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Cross-correlations between weather variables in Australia
ARTICLE IN PRESS
Building and Environment 42 (2007) 1054–1070 www.elsevier.com/locate/buildenv
Cross-correlations between weather variables in Australia L. Guana, J. Yanga,, J.M. Bellb a
School of Urban Development, Queensland University of Technology, 2 George Street, GPO Box 2434, Brisbane, QLD 4001, Australia Centre for Built Environment and Engineering Research, Queensland University of Technology, 2 George Street, GPO Box 2434, Brisbane, QLD 4001, Australia
b
Received 1 June 2005; received in revised form 22 August 2005; accepted 19 January 2006
Abstract The information on climate variations is essential for the research of many subjects, such as the performance of buildings and agricultural production. However, recorded meteorological data are often incomplete. There may be a limited number of locations recorded, while the number of recorded climatic variables and the time intervals can also be inadequate. Therefore, the hourly data of key weather parameters as required by many building simulation programmes are typically not readily available. To overcome this gap in measured information, several empirical methods and weather data generators have been developed. They generally employ statistical analysis techniques to model the variations of individual climatic variables, while the possible interactions between different weather parameters are largely ignored. Based on a statistical analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper reports on the finding of strong correlations between several specific weather variables. It is found that there are strong linear correlations between the hourly variations of global solar irradiation (GSI) and dry bulb temperature (DBT), and between the hourly variations of DBT and relative humidity (RH). With an increase in GSI, DBT would generally increase, while the RH tends to decrease. However, no such a clear correlation can be found between the DBT and atmospheric pressure (P), and between the DBT and wind speed. These findings will be useful for the research and practice in building performance simulation. r 2006 Elsevier Ltd. All rights reserved. Keywords: Climatic variables; Cross-correlation; Building simulation; Australia
1. Introduction One of the main functions of buildings is that they act as a climatic modifier, separating the indoor built environment from the external climate. Nevertheless, the climate of a particular location can still have a significant influence on the design of architectural features such as shapes and forms of the buildings, and dictate the types of environmental controls required [1]. The quality of climatic data and information will therefore have a significant impact on the effectiveness of building design strategies and the accuracy of design load and energy calculations [2]. In order to study the impacts of climate variations on the built environment, building simulation programmes are often employed. These computer-based programmes norCorresponding author. Tel.: +617 3864 1028; fax: +617 3864 1170.
E-mail address: [email protected] (J. Yang). 0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.01.010
mally require the inputs of series of hourly weather characteristics, including solar radiation, dry bulb temperature (DBT), air humidity, atmospheric pressure and wind speed and direction [3], to simulate building thermal behaviour in order to assess and evaluate their thermal comfort and energy performance. However, in most cases, the recorded meteorological data are incomplete and unsuitable for the purpose of building simulation. First, the recorded data may be only available in a limited number of representative locations. Then, the number of recorded climatic variables can also vary from one meteorological station to another; some stations may only record temperature while the others could record all the key weather parameters. Moreover, the climatic data are also often recorded in either 3 hourly intervals, or even only twice daily (9 a.m. and 3 p.m.) [4]. In order to overcome this gap in measured information, several empirical methods and weather data generators
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have been developed [5–13]. These generators often use statistical analysis techniques to model the individual climatic variables, and generate further details of weather parameters through a random choice based on their statistical distribution (daily and hourly) and autocorrelation [12]. The possible interaction between different weather parameters has often not been considered. Despite the fact that the weather conditions may be constantly changing, it is also widely believed that there could exist some ‘‘hidden’’ connection between different weather parameters [13,14]. Because the source of heat energy supplied to the Earth’s surface and the atmosphere comes predominantly from the Sun, the variation in solar radiations could have a major impact on the weather conditions on the Earth, and in particular, leading to a fluctuation in air temperatures. The air temperature variation will then bring about a change in water evaporation and air saturation, leading to the changed air humidity. Furthermore, the air temperature differences between different locations will also cause air pressure differences, which in turn would produce air movement, thereby wind (direction and speed). Thus, it could be reasonably expected that all weather variables on the Earth will more or less be affected by the solar radiation (Fig. 1). The above theory of correlations between different weather parameters has now been used in a number of studies to estimate unknown climatic variables. For example, through the pre-assumed correlations, global solar irradiation (GSI) had been estimated in a number of studies by the known climatic parameters of bright sunshine duration [15–17], cloud fraction [18,19], air temperature range [20,21], precipitation status [22], both
Water evaporations & Air saturation
Changes
Air Humidity
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temperature and rainfall [23,24] and both sunshine duration and cloud [25,26]. Because these works generally adopt the top-down approach using the pre-assumed formulae, the real cross-correlation between different weather variables (or bottom-up method) has not been assessed. Based on an analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper seeks to assess and confirm the cross-correlation between a number of different weather variables. Contrary to previous studies, a bottom-up approach is instead used in this research. Since air temperature is one of the most important meteorological parameters and has been recorded most commonly in a meteorological station, its relationship with other key meteorological parameters such as solar radiation, air humidity, atmospheric pressure and wind speed will be examined. The concept and theory/ principle of these key weather variables will also be discussed. It is expected that the results of this study would be useful for not only supplementing the ‘‘missing’’ weather data records but also the validation of weather data generators. 2. Weather database and study approach In order to explore the cross-correlation between different weather variables in Australia, hourly variations of key weather variables will need to be calculated and analysed. Using the observed weather database, the Pearson product moment correlation (called Pearson’s correlation for short) will be used to measure the degree to which the variables are related. The regression analysis will then be employed to find their trendlines for each case. These trendlines can not only graphically display trends of the studied data series but also be used to analyse the accuracy of the prediction.
Controls Solar Radiation
Causes
2.1. Weather database
Air Temperature variations Controls Air Pressure Difference
Drives
Wind Speed and Direction
Fig. 1. Relationship between different weather variables.
In this study, historic climatic data for all capital cities in Australia (Table 1), as supplied by ACADS-BSG, are used to establish the relationship between different weather variables. The ACADS-BSG is a consulting company based in Melbourne, Australia, which supplies weather
Table 1 Information of studied sites in Australia W.M.O index no.
Locality
Latitude
Longitude
Elevation (m)
Years between
Test reference year
94675 94578 94925 94121 94970 94868 94608 94768
Adelaide RO Brisbane AMO Canberra City Darwin RO Hobart RO Melbourne RO Perth RO Sydney RO
34.9 27.4 35.3 12.5 42.9 37.8 32 33.9
138.6 153.1 149.1 130.8 147.3 145 115.9 151.2
47 4 564 27 55 112 19 42
1978–1987 1978–1988 1978–1989 1969–1973 1968–1987 1967–1987 1972–1987 1978–1987
1987 1986 1978 1973 1984 1971 1982 1981
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Although the rule used to interpret correlations can be arbitrary and the cut-off values for different situations may be different, generally, it is believed that a Pearson’s correlation between 0.5 and 0.5 indicates a weak, little or no association between two variables. A Pearson’s correlation between 1 and 0.5 would indicate a strong negative association, while a correlation between 0.5 and 1 would indicate a strong positive association.
data for building simulation research and practice in Australia, New Zealand, Hong Kong and Singapore. The test reference year (TRY) in Table 1 is the year selected to represent the average weather patterns that would typically be found in a multi-year dataset for a particular location [27]. It is a whole natural calendar year data derived from observation at a specific location by the national weather service or meteorological office. This concept is in parallel to another related concept called the Typical Meteorological Year which instead consists of linked monthly segments of weather data selected from the (different-year) historical meteorological records [28]. The weather variables contained in the above Australian climatic database have included the detailed records of the DBT, humidity ratio, atmospheric pressure, wind speed and direction, cloud cover, GSI on a horizontal plane, diffuse solar irradiance on a horizontal plane and direct solar irradiance on a plane normal to the beam. In this study, however, only five key climatic variables will be examined which include GSI on a horizontal plane, DBT, humidity ratio, atmospheric pressure and wind speed.
2.3. Regression analysis Regression analysis is a method often used for the formulation of the trendline for a database. It is a form of statistical analysis used to relate variables, assess their relationships and make predictions based on known information. Regression analysis seeks to establish the relationship between different variables so that a given variable can be predicted from one or more other variables. By using regression analysis, a trendline may be extended in a chart beyond the actual available data to predict future values [30]. Both types of Linear and Polynomial (or curvilinear) trendlines are employed in this study. Such trendlines are created by using linear or polynomial equations to calculate the least-squares fit through points. The R2 value, which is a number from 0 to 1.0 and is also known as the coefficient of determination, is then calculated for each case to show the closeness of the estimated values from the trendline to the actual data. A trendline is most reliable when its R2 value is at or close to one. The formulas used for linear trendline, polynomial trendline and the R2 value are listed in Table 3. Because the DBT is one of the most important and commonly recorded meteorological parameters, and has relations to all other key climatic variables, such as solar
2.2. Pearson product moment correlation The correlation between two variables reflects the degree to which the variables are related [29]. The most common measure of correlation is the Pearson’s correlation which can take on the values from 1.0 to 1.0, where 1.0 is a perfect negative (inverse) correlation, 0.0 is no correlation and 1.0 is a perfect positive correlation. The closer the correlation is to 71, the closer to a perfect linear relationship. The formula for Pearson’s correlation takes on many forms. A commonly used formula is shown in Table 2 [29]. Table 2 Formulas for the calculation of Pearson’s correlation Equation Pearson’s correlation (r)
Notes
P P P XY X Y =N r ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P 2 P 2 P 2 P 2 X
X
N
Y
Y
N is the total number of data series
N
Table 3 Formulas for the linear trendline, polynomial trendline and the R2 value Equation
Notes
Linear trendline
Y ¼ mX+b
m is the slope and b is the intercept
Polynomial trendline R2 value
Y ¼ b+C1X+C2X2+C3X3+y+C6X6 P 2 ðY Y Þ R2 ¼ 1 P iP i 2 .
