Reducing Multi-sensor Monthly Mean Aerosol Optical Depth Uncertainty Part II: Optimal Locations for Potential Ground Observation Deployments

Abstract

Surface remote sensing of aerosol properties provides “ground truth” for satellite and model validation, and is an important component of aerosol observation system. Due to the different characteristics of background aerosol variability, information obtained at different locations usually have different spatial representativeness, implying that the location should be carefully chosen so that its measurement could be extended to a greater area. In this study, we present an objective observation array design technique that automatically determines the optimal locations with the highest spatial representativeness based on the Ensemble Kalman Filter (EnKF) theory. The ensemble is constructed using aerosol optical depth (AOD) products from five satellite sensors. The optimal locations are solved sequentially by minimizing the total analysis error variance, which means that observations at these locations will reduce the background error variance to the largest extent. The location determined by the algorithm is further verified to have larger spatial representativeness than some other arbitrary location. In addition to the existing active AERONET sites, the 40 selected optimal locations are mostly concentrated on regions with both high AOD inhomogeneity and its spatial representativeness, namely the Sahel, South Africa, East Asia and North Pacific Islands. These places should be the focuses of establishing future AERONET sites in order to further reduce the uncertainty in the monthly mean AOD. Observations at these locations contribute to approximately 50% of the total background uncertainty reduction.

1. Introduction

Compared to satellite remote sensing, surface measurements using sun photometers provide better constraint on column aerosol optical depth and other physical properties, and has thus become an important component in the aerosol observation system. Aerosol Robotic Network (AERONET, Holben et al., 1998) is currently the most extensive surface sun photometer network with over 400 stations operating at worldwide locations. Due to its accurate measurements and high data quality, AERONET has become the standard dataset for satellite retrieval validation (Kahn et al., 2005; Levy et al., 2010; Sayer et al., 2013; Ahn et al., 2014; Huang et al., 2016) as well as model calibration (Kinne et al., 2003, 2006; Li et al., 2010; Lamarque et al., 2013).

For better application of the AERONET dataset, in Part I of this series (Li et al., 2016), we evaluated the spatial representativeness of 77 AERONET sites with relatively complete data time series in terms of monthly variability. The study showed that these sites are effective in reducing uncertainties in monthly mean AOD represented by the spread of multi-sensor satellite datasets. Nonetheless, considerable spread still remains in the multi-sensor ensemble (see Figure 9 in Part I for the distribution of the remaining spread). To further reduce monthly mean AOD uncertainty, we need to collect information at additional locations. While currently AERONET has far more stations than the 77 sites selected, not all sites are active at all time, and there are still some major pollution source regions without sufficient AERONET coverage, such as Central and East China. Moreover, the observation density at some locations with complicated and variable aerosol properties may also need to be increased, in order to fully resolve the aerosol spatial variability there.

In this second part, we extend Part I to further seek “optimal” locations for AERONET deployment that help to reduce the remaining uncertainties in the monthly mean AOD. To our knowledge, there is still no systematic investigation as to what should be the best locations for additional AERONET sites. Shi et al. (2011) made recommendations for potential AERONET deployment locations based on the differences between MODIS and MISR AOD data. Places with the most disagreements, corresponding to the largest uncertainty, are where one desires ground truth, and if few AERONET stations are found within the area, more should be deployed. Surely the uncertainty of background AOD is an important factor to consider. In addition, as pointed out in Part I, the spatial representativeness of the sites also needs to be taken into account, as this matters how far information at one site can be extended spatially, i.e., high representative sites can potentially provide more spatial information than low representative sites. For example, we found that the Banizoubmou site in West Africa is more representative than the Beijing site in North China, which means that having a site at Banizoumbou is more spatially informative than one at Beijing. Specifically, this representativeness is quantified as the reduction in the total background error using the Ensemble Kalman Filter (EnKF) based assessment technique (see Part I for details). Similarly, one can use the error reduction as a criterion for the determination of optimal AERONET locations.

