Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103

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Journal of Atmospheric and Solar-Terrestrial Physics

1364-68

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/jastp

Statistical estimation of tropospheric radio refractivity derived from 10 yearsmeteorological data

Safdar Ali �, Shahzad A. Malik, Khurram Saleem Alimgeer, Shahid A. Khan, Rana Liaqat Ali

Electrical Engineering Department, COMSATS Institute of Information Technology, Islamabad, Pakistan

a r t i c l e i n f o

Article history:

Received 16 August 2011

Received in revised form

30 November 2011

Accepted 1 December 2011Available online 13 December 2011

Keywords:

Radio refractivity

Meteorology

Troposphere

ITU-model

26/$ - see front matter & 2011 Elsevier Ltd. A

016/j.jastp.2011.12.001

esponding author. Tel.: þ92 51 9049317; fa

ail address: safdarali06@live.com (S. Ali).

a b s t r a c t

Estimation of radio refractivity is critical in planning and design of radio links/systems for achieving

optimal performance. The objective of this work is to estimate statistical variation of radio refractivity

due to meteorological conditions dependent on the geographical region under consideration. These

statistical estimations of tropospheric radio refractivity have been computed using the method

recommended by International Telecommunication Union (ITU). A MATLAB software tool has been

developed for this purpose. The sensitivity of radio refractivity to temperature, pressure and humidity

has been evaluated for a period of 10 years from 2000 to 2009. Results have been obtained for

tropospheric radio refractivity taking into consideration the location height, as well as the scale height

parameters. These results have been analyzed in terms of statistical measures such as the moving

averages, cumulative probability, monthly mean values, and the corresponding standard deviations. It

has been observed that radio refractivity attains peak values during hot and humid months of July–

August over the period of study. Moreover, a significant deviation from mean values is also observed

that is required to be taken into consideration for optimal performance of radio link/systems design.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

All radio wave propagations are affected by the properties ofthe atmosphere. They can be reflected, refracted, scattered, andabsorbed by different atmospheric constituents. The part ofatmosphere most closely related to human life is troposphere; itextends from the earth surface to an altitude of about 10 km atthe earth’s poles and 17 km at the equator. The degree of atmo-spheric effects depends mainly upon the frequency, power of thesignal and on the state of the troposphere through which theradio wave propagates. The characterization of troposphericvariability has great significance to radio communications, aero-space, environmental monitoring, disaster forecasting, etc. Forinstance, worse propagation conditions lead to increased fadingon communication links and consequently decreased powerlevels at receiver.

Quality of propagation of radio waves between the transmitterand receiver mostly depends on performance and reliability of thelink. Generally for radio link design, the measured signal strengthdata for specific locations is required by radio-planning-engi-neers. Consequently, a radio propagation model is required to beused for the evaluation of signal level variations that occur atvarious locations of interest over different times of the year. An

ll rights reserved.

x: þ92 51 9247006.

important element of such type of radio propagation model is thevariation of radio refractive index in the troposphere.

It was observed that sometime microwave systems couldbecome unavailable due to seasonal variation of refractive index(Serdega and Ivanovs, 2007). Therefore, the accurate knowledgeof radio refractive index of the lower atmosphere is important inthe planning and design of terrestrial radio links for communica-tion networks, radar and propagation applications (Caglar et al.,2006; Naveen et al., 2011). Any model, therefore, should take intoaccount refractive index variations both in time and space.

Refractive index, n, of a medium is defined as the ratio of thevelocity of signal in free space to its velocity in a specifiedmedium (Freeman, 2007). The following relation signifies therefractive index, n, of the medium:

n¼ Vfs=Vm ð1Þ

where Vfs is the velocity of signal in free space and Vm is itsvelocity in the medium.

Consider a plane wave transmitting in a medium of constantrefractive index, n; the amplitude, E(r,t) varies in space (r) andtime (t) and can be expressed as

Eðr,tÞ ¼ E0 exp½iðk0n � r�wtÞ� ð2Þ

where E0 is the amplitude at t¼0, w¼2pf is the angular frequency(f¼frequency) and k0 is free space wave vector that shows thedirection in which wave travels. Refractive index is not constant inthe atmosphere and its space-time distribution results in scattering,sub-refraction, super-refraction, ducting and absorption phenomena

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103 97

(Adeyemi, 2006). Refractive index depends on properties of themedium and the boundary conditions and it varies on the scale ofwavelength at radio frequencies. In this case, even the magnitude ofE(r,t) will, in general, vary with r and it may now be written as

