When calibrating simulations of dust clouds, both the intensity and
the position are important.
Intensity errors arise mainly from uncertain emission and sedimentation strengths,
while position errors are attributed either to imperfect emission timing or to uncertainties in the transport.
Though many studies have been conducted on the calibration or correction of dust simulations,
most of these focus on intensity solely and leave the position errors mainly unchanged.
In this paper, a grid-distorted data assimilation,
which consists of an image-morphing method and an ensemble-based variational assimilation,
is designed for realigning a simulated dust plume to correct the position error.
This newly developed grid-distorted data assimilation
has been applied to a dust storm event in May 2017 over East Asia.
Results have been compared for three configurations:
a traditional assimilation configuration
that focuses solely on intensity correction,
a grid-distorted data assimilation that focuses on position correction only and the
hybrid assimilation that combines these two.
For the evaluated case, the position misfit in the simulations is shown to be dominant in the results.
The traditional emission inversion only slightly improves the dust simulation, while the grid-distorted
data assimilation effectively improves the dust simulation and forecasting.
The hybrid assimilation that corrects both position and intensity of the dust load provides
the best initial condition for forecasting of dust concentrations.
Introduction
Dust storms are a result of wind erosion
liberating particles from exposed dry surfaces .
They occur commonly in arid or semi-arid regions, e.g.
North Africa, the Middle East, Southwest Asia and East Asia .
During dust events, fine dust particles can be lifted several kilometres high into the atmosphere and carried over thousands of kilometres .
It is estimated that 2000 Mt dust is emitted into the atmosphere annually .
Such a huge amount of atmospheric mineral dust has profound effects on the Earth system,
e.g. the cycles of energy, carbon and water .
Specifically, dust particles are recognized in fertilizing terrestrial and ocean ecosystem ,
enhancing precipitation by acting as droplet nuclei and
interacting with atmospheric radiation, and may therefore significantly modify
the Earth radiative balance .
Apart from the influence on the environment,
dust storms pose
a great threat to human health by carrying thousands of tonnes of
particulate matter as well as bacteria, viruses and
persistent organic pollutants to densely populated regions .
Reported illnesses include dust pneumonia, strep throat,
cardiovascular disorders and eye sicknesses
.
The low visibility caused by dusts can also lead to severe disruptions of
air and other traffic. For example, more than 1100 flights were delayed or cancelled in Beijing
after it was struck by an extreme dust event in May 2017.
Together with growing interest in dust storms, the understanding of the physical
processes associated with dust storms has increased rapidly over the
last decades .
Large efforts have been made to develop dust modelling systems
,
which mathematically simulate the life cycle
of dust including emission, transport and deposition.
Large-scale global dust transport models, e.g. CAMS-ECMWF , or regional ones,
e.g. NASA-GEOS-5
and BSC-DREAM8b ,
are essential parts of larger Earth system models.
The most important application of these models is to forecast dust concentrations over
a few hours to a few days in order to reduce the potential threats to society.
Though these systems are usually able to predict the starting and ending of a dust event,
large differences are found in emission and deposition burdens and spatial
distribution of dust clouds
.
Dust simulations could differ from observations by up to 2 orders of magnitude .
The modelling skills are limited due to several aspects,
e.g. the insufficient knowledge of aerosol size distribution , mismatch in
aerosol removal
and in particular to the inaccurate quantification of erosive dust emission .
In addition, the quality of the meteorological data,
e.g. wind fields and soil moisture, might strongly impact the prognostic quality of dust emission and transport.
In addition to the efforts of upgrading the physical descriptions in numerical models,
data assimilation techniques have been developed to improve
simulation of dust loads.
Data assimilation aims here to estimate the state of
dust concentrations by combining a dynamical model with available observations.
An assimilation system could for example adjust model parameters
within an allowed range such that a simulation is in better agreement with the observations.
Various types of observations have been used to adjust dust simulations, for example particular matter (PM) measurements and visibility records
from ground-based monitoring networks,
aerosol optical depth (AOD) from sun photometers
in the global Aerosol Robotic Network (AERONET), and the satellite-retrieved AOD .
Those studies focused either on updating atmospheric dust concentrations directly or on optimizing emission parameters that lead to better simulations.
In both cases, only the intensity of either concentrations or emissions is adjusted,
while other input parameters are assumed to be known, and processes of transport and removal are assumed to be certain.
In our previous studies, ground-based PM10
(total particulate matter with diameter less then 10 µm) measurements
and geostationary satellite AOD
were assimilated with the LOTOS-EUROS simulation model for dust storm forecasts over East Asia.
Also these studies solely focused on correcting emission intensities.
Data selection and
observation bias correction were important aspects here
to ensure that the available measurements were used correctly.
In addition, an adjoint method was used to
identify potential new dust emission sources in case the
empirical dust emission and its uncertainty scheme
cannot fully resolve the observation
.
Severe dust storm events in May 2017 over East Asia were used as test cases,
and the assimilation procedure was shown to improve the simulated dust concentrations
at the time of observation but also to improve forecasts of dust levels over windows of up to 24 h.
