IntroductionThis is a new fascicle relates to the testing and validation of methods in Recommendations ITU-R P.836 and P.676. It takes information previously available in “Fascicle concerning the statistical distribution of integrated water vapour and liquid water contents given in Recommendations ITU-R P.836-4 and ITU-R P.840-4” and Document 3J/14 relating to the new method for computing the Zenith path water vapour attenuation.

Radiocommunication Study Groups

INTERNATIONAL TELECOMMUNICATION UNION

Source: Document 3J/TEMP/13

Subject: Integrated water vapour statistical distributions and slant path water vapour attenuation prediction

Document 3J/FAS/5-E4 July 2016English only

Working Party 3J

FASCICLE

ON STATISTICAL DISTRIBUTIONS OF INTEGRATED WATER VAPOUR (REC. ITU-R P.836-5) AND THE PREDICTION METHOD FOR WATER

VAPOUR ATTENUATION FOR A SLANT PATH IN REC. ITU-R P.676-10

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FASCICLE ON STATISTICAL DISTRIBUTIONS OF INTEGRATEDWATER VAPOUR (REC. ITU-R P.836-5) AND THE PREDICTION

METHOD FOR WATER VAPOUR ATTENUATION FORA SLANT PATH IN REC. ITU-R P.676-10

Table of contentsAbstract...................................................................................................................... 3

Part 1: Statistical distributions of integrated water vapour (P.836-5)........................ 4

1 Introduction....................................................................................................... 4

2 Review of NWP products and ITU-R Recommendations................................ 5

3 New maps derived from the ERA40 product................................................... 6

3.1 Total columnar water vapour content............................................................... 6

3.2 Ground water vapour density............................................................................ 8

3.3 Water vapour scale height................................................................................ 9

4 Technique for scaling of the total water vapour content to the height of the receiver 10

5 Validation of ERA40 derived maps using RAOBS data.................................. 11

6 Accuracy assessment of the ERA 40 data using ground measurements........... 12

6.1 Comparison between ERA40 and radiometric retrievals................................. 13

7 Probabilistic modelling for ERA40 water vapour............................................ 14

8 Acknowledgments............................................................................................ 16

9 References......................................................................................................... 17

Part 2: Proposed update to the method for water vapour attenuation prediction in P.676-10 19

1 Introduction....................................................................................................... 19

2 The radiosonde observation dataset.................................................................. 19

3 Water vapour attenuation.................................................................................. 20

3.1 The reference methodology.............................................................................. 20

3.2 The simplified ITU-R model............................................................................ 22

3.3 Model refinement.............................................................................................. 23

4 Accuracy evaluation......................................................................................... 28

5 Acknowledgments............................................................................................ 31

6 References......................................................................................................... 31

Overall conclusions.................................................................................................... 32

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AbstractThis document provides useful information on the statistical distributions of integrated water vapour included in Recommendation ITU-R P.836-5 and on a proposed update to the method for water vapour attenuation prediction in Recommendation ITU-R P.676-10. Accordingly, the document is divided in two parts.

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PART 1

Statistical distributions of integrated water vapour (Rec. ITU-R P.836-5)

1 IntroductionThe accuracy of modelling of propagation effects due to atmospheric components depends on the accuracy, the resolution (both statistical and spatial) and the statistical range of applicability of the radio-climatological input parameters, in particular with regard to water vapour, clouds and rain.

Study Group 3 activities put in evidence that the maps derived from long-term global re-analysis products of Numerical Weather Prediction (NWP) systems, provide an improvement of prediction models accuracy, with particular regard to the atmospheric attenuation for radio systems operating at millimetric wavelengths. Hence ITU-R Recommendations initiated to provide NWP derived maps since 1998 [1].

At the same time, NWP systems experienced a fast evolution in terms of period of observation, spatial resolution and quality products, as an effect of an increasing number of Earth Observation systems, better atmospheric models and the adoption improved assimilation and forecast numerical techniques. As a result, new re-analysis products characterized by a longer observation period, higher spatial resolution and increased accuracy of meteorological quantities, have been made available to the scientific community (e.g. ECMWF ERA-15 [2] and ERA-40 [3]).

WP 3J activities also benefited from this trend and in 2007 the Recommendation ITU-R P.837-5 was updated to include maps of rain parameters derived from the ECMWF ERA-40 product [4]. SG 3 also recommended to participants to pursue the analysis of NWP products also for water vapour and cloud attenuation.

