Capsoni, C.; Luini, L.; Paraboni, A.; Riva, C.
Politecnico di Milano, ITALY

At frequencies above 10 GHz one of the most important impairment on radio wave propagation is attenuation due to rain. The fade values of interest depend on the system requirements, ranging from a few dBs for low availability user terminals to some tens of dB for feeder links or gateways. In order to provide to system engineers the information needed for the link design, many statistical prediction models of rain attenuation have been developed and almost all of them make no distinction between the types of precipitation, only few taking into account explicitly meteorological phenomena other than rain frequently encountered along the earth-space path as, for example, the bright band.

This contribution is aimed to present an improved version of the EXCELL rain attenuation model (str-cnv EXCELL), which, analogously to the original one, predicts attenuation through a rain cellular representation of the meteorological environment. The new model computes separately the contributions from stratiform and convective rain described in terms of P(R)s, which were obtained from the yearly P(R) through an algorithm that discriminates between the two different precipitation phenomena. The new model makes use of two different rain heights, derived from ERA-15 database, for stratiform and convective rain respectively. When considering stratiform rain the bright band contribution to attenuation is added. The total predicted attenuation CDF is the combination of the contributions due to both stratiform and convective rain.

The sensitivity of the model to the few input parameters that have to be defined and that are expected to be latitude dependent (the amounts of the rain plateau both for stratiform and convective precipitation that account for the low rain in which rain cells are embedded, the depth of the bright band and the particle medium density within it), has been investigated by comparing predicted and measured attenuation CDF in different parts of the globe and at different frequencies. One example of the comparison is shown in the figure where the measured (black continuous line with point markers) and the predicted attenuation CDFs from the original EXCELL (blue continuous line with circle markers) and the str-cnv EXCELL (red dashed line) are reported (Spino d’Adda, Italy, 49.5 GHz).

Spatial and temporal rain dynamics is a research topic of great interest in several fields including, for example, hydrology, climatology, weather now-casting/forecasting. In the radio propagation context, communication systems using frequencies above about 10 GHz are mainly impaired by rain. This has led to the study and modelling of space-time rain fields in a number of different ways, e.g., assuming regular shapes of rain cells (ellipses or circles, Gaussian or exponential decay functions,...), using fractal methods, etc.

This work describes a new methodology for assessing and characterizing rain cell dynamics from weather radar image (WRI) sequences. WRIs are broken down into three regions: no-rain, stratiform rain and convective rain.

This research problem has been addressed by using a 2-D, 3-state probabilistic cellular automata (CA) to assess rain cell dynamics contained in sequences of WRIs after some good results achieved using a 2-D 2-state CA [1].

The proposed approach, based on [2], has been carried out in the following steps:

* Applying a threshold, Zi, of:

- 23 dBz (1 mm/h) to the WRI sequence to separate the stratiform rain from no-rain.

- 39 dBz (10 mm/h) to the WRI sequence to separate the convective rain from stratiform rain.

* Defining and determining the extent of a neighbourhood (template) to be applied to the WRIs:

- Proposing the limits and structure of the so-called, Master Template (MT).

- Simplifying the MT using a genetic algorithm to find the Best Template (BT) that reproduces the observed rain cell dynamics.

* Establishing a mapping function (CA rule) and making predictions from real images.

* Carrying out a quantitative performance assessment for the obtained rule.

* Applying two morphological operations: area thresholding and gap filling, to improve the resulting image.

The WRIs used in this study were collected by the weather radar of the Spanish Meteorological Office located near A Coruña in the Spanish North-West coast. The WRIs are 240x240 pixels in size with a resolution of 1x1 km2 per pixel and were recorded every ten minutes.

The proposed methodology has been tested for several study cases corresponding to different spatial and temporal scales (see given example in fig. 1). This method seems to capture with fairly good accuracy the dynamical behaviour of rain cells in the study cases, and it also allows extracting information on the advection trend of rain fields from the input space structure (Best Template).

