The relevance of particulate radon progeny measurements for an estimation of the mixing height was recently established. Here, an attempt at a shortrange forecast of radon concentration is presented using a neural-network model applied at a 2-hour based time series. This forecasting activity leads to useful predictions of the mixing height during stability conditions

Ameli, F.

Pasini, Antonello

Pelino, V.

English

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NOTE BREVIIL NUOVO CIMENTO Vol. 24 C, N. 2 Marzo-Aprile 2001A neural-network approach to radon short-rangeforecasting from concentration time seriesA. Pasini(1), F. Ameli(2) and V. Pelino(3)(1) CNR - Istituto sull’Inquinamento Atmosferico - via Salaria Km. 29,300I-00016 Monterotondo Stazione (Roma), Italy(2) Dipartimento di Fisica, Universita` di Roma “La Sapienza”P.le Aldo Moro 2, I-00185 Roma, Italy(3) Servizio Meteorologico dell’Aeronautica, CNMCA - Aeroporto “De Bernardi”I-00040 Pratica di Mare (Roma), Italy(ricevuto l’ 8 Novembre 2000; revisionato il 16 Febbraio 2001; approvato il 26 Febbraio 2001)Summary. — The relevance of particulate radon progeny measurements for an es-timation of the mixing height was recently established. Here, an attempt at a short-range forecast of radon concentration is presented using a neural-network modelapplied at a 2-hour based time series. This forecasting activity leads to useful pre-dictions of the mixing height during stability conditions.PACS 92.60.Fm – Boundary layer structure and processes.PACS 05.45.Tp – Time series analysis.PACS 07.05.Mh – Neural networks, fuzzy logic, artificial intelligence.1. – IntroductionSince late 70s, Fontan, Guedalia and co-workers recognised the relevance of radonprogeny measurements to establish an index of the diffusion properties of the boundarylayer [1-3]. More recently, an estimation of the mixing height through a box modelusing radon concentration data was successfully performed during stability conditions [4].Furthermore, some qualitative relationships between radon concentration and the heightof the mixed layer were shown also in advective situations [5].Several groups performed new measurement campaigns during the last years, espe-cially stressing observational features (vertical distribution, radon exhalation, etc.) [6-9].Here, instead, we present an attempt at forecasting radon concentration by means of aneural-network model, in order to obtain useful short-range predictions of the mixingheight through application of the cited box model.c© Societa` Italiana di Fisica 331332 A. PASINI, F. AMELI and V. PELINOFig. 1. – A subset of the 2-hour time series (3 October (h. 17)–8 October (h. 15) 1997). Note thetransition from a stable condition to a moderate advective situation (after 5 October, 9 a.m.).2. – Data setThe data set used in our analysis comes from a 1-year monitoring activity (1 January–31 December 1997) of radon detection on a 2-hour basis at Pratica di Mare, a site nearRome and very close to the Tyrrhenian Sea. The instrument used was a prototype similarto the ADM 9000 [4], specifically developed by CNR-IIA. This is a beta gauge monitor,which samples particulate on membrane filters and detects the short-lived radioactivityassociated with particles by means of a Geiger-Mu¨ller detector.3. – Brief statistical considerationsAs in other studies (see, for instance, [10]), our time series of beta counts (directlyproportional to radon concentration) shows the typical pattern with maxima and minimaduring stability conditions, due to the diurnal thermal cycle, and an asymptotic quasi-constant plateau during advective episodes (see fig. 1). Furthermore, an accurate analysisof our time series leads to recognise frequent bimodal structures in the nocturnal maximaand a Fourier analysis allows us to reveal the 24-hour peak of the diurnal cycle, butalso several further peaks in the spectrum (see fig. 2), a clear sign of high-frequencyperiodicities. At the present stage of our study we are not able to determine the processesresponsible for these further peaks, even if they should be identified in those physicalprocesses in the PBL endowed with short evolution time.Finally, an autocorrelation analysis shows that data at t: ∆t = t0 − t = 20, 22, 24, 26,28 hours reveal good correlation with data at time t0. They are characterised by high-correlation coefficients, substantially comparable with those related to t: ∆t = 2, 4, 6(see fig. 3). In particular, this confirms the periodicity of 24 hours.4. – Neural and box modelsThe ability of neural networks to grasp the dynamical content hidden in a time serieswas extensively recognised in several fields (see [11] for a general reference). Recently,attempts at neural forecasting applied to time series of atmospheric variables appearedin the literature [12, 13]. Due to the features briefly discussed in the previous section,A NEURAL-NETWORK APPROACH TO RADON SHORT-RANGE ETC. 333Fig. 2. – Fourier spectrum of our time series.in particular the evidence of a complex dynamical content in our data, it is interestingto test the ability of a neural network in forecasting radon concentration (some stepsahead). Soon afterwards, the results of this forecasting activity will be used as inputsfor the box model described in [4], in order to obtain useful short-range predictions ofthe