Reducing multisensor satellite monthly mean aerosol optical depth uncertainty: 1. Objective assessment of current AERONET locations

Abstract

Various space-based sensors have been designed and corresponding algorithms developed to retrieve aerosol optical depth (AOD), the very basic aerosol optical property, yet considerable disagreement still exists across these different satellite data sets. Surface-based observations aim to provide ground truth for validating satellite data; hence, their deployment locations should preferably contain as much spatial information as possible, i.e., high spatial representativeness. Using a novel Ensemble Kalman Filter (EnKF)-based approach, we objectively evaluate the spatial representativeness of current Aerosol Robotic Network (AERONET) sites. Multisensor monthly mean AOD data sets from Moderate Resolution Imaging Spectroradiometer, Multiangle Imaging Spectroradiometer, Sea-viewing Wide Field-of-view Sensor, Ozone Monitoring Instrument, and Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar are combined into a 605-member ensemble, and AERONET data are considered as the observations to be assimilated into this ensemble using the EnKF. The assessment is made by comparing the analysis error variance (that has been constrained by ground-based measurements), with the background error variance (based on satellite data alone). Results show that the total uncertainty is reduced by ~27% on average and could reach above 50% over certain places. The uncertainty reduction pattern also has distinct seasonal patterns, corresponding to the spatial distribution of seasonally varying aerosol types, such as dust in the spring for Northern Hemisphere and biomass burning in the fall for Southern Hemisphere. Dust and biomass burning sites have the highest spatial representativeness, rural and oceanic sites can also represent moderate spatial information, whereas the representativeness of urban sites is relatively localized. A spatial score ranging from 1 to 3 is assigned to each AERONET site based on the uncertainty reduction, indicating its representativeness level.

1. Introduction

Aerosols affect the Earth’s climate on multiple spatial and temporal scales, mostly due to their inhomogeneous distribution and relatively short lifetime. Nonetheless, recent modeling studies of global climate change, such as those in the Intergovernmental Panel on Climate Change reports [Intergovernmental Panel on Climate Change, 2013], suggest that many climate problems, including aerosol-induced temperature and circulation changes, can be studied using monthly mean aerosol properties [e.g., Booth et al., 2012; Shindell et al., 2013]. In addition, as most climate model outputs are on monthly mean time scales, the validation of modeled aerosol fields also relies heavily on monthly averaged observations [Kinne et al., 2003, 2006].

In characterizing aerosol properties, aerosol optical depth (AOD) is the first-order quantity that is directly related to columnar aerosol loading and varies approximately linearly with direct aerosol forcing [Anderson et al., 2003]. Therefore, accurate estimation of aerosol radiative effects on climate scale critically depends on having precise knowledge of monthly mean AOD.

Remote sensing is currently the most extensively used technique to obtain aerosol information on large scales [Kaufman et al., 2002; de Leeuw and Kokhanovsky, 2009]. Until now, quite a few space-based sensors have been launched and corresponding algorithms developed to retrieve aerosol properties from space, primarily focusing on the midvisible AOD parameter. Whereas these different AOD products have all been validated and compare qualitatively well in space and time [Zhang and Reid, 2010; Sayer et al., 2012; Li et al., 2013, 2014a], quantitative disagreements still exist that hinder the accurate estimation of aerosol forcing using satellite measurements [Kahn et al., 2007, 2009; Shi et al., 2011]. Even in the monthly mean AOD, systematic differences due to instrument viewing geometry and sampling strategies, cloud screening, surface parameterization, and retrieval assumptions can still be significant. Previous comparison studies have shown noticeable differences in the monthly mean AOD products among various satellite sensors and ground-based measurements [e.g., Liu et al., 2006; Li et al., 2014b; Popp et al., 2016]. Even for coincident satellite measurements such as those from Terra Moderate Resolution Imaging Spectroradiometer (MODIS) and Multiangle Imaging Spectroradiometer (MISR), which are exempt from differences attributable to sampling issues, monthly mean AODs still do not always agree [e.g., Kahn et al., 2009, 2010; Shi et al., 2011]. These studies indicate that current satellite monthly mean AOD measurements still have nonnegligible uncertainties in many places.

Unlike satellite aerosol retrievals, ground-based remote sensing of aerosol optical depth using direct beam measurements does not rely heavily on the parameterization of the surface and assumptions of the aerosol model and can thus achieve much higher accuracy. The most extensive surface aerosol remote sensing network, the Aerosol Robotic Network (AERONET) [Holben et al., 1998], has become the standard data set for validating satellite AOD retrievals. For places where the disagreement between satellite data sets reveals large uncertainties, it is desirable to have AERONET sites so that the AOD uncertainty can be reduced using “ground truth” measurements. In fact, Shi et al. [2011] made recommendations for future AERONET deployments based on the spatial distribution of MODIS-MISR discrepancies and the current AERONET site density; i.e., Sun photometers should be deployed at locations where the difference between MODIS and MISR is large, but AERONET sites are sparse. However, the spatial information represented by a particular AERONET location is also critical because its measurement will be the most useful if it can represent the variability over a large area. In other words, the most desirable locations for surface observation sites are where, by considering the attributes of the locations, the total uncertainty of the AOD field is reduced to the greatest possible extent.

The spatial range of uncertainty reduction when considering a certain site can be characterized as the spatial representativeness of this site. Some AERONET sites’ spatial representativeness has been moderately addressed in previous studies, usually by correlating the time series of station measurements with the surrounding area [Hoelzemann et al., 2009] or by comparing station measurements with satellite data averaged over different spatial domains [Santese et al., 2007]. These studies were generally confined to a particular region and/or focused on specific aerosol types and only yielded qualitative results. Li et al. [2014a] evaluated satellite AOD against AERONET using the MCA (Maximum Covariance Analysis) technique and indicated that the MCA patterns can be partly explained by the representativeness of the sites. However, the patterns found by Li et al. [2014a] only reflect how similar a particular satellite data set is to AERONET, rather than the representativeness of the AERONET station.

