and adjoint linear operators, which are very difficult to obtain for nonlinear model operators, POD 4DVar can make the implicit optimization problem explicit by capturing the spatiotemporal evolutionary characteristics of the data with a set of basis vectors. This approach not only simplifies the data assimilation process but also retains two significant advantages of traditional 4DVar data assimilation: ① The physical model provides a strong dynamic constraint, and ② observations from multiple periods can be introduced simultaneously in a single assimilation window. The assimilation effect is pronounced when the POD 4DVar method is used for the data assimilation of models with significant initial field errors and forecasted model uncertainties. For conventional 4DVar data assimilation, the cost function (Eq. 1) is constructed from the difference between the simulated values of the model and the observed values, and the a posteriori anthropogenic carbon emissions are obtained by deriving the cost function (

J (\vec{x_{0}})

(1)

J (\vec{x_{0}}) = {(\vec{x_{0}} - \vec{x_{b}})}^{T} B^{- 1} (\vec{x_{0}} - \vec{x_{b}}) + \sum_{j = 1}^{S} {[\vec{y_{j}} - H_{j} (\vec{x_{j}})]}^{T} R_{j}^{- 1} [\vec{y_{j}} - H_{j} (\vec{x_{j}})]

(2)

\vec{x_{j}} = M_{t_{0} \to t_{j}} (\vec{x_{0}})

where the superscript

T

represents the matrix transpose,

\vec{x_{b}}

is a background value,

j

represents the CO₂ concentration observation time series,

H_{j}

represents the observation operator, the

\vec{y_{j}}

represents the observation at a series of times

t_{j}

j = 1, \dots, S

M_{t_{0} \to t_{j}}

represents the forecast model, and the matrices B and R represent the flux background error and concentration observation error covariance, respectively.

\vec{x_{0}}

represents the control variables at the initial moment of the assimilation window. In the cost function, the control variable

\vec{x_{0}}

is connected with

\vec{x_{j}}

through the forward integration of Eq. 2. It is clear that the cost function on the gradient value of

\vec{x_{0}}

is difficult to obtain. However, the POD 4DVar method greatly simplifies its calculation. In the POD 4DVar assimilation algorithm, assuming that there are S time series in the assimilation window, N random perturbation fields are generated using the Monte Carlo method, and each perturbation field is added to the initial background field at

t = t_{0}

to produce N initial fields

\vec{x_{n}} (t_{0})

, n = 1, 2, …, N. The state variables of all sets within the used assimilation window (

\vec{X_{n}}

) are obtained by means of Eq. 3.

(3)

\vec{X_{n}} = (\vec{x_{n}} (t_{0}), \vec{x_{n}} (t_{1}), \dots, \vec{x_{n}} (t_{S})), n = 1, 2, \dots, N

The next point is how to obtain the appropriate basis vectors. The average of the N set state vectors is represented as follows:

(4)

\bar{X} = \frac{1}{N} \sum_{n = 1}^{N} \vec{X_{n}}

(5)

δ X_{n} = \vec{X_{n}} - \bar{X}, n = 1, \dots, N

In the construction of the matrix

A (M \times N) = (δ X_{1}, \dots, δ X_{n})

M = M_{g} \times M_{v} \times (S + 1)

, where

M_{g} a n d M_{v}

denote the number of model space lattice points and the number of model variables, respectively (here, only anthropogenic carbon emissions are represented). To calculate the POD modes, it is necessary to solve the eigenvalue problem.

(6)

{(A A^{T})}_{M \times M} V = λ V

In practice, M >> N; therefore, to efficiently and conveniently solve the problem, the problem is transformed into an N × N eigenvalue problem, as follows:

(7)

{A A}^{T} (A V) = λ (A V)

This translates into the problem of finding the eigenvalues of an N × N matrix, and the computational efficiency is greatly improved, which can meet the need for efficient computation of regional assimilation systems with large dimensional characteristics and high spatial and temporal resolution.

