Evaluation of the Accuracy of an Inverse Image-Based

International Journal of Artificial Intelligence, ISSN 0974-0635; Int. J. Artif. Intell. Atumun (October) 2012 , Volume 9, Number A12 Copyright © 2012 by IJAI (CESER Publications)

Evaluation of the Accuracy of an Inverse Image-Based Reconstruction Method for Chemical Weather Data Victor Epitropou1, Kostas D. Karatzas1, Jaakko Kukkonen2 and Julius Vira2 1 Informatics Systems and Applications Group, Dept. of Mechanical Engineering, Aristotle University of Thessaloniki, P.O. Box 483, 54124 Thessaloniki, Greece, Email: {vepitrop, kostas}@isag.meng.auth.gr 2 Finnish Meteorological Institute, Erik Palmenin aukio 1, P.O. Box 503, FI-00101 Helsinki Email: {jaakko.kukkonen, julius.vira}@fmi.fi

ABSTRACT It is common practice to publish environmental information via the Internet. In the case of geographical coverage information such as pollutant concentration charts and maps in chemical weather forecasts, such data are published as web-resolution images. These forecasts are commonly presented with an associated value-range pseudocolor scale, which represents a simplified version of the original data obtained through, dispersion models and related post-processing methods. In this paper, the numerical and signal processing performance of a method to reconstruct numerical data from the published coverage images is evaluated by comparing the reconstructed data with the original forecast data.

Keywords: numerical models, image processing, data reconstruction Mathematics Subject Classification: 68T99, 62M45, 92B20 Computing Classification System: I.5 1. INTRODUCTION The introduction of Web 2.0 and related technologies, coupled with an increased public awareness over environmental, health and Quality of Life (QoL) issues, generated an increased demand for environmental services (Karatzas et al., 2003; Karatzas 2005; Karatzas and Kukkonen, 2009). In general, these services trade off data source accuracy for perceived end-user friendliness and presentation/implementation simplicity. For example, information may have to be simplified in order to be presented to the final user, and the information itself may be retrieved through crowdsourcing or textual data mining techniques, rather than through the direct output of a traditional model (www.everyaware.eu). In general, there’s a problem of data underutilization: Chemical Weather Model providers (Kukkonen et al., 2012), typically produce coverage data with relatively high resolution, accuracy and volume. This is also the case of Chemical Weather (CW) model results produced by the participating partners in the Open Access European Chemical Weather Portal (Balk et al., 2011; Kukkonen et al. 2009). www.ceserp.com/cp-jour www.ceser.in/ijai.html www.ceserpublications.com

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However, the original data corresponding to the published figures may not be available, or alternatively, it may be available only on specific request. Even in cases, in which the original data is available, the file formats, geographic projections and domains, and other technical details are variable, and there is no general procedure for easily converting these data to a harmonized format. All these technical limitations render all this data de-facto unusable by Web 2.0 applications. A major consequence of this situation is that CW numerical data is often not made directly available to the general public through web mashups and SOA (Service Oriented Architecture)-compatible channels such as AJAX APIs, plain text or XML feeds, which are usually the driving data sources behind the SOA model (Bell 2008). On the contrary, the predominant form of publishing most coverage-type CW data is through static bitmap images which represent the coverage data (e.g. pollutant concentrations) in terms of a color-coded scale over a geographical map. Such maps are readily interpretable by humans, but they cannot be compared, combined or reused, while they are nearly useless for automated machine processing and SOA integration, and thus require additional image-processing steps to be converted back to usable numerical data, in scenarios where access to their backing numerical data is limited or unavailable (Epitropou et al., 2010). A system to perform this conversion has already been presented in (Epitropou et al. 2010; Epitropou, et al. 2011), called the “AirMerge” system. The process involved can be described as the inverse reconstruction of CW data (pollutant concentration values) from color-coded, georeferenced bitmap images, but it is possible to generalize to any type of coverage data which is published in a similar form. The use of such a system allows to bridge the two worlds (flexible web services on the one hand, and traditional CW computing and modeling on the other) generating the potential for interesting synergies and added value services. However, since the image-to-data reconstruction process is lossy, similar to the data-to-image process used during publishing, it is of interest to investigate the informational loss and errors introduced by the entire data publishing and reconstruction process. In this paper, we firstly describe (in brief) the way that the data reconstruction is being performed with the aid of a reverse-engineering, image processing algorithm. Then, the results of this phase are evaluated: the data reconstructed from specific CW forecast images are compared to their originating data, and the relative dynamic range (concentration values) and positional (geographical location) errors and distortions introduced by the publishing/inverse reconstruction procedure are computed. 2. CHEMICAL WEATHER FORECASTS AS SIGNALS 2.1 Visualization of model output The typical procedure used by providers of CW modeling information in order to publish their forecasts, is to visualize their simulations’ results (usually a set of data points) using appropriate data visualizing software, creating a many-to-one relationship between the originating data and the published images (Kukkonen et al. 2012). The simulations’ output, for the purposes of this analysis, can be treated most of the time as a two-dimensional signal on a discrete, regular x-y grid, whereas 153