Finding the covariability of the monthly mean AOD field is critical to evaluating the spatial representativeness of surface sites, as places where aerosol properties covary can be represented by the same site. Yet this quantity is impossible to accurately determine because neither do we have true AOD measurements and their associated uncertainties nor can we estimate it using previous correlation or MCA-based methods because these methods only reflect the covariability (or similarity) between AERONET and a single satellite data set. In this study, we present a novel approach based on the Ensemble Kalman Filter (EnKF) technique to objectively assess the spatial information represented by AERONET site locations. This idea is quite suitable for the multisensor problem here in that each satellite retrieval has its own characteristics and uncertainty, so they can be viewed as statistical samples of the same physical parameter—AOD. As a result, the AOD background covariance can be approximated by the sample covariance matrix. Ground-based observations, on the other hand, can be treated as observations to be assimilated into this multisensor ensemble. The uncertainty reduction after incorporating ground observations can then be quantified as the difference between the background error variance and the updated analysis error variance field. Our monthly mean AOD ensemble is constructed by combining monthly AOD anomaly time series from five widely used satellite data sets. To our knowledge, this is the first study that applies the EnKF technique to multisensor and ground-based aerosol observations, and as we show in the following sections, this methodology is both effective and physically justified.

Section 2 introduces the data sets used in this study. The procedure of the EnKF approach is described in section 3. Detailed analysis results are presented in section 4. Section 5 concludes the study with a short discussion of future work.

2. Data Sets

2.1. Satellite AOD Data Sets

To construct an appropriate ensemble with large enough spread, we incorporate several widely used satellite AOD products. Monthly mean AOD retrieval products from five sensors are used, namely, MODIS Terra, MISR, Sea-viewing Wide Field-of-view Sensor (SeaWiFS), Ozone Monitoring Instrument (OMI), and Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL). These five data sets have all been validated against ground-based observations within the expected accuracy level and are extensively used in aerosol and climate research. Their characteristics are described below.

The MODIS (Moderate Resolution Imaging Spectroradiometer) instrument is a multispectral radiometer, which has the capability of retrieving aerosol optical depth over land and ocean and a particle size constraint over dark water [Tanré et al., 1997]. It has a 2330 km swath width and realizes daily global coverage (each other data over the tropics). The official Level 3 monthly mean 550 nm AOD product at 1° × 1° resolution from MODIS on board the Terra platform is used for this study (MOD08_M3, collection 6, available from ftp://ladsweb.nasacom.nasa.gov/allData/6/MOD08_M3). The combined dark target and deep blue retrievals [Levy et al., 2013; Hsu et al., 2013; Sayer et al., 2014] are used to provide full global coverage. Validation of MODIS C6 AOD has been performed by Levy et al. [2013] (dark target) and Sayer et al. [2013] (deep blue). The time series of the data used spans from February 2000 to December 2014.

MISR (the Multiangle Imaging Spectroradiometer) is a multiangle sensor with nine pushbroom cameras also on board the Terra platform. The zonal overlap of the common swath of all nine cameras is at least 360 km, providing multiangle coverage in 9 days at the equator and 2 days at the poles [Diner et al., 1998]. In this study, we use the version 31 Level 3 gridded monthly AOD products (validated by Kahn et al. [2005, 2009]), available from http://eosweb.larc.nasa.gov. The original 0.5° × 0.5° data resolution has been rescaled to 1° × 1°. The rescaling is performed by assigning equal weights to each subgrid, and the final 1° × 1° grid is considered valid only when more than half of the subgrids have valid data. To be consistent with MODIS-Terra, 550 nm AOD from February 2000 to December 2014 is used.

The SeaWiFS (Sea-viewing Wide Field-of-view Sensor) sensor, launched on the SeaStar spacecraft in August 1997, is also a wide-view imager with a swath width of 1502 km that covers the globe in approximately 2 days. The SeaWiFS over land aerosol retrieval uses the deep blue algorithm developed by Hsu et al. [2004, 2006]. The AOD data over land have been validated using AERONET measurements [Sayer et al., 2012]. Here we use the standard Level 3 Version 004 monthly mean 550 nm AOD product (available from http://mirador.gsfc.nasa.gov/) covering the entire satellite lifetime from September 1997 to December 2010.

OMI (Ozone Monitoring Instrument) [Levelt et al., 2006] is a hyperspectral wide-view imager launched on the EOS Aura satellite in October 2005. Its 2666 km swath width produces near-daily global coverage. The AOD data used here are derived from the UV algorithm (OMAERUV) [Torres et al., 2007, 2013]. OMAERUV makes use of the instrument’s two near-UV channels to retrieve AOD and single-scattering albedo at 388 nm, and the 500 nm AOD reported in the standard product is converted according to the spectral dependence of the assumed aerosol model [Torres et al., 2007, 2013; Ahn et al., 2008]. Validation against AERONET and other satellite data sets is provided by Ahn et al. [2014]. Here we use Collection 003 data from the upgraded algorithm by Torres et al. [2013] at 1° × 1° spatial resolution, available from Goddard Earth Sciences Data and Information Services Center (http://mirador.gsfc.nasa.gov/). Because the current OMI aerosol product does not explicitly account for ocean color effects, retrievals over ocean are limited to absorbing aerosols as identified by the aerosol index. As a result, only data over land are used in constructing the ensemble (ocean data are obtained from PARASOL, which will be described in the next paragraph). The time period spans from October 2005 to December 2012, and the data have been linearly extrapolated to 550 nm using the 380 nm and 500 nm measurements. The extrapolation of OMI AOD depends on the assumed aerosol model by the OMI algorithm [Torres et al., 2007; Jethva and Torres, 2011], which might introduce additional uncertainty. Nonetheless, as we are only interested in the variability, any systematic biases caused by extrapolation should have been removed. Overall, we find reasonable agreement between the variability of extrapolated OMI AOD and the other data sets (figure not shown).

PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) is the third POLDER (Polarization and Directionality of the Earth Reflectance) [Deschamps et al., 1994] instrument. It was launched in December 2004 on the CNES/Myriade microsatellite. It measures light at multiple angles in eight spectral bands, three of which are polarized, for retrieving aerosol and cloud properties [Tanré et al., 2011]. Tanré et al. [2011] also validated PARASOL AOD products against AERONET observation. The originally reported 865 nm ocean AOD has been extrapolated to 550 nm using the 670–865 nm Angstrom Exponent product. We also downscaled the monthly mean Level 3 product from the 1/6° resolution (available at http://www.icare.univ-lille1.fr/parasol/) to 1° for consistency with the other data sets, using the same method as that for MISR. PARASOL AOD over ocean covers both fine- and coarse-mode aerosols, whereas over land, due to unknown surface properties, only fine mode is retrieved [Tanré et al., 2011]. We therefore use ocean data only to complement OMI data, for the period from October 2005 to December 2012.

In total, we have 179 monthly AODs from MODIS (from February 2000 to December 2014), 179 from MISR (also from February 2000 to December 2014), 160 from SeaWiFS (from September 1997 to December 2010), and 87 from OMI and PARASOL combined data set (from October 2005 to December 2012), which comprise the 605-member ensemble used for the EnKF implementation.

2.2. AERONET AOD Data

AERONET (Aerosol Robotic Network [Holben et al., 1998], http://aeronet.gsfc.nasa.gov/) is currently the largest surface aerosol remote sensing network in existence. It uses the CIMEL Sun photometer that measures spectral solar irradiance and sky radiances, operating at more than 400 locations worldwide. The AERONET AOD is derived from direct beam solar measurements [Holben et al., 2001] at two UV channels, 340 nm and 380 nm, and five visible/near-IR channels, 440 nm, 500 nm, 675 nm, 870 nm, and 1020 nm, with newer instruments also including the 1640 nm channel. The reported accuracy of quality assured Level 2.0 AOD data is ±0.01 at 440 nm [Holben et al., 1998]. For the EnKF analysis, only the locations, AOD values, and uncertainties are needed for AERONET. However, because not all sites have sufficient measurements to properly represent monthly mean aerosol variability, we first use Level 2.0 all-point AOD data availability to screen the stations with a hierarchy of criteria. Specifically, for a site to be selected, we require it to have at least four measurements per day, at least 20 days of data per month and at least 36 months of data with multiyear monthly means available for each month during the 2000 to 2012 period. This appears to be a strict set of criteria, leaving only 77 qualified stations, whose names and locations are listed in Table 1. Nonetheless, these stations cover most of the major aerosol source regions and types.

Table 1.

Information of the AERONET Sites Selected for the Study

Site	Longitude (°E)	Latitude (°N)	Dominant Aerosol Type	Reference	Spatial Scor
Agoufou	−1.48	15.34	Dust	Lee et al. [2010]	3
Alta_Floresta	−56.10	−9.87	BB	García et al. [2012]	3
Arica	−70.31	−18.47	Rural	Kahn et al. [2010]	1
Ascension_Island	−14.41	−7.98	Oceanic	Kahn et al. [2010]	3
Avignon	4.88	43.93	Urban	Kahn et al. [2010]	1
BSRN_BAO_Boulder	−105.01	40.05	Rural	Kahn et al. [2010]	1
Banizoumbou	2.67	13.54	Dust	García et al. [2012]	3
Barcelona	2.12	43.19	Urban	AERONET website	1
Beijing	116.38	39.98	Urban	García et al. [2012]	2
Birdsville	139.35	−25.90	Dust	Kahn et al. [2010]	1
Burjassot	−0.42	39.51	Urban	AERONET website	1
CASLEO	−69.31	−31.80	Rural	AERONET website	1
CEILAP-BA	−58.5	−34.57	Rural	Hoelzemann et al. [2009]	2
Camaguey	−77.85	21.42	Urban	AERONET website	1
Canberra	149.11	−35.27	Urban	AERONET website	1
Cape_San_Juan	−65.62	18.38	Oceanic	AERONET website	3
Capo_Verde	−22.94	16.73	Dust	Russell et al. [2010]	3
Carpentras	5.06	44.08	Urban	AERONET website	1
Cart_Site	−97.49	36.61	Rural	Kahn et al. [2010]	1
Chen-Kung_Univ	120.22	23.00	Urban	Lee et al. [2010]	2
Cordoba-CETT	−64.46	−31.52	Rural	Kahn et al. [2010]	2
DMN_Maine_Soroa	12.02	12.22	Dust	Kahn et al. [2010]	3
Dakar	−16.95	14.39	Dust	Giles et al. [2012]	3
Dalanzadgad	104.42	43.58	Dust	García et al. [2012]	1
Dhadnah	56.32	25.51	Dust	Eck et al. [2008]	3
Eilat	34.92	29.50	Rural	AERONET website	3
El_Arenosillo	−6.73	37.11	Rural	Kahn et al. [2010]	1
Evora	−7.91	38.57	Rural	AERONET website	1
Frenchman_Flat	−115.94	36.81	Dust	AERONET website	2
GSFC	−76.84	38.99	Urban	García et al. [2012]	2
Granada	−3.61	37.16	Rural	AERONET website	1
Guadeloup	−61.50	16.33	Oceanic	AERONET website	3
ICIPE-Mbita	34.20	−0.42	Rural	AERONET website	2
IER_Cinzana	−5.93	13.28	Dust	Kahn et al. [2010]	3
IMS-METU-ERDEMLI	34.26	36.57	Rural	AERONET website	1
Ispra	8.63	45.80	Urban	García et al. [2012]	1
Izana	−16.50	28.31	Dust	AERONET website	2
KONZA_EDC	−96.61	39.10	Rural	Kahn et al. [2010]	2
Kanpur	80.23	26.51	Urban	Giles et al. [2012]	2
La_Jolla	−117.25	32.87	Oceanic	Kahn et al. [2010]	1
La_Laguna	−16.32	28.48	Dust	AERONET website	2
La_Parguera	−67.05	17.97	Oceanic	AERONET website	3
Lake_Argyle	128.75	−16.11	BB	Qin and Mitchell [2009]	1
Lampedusa	12.63	35.52	Dust	AERONET website	2
MD_Science_Center	−76.62	39.28	Urban	Kahn et al. [2010]	1
Malaga	−4.48	36.72	Urban	AERONET website	1
Maricopa	−111.97	33.07	Rural	Kahn et al. [2010]	2
Mezaira	53.78	23.15	Dust	Eck et al. [2008]	3
Midway_Island	−177.38	28.21	Oceanic	Kahn et al. [2010]	1
Mongu	23.15	−15.25	BB	García et al. [2012]	2
Monterey	−121.86	36.59	Urban	AERONET website	1
Nauru	166.92	−0.52	Oceanic	García et al. [2012]	1
Nes_Ziona	34.79	31.92	Dust	Kahn et al. [2010]	1
OHP_OBSERVATOIRE	5.71	43.94	Rural	AERONET website	1
Ouagadougou	−1.40	12.20	Dust	Giles et al. [2012]	3
REUNION_ST_DENIS	55.48	−20.88	Oceanic	AERONET website	1
Ragged_Point	−59.43	13.17	Oceanic	AERONET website	3
Railroad_Valley	−115.96	38.50	Dust	AERONET website	1
Rome_Tor_Vergata	12.65	41.84	Urban	Kahn et al. [2010]	1
SEDE_BOKER	34.78	30.86	Dust	Giles et al. [2012]	3
SERC	−76.50	38.88	Rural	AERONET website	2
Saada	−8.16	31.63	Dust	Garcia et al. [2012]	1
Santa_Cruz_Tenerife	−16.25	28.47	Dust	García et al. [2012]	2
Sevilleta	−106.89	34.36	Rural	García et al. [2012]	1
Shirahama	−35.36	33.69	Urban	García et al. [2012]	2
Sioux_Falls	−96.63	43.74	Rural	Kahn et al. [2010]	1
Skukuza	31.59	−24.99	BB	García et al. [2012]	1
Solar_Village	46.40	24.91	Dust	Garcia et al. [2012]	3
TABLE_MOUNTAIN_CA	−117.68	34.38	Rural	AERONET website	2
Tinga_Tingana	139.99	−28.98	BB	Kahn et al. [2010]	1
Toulon	6.01	43.14	Urban	AERONET website	1
Trelew	−65.31	−43.25	Urban	AERONET website	2
UCSB	−119.85	34.42	Oceanic	Kahn et al. [2010]	1
Villefranche	7.33	43.68	Urban	AERONET website	1
White_Sands_HELSTF	−106.34	32.64	Dust	AERONET website	1
XiangHe	116.96	39.75	Rural	Giles et al. [2012]	2
Zinder_Airport	8.99	13.78	Dust	Ginoux et al. [2012]	3