b and C1yC6 are constants i is the time series and n the total number of data series
Y 2i
Yi
n
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radiation, air humidity, atmospheric pressure and wind, the hourly corresponding variations between DBT and other four variables will be first used to calculate the Pearson’s correlation in this paper. Then, the hourly variations of DBT will be plotted against the hourly variations of other four variables to find their trendlines for each case. Although it may be seen from the graphical display of studied data series that a linear correlation could exist for the studied climatic parameters, the polynomial correlation has to be still tested in this paper to confirm the uniformity of data distribution or the visual judgment of the graphics. As shown below, there is generally little difference between the accuracy of these two fitting methods. 3. Results and discussion 3.1. Solar radiation Solar radiation, which is defined as the total electromagnetic energy emitted by the Sun, drives almost every known physical and biological cycle in the Earth system [31]. Solar radiation reaches the Earth’s surface either by being directly transmitted through the atmosphere (direct solar radiation), or by being scattered or reflected to the Earth’s surface (diffuse sky radiation) [32]. It is estimated that about 50% of solar (or shortwave) radiation is reflected back into space, while the remaining shortwave radiation at the top of the atmosphere is absorbed by the Earth’s surface and re-radiated as thermal infrared (or long-wave) radiation. Insolation (an acronym for INcoming SOLar radiATION) is the rate at which solar radiation is received by a unit horizontal surface area at any point on or above the surface of Earth (direct solar radiation). The insolation received at the surface of the Earth depends upon the solar constant (the rate at which solar radiation is received outside the Earth’s atmosphere), the distance from the Sun, inclination of the Sun’s rays, and the amount of insolation depleted while passing through the atmosphere [14]. On a clear day, the direct normal irradiation or solar intensity IDN can be expressed as [33] I DN ¼ A=½exp ðB= sin bÞ,
(1)
where A is the apparent solar constant irradiation at air mass ¼ 0 (W/m2), B the atmospheric extinction coefficient (dimensionless) and b the solar altitude angle (angle above the horizon). The direct solar radiation ID is the product of the direct normal irradiation IDN and the cosine of the angle of the incidence y: I D ¼ I DN cos y,
(2)
where y is the angle between the incoming solar rays and a line normal (perpendicular) to the surface. It is noted that the values of A and B in Eq. (1) vary throughout the year because of the changing Earth–Sun
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distance and because of seasonal changes in the dust and water vapour content of the atmosphere. The diffuse radiation falling on any surface consists of radiation from the sky and part of the reflected solar radiation from adjacent surfaces, particularly the ground lying south (or north in the North Hemisphere) of the surface. The radiation does not come uniformly from all parts of the sky. A simplified general relation for the diffuse solar radiation Ids that falls on any surface from a clear sky is approximately given as [33] I ds ¼ CI DN F ss ,
(3)
where C is the diffuse radiation factor (dimensionless) and Fss is the angle factor between the surface and the sky, i.e. the fraction of shortwave radiation emitted by the sky that reaches the tilted surface (dimensionless). For vertical surfaces, F ss ¼ 0:5, while for horizontal surfaces, F ss ¼ 1:0. For other surfaces, Fss ¼ (1.0+cos S)/2, where S is the tilt angle measured upward from the horizontal plane. From the above discussion, it can be seen that for a specific location, both direct and diffuse solar radiation are determined by the Sun’s position (or incident solar angle), Sun–Earth distance and the sky condition (i.e. cloud cover). The GSI, which is the sum of direct solar radiation and diffuse solar (sky) radiation, therefore varies throughout a year with monthly maximum solar radiation reaching the highest value in summer and falls to the lowest value in winter. From Fig. 2, it can be seen that the variations of solar radiation during a year are different for different locations, with the greatest being Melbourne and the smallest being Darwin. It is also noted that the difference of solar radiation between different locations also varies during the year, the difference being largest in winter and smallest in summer. During a day, the solar radiation heat gradually increases to reach its maximum at midday and then gradually decreases to zero after sunset, following the pattern of cosine bell. This pattern may be demonstrated and illustrated through the daily solar radiation on the day of 16th June of TRY for each of the capital cities in Australia (Fig. 3). It can be seen that different cities have different scales of variations in solar radiation, and reach different levels of daily peak solar radiation. It is expected that the difference of peak solar radiation between different cities would be greater in winter time and smaller in summer time. 3.2. Air temperature Air temperature is a measure of the heat content of air. Three different temperature measurements, called as DBT (the measure of molecular motion), wet bulb temperature (reflection of the cooling effect of evaporating water) and dew point temperature (the temperature below which moisture will condense out of air) are used in the psychrometric chart to represent different types of air
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Monthly maximum global solar irradiation (W/m²)
1200
1000
Adelaide
800
Brisbane Canberra Darwin 600
Hobart Melbourne Perth Sydney
400
200
0 0
2
4
6
8
10
12
14
Month
Fig. 2. Monthly maximum solar radiation of TRY for the capital cities in Australia. 700 Adelaide Brisbane 600
Canberra
Global Solar Irradiation (W/m²)
Darwin Hobart 500
Melbourne Perth Sydney
400
300
200
100
0 0
5
10
15
20
Hours
Fig. 3. Daily solar radiation on the day of 16th June of TRY for Australian cities.
properties. In this study, unless specifically noted, the air temperature used is referred to DBT. Air temperature indicates the degree of hotness or coldness. It may therefore be considered as a measure of heat intensity. The air temperature is undoubtedly the most important climatic parameter, with its variation being primarily controlled by incoming solar energy and outgoing earth energy, as illustrated in Fig. 4 [34]. Fig. 5 shows a typical example of diurnal cycle of incoming GSI and air temperature in Brisbane on 16th June 1986. It can be seen that as the solar irradiation increases, the air temperature also increases, although there is a time lag, which is caused
by the effect of earth thermal storage (thermal mass). This can lead to a situation where the solar radiation decreases while the air temperature still increases, or solar radiation starts increasing but air temperature is still decreasing. Fig. 6 shows the hourly variations of DBT as plotted against the hourly variations of GSI on a horizontal plane for TRY of Australian capital cities. Because of the natural diurnal pattern of solar radiation as shown in Fig. 3, only these hours with solar radiation (i.e. the time between sunrise and sunset) are considered. It can be seen that there is a good correlation between hourly variations of GSI on a horizontal plane and DBT. The Pearson’s correlations, as
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tabulated in Table 4, are larger than 0.65 with the exception of Melbourne, which indicates good association between DBT and GSI. The average Pearson’s correlation for all eight capital cities is 0.69. The equations of the trendlines and their R2 value for different locations are tabulated in Table 5. Both types of linear and polynomial (or curvilinear) trendlines are examined. By comparing their R2 values, it can be seen that the curvilinear trendlines represent only a slightly better fit for the data series than that of the linear trendline, and the overall difference of R2 values between the linear and curvilinear trendlines is very small. Therefore, the linear correlation as judged from the graphical visual observation is correct, and in the following discussion, only the linear trendline will be used to represent the general trends of corresponding change between DBT and GSI. Fig. 7 shows the linear trendlines for TRY of each of the capital cities in Australia. It can be seen that these trendlines have different slopes and intercepts. This may
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be due to the effect of local geological factors. It also indicates that the linear correlation between GSI and DBT is locally dependent. The sensitivity of DBT response to the change of GSI, from strong to weak, are Canberra, Adelaide, Brisbane, Hobart, Perth, Sydney, Darwin and Melbourne. In order to test the consistency of the found correlation to a given location, the linear trendlines for each individual year of the 10 years between 1978 and 1987 of Brisbane and Sydney, Australia, are illustrated in Fig. 8. It can be seen that the correlation between DBT and GSI are remarkably consistent for a given location. The above discussion gives evidence to the fact that there is a clear correlation between DBT and GSI, which supports the postulate that the variation of air temperature is primarily controlled by the variation of solar energy. However, because these correlations are dependent on localities, the potential of their applications may somehow be limited. Despite this condition, for a specific location, where for example there are missing solar data for 1 or 2 years, the found correlation can still be used to supplement the available data. According to the comparison of recorded temperature between different years, it is possible to make necessary adjustment to the data recorded in 1 year for use in the missing year. 3.3. Atmospheric pressure
Fig. 4. March of incoming solar radiation and outgoing earth radiation for a day at about the time of an equinox.
Atmospheric pressure is the force per unit area exerted by the atmosphere in any part of the atmospheric envelope. Although the pressure varies on a horizontal plane from day to day, the greatest pressure variations are with changes in altitude (Fig. 9) [35]. Because air pressure at any given altitude within the atmosphere is determined by the weight of the atmosphere pressing down from above, the
30
700 16th June 1986, Brisbane
Incoming Global Solar Irradiation Daily Temperature
600
28
500
24 22
400
20 300
18 16
200
14 100 12 0
10 0
5
10
15
20
Hours
Fig. 5. Diurnal cycle of global solar radiation and air temperature on 16th June 1986, Brisbane.
Air temperature (°C)
Global Solar irradiation (W/m²)
26
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Fig. 6. Hourly corresponding variations between DBT and GSI.
pressure decreases with altitude gains. Atmospheric pressures are greatest at lower elevations because the total weight of the atmosphere is greatest at these points. The barometric pressure could influence the calculation of wet bulb temperatures and relative humidity (RH) [10].
