4 Brazilian tropical and equatorial propagation data

This Chapter presents the rain characteristics of the regions of interest in

this work: tropical (also including subtropical areas) and equatorial portions of the

Brazilian territory. The climatologic description herein has its main focus on the

precipitation characteristics and the propagation impairments caused by them.

Furthermore, the following topics are subjects of this Chapter: raw Brazilian

propagation data treatment and processing and extraction of isolated rain

attenuation events.

4.1. Precipitation characteristics in Brazil

The Brazilian territory covers an area of about 8.5 million square

kilometers. For comparison purposes, such an area is about twice the size of the

European Union. Brazil is located between the latitudes of +5.27° and -33.75° and

the longitudes of 286.00° and 325.20°. The country is roughly divided into three

main macroclimatic regions: equatorial, covering the northern Brazilian area,

subtropical, covering the southern part, and tropical, which is everywhere else.

Most of the country receives a large amount of rain throughout the year, with the

exception of the inland northeast, where rainfall struggles to reach more than 300

mm in an average year; this region experiences the dry tropical climate. To

illustrate that fact, Figure 22 shows the 60-year average of the accumulated

rainfall in Brazil, together with the macroclimatic regions (roughly defined). It is

possible to notice the large number of distinct rainfall areas, even within the

macroclimatic regions.

Many studies on tropical and equatorial climates were performed throughout

the Brazilian territory. The Center for Telecommunications Studies of PUC-Rio

has a considerable database of raingauge, radiometer and beacon data and the

statistics retrieved from this collection of data as well as statistical modeling are

reported in publications [37-43], just to mention a few.

78

The equatorial climate region is characterized by little seasonal variation in

temperature and humidity. The humidity is very high (mean average around 90 %)

as is also high the rain amount accumulated during the year (above 2500

mm/year), compared with the tropical regions.

The tropical region is characterized by the major common feature that is the

absence of a cold season; the mean temperature for the coolest month of the year

is around 18o

C at sea level. On the other hand, the climate is also characterized by

variability in the temperature and humidity throughout the year, with the cooler

season coinciding with the drier months.

For some locations belonging to the group of most populated areas in Brazil,

Figure 23 shows accumulated monthly rainfall measured over a 30-year period.

For each location, the climates and reference coordinates are: Belém (equatorial

climate; lat: -1.45o; lon: 311.50

o), Manaus (equatorial climate; lat: -3.15

o; lon:

299.70o), Brasília (tropical climate; lat: -15.80

o; lon: 312.17

o), Recife (dry tropical

coastal climate; lat: -8.05o; lon: 325.10

o), Rio de Janeiro (tropical coastal climate;

lat: -22.92o; lon: 316.50

o) and São Paulo (tropical highlands / subtropical climate;

lat: -23.53o; lon: 314.60

o).

Figure 22 – Accumulated rainfall in Brazil: 60-year average

(1931-1990). Reproduced from INMET (Brazilian Institute for

Meteorology)

79

Figure 23 – Accumulated monthly rainfall in some representative locations in Brazil: 30-

years average

4.2. Rain and propagation measurements campaigns over Brazilian territory

A description of the most relevant information about the measurements

campaigns over the Brazilian territory, done by CETUC (at PUC-Rio) is found in

this Section. Information on the setup for data acquisition and the storage process

are given.

Terrestrial, beacon/radiometer and rain-gauge data are digitally stored in

local Data Acquisition Units (DAU’s) – which are specialized computers for data

logging – and transferred via modem by telephone line afterwards. From the

output of the DAU’s are generated compacted files containing radio-propagation

and/or rainfall information, according to the type of measurement campaign. Raw

beacon and radiometer propagation data are composed of hourly files, sampled at

1 Hz (one sample per second). The power resolution is about 0.1 dB, assessed

through the application of the calibration curve for the DAU in each site, as

described next.

The beacon receiver antennas have a diameter of 3.6 m, except at

Mosqueiro, where a 4.5 m antenna was used to provide a larger dynamic range

necessary to account for the very deep rain attenuation events experienced in its

equatorial climate. The antennas are pointed towards INTELSAT 705, located at

50° W. The beacon frequency is 11.452 GHz (approximated by 11.5 GHz from

now on in this text), the polarization is clockwise circular and the satellite beacon

transmitted power is 7 dBW. The dynamic ranges of the receivers are in excess of

25 dB, being large enough to allow the observation of severe attenuation events,

80

especially at Mosqueiro where an antenna with larger diameter was used.

Attenuation levels up to about 30 dB are observed and measured at this equatorial

site.

The tipping bucket rain-gauges have a collection area of 800 cm2. As the

manufacturer specified bucket capacity is 8 ml, one tip corresponds to 0.1 mm of

rain accumulation. The rain-gauge models used for collection of rain allowed for

data to be sampled at the same rate of beacon data (1 Hz); the only rain-gauge

information to be stored is the instant of each tip. The rain-gauge data are stored

in the same file as the propagation ones, for the sites with concurrent rain-gauge

and beacon and/or radiometer acquisition equipment. When only rainfall is being

measured, a simpler digital logging device can be employed, still maintaining the

capacity of a maximum sampling rate of 1 Hz. Table 1 presents the most relevant

information regarding the propagation measurements campaigns, indicating

concurrent precipitation (rain-gauge) measurement where it is the case. In the

table, measurement types are defined as:

− RG for rain-gauge measurements.

− Sat (Rad) for radiometer measurements.

− Sat (Rad/Beacon) for radiometer and satellite beacon measurements.

− Terrestrial for signal measurements in point-to-point links composed by

terrestrial stations.