As the location of the AERONET sites is the major factor of consideration in determining their spatial representativeness, we further categorize the 77 sites into five location types: dust, biomass burning, urban, rural, and oceanic. The characterization is mainly based on previous published works listed in the fifth column of Table 1. For some stations not discussed in these publications, we rely on the site description on the AERONET website and the aerosol properties of nearby sites. Figure 1 shows the geographical distribution and types for the selected sites. Note that this classification mainly refers to the site type rather than aerosol species; e.g., dust sites are located in deserts, biomass burning sites are located over regions primarily dominated by biomass burning activates, urban sites are located in cities, rural sites in rural area, and oceanic sites are located on islands. It is also only approximate, as some sites have seasonally varying aerosol properties and/or are dominated by complex aerosol species.

Figure 1.

Location of the 77 selected AERONET stations colored by site type. Orange: dust; black: biomass burning; red: urban; green: rural; and blue: oceanic.

3. Methodology

Ensemble Kalman Filter (EnKF) is a popular technique in data assimilation applications [Evensen, 1994, 2003, 2009]. It is a Monte Carlo implementation of the classic Kalman Filter developed for high-dimensional, and often nonlinear, systems. In the EnKF, the background error is assumed Gaussian and expressed as the ensemble background covariance matrix:

$$P^b=\frac{1}{m-1}{A}^b{\left(A^b\right)}^T$$ (1)

where A^b is an ensemble with m members and superscript T denotes matrix transpose. Hereafter, the superscript “b” denotes background variable (i.e., background ensemble and covariance matrix, containing satellite data alone) and the superscript “a” denotes the analysis ensemble, updated with assimilated AERONET data. As discussed subsequently, “error” in the current context is determined by the covariance among the measurements, i.e., diversity rather than deviation from the (unknown) truth. According to the EnKF theory [Evensen, 1994], after assimilating a set of observations with observation operator matrix H, the error covariance matrix is updated according to the minimum variance estimation as

$${\text{P}}^{\text{a}}=\left[\text{I}-\frac{{\text{P}}^{\text{b}}{\text{H}}^{\text{T}}\text{H}}{(\text{H}{\text{P}}^{\text{b}}{\text{H}}^{\text{T}}+\text{R})}\right]{\text{P}}^{\text{b}}$$ (2)

where

$$H=\left(\begin{array}{c}{h}_1\\ h_2\\ ⋮\\ h_n\end{array}\right)$$ (3)

is the observation operator matrix that interpolates the state vector to the observation vector. The elements of H are coefficients that interpolate the latitude and longitude of each satellite grid box to the location of the AERONET sites. R is the observation error matrix that usually consists of the absolute error and the representation error. The absolute error is AERONET AOD measurement accuracy, which is ±0.01 [Holben et al., 1998]. For simplicity, the representation error is chosen as the variance of monthly mean AOD within each grid box using MODIS data, which has the most frequent sampling of the available data sets and full global coverage. This treatment is consistent with previous data assimilation works such as Zhang et al. [2008] and Schutgens et al. [2010]. Nonetheless, it could still represent an underestimate due to limitations in temporal sampling; i.e., the MODIS Terra observations are snapshots taken at about 10:30 A.M. local time.