(8)

T^{*} V_{n} = λ_{n} V_{n}, n = 1, 2, \dots, N

where

T^{*} = {(A^{T} A)}_{N \times N}

V_{n}

is the nth column of eigenvector V, and

λ_{n}

is the eigenvalue λ of the nth row. The nonzero eigenvalues

λ_{n}

(

1 \leq n \leq N

) are selected for the orthonormal, and the POD pattern is given by

ϕ_{n} = \frac{A V_{n}}{\sqrt{λ_{n}}}

(

1 \leq n \leq N

). In the 4D space, analysis variable

\vec{X_{a}}

can be rewritten in POD, which is represented as follows:

(9)

\vec{X_{a}} = \bar{X} + \sum_{n = 1}^{p} β_{n} ϕ_{n}

where P is the number of POD modes, the size of which is determined according to the following equation:

(10)

p = m i n \{p, I (P) = \frac{\sum_{n = 1}^{p} λ_{n}}{\sum_{n = 1}^{N} λ_{n}} : I (P) \geq γ\}

where 0 < γ < 1 denotes the percentage of the total information captured by the reduced dimensional space

D^{p} = s p a n {ϕ_{1}, \dots, ϕ_{p}}

. To capture most information of the POD group, γ is allowed to take values of approximately 1. Reconstructing the cost function Eq. 1 according to Eq. 9, the control variable

β = {(β_{1}, β_{2}, \dots, β_{p})}^{T}

replaces the state variable at the initial moment

\vec{X_{0}}

so that the control variables are treated explicitly in the cost function, and the tangent operator and the adjoint mode are not needed to determine the minimum cost function. The problem of finding the minimum of the cost function is transformed into a general optimization algorithm to find

β

. However, the problem still requires an iterative process, and it is still computationally intensive to find β. This problem is solved according to the following flow. First, the POD model matrix is constructed as follows:

(11)

Φ = (ϕ_{1}, ϕ_{2}, \dots, ϕ_{p})

where

ϕ_{n} = {(ϕ_{n} (t_{0}), ϕ_{n} (t_{1}), \dots, ϕ_{n} (t_{S}))}^{T}, n = 1, 2, \dots, p

. The transformation in Eq. 11 is given by

(12)

Φ = {(Φ_{0}, Φ_{1}, \dots, Φ_{S})}^{T}

where

Φ_{j} = (ϕ_{1} (t_{j}), ϕ_{2} (t_{j}), \dots, ϕ_{p} (t_{j}))

. Eq. 9 is rewritten as follows:

(13)

\vec{X_{a}} = \bar{X} + Φ β

Rewriting the cost function using Eq. 13,

(14)

+ \sum_{j = 1}^{S} {[\vec{y_{j}} - H_{j} \bar{x} (t_{j}) - H_{j} Φ_{j} β]}^{T} R_{j}^{- 1} [\vec{y_{j}} - H_{j} \bar{x} (t_{j}) - H_{j} Φ_{j} β]

where

\vec{y_{j}} = (y_{j 1}, \dots, y_{j m_{j}})

is the CO₂ concentration observation vector, and

m_{j}

is the size of

\vec{y_{j}}

. The N sets of observations can be generated by perturbing the observations using a Gaussian distribution perturbation with an uncertainty based on the site observation accuracy, which is represented as follows:

(15)

Y_{i, j} = \vec{y_{j}} + ε_{i}, i = 1, \dots, N

where

ε_{i} = {(ε_{i, 1}, ε_{i, 2}, \dots, ε_{i, m_{j}})}^{T}

; the mean value of perturbation of the N sets is 0, which is represented by the matrix as

E_{j} = (ε_{1}, ε_{2}, \dots, ε_{N})

; and the observation error covariance matrix can be evaluated as follows:

(16)

R_{j} = \frac{E_{j} E_{j}^{T}}{N - 1}, j = 1, \dots, S

The background error covariance B is constructed in a similar way to the observation error covariance R.

Since

R_{j}^{- 1}

is a symmetric matrix, the gradient of the cost function (

\nabla J (β)

) is easily obtained by a simple calculation:

(17)

\nabla J (β) = {(Φ_{0})}^{T} B^{- 1} (\bar{x} (t_{0}) - \vec{x_{b}} + Φ_{0} β) + \sum_{j = 1}^{S} - {[H_{j} Φ_{j}]}^{T} R_{j}^{- 1} \times [\vec{y_{j}} - H_{j} \bar{x} (t_{j}) - H_{j} Φ_{j} β]

To find the minimum value of the cost function, it is necessary to calculate ∇J(β) = 0; that is,

(18)

= \sum_{j = 1}^{S} {[H_{j} Φ_{j}]}^{T} R_{j}^{- 1} [\vec{y_{j}} - H_{j} \bar{x} (t_{j})] - {(Φ_{0})}^{T} B^{- 1} (\bar{x} (t_{0}) - \vec{x_{b}})

After the above series of transformations, Eq. 18 can be obtained directly without an iterative process, which greatly simplifies the computation and improves the efficiency of the assimilation inversion.