References:

[1] Núñez, A., Pastoriza, V., Mariño,P., and Fontán, F.P., "An Approach for the Modelling of the Dynamics in Individual Raincells Using Cellular Automata", in 'Radiowave Propagation Modelling and Measurements for SatCom and SatNav Systems' ESA Propagation Workshop, 23-25 November 2005, ESA/ESTEC, Noordwijk, The Netherlands.

[2] F.C. Richards, T.P. Meyer, and N.H. Packard, "Extracting Cellular Automaton Rules Directly from Experimental Data", Physica D, vol. 45, pp. 189-202, September 1990.

This paper deals with the analysis of the spatial structure of rain in the Amazon region. This analysis was based on rain gauge and radar measurements carried out in the period from June 2004 to May 2005. Tipping bucket gauges with 0.1 mm capacity and 1 minute integration time and S-band meteorological radars were used in this study. Experimental data presented here are from a research program which was developed under the responsibility of the Military Institute of Engineering (IME) with financial support from the National Scientific and Technological Development Council (CNPq). As depicted in Figure 1, rain gauge and radar stations are co-located, covering all the region of interest.

Fig. 1 – Amazon region – rain gauge and radar networks

The conversion from radar reflectivity to rainfall rate was based on the classical relation Z(mm⁶/m³) = a[R(mm/h)]^b. Parameters a and b were carefully derived to guarantee the accuracy of this formula. Regarding the horizontal distribution of rain, more than 20,000 CAPPI (Constant Amplitude Plan Position Indicator) scans were available in each radar site. Echoes larger than 30.5 dBZ, corresponding to a minimum rain rate around 5 mm/h, were examined. This large sample of precipitation elements, collected at the altitude of 1.5 km from the ground, has allowed to investigate some topics of interest to rain attenuation modeling. In this context, it should be detached the following results: a) The distribution of rain cell size for different values of precipitation rate exceeded over the cell; b) The shape of rain cells and the corresponding rain cell diameter; c) The spatial correlation of rain. On the other hand, the vertical profile of precipitation was studied for different types of rain. In this case, experimental data were taken from RHI (Range Height Indicator) radar images. Emphasis was given to the analysis of rain height in convective rain (showers and deep convection). As expected, radar images have shown that convective rain height is highly variable. This behaviour is a potential source of error when developing a rain attenuation prediction model for slant paths.

Starting from rain rate time series, collected at a site with a rain gauge, the Synthetic Storm Technique can generate rain attenuation time series (useful to design communications satellite systems) at any frequency and polarisation, and for any slant path above about 10°, as long as the hypothesis of isotropy of the rainfall spatial field holds, in the long term. For slant paths of lower elevation angles, and thus longer paths in the troposphere, isotropy cannot hold, especially for rainfall of moderate and medium intensity.

The purpose of the paper is to show that the Synthetic Storm Technique can be applied also to slant paths of very low elevation angle, but with caution and some limits. To this end, we have processed the rain attenuation measurements collected in the years 1999 and 2000, in a 5° and 28km slant path radio link at 44.5 GHz between the top of Pic du Midi (altitude 2865 m) and Lannemezan (altitude 600 m), in the French Pyrénées (experiment known as CELESTE), to obtain the probability distributions of rain attenuation and fade duration. Then we have compared the experimental distributions to those predicted by the Synthetic Storm Technique. We have found that if the rainy path length assumed in the Synthetic Storm Technique modeling is limited to 13~15 km, then, for a large attenuation range: (a) the probability distribution of rain attenuation is well reproduced; (b) the experimental probability distribution of fade duration is well reproduced for fade durations longer than about 10 minutes.

