=Paper=
{{Paper
|id=Vol-3006/38_short_paper
|storemode=property
|title=Determining the likely localization of methane sources using forecast time series and satellite data
|pdfUrl=https://ceur-ws.org/Vol-3006/38_short_paper.pdf
|volume=Vol-3006
|authors=Marina V. Platonova,Ekaterina G. Klimova
}}
==Determining the likely localization of methane sources using forecast time series and satellite data==
https://ceur-ws.org/Vol-3006/38_short_paper.pdf
Determining the likely localization of methane
sources using forecast time series and satellite data
Marina V. Platonova1,2 , Ekaterina G. Klimova1,2
1
Federal Research Center for Information and Computational Technologies, Novosibirsk, Russia
2
Novosibirsk State University, Novosibirsk, Russia
Abstract
The paper is devoted to the topical problem of determining the sources of methane from observational
data. An algorithm based on the statistical optimization method used to estimate a time constant
parameter is considered. To implement the algorithm, a variant of ensemble smoothing is used, which is
an optimal estimate of the desired parameter based on observational data and forecast for a given time
interval. This paper presents the implementation of the algorithm for real observational and forecast data,
the results of a three-dimensional transport and diffusion model are taken as a mathematical model, and
satellite measurement data are used as observational data. Methane fluxes are estimated in subdomains
of the Earth’s surface for specified time intervals. The paper contains a mathematical formulation of the
problem, a scheme for its numerical implementation. The results of numerical experiments with model
and real data are presented.
Keywords
Methane sources, forecast, satellite data.
1. Introduction
The task of searching for methane sources is modern and urgent; interest in solving this
problem has been growing more and more recently. International interest is associated with
various political and economic factors, including a carbon tax. A common practice is when data
assimilation systems are used for such a task [1, 2, 3]. In this work, the problem of probabilistic
localization of methane fluxes is solved using the system of data assimilation for the model
of transport and diffusion in the atmosphere [4, 5, 6]. The use of a mathematical model and
satellite data to solve the problem is currently a relevant method using data assimilation as a
basis. In the case of modern models with high spatial resolution, the algorithm is very laborious
due to the high dimension of the vectors of predicted variables and observational data [7, 8].
This article discusses an approach to solving this problem based on the decomposition
of the model area. Methane sources on the Earth’s surface are considered as an estimated
parameter. The authors present the results of model numerical experiments with real data on
the implementation of a part of the analysis step the data assimilation algorithm in the case of a
global model of transport and diffusion.
SDM-2021: All-Russian conference, August 24–27, 2021, Novosibirsk, Russia
" gumoznaya@gmail.com (M. V. Platonova); klimova@ict.nsc.ru (E. G. Klimova)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
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Marina V. Platonova et al. CEUR Workshop Proceedings 323–329
2. Using time-series forecasts and satellite data to determine the
likely localization of methane sources
2.1. The ensemble Kalman filter for methane fluxes estimation
Following [1, 2, 3, 4, 5], we will make an estimate based on the data of satellite observations
from a given time interval. Methane flux values will be estimated from observational methane
concentrations. This version of the algorithm is considered in many modern works [1, 2, 3, 4, 5].
The estimation of the values of the flow averages over the subdomains from the observational
and forecast data is carried out according to the standard formula of the Kalman filter (analysis
step) [9, 10]:
𝑥𝑎 = 𝑥𝑓 + 𝐾 [𝑦0 − 𝐻(𝑥𝑓 )] , (1)
(︁ )︁−1
𝐾 = 𝑃 𝑓 𝐻 𝑇 𝐻𝑃 𝑓 𝐻 𝑇 + 𝑅 . (2)
Here 𝑥𝑎 — estimation of the average flow over the subdomains, 𝑥𝑓 is the forecast by the
model and 𝑦0 is the observational data. To implement the ensemble Kalman filter, it is necessary
to specify an ensemble of perturbations of the estimated quantity [1, 2, 3, 4, 5]:
1 [︁ 𝑓 ]︁𝑇
𝐷𝑥𝑓 = 𝑑𝑥1 , . . . , 𝑑𝑥𝑓𝑁 ,
𝑁
where 𝑁 is the size of the ensemble. Matrix 𝑃 𝑓 is evaluated by the ensemble:
𝑃 𝑓 = 𝐷𝑥𝑓 (𝐷𝑥𝑓 )𝑇 ,
[︁ ]︁−1
𝐾 = 𝐷𝑥𝑓 (𝐻𝐷𝑥𝑓 )𝑇 𝐻𝐷𝑥𝑓 (𝐻𝐷𝑥𝑓 )𝑇 + 𝑅 .