2.5. CCMVS-R experimental program settings

In this paper, the simulation effect of the system is verified by two sets of experimental schemes. Scheme 1 verifies the system’s validity and convergence; therefore, the observation data are also assumed to be pseudo-observations. Scheme 2 is based on the high-precision ground-based observation data from Shanxi Province, and an assimilation inversion of the anthropogenic carbon emissions in Shanxi in 2019 is performed. The two experimental schemes maintain the same settings except for the different observation data and use two layers of regional nested simulations with resolutions of 27 and 9 km, in which the numbers of grid points in the x–y directions for the two domains are 64

\times

56 and 64

\times

91, respectively. The core nested area is selected from Shanxi, a province with large carbon emissions (Fig. 2), where the green circles represent six CO₂ concentration observation stations. The assimilation inversion is only performed for the 9 km nested region, with the first layer providing the boundary conditions for this region.

In this experiment, we set the assimilation window size to eight days, the simulation time to nine days, and the spin-up to one day to make the meteorological field simulation results as stable as possible (Fig. 3). As a key parameter in the assimilation system, the size of the assimilation window must be set according to the actual conditions of the ground-based and satellite observations. The primary physical process parameterization schemes used in the WRF-GHG simulations include rapid radiative transfer model (RRTM) longwave radiation [43], Dudhia shortwave radiation [44], Yonsei University (YSU) boundary layer parameterization [45], the Noah land surface model (LSM) [46], and Kain–Fritsch cumulus parameterization [47]. These physical parameterization schemes have been verified by numerous experiments and have good simulation effects.

In this paper, 80 ensemble members are used for assimilation inversion. In theory, a sufficiently large number of samples can cover more information on state variables, and the assimilation effect should be better. However, considering the computational and time costs, the ensemble size should be reasonably allocated according to the computational resources. In addition, ten nodes with approximately 300 cores are involved in the assimilation inversion computation. The details of the Scheme 1 are outlined below.

(1) Assuming that the raw data of the Emissions Database for Global Atmospheric Research (EDGAR) are ideal carbon emissions, the CO₂ concentrations simulated based on this inventory are used as pseudo-observations to participate in the assimilation of the ideal experiment.

(2) An uncertainty of 500% is added to the original EDGAR inventory, FFpri = FF + FF×rand, as the initial emission data to participate in the assimilation (where the resulting negative values are taken as absolute values), where FFpri is the a priori anthropogenic carbon emissions, FF is the assumed ideal anthropogenic carbon emissions, and rand is the random disturbance factor.

(3) The CO₂ concentration and boundary field data are from the CarbonTracker system (1° × 1°).

(4) The VPRM mode input data are from MOD09A1 data (500 m, 8 d).

(5) The WRF meteorological boundary field data are from FNL data (2019, 1° × 1°).

(6) There are six pseudo-observation stations whose locations are at the six CO₂ concentration monitoring stations in Shanxi (Fig. 2). The red symbol marks the location of a hypothetical ideal validation station not involved in assimilation (Fig. 2).

The Scheme 2 is consistent with the ideal scenario setup in terms of meteorological driving data, boundary conditions, and initial conditions, but the observation data are from six high-precision ground stations in Shanxi Province, and the 2018 EDGAR emission inventory is used to provide the a priori anthropogenic carbon emissions to participate in the assimilation.