Site Lat. Lon. Type Freq. Pol. Elevation/

Distance Periods

Belém 01o 27' S 48

o 29' W Sat (Rad) + RG 12 GHz V 70

o 32'

dec/87 –

nov/89

Brasília 15 o 48' S 47

o 50' W Sat (Rad) + RG 12 GHz V 62

o 53'

mar/91 –

dec/92

Manaus 03 o 09' S 60

o 01' W Sat (Rad) + RG 12 GHz V 83

o 05'

dec/87 –

nov/89

Ponta das

Lages 03

o 06' S 59

o 54' W Sat (Rad) + RG 12 GHz V 82

o 58'

dec/88 –

nov/89

Rio de

Janeiro 22

o 55' S 43

o 30' W Sat (Rad) + RG 12 GHz V 53

o 52'

dec/87 –

aug/89 |

jan/91 -

dec/93

São Paulo 23 o 32' S 46

o 37' W Sat (Rad) + RG 12 GHz V 55

o 34'

feb/91 –

jan/93

Curitiba 25 o 25' S 49

o 17' W

Sat (Rad/Beacon) +

RG 11.45 GHz C 60

o mar/97 –

feb/99

Porto

Alegre 30

o 03' S 51

o 10' W Sat (Rad) + RG 11.45 GHz C 55

o mar/98 –

feb/99

Rio de

Janeiro 22

o 55' S 43

o 30' W

Sat (Rad/Beacon) +

RG 11.45 GHz C 63

o dec/97 –

feb/99

81

Site Lat. Lon. Type Freq. Pol. Elevation/

Distance Periods

Mosqueiro 01 o 27' S 48

o 29' W

Sat (Rad/Beacon) +

RG 11.45 GHz C 89

o oct/96 –

aug/98

Recife 08 o 03' S 34

o 54' W

Sat (Rad/Beacon) +

RG 11.45 GHz C 69

o dec/97 –

feb/99

Rio de

Janeiro 22

o 55' S 43

o 30' W

Terrestrial +

4 RGs along the

path

28 GHz V/H 2.98 km mar/00 –

may/00

Brasília 15 o 48' S 47

o 50' W Terrestrial + RG 23 GHz V 4.48 km

oct/03 –

sep/03

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 14.55 GHz V 12.79 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 14.55 GHz H 12.78 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 18.61 GHz V 12.78 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 14.50 GHz V 18.38 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 14.53 GHz V 21.69 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 18.59 GHz V 7.48 km

jan/94 –

aug/97

São Paulo 23 o 32' S 46

o 37' W Terrestrial + RG 14.52 GHz H 42.99 km

jan/94 –

aug/97

Tabatinga 04 o 14' S 59

o 56' W RG - - -

sep/03 –

aug/04

Manaus 03 o 05' S 60

o 04' W RG - - -

sep/03 –

aug/04

Boa Vista 02 o 47' N 60

o 41' W RG - - -

sep/03 –

aug/04

São

Gabriel 00

o 07' S 67

o 04' W RG - - -

sep/03 –

aug/04

Santarém 02 o 30' S 54

o 43' W RG - - -

sep/03 –

aug/04

Macapá 00 o 02' N 51

o 05' W RG - - -

sep/03 –

aug/04

Porto

Velho 08

o 46' S 63

o 54' W RG - - -

sep/03 –

aug/04

Cruzeiro

do Sul 07

o 36' S 72

o 40' W RG - - -

sep/03 –

aug/04

Belém 01 o 23' S 48

o 26' W RG - - -

sep/03 –

aug/04

Table 1 – Propagation and precipitation measurements in Brazil

The beacon data used in this work are from measurements performed in four

Brazilian locations: Rio de Janeiro (RIO), Mosqueiro (MOS), Curitiba (CUR) and

Porto Alegre (POA).

82

4.3. Raw data treatment and processing

To develop this work, part of the raw data acquired in the course of the

measurement campaigns listed in Table 1 was used. In this Section it is described

the processes through which the raw data must go in order to be ready for use. In

the literature, the ensemble of tasks encompassed by this primordial activity is

referred to by the use of different denominations. In this work it is called data

treatment. Afterwards, when the data has the best possible quality determined by

the methods used to data treatment, the data processing takes place. Basically,

these are the activities intended to obtain the rain attenuation from the measured

signal and then to extract stationary and dynamic rain attenuation characteristics.

These information are then used to statistically characterize the rain attenuation

under study, obtaining parameters to be used in the propagation channel modeling.

4.3.1. Raw propagation data treatment: reading and cleaning-up

In the next two Sections the task of reading the raw data stored as

compacted binary files and the work done to perform all necessary corrections in

the data are explained.

4.3.1.1. Raw data reading

In order to define a reliable ensemble of data to be used in this work, the

databases of recordings from measurements campaigns for each site were

assessed, with the intention of:

− To analyze the header structure of the compacted binary files in order to

be able to build a convenient raw data reader.

− Once the raw data reader is implemented and working, to verify the

quality of the stocked data. By doing this, it is possible to rank the

actions to be executed in order to try to correct any faulty data and then

to choose a period of measurements with proper up-time.

83

The discussion in the sequence is focused on the analysis of beacon data,

which is the most important data for the work. If not explicitly stated, the

treatment to be described is also done for radiometer. Rain-gauge information is

dealt in a substantially different way, from the software tool to data reading to the

treatment and processing.

Received beacon signal level collected on the field is stored as integers in

the DAU, in a proprietary format. A MATLAB function was developed to:

− Read hourly DAU data values checking for the existence of invalid data

(NaN – Not a Number). For each file, a vector of 86400 elements if

filled with the DAU values of every second of a day. After the header

identifying the day and hour, every first second of a DAU file has its

value (always an integer) stored in hexadecimal, with two bytes. All

remaining seconds in the hour are registered as integer offsets to the

predecessor second, in decimal format.

At this time, nothing is done with respect to NaN values.

− Put every hourly file read for a day in the appropriate position in the

daily vector. A check for eventual missing hours is done – in this case

the corresponding hour in the daily vector is filled with NaN – and a

summary file with this information is output. At this step in the process

we have a matrix with two columns: a time stamp, in seconds; and the

integers representing the DAU received beacon signal strength.