The first part of this document describes the new statistical maps of total water vapour and water vapour scale height derived from the ECMWF ReAnalysis project ERA40, in response to the SG 3 work plan. The validation of the new maps has been performed using radiosonde observations from a selected number of stations distributed worldwide.

Measurements of the total water vapour content and of the attenuation due to water vapour performed using ground based radiometer and beacon measurements in the K, Q and V frequency bands in the framework of the ITALSAT experiment, confirmed the improvement of accuracy provided by the ERA-40 derived maps.

Water vapour is characterized by a relevant vertical variation along the atmosphere, therefore the difference between the height of the radio link and the system of reference of the input map of total water vapour should be accounted for and properly scaled, in order to improve the modelling accuracy. This issue can be addressed by introducing an additional climatological parameter, the water vapour scale height whose spatial and statistical distribution can also be derived from NWP products.

The results and the discussion contained in the first part of this document provide the background and the rationale for the modification of the Recommendation ITU-R P.836-3.

This document is divided into the following chapters:• Review of NWP products and ITU-R Recommendations• New maps derived from the ERA40 product

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• Technique for scaling of the total water vapour content to the height of the receiver• Validation of ERA40 derived maps using RAOBS data• Accuracy assessment of the ERA 40 data using ITALSAT campaign ground

measurements• Probabilistic modelling for ERA40 Vapour • Conclusions.

2 Review of NWP products and ITU-R RecommendationsIn this chapter a brief introduction on the use of NWP products in ITU-R SG 3 activities is given. An introduction on general use of meteorological, NWP and experimental data for propagation modelling can be found in [4].

NWP systems generate weather spatial fields at regular interval of times by means of two separate analysis and forecast processes (see Fig. 1 from [1]).

FIGURE 1

Example of NWP data assimilation using a 6 hour cycles

The analysis process assimilates observations (e.g. from radiosonde or satellite observations of the earth) and previous forecast data into a numerical atmospheric model using 3D/4D-Var techniques [6] to produce an estimate of the state of the atmosphere on a regular 3 dimensional grid and fixed intervals of time. The output parameters of this process are also characterized by the reduction of the original instrumental biases at the cost of a reduced spatial and temporal resolution.

Therefore analysis products are intended to provide the best estimate of the atmospheric model even if they can be characterized by issues like the degradation of accuracy results along the land and sea separation.

NWP systems can be distinguished between operational and re-analysis activities. In NWP operational systems improved processes for assimilation, modelling and spatial resolution are regularly introduced to increase of accuracy fields but at the cost of having temporal discontinuities into spatial fields. Therefore re-analysis products, in which all the observations over collected over a long-period (i.e. more than 10 years) are reprocessed using consistent analysis, are usually preferred over operational data for climatological analyses.

Atmospheric profiles of air total pressure, specific humidity and air temperature (P, q and T) are generated by the assimilation process, while parameters related to precipitation are generated by the forecast process.

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The maps provided by Recommendation ITU-R P.836-3 (Annex 2) have been derived from two years (the NA4 ECMWF dataset covering 1992-1993) of initialization data of the numerical weather forecast of the European Centre for Medium-range Weather Forecast (ECMWF). After the NA4 dataset, ECMWF produced two additional complete re-analyses products, the ERA15 [1] and the ERA40 [2]. ECMWF used for every new product new assimilation and forecast procedures and increased the number of input observations, the observation period and the horizontal and vertical resolution of global weather fields. The precipitation data of the ERA40 project have been already used to generate the rainfall map currently described in Recommendation ITU-R P.837-5.

Each product is characterized by its specific accuracy and characteristics, e.g. the land/sea mask, the topography of ground reference levels etc. It is therefore advisable to use for propagation prediction models like the ones described in Recommendation ITU-R P.618-12 a coherent set of input climatological maps, in particular for atmospheric precipitation, water vapour content and cloud liquid content.

The characteristics of the ERA40 dataset used for the maps presented in this document are described in Table 1.

TABLE 1

Main characteristics of NA4, ERA15 and ERA40 ECMWF products used for ITU-R SG 3 activities

NA4 ERA15 ERA40

Period of Observations

1992-1994 1978-1992

1959-2001(Precip Forec)

1985-2000 (P,q,T) Analysis

Horizontal Resolution

(lat long) (deg)1.5 × 1.5 1.5 × 1.5 1.125 × 1.125

Number of model vertical

levels23 31 47

Rec. ITU-R P.836-3840-31510-0

835-4 (Annex 2)834-6 (chap. 6)

837-5

3 New maps derived from the ERA40 product

3.1 Total columnar water vapour content

The maps of the total columnar water vapour content, Vgd (kg/m2) or (mm), have been calculated for the following exceedance percentages of the year: 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, 30, 50, 60, 70, 80, 90, 95 and 99%.