During these studies it was noted that although the modelling system in general
provided an accurate forecast of the dust plume, a severe position error
was present when the plume travelled over a large distance.
Specifically, forecasts by the model simulation
reported the dust arrival and departure 1 to 10 h prior to reality,
as is also illustrated in Sect. .
Position errors are a common problem in meteorology, for example in forecasting
hurricanes, thunderstorms, precipitation or meteorology-governing events like wildfires .
In geophysical disciplines, a positional error is often considered together with intensity errors to explain differences between two estimates .
A misfit in position usually leads to significant degradation of forecasts .
When discussing the accuracy of a dust forecast,
the shape and position of the plume is a key element as well as the intensity.
The position forecast determines which locations will be affected,
when the storm will arrive and for how long it will last, while the intensity
only describes the actual dust level.
A dust forecast with position misfit directly results in incorrect
timing profiles of dust loads.
The information about dust arrival and departure is sometimes more important than
the magnitude of dust load in the early warning system, but until now it has attracted only little attention.
Facing the unresolved positional mismatch,
the aforementioned data assimilation focusing solely on intensity
correction is less effective,
as is illustrated in Sect. .
Similarly to intensity feature misfits, positional misfits in model simulations
can also be adjusted to better resemble observations using data assimilation techniques.
Dust simulations suffer from position errors due to for example incorrect emission timing profiles or uncertainties in the transport, both driven by uncertain meteorology fields.
To be able to use data assimilation techniques for position correction,
it is essential to have a description of
these uncertainties.
However, position errors are much likely to be non-Gaussian and not easily captured by a static error covariance model .
For dust simulation, position errors could be caused by uncertainties
in the transport, in particular the wind field.
These uncertainties accumulate during
the time period from emission in remote desert areas to
arrival at observation networks in downwind
populated areas.
Position discrepancies might also arise from incorrect timing profiles of emissions,
which is not the case for our test event, as is explained
in Sect. .
However, determining the covariance either for transport or for emission timing profile is difficult.
Even if there is a complex covariance model that could account for the accumulation
of uncertainties along the long track of the plume, a substantial number of observations would then be required to constrain the optimal transport pattern.
Data assimilation methods based on static covariance models are therefore
often not suitable for dealing with position errors.
Instead, techniques from the field of image processing
could be combined with data assimilation
to avoid the need for a static covariance that
describes the origin of the position error.
This has been described as phase-correcting data assimilation
in numerical weather prediction ,
image-morphing ensemble Kalman filter (EnKF) for wildfire models ,
grid distortion data assimilation in oil reservoir modelling ,
and in general as position error correction in variational data assimilation .
The common approach in all these applications is to reposition the simulation using an image-morphing technique,
where the optimal morphing
parameters are adjusted to obtain the best fit with
the observations using data assimilation techniques.
In an application with dust plume simulations, the use of image morphing in the data assimilation avoids the need for developing a complex covariance model to describe uncertain transport or emission timing.
In this study, we propose a grid-distorted data assimilation method
to correct position misfits in a simulated dust plume,
which is a novel approach in the context of atmospheric dust modelling.
The implemented method offers an efficient way to correct
for a phase misfit between a dust simulation and available observations
without changing the transport
scheme and/or the emission timing profile.
The grid-distorted data assimilation is then combined with the emission
intensity inversion described in for a hybrid method.
The hybrid method is capable of optimizing the dust plume
in case both position and intensity misfits are presented in a dust simulation.
Starting from the initial condition using the hybrid assimilation posterior,
dust forecasting accuracy (in terms of both
arrival and departure and in actual dust load) is further ensured.
The paper is organized as
follows.
Section introduces the simulation model and observations used to represent the dust intensity.
Section shows an example of a dust position error in a dust simulation.
The error source is explained and identified to be the
uncertainty in long-distance transport process,
and it is illustrated that this uncertainty cannot be explained from the known spread in meteorological forecasts.
In Sect. ,
the necessity of position error correction is emphasized first,
and then the methodology of grid-distorted data assimilation is introduced.
A hybrid assimilation method is designed by combining
the grid-distorted data assimilation and emission inversion
in Sect. .
The new method is evaluated against assimilation focusing solely on emission intensities or position correction.
Section summarizes the conclusion and the added value of
using grid-distorted data assimilation to resolve model position error.
Dust model and observationsSimulation model
In this study,
the dust storm is simulated using a regional chemical transport model, LOTOS-EUROS v2.1
.
LOTOS-EUROS has been used for a wide range of applications supporting scientific research
and operational air quality forecasts both inside and outside Europe.
At present, the operational forecasts over China are released via the
MarcoPolo–Panda projects
through http://www.marcopolo-panda.eu/forecast/ (last access: July
2020).
Additionally, it is also implemented in the World Meteorological Organization (WMO) Sand and
Dust Storm Warning Advisory and Assessment System to provide short-time forecasting of the
dust load over the North Africa–Middle East–Europe areas; the online forecast product
is delivered via
http://sds-was.aemet.es/forecast-products/dust-forecasts/compared-dust-forecasts
(last access: July 2020).
