Measuring scales for daily temperature extremes, precipitation and wind velocity



The extreme values of meteorological elements and weather phenomena (extreme events) have a profound influence on human activity. It has long been accepted as part of a weather forecaster's task to predict their occurrence and severity, but without any accepted scales. Here, measuring scales of daily temperature extremes, precipitation and wind velocity have been defined and described. The scales are: standard frequency distribution for daily temperature extremes, decile method for precipitation and the Beaufort scale for wind velocity. Their units are: standard deviation, decile of frequency and unit of the Beaufort scale, respectively. The step ‘normal’ and three steps for each threshold scale of positive departure from normal are defined: above normal, well above normal and extraordinarily above normal. Also, three steps for each threshold scale of negative departure from normal are defined: below normal, well below normal and extraordinarily below normal. The scales of standard frequency distribution and the decile method can be applied to other extreme values of meteorological elements and weather phenomena if they follow these types of frequency distributions. Examples drawn from the observations of the Meteorological Observatory in Belgrade for the climate period 1961–1990 are presented. Copyright © 2012 Royal Meteorological Society

1. Introduction

Extreme values of meteorological elements and weather phenomena are nowadays becoming an extraordinary problem in human life and human activity (Jewson and Caballero, 2003; Meze-Hausken et al., 2009; Leblois and Quirion, 2011). Extreme events can have severe consequences, especially during extreme seasons (summer and winter) for different social and economic sectors because they may generate serious health problems to the population or may disturb transportation, construction and tourism activities. Also, agricultural crops and yields are very sensitive to extreme climatic events, especially those related to temperature and precipitation. In the general context of climate change, it is considered that temperature, precipitation and wind will be some of the most affected climatic parameters. The changes implied will be in frequency, intensity and persistence. For this reason, in the last decade many researchers have tried to define extreme events in many different ways (IPCC, 2007; Varfi et al., 2009; El Kenawy et al., 2011; Radinović and Ćurić, 2011; Smith and Lawson, 2012). Even if inside the meteorological community there are reasons for specific indices, the general opinion is that the more indices are used, the better and more reliable view of the changes in the extremes is presented (Perry and Hollis, 2005).

Meteorology today has progressed from a general art and science to a highly sophisticated body of knowledge and technology that may be applied to a wide range of practical activities. In order to realize the full benefit of these applications to the needs of society it is essential to provide professional meteorologists and non-meteorologists with some basic unification for measuring extremes of the meteorological events. Clearly, the time has arrived to provide a method that will allow professionals to identify meteorological thresholds which will become relevant and valuable. For example, knowledge and forecasts about weather conditions continue to be intensely interesting to people (Thornes and Stephenson, 2001). In line with this, even if the forecast is very accurate the users of weather forecasts have to know what ‘normal temperature’ or ‘extraordinary wind speed’ mean, and whether these reports are based on the historical archive for a given location. The term ‘normal’ is region-dependent and will vary from one region to another. Therefore, it is very important to know the meteorological thresholds of extreme events which are obtained using the same methodology and which can be used in weather reports and weather forecasts.

2. Methodology for defining the thresholds

The thresholds can be calculated in different ways (Smith and Lawson, 2012), but experience has shown that for weather elements whose departures from normal follow the normal distribution it is suitable to use the Gaussian curve of frequency distribution (for example, for temperature and pressure). For such weather elements the normal curve of frequency distribution may be used for classification of thresholds (Gibbs, 1987; Wilks, 1995; Changnon, 1998; Coles, 2001; Chan, 2010). The standard deviation (σ) is used in defining thresholds, as shown in Table 1. For weather elements whose departures from normal do not follow the normal distribution (precipitation amounts), a decile method may be used (Gibbs, 1987; Coles, 2001; Radinović and Ćurić, 2009). For such weather elements the seven thresholds are shown in Table 2. For wind speed thresholds the Beaufort scale can be used as shown, as in Table 3 (Radinović, 1997; Coles, 2001; WMO, 2006).