The concept of optimal observation array has been previously explored in ocean observations by Sakov and Oke (2008). They presented an efficient and versatile ensemble-based method to objectively design an observation array for the Indian Ocean. Their algorithm seeks optimal observations sequentially, which is selected as the location resulting in the maximum reduction of the total background error variance. The physical basis and the effectiveness of this method were also verified in their study. This algorithm has since been used for the processing of observation data for assimilation (Li et al., 2010) and synoptic survey (Frolov et al., 2014).

In the Sakov and Oke (2008) approach, the selection of the background ensemble appeared critical as the optimal observations solely depend on the covariance of this ensemble. In the aerosol research field, the availability of multiple satellite retrieved aerosol products provides a unique opportunity for the application of this EnKF approach. AOD retrievals from different sensors can be viewed as independent samplings of the true AOD field, so that they can be summed up into an ensemble space. This is exactly the multi-sensor ensemble used in Part I, which shows that it has adequate spread and represents the background covariance well. Therefore, we have confident that the objective array design technique developed for ocean observation systems can be successfully adapted for finding optimal ground aerosol observation sites.

Therefore, in this part of the project we will apply the Sakov and Oke (2008) approach to the multi-sensor AOD ensemble to determine where additional AERONET sites should be established. In the later parts of this paper, we describe the method and its adaptation to aerosol observations, and present the optimal locations with a brief discussion of the results. This work aims at providing a theoretical reference for considering locations for future AERONET deployments.

2. Methodology

The idea of finding the optimal locations is similar to the EnKF based representativeness assessment presented in Part I, which treats multiple satellite AOD datasets as the ensemble, and ground measurements as observations to be assimilated. The major difference is that in Part I, the observational sites are known, whereas here they need to be identified. Consistent with Part I, we use the same 605-member ensemble constructed from de-trended, de-seasonalized monthly mean AOD products from MODIS, MISR, SeaWiFS, OMI and PARASOL. It consists of 179 monthly AOD anomalies 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 (land) and PARASOL (ocean) combined dataset (from October 2005 to December 2012). To save space, we skip the detailed description of the five datasets here. Interested readers can refer to Part I instead. The ensemble A^b can be expressed as

$${\mathbf{A}}^{\mathbf{b}}=\left[{\mathbf{X}}_{\mathbf{M}\mathbf{O}\mathbf{D}\mathbf{I}\mathbf{S}};{\mathbf{X}}_{\mathbf{M}\mathbf{I}\mathbf{S}\mathbf{R}};{\mathbf{X}}_{\mathbf{S}\mathbf{e}\mathbf{a}\mathbf{W}\mathbf{i}\mathbf{F}\mathbf{S}};{\mathbf{X}}_{\mathbf{O}\mathbf{M}\mathbf{I}}\left(\mathrm{Land}\right);{\mathbf{X}}_{\mathbf{P}\mathbf{A}\mathbf{R}\mathbf{A}\mathbf{S}\mathbf{O}\mathbf{L}}\left(\mathrm{Ocean}\right)\right]$$ (1)

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

$$\mathbf{X}=\left[\begin{array}{ccc}{x}_{1,1}& \cdots & x_{1,t}\\ ⋮& \ddots & ⋮\\ x_{l,1}& \cdots & x_{l,t}\end{array}\right]$$ (2)

where l is the number of geolocations (grid boxes) and t is the length of the time series (i.e., the number of monthly mean AODs at each grid).

The background covariance matrix P^b is used to represent background uncertainty, which is calculated as

$${\mathbf{P}}^{\mathbf{b}}=\frac{1}{m-1}{\mathbf{A}}^{\mathbf{b}}{\left({\mathbf{A}}^{\mathbf{b}}\right)}^{\mathbf{T}}$$ (3)

The superscript T denotes matrix transpose. After assimilating a set of n observations, the background ensemble is updated and the analysis covariance matrix is then expressed as

$${\mathbf{P}}^{\mathbf{a}}=\frac{1}{m-1}{\mathbf{A}}^{\mathbf{a}}{\left({\mathbf{A}}^{\mathbf{a}}\right)}^{\mathbf{T}}$$ (4)