height of the nocturnal stable layer.The neural model used in the present application was extensively described in [14].Here we stress that in our model we use a feed-forward neural network with standardback-propagation training and weight updating, performed via a generalised Widrow-Hoff rule containing both gradient descent and momentum terms (see [15,16] for generalintroductions to this kind of networks).Unlike our previous application (see, for instance, [14]), when we used input patternscoming from a synchronous set of meteorological observations, in the present approachtime-delayed truncated series of radon data are considered as input patterns, in orderto test if the information contained therein is sufficient for allowing good forecasts inthis particular problem. The alternative multivariate approach used in [14], when theinput represents an “initial state” of the PBL formed by several variables at the sameFig. 3. – Autocorrelation graph.334 A. PASINI, F. AMELI and V. PELINOtime t0, is now under test for radon forecasting and the results of its implementation willbe presented in a forthcoming paper. Furthermore, due to the recognition of a seasonalchange effect on forecasting results, in the present attempt we use a moving windowtraining, as in [14]. Here, we fix a “2-month memory” of training cases and update it atevery new forecast, thus limiting the training to the same “season” of any forecast case.As far as the box model using radon concentration data is concerned, its comprehen-sive description and application in order to estimate the height of the nocturnal stablelayer are presented in [4]. Here, we remember that, under some simplifying hypotheses(valid for periods of nocturnal stability), the model allows us to estimate an equivalentmixing height he that was shown to be strongly correlated with an independent meteo-rological estimation of the mixing height, thus giving us a new method for monitoringthe nocturnal stable layer depth. The equivalent mixing height at the time t can beestimated by the relationhe(t) =Φ∆tC(t)− C0 ,(1)where Φ is the radon flux at the surface, ∆t is the time from the start of the accumu-lation, C(t) is the radon concentration at time t and C0 is the radon concentration atthe beginning of accumulation. At present, a consistent effort is devoted to improve thismodel by considering some effects previously neglected, such as radon decay and entrain-ment from the top of the box in cases of nocturnal fluctuations. This improvement leadsto a better estimation of nocturnal PBL depth fluctuations, whose fingerprint is veryevident in radon patterns as well as in the concentrations of several pollutants [17].5. – ResultsWhen dealing with multi-layer neural-network models, an important activity is thechoice of the optimal architecture, both in terms of number and kind of inputs and interms of number of hidden neurons and layers. The aim is to choose a topology whichleads to a good representation of the underlying function that we want to reproduceand, at the same time, allows us to avoid the phenomenon of overfitting, often using anearly-stopping method, too. Here, for lack of space, we do not discuss about this activity,but present directly the optimal architecture found for our forecasting problem.After several attempts and following theoretical and empirical rules (see [18] for areview of such methods), we chose a network endowed with one hidden layer with 8neurons, one output neuron and N inputs in the input layer (N chosen as the numberof delayed data with a correlation higher than 0.65 in the autocorrelation graph). Anearly-stopping rule was also applied, in order to prevent overfitting.In order to test the forecasting performance of the model, we calculate the linear cor-relation coefficient R between observed and forecast data and a Generalisation Coefficient(GC), calculated as follows (see [14]: now we have only one output unit):GC = 1−√∑Mµ=1[(Oµ − Tµ)− (Oµ − Tµ)]2M,(2)where M is the total number of test patterns, Oµ and Tµ are the output (forecastvalue) and the target (verification value: detected) respectively, for every pattern µ, andA NEURAL-NETWORK APPROACH TO RADON SHORT-RANGE ETC. 335Fig. 4. – Performance of the neural model on the test set (1 March–31 December 1997) as theforecast horizon increases: in terms of GC (solid line) and R (dotted line).(Oµ − Tµ) is the systematic error of the network (usually very low). Note that, as usualin neural modelling, input, target and output values are normalised between 0 and 1.Therefore, 0 ≤ GC ≤ 1 and the closer it is to 1, the better are the forecasts of the neuralnetwork.The performance of neural forecasts is presented in fig. 4 for 3 steps ahead (t+2, t+4and t+6hours). Each forecast is obtained by a long step method, and for the second andthe third step we directly forecast radon concentration starting from purely detected data.An alternative recursive method, performing always a t+2hours forecast, via insertion offorecast values into the input patterns for the t+4 and t+6hours forecast, leads to lowerperformance in our case, as also properly supposed from theoretical considerations [19].These results bear witness to the good general forecasting properties of our model, ofcourse with a moderate decrease in performance as the time horizon increases. Further-more, a