Communication systems operating at higher frequency bands suffer from severe attenuation due to rain, which is highly variable in time and space. However, the temporal and spatial inhomogeneity of rain fields can be exploited to improve the availability of the communication link. Knowledge of rain cell size distribution is relevant for the modelling of earth-space propagation in radio communication. To determine the spatial structure of rain cells, long term rain rate time series can be processed by applying the synthetic storm technique assuming some known value of storm translation speed. The underlying hypothesis is that rain patterns move along a line with a constant speed and that advection is the predominant mechanism to account for the spatial variability of rain-rate. The hypothesis holds when a statistical description of rain structure is required, rather than the exact space distribution of rain. Furthermore, as rainfall patterns move over a rain gauge, it is possible to estimate the horizontal extent of rain cells from the duration of various rain rate thresholds as recorded by the rain gauge if a mean advection velocity of rain cells is assumed.

In this paper, advection velocity is modelled using radar Doppler velocity measurements recorded in Chilbolton England and local wind speed measurements at Brize Norton, some 20 km from the radar location. The distribution of rain cell diameters is then determined by applying the modelled translation velocity. In an alternative approach, the PPI (Plan Position Indicator) radar scans of different rain events were analysed to determine the size distribution of various rain-rate thresholds. The rain cell size distributions obtained using the two methods are compared, and the implications of these results on the configuration of site diversity in earth-space communication systems are discussed.

With increasing capacity requirements by radio transmission services, being associated with the need for higher frequencies (millimeter waves), scattering and absorption by solid (frozen) or mixed phase precipitation particles can no longer be neglected. Though Rec. ITU-R P.530-10 states that, on paths at high latitudes or high altitude paths at lower latitudes, wet snow can cause significant attenuation, little is known on the exact scattering behaviour of individual snowflakes.

Scattering of electromagnetic waves by homogeneous and coated spherical particles composed of isotropic materials can be computed in a mathematically exact way using the conventional Mie-theory or its modifications. However, many frozen particles have non-spherical overall shapes and lack a spherically symmetric internal structure. They exist in a huge variety of shapes and exhibit different mixtures of ice, water and air. Therefore, the ability to accurately compute scattering by non-spherical particles in order to clearly understand the effects of particle non-sphericity on scattering patterns is desirable.

Precipitation particle imaging data were obtained by means of 2D-Video-Distrometer (2DVD) observations, providing individual particles’ front and side views, as well as fall velocities and size distributions. 2DVD precipitation data for different types of solid precipitation were analyzed and ranges for parameters observed with each type were found. In this study a number of representative shapes were modeled in a CAD tool and their scattering parameters exactly calculated by means of a Finite Element Method (FEM) algorithm. Several examples show that, for wavelengths small compared to the particle’s diameter, the scattering parameters of non-spherical precipitation particles can differ significantly from those of equivolumetric spheres.

Sample results are shown here for the backscattering cross section, considering three solid precipitation events (dry snowflakes, ice pellets, rimed graupel). Calculations were carried out for frequencies 5.6, 9.6, 14, 24, 35 and 78 GHz. The results for the three different precipitation types occupy significantly different ranges in backscatter. Future work is planned to obtain results for absorption and forward propagation parameters as well.

Introduction

In this work an N-state Markov Chain Model [1] will be used to generate attenuation time series. The model parameters will be derived from the fade slope statistics of measured attenuation data on point-to-point microwave links. This measurements were performed in Hungary in 2005. In our previous work [2] we showed, that the CCDF (Component Cumulative Distribution Function) of the generated time series estimated well the CCDF of the measured data. In this contribution our goal is to show, that the second order statistics i.e. fade duration or level crossing rate of the measured data can be also estimated quite well with this presented N-State Markov chain model. Results on fade duration and level crossing statistics calculated analytically from the model parameters and from the measurement will be compared.

The Considered Markov Chain model

Our considered Markov Chain Model applies quite fine resolution of the generate time series in term of attenuation and the number of states. The model is dependent for the maximum attenuation occur on the modeled microwave connection. The state transition probability parameters of the model can be determined from fade slope statistics of measured attenuation based on the Gaussian fade slope model [2].