The optimal observations should have the property of minimizing the norm of the analysis error variance, i.e.,

$${\mathbf{H}}^{\mathbf{opt}}=\arg \min \Vert {\mathbf{P}}^{\mathbf{a}}\Vert$$ (5)

where H^opt is the observation operator of the optimal sites that we are looking for. Because according to the EnKF theory,

$${\mathbf{P}}^{\mathbf{a}}=\left[\mathbf{I}-\frac{{\mathbf{P}}^{\mathbf{b}}{\mathbf{H}}^{\mathbf{T}}\mathbf{H}}{\mathbf{H}{\mathbf{P}}^{\mathbf{b}}{\mathbf{H}}^{\mathbf{T}}+\mathbf{R}}\right]{\mathbf{P}}^{\mathbf{b}}$$ (6)

and because trace(AB)=trace(BA), equation (5) can be re-written as:

$${\mathbf{H}}^{\mathbf{o}\mathbf{p}\mathbf{t}}=\arg \max \mathrm{trace}\frac{{\mathbf{P}}^{\mathbf{b}}{\mathbf{H}}^{\mathbf{T}}\mathbf{H}{\mathbf{P}}^{\mathbf{b}}}{\mathbf{H}{\mathbf{P}}^{\mathbf{b}}{\mathbf{H}}^{\mathbf{T}}+\mathbf{R}}$$ (7)

R in (6) and (7) denotes the observation error matrix consisting of both the absolute error and representation error, as described in Part I.

Because H^opt may involve multiple elements, the solution to (7) is non-trivial. However, Bierman (1977) and Sakov and Oke (2008) proved the equivalence of serial assimilation to parallel assimilation assuming no correlated errors in the observation, i.e., assimilating observations one by one results in the same analysis error as assimilating all observations at once. Therefore, we can simplify the problem by solving for optimal observations serially. In this case, H^opt reduces to a row vector H=h(k) such that h_i(k)={0, i≠k; 1, i=k}, and R becomes a scalar, R=r(k). Equation (7) them becomes

$$k=\arg \max \left[\frac{1}{{\mathbf{P}}_{ii}^b+r\left(i\right)}\sum _{j=1}^n{\left({\mathbf{P}}_{ij}^b\right)}^2\right]$$ (8)

After finding the first optimal location, we update the P^b to P^a, and the second optimal location can be found by minimizing the new P^a using equations (6) and (8), and so on.

In practice, the storage and manipulation of the ensemble covariance matrices is usually memory costly. For example, for the 1° resolution satellite ensemble, the dimension of the covariance matrix will be 64800×64800. We therefore follow the simplification strategy by Sakov and Oke (2008) again and substitute

$$\mathbf{P}=\frac{1}{m-1}\mathbf{A}{\mathbf{A}}^{\mathbf{T}}$$ (9)

into (7) as

$${\mathbf{H}}^{\mathbf{o}\mathbf{p}\mathbf{t}}=\arg \max \mathrm{trace}\frac{\mathbf{H}\mathbf{A}\left({\mathbf{A}}^{\mathbf{T}}\mathbf{A}\right){\left(\mathbf{H}\mathbf{A}\right)}^{\mathbf{T}}}{\mathbf{H}\mathbf{A}{\left(\mathbf{H}\mathbf{A}\right)}^{\mathbf{T}}+\left(m-1\right)\mathbf{R}}$$ (10)

and

$$k=\arg \max \frac{{\mathbf{A}}_{\mathbf{i}}\left({\mathbf{A}}^{\mathbf{T}}\mathbf{A}\right){\mathbf{A}}_{\mathbf{i}}^{\mathbf{T}}}{{\mathbf{A}}_{\mathbf{i}}{\mathbf{A}}_{\mathbf{i}}^{\mathbf{T}}+\left(m-1\right)r\left(i\right)}$$ (11)

