Atmospheric Environment 33 (1999) 2427}2434
Short Communication The representative day T. Tirabassi*, S. Nassetti Institute FISBAT of CNR, via Gobetti 101, I-40129 Bologna, Italy Received 30 April 1998; received in revised form 16 October 1998; accepted 17 October 1998
Abstract The work presents a daily trend of pollutant concentrations, referred to as the &&representative day'', i.e. the day for which the overal sum of the mean-square di!erences between its concentration, averaged within each hour, and the concentrations for all other days at the same hour, is a minimum. The approach also allows the identi"cation of the &&least representative day'' (the daily series that maximises the mean sum of squared residuals), which usually indicates an anomalous situation in pollutant dispersion, characterised by concentration maxima at the ground. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: Air pollution; Daily trends; Data sets
1. Introduction The interpretation of phenomena governing air pollution di!usion presupposes a synthesis of information derived from temporal data series. The recording of air pollution concentration values involves the measurement of a large volume of data, giving rise to the need for a rapid method of summarising such information. Generally, automatic selectors and explicators are used, many of which are provided by statistics: f f f f f f
probability density function; mean, standard deviation, median, quantiles; time-series trend; spectral analysis; principal components analysis; cluster analysis.
* Corresponding author. Tel.: 0039 051 639 9601; fax: 0039 051 639 9658; e-mail:
[email protected].
Currently, hourly concentration means are the most widespread method employed and represent the maximum disaggregation with which pollution data are generally collected. It is often adopted in applications and allows the evaluation of average concentrations over long periods, such as a day, a season or a year. In addition, hourly concentrations are used to de"ne speci"c &&typical'' periods that may be of particular interest in the study of pollutant di!usion (for example, a typical working day, a typical holiday, a typical seasonal day, etc.). The purpose of such typifying is that of outlining characteristic scenarios for a given period under investigation. Mathematical models make it possible to attempt simulations of a typical period trend, without the need to simulate all the days of the time interval covered by the typical period. This work presents a new representation of data, called the &&representative day'', that is, a daily series of hourly means that minimises the sum of squared residuals (the di!erences between the values of the representative day and the values of the other days) with respect to all the days of a temporal series.
1352-2310/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 2 - 2 3 1 0 ( 9 8 ) 0 0 3 7 1 - 9
2428
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
2. The representative day
cal matrix with all zeros in the diagonal)
A form of data representation widely used in Italy is the typical day (Tirabassi and Rizza, 1993), where each hourly concentration is expressed by the mean value (CM ) k of the concentrations (c ), referring to the same time of ik day, calculated over the period under consideration. The typical day could therefore be de"ned as a &&"ctional'' day, whose hourly concentrations are given by the concentration means, calculated, hour by hour, over all the days of the period of study. The period may be a month, season, year or grouping of particular days which share the features one wishes to study. The typical day can be mathematically expressed by 1 N CM " + c , k"1224, k N ik i/1
(1)
where CM is the kth hour of the typical day, N is the k number of days making up the time interval for which the typical day is calculated and c is the mean hourly ik concentration of the pollutant of the ith day at the kth hour. However, this form of evaluation provides a presentation averaged over the hourly trend, which cannot take account of the variations characterising the real behaviour of the quantity under examination. In addition, when using mathematical models, the day thus calculated requires the use of meteorological variables averaged in a similar way. Because of the nonlinearity of the phenomena involved (Seinfeld and Pandis, 1998), such averaging may lead to the loss of a considerable amount of information, and give rise to incorrect results. Hence the need for a new method of representing hourly trends of pollutant concentrations which, while preserving the concise characteristic of the typical day, gives a more realistic representation of the actual data. What we call a &&representative day'' is a 24 h data set, actually recorded at a "eld station, which is characterised by the least di!erences with respect to all the 24-h measurements of that station's temporal series: that is to say, the daily series whose sum of the squared di!erences over 24 h turns out to be the smallest compared to all the other days of the period under consideration. In mathematical notation, the least-squares matrix is indicated by A: 24 A " + (c !c )2, i, j"1, 2 2N, ij ki kj k/1
(2)
where N is the number of days in the time period for which the representative day is calculated and c is the ki pollutant concentration of the ith day at the kth hour. We adopt A to indicate the sum of all the squared i residuals of the ith line (or column, A being a symmetriij
A
B
N (3) + A . ij j/1 The representative day (RD) is the one with the lowest sum, i.e. the ith day where A is the smallest of the i quantities obtained A" i
min(A )NRD. (4) i The main advantage of the representative day, compared to the typical day, lies in the fact that it is an actual day, identi"ed by a precise date; this allows us to know the actual meteorological parameters to which it is associated, and which have contributed to de"ning the properties of atmospheric dilution and transport, ultimately determining the concentrations measured. The day determined can be used in the study of pollutant dispersion with mathematical models which have scenarios that characterise the time period considered, employing as input meteorological and pollutant emission values not averaged over the entire period, but relating instead to a precise and de"ned period of time.