Previous results on comparison the CCDF of the generated time series and the measured data are depicted on Fig. 1. In this case the data measurement was performed in HU11 terrestrial microwave link in Hungary. Please observe the two CCDFs are really very similar.

Second Order Statistics of The Generated Time Series

In order to profusely compare the generated and the measured time series second order statistics of attenuation must be also examined besides the CCDF of attenuation. Fade duration gives the length of the time interval during which attenuation exceeds a given threshold, while level crossing rate defines how often the signal envelope crosses a certain threshold with positive (or negative) fade slope. These second order statistics of the generated time series will be determined directly from the transition probability parameters of the presented Markov Chain model. In this contribution a comparison will be given of second order statistics of the measured data and of the generated time series. We expect, that fade duration statistics and the level crossing rate of the generated time series will estimate the statistics of the measured data well applying our method for determine the transition probability parameters of the N-State Markov Chain model based on the Gaussian fade slope assumtions.

Acknowledgement

This work was carried out in the framework of IST FP6 SatNex NoE project and supported by the Mobile Innovation Center, Hungary.

References

[1]L. Castanet, T. Deloues, J. Lemorton, "Channel Modeling Based on N-State Markov Chain for Satcom Systems Simulation", ICAP 2003 Conference, Exeter, UK, pp 119- 122, April 2003

[2]Balázs Héder, János Bitó, "General N-state Markov Model Applicable for Attenuation Time Series Generation Parametrised from Gaussian Fade Slope Model", WSEAS-EHAC 2006 Conference, Madrid, Spain, February 2006

Fade duration is one of the most important dynamic aspects of path attenuation that corresponds to the time length during which a fixed threshold is exceeded by path attenuation. Similarly, to characterize the periods of time between two fades, the statistics of interfade duration can be used. The estimation of the fade and interfade duration parameter is essential in the design process of different wireless communication systems.

In this paper we are presenting a digital model with an N-state Markov chain for the statistical prediction of fade and interfade duration at different attenuation levels. The proposed Markov model is able to generate the stochastic fade and interfade duration time process beside the accurate prediction of the distribution functions according [1] and [2]. The model is a partitioned Fritchman’s Markov chain where the elements of the state transition matrix and the steady state probabilities can be determined by linear regression of the logarithmical complementary cumulative distribution function of a real measurement fading statistics. The parameterized Markov chain can be applied to model the CCDF of fade and interfade durations.

The parameter set of the digital model has been derived from the fading statistics of a high frequency radio link. According to [3] the modeling of fade and interfade durations are showing a good agreement with the original measurement data as Fig. 1 and 2 depicts.

Our results published in [3] shows that the Markov model of fade duration can not be used for interfade duration modeling and vice versa. The new and modified Markov model introduced in this contribution helps to create a joint modeling method the two dynamic aspect of the radio channel.

References:

[1] János Bitó: "Digitale Mobilfunk-Kanalmodelle unter besonderer Berücksichtigung von adaptiven digitalen Modellen", (Modelling of digital mobile radio channels with special emphasis on adaptive digital channel models), Dissertation, Technische Universität Berlin, 1996.

[2] László Csurgai-Horváth, János Bitó: "Fade Duration Modeling with Partitioned Markov Model", ESA Wave Propagation Workshop, Noordwijk, Netherland, November 2005

[3] László Csurgai-Horváth, János Bitó: "Fade Duration Modeling of Satellite Links Applying Markov Chain", ASMS 2006, Herrsching am Ammersee, Germany, May 2006 (accepted paper)

[4] Laurent Castanet, Thierry Delouses, Joël Lemorton, "Channel Modelling based on N-state Markov Chains from Satcom Systems Simulation", ICAP 2003, Exeter, United Kingdom, April 2003.

[5] Paraboni, A. and C. Riva (1994): "A new method for the prediction of fade duration statistics in satellite links above 10 GHz", Int. J. Sat. Com., 12, 387-394.