Vgd is relative to the height above mean sea level of the ERA40 grid point, derived according to the Recommendation ITU-R P.1511-1 (Annex 1).

The spatial distribution of the difference and the relative difference of ERA40 total columnar vapour content values with respect to Recommendation ITU-R P.836-3 for 1% of the annual time are given in Figure 2 and Figure 3.

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FIGURE 2

Difference between ERA40 and Recommendation ITU-R P.837-3 total columnar vapour content at 1% of the year

FIGURE 3

Relative difference [%] between ERA40 and Recommendation ITU-R P. 837-3 total columnar vapour

content at 1% of the average year (white pixel indicate values higher than the 50%)

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3.2 Ground water vapour density

The maps of the water vapour density at ground, vapd (g/m3), have been calculated for the following exceedance percentages of the year: 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, 30, 50, 60, 70, 80, 90, 95 and 99%.

vapd is relative to the height above sea mean level the ERA40 grid point, derived according to the Recommendation ITU-R P.1511-1 (Annex 1).

The spatial distribution of difference and relative difference of ERA40 water vapour density at ground with respect to Recommendation ITU-R P.836-3 for 1% of the annual time are given in Figure 4 and Figure 5, respectively.

FIGURE 4

Difference between ERA40 and Recommendation ITU-R P.837-3 water vapour ground density at ground at 1% of the year

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FIGURE 5

Relative difference [%] between ERA40 and Recommendation ITU-R P.837-3 water vapour

ground density at 1% of the average year (white pixel indicate values outof the colour-bar range

3.3 Water vapour scale height

The maps of the values of water vapour scale height, Vsch [, (km), have been calculated for the following exceedance percentages of the year: 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, 30, 50, 60, 70, 80, 90, 95 and 99%.

Samples of water vapour scale height has been derived from simultaneous values of ERA40 total columnar water content and water vapour density using Equation 2 (see section 4).

The map of values of water vapour scale height exceeded for 1% of the year is given in Figure 6.

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FIGURE 6

Spatial distribution of ERA40 water vapour scale height (km) exceeded for 1% of the year

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Water Vapour Scale Height (km) exceeded for 1% of the year

Longitude (degrees)

Latit

ude

(deg

rees

)

-150 -100 -50 0 50 100 150

-80

-60

-40

-20

0

20

40

60

80

4 Technique for scaling of the total water vapour content to the height of the receiver

The distribution of water vapour density the atmosphere, hv (g/m3), can be modelled as a negative exponential of the altitude, h (km), in:

V

gdvgdv h

hhh exp

(1)

where hgd (km) is the altitude above mean sea level of the ground, vgd (g/m3) is the water vapour density at the ground and hV (km) is the scale height of water vapour.

The integrated total columnar water vapour content above ground, Vgd (kg/m2) or (mm), is given by:

Vvgdh V

gdvgdgd hz

hhz

Vgd

dexp(2)

By using Equations 1 and 2 the following relationship can be derived for the integrated total columnar water vapour content, Vh (kg/m2), above a generic height above mean sea level, h (km):

V

gdgd

h V

gdgdh h

hhVz

hhz

V expdexp(3)

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The statistical analysis revealed that in average vgd and Vgd and have a positive correlation so Equation 3 can be used also to derive Vh(P) from Vgd(P), and hV(P) exceeded for the percentage, P (%), of the year :

Phhh

PVPVV

gdgdh exp

(4)

Therefore, considering on one hand the exponential variation of the total columnar water vapour content along the height and on the other hand the need to preserve the original information provided by the ERA40 maps, the spatial interpolation procedure used to derive the total columnar water vapour at the position of the station from ERA40 grid points, has to be performed after scaling in height the ERA40 values of VE40 from hE40 to hst using Equation 4, Vst (kg/m2), located at the position identified by latitude, longitude and height Latst, Longst (deg) and from the values of the total water vapour of the nearest ERA40 grid points, VE40 (kg/m2), located at an altitude above mean sea level hE40 (km).