where A_i=h(i)A is the ith row of A. We pre-calculate the matrix A^TA which is of much lower dimension than the covariance matrix P. This treatment greatly saves computational and memory cost. Substituting P using (9) requires updating the ensemble after finding each optimal location so that the covariance matrix calculated by (9) is equivalent to that calculated by (6). We use the solution given by the ensemble transform Kalman Filter (Bishop et al., 2001) as follows:

$${\mathbf{A}}^{\mathbf{a}}={\mathbf{A}}^{\mathbf{b}}\mathbf{T}$$ (12)

and

$$\mathbf{T}={\left[\mathbf{I}+\frac{1}{m-1}{\left(\mathbf{H}{\mathbf{A}}^{\mathbf{b}}\right)}^{\mathbf{T}}{\mathbf{R}}^{-1}\mathbf{H}{\mathbf{A}}^{\mathbf{b}}\right]}^{-1/2}.$$ (13)

As a brief summary, we first calculate the background covariance matrix P^b, and find the location of the first optimal site using equation (8). Then, we update the background ensemble by assimilating an observation at the first optimal site according to the ensemble transform Kalman filter indicated by equations (12) and (13). Using this updated ensemble, we calculate the updated ensemble covariance matrix P^a and subsequently find the second optimal location using equation (8), by substituting P^b with P^a(note now the updated covariance matrix becomes the new background covariance matrix). This process is repeated until the desired number of optimal sites is reached (in our case 40).

Till December 2015, there are 170 active AERONET sites globally. These sites are considered as the initial observation array, whose uncertainty reduction is first evaluated using the EnKF technique introduced by Part I. Then using the above procedure, we calculate H^opt for 40 additional sites beyond the initial 170 sites. Because AERONET sites should be preferably established over land area, we further constrain that the location of the optimal location be on continents or islands using a 1°×1° land ocean mask, i.e., the location must be a land grid box as indicated by the mask.

3. Results

We first screened the existing AERONET sites and find 170 sites having data updated till December 2015. These sites are thus considered active sites, and the selection of optimal locations aims at places not covered by these sites. Before carrying out optimal array design, the spatial representativeness of these sites is first evaluated according to the method introduced in Part I. Specifically, AERONET AOD at these sites are assimilated into the satellite AOD ensemble, and the analysis error field and background error field are compared and uncertainty reduction calculated. Figure 1 shows the evaluation results. Overall, by considering measurements at the initial 170 sites, the background error is reduced by ~50%. This result is quite encouraging, indicating the effectiveness of these sites. Nonetheless, according to Figure 1b, relatively large uncertainty level, up to 0.15, still remains at some places, especially over North Pacific, East China, South Africa coast and the Arabian Sea. Therefore future AERONET deployment should focus on reducing these remaining uncertainties.

Figure 1.

Background error (a), analysis error (b), error reduction (c) and relative error reduction (d) by assimilating the 170 active AERONET sites into the original satellite AOD ensemble. Red triangles overlaid on panels c and d mark the locations of the AERONET sites.

Using the method described in the previous section, we obtained the geolocations of 40 additional “optimal” sites, ranked from 1 to 40. This means that Site 1 will reduce the most uncertainty in the initial background monthly mean AOD field, Site 2 will reduce the most remaining uncertainties after incorporating Site 1 and so on. Figure 2 a&b show their positions superimposed on the background error field and the uncertainty reduction field respectively. The background error (Figure 2a) here is the analysis error after assimilating the initial 170 sites and is identical to Figure 1b (simply plotted on a different color scale). The uncertainty reduction field (Figure 2b) is the difference between the analysis error with the additional 40 sites assimilated and the background error, i.e., the reduction of uncertainty due to the assimilation of observations at these additional 40 sites. From Figure 2b, first we note that by adding the information obtained at these 40 sites, the global mean uncertainty is further reduced from 0.033 to 0.017, approximately 50%. This amount is comparable to the effect of the original 170 sites combined (see Figure 1d). Next, we can see that the objectively determined sites are mostly concentrated over North Pacific, East Asia, the Sahel, West and South African coast, and the Arabian Sea. Many sites are chosen as island sites because over land the observation is already quite dense. Quite a number of sites clustered in the North Pacific area. This is primarily due to the high overall uncertainty there, which might be partly related to cloud contamination as discussed in Part I. This issue may mask the identification of “real” optimal sites to some extent. However, this error is difficult to quantify and is beyond the scope of this study. On the other hand, because satellites have difficulty in obtaining aerosol information at these cloud contaminated regions whereas ground observation is less prone to this issue, it is still desirable to establish sites here for more accurate information of aerosol properties. Another feature to note is that while most sites do locate at regions with the largest uncertainty, this is not the case for some sites such as those over West African coast. This is because the site selection criteria is the highest reduction of the analysis error (trace(P^a)) rather than the maximum background error (trace(P^b)), and the locations of the optimal sites thus not only depend on the local variance, but also on its covariance with the other places. Sites with larger spatial representativeness can contribute to more global error reduction, and are thus favorably picked by this algorithm. West Africa has been shown to have large AOD spatial representativeness in Part I, therefore sites over this region will result in higher global variance reduction.