− Generate a log of the batch process, which is the process of reading an

entire period of days specified by the user. The log file contains

information about missing days in the period and missing hours in the

days.

Each daily data output by this function is stored as a matrix (in columns as

just described) generating its own .mat (MATLAB format) file. From this moment

on, original binary files are useless (although they are kept stocked in the

database) and a next step starts: first analysis of up-time and correction of the

measured data.

84

4.3.1.2. First analysis of up-time

Aiming at the provision of non-biased statistics, every chosen period for

statistical analysis must be composed of a multiple of the twelve months of the

year, with no month appearing more times than the others. Otherwise, there is a

risk of inserting a bias in the results, making then to have a false trend towards

rainy of clear sky behavior. It would be specially an issue for non-equatorial

regions, which have more defined dry and wet seasons. Although – statistically

wise – it is the most adequate decision, it may lead to the discarding of months of

measurements, which is generally not desired. As it was not developed a

technique for considering uneven periods of months assuring that no bias in

results is generated, due to the sensitivity of the models – whose parameters are

derived from these data – the choice was to keep just periods in agreement with

what was stated in the beginning of this paragraph.

In order to choose the group of daily .mat files to proceed to next step (for

each site), a first analysis of up-time is performed. It is a quite simple task

consisting of the search for the largest period of time, in accordance to the stated

above, giving the highest possible up-time. Because of the fact that some days

have holes of data (NaN values) on them, up-time must be computed not on a

daily basis, but on a seconds basis, which is a most precise way in this case.

Therefore, a range of .mat daily files was chosen for each site and, from now on,

this range will be referenced in the text as period.

Although the DAU’s have shown considerable reliability through the course

of years of measurements, some failures in the data storage were verified. The

following Section explains the identification and correction of such problems.

4.3.1.3. Raw data cleaning-up

Faults in raw data were mainly verified in the process of data saving and

manifested as intervals with missing of data (caused also by equipment

maintenance and then substituted by NaN) and power shift, this last one being

very common in the transitions of hours, as shown in Figure 24, left.

85

Every incorrect daily time series is classified in one of two well defined

groups, according to the severity of the situation: correctable or uncorrectable

data. Basically, there are three situations which state that the data cannot be

corrected: huge vertical offset causing a dead signal which cannot be recovered;

hard to clean compositions of many consecutive offsets (see Figure 24, right) and

severe attenuation giving rise to receiver loss of lock. Note that the third situation

is not due to any DAU failure, having to do only with the dynamic range of

measurements. Every other situation which is not one of these three stands in the

category of correctable daily files and the correction was made by means of a

semi-automatic tool developed for this specific purpose.

Figure 24 – Samples of daily raw beacon time series (without correction)

Aiming at the correction of every data pertaining to the group of correctable

days, it was developed a MATLAB function which allowed for the graphical

edition of daily received beacon signal time series. Edition capabilities include:

− Vertical shift (the most used tool): this is the case exemplified on the first

part of Figure 25. Vertical offsets are the most common type of failure

encountered on raw data files. This occurrence is characterized by the fact

that the quality of the measurement is just fine but, for some reason, the

storage of data in the DAU unit had some offsets clearly identified. After

reading the daily file, the developed tool searches for discontinuities in the

data. Discontinuities were defined as a difference of 25 DAU units

between two consecutive data samples (this value was empirically chosen

86

to give good results for discontinuities catching). The user then marks,

over the time series plot, the interval he/she wants to correct. As a single

plot represents an entire day in the graph, it would be a tough task (even

impossible) for the user to find and click exactly over the point of

discontinuity; so, the tool corrects the chosen point to the closer

discontinuity in a range of 10 minutes of the original point marked by the

user. After both ends of the interval are selected, the offset is

automatically done and the user can visually inspect (by zoom) the quality

of the correction.

Usually, the tool works just fine. Any imprecision in the offset, in the

order of few DAU units, will be translated in decimals of dB after data

calibration which is not of a concern because data filtering to be

performed afterwards can smooth every small imperfection.

Due to the nature of the vertical offset feature, it is not always possible to

compute the amount of offset for a precise correction. For these kind of

situations, it is provided a fully manual tool: the user marks not only the

ends of the discontinuities but also – and here is the difference from the

semi-auto utility – the size of the offset.

− Fill gap: all holes in data (marked with NaN) can be filled by linear

interpolation between the ends of the missing data interval.

After analyzing some cases, the decision was not to use this feature due to

a simple but important reason: the only motivation to do such a task would

be the improvement in up-time. However, the improvement achieved

would be marginal for most of the cases. On the other hand, a straight line

joining two ends of a hole in the data could be not good for statistics of

fade events duration and slope.

− Remove levels (including spikes): some portions of the data present

extremely fast and high transitions of levels, clearly identifiable as being

due to equipment failure. The selection of the borders of such occurrences

(always very small in duration) removes the spike by joining the ends of it

just before and after the discontinuities.

− Delete interval: sometimes a file considered as having good data for most

part of the day has some bad piece of data hard to be correct recovered. In

order to not discard the entire day, the faulty interval can be removed

87

leading to a minor damage in up-time than the deletion of an entire day

would cause.

Furthermore, for the treatment of errors spanning across two days, the

joining of consecutive time series is possible, saving them as two separate files

afterwards. Figure 25 presents examples of raw beacon data cleaning. The upper

part of it shows the process of vertical offset with the red portion being joined to

the correct mean signal level and then the resulting time series is shown in the

right. In the second part, close inspection shows that signal fluctuations in the

marked region are compatible with the ones found just before and after the

discontinuity; so, the data is corrected by the same process illustrated in the upper

figure. Sometimes, this kind of inspection shows that in fact the signal in the

discontinuity is a “dead signal” meaning that there is no measurement in that time

interval (it is easy determined by the lack of fast fluctuations, being the signal

almost flat). In these cases, if the duration of such an interval is small enough

compared to the duration of the day, the interval is removed and the rest of the day

is saved.