3. Results and discussion

3.1. Evaluating assimilation effects based on ideal experiments

The ideal experiments designed in this paper are all conducted in the model to examine whether the constructed CCMVS-R carbon assimilation system can assimilate well to invert anthropogenic carbon emissions. Fig. 4(a) shows the assumed ideal anthropogenic carbon emissions using the 2018 EDGAR emission inventory. It is evident from the distribution that some regions, such as Taiyuan, Linfen, Changzhi, and Datong, have higher emissions, while other areas have lower emissions, which is closely related to the distribution of industrial and residential areas in Shanxi. Fig. 4(b) shows the distribution obtained by randomly assigning a 500% uncertainty perturbation to each grid based on ideal anthropogenic carbon emissions. From this, it can be seen that the whole distribution is significantly higher than the ideal anthropogenic carbon emissions, which we take as a priori anthropogenic carbon emissions for the analysis of the CCMVS-R assimilation effect. Fig. 4(c) shows the distribution of anthropogenic carbon emissions after assimilation. The spatial distribution tends to be relatively similar to the assumed ideal anthropogenic carbon emissions, and some high-value areas of anthropogenic carbon emissions before the assimilation are corrected. For the statistical analysis of the corresponding grid of ideal anthropogenic carbon emissions, a priori anthropogenic carbon emissions, and a posteriori anthropogenic carbon emissions, the correlation between a priori anthropogenic carbon emissions and ideal anthropogenic carbon emissions is 0.89 with a root-mean-square error (RMSE) of 4.89 × 10⁴ mol·km²·h⁻¹. The correlation between the assimilated and ideal anthropogenic carbon emissions is improved to 0.94 with an RMSE of 5.18 × 10³ mol·km²·h⁻¹. Although the correlation does not improve much, with an increase of 5.5% relative to the a priori anthropogenic carbon emissions, the RMSE decreases significantly, with a decrease of 89.4% relative to the a priori anthropogenic carbon emissions and a noticeable assimilation effect.

Fig. 5(a) shows a cumulative histogram of anthropogenic carbon emissions in Shanxi Province during one assimilation process; the ideal carbon flux is 5.24 × 10⁶ mol·h⁻¹, the a priori carbon flux after the perturbation is 1.82 × 10⁷ mol·h⁻¹, and the a posteriori anthropogenic carbon emissions after the assimilation are 5.97 × 10⁶ mol·h⁻¹. The a priori anthropogenic carbon emissions are 3.47 times the ideal anthropogenic carbon emissions, and the a posteriori anthropogenic carbon emissions are 1.14 times the ideal anthropogenic carbon emissions. Fig. 5(b) shows the difference between the anthropogenic carbon emissions and the corresponding grid points of the ideal anthropogenic carbon emissions before and after assimilation. The black line shows the difference between the a priori and ideal anthropogenic carbon emissions, while the red line is the difference between the a posteriori anthropogenic carbon emissions and ideal anthropogenic carbon emissions. It can be seen from the figure that the difference between the grid points after assimilation is mainly concentrated near the 0 axis line. The anthropogenic carbon emissions after assimilation have very obviously improved.

Fig. 4, Fig. 5 display the assimilation effect in terms of the spatial distribution and emission statistics. In contrast, Fig. 6 analyzes the assimilation effect in terms of the difference between the simulated and pseudo-observed CO₂ concentrations before and after assimilation. The black line represents the pseudo-observed CO₂ concentrations, the red line represents the simulated CO₂ concentrations before assimilation, and the blue line represents the simulated CO₂ concentrations after assimilation, where Fig. 6(a) and (b) show the hourly average CO₂ concentrations at the validation station that did not participate in assimilation and at the Taiyuan station. The simulated values of CO₂ concentrations before and after assimilation at validation station Site B—which did not participate in the assimilation—agree with the pseudo-observation data, despite some deviations. Fig. 6(c) and (d) show the simulated hourly CO₂ concentrations in one assimilation process at the Taiyuan station and at the validation station without assimilation, which aligns with Fig. 6(a) and (b). The simulation effect is improved after assimilation, the correlation between the CO₂ concentration after assimilation and the ideal result at the two monitoring stations is close to 1, and the RMSE is close to 0. These results indicate that the CCMVS-R can capture the daily variation information of the stations well in the ideal experiment and is expected to assimilate the inverse regional anthropogenic carbon emissions with higher accuracy based on high-precision ground-based observation data.

3.2. Inverse anthropogenic CO₂ emissions at high resolution in Shanxi

Fig. 7 shows a comparison of 9 km a posteriori anthropogenic carbon emissions and a priori anthropogenic carbon emissions in Shanxi Province in 2019 by means of CCMVS-R inversion. This comparison indicates that the bottom-up statistical method may underestimate the emissions in this region. The overall distribution of anthropogenic carbon emissions in Shanxi is stronger in the central part and weaker in the eastern and western parts. In the central region, anthropogenic carbon emissions are linearly clustered in a north–south direction. Three emission centers with high intensity are located at the junction of Shuozhou–Datong, the south side of Taiyuan, and the junction of Linfen–Yuncheng, respectively.