Eðr,tÞ � E0 exp½iðk0nðrÞ � r�wtÞ� ð3Þ

The variation of refractive index is due to various phenomenaaffecting the propagation of radio signal, which for instanceinclude refraction, bending, ducting and scintillation, range andelevation errors in radar acquisition and radio-station interfer-ence (Maitham and Asrar, 2003; Freeman, 2007; Jan and Ewa,2009; Grabner and Kvicera, 2003; Tom, 2006). The variation ofrefractive index as well as specific attenuation of micro/radiowave may be estimated indirectly with the measurement oftemperature, pressure and relative humidity. The effect of tem-perature and relative humidity on specific attenuation of micro-wave was studied by different researchers (Ihara, 1994;Tamosiunaite et al., 2010). For example, the 10% increase intemperature could increase the specific attenuation of microwaveby 72.73�10�5 dB/km whereas 10% increase in relative humiditycould increase the specific attenuation by 2.51�10�2 dB/km.

The establishment of a radio refractive index database isnecessary because the knowledge of radio refractive index isalways required when measurements are made in air (Nelet al.,1988; Guanjun and Shukai, 2000; Valma et al., 2010). Inthe absence of reliable local data, wireless service providers usethe radio refractive index and other data from world charts andglobal numerical maps provided by International Telecommuni-cation Union (ITU). In Pakistan, however no local reliable data onatmospheric radio refractivity is available. The paper estimatesand characterizes thorough statistical analysis the radio refractiveindex variations derived from radiosonde data over a decade(2000–2009) for Lahore, Punjab, Pakistan.

2. Methodology and calculation of radio refractivity

The refractive index of the atmosphere is dependent uponthree factors: humidity (water vapor), temperature and pressure.As we move vertically up into the atmosphere, all these threeparameters vary and consequently refractive index, n, alsochanges. Near the surface of earth, this number, n, is slightlygreater than unity and approaches to about 10–5. The deviation ofatmospheric refractive index, n, from unity is mainly due to twofacts:

(i)

Polarization of the air molecule constituents (generally; oxy-gen, nitrogen, carbon dioxide and water vapor) of loweratmosphere; this is primarily due to the interaction ofelectromagnetic signal with air molecules up to millimeterwaves at varying values of pressure, humidity/water vaporand temperature.

(ii)

Quantum mechanical molecular resonance effect, which islimited to narrow frequency bands, around 22 GHz and60 GHz.

For convenience, a derived quantity referred to as radiorefractivity, N, is used in many scientific studies, and is mathe-matically formulated as follows:

N¼ 106ðn�1Þ ð4Þ

Although N is a dimensionless quantity, it is expressed inN-units. Radio refractivity, N, depends on the pressure P (mbar),the absolute air temperature T (K), and the vapor pressure e

(mbar). Radio refractivity is related to these meteorologicalparameters with the following formula (ITU, 1970–1986–1990–

1992–1994–1995–1997–1999–2001–2003):

N¼77:6

TPþ4810

e

T

� �¼NdryþNwet ðN-unitsÞ ð5Þ

where

Ndry ¼ 77:6P

Tð6Þ

and

Nwet ¼ 3:73� 105 e

T2ð7Þ

Ndry and Nwet are often referred to as dry and wet terms ofatmospheric radio refractivity, respectively. The dry term is due tonon-polar nitrogen and oxygen molecules. It is proportional topressure, P, and therefore, related to the air density. The wet termis proportional to vapor pressure and dominated by polar watercontents in the troposphere. The expression in (7) might well beused for all frequencies up to 100 GHz with an error less than0.5%. Near the surface of the earth with relatively warm tem-peratures, most of the spatial variability in N results from thechange in the second term of (5). The water vapor pressure, e, canbe calculated from relative humidity as from given:

e¼RHes

100ð8Þ

with

es ¼ a expbt

tþc

� �ð9Þ

where RH is the relative humidity (%), t the temperature (1C), e thesaturation vapor pressure (hPa) at the temperature t (1C) and thecoefficients for water a¼6.1121, b¼17.502, and c¼240.97 (validfrom –20 1C to þ50 1C, with an accuracy of70.20%). The refrac-tivity shows exponential behavior with the height in troposphere:

Nh ¼N exp�h

Hs

� �ð10Þ

where Nh is radio refractivity at height, h, above from the station’slocation, N is the radio refractivity at the station’s location, and Hs

is the scale height, which incorporates the temperature variationdue to change of height. Eq. (10) may serve as practical tool forthe study of radio refractivity variations near the earth’s surfaceand the apparent boresight angle (ITU, 1992–1994–1997–1999–2003–2005–2007). The parameters N and Hs can be determinedstatistically for different climates. It is obvious that their changemay affect the value of Nh.