The barometric equation, which expresses the above discussion, is dP ¼ rg, dZ
(4)
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Table 4 Pearson’s correlation between DBT and GSI Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.730 0.000 4347
0.809 0.000 4360
0.713 0.000 4346
0.691 0.000 4367
0.667 0.000 4361
0.519 0.000 4553
0.721 0.000 4347
0.687 0.000 4344
Table 5 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Linear: y ¼ 0:007x þ 0:3992 Polynomial: y ¼ 3E 07x2 þ 0:007x þ 0:3948 Linear: y ¼ 0:0066x þ 0:4279 Polynomial: y ¼ 1E 06x2 þ 0:0066x þ 0:4518 Linear: y ¼ 0:0077x þ 0:5681 Polynomial: y ¼ 3E 06x2 þ 0:0077x þ 0:6 Linear: y ¼ 0:0041x þ 0:2781 Polynomial: y ¼ 3E 06x2 þ 0:0041x þ 0:33 Linear: y ¼ 0:0062x þ 0:2912 Polynomial: y ¼ 5E 06x2 þ 0:0062x þ 0:3434 Linear: y ¼ 0:0035x þ 0:3738 Polynomial: y ¼ 9E 07x2 þ 0:0035x þ 0:3577 Linear: y ¼ 0:0058x þ 0:4766 Polynomial: y ¼ 2E 06x2 þ 0:0058x þ 0:5044 Linear: y ¼ 0:0049x þ 0:3273 Polynomial: y ¼ 3E 06x2 þ 0:0049x þ 0:3639
0.5331 0.5331 0.6553 0.6557 0.5077 0.5085 0.4774 0.4804 0.4456 0.4494 0.2693 0.27 0.5204 0.521 0.4719 0.4737
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
where P is the atmospheric pressure (Pa), Z the altitude (m), r the air density (kg/m3) and g the gravitational acceleration (m/s2). From Eq. (4), it can be seen that there will be a change of pressure whenever either the mass (density) of the atmosphere or the accelerations of the molecules within the atmosphere are changed. Although altitude exerts the dominant influence, it is noted that the air temperature and moisture level can also alter pressure at any given altitude, especially near Earth’s surface where heat and humidity are most abundant [14]. For a certain amount of air mass at a given altitude, the relationship between pressure and temperature can be expressed through the ideal gas law P ¼ rRT,
Fig. 10 illustrates the hourly variation of atmospheric pressure as plotted against hourly variation of DBT for TRY of all Australian capital cities. It can be seen that when the temperature increases, the pressure actually decreases, which may be in contrast to the first glance of Eq. (5). However, in a free atmosphere, a temperature increase frequently leads to the expansion of the air, resulting in a decrease in the air density [14]. Moreover, a temperature increase allows an increase in moisture content, which would also decrease air density (density of vapour is lower than that of dry air). These two factors combined can therefore often result in a decrease in air density to the extent which outweighs the effect of temperature increase, leading to a decreased pressure, as shown in Fig. 10. The Pearson’s correlations between DBT and atmospheric pressure are tabulated in Table 6. It can be seen that the values vary between 0.26 and 0.13, which indicates weak or little negative association between DBT and atmospheric pressure. The average Pearson’s correlation for all eight capital cities is 0.195. The equations of the trendline and their R2 values for Fig. 10 are also listed in Table 7. Correspondingly, it can also be seen that all these trendlines have very low R2 values (less than 0.07), which also indicates a low reliability of estimated values. In the absence of clear correlation between hourly corresponding variations of atmospheric pressure and air temperature, it is suggested that for a given location, the set of observed weather data may have to be used for a missing year. It may also be noted that from the analysis of actual record of hourly pressure and DBT for TRY of all the capital cities in Australia, the change in pressure is fairly small (o6 kPa oro6%) with a wide range of variation in temperature (16–42.3 1C). 3.4. Air humidity
(5)
where P is the absolute pressure (kPa), r the air density (kg/m3), R the universal gas constant 8.314 (kJ/kg K) and T the absolute temperature, K ¼ 1C+273.15. It can be seen from Eq. (5) that if the left side of the equation (pressure) changes, a corresponding change must occur on the right side (either in the density or temperature) to make the equation equal again. With the change of temperature, air density would also be changed. Therefore, the final change of pressure due to changing temperatures is dependent on the product of new r and T.
Atmospheric air contains many gaseous components, such as dry air, as well as water vapour and miscellaneous contaminants, including smoke, pollen and gaseous pollutants. Although the quantity of water vapour in a saturated volume of atmosphere is independent of the air pressure, it is significantly influenced by the air temperature. At a higher temperature, more vapour will be injected into a given volume before the saturated state changes to dew or fog forms. On the other hand, cooling a saturated volume of air may force some of the vapour to condense out as the quantity of vapour in the volume diminishes [14].
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3.0
Hourly variation in DBT (°C)
2.0
1.0
0.0 -300
-200
-100
0
100
200
300 Adelaide Brisbane
-1.0
Canberra Darwin Hobart Melbourne
-2.0
Perth Sydney
-3.0 Hourly variation in GSI (W/m²)
Fig. 7. Linear trendlines between hourly variations of DBT and GSI for TRY of Australian capital cities.
Sydney
3.0
3.0
2.0
2.0
1.0
0.0 - 300
-200
-100
0
100
-1.0
-2.0
-3.0
200
Y87 300 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
Hourly variation in GSI (W/m²)
Hourly variation in DBT (°C)
Hourly variation in DBT (°C)
Brisbane
1.0
0.0 - 300
-200
-100
0
100
-1.0
-2.0
-3.0
200
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
300
Hourly variation in GSI (W/m²)
Fig. 8. Linear trendlines between hourly variations of DBT and GSI for 10 years historic weather data in Brisbane and Sydney, Australia.
same temperature and pressure: xw pw ¼ , f¼ xws t;p pws t;p
Fig. 9. Vertical pressure profile.
To show the degree of saturation or determine how close the air is to the saturation point, the concept of RH f is introduced, which is defined as the ratio of the mole fraction of water vapour xw in a given moist air sample to the mole fraction xws in an air sample, saturated at the
(6)
where pw is the partial pressure of water vapour and pws the saturation pressure of water vapour in the absence of air at the same given temperature, which is only a function of temperature and may differ slightly from the vapour pressure of water in saturated moist air. Fig. 11 shows the hourly variation in RH as plotted against the hourly variation in DBT for TRY weather data of all Australian capital cities. It can be seen that there is a good correlation between RH and DBT. The Pearson’s correlations, as tabulated in Table 8, are between 0.72 and 0.85, which indicates a very strong association between DBT and RH. The average Pearson’s correlation for all eight capital cities is 0.793. From Fig. 11, it can also be seen that with increasing DBT, RH is generally decreasing. This agrees with Lutgens
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Fig. 10. Hourly corresponding variations between DBT and atmospheric pressure.
and Tarbuck’s finding [34], which showed that there is a corresponding daily variation for temperature and RH (Fig. 12). This may be due to a stronger influence of
temperature on the saturation pressure of water vapour than that on the partial pressure of water vapour (due to the increased evaporation). However, it is also noted that
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Table 6 Pearson’s correlation between DBT and atmospheric pressure Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
–0.158 0.000 8759
0.131 0.000 8759
0.253 0.000 8759
0.184 0.000 8759
0.232 0.000 8783
0.228 0.000 8759
0.202 0.000 8759
0.170 0.000 8759
Table 7 Equation of the trendline and its R2 value for P and DBT in Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Polynomial: y ¼ 5E 06x2 0:0028x 0:0166 Linear: y ¼ 0:0028x þ 0:0003 Polynomial: y ¼ 8E 06x2 0:002x 0:0275 Linear: y ¼ 0:002x 0:0001 Polynomial: y ¼ 7E 06x2 0:0052x 0:0242 Linear: y ¼ 0:0052x 0:0004 Polynomial: y ¼ 2E 06x2 0:002x 0:0071 Linear: y ¼ 0:002x 0:0002 Polynomial: y ¼ 4E 06x2 0:0028x 0:0184 Linear: y ¼ 0:0028x 0:001 Polynomial: y ¼ 3E 06x2 0:0032x 0:0122 Linear: y ¼ 0:0032x þ 0:0002 Polynomial: y ¼ 9E 06x2 0:0036x 0:0269 Linear: y ¼ 0:0036x þ 0:0001 Polynomial: y ¼ 5E 07x2 0:0019x þ 0:002 Linear: y ¼ 0:0019x 0:0001
0.0259 0.025 0.0187 0.0171 0.0658 0.0641 0.0341 0.0339 0.0551 0.0536 0.0523 0.0518 0.0432 0.0407 0.0288 0.0288
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
the change of precipitation status (e.g. precipitation starting or stopping) could change the above relationship, as precipitation is also able to change the moisture content of the environmental air. In such a situation, with the DBT increasing, the RH may instead be still increasing, and vice versa. Moreover, because at different times the moist air may have different absolute humidity content, with the same temperature variation, the corresponding change in RH could be different, which leads to a number of points in Fig. 11 being dispersed from the trendline. The equations of the trendlines and their R2 value for different locations are tabulated in Table 9. By comparing their R2 values, it can be seen again that the curvilinear trendline represents only a slightly better fit for the data series than that of the linear trendline, and the overall difference in R2 values between these two methods is insignificant. Therefore, in the following discussion, the linear trendline is again used to represent the general trends of corresponding change between DBT and RH. Fig. 13 shows the linear trendlines for TRY weather data in all capital cities of Australia. These lines are almost identical except for the small difference in their slopes. This may indicate that the correlation between DBT and RH is
largely independent of location. This seems to be further supported by the data for each individual year of the 10 years historic weather data between 1978 and 1987 for Brisbane and Sydney (Fig. 14). It can be seen that there is almost no difference in the relationship for different cities and different years. Similar to Section 3.2, the correlation found between DBT and RH can also be potentially used to supplement the missing weather information from one year to another for a specific location. Moreover, because the correlation between DBT and RH is independent of localities, their potential use would be much wider, and it can also be used to supplement air humidity data from one location to another. For example, if there are two nearby places A and B, in Place A (i.e. Brisbane), there are recorded weather data for temperature and air humidity, but in Place B (i.e. Ipswich, 30 km South-West of Brisbane), there is only recorded temperature available. Without these correlations, the air humidity data recorded in Place A have to be used directly for Place B. However, with these correlations, necessary adjustments can be made to the data recorded in Place A for use in Place B, according to the comparison of recorded temperature between these two areas. This presents a significant advantage for the quality of weather data. 3.5. Wind The Sun’s radiation is the energy that sets the atmosphere in motion, both horizontally and vertically [14]. The rising and expanding of the air when it is warmed or the descending and contracting of the air when it is cooled causes the vertical motion. The horizontal motion is caused by different temperatures due to the inequalities in gain and loss of heat. Temperature differences cause pressure differences, which in turn cause air movements. The variation in heating (and consequently the variation in pressure) from one locality to another is an important factor that produces movement of air or wind. Fig. 15 shows the hourly corresponding variations between DBT and wind speed for each of all the major cities in Australia in the TRYs. It can be seen that with temperature increase, the wind speed also increases. This is consistent with the finding by Peterson and Parton [36] that the wind speed and air temperature have
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Fig. 11. Hourly corresponding variations between DBT and RH.
the same pattern of mean monthly diurnal variation and these patterns change seasonally in the same manner. For this reason, they used the model for the simulation of
diurnal variation in air temperature to represent diurnal variations of surface wind speeds at a short-grass prairie site.