The inversion results were compared with five sets of anthropogenic carbon emission inventory products—namely, global infrastructure emission database (GID), open-source data inventory for anthropogenic CO₂ (ODIAC), EDGAR, China high-resolution emission gridded data (CHRED), and global carbon project (GCP). The comparison results (Table 3) show that the statistical values of the a posteriori inventory in each city of Shanxi Province are closer to those of CHRED. However, in general, the a posteriori anthropogenic carbon emissions from the CCMVS-R assimilation inversion are approximately 28.6% (17%–38%) higher than those of the five inventory products, especially the emissions of the ODIAC anthropogenic carbon emission inventory product, which may be considerably underestimated.

Fig. 8 portrays a statistical histogram of the a posteriori anthropogenic carbon emissions and five sets of emission inventory products for prefecture-level cities in Shanxi, which shows that the region with the highest a posteriori anthropogenic carbon emissions is the city of Linfen. Taking Linfen and Datong—the two major carbon-emitting cities in Shanxi Province—as an example, the statistical analysis is based on the a posteriori emissions and the three inventory products GCP, GID, and ODIAC in 2019. The results show that the statistical value of the anthropogenic carbon emissions of the GID data product for Linfen is greater than that for Datong, which is consistent with the statistical results of the a posteriori emissions; however, for the other two sets of inventories (GCP and ODIAC), Datong has higher carbon emissions.

To verify the reasonableness of the a posterior anthropogenic carbon emissions and analyze the pollution concentration of CO₂'s associated gas CO in the atmosphere, CO pollution concentration observations were obtained from the China National Environmental Monitoring Center^†(^† https://www.cnemc.cn/.), and the collected CO concentration observations from 6 + 6 monitoring stations within Datong and Linfen in 2019 were statistically analyzed by city where the stations are located, by month. The analysis was used to represent the average observed concentrations in Datong and Linfen. Fig. 9(a) shows the monthly average CO concentration observations in Datong (black line) and Linfen (red line). Except for March, May, and July, when those in Linfen are lower than those in Datong, the CO concentration observations in Linfen are similar to or significantly higher than those in Datong, especially in winter. Fig. 9(b) shows the annual average observation of CO concentrations in Datong and Linfen. Those in Linfen (red bar) are approximately 0.16 mg·m⁻³ higher than those in Datong (black bar), and the area of Linfen is approximately 1.43 times larger than that of Datong. These findings verify that the a posteriori anthropogenic carbon emissions in Linfen are higher than those in Datong, which is reasonable. ODIAC and GCP are inventory products with a time lag that use bottom-up statistical methods to determine the emission factors—methods that vary greatly and have large errors [48], [49]. Thus, the obtained results may have a significant bias.

Fig. 10 shows scatter plots of the simulated CO₂ concentration of the CCMVS-R system before and after the assimilation of anthropogenic carbon emissions from 1 February to 30 April 2019 at the Datong and Taiyuan monitoring stations in Shanxi, compared with the daily average (24 h) of the observed values. The horizontal axis represents the observed values, while the vertical axis represents the simulated values before and after the assimilation. The correlation coefficients between the simulated and observed CO₂ concentrations after assimilation by the CCMVS-R system at the Datong and Taiyuan monitoring stations are as high as 0.80 and 0.83, respectively, with mean deviations of −0.25 and 1.01 ppm. Compared with the correlation coefficients of 0.60 and 0.76 and mean deviations of −5.92 and −11.1 ppm at the Datong and Taiyuan monitoring stations before assimilation, there is a significant improvement. The simulation effect before the assimilation is similar to that reported in other studies, such as in the work of Diao et al. [50]. In their study using the WRF-GHG model without the assimilation of atmospheric CO₂ data, Diao et al. obtained a correlation coefficient of approximately 0.64 and an average deviation of approximately 6.87 ppm compared with the observed values. Those results showed that the emissions were closer to the actual emissions after the optimization of anthropogenic carbon emissions. The results provided in Fig. 10 show that the deviation between the system-simulated values and the observed values is larger for some dates (especially within the purple rectangle), which is strongly related to the system deviation, the observation error, and the difficulty of capturing small-scale anthropogenic carbon emission events. However, in general, the system-simulated values after the assimilation can capture well the daily averaged variation in CO₂ concentration information.