The detailed procedure to derive the values of total columnar water vapour content above the station, Vst(P), from VE40(P) values exceeded for the percentage of the year P (%), is:1) For each percentage of the year, P (%), and for each ERA40 grid point around the

station calculate the height of the total columnar water vapour content above the mean

sea level PhV stE ,40 , using the following equation:

PhhhPVPhV

EV

EstEstE

40

404040 exp,

where:VE40(P) is the total columnar water vapour content above the height above mean sea

level of the ERA40 grid point, hE40 (km), hV-E40 (km);hv(P) is the water vapour scale height of the ERA 40 grid point exceeded for the P

percentage of the year;hst (km) is the height of station above mean sea level.

2) Derive the total columnar water vapour content above the station, Vst(P) performing a

bilinear interpolation with the values PhV stE ,40 of the nearest ERA40 grid points.

5 Validation of ERA40 derived maps using RAOBS dataThe validation of the new maps derived from ERA40 has been performed by using a dataset of radiosonde observations (RAOBS) performed in 24 stations. Those stations are a subset of the ESA RAOBS FERAS database covering the world for an observation period of 10 years starting from 1980. The FERAS database includes both ground and upper air meteorological measurements and it has been used to generate the reference standard atmospheres described in Rec. ITU-R P.835-4 (Annex 2). The validation stations, listed in Annex 1, have been selected according to data availability and quality selection criteria. The station number reported in Annex 1 is used as station reference in the abscissa of the following diagrams.

The mean and rms of the difference between Recommendation ITU-R P.836-3 (Annex 2), ERA15 data (previously distributed in SG 3), ERA40 and FERAS data are given in Figure 7 and Figure 8.

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FIGURE 9

Mean value of the difference between FERAS RAOBS data and ERA40, ERA15 and Recommendation ITU-R P.836-3 values of total water vapour content

FIGURE 10

rms value of the difference between FERAS RAOBS data and ERA40, ERA15 and Recommendation ITU-R P.836-3 values of total water vapour content

The rms residual error of the ERA40 data is lower than the rms of the residual error of the Rec. ITU-R P.836-3 of a factor 2 (at least) and is characterized by a minimum residual bias (almost 0 vs more than 2 mm).

6 Accuracy assessment of the ERA 40 data using ground measurementsThe testing of ERA40-derived maps of Vtot has been conducted with data collected at Spino d’Adda (latitude 45.4°N, longitude 9.5°E, altitude a.m.s. l. 84 m). The ground station located at Spino d'Adda received since 1993 the signals of the three ITALSAT beacons (at 18.7, 39.6 and 49.5 GHz) with an offset of 3.5 m diameter antenna equipped with de-icing and tracking systems. These signals were coherently detected, sampled at the rate of 1 Hz, stored, edited and analysed off-line by

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the Centro di Studio sulle Telecomunicazioni Spaziali (CSTS-CNR) at Politecnico di Milano. The station was equipped since 1994 with a set of noise injection radiometers at 13.0 GHz, 23.8 GHz and 31.65 GHz to evaluate liquid water and water vapour atmospheric content. A set of traditional meteorological instruments (thermometer, hygrometer, barometer and tipping bucket rain gauge) was also available.

Data from different sources have been exploited. Specifically:• FERAS (FUB-ESA Radiosonde, being FUB the acronym for Fondazione Ugo Bordoni)

radiosoundings provided by the European Space Agency (ESA), which have been derived from a NCAR (National Center for Atmospheric Research) database: vertical profiles of pressure, temperature and relative humidity, collected routinely twice a day (0 and 12 Coordinated Universal Time UTC) for ten years (1980-1989) in non rainy condition at Milano/Linate airport (45.26° N; 9.17° E, 122 m amsl), which is 20 kilometres West of Milano/Linate.

• radiometric measurements: 1-s sampled brightness temperatures collected at Spino d’Adda in the period 1992-2001 by a dual-channel radiometer (23.8 GHz and 31.6 GHz, 37.7° elevation angle) manufactured by Elecktronic Centralen. The instrument was calibrated weekly with the tip curve procedure [2] and once a year with a cold reference load [3]. The radiometric resolution is about 0.1 K and the radiometric precision is estimated to be lower than 2 K. This corresponds to a precision of radiometric retrieval of about 0.1 mm and 3 mm for cloud liquid and total vapour content, respectively.