To establish a dust simulation over East Asia, the model is
configured on a domain from 15 to 50∘N
and 70 to 140∘E, with a resolution of about
0.25∘×0.25∘.
Vertically, the model consists of eight layers, with a top at 10 km.
The dust simulation is driven by European Centre for
Medium-Ranged Weather Forecasts (ECMWF) operational
forecasts over 3–12 h, retrieved at
a regular longitude–latitude grid resolution of about 7 km.
An interface to the ECMWF output set is designed,
which not only interpolates the default 3 h
ECMWF short-term forecast meteorology to hour values but also averages the forecast to fit the LOTOS-EUROS spatial resolutions .
Physical processes included are wind-blown dust emission,
diffusion, advection, dry and wet deposition, and sedimentation.
Distribution of the barren region over East Asia and the China Ministry of Environmental Protection (MEP) observing network.
Original PM10(a.1), bias-corrected dust observations (a.2),
the a priori surface dust concentration (b), maximum over the ensemble simulations driven by ensemble meteorology (c),
posterior dust simulation of the emis inversion(d), grid-distorted assim posterior (e)
and hybrid assim posterior simulation (f) at 15:00 CST on 5 May. SDC: surface dust concentration.
Definitions of emis inversion, grid-distorted assim and hybrid assim
can be found in Table .
Observation network
The observations used in this study consist of hourly PM10 concentrations
from the China Ministry of Environmental Protection (MEP) air quality monitoring network,
which is shown in Fig. .
By now, the network has over 1700 stations and hence offers an opportunity
to track the whole dust plume
while it moves through the region.
All these PM10 measurements are actually
a sum of dust and airborne particles (black carbon, sulfate, etc).
Since the analysed event
is an extremely severe
case, these PM10 measurements were
directly used to quantify the dust load in .
In this study however,
an observational bias correction is performed to
make the PM10 measurements fully representative of the dust loads.
First, non-dust aerosol levels are calculated using
a LOTOS-EUROS simulation following the MarcoPolo–Panda configuration but with the dust tracers disabled.
Using these simulations, bias-corrected dust observations were calculated by subtracting the non-dust loads
from the original PM10 observations.
The original PM10 measurements vs. the pure dust observations can be seen in
Figs. a.1 and a.2
and a.1 and a.2.
As dust aerosols are far more dominant during the severe dust storm,
the bias-corrected dust observations are actually very close
to the original PM10 measurements.
Position error
Numerical dust models are expected to provide correct timing profiles and intensity of dust loads.
However,
a discrepancy between observations and simulations is relatively common in terms of both position and intensity.
Unlike the intensity estimation that has been widely investigated already,
the position
error has received less attention, but it has been the main focus of this study.
Position error in dust simulation
The test case investigated in this study is a
severe dust storm event that occurred over East Asia in May 2017.
The detailed calibration of the model simulations
on this test case can be found in .
The dust emission occurred from 2 May in the Mongolia, Gobi and Alxa deserts,
of which the location can be seen in Fig. .
The dust particles lifted up from these regions
were then transported in the south-east direction.
After 2 to 3 d
of transport, the dust plume arrived in central China,
where according to the surface observations a positional error was present in the simulations.
The position error in the simulation
is illustrated in
Fig. , which
shows the original PM10 measurements,
bias-corrected dust observations and the a priori
surface dust concentration (SDC) simulation
on 5 May at 15:00 (China Standard Time, CST).
The measurements of PM10 are strongly elevated when the dust plume passes
and could increase to values over 2000 µgm-3.
Under normal conditions the observations (non-dust aerosols)
usually do not exceed values of 200 µgm-3,
and therefore the location of a dust plume is clearly visible
in the bias-corrected dust observations as well as in these original PM10 observations.
According to the observations in panel (a),
the dust plume forms a band from the west to the east
over central China.
The corresponding simulation in panel (b)
shows a plume with a similar shape but at a location farther to the south-east.
This is indicated by the markers that are added to the plumes.
For the observations the markers for the left part of the plume are around 35∘ N, and
the right one stays around 37.5∘ N,
while for the simulation they are around 32.5 and 36∘N.
The dust plume is therefore positioned about 200 km too far to the south;
with a wind speed of 40 kmh-1 this implies
a difference in arrival time of 5 h.
The simulated plume, in particular the left part, is also broader than the rather sharp band that
is seen in the observations.
To quantify the simulation-minus-observation mismatch,
the root mean square error (RMSE) between dust simulation and bias-corrected
dust observation has been computed over all stations
in central China (marked by the black framework in
Fig. a). The RMSE of the a priori dust simulation is as high as 388.1 µgm-3. This vast mismatch is attributed to the sum of intensity and position error (mainly), as is explained in Sect. .
PM10 observations (a)
and the a priori dust simulation (b) at 15:00 CST on 4 May.
SDC: surface dust concentration.
Illustration of intensity-centred assimilation only (a)
versus assimilation after position error correction (b).
Uncertainty in emission timing profile
One potential origin of the position error is an incorrect emission time profile.