Figure 2.

The location of the 40 optimal sites overlaid on the background error (a) and the error reduction (b). Error reduction is the difference between updated error with the 40 sites assimilated and the original error fields. The numbers in the upper right corner indicate global mean value.

Another feature to note in Figure 2 is that some high uncertainty regions do not have optimal sites. A typical example is Europe. This is again associated with spatial representativeness. Due to the high population density and urbanization, there are many localized aerosol emission sources in Europe, which results in the highly inhomogeneous aerosol property there. To further examine this feature, we compare the spatial correlation patterns for the 1^st optimal site and an arbitrary location in Europe. The spatial correlation is defined as the correlation between the de-trended, de-seasonalized monthly mean AOD time series measured at the optimal location and that measured at all of the other grid boxes of the satellite ensemble. The results are shown in Figure 3, which indicates a sharp contrast between both the pattern and the extent of the spatial correlation map for these two sites. Optimal location 1, situated in the Sahel, is representative of aerosol variability over the entire Sahel region and also part of Northwest Africa. These regions are most dominated by dust but also with some biomass burring smoke in the winter dry season. Both these two aerosol types have very high spatial representativeness as indicated in Part I. The European site, on the other hand, only represents a very small local area, and with some scattered low correlations remotely. Many of these remote correlations might not be real, but rather spurious correlations resulting from factors such as insufficient sampling, especially for the high latitudes where satellite retrievals are usually not available during the winter season. According to this result, having a site at the Sahel appears more informative of the spatial information of the background AOD than a site in Europe. However, this is not saying that we do not need observations in Europe. Instead we need a denser network in order to resolve the high aerosol spatial variability there.

Figure 3.

Spatial representativenss of optimal location 1 situated on Borneo Island vs. and arbitrary location in Europe. The spatial representativeness for the Indonesian site is clearly much higher than the European site.

Furthermore, in Figure 4 we plot the error reduction by each optimal site and the cumulative reduction, in order to examine the effectiveness of incorporating information at these optimal sites. The first 3 sites appear to be the most representative, jointly reducing ~15% of the total uncertainty. The rest 37 sites exhibit gradually decreasing representativeness. In total, these additional 40 sites reduce 49% of the background error variance.

Figure 4.

Percentage of error reduction and cumulative reduction for the 40 optimal sites.