Experimental research in the Department of Microwave Communications in TESTCOM is focused on the stability of a received signal on terrestrial radio and optical paths. Hydrometeors, i.e. rain, snow, hail, and fog as well as their possible combinations can cause serious attenuation of electromagnetic waves in the frequency bands over 10 GHz. Attenuation due to rain on terrestrial path can be calculated from measured rainfall intensities with an integration time of 1 min (average 1-minute rainfall intensities) according to Rec. ITU-R P.530-11. Therefore, our experimental research is also focused on measurement of rainfall intensities.

One siphon raingauge and two tipping-bucket raingauges with different collecting areas are used for the measurement of rainfall intensities. Rainfall intensities have been measured since February 1992 by means of a heated siphon raingauge having the collecting area of 250 cm². Since December 2002, rainfall intensities have also been measured by means of another two heated tipping-bucket raingauges. One of them has the collecting area of 500 cm², and the rain amount per one tip is 0.1 mm. The other one has the collecting area of 200 cm², and the rain amount per one tip is 0.2 mm. These three raingauges are located very close to each other to avoid the influence of space inhomogeneity of rainfall events. Since June 2003, rainfall intensities have also been measured by means of a rain detector which is integrated into the Present Weather Detector PWD11 of the VAISALA equipment. All rainfall intensity data are recorded.

It is generally known that higher rainfall intensities measured by tipping-bucket raingauges are overestimated. Therefore, both tipping-bucket raingauges and the heated siphon raingauge will be dynamically calibrated by flowmeters in early spring 2006. The used method of dynamic calibration of tipping-bucket raingauges and our experience obtained will be described. Data obtained from these three dynamically calibrated raingauges and from the rain detector will be statistically processed at least over one month period. The methods of rainfall intensity data processing will be described. The cumulative distributions of average 1-minute rainfall intensities obtained from individual tipping-bucket raingauges, with and without dynamic calibration involved, will be presented. The results obtained will be compared and discussed.

The radio spectrum is a finite resource, and is becoming increasingly congested. In the UK, this has prompted a number of studies investigating methods of improving spectral efficiency and opening up higher frequencies (10 GHz and above) to commercial exploitation.

Current systems operating at frequencies above 10 GHz allocate a fixed fade margin to compensate for the attenuating effects of rain, clouds and atmospheric gases. However, as the operational frequency of radio systems increases, the fade margin also increases until it is no longer economical, practical, or spectrally efficient.

Rain is the dominant attenuator for frequencies above 10 GHz. Some methods proposed in the literature to compensate for the effects of rain fading rely on the spatio-temporal inhomogeneity of rain fields for their effective operation. Correctly configuring systems that can dynamically compensate for rain fading requires a detailed knowledge of spatial and temporal rain field variation. Ideally, this would be provided by a database of meteorological radar measurements. Unfortunately, such data is scarce, and often does not achieve the spatial and temporal resolutions required for accurate radio channel modelling.

Alternatives to radar measurements are methods for simulating rain fields in time and space. Some published methods use fractal techniques, as the fractal nature of rain has been extensively studied in past years. Fractal methods can be used to analyse and synthesise the spatial and temporal variation of rain fields, producing visually and statistically realistic synthetic rain fields. These simulated fields may be customised for different climactic regions, converted to simulated attenuation time series, and then applied to communications engineering scenarios where measured data is not available.

This paper discusses a monofractal, additive (in the logarithmic domain) discrete cascade model for simulating rain fields in two spatial dimensions. Further modification allows extension into a third spatial dimension, or a temporal dimension. The model produces events-on-demand, customised to an input rain rate parameter and desired rain event type (stratiform or convective). In order to test the long term statistics of a proposed radio system, simulated rain field datasets are required which will reproduce the annual rain statistics for the average year. A method to convert from a set of single events into a set capable of reproducing annual statistics is presented in this paper.

Acknowledgement: The research presented in this paper was funded by the UK' s Ofcom as part of the Spectrum Efficiency Scheme.