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Table 8 Pearson’s correlation between DBT and RH Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.785 0.000 8759
0.828 0.000 8759
0.849 0.000 8759
0.724 0.000 8759
0.775 0.000 8783
0.814 0.000 8759
0.791 0.000 8759
0.776 0.000 8759
Fig. 12. Typical daily variations in temperature and relative humidity during a spring day at Washington, DC, USA.
Table 9 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Linear: y ¼ 3:4407x þ 0:0005 Polynomial: y ¼ 0:0985x2 3:4851x 0:1029 Linear: y ¼ 3:8976x 0:0016 Polynomial: y ¼ 0:1157x2 3:9784x 0:1035 Linear: y ¼ 3:9888x þ 0:0011 Polynomial: y ¼ 0:0765x2 4:0264x 0:1073 Linear: y ¼ 3:6774x 0:0004 Polynomial: y ¼ 0:4673x2 3:5221x þ 0:2394 Linear: y ¼ 3:9072x 0:0023 Polynomial: y ¼ 0:2223x2 3:9922x 0:1368 Linear: y ¼ 3:9098x 0:0023 Polynomial: y ¼ 0:1188x2 3:9626x 0:0895 Linear: y ¼ 3:5176x þ 0:0012 Polynomial: y ¼ 0:4174x2 3:8474x 0:3737 Linear: y ¼ 3:9485x þ 0:0011 Polynomial: y ¼ 0:0354x2 3:9281x þ 0:0198
0.616 0.6176 0.6853 0.6863 0.72 0.721 0.5245 0.5371 0.601 0.6046 0.6625 0.6644 0.626 0.6405 0.6029 0.603
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
The equations of the trendline and their R2 values for Fig. 15 are listed in Table 11. It can be seen that, consistent with Pearson’s correlation, all these trendlines have very low R-square values (less than 0.1), which indicates a low reliability of estimated values. It is noted that an unclear correlation between DBT and wind speed may indicate that wind speed is predominated by the temperature or pressure gradients on a large scale. For a ‘‘stable’’ location, which can be selected as meteorological record point, the variation of local air temperature or pressure would only have a small effect on wind speed (or the third order of atmospheric circulations). However, for a place in the valley or on rolling hills, for instance, the variation of local air temperature or pressure may then have a much larger effect on the wind speed. In the absence of clear correlation between hourly corresponding variations of wind speed and air temperature, it is suggested that for a given location, the set of observed weather data may have to be used for a missing year. 4. Conclusion
The Pearson’s correlations between DBT and wind speed are tabulated in Table 10. It can be seen that the values vary between 0.1 and 0.35, which indicates a weak or little association between DBT and wind speed. The average Pearson’s correlation for all eight capital cities is 0.241.
Based on the historic weather data for all capital cities in Australia, a study has been undertaken on the five key weather parameters of solar irradiation, air temperature, atmosphere pressure, air humidity and wind, to assess their possible correlation. Because dry bulb temperature (DBT)
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25 Adelaide
20
Brisbane Canberra Darwin
15
Hobart
Hourly variation in RH (%)
Melbourne
10
Perth Sydney
5 0 -5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -10 -15 -20 -25 Hourly variation inDBT (°C)
Fig. 13. Linear trendlines between hourly variations of DBT and RH for TRY of Australian capital cities.
Brisbane
Sydney
20 15 Hourly variation in RH (%)
25
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
10 5
15
0 -5
-4
-3
-2
-1
0
1
2
3
4
-5 -10 -15 -20 -25
Hourly variation in DBT (°C)
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
20
5
Hourly variation in RH (%)
25
10 5 0 -5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -10 -15 -20 -25
Hourly variation in DBT (°C)
Fig. 14. Linear trendlines between hourly variations of DBT and RH for 10 years historic weather data in Brisbane and Sydney, Australia.
is one of the most important and commonly recorded meteorological parameters, and has relations to all other key climatic variables, it has been used as the reference parameter in this study to explore its correlation with other four key weather parameters. It has been found that there appears to be a strong linear correlation between hourly variations of global solar irradiation (GSI) and air DBT. With an increasing GSI, the air temperature is generally on the rise. Where the GSI is decreasing, the air temperature will also be generally decreasing. By comparing the slope and intercept of trendlines for these two variables, it has been found that these linear trendlines can be significantly affected by localities. It has also been found that there appears to be a strong linear correlation between hourly variations of relative humidity (RH) and air DBT. With an increasing air
temperature, the air RH is generally decreasing. Where the air temperature is decreasing, the air RH is generally increasing. By comparing the slope of trendlines at different locations, it has been found that these linear trendlines are generally independent of localities. From the analysis of hourly variation of DBT and atmospheric pressure, and corresponding variations between DBT and wind speed, it appears that with an increasing air temperature, the atmospheric pressure may be decreasing, while the wind speed would rise. However, because of scattering distribution of data points, there is only weak or little association between DBT and atmospheric pressure, and between DBT and wind speed. In the absence of clear correlation, it is suggested that the observed weather data be used in place of the missing data. However, cautions are necessary to ensure the
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Fig. 15. Hourly corresponding variations between DBT and wind speed.
smooth transition of weather data to maintain a sensible diurnal weather pattern. The above findings will be useful for the research and practice in building performance simulation. For example, the relationships between different weather parameters can
be used to supplement the ‘‘missing’’ weather data records and the validation of weather data generators. The bottomup approach used in this paper also complements the previous top-down approaches in the study of crosscorrelation between different climatic variables.
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Table 10 Pearson’s correlation between DBT and wind speed Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.304 0.000 8759
0.283 0.000 8759
0.347 0.000 8759
0.105 0.000 8759
0.195 0.000 8783
0.298 0.000 8759
0.188 0.000 8759
0.171 0.000 8759
Table 11 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Polynomial: y ¼ 0:0052x2 þ 0:245x þ 0:0057 Linear: y ¼ 0:2426x þ 0:0002 Polynomial: y ¼ 0:0779x2 þ 0:3936x þ 0:0688 Linear: y ¼ 0:3391x þ 0:0001 Polynomial: y ¼ 0:0004x2 þ 0:224x 0:0004 Linear: y ¼ 0:2242x þ 0:0002 Polynomial: y ¼ 0:0059x2 þ 0:1583x 0:0029 Linear: y ¼ 0:1603x þ 0:0001 Polynomial: y ¼ 0:0279x2 þ 0:2836x þ 0:0172 Linear: y ¼ 0:2729x þ 0:0003 Polynomial: y ¼ 0:0246x2 þ 0:2324x 0:0182 Linear: y ¼ 0:2434x 1E 04 Polynomial: y ¼ 0:0524x2 þ 0:2185x þ 0:0468 Linear: y ¼ 0:1771x 0:0003 Polynomial: y ¼ 0:0034x2 þ 0:2152x þ 0:0019 Linear: y ¼ 0:2132x þ 0:0001
0.0924 0.0923 0.0869 0.0799 0.1202 0.1202 0.011 0.011 0.0387 0.038 0.0914 0.0887 0.0404 0.0353 0.0293 0.0292
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
References [1] Lam JC, Tsang CL, Yang L, Li DHW. Weather data analysis and design implications for different climatic zones in China. Building and Environment 2005;40(2):277–96. [2] Hui SCM, Cheung KP. Climatic data for building energy design in Hong Kong and Mainland China. Proceedings—the CIBSE national conferences 1997, 5–7 October. London (paper for CIBSE virtual conference 1997). [3] Crawley DB, Hand JW, Lawrie LK. Improving the weather information available to simulation programs. In: Building Simulation’99, vol. 2, 1999. p. 529–36. [4] Mason M, Kingston T. Let’s talk about the weather. In: Building simulation’93. p. 487–94. [5] Hirschmann. The cosine function as mathematical expression for the processes of solar energy. Solar Energy 1974;16(2):117–24. [6] Parton WJ, Logan JA. A model for diurnal variation in soil and air temperature. Agricultural Meteorology 1981;23:205–16. [7] Richardson CW. Stochastic simulation of daily precipitation, temperature and solar radiation. Water Resources Research 1981; 17(1):182–90. [8] Weiss A. Algorithms for the calculation of moist air properties on a hand calculator. Transactions of the ASAE 1977;20:1133–6. [9] Nfaoui H, Buret J, Sayigh AAM. Stochastic simulation of hourly average wind speed sequences in Tangiers (Morocco). Solar Energy 1996;56(3):301–14. [10] Degelman LO. A statistically based hourly weather data generator for driving energy simulation and equipment design software for buildings. In: Building simulation’91. p. 592–9.