The data cleaning-up ends when all the period is analyzed. Next steps are

the calibration of daily data files, to convert the beacon received signal level from

DAU units to dBm, the convenient unit to deal with from now on.

4.3.1.4. Applying calibration curves and assessing data resolution

Before being put in use and sometimes during their service life, the beacon

receivers were calibrated by means of a signal generator connected to the receiver

input. A table relating received signal level (in dBm) with DAU value is then

generated by varying the injected power from the maximum expected (generally,

few dB’s above nominal level, for clear sky condition) to the minimum one

(corresponding to the higher expected attenuation which could be measured,

leading to loss of lock at the receiver). The next step is to best fit a curve through

the points (DAU units X signal generator (dBm)). The fit for every site as well as

any relevant comments are presented next.

88

Figure 25 – Example of use of the tool designed to clean raw beacon time series

The best fit is found by the application of the internal MATLAB function

called polyfit. Given a degree input by the user, this function searches for the

polynomial which best fits a data interval (on a least RMS error sense). In order to

enhance the quality of the fit, the two extremes, corresponding to very low power

values (next to the receiver “loss of lock”) and to the high ones (close to receiver

saturation) are eliminated. In these ranges, which correspond to just a small part of

the data set to be fit, the relation between DAU and dBm values differs

considerably from the almost linear relation verified for most part of the data. To

89

even enhance the quality of the fit, it was done just in the data interval comprised

between the maximum and minimum recorded DAU values for the whole period

of measurement.

Polynomial fits of order one to three are then made in the data, as presented

in Table 2 and Table 3. Table 2 shows the RMS errors between the polynomial of

each degree and the curve to be fit. The one leading to the smallest error is chosen

for the fit and so for the calibration, as presented in Table 3 and Figure 26. Note

that for Rio de Janeiro calibration was done twice along the measurement period,

so both are described here.

Site RMS error for polynomial

of 1st degree

RMS error for polynomial

of 2nd

degree

RMS error for polynomial

of 3rd

degree

POA 0.3262 0.0630 0.0522

MOS 0.1551 0.1094 0.0879

RIO 0.0601 0.0670 0.0553 0.0493 - 0.0482

CUR 0.2307 0.1659 0.0809

Table 2 – RMS errors in the polynomial fit for DAU data calibration

Site Chosen polynomial for DAU data calibration

POA [-8.6030e-9 2.7008e-5 0.0301 -116.8993]

MOS [-5.8912e-9 9.8421e-6 0.0526 -107.7337]

RIO [2.3315e-6 0.0901 -119.9662] [-5.6050e-9 1.0731e-5

0.0859 -119.6895]

CUR [-3.0874e-8 4.8393e-5 0.0430 -108.9110]

Table 3 – Chosen polynomial for DAU data calibration (highest to lowest order)

After calibration, because the data will be used to parameters extraction, test

and comparison of channel models among themselves and also among the four

Brazilian sites, putting every data property on a standard basis for comparison in

an important issue. At the current point in data treatment, the time resolution is

already known (one second) and the power resolution, in dB, can be assessed in

the following way. For every consecutive DAU value (step = 1) in the range

defined for calibration, the correspondent dBm value is computed, using the

appropriate polynomial. Then, the difference between successive power values, in

dB, is calculated. As all the curves present high linearity (in fact, the choice for

2nd

and 3rd

order polynomials is quite rigorous), the standard deviation of the set

of subtractions is very low. The maximum value of these computed differences,

90

for all periods and all locations analyzed, is just slightly lower that 0.1 dB.

Therefore, 0.1 dB is the adopted resolution to be used for every data in this work.

Figure 26 – Chosen polynomial fit on the receiver calibration curves for each Brazilian site

Provided that calibration curves for all locations and periods are supplied as

a text in an appropriate format (.dat file presented in Figure 27), a script

implemented to perform the task of converting DAU units to received power in

dBm is used. Once .mat files for each site are in the database, the batch text

depicted in Figure 27 is input in the function to generate as output an ensemble of

91

daily .mat files containing, each one, a matrix with two columns: a time stamp

with every second in a day; beacon received power level, in dBm. After

calibration, the same script is responsible to converting every power value to a

resolution of one decimal unit, as stated in the above paragraph.

Figure 27 – Batch .dat file to apply receiver calibration to Brazilian

data

The so-called data treatment ends here. The next step, which is the

beginning of data processing, consists in the extraction of rain attenuation

information from the beacon time series. This is the last step before statistics as

well as parameters for channel modeling can be retrieved from attenuation data.

4.3.2. Raw propagation data processing: rain attenuation assessment and computation of statistics

Received signal strength is influenced by many factors, generally including

atmospheric or transmitter/receiver equipment issues. Besides the propagation

factors affecting every wireless communication, satellite links may suffer

additional influence from higher layers in the atmosphere (clouds in the

troposphere and reflections in the ionosphere, although this last one is less critical

for millimetric waves) and also from the fact that satellites, although stationary in

relation to the Earth, are not absolutely static and so partial decoupling between

onboard and terrestrial antennas can take place.

92

Therefore, as the interest is to model the channel affected by rain induced

attenuation, some technique must be applied to assure that every other effect is

removed or smoothed to an acceptable level.

4.3.2.1. Template removal

Satellites present a natural oscillation and are also periodically commanded

to make small position adjustments inside their orbit. In clear sky conditions, the

natural satellite movement causes the nominal received beacon signal to fluctuate

as presented in Figure 28. This effect is easily spotted in the plot of a daily time

series; depending on the link inclination this effect can be more or less noticeable,

so the plot of two or three consecutive days may be necessary to put the effect in

evidence. The man-commanded adjustment is sometimes less clear in the plot but

its large scale behavior makes it as traceable as the natural satellite movement. In

the figure, the first plot shows a natural oscillation along a day; the other samples

present three consecutive days of man-made periodic adjust in the satellite

position. Both signals were measured at Curitiba site.