Operator 𝐻 includes model prediction at the time of observation, interpolation from grid
nodes to observation points. When working with satellite data, the operator includes vertical
averaging with known coefficients (using the average kernel). We will assume that the equation
of changes in flows from time to time is constant and flows do not change (the forecast step is a
change in the variable at the forecast step according to the model), i.e.:
𝑥𝑛+1
𝑓 = 𝑥𝑛𝑓 ,
𝑛 is the number step of the time.
Observational data on the concentration of greenhouse gases at the moment of time 𝑡𝑛 can
be represented in the form:
𝑦0𝑛 = 𝐻 [𝑓 (𝑞𝑡𝑛 ) + 𝑥𝑛𝑡 ] + 𝜀0 ,
where 𝑓 is the operator of the model, i.e. the model describing the time variation of the
concentration 𝑞𝑡𝑛 is included in the observation operator. To implement the analysis step, you
need to specify an ensemble of errors. We write the observation operator in the form:
𝐻(𝑑𝑥𝑖𝑓 ) = 𝐻1 𝑓 (𝑞𝑡𝑛 ) + 𝑥𝑛𝑡 + 𝑑𝑥𝑖𝑓 − 𝑓 (𝑞𝑡𝑛 ) + 𝑥𝑛𝑡 ,
[︀ ]︀
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where 𝐻1 is the operator of the interpolation to the observation point. In the case of satellite
data on greenhouse gas concentrations, the data contains information about the mean in a
vertical column:
𝐿
∑︁
𝑦0 = 𝛽𝑙 𝑞𝑙0 ,
𝑙=1
the sum with the weights of the values at 𝐿 levels along the vertical.
2.2. Deterministic version of the LETKF algorithm
Consider a deterministic version of the local data assimilation algorithm. The data assimilation
algorithm consists of alternating forecasting steps and model analysis steps. The analysis stage
is an optimal estimate based on observational and forecast data [9, 11]. We will consider a
variant of the ensemble Kalman filter, in which the covariance matrix of the forecast errors is
specified at the initial moment and considered constant over time.
Let us define an ensemble of forecast errors:
1 [︀ 1 ]︀𝑇
𝐷𝑥𝑓 = 𝑑𝑥𝑓 , . . . , 𝑑𝑥𝑁
𝑓 .
𝑁
The covariance matrix of forecast errors can be represented as 𝐷𝑥𝑓 (𝐷𝑥𝑓 )𝑇 . The analysis
step of the assimilation procedure has the form (1)–(2). Consider the implementation of the
analysis step algorithm based on the deterministic LETKF algorithm [10, 11]:
𝑥𝑎 = 𝑥𝑓 + 𝐷𝑥𝑓 𝑃 𝑎 (𝐻𝐷𝑥𝑓 )𝑇 𝑅−1 , (3)
]︀−1
𝑃 𝑎 = (𝑁 − 1)𝐼 + (𝐻𝐷𝑥𝑓 )𝑇 𝑅−1 𝐻𝐷𝑥𝑓 (4)
[︀
.
In this case, the analysis algorithm becomes local. It can be implemented for any grid node
independently [10, 11]; in this case, operations are performed with the ensemble dimension
matrices. Additional localization can be performed by element-wise multiplication of the matrix
𝑅 by a function that decreases with distance. This algorithm can be implemented in a simplified
deterministic version in which the ensemble of disturbances is not recalculated according to
the model.
Using the formulas of this algorithm, following [1, 2, 3, 4, 5], we will make an estimate based
on the data of satellite observations for a given time interval. Methane flux values will be
estimated from observational data using methane concentration information. This version of
the algorithm is considered in many modern works [1, 2, 3, 4, 5].
2.3. Implementation of the analysis step for real observational and forecast
data
In the process of implementing the algorithm for finding the estimate of methane sources,
it is possible to distinguish several stages. Note that the estimate is carried out for a given
time interval, in which the fluxes are considered constant. In algorithms for processing large
amounts of satellite data, it is customary to evaluate for a given time interval (for example, a
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week), assuming that the fluxes values are constant during this period. In this case, the data
vector contains all observational data from this period, and the forecast from the transport and
diffusion model is included in the interpolation operator.
It should be noted that the use of the deterministic variant is possible only in experiments
using a 6-hour time interval.
2.4. Surface area decomposition
Due to the specificity of the used algorithm, it is possible to perform the analysis step locally.
We assume that the data is known on the surface of the Earth. We have divided the entire
surface area of the Earth into subdomains of approximately 1000×1000 km. Further, the work
of the formulas of the algorithm will be carried out within each subdomain.