[11] Knight KM, Klein SA, Duffie JA. Methodology for the synthesis of hourly weather data. Solar Energy 1991;46(2):109–20. [12] Adelard L, Boyer H, Garde F, Gatina JC. A detailed weather data generator for building simulations. Energy and Buildings 2000;31(1): 75–88. [13] van Paassen AHC, Luo QX. Weather data generator to study climate change on buildings. Building Services Engineering Research and Technology 2002;23:251–8. [14] Aerographer’s Mate. Module 05–Basic Meteorology, 2004. Integrated publishing: http://www.tpub.com/content/aerographer/14312/ index.htm [15] Benson RB, Paris MV, Sherry JE, Justus CG. Estimation of daily and monthly direct, diffuse and global solar radiation from sunshine duration measurements. Solar Energy 1984;32(4):523–35. [16] Boisvert JB, Hayhoe HN, Dube´ PA. Improving the estimation of global radiation across Canada. Agricultural and Forest Meteorology 1990;52:275–86. [17] Abdul-Aziz J, A-Nagi A, Zumailan AAR. Global solar radiation estimation from relative sunshine hours in Yemen. Renewable Energy 1993;3(6–7):645–53. [18] Norris DJ. Correlation of solar radiation with clouds. Solar Energy 1968;12:107–12. [19] Kasten F, Czeplak G. Solar and terrestrial radiation dependent on the amount and type of cloud. Solar Energy 1980;24(2):177–89. [20] Bristow KL, Campbell GS. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agricultural and Forest Meteorology 1984;31:159–66. [21] El-Shal AO, Mayhoub AB. Estimating solar radiation as a function of air temperature using Fourier series. Theoretical and Applied Climatology 1996;54(3–4):153–9. [22] McCaskill MR. Prediction of solar radiation from rainday information using regionally stable coefficients. Agricultural and Forest Meteorology 1990;51:247–55. [23] Hansen JW. Stochastic daily solar irradiance for biological modeling applications. Agricultural and Forest Meteorology 1999;94(1):53–63. [24] Bindi M, Miglietta F. Estimating daily global radiation from air temperature and rainfall measurements. Climate Research 1991;1(2): 117–24. [25] Tasdemiroglu E, Sever R. Estimation of total solar radiation from cloudiness in Turkey. Renewable Energy 1991;1(5–6):775–8. [26] Ododo JC, Agbakwuru JA, Ogbu FA. Correlation of solar radiation with cloud cover and relative sunshine duration. Energy Conversion and Management 1996;37(10):1555–9. [27] Adelard L, Garde F, Pignolet-Tardan F, Boyer H, Gatina JC. Weather sequences for predicting HVAC system behaviour in residential units located in tropical climates. In: Building simulation’97, vol. 3, 1997. p. 49–56. [28] Hui SCM, Cheung KP. Multi-year (MY) building simulation: is it useful and practical? In: Proceedings of building simulation’97, vol. 2, 1997. p. 285–92. [29] Lane DM. HyperStat online textbook, 2003, http://davidmlane.com/ hyperstat/index.html [30] Microsoft Corporation. Microsoft Office Excel 2003—help manual, 2003. [31] NASA (National Aeronautics and Space Administration). Educational brief—solar radiation and the earth system, 2005,
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http://edmall.gsfc.nasa.gov/inv99Project.Site/Pages/science-briefs/ ed-stickler/ed-irradiance.html [32] National Snow and Ice Data Centre. Arctic Climatology and Meteorology—solar radiation, 2005, http://nsidc.org/arcticmet/ factors/radiation.html [33] ASHRAE. ASHRAE handbook: fundamentals. Atlanta: American Society of Heating Ventilating and Air-Conditioning Engineers (ASHRAE); 1989.
[34] Lutgens FK, Tarbuck EJ. The atmosphere—an introduction to meteorology. Englewood Cliffs, NJ: Prentice-Hall, Inc.; 1979. [35] Wayne State University website, http://sun2.science.wayne.edu/ geology/GEL-1350-ch-1.ppt [accessed at 17 February 2005]. [36] Peterson TC, Parton WJ. Diurnal variations of wind speeds at a shortgrass prairie site—a model. Agricultural Meteorology 1983;28: 365–74.
Building and Environment 42 (2007) 1054–1070 www.elsevier.com/locate/buildenv
Cross-correlations between weather variables in Australia L. Guana, J. Yanga,, J.M. Bellb a
School of Urban Development, Queensland University of Technology, 2 George Street, GPO Box 2434, Brisbane, QLD 4001, Australia Centre for Built Environment and Engineering Research, Queensland University of Technology, 2 George Street, GPO Box 2434, Brisbane, QLD 4001, Australia
b
Received 1 June 2005; received in revised form 22 August 2005; accepted 19 January 2006
Abstract The information on climate variations is essential for the research of many subjects, such as the performance of buildings and agricultural production. However, recorded meteorological data are often incomplete. There may be a limited number of locations recorded, while the number of recorded climatic variables and the time intervals can also be inadequate. Therefore, the hourly data of key weather parameters as required by many building simulation programmes are typically not readily available. To overcome this gap in measured information, several empirical methods and weather data generators have been developed. They generally employ statistical analysis techniques to model the variations of individual climatic variables, while the possible interactions between different weather parameters are largely ignored. Based on a statistical analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper reports on the finding of strong correlations between several specific weather variables. It is found that there are strong linear correlations between the hourly variations of global solar irradiation (GSI) and dry bulb temperature (DBT), and between the hourly variations of DBT and relative humidity (RH). With an increase in GSI, DBT would generally increase, while the RH tends to decrease. However, no such a clear correlation can be found between the DBT and atmospheric pressure (P), and between the DBT and wind speed. These findings will be useful for the research and practice in building performance simulation. r 2006 Elsevier Ltd. All rights reserved. Keywords: Climatic variables; Cross-correlation; Building simulation; Australia
1. Introduction One of the main functions of buildings is that they act as a climatic modifier, separating the indoor built environment from the external climate. Nevertheless, the climate of a particular location can still have a significant influence on the design of architectural features such as shapes and forms of the buildings, and dictate the types of environmental controls required [1]. The quality of climatic data and information will therefore have a significant impact on the effectiveness of building design strategies and the accuracy of design load and energy calculations [2]. In order to study the impacts of climate variations on the built environment, building simulation programmes are often employed. These computer-based programmes norCorresponding author. Tel.: +617 3864 1028; fax: +617 3864 1170.
E-mail address: [email protected] (J. Yang). 0360-1323/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2006.01.010
mally require the inputs of series of hourly weather characteristics, including solar radiation, dry bulb temperature (DBT), air humidity, atmospheric pressure and wind speed and direction [3], to simulate building thermal behaviour in order to assess and evaluate their thermal comfort and energy performance. However, in most cases, the recorded meteorological data are incomplete and unsuitable for the purpose of building simulation. First, the recorded data may be only available in a limited number of representative locations. Then, the number of recorded climatic variables can also vary from one meteorological station to another; some stations may only record temperature while the others could record all the key weather parameters. Moreover, the climatic data are also often recorded in either 3 hourly intervals, or even only twice daily (9 a.m. and 3 p.m.) [4]. In order to overcome this gap in measured information, several empirical methods and weather data generators
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have been developed [5–13]. These generators often use statistical analysis techniques to model the individual climatic variables, and generate further details of weather parameters through a random choice based on their statistical distribution (daily and hourly) and autocorrelation [12]. The possible interaction between different weather parameters has often not been considered. Despite the fact that the weather conditions may be constantly changing, it is also widely believed that there could exist some ‘‘hidden’’ connection between different weather parameters [13,14]. Because the source of heat energy supplied to the Earth’s surface and the atmosphere comes predominantly from the Sun, the variation in solar radiations could have a major impact on the weather conditions on the Earth, and in particular, leading to a fluctuation in air temperatures. The air temperature variation will then bring about a change in water evaporation and air saturation, leading to the changed air humidity. Furthermore, the air temperature differences between different locations will also cause air pressure differences, which in turn would produce air movement, thereby wind (direction and speed). Thus, it could be reasonably expected that all weather variables on the Earth will more or less be affected by the solar radiation (Fig. 1). The above theory of correlations between different weather parameters has now been used in a number of studies to estimate unknown climatic variables. For example, through the pre-assumed correlations, global solar irradiation (GSI) had been estimated in a number of studies by the known climatic parameters of bright sunshine duration [15–17], cloud fraction [18,19], air temperature range [20,21], precipitation status [22], both
Water evaporations & Air saturation
Changes
Air Humidity
1055
temperature and rainfall [23,24] and both sunshine duration and cloud [25,26]. Because these works generally adopt the top-down approach using the pre-assumed formulae, the real cross-correlation between different weather variables (or bottom-up method) has not been assessed. Based on an analysis of 10 years historical hourly climatic data over all capital cities in Australia, this paper seeks to assess and confirm the cross-correlation between a number of different weather variables. Contrary to previous studies, a bottom-up approach is instead used in this research. Since air temperature is one of the most important meteorological parameters and has been recorded most commonly in a meteorological station, its relationship with other key meteorological parameters such as solar radiation, air humidity, atmospheric pressure and wind speed will be examined. The concept and theory/ principle of these key weather variables will also be discussed. It is expected that the results of this study would be useful for not only supplementing the ‘‘missing’’ weather data records but also the validation of weather data generators. 2. Weather database and study approach In order to explore the cross-correlation between different weather variables in Australia, hourly variations of key weather variables will need to be calculated and analysed. Using the observed weather database, the Pearson product moment correlation (called Pearson’s correlation for short) will be used to measure the degree to which the variables are related. The regression analysis will then be employed to find their trendlines for each case. These trendlines can not only graphically display trends of the studied data series but also be used to analyse the accuracy of the prediction.
Controls Solar Radiation
Causes
2.1. Weather database
Air Temperature variations Controls Air Pressure Difference
Drives
Wind Speed and Direction
Fig. 1. Relationship between different weather variables.
In this study, historic climatic data for all capital cities in Australia (Table 1), as supplied by ACADS-BSG, are used to establish the relationship between different weather variables. The ACADS-BSG is a consulting company based in Melbourne, Australia, which supplies weather
Table 1 Information of studied sites in Australia W.M.O index no.
Locality
Latitude
Longitude
Elevation (m)
Years between
Test reference year
94675 94578 94925 94121 94970 94868 94608 94768
Adelaide RO Brisbane AMO Canberra City Darwin RO Hobart RO Melbourne RO Perth RO Sydney RO
34.9 27.4 35.3 12.5 42.9 37.8 32 33.9
138.6 153.1 149.1 130.8 147.3 145 115.9 151.2
47 4 564 27 55 112 19 42
1978–1987 1978–1988 1978–1989 1969–1973 1968–1987 1967–1987 1972–1987 1978–1987
1987 1986 1978 1973 1984 1971 1982 1981
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Although the rule used to interpret correlations can be arbitrary and the cut-off values for different situations may be different, generally, it is believed that a Pearson’s correlation between 0.5 and 0.5 indicates a weak, little or no association between two variables. A Pearson’s correlation between 1 and 0.5 would indicate a strong negative association, while a correlation between 0.5 and 1 would indicate a strong positive association.
data for building simulation research and practice in Australia, New Zealand, Hong Kong and Singapore. The test reference year (TRY) in Table 1 is the year selected to represent the average weather patterns that would typically be found in a multi-year dataset for a particular location [27]. It is a whole natural calendar year data derived from observation at a specific location by the national weather service or meteorological office. This concept is in parallel to another related concept called the Typical Meteorological Year which instead consists of linked monthly segments of weather data selected from the (different-year) historical meteorological records [28]. The weather variables contained in the above Australian climatic database have included the detailed records of the DBT, humidity ratio, atmospheric pressure, wind speed and direction, cloud cover, GSI on a horizontal plane, diffuse solar irradiance on a horizontal plane and direct solar irradiance on a plane normal to the beam. In this study, however, only five key climatic variables will be examined which include GSI on a horizontal plane, DBT, humidity ratio, atmospheric pressure and wind speed.