Besides satellite movement, the received power time series contains, in

various degrees, signal variations due to effects other than attenuation caused by

rain, such as those caused by emission power changes, antenna misalignment,

attenuation due to clouds and noise generated by the receiver equipment.

Therefore, under rain conditions, special care should be taken to make a

distinction between the real rain events and larger scale fluctuation due to any

other causes. The presence of such signal variations makes necessary the

application of a detrending process in order to determine the reference level for

rain attenuation.

The detrending process can be also called template removal and some

approaches to it can be implemented, being the degree of efficiency, speed of

treatment and ease of use different from one method to another. A quite simple

solution is the use of 30 minutes averages of the received signal as reference to

allow for the distinction between rain attenuation events and all other

aforementioned causes of signal variations. If the signal variance or the signal

peak-to-peak variations in a 30 minutes period do not exceed preset values, the

93

reference is updated with the new average. Otherwise, if the variance or variation

exceeds these thresholds, the reference obtained in the previous 30 minutes is

used.

Figure 28 – Satellite movement

In the method just presented, the determination of the thresholds is site

specific and not easy. Besides it, in some rare cases a rain event can be masked.

The solution created at ONERA, improved and used with Brazilian data for this

work, approaches the problem in a different way: the large scale behavior of the

time series is mapped by a curve describing the nominal level at each point. The

tool, depicted in Figure 29, can be summarized in the following steps:

94

1. Presentation, in the interface, of the daily received signal time series

together with the rain rate time series, when available.

2. Graphical definition, via the user interface, of the data intervals to be

considered or to be eliminated in the large scale mapping of the time

series. As the goal is to retrieve the nominal signal level, rain events

should not be left to be mapped otherwise they would be masked. An

example is marked in red in Figure 29.

3. Decision of the technique, between polynomial and Fourier fit.

− Polyfit: based on the shape and degree of oscillations of the time

series, the user chooses the order of a polynomial to be fitted. The

polynomial coefficients are computed considering just the signal

levels corresponding to the selected subset of the time vector. Finally,

the polynomial is evaluated for all points in the time series, being

plotted in the interface. Although polyfit can give good results, in

more complex templates it fails.

− Fourier: also based on the general shape of the time series, the user

chooses the number of frequencies for a fast Fourier transform (FFT).

To perform the FFT, some steps are necessary: interpolation of the

selected portion of the time series in order to have all data values

sampled at the same rate (this process is reverted at the end of

template assessment); linear correction of the time series to make

initial and final power levels the same, otherwise the FFT routine does

not perform well because the theory requires the signal to be periodic.

This correction is also reverted at the end, just before reverting the

interpolation. The current version of the tool works well even in the

existence of gaps (data holes) in the series. Usually, less oscillatory

time series are well resolved using around eight frequencies. For more

complex ones, twenty or even more is a good number.

4. At this step, the template is assessed. After converting its values to the

original resolution of 0.1 dB, it is plotted in the interface for user

inspection. If the user validates the template definition, the last task is

performed: subtraction of the original time series from the template. The

result is the attenuation time series expressed with positive values, in dB.

95

5. This process is performed for every single day, generating daily .mat

files with two columns: time stamp (in seconds) and the attenuation

value (in dB). To reduce processing time and also to make a more

precise template extraction in the cases when a rain event spans

midnight, this version allows for the treatment of two joined days at a

time, saving them as two separate files afterwards.

Figure 29 – Example of use of the tool for template removal of received signal time

series

In the left plot of Figure 29, it is presented the received signal time series

concurrently with rain rate time series. At right in the same figure, the lower plot

is the final attenuation time series, after template removal (i.e. after subtraction of

the received signal time series from the detrending curve plotted in cian).

Still regarding template extraction, Figure 30 highlights an example to show

how tricky and error inducing some cases can be. In the left plot, the rain rate time

series totally correlates with the one of received signal, remaining no doubt that

the shape of the power level during the event is mainly due to rain attenuation. On

the other hand, in the right plot, although received signal returns to nominal level

with a shape quite similar to the one verified in the left, rain gauge measurement

indicates no rain at that time. Therefore, based on the fact that both situations

occur in the same site (Curitiba), at a just moderate inclination (60o), and also

considering that the left plot clearly shows how a typical end-of-event shape can

be, it is highly probable that the event on the right plot is of the same kind, with

the difference that the rain event ended first in the rain-gauge location but

continued somewhere else along the Earth-satellite link.

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Figure 30 – Importance of concurrent rain rate and received signal time series plot

An useful way to check the performance of the detrending process is to

construct an histogram of the attenuation values in the entire period of the rain

attenuation time series. For each single day, it is expected that the most frequent

value is zero dB, indicating that clear sky oscillations are uniformly distributed

around the null attenuation value. A faulty template extraction would generally

cause an offset for the clear sky instants of time. This check was done for every

site and the results showed that, from the offset generation point of view, the

detrending task was successful. For the entire period in each site, the number of

days having offset different from zero, as well as the most frequent value, are

given below.

− Curitiba: no days with offset different from zero

− Mosqueiro: one day (-0.1 dB)

− Porto Alegre: one day (-0.1 dB)

− Rio de Janeiro: no days with offset different from zero

From these results it can be concluded that, for every case with offset

different from zero, the mapping of the large scale (low frequency) attenuation

made by the use of FFT/IFFT in the raw beacon time series was offset by just one

resolution step (0.1 dB), which is acceptable specially after verifying above that

these occurrences were very rare.

Table 4 presents the final definition of periods for the four sites used in this

work. The most important site characteristics as well as up-times are also shown.