The computation of P^a in (2) requires inverting the ensemble covariance matrix which is often of large dimension. For example, for satellite AOD data with 1° resolution, the dimension of each ensemble member will be 360 × 180 = 64800. This is much larger than the ensemble size m (in our case 605). Therefore, to avoid the manipulation of the high-dimensional covariance and to reduce computational cost, Bishop et al. [2001] proposed a method to simplify the calculation of the analysis covariance matrix P^a by updating the background ensemble, namely, the ensemble transform Kalman Filter. In this method, the updated ensemble A^a can be obtained by the ensemble transform function:

$${\text{A}}^{\text{a}}={\text{A}}^{\text{b}}\text{T}$$ (4)

and

$$T{\left[I+\frac{1}{m-1}{\left(H{A}^b\right)}^T{R}^{-1}H{A}^b\right]}^{-1/2}$$ (5)

The inversion of T can be accomplished using an eigenvalue decomposition of the matrix in square brackets as follows:

$$I+\frac{1}{m-1}{\left(H{A}^b\right)}^T{R}^{-1}H{A}^b=U\Lambda U^T$$ (6)

where U is an orthonormal matrix and Λ is a diagonal matrix consisting of eigenvalues. Therefore, T can be obtained by

$$T=U{\Lambda }^{-1/2}{U}^T$$ (7)

In our implementation, the background ensemble is constructed as a combination of all satellite monthly mean AOD data sets as

$$A^b=\left[X_{\text{MODIS}};X_{\text{MISR}};X_{\text{SeaWiFS}};X_{\text{OMI}}\left(\text{Land}\right);X_{\text{PARASOL}}\left(\text{Ocean}\right)\right]$$ (8)

Each X is the data matrix from a satellite sensor, organized as

$$X=\left[\begin{array}{ccc}{X}_{1,1}& \cdots & X_{1,t}\\ ⋮& \ddots & ⋮\\ X_{I,1}& \cdots & X_{I,t}\end{array}\right]$$ (9)

where l is the number of geolocations (grid boxes) and t is the length of the time series (i.e., the number of monthly means) of each data set. We also remove the known variability, including linear trends and multiyear averaged seasonal cycles from each grid box of each data set so that the remaining anomalies better represent the short-term variability of the background AOD field. For the time series at each grid box, the multiyear averaged seasonal cycle is obtained by taking the overall AOD average for each month:

$$\overline{X_i}=\frac{1}{M}\sum _{j=1}^M{X}_{i,j}$$

where X_i,j is the monthly mean AOD at month i and year j and M is the total number of the years. Then a least squares linear regression is performed on the deseasonalized time series to obtain the linear trend

$$X_t=a{T}_t+b+\epsilon$$

where X_t is the AOD time series of each grid box, T_t is the time vector, a is the linear trend, b is the offset, and ε is the noise term.

This trend is further removed by

$$X_{t,\text{detrended}}=X_t-\left(a{T}_b+b\right)$$

Because the multiyear averaged seasonal cycle is removed, the mean AOD is also removed, and thus, any bias in the mean AOD among different data sets is also removed during this procedure. In this way, each grid box now has four monthly deseasonalized time series (three individual satellite data and one land/ocean combined). These four series are serially combined to form a 605-member ensemble for each grid box. For the seasonal ensembles, only the months for each season are selected and serially combined, so that each seasonal ensemble consists of ~151 members. Please note that we do not require different data sets to agree but rather treat them as individual samples. In fact, the diversity among different data sets increases the ensemble spread which actually contributes to the reliability of the ensemble.

4. Results

4.1. Ensemble Spread

The annual and seasonal ensemble spreads are shown in Figures 2 and 3. Overall, the global average of the ensemble spread is ~0.07. Regions with the largest spread correspond to major aerosol source regions, including West Africa, South America, East Asia, and Southeast Asia. This is not surprising as these regions also have the highest aerosol loading, and many also exhibit complex aerosol mixtures, such as the Sahel, North India, and East Asia. North Pacific also exhibits large spread, which is affected by aerosol transport from East Asia and possibly cloud contamination. A sharp land-sea contrast in the spread maps is observed off South Africa coast, which might also be due to cloud contamination as this region is dominated by marine stratus clouds, although the exact cause needs further investigation. The ensemble spread also exhibits clear seasonal features that reflect seasonal variability of aerosol types. For example, in northern spring, most of the variance is found over regions with dust emission or transport such as West Africa, East Asia, and North Pacific. The ocean area off the North African coast also has high variability; however, the overall spread among the satellite products over the Sahara desert is relatively low. The Saharan dust activity is subject to wind anomalies and exhibits strong seasonal and often interannual variability. The lack of expected variability and the inconsistency between land and ocean for the products used (except for MISR in this case, though not shown) may suggest potential problems in some of the satellite land-retrieval algorithms. This warrants further examination, beyond the scope of the current paper. In boreal fall, the signals mostly come from biomass burning regions including South America, South Africa, and Southeast Asia. Note that the spread in East Asia is high throughout the year, indicating that the retrieval uncertainty or aerosol variability over this region is high irrespective of season or aerosol type.

Figure 2.

Spread (standard deviation) of the annual ensemble with 605 members. The number on the upper right corner is the global mean value.

Figure 3.

Spread of the four seasonal ensembles, each with ~151 members. The numbers on the upper right corner of each panel denotes global mean values.

4.2. EnKF Case Studies

To illustrate the usage of EnKF in evaluating the spatial representativeness of AERONET locations, we perform case studies respectively for one high representative site, Banizoumbou, and one low representative site, Beijing. The differences between the analysis error field (A^a) after assimilating the observations with uncertainty R and the background error field (A^b) at these two sites are shown in Figures 4a and 4b, respectively. Note that because we do not have the “true” AOD, the error fields refer to the sample error which are deviations from the ensemble mean and should be considered as uncertainty rather than the true error.

Figure 4.