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the signal’s “amplitude” represents the physical quantity or other property being modeled (Oppenheim et al. 2009). The mapping is often many-to-one or quantized in the amplitude domain, because of the use of a finite range of colors to represent concentration values (a continuous and not discrete quantity). A time step parameter, if present, could be considered as yet another dimension which however separates the simulation output into independent instances (and therefore images), which can be analyzed separately from the others, at least if no use of temporal inter-correlation is made. In this paper, the focus will be on single time-instances, therefore CW forecasts and their reconstructions will be treated as “frames” of 2D signals. 2.2 Model output loss of information Most model simulations operate on discrete-step grids located on specific geographic regions, therefore single data points often represent finite geographic arealets (model grid resolutions are usually measured in terms of actual area equivalents, e.g. in case of regional and continental scale CW forecasts these can be of the order of 10 x 10 km2 rectangular areas or in terms of fixedlatitude/longitude steps, e.g. 0.5º). This relatively rigid area quantization, often also implies a maximum –and optimum- raster resolution for the associated published images. Choosing a different raster resolution than the one of the grid itself will inevitably introduce some degree of spatial distortion, except under very specific circumstances dictated by the frequency content and statistical properties of the signal itself (Shannon 1949; Oppenheim et al. 2009). The data points of the output signal, even though they are constrained on a discrete-step grid, usually consist of floating-point values and can be considered continuous for the purpose of signal analysis, while more rarely they consist of discrete/enumerated states. In the case of floating-point values, often their distribution is continuous over a certain range, even though their histogram may not be necessarily uniform. For example, a CW simulation for which final output are pollutant concentrations, will usually contain zero-inclusive positive data values ranging from zero (0.0) up to a maximum physical value (the value range), expressed in the proper pollutant concentration unit (most commonly g/m3). The dynamic range of the original values can theoretically be infinite, at least within the limits of the exact numerical data type used (in this work, the simulation results used were available as 32bit floating point data in IEEE 754 format). In general, the process of converting the dispersion model simulation output to web-resolution images for reasons of on-line publishing causes irreversible signal degradation in both the x-y space and signal amplitude domains. For example, continuous ranges of pollution concentration values may be quantized using value interval scales with as few as five (5) steps, and rarely more than 10-15. . In addition, the steps’ intervals are often not equally spaced, but instead adopt logarithmic or quadratic relationships, with a typical spacing being, e.g., [0.1, 0.2, 0.5, …, 50.0, 100.0, 200.0], a process which can be equated with a coarse, non-linear quantization (Oppenheim et al. 2009). Of course, this causes a dramatic compression of the data’s dynamic range as well as an ambiguity in interpreting the quantized values back into original values.

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>

Given a real-valued continuous interval I : a, b  ƒ and an arbitrary quantization

q of said interval

> @

*r, n

in n , discrete, monotonically increasing, non-overlapping intervals ri , i  1, n such that I

i i

ri  >ai , bi where ai , bi  ƒ , then a real value x, where a d x d b will be assigned to the unique interval ri where a i d x d bi . Since this is obviously a many-to-few mapping, the original value of a data point which was classified into a particular interval ri will be by definition unrecoverable, as the inverse operation would be a fewto-many mapping. The most trivial approaches used consist of considering only the floor (minimum), ceiling

(maximum)

or

the

min ri ai , min ri bi , avg ri

mean

values

of

a

given

interval

ri

:

e.g.

bi  ai . 2

The only ways to improve the reconstruction of quantized values is to make very specific assumptions about the quantization criteria applied, the value distributions, their spatial properties and mutual correlations, as well as the overall signal’s frequency contents (Shannon 1949). An example of a more refined approach would be assuming that sample points values located at the boundary between two regions A and B containing values belonging to two contiguous quantization intervals s i and s i 1 , could be considered as having the maximum and minimum values allowed by their respective value ranges, and that intermediate values form a continuous gradient along the direction of the normal (Figure 1).

A

B

Figure 1: Representation of two neighboring regions A and B of a CW forecast, containing values that belong to two continuous quantization intervals 3. IMAGE-ORIENTED DATA RECONSTRUCTION 3.1 Conversion of images to numerical data As a first step, the original images are automatically downloaded from the provider’s website, cropped and parsed into a 2D data array, based on a chroma key constructed on the basis of the color scale and the pixels of the original image. This chroma key is an RGB color/value-index pairing map, under