Table 1. Area under normal frequency distribution divided by standard deviation (σ)
Standard deviationPercent of frequencyTerm
< − 3σ0–0.15Extraordinarily below normal
− 3σ to < − 2σ0.16–2.30Well below normal
− 2σ to < − σ2.31–15.85Below normal
− σ to < + σ15.86–84.15Normal
+ σ to < + 2σ84.16–97.70Above normal
+ 2σ to < + 3σ97.71–99.85Well above normal
≥ + 3σ99.86–100.00Extraordinarily above normal
Table 2. Frequency distribution presented by decile method (D)
DecilePercent of frequencyTerm
10.1–10Extraordinarily below normal
210.1–20Well below normal
320.1–30Well below normal
870.1–80Above normal
980.1–90Well above normal
1090.1–100Extraordinarily above normal
Table 3. Thresholds scale for wind speed (B)
Beaufort scale (B)Type of windSpeed (m s−1)Term
0–1Calm to light air0.0–1.5Extraordinarily below normal
2–3Light breeze to gentle breeze1.6–5.4Well below normal
4–5Moderate breeze to fresh breeze5.5–10.7Below normal
6–7Strong breeze to moderate gale10.8–17.1Normal
8–9Fresh gale to strong gale17.2–24.4Above normal
10–11Storm to violent storm24.5–32.6Well above normal
≥ 12Hurricane wind≥ 32.7Extraordinarily above normal

3. Thresholds of extreme weather elements for Belgrade

The air temperature is considered as one of the most important climate and weather elements. It is, therefore, important to know the limits within which the air temperature should be considered as normal or how much it departs from normal. That is particularly important in situations when the air temperature becomes an extreme weather phenomenon. It represents a local climate feature and will vary from one region to another.

3.1. Thresholds of minimum daily air temperature

As a measure for cold weather, the negative departure of the minimum daily air temperature from the monthly normal value is representative. Conversely, a positive departure of the maximum daily air temperature from the monthly normal value is also representative (Toros, 2011; Smith and Lawson, 2012).

The thresholds of minimum air temperature are derived from the frequency distribution of the minimum daily temperature in 1 month during the normal climate period 1961–1990 for the Belgrade Meteorological Observatory (44°48′N, 20°28′E, 132 m a. m. s. l.). These are given in Table 4. Effectively, the values of thresholds presented are only valid for Belgrade, but the methodology used is suggested to be accepted generally.

Table 4. Thresholds of minimum daily air temperature in Belgrade (°C) for the period from 1961 to 1990
 To− 7.2− 4.4−− 0.3− 4.6
Below normalFrom− 7.3− 4.5−− 0.4− 4.7
 To− 13.3− 10.2−− 5.0− 8.2
Well below normalFrom− 13.4− 10.3−− 5.1− 8.3
 To− 20.9− 15.3− 12.6−− 2.5− 7.9− 15.0
Extraordinarily below normal≤− 21.0≤− 15.4≤− 12.7≤− 1.9≤1.6≤4.6≤9.3≤6.7≤0.4≤− 2.6≤− 8.0≤− 15.1

A great part of the human population is suffering from weather changes (Kumkel et al., 1999; Maheras et al., 2006). This has an influence on the human body, psyche and activity. For that reason, weather forecasts and weather reports are frequently accompanied by medical advice (Schaefer, 1990; WMO, 2006). Therefore, it is necessary to define the thresholds of the inter-diurnal changes of the main meteorological elements. The thresholds of the inter-diurnal minimum temperature decrease per month are presented in Table 5.