2.3. Regression analysis Regression analysis is a method often used for the formulation of the trendline for a database. It is a form of statistical analysis used to relate variables, assess their relationships and make predictions based on known information. Regression analysis seeks to establish the relationship between different variables so that a given variable can be predicted from one or more other variables. By using regression analysis, a trendline may be extended in a chart beyond the actual available data to predict future values [30]. Both types of Linear and Polynomial (or curvilinear) trendlines are employed in this study. Such trendlines are created by using linear or polynomial equations to calculate the least-squares fit through points. The R2 value, which is a number from 0 to 1.0 and is also known as the coefficient of determination, is then calculated for each case to show the closeness of the estimated values from the trendline to the actual data. A trendline is most reliable when its R2 value is at or close to one. The formulas used for linear trendline, polynomial trendline and the R2 value are listed in Table 3. Because the DBT is one of the most important and commonly recorded meteorological parameters, and has relations to all other key climatic variables, such as solar
2.2. Pearson product moment correlation The correlation between two variables reflects the degree to which the variables are related [29]. The most common measure of correlation is the Pearson’s correlation which can take on the values from 1.0 to 1.0, where 1.0 is a perfect negative (inverse) correlation, 0.0 is no correlation and 1.0 is a perfect positive correlation. The closer the correlation is to 71, the closer to a perfect linear relationship. The formula for Pearson’s correlation takes on many forms. A commonly used formula is shown in Table 2 [29]. Table 2 Formulas for the calculation of Pearson’s correlation Equation Pearson’s correlation (r)
Notes
P P P XY X Y =N r ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P 2 P 2 P 2 P 2 X
X
N
Y
Y
N is the total number of data series
N
Table 3 Formulas for the linear trendline, polynomial trendline and the R2 value Equation
Notes
Linear trendline
Y ¼ mX+b
m is the slope and b is the intercept
Polynomial trendline R2 value
Y ¼ b+C1X+C2X2+C3X3+y+C6X6 P 2 ðY Y Þ R2 ¼ 1 P iP i 2 .
b and C1yC6 are constants i is the time series and n the total number of data series
Y 2i
Yi
n
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radiation, air humidity, atmospheric pressure and wind, the hourly corresponding variations between DBT and other four variables will be first used to calculate the Pearson’s correlation in this paper. Then, the hourly variations of DBT will be plotted against the hourly variations of other four variables to find their trendlines for each case. Although it may be seen from the graphical display of studied data series that a linear correlation could exist for the studied climatic parameters, the polynomial correlation has to be still tested in this paper to confirm the uniformity of data distribution or the visual judgment of the graphics. As shown below, there is generally little difference between the accuracy of these two fitting methods. 3. Results and discussion 3.1. Solar radiation Solar radiation, which is defined as the total electromagnetic energy emitted by the Sun, drives almost every known physical and biological cycle in the Earth system [31]. Solar radiation reaches the Earth’s surface either by being directly transmitted through the atmosphere (direct solar radiation), or by being scattered or reflected to the Earth’s surface (diffuse sky radiation) [32]. It is estimated that about 50% of solar (or shortwave) radiation is reflected back into space, while the remaining shortwave radiation at the top of the atmosphere is absorbed by the Earth’s surface and re-radiated as thermal infrared (or long-wave) radiation. Insolation (an acronym for INcoming SOLar radiATION) is the rate at which solar radiation is received by a unit horizontal surface area at any point on or above the surface of Earth (direct solar radiation). The insolation received at the surface of the Earth depends upon the solar constant (the rate at which solar radiation is received outside the Earth’s atmosphere), the distance from the Sun, inclination of the Sun’s rays, and the amount of insolation depleted while passing through the atmosphere [14]. On a clear day, the direct normal irradiation or solar intensity IDN can be expressed as [33] I DN ¼ A=½exp ðB= sin bÞ,
(1)
where A is the apparent solar constant irradiation at air mass ¼ 0 (W/m2), B the atmospheric extinction coefficient (dimensionless) and b the solar altitude angle (angle above the horizon). The direct solar radiation ID is the product of the direct normal irradiation IDN and the cosine of the angle of the incidence y: I D ¼ I DN cos y,
(2)
where y is the angle between the incoming solar rays and a line normal (perpendicular) to the surface. It is noted that the values of A and B in Eq. (1) vary throughout the year because of the changing Earth–Sun
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distance and because of seasonal changes in the dust and water vapour content of the atmosphere. The diffuse radiation falling on any surface consists of radiation from the sky and part of the reflected solar radiation from adjacent surfaces, particularly the ground lying south (or north in the North Hemisphere) of the surface. The radiation does not come uniformly from all parts of the sky. A simplified general relation for the diffuse solar radiation Ids that falls on any surface from a clear sky is approximately given as [33] I ds ¼ CI DN F ss ,
(3)
where C is the diffuse radiation factor (dimensionless) and Fss is the angle factor between the surface and the sky, i.e. the fraction of shortwave radiation emitted by the sky that reaches the tilted surface (dimensionless). For vertical surfaces, F ss ¼ 0:5, while for horizontal surfaces, F ss ¼ 1:0. For other surfaces, Fss ¼ (1.0+cos S)/2, where S is the tilt angle measured upward from the horizontal plane. From the above discussion, it can be seen that for a specific location, both direct and diffuse solar radiation are determined by the Sun’s position (or incident solar angle), Sun–Earth distance and the sky condition (i.e. cloud cover). The GSI, which is the sum of direct solar radiation and diffuse solar (sky) radiation, therefore varies throughout a year with monthly maximum solar radiation reaching the highest value in summer and falls to the lowest value in winter. From Fig. 2, it can be seen that the variations of solar radiation during a year are different for different locations, with the greatest being Melbourne and the smallest being Darwin. It is also noted that the difference of solar radiation between different locations also varies during the year, the difference being largest in winter and smallest in summer. During a day, the solar radiation heat gradually increases to reach its maximum at midday and then gradually decreases to zero after sunset, following the pattern of cosine bell. This pattern may be demonstrated and illustrated through the daily solar radiation on the day of 16th June of TRY for each of the capital cities in Australia (Fig. 3). It can be seen that different cities have different scales of variations in solar radiation, and reach different levels of daily peak solar radiation. It is expected that the difference of peak solar radiation between different cities would be greater in winter time and smaller in summer time. 3.2. Air temperature Air temperature is a measure of the heat content of air. Three different temperature measurements, called as DBT (the measure of molecular motion), wet bulb temperature (reflection of the cooling effect of evaporating water) and dew point temperature (the temperature below which moisture will condense out of air) are used in the psychrometric chart to represent different types of air
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Monthly maximum global solar irradiation (W/m²)
1200
1000
Adelaide
800
Brisbane Canberra Darwin 600
Hobart Melbourne Perth Sydney
400
200
0 0
2
4
6
8
10
12
14
Month
Fig. 2. Monthly maximum solar radiation of TRY for the capital cities in Australia. 700 Adelaide Brisbane 600
Canberra
Global Solar Irradiation (W/m²)
Darwin Hobart 500
Melbourne Perth Sydney
400
300
200
100
0 0
5
10
15
20
Hours
Fig. 3. Daily solar radiation on the day of 16th June of TRY for Australian cities.
properties. In this study, unless specifically noted, the air temperature used is referred to DBT. Air temperature indicates the degree of hotness or coldness. It may therefore be considered as a measure of heat intensity. The air temperature is undoubtedly the most important climatic parameter, with its variation being primarily controlled by incoming solar energy and outgoing earth energy, as illustrated in Fig. 4 [34]. Fig. 5 shows a typical example of diurnal cycle of incoming GSI and air temperature in Brisbane on 16th June 1986. It can be seen that as the solar irradiation increases, the air temperature also increases, although there is a time lag, which is caused
by the effect of earth thermal storage (thermal mass). This can lead to a situation where the solar radiation decreases while the air temperature still increases, or solar radiation starts increasing but air temperature is still decreasing. Fig. 6 shows the hourly variations of DBT as plotted against the hourly variations of GSI on a horizontal plane for TRY of Australian capital cities. Because of the natural diurnal pattern of solar radiation as shown in Fig. 3, only these hours with solar radiation (i.e. the time between sunrise and sunset) are considered. It can be seen that there is a good correlation between hourly variations of GSI on a horizontal plane and DBT. The Pearson’s correlations, as
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tabulated in Table 4, are larger than 0.65 with the exception of Melbourne, which indicates good association between DBT and GSI. The average Pearson’s correlation for all eight capital cities is 0.69. The equations of the trendlines and their R2 value for different locations are tabulated in Table 5. Both types of linear and polynomial (or curvilinear) trendlines are examined. By comparing their R2 values, it can be seen that the curvilinear trendlines represent only a slightly better fit for the data series than that of the linear trendline, and the overall difference of R2 values between the linear and curvilinear trendlines is very small. Therefore, the linear correlation as judged from the graphical visual observation is correct, and in the following discussion, only the linear trendline will be used to represent the general trends of corresponding change between DBT and GSI. Fig. 7 shows the linear trendlines for TRY of each of the capital cities in Australia. It can be seen that these trendlines have different slopes and intercepts. This may
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be due to the effect of local geological factors. It also indicates that the linear correlation between GSI and DBT is locally dependent. The sensitivity of DBT response to the change of GSI, from strong to weak, are Canberra, Adelaide, Brisbane, Hobart, Perth, Sydney, Darwin and Melbourne. In order to test the consistency of the found correlation to a given location, the linear trendlines for each individual year of the 10 years between 1978 and 1987 of Brisbane and Sydney, Australia, are illustrated in Fig. 8. It can be seen that the correlation between DBT and GSI are remarkably consistent for a given location. The above discussion gives evidence to the fact that there is a clear correlation between DBT and GSI, which supports the postulate that the variation of air temperature is primarily controlled by the variation of solar energy. However, because these correlations are dependent on localities, the potential of their applications may somehow be limited. Despite this condition, for a specific location, where for example there are missing solar data for 1 or 2 years, the found correlation can still be used to supplement the available data. According to the comparison of recorded temperature between different years, it is possible to make necessary adjustment to the data recorded in 1 year for use in the missing year. 3.3. Atmospheric pressure
Fig. 4. March of incoming solar radiation and outgoing earth radiation for a day at about the time of an equinox.
