Morales, Randulph: Spatio-temporal kriging in estimating local methane sources from drone-based laser spectrometer measurements

Cluster-based Kriging for estimating local methane
sources from drone-based laser spectrometer
measurements
Randulph Morales1,2, Jonas Ravelid1, Béla Tuzson1, Lukas Emmenegger1, and
Dominik Brunner1
1Laboratory for Air Pollution/Environmental Technology, Swiss Federal Laboratories
for Materials Science and Technology, Empa, Dübendorf, Switzerland
2Institute of Atmospheric and Climate Science, ETH Zürich, Switzerland
MEMO2 : Methane goes Mobile- Measurements and Modelling

Drone Integrated System [03]
randulph.morales@empa.ch | 01
Cluster-based kriging [06]
Outline
Summary and outlook [12]
Controlled release experiments [04]
Motivation of the study [02]
Quantification results from release experiments [09]

Motivation of the study
A need for a lightweight but precise CH4
measurements that can be mounted on a
drone system
Commercial drone (Matrice 600, DJI) has a
vertical accuracy of ±0.50m which is not
sufficient in performing the mass balance
quantification method
Limited flight-time, limited sampling of
turbulent plumes
o CH4 is primarily emitted from diffusive sources such as landfills
or wetlands and from leaks during oil- and gas-production
o Measurements from drones offer an attractive means to sample
the plumes in 3D of individual sources to quantify their
emissions
Lightweight and precise QCLAS developed by EMPA and an accurate RTK-GPS
system mounted on the drone system
Main challenges:
World’s lightest laser-
spectrometer developed by
Empa
Implement an RTK-GPS
system which has a precision
of 2.0 mm
Design the best measurement
strategy and quantification
method for sampling
atmospheric trace gases,
particularly CH4

Drone Integrated System
© Empa 2020. All rights reserved.
[1] Graf et al., Optics Letters, 43, 2018
[2] Tuzson et al., AMTD, 2020 https://doi.org/10.5194/amt-2020-102
Weight: 2.2 kg
Precision: 1.1 ppb @ 1s
Sampling rate: 1-10 Hz
• The in-situ QCLAS instrument covered by a white polymer cover (Empa)
and the active AirCore system enclosed in a carbon fibre box (RUG)
mounted on the drone-system (Matrice 600, DJI)
• Accurate and precise RTK-GPS mounted on top of the drone
• Total weight of the system is 13 kg with an average flight time is
approximately 20 mins

Controlled release experiments in Dübendorf, Switzerland
Site: Cropland farm (Dübendorf, Switzerland)
Date: 23 Feb-14 March 2020 (9 days of active measurements)
Number of flights: 20 / 35 measurements
Source: Natural gas (92.2% CH4)
Meteorological Instruments: 2.5D and 3D sonic anemometer @
20 Hz
Flight: 314_02
• Characterize mass balance quantification methodology using controlled releases of methane

I. Clock synchronization among different
systems by cross correlating among
different GPS timestamps
II. Background CH4 were removed using the
Robust Extraction Baseline Signal
(Ruckstuhl, 2012)
III. Take-off and landing time was removed
from dataset and points were projected
into a measurement plane
Time synchronization and data pre-processing
Cross correlation between the longitude of the
QCLAS and the GPS-RTK system
Timeseries of CH4 elevations after removing background values
using REBS
Measurement points projected into a single plane. Orange
circle at the bottom signifies where the 0.00m distance is
located
CH4 elevations projected in one cross-sectional area.

Clustering of drone measurement data using
mixture models
• Standard Kriging assumes measurement points are
from a single unimodal distribution, but
background and plume signals have different
spatial correlation scales
Gas spatial distribution mapping
Ability to map background values and areas
of elevations and sharp peaks
• Cluster-Based Kriging: Measurements are clustered
into two components using Gaussian Mixture
Models
𝑆 = {𝒳1 … 𝒳 𝐾} where ∪ 𝑘
𝒳𝑙 = 𝒳
Given a set: 𝒳 = { 𝒙1, 𝑦1 , … (𝒙 𝑛, 𝑦 𝑛)}
we wish to obtain a set 𝑆
𝑛 = number of measurement points
𝐾 = number of clusters

𝑙 𝑒𝑙𝑒𝑣,ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 = 3.07 m 𝑙 𝑒𝑙𝑒𝑣,𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 = 0.28 m
𝑙 𝑏𝑔,ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 = 76.55 m 𝑙 𝑏𝑔,𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 = 48.64m
Learning Kriging parameters for each cluster
• Kriging parameters such as horizontal and vertical
length scales are learned for each cluster
• Initial length scales are provided and optimized
using Expectation-Maximization algorithm
Train an adequate Kriging model for each cluster
• Posterior probability cluster membership of
unsampled spatial points are also computed
• Combination of two mixture models using
posterior probability membership
𝑦|𝑥 = ෍
𝑙=1
𝐾
Pr(𝑥𝑙) ⋅ 𝑦𝑙
𝑦 = CH4molar fraction ppm
𝑥 = spatial location of CH4
𝑙 = cluster membership
I. Background Clusters
II. Elevated Clusters