That is, changes in the time period over which
dust is released from the source regions could
to some extent alter the position of the simulated plume.
Actually during the first 48 h after dust emission started,
the simulated dust plume was still in northern China and showed in general
the same pattern as is visible in the observations.
For example the aerosol optical depth (AOD) retrieved
from the Himawari-8 geostationary satellite showed that
the simulated plumes are correctly positioned in northern China .
The good phase match in general can also be seen from
a snapshot of the ground PM10 observation
vs. the simulated surface dust concentration on 4 May at 15:00 CST
in Fig. .
There might already be position misfits in the dust simulation at these snapshots that are not easily detected.
The magnitudes of the dust concentration showed discrepancies,
but these could be corrected by emission inversion
through assimilation of those AOD observations or PM10 measurements.
The good match in position between simulated and observed dust plume indicates
that the emission timing profile is rather accurate too.
When the dust plume is transported farther southward,
the simulated plume starts to
deviate from the available surface measurements.
Uncertainty in meteorology
Another possible origin of the position error in the simulations is the
uncertainty in the meteorological data.
In our study, the simulation model is driven by ECMWF meteorological forecasts.
The uncertainty in this input is reflected in the
ensemble forecasts that are available too .
For the studied period,
the ensemble forecast of Nmeteo=26 different members is available,
where each member is a perturbation of the deterministic forecast.
The resolution of meteorological ensemble is about 30 km,
which is comparable to the LOTOS-EUROS resolution for these experiments.
To estimate the impact of the meteorological uncertainty,
the dust simulations have been repeated Nmeteo times
using input from the meteorological ensemble.
The spread in simulated dust concentrations is computed in
terms of the maximum over the ensemble via
cmax(x,y,z,t)=maxc1(x,y,z,t),…,cNmeteo(x,y,z,t).
In here, ci represents the dust concentration field that results from
a simulation with the ith ensemble member.
This measure reflects for each location whether in any of the simulations
a severe dust load is present.
The ensemble maximum here can be used as a quick criterion:
only if the dust plume (in observational view) is covered by the maximum is meteorological uncertainty (represented by ensemble meteorological inputs) likely to resolve the dust plume position error.
A snapshot of the ensemble maximum Eq. () at 15:00 CST
is shown in Fig. c.
The map shows a broader plume, which implies that some ensemble members result
in a dust plume that is more to the north
and others more to the south than the a priori forecast.
The extended dust field is however not wide enough to cover the area with increased observation values.
The uncertainty approximated using the available meteorological ensemble therefore could not be used to fully account for
the position error. The origin might be that the required case is not represented in the ensemble but also because the
simulated dust transport in the LOTOS-EUROS model does not take all meteorological details into account or is simply not
accurate enough.
To resolve the position error,
a complex covariance matrix would then be required to fully account for
the accumulation of uncertainties along the long track of the plume.
The uncertainty in the interface that interpolates and averages
the meteorological forecast to fit our LOTOS-EUROS model resolution should also be taken into account here.
Grid-distorted data assimilation
The experiments in the previous section showed that the mismatch between dust plume simulation and observations cannot be easily explained by inaccurate emission timing or uncertainty in the meteorological data available.
We therefore propose to use a griddistorteddataassimilation to correct for the position errors without attributing this error to a specific part of the simulation model or its input.
Necessity of position error correction
Position errors pose a great challenge for data assimilation, where it is often easier to adjust amplitudes rather than a position.
This strongly limits the forecast skill, and further improvement requires the correction of position errors.
The difference between assimilation of observations
with or without correction of position errors is illustrated in
Fig. .
The panels show a hypothetical dust concentration along a coordinate,
which could be either spatial or temporal
without loss of generality.
The a priori simulation (dashed) differs from the observations
(stars) both in amplitude and shape (location and width in space or arrival and duration in time).
The underlying simulation model is therefore likely to be imperfect in
either emission strength, emission timing or transport
or
a combination of all of these.
The left panel illustrates a typical assimilation of observed concentrations
that adjust emission strengths only.
In such an assimilation, the a priori concentrations are just scaled towards the observations.
The posterior concentrations are therefore closer to the observations but only where the a priori simulations
have any concentrations at all.
On the left side of the axis the simulated concentrations are therefore
strongly reduced to match with the zero observations.
However, if initially no dust is present in the simulations,
as is the case on the right side of the axis,
then the assimilation does not suddenly introduce dust out of nothing.
The right panel illustrates how a position error correction could improve this.
Before analysing the observations, the a priori plume is shifted
and reshaped to have the best match with the observations, ignoring differences in amplitude.
If this repositioned plume is analysed with the available observations,
the posterior result is in much better agreement with the
observations along the entire axis, also where initially no dust was simulated.
The assimilation will still adjust the emission strengths, but these are
now not adjusted to correct for transport errors.
Illustration of grid distortion technique:
(a) original grid map,
(b) original dust concentrations as band,
(c) distorted grid map,
(d) distorted dust concentrations.
Definition of assimilation experiments.