more accurate analysis leads to recognise a satisfying behaviour even in specificcases of physical relevance as shown in fig. 5, where one can see as nocturnal fluctuationsare correctly grasped by the model.Finally, for the stability periods shown in fig. 5, an estimate of the nocturnal value of hehas been calculated by means of the box model previously described, both from detectedand forecast values of concentration. The relevance of this model for a correct estimationof the nocturnal mixed layer depth from detected values was shown elsewhere [4]. Here,the calculation of he from forecast values shows that it is possible to obtain a usefulforecast of this variable by means of application of neural and box models (see fig. 6).As a preliminar comment to this figure, we can say that the range of nocturnal fluctu-ations, even in the estimations from detected radon values, seems sometimes too wide forphysical consistent oscillations of the stable layer depth: this effect is due to the simpleform of the box model adopted here and it is greatly reduced in applications of a refinedmodel (now under development [17]), where radon decay and entrainment from the topof the box are included in its theoretical formulation. In spite of this, qualitatively thepatterns of nocturnal fluctuations are well predicted, even if sometimes with amplitudesdifferent from those estimated by measures. Furthermore, due to its structure, the boxmodel is more sensitive to errors of the neural model in predicting medium-low radon336 A. PASINI, F. AMELI and V. PELINOFig. 5. – Detected data (solid line) vs. forecast data (dotted line) for the period 9–13 September1997.concentrations, rather than to errors in the range of high radon concentration values.Therefore, while there are some discrepancies in the results for high values of he, themost acute episodes (very low he) are always well forecasted.6. – Conclusions and perspectivesFollowing previous works [1-5], which claim the relevance of radon progeny measure-ments for estimating the physical features of the PBL and, in particular, the nocturnalstable layer depth, in this note we present an original application of a neural-networkmodel to evaluate short-range forecasts of radon concentration at the surface. Accord-Fig. 6. – Nocturnal Equivalent Mixing Heights as calculated by the box model using detecteddata (solid line) and forecast data (dotted line).A NEURAL-NETWORK APPROACH TO RADON SHORT-RANGE ETC. 337ingly, the obtained results are encouraging and, after the further application of a boxmodel, lead to accurate short-range forecast of the nocturnal mixed layer depth.We have shown that our time series of radon concentration on a 2-hour basis containssufficient information for its short-range forecasting. Nevertheless, as a perspective offurther studies, attempts at including other physical observations (related to the bound-ary layer) into the input layer seem to be promising for better characterise the initialstate of the PBL and in order to achieve more accurate forecasts.∗ ∗ ∗A. Di Diodato (Met Service of the Italian Air Force) andM. Montagnoli (CNR -Institute of Atmospheric Polllution) are acknowledged for validation of radon data.REFERENCES[1] Fontan J., Druilhet A., Lopez A., Bernis M. J. and Cautenet G., Pollut. Atmos.,71 (1976) 231.[2] Fontan J., Guedalia D., Druilhet A. and Lopez A., Boundary Layer Meteorol., 17(1979) 3.[3] Guedalia D., Ntsila A., Druilhet A. and Fontan J., J. Appl. Meteorol., 19 (1980)839.[4] Allegrini I., Febo A., Pasini A. and Schiarini S., J. Geophys. Res., 99 (D9) (1994)18765.[5] Allegrini I., Febo A., Pasini A. and Schiarini S., Riv. Meteorol. Aeronaut., 53 (1993)51 (in Italian).[6] Lupu A. and Cuculeanu V., J. Geophys. Res., 104 (D22) (1999) 27527.[7] El-Hussein A., Mohammed A. and Ahmed A. A., Atmosph. Environ., 33 (1999) 183.[8] Duen˜as C., Fernandez M. C., Can˜ete S., Carrettero J. and Liger E., Atmosph.Environ., 33 (1999) 501.[9] Vinod Kumar A., Sitaraman V., Oza R. B. and Krishnamoorthy T. M., Atmosph.Environ., 33 (1999) 4717.[10] Porstendo¨rfer J., Butterweck G. and Reineking A., Atmosph. Environ. A, 25(1991) 709.[11] Weigend A. S. and Gershenfeld N. A., Editors, Time Series Prediction: Forecastingthe Future and Understanding the Past (Addison-Wesley, New York) 1993.[12] Mihalakakou G., Santamouris M. and Asimakopoulos D., J. Geophys. Res., 103(D16) (1998) 19509.[13] Santamouris M., Mihalakakou G., Papanikolaou N. and Asimakopoulos D. N.,Geophys. Res. Lett., 26 (1999) 337.[14] Pasini A. and Potesta` S., Nuovo Cimento C, 18 (1995) 505.[15] Hertz J., Krogh A. and Palmer R. G., Introduction to the Theory of NeuralComputation (Addison-Wesley, New York) 1991.[16] Bishop C. M., Neural Networks for Pattern Recognition (Oxford University Press, Oxford)1995.[17] Febo A., Pasini A. and Giusto M., (in preparation).[18] Swingler K., Applying Neural Networks (Academic Press, London) 1996.[19] Atija A. F., El-Shoura S. M., Shaheen S. I. and El-Sherif M. S., IEEE Trans.Neural Networks, 10 (1999) 402.

A neural-network approach to radon short-range forecasting from concentration time series

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A neural-network approach to radon short-range forecasting from concentration time series

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