randulph.morales@empa.ch | 08© Empa 2020. All rights reserved.
• Reconstruction of time series using obtained
spatially filled CH4 measurement plane
• Conversion of CH4 molar fraction [ppm] to CH4
concentration [g/m3] under normal conditions.
Quantification of methane emissions
Emission quantification:
𝑑𝑚
𝑑𝑡
= 𝑄 = ෍ 𝐶𝑖,𝑗 𝐴𝑖,𝑗 𝑈𝑗
𝐶𝑖,𝑗 = Concentration at every grid cell [g/m3]
𝐴𝑖,𝑗 = Area of each grid cell [m2]
𝑈𝑖,𝑗 = wind speed at every vertical level [m/s]
𝑄 = Emission flux [g/s]
• Wind speed used in quantification is the wind
component perpendicular to the measurement
plane

• Constant wind speed
Different treatments for wind data
Computed methane emission fluxes using different wind treatments
• Neutral logarithmic wind profile
• Project perpendicular wind
component into the location of the
drone system and perform Kriging
𝑢 𝑧 =
𝑢∗
𝜅
ln
𝑧 − 𝑑
𝑧0
𝑢 𝑧 = wind at height z
𝜅 = 0.4 karman constant
𝑧0 = surface roughness

Estimate residuals with respect to wind speed and
wind direction variability
• Lowest residuals are obtained at wind
speeds ranging from ~3-5 m/s
• Emission flux computed at wind speeds
below 2 m/s tend to be underestimated
• Large wind directional variability (>30o)
results in underestimated emission
fluxes
• Emission estimates computed with wind
direction below 20o variability tend to
provide lower residuals
• Best emission estimates were obtained
at wind speeds of > 4 m/s and wind
direction variability below 20o
* Residuals relative to true flux

randulph.morales@empa.ch | 08randulph.morales@empa.ch | 11© Empa 2020. All rights reserved.
Comparison of cluster-based ordinary kriging and ordinary based kriging
• Under optimal meteorology conditions (wind speeds > 4-5 m/s and wind direction variability below 30o), cluster-based Kriging
performs better than standard ordinary Kriging
• No significant difference between quantification using standard ordinary kriging and cluster based ordinary kriging in cases of
suboptimal weather conditions
• Methane emission estimates using cluster-based Kriging deviates 3-10% from the true flux under optimal weather conditions
• In cases of low wind speeds, both ordinary and cluster-based Kriging underestimates the true flux by an average of 70%

Summary
Controlled release experiments were performed to characterize the performance of a drone-based
mass balance approach in quantifying methane emissions.
Comparison of emission estimates obtained from Active Aircore measurements and drone-based
QCLAS in-situ measurements
Outlook
Steady wind speeds of 3-5 m/s with low variability (0-20 degrees) results to estimates close to real
emissions
Using a logarithmic wind profile in the quantification of methane emissions result to higher
estimates when compared to estimates using average wind speeds and/or projected wind speeds
Cluster based ordinary Kriging performs better than standard ordinary Kriging under optimal wind
conditions
Emission estimates obtained from cluster-based Kriging are within 3-10% away from the true flux
under optimal weather conditions

References
• Graf, M., Emmenegger, L., and Tuzson, B. , "Compact, circular, and optically stable multipass cell for mobile
laser absorption spectroscopy," Opt. Lett. 43, 2434-2437 (2018)
• Ruckstuhl, A. F., Henne, S., Reimann, S., Steinbacher, M., Vollmer, M. K., O'Doherty, S., Buchmann, B., and
Hueglin, C.: Robust extraction of baseline signal of atmospheric trace species using local regression,
Atmos. Meas. Tech., 5, 2613–2624, https://doi.org/10.5194/amt-5-2613-2012, 2012.
• Tuzson, B., Graf, M., Ravelid, J., Scheidegger, P., Kupferschmid, A., Looser, H., Morales, R. P., and Emmenegger, L.:
A compact QCL spectrometer for mobile, high-precision methane sensing aboard drones, Atmos. Meas.
Tech. Discuss., https://doi.org/10.5194/amt-2020-102, in review, 2020.

This work was supported by the ITN project Methane goes Mobile – Measurements and Modelling (MEMO2; https://h2020-memo2.eu/).
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie
Sklodowska-Curie grant agreement No 722479.
Acknowledgements

Morales, Randulph: Spatio-temporal kriging in estimating local methane sources from drone-based laser spectrometer measurements

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Morales, Randulph: Spatio-temporal kriging in estimating local methane sources from drone-based laser spectrometer measurements

Similar to Morales, Randulph: Spatio-temporal kriging in estimating local methane sources from drone-based laser spectrometer measurements (20)

More from Integrated Carbon Observation System (ICOS)

More from Integrated Carbon Observation System (ICOS) (20)

Recently uploaded

Recently uploaded (20)

Morales, Randulph: Spatio-temporal kriging in estimating local methane sources from drone-based laser spectrometer measurements