ExperimentTarget errorDescriptionA priori–Pure model, no assimilationEmis inversionIntensityEmission inversionGrid-distorted assimPositionGrid-distorted data assimilationHybrid assimPosition and intensityEmission inversion based on grid-distorted assim
Diagrams of emis inversion, grid-distorted assim and hybrid assim systems.
Grid distortion
To align the dust plume with the observations,
a grid distortion method as described by is used.
The procedure is illustrated in Fig. .
In transport models, the flow equations are usually solved on a discrete grid.
For the LOTOS-EUROS model used here, the grid is Cartesian (perpendicular in longitude and latitude) and regular in spacing (panel a of the figure).
Computed concentrations represent an average over a grid cell,
and the simulated plume therefore consists of a set of grid cells with a substantial dust load.
Panel (b) shows an example with a dust plume as a band from left to right.
The grid distortion smoothly transforms the Cartesian grid into a non-Cartesian grid.
That is, the corners of the grid cells are repositioned to a nearby location such that each distorted grid cell remains connected to its original neighbours (panel c).
The dust concentration in each grid cell (in µgm-3) is kept constant after distortion to ensure a smooth variation in dust intensities over neighbouring cells.
The dust plume is deformed together with the grid (panel d).
In mathematical formulation, let (x,y) denote the original Cartesian coordinates.
A discrete model grid with regular spacing Δx×Δy is
defined on points (xi,yj), with i and j the integer indices of the grid points in the x and y direction.
The grid distortion is defined as a coordinate transformation that projects an original location (x,y) onto a new location (λ,ψ) with
2λ=Λ(x,y)3ψ=Ψ(x,y).
Following , the grid distortion is
described using a Poisson equation.
The elliptic equation is broadly utilized
in mechanical engineering and theoretical physics to
describe how an object diffuses in space given a charge.
The repositioned grid locations (λ,ψ)
are the solutions of two 2D Poisson
equations
with the charges or
distortion functionsP and Q on the right-hand side:
4∂2Λ∂x2+∂2Λ∂y2=P(x,y)5∂2Ψ∂x2+∂2Ψ∂y2=Q(x,y).
The distortion functions P and Q that drive the grid distortion are initially unknown, and their optimal values are to be calculated as part of the data assimilation procedure described in Sect. .
The second-order derivatives in Eqs. () and () are discretized on the grid using finite differences.
For Eq. (), the discretization is
λi+1,j-2λi,j+λi-1,j(Δx)2+λi,j+1-2λi,j+λi,j-1(Δy)2=Pi,j,
and Eq. () gives a similar discretization.
When this system is solved for a given right-hand side,
the result is a grid of 2D locations (λi,j,ψi,j) corresponding to
the distorted positions of the original grid points (xi,yj).
This system can be solved using a numerical method for
linear equations.
In our experiments, we use the red–black ordering
Gauss–Seidel method
to solve the discrete system of linear equations.
The distorted dust plume is
interpolated back to the Cartesian grids using the nearest searching method
for comparison with observations (that are defined on longitude–latitude coordinates),
and to serve as initial fields for the following simulation steps.
Distortion estimation using 4DEnVar
The grid distortion method provides a new way of repositioning
the dust plume without adjusting the long-distance dust transport.
We use the ensemble-based variational (4DEnVar) data assimilation algorithm to optimize the grid distortion.
To find the optimal distortion, the initial value and covariance of P and Q need to be defined first.
Each element in the two distortion equations is assumed to have
a zero mean and a standard deviation, empirically chosen to be 0.015.
To enforce a smooth grid distortion, we also prescribe a correlation c between two elements P(xi,yj) and P(xk,yl)
(and similar for Q):
c=e-d(xi,yj;xk,yl)/L,
where d represents the spatial distance in kilometres, and L is
an empirical length scale that is set to 1000 km.
The parameters used in this study (standard deviation, correlation length scale) were chosen based on experiments for the described dust event; for other events they might need to be revised.
In our 3D model, the grid distortion is applied in the horizontal direction only, changing each layer in the same way.
This is mainly to reduce the degrees of freedom in the distortion since no information on the 3D structure of
the plume is available from the current observations (surface data and satellite-retrieved column information).
It is however also possible to use a 3D distortion with a few degrees of freedom in the vertical
for dust events where measurements of the vertical structure are available, e.g. lidar backscatter coefficient
.
An ensemble of random distortion fields is generated using the assumed prior value (zero) and the assumed covariance.
Each member is a vector s collecting all elements of P and Q on the discrete grid:
[s1,…,sN].
In our experiments the ensemble size N was set to 100.
For each of these ensemble members, the distorted grid (λ,ψ)
is solved from the system of the discrete Poisson equations as described in Sect. .
With this an ensemble of distorted dust maps is formed
from the a priori dust field x:
[x(s1),…,x(sN)],
where x(si) represents the distorted dust field using distortion si.
Denote the ensemble perturbation matrix or covariance square root by
S′=1N-1[s1-sb,…,sN-sb],
where sb is the (zero) prior value.
In a 4DEnVar assimilation, the optimal distortion vector sa is defined to be a weighted sum of the columns of the perturbation matrix S′ using weights from a control variable vector w:
sa=sb+S′w.