Table 5. Thresholds of inter-diurnal minimum temperature decrease in Belgrade (°C) for the period from 1961 to 1990
 To− 2.5− 2.5− 2.2− 2.4− 2.2− 1.9− 2.0− 2.3− 2.4− 2.6− 2.6− 2.4
Below normalFrom− 2.6− 2.6− 2.3− 2.5− 2.3− 2.0− 2.1− 2.4− 2.5− 2.7− 2.7− 2.5
 To− 5.5− 5.6− 5.5− 6.0− 5.0− 4.9− 4.5− 4.9− 4.9− 5.7− 5.4− 5.4
Well below normalFrom− 5.6− 5.7− 5.6− 6.1− 5.1− 5.0− 4.6− 5.0− 5.0− 5.8− 5.5− 55
 To− 10.5− 13.2− 8.7− 11.9− 11.2− 6.4− 8.9− 8.5− 7.6− 8.7− 11.1− 9.3
Extraordinarily below normal≤− 10.6≤− 13.3≤− 8.8≤− 12.0≤− 11.3≤− 6.5≤− 9.0≤− 8.6≤− 7.7≤− 8.8≤− 11.2≤− 9.4

From Table 5 it can be seen that unexpected uniform values of inter-diurnal minimum temperature change from month to month in a year. The normal inter-diurnal changes of minimum daily temperature through the year occurred in the limits between − 2.6 and 3.5 °C. Below normal temperatures appear between − 6.0 in April and − 2.0 °C in June, while extraordinarily below normal temperatures appear between ≤− 6.5 °C in June and ≤− 13.3 °C in February. The last threshold is under the influence of the sudden temperature drop during the winter surge of cold air (Milosavljević, 1987).

3.2. Thresholds of maximum daily air temperature

The thresholds of maximum daily air temperature in Belgrade are presented in Table 6. From this table it can be seen that the differences between thresholds are smaller in the summer than in the winter months. The maximum daily temperature is considered to be in normal limits on average in January from − 2.0 to 9.4 °C and in July from 23.1 to 31.6 °C. The daily maximum temperature above normal is considered to be from 9.5 to 14.5 °C in January and from 31.7 to 35.3 °C in July. The threshold of extraordinarily above normal of daily maximum air temperature varies between 20.3 °C in January and 40.2 °C in July. These extremes in the summer months are mainly related to heat waves which affect human health, cause damage to the urban infrastructure, or disrupt services due to the excessive consumption of energy for cooling (Kalkstein, 1991; Beniston and Diaz, 2004; Radinović and Ćurić, 2011).

Table 6. Thresholds of maximum daily temperature in Belgrade (°C) for the period from 1961 to 1990
NormalFrom−− 0.1
Above normalFrom9.513.017.722.927.330.031.731.928.823.917.711.3
Well above normalFrom14.619.524.427.330.633.235.435.432.527.822.916.4
Extraordinarily above normal≥ 20.3≥ 23.1≥ 28.9≥ 29.8≥ 34.1≥ 35.7≥ 40.2≥ 38.7≥ 34.5≥ 29.3≥ 28.4≥ 22.6

The thresholds of the inter-diurnal maximum temperature changes per month in Belgrade are shown in Table 7. From this table it can be seen that the thresholds for normal changes of daily maximum temperature are from − 3.8 °C in November to 4.1 °C in March. The thresholds for inter-diurnal maximum temperature changes above normal are between 3.0 °C in October to 8.0 °C in November. The inter-diurnal rise of maximum temperature over 9.7 °C in June and 13.7 °C in July is considered to be extraordinarily above normal.

Table 7. Thresholds of inter-diurnal maximum temperature increase in Belgrade (°C) for the period from 1961 to 1990
NormalFrom− 3.6− 2.9− 3.5− 3.7− 3.3− 3.3− 3.4− 3.4− 3.6− 3.4− 3.8− 3.2
Above normalFrom3.
Well above normalFrom7.
Extraordinarily above normal≥ 12.6≥ 10.1≥ 10.4≥ 10.4≥ 13.6≥ 9.7≥ 13.7≥ 10.1≥ 11.7≥ 10.4≥ 11.8≥ 12.1

3.3. Thresholds of extreme daily precipitation amount

On many rainy days the amount of rainfall is relatively small. However, even small amounts of rain may create serious problems in many activities, for example during construction. Light rain may make roofing impossible and surveying difficult, whereas heavy rainfall or large rainfall amounts may bring such operations to an extended halt. Many modern roofing materials must be installed during dry periods (Haggard and Mc Cown, 1985). Therefore, extremely small as well as extremely high amounts of precipitation are of interest for statistics (Gibbs, 1987; Donald and Davis, 1992; Coles, 2001; Radinović and Ćurić, 2009; Xuanyi and Xuefeng, 2010). The thresholds for all daily precipitation amounts can be found at the base of Table 2.