The statistical distribution of radio refractivity has beencomputed using the method given in recommendation (ITU-RP.453-9–1970–1986–1990–1992–1994–1995–1997–1999–2001–2003). A software tool in MATLAB has been developed forthe computation of the radio refractivity and other parameters.Raw data for temperature, pressure and relative humidity col-lected over 10 years (2000–2009) is converted into suitable inputformat for processing using the software tool; the values of N, andNh are then computed using Eqs. (4)–(10).

3. Input data

The geographical area under investigation is the city of Lahore,the capital of Punjab province, Pakistan. Table 1 provides infor-mation about the location under study. Radio refractivity varia-tions have been computed using the local reliable data obtainedfrom Lahore airport.

The datasets used in this study were based on the radiosondemeasurements of temperature, pressure and relative humidity

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–10398

taken every hour for the period of 10 years (2000–2009) obtainedfrom the Pakistan Meteorological Department.

Fig. 1 shows the complete measured input data profiles for adecade (years 2000–2009) of temperature, pressure, and humid-ity of Lahore used in the computation of radio refractivity andother parameters. The average value of temperature, pressure,and humidity for each day is represented by a small rectanglewith gray scale values. The darkness of the rectangle showssmaller value whereas brightness shows larger value, as describedby the bar (scale) attached vertically on the right of the datasets.Such 31 small rectangles make a month in a column as shown inFig. 1. However, the months with less than 31 days are shown inblack rectangles. Then 365 small rectangles are combinedtogether to form a column of 12 months i.e., one columnrepresents complete one year data. Horizontal scale shows yearsfrom 2000 to 2009. A large rectangle is formed from 10 columns(each column equivalent to 1 year) and 365 rows. Three differentprofiles namely, temperature, pressure, and humidity are repre-sented by three separately large rectangles.

4. Results and analysis

4.1. Sensitivity analysis of radio refractivity (N)

In general, changes in temperature (T), atmospheric pressure(P) and water vapor pressure (e) cause changes in the radio

Table 1Information about the location/area under investigation.

Country Pakistan

Region Lahore, Punjab

Latitude 3113205900N

Longitude 7412003700E

Elevation 213 m

Average extreme

temperature

40–48 1C (in May–July)

Highest maximum

temperature

48 1C, recorded on June 10, 2007

Monsoon seasons From late June till August, with heavy rainfall (highest

rainfall recorded during 24 h is 221 mm (8.7 in) on

August 13, 2008

Fig. 1. Ten-year (2000–2009) measured input dataset of temperature

refractivity, N. The relative importance of these parameters(T, P, e) particularly water vapor content could also be observedfrom the differentials of Eq. (4):

dN ¼ 77:6dP

T� 77:6

P

T2þ7:46� 105 e

T3

� �dTþ3:73� 105 de

T2ðN-unitsÞ

ð11Þ

For typical atmospheric conditions, pressure P¼1000 hPa, rela-tive humidity RH¼60%, temperature T¼290 K and e¼13.7 hPa,above Eq. (11) reduces to

dN¼ 0:268dP�1:289dTþ4:435de ð12Þ

It has been seen that the contribution of e is large relative to T

and P in the gradients of radio refractivity. This is primarily due tothe fact that water vapor molecules become polarized on inter-action with the radio signal. This effect causes the dielectricconstant of water vapor to rise resulting in relatively largercontribution in N than T and P. In standard atmosphere

, pressure, and humidity from Lahore used in the present study.

Fig. 2. Variation of N to atmospheric temperature and relative humidity, assuming

pressure is constant.

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103 99

conditions, the P, T, and e also decrease with height resulting indecreasing N with a gradient of �40 N/km.

It is observed from Fig. 1 that pressure remains stable around1000710 hPa. Therefore, the contribution of pressure to thevariation in radio refractivity, N, is insignificant. It is customaryto analyze the sensitivity of N to temperature and water vaporpressure (i.e., humidity).