The optimal control variables are then calculated through minimizing of the cost function:
J(w)=12wTw+12(HXSb′w+d)TR-1(HXSb′w+d).
In here, d is referred to as the innovation
that describes the difference between observations y and simulations on the distorted grid:
d=Hx(sb)-y.
In here, H is the observation operator
that simulates the observed value on the distorted grid, which here simply takes the model simulation
from the grid cell holding the observation location.
The distortion uncertainty is transferred into the observation space through
application of H on the ensemble members:
HXSb′≈1N-1[Hx(s1)-Hx(sb),…,Hx(sN)-Hx(sb)].
The observation error covariance matrix
R describes the possible differences
between simulations and observations due to observation representation errors.
R here is defined as a diagonal matrix,
in which each representation error is set to
an observation-dependent value ranging from 100 to 200 µgm-3
following .
To ensure that the position correction is not too much influenced
by differences in dust intensity, both the observations y
and prior dust simulations x are normalized using their maximum values.
Elements in R
are also then scaled using the square of the
maximum observed value.
The computation of the N=100 grid distortions is the
most time-consuming part of the 4DEnVa-based grid-distorted data assimilation method;
each of them costs around 2 min in our computing platform (CPU: Intel Xeon(R) E5;
programming language: Python 3.7.6). The computation of the ensemble distortions
could be re-implemented in a more efficient language but also be easily parallelized;
the grid-distorted assimilation method is therefore expected to be computationally
efficient enough to allow implementation in an operational forecast.
Dust storm data assimilation
The grid-distorted data assimilation
was introduced for repositioning the simulated dust clouds.
To evaluate the effectiveness,
assimilation experiments including grid distortion have been performed and compared with a traditional assimilation configuration focusing on intensities only and a hybrid assimilation that combines these two.
An a priori simulation serves as a reference for all assimilation experiments. The
emission inversion assimilation corrects for the dust intensity errors only, while the grid-distorted assimilation only corrects for the position error.
The hybrid assimilation combines both in order to correct for the intensity as well as the position error.
Assimilation methods
Figure shows the
schematic overview of the three assimilation methods
listed in Table .
The left panel shows the
set-up of the emission inversion,
as described in detail in .
The inversion combines the transport model (LOTOS-EUROS)
with a four-dimensional variation (4DVar) data assimilation using a reduced-tangent linearization .
The system assumes that the processes of dust transport and removal are
simulated correctly, while only the emission
is imperfect.
The uncertainty in the emissions was
parameterized as a sum of two sources:
the uncertainty in the friction velocity threshold
and in the erosive wind fields.
The dust emission intensity in the source regions
is then optimized such that the amplitude of
the simulated concentrations is as close to
the observations as possible. The optimized
emission fields could then be used to drive
simulations that have a better forecast skill than simulations with the original emissions.
The grid-distorted assim
is designed to adjust the position of the simulated dust plume only.
As described in Sect. ,
the impact of the actual dust concentrations
is avoided by normalizing the dust simulations and observations
using their maximum values before calculation of the distortion;
afterwards, the distorted dust field is multiplied by the same maximum value again.
The right panel of Fig.
shows the set-up of the hybrid assim.
Different from the emis inversion
and grid-distorted assim,
the hybrid assim performs two assimilations sequentially.
First the grid-distorted assim
is conducted for repositioning the simulated dust plume.
Then, the position-corrected dust plume is used as a prior in the second assimilation
(similar to an emis inversion) to adjust the
emissions to have the best possible match between actual (not normalized) observations and position-corrected simulations.
The posterior dust field from the hybrid assim
is then used as the initial condition for forecast simulations.
In
all assimilation tests,
only observations from the snapshot of 5 May at 15:00 CST are used for
fair comparison.
The repositioned plume is only available for this single moment;
measurements at earlier times
can therefore not be accurately assimilated in hybrid assim since the corresponding simulation still has a position error then.
In the emis inversion,
the assimilation window is set
from 2 May, 08:00 CST, which fully
covered the related dust emission for this event.
Optimized plume position and dust load
The a priori dust plume described in Sect. is
assimilated with observations using the emis inversion, the grid-distorted assim or the hybrid assim.
The posterior surface concentrations
are shown in Fig. d–f, respectively.
The optimized dust plumes are evaluated
by their position and the RMSE metric that was introduced in Sect. to quantify the difference with observations.
Note that observations that are used to evaluate the posterior performance
are the same as those that have been assimilated. When evaluating the method over a longer time period (multiple dust events),
validation with independent observations should be considered.
Panel (d) shows the posterior dust plume using the emis inversion.
The markers indicate that it has
in general the same position as the a priori,
and hence the position error has not been corrected yet.
In terms of root mean square error (RMSE), the emis inversion posterior simulation is improved, but only slightly;
the RMSE is reduced from 388.1 µgm-3
for the a priori simulation to 362.9 µgm-3. The emis inversion also has little effect on
the dust simulation at earlier periods of the dust event, which can be found through
a comparison of the a priori and emission-inversion-only
simulations on 3 May at 13:00 CST in Fig. S1 in the Supplement.