Comparison between assimilating Banizoumbou and Beijing, (a and b) error (standard deviation of the ensemble) reduction and (c and d) spatial correlation pattern calculated by correlating the data at the AERONET location with the rest of the globe.

Comparing these two panels, it is clearly seen that the spatial extent with observable uncertainty reduction is much larger for Banizoumbou than for Beijing. The Banizoumbou site impacts almost the entire West Africa, whereas for Beijing, the error reduction only concentrates on a small area surrounding the site. Banizoumbou is mainly affected by Saharan dust and periodically by biomass burning smoke in boreal winter. Both of these aerosol types are relatively uniformly distributed; they come mainly from upwind sources and tend to be transported over long distances. Beijing, in contrast, has much more complex aerosol-type distributions and variability. Moreover, the mountainous area to the northwest of the city blocks the effective transport of aerosols from that direction. These factors result in spatially inhomogeneous aerosol properties around Beijing and correspondingly low spatial representativeness for a single sampling station. To explain in more detail, the representativeness is proportional to the size of the spatial domain over which the uncertainty within the satellite ensemble is reduced by assimilating AERONET observations. The degree of representativeness depends on the covariability between AOD at the AERONET site and the surrounding area; high AOD variability will lead to low spatial correlation and correspondingly a low uncertainty reduction around the AERONET site. This effect shows up in the result as a smaller domain with observable uncertainty reduction.

Further, if we compare these results with the spatial distribution of the correlation coefficients calculated between AOD at these two sites and the rest of the globe (Figures 4c and 4d), we can see that the patterns of each pair (Figures 4a and 4c and 4b and 4d) agree quite well. This demonstrates that the spatial representativeness of a site can be well captured by the EnKF analysis. Also, by calculating the reduction of the total variance after assimilating the observation at this location, its representativeness can be quantified. For example, the reduction of the total global background variance by assimilating the Banizoumbou data is 0.00053, about twice as large as assimilating the Beijing data (0.00028). According to this result, we conclude that establishing a site at Banizoumbou will be informative over a larger area, or conversely, that a denser distribution of observations is likely required to resolve the highly spatially inhomogeneous aerosol properties in places such as Beijing.

4.3. Analysis of the Annual Ensemble

The selected 77 AERONET locations are first assimilated into the annual ensemble using the method described in section 3. In this procedure, AERONET AOD is considered to be closer to the true AOD field than the satellite data sets, and the goal is to assess how much the background uncertainty is reduced by assimilating the AERONET observations. The original satellite ensemble A^b is first updated to the analysis ensemble A^a by equations (4) to (7). Then the background error field ${\sigma }_{A^b}$ and analysis error field ${\sigma }_{A^a}$ are calculated as the standard deviation at each grid of A^b and A^a, respectively. The absolute and relative reductions of the background uncertainty after the assimilation, which amount to reductions in the diversity among the values rather than deviation from “truth,” are shown in Figures 5a and 5b, respectively. The uncertainty reduction is defined as ${\sigma }_{{\text{A}}^{\text{a}}}-{\sigma }_{{\text{A}}^{\text{b}}}$, and the relative reduction is defined as $\left({\sigma }_{A^a}-{\sigma }_{{\text{A}}^{\text{b}}}\right)/{\sigma }_{{\text{A}}^{\text{b}}}$, where σ denotes standard deviation. Global mean uncertainty reduction is 0.02, accounting for more than 20% of the global mean background uncertainty. Regionally, the difference can be much larger. The highest uncertainty reductions are found over South America, West Africa, and the Arabian Peninsula, where the overall absolute error is reduced by more than 0.1. This suggests that AERONET sites at these locations are more spatially representative than elsewhere.

Figure 5.

(a) Error reduction and (b) relative reduction by assimilating the 79 sites into the annual ensemble. Overall, the background error has been reduced by ~27%.

Also note that for some places where no qualified AERONET site is available, the uncertainty in the satellite data sets can also be reduced to some extent, e.g., Indonesia and Southeast China. This is because aerosol properties over these regions covary with other locations having qualified AERONET sites, either due to similar climate mechanisms that govern the emission or transport of pollutants or because it is downwind of an AERONET site, so the impact of aerosol properties at these AERONET sites is extended to more remote places through spatial covariation. For example, both Indonesia and South America are dominated by biomass burning aerosols in some seasons. Moreover, the interannual variability of biomass burning intensity over these two tropical regions is strongly influenced by meteorological conditions tied to tropical ocean variability, namely, the El Niño–Southern Oscillation (ENSO) [Thompson et al., 2001; van der Werf et al., 2006]. The footprint of the ENSO signal on local climate thus connects aerosol variability over South America and Indonesia, implying that aerosol information observed at South American sites can explain part of the aerosol variability of Indonesia. For the North Pacific, the change is subtle and is mainly associated with pollution transport from East and Northeast Asia by the prevailing midlatitude westerlies [Wilkening et al., 2000; Eck et al., 2005]. However, the uncertainty over North Pacific is still significant, which might be related to factors other than aerosol variability, such as cloud contamination. Aerosol variability in Southeast China is likely attributable to a combination of both climate and transport factors. On one hand, the entire East Asia climate is impacted by the Siberian High in winter and East Asian monsoon in summer, which interacts with local weather and modulates aerosol variability. On the other hand, aerosols emitted from mega cities such as Beijing can occasionally be transported downwind to South China. In addition, most of East China is affected by dust transport from the desert regions in Northwest China and Mongolia [Wang et al., 2008; Tan et al., 2012].

The relative uncertainty reduction (Figure 5b) displays a similar but more localized spatial pattern, with the reduction increasing toward each AERONET site. On average, the uncertainty has been reduced by 27%, and around highly representativeness sites, such as those in South America and the Arabian Peninsula, it can be reduced by more than 50% and reaches 80%.