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Site Coordinate

(degrees)

Altitude

above sea

level (m)

Link

inclination

(degrees)

Climate Data intervals

Mosqueiro (MOS) Lat: -1.11

Lon: 311.57 24 89.0 Equatorial

09/96 – 08/97 (ut = 88.9 %)

11/97 – 10/98 (ut = 84.6 %)

Rio de Janeiro (RIO) Lat: -22.92

Lon: 316.50 30 63.0 Tropical 03/98 – 02/99 (ut = 89.3 %)

Curitiba (CUR) Lat: -25.42

Lon: 310.72 915 60.0 Subtropical 03/98 – 02/99 (ut = 74.2 %)

Porto Alegre (POA) Lat: -30.05

Lon: 308.83 70 55.0 Subtropical 05/98 – 04/99 (ut = 86.4 %)

Table 4 – Brazilian beacon data used in the study

4.4. Extraction of rain attenuation events

The extraction of isolated events from the rain attenuation time series is

necessary for some reasons, listed below.

− Creation of the data structure to be used in the microscopic portion of

the two-state Markov chain channel model (see Section 3.4.3.4 and

Appendix A). The structure is generated by putting the three relevant

characteristics to the MKod microscopic model – the duration,

maximum attenuation and instant of the maximum attenuation – in an

organized disposition for input to the on-demand generation of rain

events.

− Determination of the probability of rain, p1 . It is shown in Section 4.6

that the use of isolated experimental events to the computation of this

parameter leads to a much more precise result to be used as input to the

macroscopic portion of the two-state Markov chain channel model. In

the case of the long-term channel models based on the Maseng-Bakken

theory, the use of the p1 parameter computed by extracted events –

instead of directly from the long-term attenuation time series – does not

modify the final result in statistics in an important way. In fact, the

choice of a different value for p1 impacts in two ways the determination

of input parameters for these models: the limiting percentage of time for

lognormal fit on the attenuation CCDF; and the value for Aoffset . For the

four analyzed Brazilian sites, the differences were marginal.

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− Correction of the original attenuation time series. In order to eliminate

the oscillation – not due to rain – in the instants of clear sky, isolated

extracted events are used, as explained in Section 4.6. This third reason

is directly linked to the previous one because the determination of p1 is

made from the new attenuation CCDF obtained after correction of the

original times series by the use of the extracted rain attenuation events.

− Testing of the physical soundness of the isolated events. An “event-

based” methodology (refer to Section 5.2) is used for these tests.

A technique must be created to identify and extract rain attenuation events.

In order to be able to develop a semi-automatic tool, a common approach has to

be defined to detect events and to approximate their length, for proper extraction.

Two methodologies were developed in the course of this work: a fully automatic

one and a semi-automatic one (requiring user intervention).

4.4.1. Fully automatic tool for events extraction

Basically, to extract events in a fully automatic fashion, it is necessary to set

a threshold level to detect events, named detection threshold. This threshold is the

attenuation level above which almost every attenuation occurrence is due to rain.

As the interest is to retrieve just the effect of rain, low-pass filtering is

necessary prior to events extraction. Cutoff frequency is 0.025 Hz, considered in

the literature [9] – [12] a typical value above which the spectrum of attenuation

starts to be highly influenced by atmospheric scintillation. The filter used is of

squared cosine type, the same adopted for the computation of statistics. The filter

is similar to a moving-average one, but before averaging it multiplies the samples

by a cos2-shaped function. The results of analysis reported in [16] show that the

effective time length to be used in such filter should be 0.719/fc , where fc is the

cutoff frequency.

Another option would be the use of a Butterworth filter (5th

order is

appropriate), which provides the flattest possible shape (no spikes) for the passing

band. In order to be consistent with the validated work already done for temperate

climate (and so to be able to compare results in the same basis) and also because

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of an artifact presented by the Butterworth filter (highlighted in Figure 31, where

the plot in the left leads to a huge discontinuity), it was decided to keep the

squared cosine filter for every filtering task in this work.

For the adopted methodology, based on a summarized description presented

in [18], two attenuation thresholds must be defined: detection and definition

thresholds. The first one indicates that an event exists and therefore it should be a

level above which almost every attenuation occurrence is due to rain; after

detected, the definition threshold defines both ends of an event.

To find an event, the function parses the attenuation time series storing the

blocks of occurrences of values greater than the detection threshold. For each

block, the function goes left and right until it crosses the definition threshold for

the first time, completely defining the event. Both thresholds are user input to the

function and so the appropriate choice must be made with care. A bad choice of

definition threshold would extend the attenuation event to outside the duration of

the rain or cut the event before the rain finishes. Comparison with rain events

extracted from rain rate time series computed for a location with high inclination

(high correlation between rain-gauge and beacon measurements) is useful to get

an insight of a good value. For Brazilian data, the chosen value for the definition

threshold is 0.1 dB. On the other hand, in order to find the most appropriate value

for the detection threshold, one should know the minimum attenuation level which

is certainly caused by rain. To aid in this task, the histogram of occurrence of low

attenuation levels (for all the period of measurements of a site) is plotted, as

exemplified in Figure 32. Analyzing this figure it can be concluded that 0.4 or 0.5

dB are good choices for the threshold because the number of positive (attenuation)

values are much higher than the negative ones, indicating that attenuation in the

long-term time series is not due to clear air oscillation anymore, it is due to rain.

The chosen value for the detection threshold is then 0.5 dB.

The extraction of every event from the ensemble of time series is also an

efficient way to check if all previous steps of data treatment were well done. By

visual analysis of events, the treatment done for faulty DAU logs and the template

removal can be validated, especially for the most critical days. A tool was

designed to make easy the visualization of the non-filtered daily attenuation time

series together with every extracted event in the day (conjugated with rain-rate

time series, when available). Figure 33 presents an example.

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Experimental time series are daily files and so the extraction tool accounts

for the existence of events which encompass more than one file. This is specially

treated in the tool and at this point filtering effects can take place and be an issue.

Therefore, in order to have a smooth transition between two data files for an event

spanning from one day to the next one, whenever it is automatically identified that

this situation will occur, both data files are joined before filtering. This procedure

and the use of the squared cosine filter guarantees that no discontinuity will take

place due to filtering issues.