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which the pixel colors of the original images are mapped to an integer index such as 0, 1, 2, 3 etc. based on their actual RGB value and the relative order of the legend’s colors. Those indexes can be interpreted as concentration value ranges for the purpose of numeric processing, again by using the concentration values described by the color scale. The final result of the above procedure is called recovered data, which are better suited for further processing and comparison with other available data (including their originating data because now each pixel is mapped to a precise integer index with an associated range of real values (Epitropou et al. 2011) and a precise geographical locationpixel mapping. This functionality is at the core of AirMerge, and the handling of the different modelimage configurations between different providers is accounted for automatically, via an ad-hoc configuration-driven setup. However, due to the way that CW model images are published, they often contain undesirable elements such as longitude and latitude markers, text, logos and watermarks, which do not represent actual pollutant concentration data, and often do not map to any of the color-code values represented by their color legend, thus allowing their identification as noise. A possible approach is to mark such regions as “holes” or “void”, but unless such areas are particularly extended (as is the case of some models which actually have deliberately void areas) they usually can be treated as isolated noise/small errors and thus be corrected to some degree. The typical “holes” left behind after parsing such images are usually pixel-sized, or in the form of thin, horizontal lines (not necessarily continuous), so using an interpolation/error correction scheme is viable and not particularly time consuming, while increasing the coverage of the recovered data by transforming it into a continuous data region. The “holes” or “void” are therefore marked as unwanted noise in the images and removed during a noiseremoval step, detailed below. 3.2 The NADI algorithm for small-scale error removal One of the methods that were applied for correcting aforementioned small errors was based on Artificial Neural Networks, a common approach in image processing tasks (Cristea, 2009, Fengmei and Keming, 2008), and more specifically the NADI (Neural Adaptive Data Interpolator) algorithm (Epitropou et al. 2010). NADI exploits the similarities in small-scale rectangular domains of size 3x3 of a CW forecast image, in order to train a neural network, and subsequently uses this neural network’s stored patterns in order to correct small-scale errors (missing data) on an image I, intended as a 2D discrete grid with discrete-level data (N levels), such as indexed color 2D images. Correction is performed directly on the indexes

themselves, not on their associated physical values.

NADI works by generating single-element output based on multiple input elements, and operates on a discrete input and output domain, being designed to perform local-scale error correction by using the self-similarity of I (CWF images tend to have a high degree of self-similarity), by using discrete pattern classification for mapping incomplete patterns containing errors to known, complete patterns. In this respect, it is similar to the methods used in (Fengmei and Keming 2008) and (Maxwell et al. 2006),

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which also place emphasis on reconstructing data based on local or external information, rather than a holistic function estimation of the model output or of the noise itself. Since NADI is designed to accept input and generate output only from a discrete 2D domain of cardinality N, the necessary multi-level neural input and output is simulated by using bundles of N Perceptron neurons, though a pure multi-level neuron implementation is being considered. The input layer contains a 3 u 3 array (or mask) of neuron bundles; therefore for an image with N discrete levels, there will be a total of 3 u 3 u N input neurons. These neurons are connected by trainable weight connections Wij to a hidden layer containing a multiple of the input neurons, and the hidden layer itself is connected to an output neuron containing an output bundle of size N matching that of the input neurons. The 3u 3 mask is positioned and the training procedure is calibrated in such as way, that the central element (bundle 0) of the mask is considered as the “goal”, generated by the input of the other 8 elements in the mask (bundles 1 through 8), as illustrated in Figure 2. The correction procedure, illustrated in Figure 3, consists of centering the 3 u 3 mask (Figure 4) over error positions,

Wij

OUTPUT LAYER

INPUT

INPUT LAYER

and using the output value of the NADI ANN as the corrected one.

HIDDEN LAYER

OUTPUT

GOAL Figure 2: Representation of NADI’s training procedure.

CORRECTION

Wij HIDDEN LAYER

ERROR INPUT

Figure 3: Representation of NADI’s error-correction procedure.

157

OUTPUT LAYER

INPUT LAYER

INPUT

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8

1

2

7

0

3

6

5

4

Figure 4: Representation of NADI’s sliding mask, with bundle position numbers. In this way, quasi-complete patterns that contain a small amount of errors (e.g. 1-point errors in 3u 3 masks) can be filled with somewhat greater accuracy than using simple interpolation (Epitropou et al., 2010). The process can be repeated, in order to handle errors of larger magnitude or larger data gaps and “learn” from freshly corrected patterns. The maximum number of errors present in any of the possible 3 u 3 patterns contained in an image is called the “error class”, and lower error classes are corrected first. The worst-case running time of NADI can be approximated by:

§ · § · § « k »· O¨ 2n  k ¨¨ max¨¨ ord « » ¸¸c(n  H )t  4n ¸¸  3n(n  H ) ¸ ¨ ¸ m ¬ ¼¹ © © ¹ © ¹ where n is the total number of elements in the image,  is the total number of errors to correct,

k

2  maxDChebychev is a parameter which is set according to the maximum Chebychev distance

of the data gaps present in an image, c is a time constant which depends on the performance of ANN retraining, m is a parameter indicating how often an unconditional retraining of the ANN should take place (lower values cause more frequent retraining), max ord ¬"¼ is a computed parameter measuring the largest error class currently present in the image under processing. The general case