Fig. 2 shows the sensitivity to atmospheric temperature andrelative humidity variations, if pressure is kept constant. As therelative humidity increases, the value of N also increases. FromFig. 2, it is seen that 1 1C change in temperature results in about4 N-units change in radio refractivity N at standard atmosphericconditions; for example, consider the graph of relative humidityfor RH¼60%, the value of N at temperature 20 1C is 315 N-unitswhile at 301C is 355 N-units, i.e., 10 1C change in temperatureresults in an approximate change of 40 N-units in refractivity.

In Eq. (5), the dry and wet terms in the radio refractivity dependon temperature and water vapor pressure. In case of normal water

Fig. 4. Refractivity without and with second order moving average of 31-days versus tim

observed.

Fig. 3. The monthly normalized values of Nw (wet part of N) and Nd (dry part of N)

corresponding to monthly N values (left scale) are shown by columns whereas

Nd/Nw ratio (right scale) is marked by solid triangles for years 2000–2009.

vapor content in the atmosphere, an increase in the temperaturewould decrease the wet term faster than the dry term in (5). Hence,contribution of wet term is relatively small to the value of N.However, in case of high water content in the atmosphere, thecontribution of Nwet to N is higher. This is due to the fact thatdecrease in its value due to temperature is more than compensatedby the increase due to the higher water vapor content. Conse-quently, the contribution of Nwet in the value of N is relatively largerover the period of time when atmosphere has high vapor content.This effect could also be observed from Fig. 3 where the contributionof the wet term to the value of N for the months of June–Septemberis relatively higher than the rest of months in the year. It is obviousthat the wet part Nwet contributes a smaller portion to N than thedry part Ndry. The largest contribution of Nwet to N is in the month ofJuly and August; however, its value does not exceed about 30% of N.This is due to humid and hot season from June–September of eachyear of the period under study, as is evidenced from Fig. 1 as well.

4.2. Statistical distribution of radio refractivity (N)

Application of moving averages (low pass filtering) to timedependent datasets, removes the rapid fluctuations and providesde-noised computed values of N and Hs. The statistical estimates of N

and Hs are obtained by applying the second order 31-days movingaverages. These parameters, N and Hs, have shown time seriesbehavior with periodic variations over the 10-year duration underconsideration. Fig. 4 depicts radio refractivity without and withsecond order (31-days) moving average of N versus a decade fromfirst January 2000 (day 1) to 31 December 2009 (day 3650). Thisvariation of N through the whole year can be correlated with changesin temperature, pressure and relative humidity presented in Fig. 1.

It is observed from Fig. 4 that radio refractivity decreases fromJanuary reaching a minimum value of the year in month of May.From June, the value of refractivity starts to increase and attains apeak value (highest value of year) in the month of August. Thevalue of refractivity then starts decreasing until September afterwhich it shows an increase and a small peak is observed inOctober, where it reaches a second peak, smaller than the previousone. After October, for the rest of winter period, radio refractivityshows a decreasing trend.

e (day). A periodic variation of N with respect to time for a decade (2000–2009) is

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103100

Fig. 5 shows scale height Hs without and with second ordermoving average (31-days) versus the day over a decade (2000–2009). The scale height (Fig. 5) follows the similar trend but withlower variation than N (Fig. 4).

A year is divided into following three time windows for thestudy of N: (i) from October to May, (ii) from May to August, and(iii) from August to October. More insight about variations inrefractivity could be revealed from the examination of Fig. 6. Itillustrates comparative study of radio refractivity variations ineach month for every year of entire period under consideration.From October to May, a decreasing trend in monthly mean valuesof N has been observed. From May to August, a strictly increasingbehavior in monthly mean values of N is clearly visible whereasfrom August to October, a strictly decreasing trend is seen. Thehigher values of monthly mean N were seen in July and August for

Fig. 6. Variation of monthly mean-values of refractivity again

Fig. 5. Scale height without and with second order moving average of 31-days v

all years, owing to hot and heavily humid months. It is observedthat the values of the radio refractivity in the months of July andAugust of years 2005 and 2007 were highest among all the yearsinvestigated.