Atmospheric pressure is the force per unit area exerted by the atmosphere in any part of the atmospheric envelope. Although the pressure varies on a horizontal plane from day to day, the greatest pressure variations are with changes in altitude (Fig. 9) [35]. Because air pressure at any given altitude within the atmosphere is determined by the weight of the atmosphere pressing down from above, the
30
700 16th June 1986, Brisbane
Incoming Global Solar Irradiation Daily Temperature
600
28
500
24 22
400
20 300
18 16
200
14 100 12 0
10 0
5
10
15
20
Hours
Fig. 5. Diurnal cycle of global solar radiation and air temperature on 16th June 1986, Brisbane.
Air temperature (°C)
Global Solar irradiation (W/m²)
26
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Fig. 6. Hourly corresponding variations between DBT and GSI.
pressure decreases with altitude gains. Atmospheric pressures are greatest at lower elevations because the total weight of the atmosphere is greatest at these points. The barometric pressure could influence the calculation of wet bulb temperatures and relative humidity (RH) [10].
The barometric equation, which expresses the above discussion, is dP ¼ rg, dZ
(4)
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Table 4 Pearson’s correlation between DBT and GSI Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.730 0.000 4347
0.809 0.000 4360
0.713 0.000 4346
0.691 0.000 4367
0.667 0.000 4361
0.519 0.000 4553
0.721 0.000 4347
0.687 0.000 4344
Table 5 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Linear: y ¼ 0:007x þ 0:3992 Polynomial: y ¼ 3E 07x2 þ 0:007x þ 0:3948 Linear: y ¼ 0:0066x þ 0:4279 Polynomial: y ¼ 1E 06x2 þ 0:0066x þ 0:4518 Linear: y ¼ 0:0077x þ 0:5681 Polynomial: y ¼ 3E 06x2 þ 0:0077x þ 0:6 Linear: y ¼ 0:0041x þ 0:2781 Polynomial: y ¼ 3E 06x2 þ 0:0041x þ 0:33 Linear: y ¼ 0:0062x þ 0:2912 Polynomial: y ¼ 5E 06x2 þ 0:0062x þ 0:3434 Linear: y ¼ 0:0035x þ 0:3738 Polynomial: y ¼ 9E 07x2 þ 0:0035x þ 0:3577 Linear: y ¼ 0:0058x þ 0:4766 Polynomial: y ¼ 2E 06x2 þ 0:0058x þ 0:5044 Linear: y ¼ 0:0049x þ 0:3273 Polynomial: y ¼ 3E 06x2 þ 0:0049x þ 0:3639
0.5331 0.5331 0.6553 0.6557 0.5077 0.5085 0.4774 0.4804 0.4456 0.4494 0.2693 0.27 0.5204 0.521 0.4719 0.4737
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
where P is the atmospheric pressure (Pa), Z the altitude (m), r the air density (kg/m3) and g the gravitational acceleration (m/s2). From Eq. (4), it can be seen that there will be a change of pressure whenever either the mass (density) of the atmosphere or the accelerations of the molecules within the atmosphere are changed. Although altitude exerts the dominant influence, it is noted that the air temperature and moisture level can also alter pressure at any given altitude, especially near Earth’s surface where heat and humidity are most abundant [14]. For a certain amount of air mass at a given altitude, the relationship between pressure and temperature can be expressed through the ideal gas law P ¼ rRT,
Fig. 10 illustrates the hourly variation of atmospheric pressure as plotted against hourly variation of DBT for TRY of all Australian capital cities. It can be seen that when the temperature increases, the pressure actually decreases, which may be in contrast to the first glance of Eq. (5). However, in a free atmosphere, a temperature increase frequently leads to the expansion of the air, resulting in a decrease in the air density [14]. Moreover, a temperature increase allows an increase in moisture content, which would also decrease air density (density of vapour is lower than that of dry air). These two factors combined can therefore often result in a decrease in air density to the extent which outweighs the effect of temperature increase, leading to a decreased pressure, as shown in Fig. 10. The Pearson’s correlations between DBT and atmospheric pressure are tabulated in Table 6. It can be seen that the values vary between 0.26 and 0.13, which indicates weak or little negative association between DBT and atmospheric pressure. The average Pearson’s correlation for all eight capital cities is 0.195. The equations of the trendline and their R2 values for Fig. 10 are also listed in Table 7. Correspondingly, it can also be seen that all these trendlines have very low R2 values (less than 0.07), which also indicates a low reliability of estimated values. In the absence of clear correlation between hourly corresponding variations of atmospheric pressure and air temperature, it is suggested that for a given location, the set of observed weather data may have to be used for a missing year. It may also be noted that from the analysis of actual record of hourly pressure and DBT for TRY of all the capital cities in Australia, the change in pressure is fairly small (o6 kPa oro6%) with a wide range of variation in temperature (16–42.3 1C). 3.4. Air humidity
(5)
where P is the absolute pressure (kPa), r the air density (kg/m3), R the universal gas constant 8.314 (kJ/kg K) and T the absolute temperature, K ¼ 1C+273.15. It can be seen from Eq. (5) that if the left side of the equation (pressure) changes, a corresponding change must occur on the right side (either in the density or temperature) to make the equation equal again. With the change of temperature, air density would also be changed. Therefore, the final change of pressure due to changing temperatures is dependent on the product of new r and T.
Atmospheric air contains many gaseous components, such as dry air, as well as water vapour and miscellaneous contaminants, including smoke, pollen and gaseous pollutants. Although the quantity of water vapour in a saturated volume of atmosphere is independent of the air pressure, it is significantly influenced by the air temperature. At a higher temperature, more vapour will be injected into a given volume before the saturated state changes to dew or fog forms. On the other hand, cooling a saturated volume of air may force some of the vapour to condense out as the quantity of vapour in the volume diminishes [14].
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3.0
Hourly variation in DBT (°C)
2.0
1.0
0.0 -300
-200
-100
0
100
200
300 Adelaide Brisbane
-1.0
Canberra Darwin Hobart Melbourne
-2.0
Perth Sydney
-3.0 Hourly variation in GSI (W/m²)
Fig. 7. Linear trendlines between hourly variations of DBT and GSI for TRY of Australian capital cities.
Sydney
3.0
3.0
2.0
2.0
1.0
0.0 - 300
-200
-100
0
100
-1.0
-2.0
-3.0
200
Y87 300 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
Hourly variation in GSI (W/m²)
Hourly variation in DBT (°C)
Hourly variation in DBT (°C)
Brisbane
1.0
0.0 - 300
-200
-100
0
100
-1.0
-2.0
-3.0
200
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
300
Hourly variation in GSI (W/m²)
Fig. 8. Linear trendlines between hourly variations of DBT and GSI for 10 years historic weather data in Brisbane and Sydney, Australia.
same temperature and pressure: xw pw ¼ , f¼ xws t;p pws t;p
Fig. 9. Vertical pressure profile.
To show the degree of saturation or determine how close the air is to the saturation point, the concept of RH f is introduced, which is defined as the ratio of the mole fraction of water vapour xw in a given moist air sample to the mole fraction xws in an air sample, saturated at the
(6)
where pw is the partial pressure of water vapour and pws the saturation pressure of water vapour in the absence of air at the same given temperature, which is only a function of temperature and may differ slightly from the vapour pressure of water in saturated moist air. Fig. 11 shows the hourly variation in RH as plotted against the hourly variation in DBT for TRY weather data of all Australian capital cities. It can be seen that there is a good correlation between RH and DBT. The Pearson’s correlations, as tabulated in Table 8, are between 0.72 and 0.85, which indicates a very strong association between DBT and RH. The average Pearson’s correlation for all eight capital cities is 0.793. From Fig. 11, it can also be seen that with increasing DBT, RH is generally decreasing. This agrees with Lutgens
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Fig. 10. Hourly corresponding variations between DBT and atmospheric pressure.