3. The least representative day A further feature of the procedure presented here is that it also allows the calculation of the &&least representative day'' (LRD). This day is the one that maximises the sum of squared residuals, that is, the day when the quantity (3) is greatest. max(A )NLRD. (5) i The least representative day identi"es an anomalous situation of pollutant dispersion, often (although not always) characterised by maximum ground concentrations.
4. Normalisation of results To compare the degree of representativity of the most or least representative days with that obtained for other time periods and/or in other measurement stations (also in completely di!erent areas), a normalisation is required in order to make the day independent of the length of the measurement series, sampling period and characteristics of the area under study. The &&representativity'' of a representative day can be quanti"ed by introducing the following adimensional index: J+N +24 (C !c )2 i/1 k/1 k ik , DI" J+N +24 (C1 !c )2 i/1 k/1 k ik
(6)
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
where C1 is the mean hourly concentration of the typical k day at the kth hour and ! is the mean hourly concentrak tion of the representative day at the kth hour. DI is an adimensional quantity (DI*1), which is closer to unity the more RD is representative of the period under consideration. The limit value of DI is 1, when the most representative day coincides with the typical one. The least representative day can also be normalised in the same way: one simply substitutes in Eq. (6) the hourly concentration of RD (! ) with the least representative k ones. In this case the value of DI will be greater than one, providing an indication of the low degree of representativity of the day obtained; the more DI is greater than one, the more the least representative day is &&anomalous'', compared to the trend of RD. The normalisation procedure described above presents two important features: (1) independence from the size of the measured concentrations: if the concentrations are multiplied by a factor, the results of the normalisation do not change; (2) independence from the number of days (N) included in the time period considered: the quantities of the numerator and denominator of Eq. (6) are calculated over all the N days of the period under consideration.
5. Example of application We applied the method to the industrial area of Ravenna, which is situated on completely #at terrain with the Apennine foothills 60 km southwest and the Alps some 100 km to the north. The town of Ravenna is 10 km from the sea, while the industrial area, mainly comprising power stations and petrochemical plants, is situated between the sea and the town (Fig. 1). The climate is basically continental but is rendered more temperate by the proximity to the coast. The entire area is subject to a series of weak local circulations, frequent inversion phenomena and ensuing high relative humidity, particularly during extended periods of anticyclonic conditions (Tirabassi et al., 1991). Use was made of ground level concentrations measured in 4 stations of the air monitoring network during 1995. The data were made available by the ARPA (regional environmental agency) of Ravenna. In particular, we considered the hourly mean series of data measured during 1995 of SO , NO and CO by stations 1, 8, 10, 15 2 2 shown in Fig. 1. Figs. 2}4 show the data relating to SO , NO and CO, 2 2 respectively. Examining them, one sees how the behaviour of the various pollutants di!ers. While the typical and representative days present the same behaviour (remembering, however, that, although similar, the representative day has an advantage over the typical in that it
2429