§

§ 1 ·· ¸ ¸¸ , where p  >0,1.0 is an “escape parameter” forcing the © H ¹¹

is closer to O¨¨ kcn  n log1 p ¨

©

termination of the NADI algorithm if the percentage of uncorrected errors doesn’t drop below a certain threshold after a set number of iterations, in order to guarantee algorithmic termination. In such cases, the remaining errors are handled by a conventional interpolation algorithm. 4. FMI’S ORIGINAL DATA, MODELING AND PUBLISHING SETUP In order to compare the results of the reverse engineering of CW images with the actual CW forecasts, we made use of the numerical form of the forecasts, as produced by the Finnish Meteorological Institute. The forecasts are produced using the SILAM chemistry transport model (Sofiev et al., 2006) for several nested regions. In this paper, we focused on the “North Europe” region, which is geographically defined by the model’s input data to be contained into a bounding box of (4.5°W, 53.5°N)-(32.675° W, 71.52° N). This corresponds to an approximate area of (1800 x 2002) km2. For reasons of generalization of the methodology applied, we assumed no prior or “insight” knowledge of the studied CW data, apart from having full access to both the numerical model results (forecasts) as well as to the corresponding images of CW forecasts published on-line. 158

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4.1 Description of the chosen regions and data formats For the “North Europe” region, separate CW forecasts are provided for the concentrations of the following pollutants: SO2, NO, NO2, CO, O3, PM10 and PM2.5. These forecasts are repeated for 4 different altitudes (surface altitude (SURF), SURF+500m, SURF+1000m, SURF+3000m) and over a time extension of 48 hours with a time resolution of one hour. Hour offsets may range from 01 to 48 and are relative to standard UTC time. The values computed represent the average hourly concentrations of the modeled pollutants (in g/m3). Therefore, there is a daily production of 6×4×48=1152 different data layers just for the North Europe region. The simulation’s output consists of fixed-resolution gridded numerical data with dimensions of 245×265 points/pixels (width × height) with the smallest resolution (width) corresponding to the geographical longitude, and each point corresponding approximately to 7.5 km of actual spatial resolution. This setup is common between all computed layers of the same region. In order to divulgate simulation results to the public, the data are converted to images having the general format indicated in Figure 5, which is common for all published SILAM model forecasts within the “North Europe” region. These images are in PNG format, have an overall resolution of 600x750 pixels, and contain three sub-images, of which the largest one has 402x297 pixels spread over a geographical area matching that of the model. This largest sub-image is also the one which is the focus of this paper, as it contains the concentration data for a particular pollutant (the two smallest ones contain the dry and wet depositions, not available for all pollutants). For the purposes of analysis by the AirMerge system, this larger image is cropped from the rest of the graphic, and its colors are interpreted as numerical value ranges, handling transparent/non-data regions as well as unwanted noise (geomarkers, text, etc.) appropriately. The color scale associated with this particular image, visible below the data area itself, associates each color present in the image with a range of possible values. The minimum value is not explicitly stated and is assumed to be zero; the maximum value is assumed to be four times the biggest explicit value. The image also contains white non-data regions which are not covered by the model, and are treated as void in the subsequent computations (namely, they don’t contribute to the gathering of statistics).

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Figures 5a-c: Typical SO2 chemical forecast images using the SILAM model format. The notation 01Z25NOV2011 means that the forecast corresponds to the UTC time of 01.00 on 25 Nov 2011. Concentrations are presented in the above figure, and dry and wet deposition in the two lower figures

Figure 6: Visualization of a cleaned data region from the concentration forecast in Fig. 5a, using AirMerge.

The information necessary to parse valid colors and detect unwanted noise and transparent areas is part of AirMerge’s configuration and is unique for each CW model provider, depending on the exact specifications of the publishing format used. In the present case, the color scale contains 11 values for all considered pollutants; the continuous range of concentration values is therefore quantized to just 11 levels regardless of what the actual value ranges are. Of course, this will result in comparatively larger quantization error for scales that extend over a wider value range (Bruce 1965; Cover et al. 1991). 4.2 Reconstructed data and sources of errors The result of AirMerge’s parsing procedure is a “cleaned up” version of the desired data region, which associates colors with concentration value ranges, and contains no superfluous information. This constitutes the reconstructed data, created by interpreting the visualized values directly by selecting samples and processing those, without any smoothing or interpolation. Interpretation of colors as 160

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concentration values is made ambiguous by the fact that a single published color may correspond to more than one original data value, and thus a color could be interpreted as any value between its stated minimum and maximum (Cover et al. 1991). Other than color quantization, other factors that may adversely affect the quality of reconstructed datasets are spatial quantization and reconstruction errors. These can be introduced by all of the following factors:

x Mismatch between estimated/computed geographical registration of reconstructed data (in the present cases this was minimized, due to access to the actual numerical values).