and Tarbuck’s finding [34], which showed that there is a corresponding daily variation for temperature and RH (Fig. 12). This may be due to a stronger influence of
temperature on the saturation pressure of water vapour than that on the partial pressure of water vapour (due to the increased evaporation). However, it is also noted that
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Table 6 Pearson’s correlation between DBT and atmospheric pressure Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
–0.158 0.000 8759
0.131 0.000 8759
0.253 0.000 8759
0.184 0.000 8759
0.232 0.000 8783
0.228 0.000 8759
0.202 0.000 8759
0.170 0.000 8759
Table 7 Equation of the trendline and its R2 value for P and DBT in Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Polynomial: y ¼ 5E 06x2 0:0028x 0:0166 Linear: y ¼ 0:0028x þ 0:0003 Polynomial: y ¼ 8E 06x2 0:002x 0:0275 Linear: y ¼ 0:002x 0:0001 Polynomial: y ¼ 7E 06x2 0:0052x 0:0242 Linear: y ¼ 0:0052x 0:0004 Polynomial: y ¼ 2E 06x2 0:002x 0:0071 Linear: y ¼ 0:002x 0:0002 Polynomial: y ¼ 4E 06x2 0:0028x 0:0184 Linear: y ¼ 0:0028x 0:001 Polynomial: y ¼ 3E 06x2 0:0032x 0:0122 Linear: y ¼ 0:0032x þ 0:0002 Polynomial: y ¼ 9E 06x2 0:0036x 0:0269 Linear: y ¼ 0:0036x þ 0:0001 Polynomial: y ¼ 5E 07x2 0:0019x þ 0:002 Linear: y ¼ 0:0019x 0:0001
0.0259 0.025 0.0187 0.0171 0.0658 0.0641 0.0341 0.0339 0.0551 0.0536 0.0523 0.0518 0.0432 0.0407 0.0288 0.0288
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
the change of precipitation status (e.g. precipitation starting or stopping) could change the above relationship, as precipitation is also able to change the moisture content of the environmental air. In such a situation, with the DBT increasing, the RH may instead be still increasing, and vice versa. Moreover, because at different times the moist air may have different absolute humidity content, with the same temperature variation, the corresponding change in RH could be different, which leads to a number of points in Fig. 11 being dispersed from the trendline. The equations of the trendlines and their R2 value for different locations are tabulated in Table 9. By comparing their R2 values, it can be seen again that the curvilinear trendline represents only a slightly better fit for the data series than that of the linear trendline, and the overall difference in R2 values between these two methods is insignificant. Therefore, in the following discussion, the linear trendline is again used to represent the general trends of corresponding change between DBT and RH. Fig. 13 shows the linear trendlines for TRY weather data in all capital cities of Australia. These lines are almost identical except for the small difference in their slopes. This may indicate that the correlation between DBT and RH is
largely independent of location. This seems to be further supported by the data for each individual year of the 10 years historic weather data between 1978 and 1987 for Brisbane and Sydney (Fig. 14). It can be seen that there is almost no difference in the relationship for different cities and different years. Similar to Section 3.2, the correlation found between DBT and RH can also be potentially used to supplement the missing weather information from one year to another for a specific location. Moreover, because the correlation between DBT and RH is independent of localities, their potential use would be much wider, and it can also be used to supplement air humidity data from one location to another. For example, if there are two nearby places A and B, in Place A (i.e. Brisbane), there are recorded weather data for temperature and air humidity, but in Place B (i.e. Ipswich, 30 km South-West of Brisbane), there is only recorded temperature available. Without these correlations, the air humidity data recorded in Place A have to be used directly for Place B. However, with these correlations, necessary adjustments can be made to the data recorded in Place A for use in Place B, according to the comparison of recorded temperature between these two areas. This presents a significant advantage for the quality of weather data. 3.5. Wind The Sun’s radiation is the energy that sets the atmosphere in motion, both horizontally and vertically [14]. The rising and expanding of the air when it is warmed or the descending and contracting of the air when it is cooled causes the vertical motion. The horizontal motion is caused by different temperatures due to the inequalities in gain and loss of heat. Temperature differences cause pressure differences, which in turn cause air movements. The variation in heating (and consequently the variation in pressure) from one locality to another is an important factor that produces movement of air or wind. Fig. 15 shows the hourly corresponding variations between DBT and wind speed for each of all the major cities in Australia in the TRYs. It can be seen that with temperature increase, the wind speed also increases. This is consistent with the finding by Peterson and Parton [36] that the wind speed and air temperature have
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Fig. 11. Hourly corresponding variations between DBT and RH.
the same pattern of mean monthly diurnal variation and these patterns change seasonally in the same manner. For this reason, they used the model for the simulation of
diurnal variation in air temperature to represent diurnal variations of surface wind speeds at a short-grass prairie site.
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Table 8 Pearson’s correlation between DBT and RH Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.785 0.000 8759
0.828 0.000 8759
0.849 0.000 8759
0.724 0.000 8759
0.775 0.000 8783
0.814 0.000 8759
0.791 0.000 8759
0.776 0.000 8759
Fig. 12. Typical daily variations in temperature and relative humidity during a spring day at Washington, DC, USA.
Table 9 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Linear: y ¼ 3:4407x þ 0:0005 Polynomial: y ¼ 0:0985x2 3:4851x 0:1029 Linear: y ¼ 3:8976x 0:0016 Polynomial: y ¼ 0:1157x2 3:9784x 0:1035 Linear: y ¼ 3:9888x þ 0:0011 Polynomial: y ¼ 0:0765x2 4:0264x 0:1073 Linear: y ¼ 3:6774x 0:0004 Polynomial: y ¼ 0:4673x2 3:5221x þ 0:2394 Linear: y ¼ 3:9072x 0:0023 Polynomial: y ¼ 0:2223x2 3:9922x 0:1368 Linear: y ¼ 3:9098x 0:0023 Polynomial: y ¼ 0:1188x2 3:9626x 0:0895 Linear: y ¼ 3:5176x þ 0:0012 Polynomial: y ¼ 0:4174x2 3:8474x 0:3737 Linear: y ¼ 3:9485x þ 0:0011 Polynomial: y ¼ 0:0354x2 3:9281x þ 0:0198
0.616 0.6176 0.6853 0.6863 0.72 0.721 0.5245 0.5371 0.601 0.6046 0.6625 0.6644 0.626 0.6405 0.6029 0.603
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
The equations of the trendline and their R2 values for Fig. 15 are listed in Table 11. It can be seen that, consistent with Pearson’s correlation, all these trendlines have very low R-square values (less than 0.1), which indicates a low reliability of estimated values. It is noted that an unclear correlation between DBT and wind speed may indicate that wind speed is predominated by the temperature or pressure gradients on a large scale. For a ‘‘stable’’ location, which can be selected as meteorological record point, the variation of local air temperature or pressure would only have a small effect on wind speed (or the third order of atmospheric circulations). However, for a place in the valley or on rolling hills, for instance, the variation of local air temperature or pressure may then have a much larger effect on the wind speed. In the absence of clear correlation between hourly corresponding variations of wind speed and air temperature, it is suggested that for a given location, the set of observed weather data may have to be used for a missing year. 4. Conclusion
The Pearson’s correlations between DBT and wind speed are tabulated in Table 10. It can be seen that the values vary between 0.1 and 0.35, which indicates a weak or little association between DBT and wind speed. The average Pearson’s correlation for all eight capital cities is 0.241.
Based on the historic weather data for all capital cities in Australia, a study has been undertaken on the five key weather parameters of solar irradiation, air temperature, atmosphere pressure, air humidity and wind, to assess their possible correlation. Because dry bulb temperature (DBT)
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25 Adelaide
20
Brisbane Canberra Darwin
15
Hobart
Hourly variation in RH (%)
Melbourne
10
Perth Sydney
5 0 -5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -10 -15 -20 -25 Hourly variation inDBT (°C)
Fig. 13. Linear trendlines between hourly variations of DBT and RH for TRY of Australian capital cities.
Brisbane
Sydney
20 15 Hourly variation in RH (%)
25
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
10 5
15
0 -5
-4
-3
-2
-1
0
1
2
3
4
-5 -10 -15 -20 -25
Hourly variation in DBT (°C)
Y87 Y86 Y85 Y84 Y83 Y82 Y81 Y80 Y79 Y78
20
5
Hourly variation in RH (%)
25
10 5 0 -5
-4
-3
-2
-1
0
1
2
3
4
5
-5 -10 -15 -20 -25
Hourly variation in DBT (°C)
Fig. 14. Linear trendlines between hourly variations of DBT and RH for 10 years historic weather data in Brisbane and Sydney, Australia.
is one of the most important and commonly recorded meteorological parameters, and has relations to all other key climatic variables, it has been used as the reference parameter in this study to explore its correlation with other four key weather parameters. It has been found that there appears to be a strong linear correlation between hourly variations of global solar irradiation (GSI) and air DBT. With an increasing GSI, the air temperature is generally on the rise. Where the GSI is decreasing, the air temperature will also be generally decreasing. By comparing the slope and intercept of trendlines for these two variables, it has been found that these linear trendlines can be significantly affected by localities. It has also been found that there appears to be a strong linear correlation between hourly variations of relative humidity (RH) and air DBT. With an increasing air
temperature, the air RH is generally decreasing. Where the air temperature is decreasing, the air RH is generally increasing. By comparing the slope of trendlines at different locations, it has been found that these linear trendlines are generally independent of localities. From the analysis of hourly variation of DBT and atmospheric pressure, and corresponding variations between DBT and wind speed, it appears that with an increasing air temperature, the atmospheric pressure may be decreasing, while the wind speed would rise. However, because of scattering distribution of data points, there is only weak or little association between DBT and atmospheric pressure, and between DBT and wind speed. In the absence of clear correlation, it is suggested that the observed weather data be used in place of the missing data. However, cautions are necessary to ensure the
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Fig. 15. Hourly corresponding variations between DBT and wind speed.
smooth transition of weather data to maintain a sensible diurnal weather pattern. The above findings will be useful for the research and practice in building performance simulation. For example, the relationships between different weather parameters can
be used to supplement the ‘‘missing’’ weather data records and the validation of weather data generators. The bottomup approach used in this paper also complements the previous top-down approaches in the study of crosscorrelation between different climatic variables.
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Table 10 Pearson’s correlation between DBT and wind speed Location
Adelaide
Brisbane
Canberra
Darwin
Hobart
Melbourne
Perth
Sydney
Pearson’s correlation Significance (2-tailed) No. of cases
0.304 0.000 8759
0.283 0.000 8759
0.347 0.000 8759
0.105 0.000 8759
0.195 0.000 8783
0.298 0.000 8759
0.188 0.000 8759
0.171 0.000 8759
Table 11 Equation of the trendline and its R2 value for Australian capital cities Location
Equation of the trendline
R2 value
Adelaide
Polynomial: y ¼ 0:0052x2 þ 0:245x þ 0:0057 Linear: y ¼ 0:2426x þ 0:0002 Polynomial: y ¼ 0:0779x2 þ 0:3936x þ 0:0688 Linear: y ¼ 0:3391x þ 0:0001 Polynomial: y ¼ 0:0004x2 þ 0:224x 0:0004 Linear: y ¼ 0:2242x þ 0:0002 Polynomial: y ¼ 0:0059x2 þ 0:1583x 0:0029 Linear: y ¼ 0:1603x þ 0:0001 Polynomial: y ¼ 0:0279x2 þ 0:2836x þ 0:0172 Linear: y ¼ 0:2729x þ 0:0003 Polynomial: y ¼ 0:0246x2 þ 0:2324x 0:0182 Linear: y ¼ 0:2434x 1E 04 Polynomial: y ¼ 0:0524x2 þ 0:2185x þ 0:0468 Linear: y ¼ 0:1771x 0:0003 Polynomial: y ¼ 0:0034x2 þ 0:2152x þ 0:0019 Linear: y ¼ 0:2132x þ 0:0001
0.0924 0.0923 0.0869 0.0799 0.1202 0.1202 0.011 0.011 0.0387 0.038 0.0914 0.0887 0.0404 0.0353 0.0293 0.0292
Brisbane Canberra Darwin Hobart Melbourne Perth Sydney
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