According to the daily amounts of precipitation in Belgrade, and using the decile method of frequency distribution, the thresholds shown in Table 8 were obtained. From Table 8 it can be seen that daily amounts between 8.1 and 21.0 mm are considered normal. Amounts between 21.1 and 25.6 mm per day are above normal, amounts 25.7–33.6 are well above normal and daily amounts ≥ 33.7 mm are considered to be extraordinarily above normal. The last threshold corresponds to reports of local flooding (Milosavljević, 1987).

Table 8. Thresholds of daily precipitation amounts in Belgrade (mm) for the period from 1961 to 1990
ScaleDecilesAmounts (mm)
Extraordinarily below normal10.1–1.7
Well below normal21.8–4.2
Below normal34.3–8.0
Above normal821.1–25.6
Well above normal925.7–33.6
Extraordinarily above normal10≥ 33.7

3.4. Wind as an extreme weather phenomenon

Insurance companies worldwide have established the standard that wind speed of Beaufort Force 8 (≥17.2 m s−1) or greater is considered to be destructive. The same is taken to be the threshold for wind speed as an extreme weather phenomenon (Changnon et al., 1997; Smith, 1999; Zielinski, 2002; WMO, 2006; Chan, 2010). Table 9 shows the frequencies of wind speed in Belgrade taking into account Table 3 and data for wind speed. From Table 9 it can be seen that the frequency of extreme wind speed (above normal and well above normal) has a very pronounced annual course. In winter they occur on average four times more frequently than in the summer. Below normal, well below normal and extraordinarily below normal wind speeds are rather uniformly distributed throughout the year. Hurricane force winds (extraordinarily above normal) should be considered as catastrophic winds. These do not appear in Belgrade during the climatological reference period.

Table 9. Number of days with wind speed between defined thresholds observed in Belgrade for the period from 1961 to 1990
ScaleType of windBeaufort scalem s–1Months
Extraordinarily below normalCalm to light air0–10.0–1.5191176173175184179191189176177172173
Well below normalLight breeze to gentle breeze2–31.6–5.4198194181188209238242240237229221226
Below normalModerate breeze to fresh breeze4–55.5–10.7241218254246251231241239235227239215
NormalStrong breeze to moderate gale6–710.8–17.1235184229233254227239242236214202223
Above normalFresh gale to strong gale8–917.2–24.4716691533124131716776182
Well above normalStorm to violent storm10–1124.5–32.64935113306511
Extraordinarily above normalHurricane wind≥ 12≥ 32.7000000000000

4. Conclusions

The basic idea exposed in this paper is to show the measuring scales for principal meteorological elements (extreme temperatures, precipitation and high winds). They represent local climate features but they are comparable with the same climate features in different regions. Effectively the values of thresholds presented in this paper are only valid for Belgrade, but it is suggested that the methodology used be generally accepted.

Meteorological information may be imprecise, incomplete and ambiguous, and will be of no use in disaster management without accurate measurement data. The unification of threshold scales and their units for extreme weather phenomena will contribute to a better understanding and quantification of these types of phenomena in different areas in the world. Also, the use of these scales in practice will improve the application of the weather reports and weather forecasts in the process of designing and implementing procedures for reducing the risk associated with the occurrence of a disaster.


The authors would like to thank the editor and the reviewers for their valuable comments. Appreciation is extended to D. Bulatović for his assistance in the preparation of data. This work was partially supported by the Ministry of Science of Serbia. Hydrometeorological Service of the Republic of Serbia provided the necessary data for this study.