Fig. 11 shows the daily average time series of the CCMVS-R system’s simulated values and station observations from 1 February to 30 April 2019 for the Datong and Taiyuan monitoring stations, with the horizontal axis representing the date and the vertical axis representing the CO₂ concentration values (ppm) of the assimilated CCMVS-R system’s simulated values (red line) versus the observed values (black line). The line graph in Fig. 11 shows that the CCMVS-R system’s simulated values can well capture the information on the average daily changes in CO₂ concentration. However, the simulation effect of the Taiyuan monitoring station is inferior to that of the Datong monitoring station—especially the deviation of the system-simulated values from the observed values in the dates marked by the purple rectangle boxes in Fig. 11. This deviation may be due to the following reasons: ① The Taiyuan monitoring station is located in an area with intensive emissions (Fig. 7), which has a significant impact on the observations; in addition, the observed data are influenced by anthropogenic emissions, which can cause the observation results to fluctuate greatly within a day. After averaging, there are significant differences between the model’s simulated values and observations and those at the Datong monitoring station. ② The surface is strongly mixed by turbulence after sunrise due to solar radiation, and vegetation photosynthesis is simultaneously enhanced; this results in the concentration of CO₂ in the near-surface atmosphere decreasing continuously and reaching the lowest value at approximately 15:00. With the subsequent continuous weakening of photosynthesis and atmospheric turbulence, the concentration of CO₂ in the near-surface atmosphere increases gradually. At night, the atmospheric boundary layer tends to stabilize; CO₂ accumulates in the atmospheric boundary layer, and its concentration increases continuously and reaches the daily maximum before sunrise. These meteorological factors directly affect the atmospheric CO₂ concentration. Therefore, the simulation accuracy of WRF-GHG on meteorological factors (including temperature and downward shortwave radiation, etc.) affects the simulation effect of atmospheric CO₂ concentration to a certain extent, which is the reason for the large deviation between the simulated and observed values during some periods.

3.3. Advantages of our CCMVS-R system

The good performance of the CCMVS-R system stems from its two main advantages: ① The CCMVS-R was developed based on the WRF model, and the inverse anthropogenic carbon emissions and CO₂ concentration data are more realistic with the combination of atmospherically driven data and a model parameterization scheme. This is a significant improvement over the anthropogenic carbon emissions obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS) and GOSAT data using model recursion by Guo et al. [51]. Guo et al.’s method lacked consideration of atmospheric transmission models, resulting in a lack of further limitations from meteorological factors, and hence had considerable uncertainty. ② The CCMVS-R is based on the 4DVar assimilation inversion method of POD to build the assimilation system, which essentially reduces the computer resources required for assimilation inversion while improving the computational efficiency and estimation accuracy. Our approach solves the critical technical issue to a certain level of high spatial and temporal resolution and huge dimensionality of the regional carbon assimilation system, operational cost, and computational efficiency limitation [49], [52], [53].

4. Conclusions

Based on the WRF-GHG regional model, we used the POD 4DVar method to construct a regional high-precision carbon assimilation system, CCMVS-R. The system realizes the assimilation inversion of anthropogenic carbon emissions at the kilometer level. It provides an effective means of accurately estimating anthropogenic carbon emissions at the regional and local scales. Two nested layers were designed with the resolutions of the outer and inner regions set at 27 and 9 km, respectively, to verify the effectiveness of the CCMVS-R system. The core nested area was within Shanxi Province, which is associated with large carbon emissions.

Two schemes were also designed for verification using six ground-based sites with high-precision CO₂ monitoring from Shanxi. Scheme 1 used simulated values from the WRF-GHG model extracted from six ground-observation stations as pseudo-observation data for assimilation inversion. In comparison, Scheme 2 used the information from six high-precision ground-observation stations for assimilation inversion, while the other settings remained the same. The simulation results of the ideal experiment showed that ① the anthropogenic carbon emissions after assimilation converged well to the assumed ideal carbon flux, with significant correction of some high-value regions of the a priori carbon flux. The correlation between anthropogenic carbon emissions and the ideal carbon flux before and after CCMVS-R assimilation improved from 0.89 before assimilation to 0.94 after assimilation, and the RMSE decreased from 4.89 × 10⁴ mol·km²·h⁻¹ before assimilation to 5.18 × 10³ mol·km²·h⁻¹ after assimilation—a decrease of 89.4%. This experiment illustrates the effective convergence of the CCMVS-R system. ② The results of the anthropogenic carbon emissions after assimilation were used as input to the CCMVS-R system. The simulation ability of CCMVS-R on CO₂ concentration was greatly improved. In this experiment, the pseudo-observations simulated by the Taiyuan monitoring station, which participates in the assimilation, and Site B, a hypothetical observation that does not participate in the assimilation, were selected to verify the simulation ability of the CCMVS-R on CO₂ concentration before and after the assimilation. The experimental results showed that the simulation effect was significantly improved after assimilation. The correlation between the CO₂ concentration after assimilation and the ideal value was close to 1, and the RMSE between them was close to 0.