The a priori and emis inversion also present a relatively similar performance in the early stage.
Using the grid-distorted assim, the repositioned dust plume in panel (e)
matches well with the ground observations shown in panel (a.2).
The marker indicating the left side of the plume is now around 35∘ N, which is in agreement with the observations; also the markers at the centre
and the right side are now better positioned.
Only the very left part of the repositioned dust plume (west of 110∘ E)
still shows a discrepancy compared to the PM10 observations.
This can be explained from the fact that this part of the dust plume has a relatively low dust load, which
makes the corresponding position error less important in the cost function Eq. ().
In addition, a rather large grid distortion is required for this part of the dust plume to match the measurements,
which is constrained with the assumed covariance of the distortion function.
The RMSE of the posterior simulation
is now significantly reduced to 251.1 µgm-3.
Though the dust plume is now correctly repositioned, the simulated dust concentration does not exactly
match the actual measurements. Especially in the plume centre, the posterior simulation
shows dust concentrations over 1200 µgm-3 that are still similar
to the a priori simulation, while the
bias-corrected observations
indicate that the dust intensity at most stations is lower than 1200 µgm-3.
The hybrid assim posterior simulation provides the best performance, as shown in panel (f).
Not only is the dust plume realigned with the observations,
but also the amplitude of the dust loads agrees better with the actual situation.
For instance, the dust concentration in the plume centre is reduced from 1500 to 1200 µgm-3,
and in the upper left part of the plume the concentration level is lifted from 100 to 200 µgm-3.
As a result, the RMSE in the hybrid assim is
reduced to 223.4 µgm-3.
PM10(a.1), bias-corrected dust observations (a.2),
the a priori forecast (b), ensemble maximum (c) dust forecast
and dust forecast driven by emis inversion posterior (d),
the grid-distorted assim posterior
(e), and hybrid assim posterior simulation (f) at 21:00 CST on 5 May. SDC: surface dust concentration.
Time series of PM10 measurements, bias-corrected dust observations, a priori simulation and forecasting driven by the initial state from emis inversion,
grid-distorted assim and hybrid assim
at Baoji (a), Xinxiang (b), Xuchang (c),
Bozhou (d), Zibo (e) and Zhaoyuan (f).
The vertical dashed black line indicates the start of the forecast.
RMSE of the a priori dust simulation and forecasting using the initial state from
emis inversion, grid-distorted assim and hybrid assim.
Forecasting of dust plume position
In an operational setting the posterior dust concentrations are used as
initial conditions for a forecast.
Starting from the analysis results,
forecast runs have been performed.
A snapshot of the resulting forecast of
the surface dust concentrations as well as the
PM10 measurements, bias-corrected dust observations
and the a priori forecast at 21:00 CST on 5 May are shown in Fig. .
The ground observations in panel a.1 and a.2 indicate that
the dust plume is now located along 35∘ N.
In both the a priori simulation and in the forecast based on emis inversion,
the right, centre and left plume markers are about 100, 300 and 200 km farther south, respectively.
However, the forecasts based on grid-distorted assim or hybrid assim
assimilation both show plumes with positions in better agreement with the observations.
The best results are obtained for the hybrid assim,
which shows better agreement for the central and upper right part
of the dust field (panel f) compared to the grid-distorted result (panel e).
Time series at stations
Figure shows times series of dust concentrations
at six different observation sites.
The locations can be found in Fig. and were selected to illustrate the general results but also challenges to be solved in future.
The time series show PM10 observations (red circles), bias-corrected observations representing the dust part (red dot),
the a priori forecast (black line)
and the forecasts driven by the three assimilation tests
starting from 15:00 CST on 5 May.
For all six sites, the a priori dust simulations estimate
an arrival time of the dust cloud that is at least 4 h too early.
The emis inversion focusing on intensity correction does not
improve the forecasting of the arrival time since it only changes the emission strength.
Ignoring the intensity of the dust load, the temporal profiles of the dust forecasts
driven by the grid-distorted assim
after 5 May at 15:00 CST
are in good agreement with the temporal profile of the dust observations.
For stations on the upper side of the plume, e.g. Baoji in panel (a),
the declining trend predicted by the a priori and emis inversion forecasts
is well reproduced by the grid-distorted assim.
For sites where the descent pattern was
not captured by the a priori simulation, the emis inversion helps little, while grid-distorted assim resolves the decreasing trend, as can be seen in Zibo and Zhaoyuan.
For stations downwind
of the plume like Xinxiang, Xuchang and Bozhou,
the dust concentrations show an up-and-down pattern caused by the arrival and departure of the plume.
The a priori and emis inversion forecasts are unable to capture the dust profile.
For instance in Bozhou, the a priori simulation indicated that the main dust plume arrived
earlier than 00:00 CST on 5 May, and it started to decline from 12:00 CST.
However, the real observation showed that the dust storm actually
arrived around 12:00 CST, with a steady increase in concentration.