x Errors due to the different data resolutions between the published forecasts and the model’s original numerical output. This makes simple point-per-point comparisons more laborious, as the two resolutions must be matched. In the case of the SILAM CW forecasts at the FMI there are notable differences in resolution and aspect ratio between the on-line published forecast images and the original data. In particular, even though the original data had an actual resolution of 245 x 265, the published forecast image has a resolution of 402 x 297 pixels (with the largest value being the longitude direction). It is therefore reasonable to assume that part of the on-line published data is actually the result of 2D spatial interpolation, and thus not part of the original dataset. This will reasonably lead to spatial inaccuracies, especially whenever there are transitions between constant-value colored zones. 5. COMPARISON METHODOLOGY The comparison was performed by computing a point-by-point Mean Squared Error (MSE) metric between the concentration values of each point of the original data versus the corresponding point in the reconstructed data. The grid resolution mismatch was bridged through the use of an adapter, which operated the following transformations as needed: original data grid o geographical area (point) o reconstructed data grid This approach is simple to implement, but of course introduces spatial distortion because it implies that a single grid point corresponds to a single, geographical point and vice versa. Also, since the reconstructed data grid is spatially denser than the original one, this means that the mapping between data points will be one o many. 5.1 Spatial resolution matching Since the original dataset’s stated spatial extension implies a longitudinal extension of 1800 km and a latitudinal one of 2002 km, a single original data point corresponds to an “arealet” with a surface area of (7.35 × 7.55) km2, while the reconstructed dataset has an artificially inflated resolution which results in a theoretical spatial resolution of (4.48 × 6.55) km2. This leads to a situation similar to the comparison of two signals sampled at different sampling rates: any processing must occur at an intermediate sampling rate which is the least common multiple (LCM) of both in order to minimize data skipping and intermodulation noise (Cover et al. 1991; Oppenheim et al. 2009).

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This can be achieved by projecting both datasets into an intermediate, higher-resolution grid before performing any statistical processing. The ideal resolution to perform this task would be

LCM (245,404)

98980 for width and LCM (297,265)

78705 for height. Since these are

impractically high values and would require prohibitively high amounts of memory and CPU time to perform, a compromise can be found by using the LCM of approximations of the actual resolutions e.g.

LCM (250,400)

2000 for width and LCM (300,270)

3000 for height. This was also the actual

intermediate grid size used for computations, with a much finer grid and thus spatial stepping compared to that of either dataset, and sufficiently high as to minimize resolution mismatch errors. Other than this spatial oversampling, the datasets themselves are not altered nor interpolated at this point. 5.2 Interpretation of color scales The statistical operations of gathering the per-point variance and MSE for even moderately-sized gridded datasets generate large amounts of data. In order to represent this amount of information intuitively, the MSE and Variance stats are presented in both a graphical (image) and numerical table summary form, including the minimum, maximum, mean and variance of the point-by-point Variance and the MSE. The MSE and Variance image maps indicate the numerical value of the MSE and Variance at a specific point by using the same color scale as the retrieved data themselves (i.e. figures 9 and 10 for sulfur and ozone, respectively), stretched and interpolated by a factor of ten (10) to better represent the more varied range of values. This stretching actually means that while in the original color scale 11 quantization levels were used, now each level is divided into 10 sublevels, to increase the accuracy of visualization. The same stretched color scale is also used to represent the original data. 5.3 Interpretation of original data values The stated values, unless specified otherwise, are always assumed to be concentration values expressed in g/m3. For the SO2 forecasts in particular, the actual numerical values contained in the original data files were halved before partaking into further calculations, since the values expressed in the forecasts actually express the concentration of sulfur (S) in g/m3 while the data contained in the numerical output of the model (NetCDF files) expresses the concentration of sulfur Dioxide (SO2), whose molecular weight is approximately double that of the atomic weight of sulfur. Finally, the issue of color quantization was solved by noting that using the minimum value of each color range for interpreting the recovered forecast data yielded the best results (lower maximum error, lower average MSE and variance). 6. CW FORECAST DATA SETS USED FOR THE EVALUATION Due to the large number of possible layers (1152) the comparisons were limited to two different pollutants (O3 and SO2), two different altitudes (surface level and +500m), and only two different time offsets (+01 and +12 hours). The forecasts and datasets used were issued for the day of November 162

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28, 2011 and were automatically retrieved from FMI’s website through the AirMerge system. The original data used for comparison was extracted from a NetCDF format file provided by FMI, containing the totality of FMI’s model simulations for the region of “North Europe” for the day of 28 November 2011. The forecasts will be referred to by the labels mentioned in Table 1. Since those datasets have markedly different statistical and value distribution properties, it is possible to predict certain of their statistical and accuracy properties during data reconstruction by taking into account their color scale quantization and value distributions. Performing a simple regression analysis (Figure 7) shows that the spacing of the color scale used for SO2 forecasts (Figure 8) is roughly logarithmic, as shown by the ln bi  ai plot in Figure 7 applied to the intervals of the SO2 color scale. By contrast, the O3 forecasts use a linear scale defined simply by a i