is an actual day with a date of reference), the least representative day shows a di!erent trend for the three pollutants. On the least representative day, while CO reveals the same trend as on the most representative one, although with higher concentrations, the trend for SO is di!erent. 2 The "gures show that CO always presents two peaks, one in the morning and one in the evening (the latter greater than the former), caused by the tra$c of the morning and evening rush-hour; instead, the values for SO corres2 pond for some part of the day but become very di!erent later on. In the case of NO we "nd an intermediate 2 behaviour: at one station on the least representative day it maintains the trend of the most representative, but not at the other. Such behaviour can be explained by the fact that SO 2 is mainly emitted from point sources located in the industrial area and therefore the measurements are greatly in#uenced by wind direction. Instead, CO is mainly emitted by road tra$c, a source that is distributed over all the area. The NO presents an intermediate behaviour because 2 it is emitted by point sources of the industrial area, tra$c, as well as sources distributed through the urban area. The wind speed and direction registered on 3 January 1995 (the data of the LRD of Fig. 2 up) (Fig. 5) explains the concentrations measured at station at the 10 a.m., as it shows a 903 change in wind direction with a corresponding doubling in speed. Table 1 provides the representativity index DI of the most and least representative days. It can be seen here that SO and CO have similar DI values, while in the case 2 of NO , the indices shows that the RD are less representa2 tive and the least representative are less anomalous.
6. Conclusions The interpretation of the phenomena governing pollutant di!usion requires a synthesis of the information given by temporal data series. The most representative day constitutes a simple and immediate method through which it is possible to characterise the hourly structure of daily trends. We have called the &&representative day'', the one which minimises the sum of squared di!erences with respect to all the daily trends in a temporal series. The attention is focused on the &&day as a unit'', without losing, however, the particular hourly structure, as partly occurs in the case of the &&typical day''. The special advantage of the representative day method derives from the fact that, being an actual day, it allows the identi"cation of the date on which the representative trend occurred and, thus, a knowledge of the meteorological and emission parameters which characterised it. It can therefore be more easily simulated with di!usion models.
2430
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
Fig. 1. Map of the Ravenna industrial area. The circles mark the monitoring points. A is a power plant, B and C are petrochemical plants.
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
2431
Fig. 2. Representative day (black circles), least representative day (black diamonds) and typical day (white squares) of SO measured in 2 station 10 (up) and station 15 (down).
2432
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
Fig. 3. Representative day (black circles), least representative day (black diamonds) and typical day (white squares) of CO measured in 2 station 10 (up) and station 1 (down).
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
2433
Fig. 4. Representative day (black circles), least representative day (black diamonds) and typical day (white squares) of NO measured in 2 station 8 (up) and station 15 (down).
2434
T. Tirabassi, S. Nassetti / Atmospheric Environment 33 (1999) 2427}2434
Fig. 5. Wind speed (continuous line) and direction (dashed line) registered on 3 January 1995 (the data of the LRD Fig. 2 up).
Table 1 The representative index DI of RD and LRD SO 2
RD LRD
NO 2
CO
Station 10
Station 15
Station 10
Station 1
Station 8
Station 15
1.01 6.34
1.02 5.14
1.04 2.70
1.03 2.89
1.02 5.49
1.02 4.71
The same approach also allows the identi"cation of the least representative day, that is, the day on which an anomalous, nearly always critical situation occurred, compared to the average trend recorded for that period. The study of the meteorological and emission parameters relating to this day, will allow a preliminary interpretation of the phenomena which brought about the situation. Acknowledgements The authors wish to thank Dr Francesco Fortezza for making the data of the Ravenna network available.
References Seinfeld, J.H., Pandis, S.N., 1998. Atmospheric Chemistry and Physics. Wiley, New York. Tirabassi, T., Rizza, U., 1993. Flux parameterization for atmospheric-di!usion models in an industrialized area. Il Nuovo Cimento 16C, 187}192. Tirabassi, T., Fortezza, F.E., Vandini, W., 1991. Wind circulation and air pollutant concentrations in the coastal city of Ravenna. Energy and Buildings 1}2, 699}704.