Another important feature to note in Figure 5 is that the background uncertainty reduction in remote places, i.e., those far away from any of the selected sites, is almost zero. This is an indication of negligible spurious correlation. Spurious correlation is a common problem that seriously degrades the reliability of EnKF results, which is often caused by inadequate size of the background ensemble [Evensen, 2003]. The results shown here further suggest that our satellite ensemble is appropriate for EnKF analysis.

4.4. Analysis of Seasonal Ensemble

As aerosols vary with climatic conditions, most places also exhibit seasonally varying aerosol properties. This includes changes in aerosol loading, aerosol mixture, or both. Because representativeness is intrinsically related to the spatial variability of aerosol properties, it is highly possible that it also changes from season to season. Therefore, we examine the seasonal representativeness of the selected sites using the seasonal ensembles.

Figures 6a, 6c, 6e, and 6g show the reduction of background uncertainty for northern spring (March-April-May, MAM), summer (June-July-August, JJA), fall (September-October-November, SON), and winter (December-January-February, DJF), and Figures 6b, 6d, 6f, and 6h indicate the relative reduction. The global averages of the uncertainty reduction for the four seasons are quite close, only slightly lower in winter. However, their spatial patterns are quite distinct. In northern spring (Figure 6a), the signals mainly come from dust sources or transport regimes, namely, West Africa, the Arabian Peninsula, and the North Pacific. The area to the south of the Sahara could also reflect some biomass burning activity in early spring. The areas around Beijing and Hong Kong and the Caribbean region also show changes in the variance. These places are reportedly affected by dust transported from Northwest China [He et al., 2008; Yu et al., 2009] and the Sahara [Prospero and Lamb, 2003], respectively, during the spring season. During boreal summer (Figure 6c), dust activity weakens compared to spring, whereas anthropogenic aerosols such as sulfates become dominant over much of the land area, especially close to mega cities in China and India. A relatively strong signal is also found over South America, which appears to be due mainly to the strong biomass burning events in August. The highest biomass burning intensity in the Southern Hemisphere happens in the boreal fall, and the uncertainty reduction pattern captures this phenomenon well (Figure 6e). The highest uncertainty reduction is found over central South America surrounding the Alta_Floresta station, South Africa, and Indonesia, where the uncertainty is reduced by more than 60% (Figure 6e). The winter signals are low overall (Figure 6g). The only place with strong uncertainty reduction is the Sahel, with a relative reduction of approximately 60% (Figure 6g). The Sahel is mostly dominated by biomass burning in northern winter due to decreased rainfall [Duncan et al., 2003].

Figure 6.

The same as Figure 5 but for seasonal ensembles. The seasonal results capture seasonal variability of aerosol types, such as dust in spring (MAM), industrial pollution in summer (JJA), Southern Hemisphere biomass burning in the fall (SON), and Sahel biomass burning in the winter (DJF).

In short, the assimilation results show quite distinct seasonal variability associated in part with seasonal shifts of dominant aerosol types and source regions. The assimilation effect is the most evident around strong pollution sources with high aerosol variability and also places where different satellite data sets have the largest differences. The latter is usually associated with differences in instrument characteristics and retrieval algorithms. The results indicate that the EnKF method can effectively reduce the ensemble spread, which represents the uncertainties. This indicates that the representativeness of the ground observations needs to be evaluated on a seasonal basis. This also suggests that when selecting locations for potential AERONET sites, the seasonal aerosol characteristics is also an important factor to consider in order to adequately resolve the aerosol variability.

4.5. Assessment of AERONET Locations by Type

The above seasonal analysis reflects the fact that different aerosol types exhibit different spatial representativeness. It is therefore desirable to independently examine different aerosol types to clarify their specific representative features. For this purpose, we separately assimilate the five groups of sites generally associated with five major aerosol types (see Figure 1 and Table 1 for detailed aerosol-type classification) into the ensemble. The results are shown in Figure 7.

Figure 7.

Uncertainty reduction and relative reduction for different AERONET site types. Results indicate that overall dust and biomass burning sites result in the highest error reduction.

Comparing the strength and spatial extent of the uncertainty reduction patterns for the different location types, it is quite clear that dust and biomass burning aerosols have the highest spatial representativeness on the multiyear 1° × 1° scale, with both high reduction and extensive spatial distribution of the signal. This reflects the high spatial correlation within the satellite AOD field over these regions. On one hand, biomass burning and dust particles are often transported over long distances, which extends their spatial representativeness. One the other hand, systematic issues in satellite retrievals, such as cloud contamination or surface parameterization differences, may also produce high correlation errors. For biomass burning aerosols it is also interesting to note the spatial inhomogeneity between different source regions. For example, South American sites have a much larger representativeness than South African sites. Compared to South America, the South African aerosol composition is more complicated. It is also periodically influenced by dust aerosols, and some sites, such as Skukuza, are located close to urban areas that have mixtures of industrial pollutions and biomass burning smoke. These factors nonetheless introduce higher AOD variability and degrade the spatial representativeness. The uncertainty reduction pattern for urban aerosols is much more localized, focusing on a narrow region around each site, whereas for rural and oceanic sites, the patterns are more broadly distributed surrounding each site. The result well reflects the differences between these two aerosol types well. At urban sites, the observed aerosol amount and property is more complex because of multiple local emission sources and pollution compositions. Rural and oceanic sites are remote locations that represent the more uniformly distributed background aerosols; thus, the information at these sites can generally be extended to larger areas. Nonetheless, the total amount of uncertainty reduction for rural and oceanic aerosols is smaller simply because there are fewer sites classified into these two types. Another important property to note in Figure 7 is that the total uncertainty reduction (sum of all five types) for different aerosol types assimilated separately (0.02) roughly equals the uncertainty reduction by assimilating all sites together (0.018). This provides the basis of evaluating different aerosol types or different sites individually by the EnKF method.

These results suggest that due to their different scales of variability, the ground truth observation density needed for different aerosol types should also be different. As might be expected for biomass burning or dust regions, a much less dense network of observing sites is required to represent the source and downwind areas than for urban aerosols.