20i  1 , bi

20i , i  >1,10@

3

g/m , which has a markedly different quantization behavior. ln(bi-ai)

Figure 7: Color scale spacing and intervals for FMI’s SO2 forecasts. Table 1: Naming of forecasts. Name

Pollutant (composition)

Elevation (m)

Time offset (h)

Forecast 1

SO2

0

1

Forecast 2

SO2

0

12

Forecast 3

SO2

500

1

Forecast 4

SO2

500

12

Forecast 5

O3

0

1

Forecast 6

O3

0

12

Forecast 7

O3

500

1

Forecast 8

O3

500

12

In addition, the histograms showing the distribution of the original data’s in the bins defined by the color scales indicate that the use and distribution of values in the color scale’s dynamic range is not always optimal and can vary widely depending on the model’s output and the general tendencies for a pollutant: for example, the averaged histogram of several SO2 forecasts at the surface level tend to fill the first 8 bins (Figure 8 a) and b)) with all values contained within a maximum of 7 g/m3, with the 163

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majority of the values filling the smallest bins in terms of range. This leads to a relatively high precision quantization, something verified later on by comparison of reconstructed data with original data. At an altitude of 500 m however, the values distributions tend to be slightly shifted upwards to wider-spaced bins and thus should lead to increased quantization errors, in terms of absolute maximum error encountered, but overall the accuracy should remain high. The histograms for O3 forecasts on the other hand display a much more coarse quantization overall due to their equallyspaced linear scale (Figure 8 c) and d)), of which they end up using only 4 bins each of which is effectively akin to a 2-bit linear quantization. This can lead to relatively large quantization errors, and a lower quality of reconstruction compared to forecasts using a logarithmic scale, because the nonlinearity of the values’ distribution is not matched by an adaptive non-linearity of the color scale (Hiroya et al. 1967).

Figure 8: Distribution histograms of the original pollutant concentration dataset for the selected forecast types. Each dataset contains n=60364 non-void data points.

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Figure 9a-b: The logarithmic sulfur(S) concentration color scale (g/m3) used in this study (a-top), and the scale used in the Figures 11, 12 and 15a (b- bottom)

Figure 10a-b: The linear ozone (O3) concentration color scale (g/m3) used in this study (a- top) and the scale used in the Figures 13, 14 and 15b (b- bottom) 7. RESULTS

Figure 11: The AirMerge-based forecasts 1-4 (top row) along with their original data (bottom row). The color scale is the one of Figure 9b.

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Figure 12: The variance (top row) and MSE (bottom row) maps for forecasts 1-4. The color scale is the one of Figure 9b.

Figure 13: The AirMerge-based forecasts 5-8 (top row) along with their original data (bottom row). The color scale is the one of Figure 10b. It is obvious just from the visualization of the forecasts and their original datasets ((Figures 11 and 13), that the quantization process does cause a loss of information. These losses are much more marked in forecasts 5 to 8 (Figure 13) since they follow a coarser quantization which does not fit the data well, resulting a loss of detail, and lower recoverability.

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Figure 14: The Variance (top row) and MSE (bottom row) error maps for forecasts 5-8. The color scale is the one of Figure 10b. The visualization of the corresponding error maps for the per-point Variance and MSE (Figures 12 and 14) and the much larger variances of the per-point variance and RMSE metrics in Tables 2 and 3 further confirm this (NOTE: even though computations and error maps used the MSE metric, the RMSE value is reported In tables, so that comparisons can be done using the same unit as the concentration) Table 2: Cumulative statistics for point-per-point variance, expressed in (g/m3). Forecast 1 0.000 3.603 0.007 0.003

Minimum Maximum Mean Variance

Forecast 2 0.000 12.162 0.025 0.065

Forecast 3 0.000 56.058 0.011 0.120

Forecast 4 0.000 56.102 0.040 0.750

Forecast 5 0.000 203.955 38.358 836.895

Forecast 6 0.000 293.173 37.661 933.874

Forecast 7 0.000 223.595 36.186 828.105

Forecast 8 0.000 228.449 34.111 808.998

Table 3: Cumulative statistics for point-per-point RMSE, expressed in g/m3.