Regarding the duration of events, the events extraction tool allows for the

definition of the minimum duration an event must have (detailed below) and the

minimum time interval between defined events for them to be considered, in fact,

two isolated events. In fact, variations in the combination of the detection and

definition thresholds and the minimum interval between events can dramatically

change the duration of extracted events. In this work, some studies were done

comparing many combinations of these three parameters. For each specific set of

extracted events, the CCDF of duration of events was compared to the one of

duration of rain events (from rain-gauge measurements). The conclusions are:

− There is no concrete answer to the best combination of the three

parameters as no clear rule could be identified from all the tested

possibilities. Furthermore, the comparison of rain attenuation with rain-

gauge time series should be made with care: it is expected that for higher

frequencies the match between the duration of rain events and rain

attenuation events be closer than for lower frequencies. For low rate

rains (under about 8 mm/h) many times it is not straightforward to tell

apart the attenuation event from the oscillations in the noisy background,

for the beacon frequency of 11.5 GHz;

− From the conclusion in the topic above, it became clear that a better

option for extraction of experimental rain events should be a semi-

automatic one: the automatic algorithm suggests the events but it is

given to the user the possibility of choosing which events to take,

joining and breaking events; every action is supported by the

simultaneous analysis of rain-gauge or radiometer time series, according

to the user choice and availability of the data.

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It is worth to say that all the tests were performed for MOS site, which

presents an almost vertical link inclination to the satellite, a paramount condition

for an analysis based on the correlation between rain-gauge and beacon data.

Since the satellite link inclination is 89o from the horizon line for MOS site, the

capture of rain by the rain-gauge placed just beside the terrestrial antenna is highly

correlated to the occurrence of rain induced attenuation in this radio link.

With respect specifically to the choice of the definition threshold,

comparison between rain rate, attenuation and radiometer time series were done.

In the beginning and ending of rain events, if the verified slope of the radiometer

was much more pronounced than the one of the attenuation time series, maybe it

could be possible to assess the most frequent attenuation value to be used as the

definition threshold. At the end, no useful conclusion could be driven in this

regard and therefore the use of 0.1 dB seemed to be coherent because it is the

resolution of the data and, also, tests in the tail of events have shown that this

choice of threshold did not lead to oscillations which could cause an unreal

prolongation of events (the choice of 0 dB for instance, is much more likely to

produce such undesired effects).

Figure 31 – Preliminary comparison between filters

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Figure 32 – Histogram of low attenuation levels for Mosqueiro

Figure 33 – Tool for events visualization

The tool for automatic events extraction tests the events according to some

characteristics to decide if they are kept or not in the database. Discarding follows

the criteria below:

− Duration less than a given threshold. It is not easy to say if small

duration events are physical or not; also, their identification in the time

series is very sensible to the way the events extraction tool (specially the

thresholds) is implemented. The default value, used for all extractions in

this work, is 1 minute.

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− Bad event definition. After event definition, the first and last attenuation

levels of the event will not be exactly equal to the definition threshold in

most of the cases, due to filtering. So, a linear correction is applied to

the events; this correction should be minimal, otherwise the events can

be deformed. The criterion is: if any of both ends of a defined event has

a value higher than [def thres + (detect thres – def thres)/4], the event is

discarded. For the chosen thresholds, this expression gives 0.2 dB.

Because data resolution (0.1 dB) is good, even this high restrictive value

leads to zero cases of discarding for experimental events and almost zero

cases of discarding for synthesized ones.

− Bad clear sky calibration. Sometimes, the definition of the nominal

received level is not well done. A criterion presented in [18] consists in

the computation of: the ratio between the lowest and the highest absolute

attenuation value in the event; and the percent of time negative

attenuation occurs. If any of both results is higher than 10 % it may

indicate a bad clear sky level definition and the event is separated for

analysis. The occurrence of many cases in the same day or couple of

consecutive days may lead to the re-treatment of the days, including new

template removal. The choice of the minimum time interval between

events greatly impacts this analysis, even for good clear sky level

definition.

− The first detected event of the period under analysis begins with

attenuation level higher than the event definition threshold. This is not

an expected situation but in the case it occurs the event is discarded.

− An event does not finish in the day (spanning event) but next day is

corrupted or missing.

4.4.2. Semi-automatic tool for events extraction

Basically, the same algorithm used for the automatic tool applies here, with

the difference that events are not immediately extracted. Instead, a graphical

interface, exemplified in Figure 34, suggests the events by marking both of their

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ends (red dots in the figure). The interface allows the simultaneous visualization

of rain rate time series or radiometer time series.

After the analysis of the events, the user has the option of performing the

following actions regarding the events: joining/breaking, deleting, creating. Every

action is performed by graphical interaction in the dots defining the events

extremes. The same discarding criteria adopted in the automatic tool are used

here.

Figure 34 – Semi-automatic events extraction

4.5. Computation of the probability of rain attenuation, p1

The interest in the calculation of this probability comes from the fact that it

is important in two steps of the modeling activity: assessment of the Aoffset

parameter (refer to Section 3.2.1.1) and parameterization of the macroscopic step

of the Markovian on-demand model (refer to Section 3.4.1).

In this work, four methodologies for p1 calculation were tried:

− Recommendation ITU-R P.837-5 [31]. This is the ITU-R

recommendation for global rain rate prediction. The relevant output for

this work is the annual percentage of rain on a given coordinate in the

planet.

− Tattelman & Scharr prediction model [44]. The model provides monthly

percentage of rain on a given coordinate in the planet.

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− Experimental beacon data.

− Experimental raingauge data.

Parameter p1 , the probability of rain attenuation in the link, is the lowest

percentage of the time for which the long-term CCDF of experimental rain

attenuation (including periods of rain and clear sky) has null value. I.e., it is the

percentage of the time rain attenuation exceeds 0 dB, directly assessed from the

rain attenuation CCDF.