In the above determination of optimal location, we did not consider the environmental information of the surrounding area, as long as the site is located over land. Practically, it is always easier to establish a site with favorable local environment and facilities, such as power, housing, etc. This is likely realized if the location corresponds to some previously active AERONET site, i.e., where observations have already been made before, as presumably these locations can be easily equipped with the necessary infrastructure. Therefore, to make a more practical recommendation, we repeat the analysis but require that the optimally determined observation locations are situated closely to a previously established AERONET site. The locations of all 862 AERONET sites are obtained from the AERONET website. When each optimal location is determined sequentially, we first evaluate whether its location is within ±0.25°of an existing site, and if not, the algorithm will automatically progress onto the next loop until a qualified site is found. The new 40 optimal site locations that are collocated with previous sites are indicated in Figure 5, with the background map showing the distribution of uncertainty reduction. Figure 5a is the global distribution while Figure 5b shows an enlarged map for Asia where many sites are clustered and difficult to identify. A first impression when comparing Figure 5 with Figure 2 is that the uncertainty reduction is lower for Figure 5. Because we enforce the collocation of optimal sites with existing AERONET sites, the selected sites are actually “sub-optimal” as compared to Figure 2, meaning that they are less effective in reducing the background uncertainty. In particular, because no AERONET site has ever been deployed over North Pacific, Figure 5 only indicates a very limited uncertainty reduction there. Among various parts of the world, North India and East Asia appear to have the densest site distribution. This can be explained by their high spatial inhomogeneity of aerosol properties due to the large population size and rapid industrial development. Although not as effective as the initial 40 optimal locations, the sites in Figure 5 combined still reduce ~30% of the total background uncertainty, suggesting that re-activating these sites can greatly contribute to our knowledge of global aerosol variability.

Figure 5.

Locations of 40 optimal sites by requiring that the locations are close to an existing site, for more practical deployment considerations. (a) shows global distribution and (b) shows distribution over the Persian Gulf and India where many sites are clustered.

4. Conclusions and Discussions

In this study, we presented an EnKF based objective observation array design technique to identify “optimal” locations for potential AERONET deployment based on the reduction of background error variance. This work is an extension of Part I (Li et al., 2016) of this series, in which we assessed how current AERONET sites contribute to reducing the uncertainty in the monthly mean AOD. The potential sites recommended by this work thus serve to further reduce the remaining uncertainty.

The “optimal” locations are determined one at a time by selecting the location corresponding to the minimum analysis error variance (trace(P^a)) of the multi-sensor AOD ensemble. In this way, the objectively designed observation network has the property of reducing the background error of the satellite ensemble to the largest extent. Note that the background error simply means the error of the satellite data, which is not necessarily that of the true AOD. This is because uncertainties in satellite retrievals, such as cloud contamination and surface parameterization, may also result in disagreements among the satellite datasets, thus causing potential errors in the “optimal” sites.

We further verify that the “optimal” sites identified indeed have larger spatial representativeness than some other arbitrary location. The current 170 active AERONET sites contribute to ~50% background error reduction, whereas the additional 40 sites alone further reduce ~50% of remaining uncertainty, which is an indication of their effectiveness. The optimal locations correspond to places with largest spatial representativeness, some also with large local variance. Specifically, North Pacific, the Sahel, East China, South and West Africa coast and the Arabian Sea should be preferentially considered for future AERONET deployments.

Considering that some of these optimal locations are remote and less favorable for establishing observation sites, we made a more practical recommendation by requiring that the “optimally” solved locations to collocate with an existing AERONET site. Results indicate that many sites in Asia, especially North India and East Asia, should be reactivated for the consideration of reducing monthly mean AOD uncertainty. We hope that this work can serve as a reference or basis for establishing new AERONET sites.

This work uses the global ensemble so that the optimal locations contribute to reducing the most global uncertainties. In many cases, one may be more interested in regional aerosol properties when setting up an observation site, however this site may not be considered optimal by the global analysis. For example, in Section 3 we mentioned that no site is chosen in Europe because this region has low AOD spatial representativeness. In this case, we need to evaluate the local ensemble error variance. The method presented here is easily adapted to regional analysis by simply replacing the global ensemble with the regional ensemble. In the future we plan to investigate this problem focusing on typical regions, such as Europe, China and India. Another limitation of current study is that we focus on interannual time scale using de-trended, de-seasonalized monthly mean AOD. Therefore the selected locations are only optimal in terms of reducing interannual AOD uncertainty. The reason of using monthly means in this study is that (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 datasets are mostly fully covered, which makes the EnKF easier to realize. However, aerosols do vary on different time scales which means that their corresponding optimal locations could also be different. A more comprehensive assessment and design of AERONET deployment sites on different time scales, especially on seasonal and weekly scales, will also be our next step.