Minimum Maximum Mean Variance

Forecast 1

Forecast 2

Forecast 3

Forecast 4

Forecast 5

Forecast 6

Forecast 7

Forecast 8

0.000 1.342 0.061 0.037

0.000 2.466 0.112 0.180

0.000 5.294 0.074 0.245

0.000 5.296 0.141 0.613

0.000 10.098 4.379 14.465

0.000 12.107 4.339 15.280

0.000 10.573 4.254 14.388

0.000 10.688 4.130 14.221

Note: the statistically gathered RMSE is defined as

V 2 by using the sample average as an estimator, and since n

the per-point RMSE is computed between single points of the original dataset and the forecast, n

RMSE

V2 . n

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Table 4: Cumulative statistics for point-per-point RMSE between pre-quantized original data and reconstructed data, expressed in g/m3. Forecast Forecast Forecast Forecast Forecast Forecast Forecast Forecast 1 2 3 4 5 6 7 8 Minimum 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Maximum 1.379 2.440 5.268 5.268 14.142 7.071 14.142 7.071 Mean 0.065 0.121 0.077 0.153 2.229 1.762 2.026 1.684 Variance 0.191 0.493 15.821 12.064 13.955 11.564 0.034 0.166

Additionally, a series of spatial error maps were constructed by first applying the same quantization procedure to the original data as the one applied to the published forecasts, before carrying out any comparisons. The only difference is that the resolution stretching from 245 × 265 to 402 × 297 pixels was not applied. This allowed identifying the errors which are introduced by spatial distortion alone. In the case of Forecasts 5 to 8 (Figure 15), this resulted in relatively low-valued error maps, in which errors were mostly concentrated around the contours of transition zones between “islets” of different quantization levels, while for Forecasts 1 to 4 the error maps and relative tables were not significantly different.

Figure 15a-b: Prequantized MSE error maps for forecasts 1-4 (a-top row) and 5-8 (bbottom row), obtained by pre-applying quantization to original data and comparing with the corresponding reconstructed data. The color scales used are presented in Figures 9b and 10b respectively. Finally, another series of statistics were gathered in order to estimate the RMSE introduced by the initial quantization process itself, by comparing the original data versus a quantized version of itself, using the same rule applied to downsample the original data to the published forecast images (rounding values down to the floor value of each bin). The results of this comparison are reported in Table 5. It is interesting to notice how the values in Table 5 are quite close to the values reported in Table 2 (the final RMSE introduced by the entire reconstruction process): the Mean and Variance rows 168

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of both tables are quite close, while only the Maximum row is clearly divergent. This is consistent with error peaks being generated near transition zones, and affecting mostly high concentration values that tend to be more coarsely quantized. Table 5: Cumulative statistics for point-per-point RMSE between the original data and its quantized form expressed in g/m3.

Minimum Maximum Mean Variance

Forecast 1 0.000 0.528 0.051 0.013

Forecast 2 0.000 1.060 0.061 0.028

Forecast 3 0.000 1.718 0.047 0.018

Forecast 4 0.000 2.819 0.071 0.107

Forecast 5 0.000 7.071 4.387 14.083

Forecast 6 0.000 7.071 4.363 14.420

Forecast 7 0.000 7.071 4.234 13.862

Forecast 8 0.000 7.071 4.177 13.604

8. CONCLUSIONS It was found that the performance of the CW data reconstruction is highly dependent on the quantization imposed by the chosen resolution and color scale, as well as the distribution of the original data values within the bins of that color scale. The use of a logarithmic scale and a majority of data points residing in the lower-valued and less widely-spaced bins of the scale results in smaller reconstruction errors and a more effective use of the color scale’s range, which resulted in an overall satisfactory reconstruction of the SO2 forecasts. On the contrary, the reconstruction of O3 forecasts suffered a lot from the linear color scale chosen, which led to decreased reconstruction fidelity. Pre-quantizing the original data in order to simulate the process by which the published forecasts were created, resulted in slightly decreased reconstruction error because no spatial distortion or watermarking was taking place. It was also revealed that, at least in coarsely quantized forecasts, the spatial resolution mismatch creates errors around the quantization levels transition zones. Such errors can be minimized by applying sufficiently fine spatial oversampling. It is important to note that, unless a particularly destructive quantization process is applied to the original data by the model’s publisher, the data reconstruction technique presented in this paper allows recuperating a significant amount of the original data, depending on the color scale chosen by part of the model provider. In the case of the SO2 forecasts studied here, the mean error and its variance are often well within the lower valued bins of its color scale, and the reconstruction itself displays similar statistical properties as the initial quantization imposed on the data, minus artifacts caused by watermark elimination and spatial distortion induced by image resizing. This suggests that a near-perfect reconstruction of at least the quantized model values should be possible, if the images used by the model provider during publishing are reasonably noise-free, the watermark removal algorithm is particularly effective, and the grid size of the published image matches that of the original data so that no spatial distortion takes place. The reliability of the reconstruction decreases around areas with high values of pollutant concentrations, as those tend to be assigned to larger bins which have a higher inherent quantization error. This uncertainty however is not expected to cause trouble in scenarios where episode