Starting from the grid-distorted assim,
the forecast shows concentrations with a trend similar to the observations,
although the increase starts a few hours too early.
The observation-minus-simulation discrepancy is further reduced for most stations using the
hybrid assim that combines the grid-distorted assim
and emis inversion.
Evaluation of forecast skills
The forecast skill of the three assimilation algorithms is also evaluated using the
RMSE indicator that was also used for the a priori and posterior dust simulations
in Sects. and .
During the period from 16:00 CST on 5 May to 07:00 CST on 6 May,
the a priori RMSE
reached values around 300 µgm-3.
The assimilation based on emis inversion helped to decrease the RMSE of
the forecast simulations with about 20 µgm-3.
The improvement is limited since position errors are dominant and still present.
The grid-distorted assim is efficient in enhancing dust forecast skills
in terms of the RMSE, which significantly reduce to less than 200 µgm-3.
When combined with emis inversion in the hybrid approach, an additional decrease in RMSE of about 20 µgm-3 is achieved.
These results show that the grid-distorted assim is capable of correcting the position error in the simulated dust plume effectively;
the hybrid assim that combines the grid-distorted assim and emis inversion provides the best initial condition to drive the dust forecast in the short term.
Summary and conclusions
Evaluation of dust storm forecasts focuses on two main criteria: the intensity of the dust load and the position of the cloud.
Various studies on improving dust forecasts focused mainly on correcting the intensity only.
However, positional misfits are unavoidable
as a result of inaccurate emission timing profile and/or
accumulation of uncertainties in long-distance transport and therefore need to be taken into account too.
An extremely severe dust storm in May 2017 over East Asia was used as the test case in this study.
A regional chemical transport model, LOTOS-EUROS, was used to reproduce the dust event.
PM10 observations are available from the China Ministry of Environmental Protection (MEP) air quality monitoring network;
bias-correction was used to process the original PM10 measurements to accurately represent the dust load.
The position misfits are obviously detected in the results,
especially when the simulated dust plume is transported thousands of kilometres away to central China.
The positional misfit in dust simulation could be corrected by data assimilation too.
Assimilation configurations for this type of application
usually require definition of a background error covariance or
an ensemble perturbation scheme that could resolve the full
observation–simulation positional discrepancy too.
This covariance could for example include the meteorological uncertainty,
as described by a meteorological ensemble forecast.
For the dust storm studied here it was however shown that the spread in the available meteorological ensemble and/or the way in which the simulation model is using it is not sufficient to explain the position error in the simulations.
Therefore, a complex covariance model that could account for the accumulation
of uncertainties along the long track of the plume would be required while using the traditional assimilation method.
Meanwhile, a substantial number of measurements would then be required to constrain the optimal transport pattern too.
Alternatively, an image-morphing method, grid distortion,
is adopted to reposition the simulated dust plume in this paper.
The method is then combined with 4DEnVar for
a griddistorteddataassimilation,
which focuses solely on correcting the dust field position to best fit the assimilated observations.
Since in reality both position and intensity errors might be present,
a hybrid assimilation algorithm is proposed. In this hybrid system,
the griddistorteddataassimilation and an intensity-centred emission inversion
are performed after each other.
Assimilation tests using either the emission inversion
or griddistorteddataassimilation only
or using the hybrid assimilation have been conducted on the studied dust event.
The posterior dust simulation and the forecast are slightly improved by using emission inversion.
This indicates that the traditional intensity-centred data assimilation
is of little help in the case that positional errors are present.
Only using the griddistorteddataassimilation,
strongly improved posterior and forecast simulations are obtained.
The best results are obtained when the hybrid assimilation is performed, with both the position and intensity errors corrected.
The grid-distorted assimilation should be seen as an extension
to traditional intensity-centred assimilation, not as a replacement.
In the presence of a position error, grid-distorted data assimilation is
a computationally efficient pre-processing procedure to correct for errors that are not resolved otherwise.
The method could be used to further explore 3D dust and aerosol structure by combining the 3D grid distortion and
observations with vertical layering information.
Code and data availability
The source code and user guidance of the CTM, LOTOS-EUROS, can be obtained from https://lotos-euros.tno.nl.
The grid-distorted data assimilation algorithm is in the Python environment and is archived on Zenodo (10.5281/zenodo.4579960; ).
The real-time PM10 data are from
the network established by the China Ministry of Environmental Protection
and accessible to the public at http://106.37.208.233:20035/.
The observations covering the dust event are also archived on Zenodo (10.5281/zenodo.4579953; ).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-14-5607-2021-supplement.
Author contributions
JJ and AS conceived the study and designed the grid-distorted data assimilation.
JJ and AS performed the control and assimilation tests and carried out the data analysis.
AS, HL, HXL, BH, XW and AH provided useful comments on the paper.
JJ prepared the manuscript with contributions from AS and all other co-authors.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Financial support
The research has been supported by the National Natural
Science Foundation of China (grant no. 42105109) and Natural Science Foundation of Jiangsu Province (grant no. BK20210664).
Review statement
This paper was edited by Christoph Knote and reviewed by two anonymous referees.
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