In Fig. 6, it is observed that the difference between themaximum and the minimum values of mean refractivity for eachmonth of the year over the 10 year study period does not remainuniform. This difference for the month of December is thesmallest and equal to 11 N-units. For the rest of months exceptfor January and June, this difference is about two times higherthan that for December. For the month of January, the differenceis found to be equal to 16.8 N-units. Whereas for the month ofJune, this difference has the largest value (i.e., 53.61 N-units),which is approximately five times than the smallest value. Thisfact can also be correlated with datasets in Fig. 1, which depicts

st time (month) for entire period of study (2000–2009).

ersus time (day) of a decade (2000–2009). A similar trend is seen as Fig. 4

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103 101

the variation of metrological conditions over the 10-year periodunder study. Fig. 7 provides the standard deviation of monthlyradio refractivity against each month for 10-year period (2000–2009). A significant change is observed during the months fromMay to August, with highest variation being experienced in themonths of June and July. The large deviation of radio refractivityfrom mean has a profound impact on radio signal propagationand needs to be properly catered for.

Fig. 8 provides the monthly mean values of scale height, Hs, versustime in month for the 10-year period under study (2000–2009). Thevariations in monthly values of Hs from year to year are quite small;approximately about 5%. However, the value of Hs during a typicalyear varies significantly. It increases from January to May, remainsstable within a certain range during May–July, attaining maximum

Fig. 7. Standard deviations of the monthly values of refractivity aga

Fig. 8. Variation of monthly mean-values of scale height, Hs versu

value of the year in this period and then decreases from August toDecember like waterfall curves. Fig. 9 depicts the standard deviationof Hs versus time in month for the 10-year period under study (2000–2009). It is seen that the behavior is quite sporadic over the months ofa typical year and from year to year over the 10 year period underconsideration. Primarily, the Hs incorporates the temperature varia-tion due to the elevation (or change of height from sea level) thatsubsequently impacts the value of radio refractivity, N. The change inthe values of N (monthly mean of 10 years) due to Hs at 100 m fromthe station height, designated as Nh (Eq. 10) is shownin Table 2.

Fig. 10 depicts the cumulative frequency distribution and thehistogram of the radio refractivity for 10-year period under study(2000–2009). Maximum number of occurrences of radio refractivity

inst time (month) for the entire period of study (2000–2009).

s time (month) for entire period of study (years 2000–2009).

Table 2Change in values of N (monthly mean of 10 years) at 100 meter from the station

height, designated as Nh due to Hs (monthly mean of 10 years).

Month Mean N Mean Nh

January 313.76 310.06

February 312.58 308.94

March 311.64 308.08

April 299.84 296.49

May 304.27 300.91

June 329.18 325.55

July 364.38 360.34

August 369.65 365.54

September 349.28 345.39

October 322.44 318.81

November 317.77 314.12

December 312.98 309.32

Year 325.65 321.96

Fig. 9. Standard deviations of the monthly values of scale height, Hs against time (month) for the entire period of study (years 2000–2009).

Fig. 10. Frequency histogram and cumulative probability plot of the radio

refractivity for 10 years (2000–2009).

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103102

is for the value 320 N-units, which has been observed during thewhole period of study.

5. Conclusion

This work has addressed the issue of estimating radio refractivityin troposphere under varying meteorological conditions along withthe effect of location height. Tropospheric radio refractivity has beendetermined by applying the method recommended by ITU.A sensitivity analysis of radio refractivity in terms of statisticalmeasures has been carried out using datasets of temperature,pressure and humidity for a 10-year period (2000–2009). Thestatistical measures used in this analysis include the moving average,cumulative probability, monthly mean and the standard deviation.The collected results indicate the strong dependence of the radiorefractivity on temperature and humidity (i.e., water vapor pressure).Three distinct time windows have been identified in respect of thevariations in the refractivity in a typical year. The monthly meanvalues attain the peak during July–August and then decrease untilApril–May from where these show an increasing trend until July. It isobserved that the values of monthly mean refractivity in 2 monthsJuly and August for years 2005 and 2007 are highest than onesobtained among all the years for the period under investigation. Thepeak values of refractivity appearing mostly during July–August areprimarily due to humid and hot period of the year. Further, thesignificant deviation from mean value of radio refractivity observedduring hot and humid period of the year has a profound impact onradio signal propagation and needs to be properly catered for. Thisvariation pattern is more or less same across the years over the 10-year period under consideration. The Hs (scale height) parameter hasbeen computed to assess the elevation effect and subsequently itsimpact on the value of radio refractivity. The results are highly criticalfor optimal planning and design of radio links.

Acknowledgments

The authors would like to express their gratefulness to theDepartment of Meteorology, CIIT, Islamabad and the PakistanMeteorological Department for providing the data used in this work.

S. Ali et al. / Journal of Atmospheric and Solar-Terrestrial Physics 77 (2012) 96–103 103

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