Scheme 2 assimilated six high-precision ground station observations in Shanxi Province to obtain inverse anthropogenic carbon emissions in 2019. The spatial distribution of the a posteriori anthropogenic carbon emissions was reasonable. Anthropogenic carbon emissions increased in most cities in Shanxi, particularly in Linfen, showing that the bottom-up emission inventory for this city may be underestimated. The results of the a posteriori anthropogenic carbon emission statistics were compared with the mean of five anthropogenic carbon emission inventory products (GID, ODIAC, EDGAR, CHRED, and GCP), showing that the a posteriori anthropogenic carbon emissions from CCMVS-R assimilation inversion were approximately 28.6% (17%–38%) higher than those of the five inventory products, especially for the ODIAC inventory products, which may be more underestimated than the other inventories due to the time lag and the error of the bottom-up statistical method.

In addition, the relationship between the simulated and observed CO₂ concentrations after assimilation at the Datong and Taiyuan monitoring stations from 1 February to 30 April 2019 was compared and analyzed. The results showed that the CCMVS-R has sound simulation effects, with the correlation coefficients between the simulated and observed CO₂ concentrations after assimilation being as high as 0.80 and 0.83, with mean deviations of −0.25 and 1.01 ppm, respectively. Their correlation coefficients and mean deviations were significantly improved compared with those before the assimilation at the Datong and Taiyuan monitoring stations. The simulated values of the system after assimilation were able to capture the information on the average daily variation in CO₂ concentration well. The inversion results show that the CCMVS-R regional high-precision carbon assimilation system has good application prospects.

The quantity and quality of observational data limited the development of the regional carbon assimilation system. In future studies, multisource CO₂ concentration observational data (i.e., ground-based observations, OCO-2/OCO-3, GOSAT/GOSAT-2, TanSat, etc.) will be introduced to the CCMVS-R, and the companion gas CO of CO₂ will be introduced into the regional atmospheric CO₂ assimilation inversion system to compensate for the low inversion accuracy in regions without sufficient observational data. This will potentially improve the inversion accuracy of the regional carbon fluxes further.

Acknowledgments

This research was supported by the General Project of Top-Design of Multi-Scale Nature-Social Models, Data Support and Decision Support System for NSFC Carbon Neutrality Major Project (42341202), and the Basic Scientific Research Fund of the Chinese Academy of Meteorological Sciences (2021Z014). The authors are grateful to all the organizations and groups that provided indispensable datasets that we used in this study. We acknowledge the CO₂ boundary conditions provided by Dr. Huifang Zhang.

Compliance with ethics guidelines

Lifeng Guo, Xiaoye Zhang, Junting Zhong, Deying Wang, Changhong Miao, Licheng Zhao, Zijiang Zhou, Jie Liao, Bo Hu, Lingyun Zhu, and Yan Chen declare that they have no conflict of interest or financial conflicts to disclose.

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1. Introduction

2. Materials and methods

2.1. Data information

2.1.1. Meteorological inputs

2.1.2. Anthropogenic carbon flux data

2.1.3. VPRM model-driven data

2.1.4. Initial and boundary CO2 concentrations

2.1.5. CO2 concentration observation data

2.2. Introduction to the WRF-GHG model

2.3. The CCMVS-R building process

2.4. Introduction of efficient assimilation methods for POD 4DVar

2.5. CCMVS-R experimental program settings

3. Results and discussion

3.1. Evaluating assimilation effects based on ideal experiments

3.2. Inverse anthropogenic CO2 emissions at high resolution in Shanxi

3.3. Advantages of our CCMVS-R system

4. Conclusions

Acknowledgments

Compliance with ethics guidelines

References

RIGHTS & PERMISSIONS

2.1.4. Initial and boundary CO₂ concentrations

2.1.5. CO₂ concentration observation data

3.2. Inverse anthropogenic CO₂ emissions at high resolution in Shanxi