Diapositiva 1

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A METHOD TO ESTIMATE DAILY MAXIMA AND MINIMA BASED ON SINGLE DAILY AIR TEMPERATURE READINGS
Michele Andrighetti, Massimiliano de Franceschi, Dino Zardi
Atmospheric Physics Group, Dept. of Civil and Environmental Engineering – University of Trento
Introduction: A problem specifically affecting series composed from measurements taken before the introduction of modern standards about observation timing and instruments (e. g. maximum and minimum thermometers) is the availability of only one
daily observation, often taken at varying hours. Even when the observer used to record at least the daily hour at which measurements were recorded, the effective diurnal timing of measurements have to be reconstructed if the adopted timing system was an
older one. Indications about the state of the weather at the time of observations, which usually were recorded as side information as well, are a very useful reference to classify the days into some weather categories. The paper proposes a method to estimate
daily temperature maxima and minima when only such single daily readings are available, taking advantage of all the available information. The method requires the availability of a representative diurnal temperature cycle (for each weather category),
determined for instance on the basis of sample of high frequency temperature measurement in the same area (of course, in more recent times). Based on linear regression, a best fit line is obtained, which provides the basis for the relationship between the
single-hour reading and daily extremes. The outcoming parameters of the best fit line provide the basis for the evaluation of maxima and minima from single daily readings. The methods provides also an estimate for the intrinsic error of the estimate.
Fig. 4. Seasonal average daily cycles for weather conditions
Fig. 1. Map of the city centre of Verona (1737). The Fig. 2. The main tower of the castle of Castelvecchio
Fig. 3. Original observations by G. Maggi (August 1768).
as indicated (FW = fair weather, PO = partly overcast, OC =
letter “M” indicates the main tower of the castle of where G. Maggi used to take measurements.
overcast). In brackets the number of days in each subset.
Castelvecchio (Fig. 2).
The test-case dataset: As a preliminary application of the method, the series of data from temperature measurements taken in Verona (Italy) from 1768 to 1774 by Giuseppe Maggi has been used.
Maggi used to be lecturer in the Military Academy of Verona in the castel of Castelvecchio (Fig. 2). In his records (Fig. 3) he used to write every day the main meteorological variables, such as air pressure, temperature, wind direction, precipitation,
water level in the Adige river and the state of the weather (see Andrighetti et al., 2007 for further details). For temperature he used the thermometer made by A. M. Lorgna for previous measurements (1765) at the same premises. He also wrote that he
used to take measurements at sunrise: this is a very important piece of information in order to infere daily temperture extrema. Indeed the hour of sunset can be easily evaluated for each day of the year through suitable algorithms (Bird and Hulstrom,
1981).
The notes about the state of the weather recorded by Maggi are extremely useful, as these allowed to include the days of the dataset in three main categories (namely “fair weather”, “partly overcast” and “overcast”) for each season, resulting in a total
of 12 subsets containing homogeneous days so as to weather and season.
Starting from recent (2003-2006) time series of air temperature taken every 1 min in Verona, suitable average daily cycles have been evaluated for each of the above subsets (Fig. 4). Comparison of each daily cycle with the corresponding average cycle
provides a useful information about deviation of that cycle from the average. In particular the differences between maximum (∆TM) and minimum (∆Tm) temperature of each day with respect to the corresponding extrema of the average cycles can be
evaluated, as well as similar differences between the temperature at a given hour between the single daily cycle and the average (Fig. 5). Suitable linear correlation between the above differences can be evalueted by suitable scatter plot and best fit lines
(Fig. 6). The resulting slope (A) and intercept (B), along with their uncertainties (∆A, ∆B) provide the coefficients for the algorithm that allows to estimate extrema starting from a single daily reading taken at a known hour (Table 1). An example of a
series of daily extrema obtained through the above metjod is shown in Fig. 7.
Table 1. Coefficients of
the least mean square
line for the conversion
of the data. A indicates
the
slope,
B
the
intercept and ∆A and
∆B their corresponding
uncertainties.
Fig. 5. A typical daily cycle of an partly overcast day in
Fig. 6. Scatter plot of temperature differences between extrema at single days
autumn (blue) compared to the corresponding average (green).
and in the average daily cycle vs. the corresponding differences at sunrise for
The relevant differences between extrema are indicated.
partly overcast summer days.
Fig. 7. Time series of temperature extrema for 1769 from Maggi’s data through the proposed method.
Acknowledgements
References
The Authors are greatly indebted with Roberto Tomasini of “MeteoVerona” for providing his
M. Andrighetti, G. Rampanelli, D. Zardi, Reconstruction and climatological analysis of the temperature series of Verona (1741 – 2006), Proceedings of the
data; with dr. Ivano Dal Prete for precious support and cooperation in discovering and
29th International Conference on Alpine Meteorology (ICAM2007) – Chambéry, France, 4-8 June 2007 – Vol. 1, pp. 245-248
interpreting Maggi’s observations; with prof. Maurizio Maugeri, Michele Brunetti, Dario
A. M. Lorgna, Della graduazione de’ Termometri a Mercurio, e della rettificazione de’ Barometri semplici: Dissertazione di A. M. Lorgna, Professore di
Camuffo and Claudio Cocheo for very fruitful discussions; with dr. Paolo Frontero for
Matematiche nel Pubblico Collegio Militare di Verona. Stamperia di Marco Moroni, Vol. IV, pag. 70. Verona 1765.
precious comments and remarks; with dr Luisa Pigatto e Rossella Miceli for kindly providing
R. E. Bird, R. L. Hulstrom, A simplified Clear Sky Model for Direct and Diffuse Insolation on Horizontal Surfaces, Solar Energy Research Institute, 1981.
access to the papers of Giuseppe Maggi at the Library of the Department of Astronomy of the
R. Geiger et al., The Climate near the ground, Rowman & littlefield publishers, inc., Oxford, United Kingdom, 2003.
University of Padova.
W. E. K. Middleton, “Meteorological Instruments”, Johns Hopkins Press, Baltimora, 1969.
Contacts
Eng. Michele Andrighetti
Eng. Massimiliano de Franceschi
Prof. Dino Zardi
E-mail: [email protected]
E-mail: [email protected]
E-mail: [email protected]