4.6. The Spatial Scores of AERONET Locations

Because the spatial representativeness is reflected in the decrease of the total global background error, we make a further attempt to quantitatively express the representativeness based on the uncertainty reduction. Specifically, we assimilate each site into the ensemble individually and calculate the total reduction of the background uncertainty, i.e., global mean of the difference between background error and analysis error. Based on this result, we grouped the sites into three representative grades and assigned each a spatial score ranging from 1 to 3. Score 3 sites (marked in red) have uncertainty reduction greater than 3 × 10⁻⁴, score 2 (marked in blue) sites have uncertainty reduction between 3 × 10⁻⁴ and 2 × 10⁻⁴, and the uncertainty reduction for score 1 sites (marked in green) is below 2 × 10⁻⁴. Figure 8 shows the distribution of the spatial scores of the 77 AERONET sites.

Figure 8.

Spatial score map for the 77 sites based on the uncertainty reduction level. Red: score 3; blue: score 2; and green: score 1.

The sixth column of Table 1 also lists the spatial score of each selected station. This spatial score to some extent reflects regional aerosol variability; i.e., regions around score 1 sites tend to have higher aerosol variability than that around score 3 sites. However, note that this may not be applicable to remote sites, as the grading is based on global error reduction, whereas for these sites, the background AOD variability is already low and the assimilation of AERONET data only results in limited error reduction. Nonetheless, we hope that this information can serve as a quantitative reference for selecting satellite validation sites and especially model comparison studies.

5. Discussion and Conclusions

The study of aerosols and their climate effects relies heavily on space-retrieved aerosol products. However, satellite aerosol retrievals still have uncertainties due to various factors such as sampling, cloud screening, surface parameterizations, and other retrieval algorithm assumptions. Surface observations are usually considered as near ground truth and used to reduce the uncertainty in satellite retrievals. The degree to which uncertainty can be reduced depends critically on the spatial representativeness of the surface observation location. This information is also a key factor to consider in the deployment of surface stations and the synergic use of satellite and ground observational data sets. This study focuses on the first step in reducing satellite AOD uncertainty using ground-based measurements, i.e., evaluating the spatial representativeness of current AERONET sites. By assimilating ground observations into the satellite data ensemble using the EnKF method, the spatial representativeness of each AERONET site is readily observed by comparing the analysis error and background error, because the information at a single location is passed to other grids through the ensemble covariance matrix and contributes to reducing the uncertainty there. By including most of the currently available satellite data sets into the ensemble, we are able to obtain a large ensemble spread which helps reduce spurious correlation (correlation between far away grids due to small ensemble spread). This increases the reliability of our analysis results.

Analysis of the 77 selected AERONET stations that well represent monthly mean aerosol variability indicates that overall, these sites reduce 27% of the uncertainty among different satellite data sets. Regionally, the reduction can be much larger, reaching 80% for some biomass burning and dust-dominated locations. The difference between satellite-only background and the AERONET-assimilated analysis error fields also exhibits strong seasonal variability that is tied to climatic conditions and aerosol types. In general, dust and biomass burning sites have the highest spatial representativeness, rural and oceanic sites can also capture background variability over an extensive area, although they may explain less variability for remote places, whereas the spatial impacts of urban sites are more localized.

We also note that the remaining diversity after assimilating these AERONET observations can still be large. Figure 9 shows the analysis error of the annual ensemble, which includes large remaining spreads over the North Pacific, East Asia, Indonesia, and the Sahel. This suggests that more observations are needed to further reduce these remaining uncertainties, possibly combined with algorithm upgrades, such as improved cloud screening and assumed aerosol types. Some regions already have sites established; however, their data do not pass our selection criteria because of either insufficient sampling or short time series. For example, Indonesia is frequently affected by cloud, so the AERONET measurements do not meet the 20 d/month standard. East Asian sites were either established in recent years or deactivated, thus having quite limited observation records.

Figure 9.

Analysis error after assimilating the 77 selected AERONET sites into the ensemble.

As just mentioned, this study addresses step one of reducing satellite AOD uncertainty using surface observations. In the future, we plan to extend and finalize this goal in three more steps. First, we will introduce and implement an objective observation array design technique that automatically determines the optimal locations for additional AERONET deployments that would contribute the most to reducing the remaining AOD uncertainty shown in Figure 9. Second, the uncertainty of surface observation itself strongly impacts on the reduction of the background error, and its information content will be less useful or even useless for this application if it comes with a large uncertainty. Aside from the known AERONET measurement accuracy, the representation error R_E heavily impacts the analysis result but is actually difficult to quantify. This term depends on the spatial and temporal variability of AOD itself. It not only is useful for data assimilation but also provides specific information on background aerosol variability. We will use high-resolution observations or aerosol modeling to explore this topic in step three. Finally, once the spatial representativeness and R_E are quantified, we will perform the data assimilation step to generate a more accurate and complete monthly mean AOD data set.

The current study only concerns monthly mean AOD mainly because (1) monthly means are usually the scale of climate forcing studies and GCM outputs and (2) for illustration purpose, this time scale can yield a complete ensemble for each grid box; i.e., the monthly mean AOD maps for different satellite data sets are mostly fully covered, which makes the EnKF easier to realize. Nonetheless, the EnKF analysis can surely be performed on different scales and different parameters. In particular, aerosol variability will be different on different time scales, which means that the spatial representativeness also tends to vary with scale. For example, for urban areas, the current 1° × 1° resolution is too coarse to reflect local aerosol characteristics, and a small-scale analysis with finer resolution is needed. The NASA DRAGON network is designed to resolve mesoscale aerosol variability and would be suitable for analysis using the technique presented in this study. In the future, we also plan to extend the current study to weekly, seasonal or even decadal scales, in order to provide a more comprehensive evaluation of aerosol variability.

Key Points:

• A novel EnKF-based approach is developed to assess spatial representativeness of AERONET ground observation using multisensor AOD data

• The spatial representativeness can be quantified as the reduction of ensemble background error after assimilating AERONET observation

• The spatial representativeness of different aerosol types and its seasonal characteristics are investigated