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predictions are important, since the reconstructed values in high-concentration zones will, in most cases, be interpreted as high values anyway, thus altering their quantitative but not their qualitative associated information. Overall, the technique displayed in this paper allows recovering large amounts of data from a previously underutilized resource, and thanks to the tier-based architecture of the underlying AirMerge system and its facilities to render data from different model providers interoperable, it will allow the development of further web-based services that exploit its data-reconstruction capabilities and its backing database of retrieved CW information. Planned developments of the AirMerge system include the introduction of enhanced data smoothing during reconstruction and exposure/licensing of its functionality to third-party services and users via a public API. 9. REFERENCES Balk, T., Kukkonen, J., Karatzas, K., Bassoukos, T., Epitropou, V. 2011, European open access chemical weather forecasting portal. Atmospheric Environment 38(45), 6917-6922. Bell, M., 2008, Introduction to Service-Oriented Modeling. Service-Oriented Modeling: Service Analysis, Design, and Architecture, John Wiley and Sons. Bruce, J.D., 1965, Technical Report 429: Optimum quantization. Cambridge: Research Laboratory of Electronics, Massachusetts Institute of Technology, Pat. No.: NASA-CR-62742, TR-429. Cover, T.M., Thomas, J.A., 1991, Elements of Information Theory. New York: Wiley and Sons. Cristea, P.D., 2009, Application of Neural Networks in image processing and visualisation. In R. De Amicis et al. (eds.), GeoSpatial Visual Analytics: Geographical Information Processing 59 and Visual Analytics for Environmental Security, © Springer Science + Business Media B.V., 59-71. Epitropou, V., Karatzas, K., Bassoukos, A., Kukkonen, J. Balk, T., 2011, A new environmental image processing method for chemical weather forecasts in Europe. Proceedings of the 5th International Symposium on Information Technologies in Environmental Engineering (Paulina Golinska, Marek Fertsch and Jorge, Marx-Gomez, eds.). Springer Series: Environmental Science and Engineering, Poznan, Poland, 781-791. Epitropou, V., Karatzas K. Bassoukos A., 2010, A method for the inverse reconstruction of environmental data applicable at the Chemical Weather portal. Geospatial Crossroads @ GI_Forum '10, (A. Car, G. Griesebner and J. Strobl., eds), Salzburg, Austria, 58-69. Fengmei, L. Keming, X., 2008, Classified image interpolation using neural networks. IEEE International Joint Conference on Neural Networks-IJCNN 2008, (IEEE World Congress on Computational Intelligence), Hong Kong, 1075–1079. Hiroya, F. and Kataoka, M., 1967, Evaluation and Optimization of Nonlinear Quantization Characteristics in PCM Transmission of Speech, Journal of the Acoustical Society of America 42(5), 1192-1192 (1 page). Karatzas, K., 2005. A quality-of-urban-life ontology for human-centric, environmental information services. C21: Towntology, WG1: Ontologies and Information Systems, Brussels, Belgium, 12–13 (http://www.towntology.net/Meetings/0512-BXL/presentations/C21_towntology_karatzas_brussels.pdf, last visited 01.03.2012) Karatzas, K., Dioudi, E., Moussiopoulos. N., 2003, Identification of major components for integrated urban air quality management and information systems via user requirements prioritization. Environmental Modelling & Software 18, 173–178. Karatzas, K., Kukkonen, J., 2009, COST Action ES0602: Quality of life information services towards a sustainable society for the atmospheric environment, Thessaloniki: Sofia Publishers. 170

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Kukkonen, J., Klein, T., Karatzas, K., Torseth, K., Fahre, Vik A., San Jose, R., Balk, T., Sofiev, M., 2009, COST ES0602: Towards a European network on chemical weather forecasting and information systems. Advances in Science and Research Journal 3, 27–33. Kukkonen, J., Olsson, T., Schultz, D.M., Baklanov, A., Klein, T., Miranda, A.I., Monteiro, A., Hirtl, M., Tarvainen, V., Boy, M., Peuch, V.-H., Poupkou, A., Kioutsioukis, I., Finardi, S., Sofiev, M., Sokhi, R., Lehtinen, K.E.J., Karatzas, K., San José, R., Astitha, M., Kallos, G., Schaap, M., Reimer, E., Jakobs, H., and Eben, K., 2012, A review of operational, regional-scale, chemical weather forecasting models in Europe. Atmospheric Chemistry Physics 12, 1-87, doi:10.5194/acp-12-1-2012 Maxwell, S.K., Schmidt G.L. & Storey, J.C. , 2006, A multi-scale segmentation approach to filling gaps in Landsat ETM+ SL-off images. International Journal of Remote Sensing 28(23), 5339–5356 Oppenheim, A.,V., Schafer, R.W., Buck, J.R., 2009, Discrete-Time Signal Processing. (3rd Edition ed.), Prentice Hall. Shannon, C.E., 1949, Communication in the presence of noise. Proc. Institute of Radio Engineers 37, 10–21. Sofiev M., Siljamo, P., Valkama, I., Ilvonen, M., Kukkonen, J., 2006, A dispersion modelling system SILAM and its evaluation against ETEX data. Atmospheric Environment 40, 674-685, DOI:10.1016/j.atmosenv.2005.09.069.

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