Although one of the ultimate goals of a channel model intended to be used

worldwide is its ability to be parameterized through the use of global

recommendations (like ITU-R ones), this work is mainly focused in the use of

experimental data to the extraction of the models parameters, leaving for a future

work the comparison of results obtained through the use of input parameters

assessed from global recommendations. Therefore, the last two methods above are

more interesting at this time.

Experimental raingauge data has the advantage of being easily obtained

since the cost of the equipment is generally not prohibitive and installation is

relatively easy; furthermore, the use of raingauge data seems to be appropriate for

the task of computing the probability of rain attenuation, since this equipment

measures exclusively rain. However, equipment precision issues limit the

minimum reliable rain rate measurement: the resolution of the available data was

not enough to allow for the assessment of p1 , which would need an instrument

capable of measuring the very low rain rates, below 1 mm/h (the necessary

extrapolation in the rain rate CCDF to reach 0 mm/h, and then to retrieve the

probability of rain, could give wrong results). Another issue is the fact that it is a

point-rainfall measurement, meaning that rain events occurring outside the

raingauge site would not be accounted. For this reason, computing p1 from

raingauge data would be especially critical for low elevation satellite links:

although the probability of rain in a site and the probability of rain in a link can be

approximated for almost vertical links, it is not the case for the much less inclined

ones.

Recommendation ITU-R P.837-5 provides the probability of rain in a point

in the globe. It would be the most reasonable source for this parameter in the

absence of experimental data, which was not the case. A comparison between the

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p1 value provided by the recommendation with the one assessed from

experimental data, showed a considerable overestimation by the ITU-R, even

considering that ITU-R database is much larger than the periods of measurements

used in this thesis (the years used in this work are not atypical and so it seems that

the verified difference with respect to ITU-R is not due to bad representativeness

of the measured data). Furthermore, the same objection in the use of raingauge

data is found here: ITU-R output comes from point rainfall rate.

Tattelman & Scharr prediction model gives point rainfall rates for some

percentages of the time, but not for p1. In order to compute p1 , the CCDF

obtained from the calculation of lower percentages of the time is extrapolated till

it crosses null rain rate, which gives p1 . The issue in this procedure comes from

the fact that – as for raingauge data – the extrapolation cannot take into account

the transition in the shape of the rain rate CCDF which occurs in the low rain rate

values (this transition tends to be especially noticeable in tropical and equatorial

climates, establishing the rough limit between convective and stratiform rain

events). The implementation of this model was done and global input parameters

were retrieved and adjusted from “Potsdam Atlas” [45] but, for the reason just

presented, its results for p1 were not used.

Besides the issues in the alternative techniques exposed above, the use of

the experimental beacon data for p1 retrieval seemed to be the most appropriate

one also due to the fact that, since the channel models presented in the thesis

generate rain attenuation time series, parameterization using attenuation data is

more natural than by the use of rain data.

4.6. Adjust on the experimental time series based on extracted attenuation events

Although the process of cleaning up the raw data files, as discussed in

Section 4.3.1.3, has led to attenuation time series of good quality, some

improvements were tried. Equipment noise and signal oscillations give rise to

non-zero attenuation levels even in clear sky conditions. For a generally well-

behaved period of time series, these oscillations are in the order of few decimals

of a dB, almost equally distributed between positive and negative attenuation

values. Cases like that could have an effect on modeling, especially at low

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attenuation levels, although it is not expected to be a real issue concerning the

overall performance of the channel models.

However, some occurrences of oscillation are substantially more powerful.

Therefore, the clear sky portion of a period of attenuation time series may be

contaminated by these so-called measurements artifacts, ultimately affecting

parameters extraction for channel modeling as well as the posterior analysis of the

models performance. Thanks to the semi-automatic tool for rain events extraction

(see Section 4.4.2 for further information), many of the false rain events

automatically detected can be manually removed from the isolated events

database through the comparison with concurrent rain-gauge measurements.

Nevertheless, these occurrences remain in the long-term time series, possibly

affecting models parameterization and validation.

The main issues arriving from the oscillatory behavior aforementioned can

be described as being:

− Erroneous identification of rain events. Although it can be largely

minimized by the use of the semi-automatic tool for events extraction,

some false rain events can still remain in the database. Furthermore,

even if it was possible the error-free rain events identification, the

experimental long-term attenuation time series would still suffer from

the problem.

− As a direct consequence of the previous topic, the existence of signal

variations with amplitude larger than a few decimals of dB have an

effect on every dynamics validation (relative number and duration of

fades and fade slope) for the long-term channel models.

− Extraction of the β parameter (refer to Section 3.2 for explanations on

this parameter, related to the reproduction of the rain dynamics). The

first linear adjust for β assessment is made on the attenuation domain.

Small scale oscillations can difficult the choice of the proper attenuation

interval for the linear fit.

− Computation of the percentage of rain. The value of the p1 parameter,

especially important for the MKod channel model, can be sensibly

altered due to the clear sky level oscillations. The CCDF of rain

attenuation is highly sensitive to the quality of the attenuation time series

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at high percentages of time (low attenuation levels). Inferring p1 from

this statistic, through interpolation, can lead to errors which will have a

decisive effect on models whose dependence upon this parameter is

important (MKod model, remarkably).

In order to quantify the problem and to use an experimental attenuation time

series with mitigated measurements artifacts in the lower level attenuation range,

the time series obtained after the data treatment step (Section 4.3.1 presents the

details on this step) passed through a cleaning of clear sky levels. The isolated

extracted events database was used to make zero attenuation every second not

pertaining to an extracted event. The procedure showed to be of relevance for the

determination of the p1 parameter, particularly affecting the macroscopic step of

the MKod model, and for long-term model validation in the low attenuation range

(up to about 2 dB and particularly for the sites whose measurements present

higher oscillatory behavior).

In this work, every task regarding parameters extraction and models

validation used as input experimental time series corrected by the extracted rain

attenuation events.