2.5. Specifics of using the data of the MOZART model
The data assimilation algorithm consists of a forecast step and an analysis step. For the forecast
step, we used the results of calculations of the mathematical model MOZART-4. This is the
MOZART-4 Global Chemical Transport Model, the source code of which is freely available. The
results of calculations of this model were provided by colleagues Anatoly A. Lagutin and Egor
Yu. Mordvin [12]. This model is autonomous, it only needs meteorological data for the duration
of the simulation. The model has a spatial resolution of 2.8×2.8∘ . The MOZART-4 model has
28 levels in height (from the surface of the Earth to a height of ∼2 hPa). This model includes
85 types of gases and 12 aerosol components. The content of each component of the model in the
atmosphere is found by solving the mass conservation equation taking into account adventive,
convective, and diffusion transfer. In addition, there is accounting for the emission component
of the underlying surface, aerosols, photochemical reactions and wet/dry deposition. In the
MOZART-4 model we used for our calculations, we used a standard set of chemical reactions.
2.6. Specifics of using AIRS data
We used data from the AIRS satellite as observational data for the analysis step. The Atmospheric
Infrared Sounder AIRS, launched into low-Earth orbit on May 4, 2002 aboard NASA’s Aqua
satellite, provides data for monitoring the Earth’s atmosphere. AIRS is one of six instruments
aboard the Aqua satellite, which is part of NASA’s Earth Observing System. AIRS measures all
the primary greenhouse gases including carbon dioxide, the largest source of anthropogenic
greenhouse gas, carbon monoxide, methane, and ozone.
The main AIRS products used in CH4 extraction are those recoverable using both AIRS
and AMSU. The AIRS instrument on NASA’s Aqua satellite orbits the Earth from pole to pole
approximately fifteen times a day. The AIRS data information products used are divided into
series 6-minute granules, and each granule is a file, there are 240 granules for each day. All
AIRS information products that were used for the calculations satisfy the measurements by the
method of least squares. To properly compare the satellite observations with model simulations,
the model data should be convolved using the averaging kernels [12].
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3. Model experiments with real data
We divide the surface of the globe into regions for which we will calculate the estimate. Since a
local algorithm is used at the analysis step, which can be used for each grid node independently,
the procedure for estimating the emission values is carried out separately for the specified
subdomains. The same approach is used in works [1, 2, 3, 4, 5], but these works use an analysis
algorithm that is not local.
The transport and diffusion model calculates a forecast based on the given initial values
of concentrations and fluxes over a time period with a given time step, then interpolation is
performed to the observation point and the time at which the observation is made. Further, the
search for the estimate is carried out according to formulas (3)–(4).
Numerical experiments were carried out with model data and with real data for the described
local deterministic data assimilation algorithm.
It is believed that predictive and observational data are known at the surface of the Earth. The
entire area is divided into regions, the analysis is carried out locally for each sub-area separately.
The possibility of performing an analysis step locally is due to the properties of the assimilation
algorithm used. From the estimates obtained within each sub-area, a general emission estimate
is compiled. Over the entire model area, the concentration value was set, observational data
were modeled.
The results of the MOZART-4 model and observational data were taken at the same time. We
have interpolated the received data into one grid.
We set up observation and forecast error matrices to work with ensembles. All generated
random variables have a normal distribution, zero mean and specified variance. As errors in the
first approximation (forecast for the initial moment), random variables with a variance of 0.08
were taken.
Figure 1 shows the spatial distribution of the distribution of the methane mixture ratio at an
altitude of ∼1500 m at 00.00 UTC on August 01, 2002.
Figure 1: Spatial distribution of the distribution of the ratio of the mixture of methane at an altitude of
∼1500 m at 00:00 UTC on August 01, 2002.
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a b
Figure 2: Results of model experiments with real data: a —model methane emission in the Siberia
subregion; b — an estimate of the localization of methane sources.
To simulate methane emissions, we have chosen one subregion with a size of 1000×1000 km.
In this case, the emission is modeled in the region — Siberia (from 50∘ 36’ to 58∘ 48’ north latitude
and from 78∘ 24’ to 86∘ 48’ east longitude). I would like to note that the order of the modeled
emission is 0.1e−08.
Data assimilation was carried out at the analysis step for one for one 6-hour interval (from
00:00 UTC August 1, 2002 to 6:00 am August 1, 2002). Results of model experiments with real
data are presented on Figure 2. Figure 2, a shows a model methane release in one sub-region
(Siberia). Figure 2, b shows an estimate of the localization of methane sources obtained from
data on methane concentration.
For a qualitative assessment of the operation of the algorithm for the probabilistic localization
of methane sources, let us compare the deviations of the geographic coordinates of the found
sources in comparison with the coordinates of the modeled emission. The maximum deviation
is ±2∘ , which is comparable to the degree measure of the grid step in the space of the Mozart-4
model.
Acknowledgments
The authors of the article express their deep gratitude to colleagues who provided materials for
the work: professor Anatoly A. Lagutin and assistant professor Egor Yu. Mordvin.
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