6.1 Comparison between ERA40 and radiometric retrievals

FERAS RAOBS were assumed as the reference data set for characterizing the non precipitating atmosphere in the Milan area. Vertical profiles of pressure, temperature and relative humidity were used as input to the Liebe MPM93 [5] mass absorption models in order to calculate the specific attenuation at each altitude layer consequently, the total path attenuation due to gases and clouds through simple linear integration along the vertical profile. The profiles of atmospheric specific attenuation were used together with the radiative transfer model (in non-scattering conditions) to simulate sky brightness temperatures at radiometric frequencies and then to derive radiometric retrieval coefficients for water vapour attenuation, AV. As well, water vapour mass absorption coefficients for the radiometric channels have been calculated and are provided for reference in Table 2.

TABLE 2

Oxygen attenuation and mass absorption coefficients zenithal path

Radiom. Channel

23.8 GHz

31.6 GHz

aV (dB/mm) 0.0243 0.009

Figure 9 shows a comparison between the statistical distribution of Vtot: the black curve is obtained from the radiometric measurements according, the back curve with circles is obtained from FERAS RAOBS, while the blue and red curves are obtained from ERA40 map and from Recommendation ITU-R P.838-6, respectively. The ERA15 data (green curve) is also shown. ERA40 and ERA15 values of water vapour content were scaled in height according to the procedure described in section 4.

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Since the radiometric curves can be considered as an independent experimental reference for this climatological parameter, it is clear from Figure 9 that the best accuracy is obtained in Spino d’Adda using ERA40 data. The difference between ERA40 values and radiometric estimate is always lower than the estimated precision of retrieval.

FIGURE 13

Statistical Distribution of Vtot (in abscissa) derived from radiometric measurements (black curve),

FERAS RAOBS (black curve with circles), ERA40 (blue curve), ERA15 map (green curve) and Recommendation ITU-R P.836-3. Probability 1 corresponds to 100% of

annual time

0 5 10 15 20 25 30 35 4010

-2

10-1

100

Total column of water vapour content (mm)

Prob

abilit

y

V RadiometerV FERASV ERA40V ITU-R P.836-3V ERA15

7 Probabilistic modelling for ERA40 water vapourThe development of channel models for total atmospheric attenuation (e.g. synthetic time series generators) requires a probabilistic model for the statistical model distribution of the climatological parameter. Such a model can be derived by regression analysis of NWP tables like the ERA40 maps discussed in this document. It has to be stressed that the probabilistic modelling constitutes actually an additional processing step, in addition to the one originally performed by the NWP system on the actual (scattered) observations and to the spatial interpolation process described in section 4. As such, it can increase the final error of the prediction with respect to the local distribution.

In [7] it has been shown that a Weibull distribution model can be used to describe the statistic of integrated columnar water vapour content provided by ECMWF ERA15:

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kVVVP

** exp)(

(5)

Therefore, the integrated columnar water vapour content is:

kppV1

ln (6)

The coefficients of the Weibull distribution model, k (mm) and derived by least square analysis of ERA40 data are provided in Figure 10 and Figure 11.

FIGURE 10

Spatial distribution of the k parameter of the Weibull distribution derived from ERA40 maps

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FIGURE 11

Spatial distribution of the parameter of the Weibull distribution derived from ERA40 maps

The spatial distribution of the rms error of the Weibull model with respect to the original ERA40 data is provided in Figure 12. The error is higher than the assumed precision of radiometric retrieval (3 mm) is some areas around the tropical and equatorial regions.

FIGURE 12

Spatial distribution of the rms error of the Weibull distribution derived from ERA40 maps with respect to the original ERA40 data

8 AcknowledgmentsThe results presented in this document have obtained in the framework of the ESA contracts 17760/03/NL/JA “Characterisation and Modelling of Propagation Effects in 20-50 GHz band”, 18278/04/NL/US “Assessment of radiowave propagation for satellite communication and navigation systems in tropical areas”, 20046/06/NL/CO “ERA40 Statistical analysis” and

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21317/07/NL/HE “Assessment of Propagation Effects in the W Frequency Band for Space Exploration” and with the support of the EU FP6 SatNex project.

9 References[1] Poiares-Baptista P., Salonen E., 1998: “Review of rainfall rate modeling and mapping”,

Proc. of URSI Commission F Open Symposium on Climatic Parameters in Radiowave Propagation Prediction (CLIMPARA’98), Ottawa, Ontario, Canada.

[2] ERA: ECMWF Re-analysis project report series, “1. ERA-15 Description”, Version 2, January 1999, European Centre for Medium-Range Weather Forecasts.

[3] ERA: ECMWF Re-analysis project report series, “ERA-40 Archive”, December 2002, European Centre for Medium-Range Weather Forecasts

[4] L. Castanet, C. Capsoni, G. Blarzino, D. Ferraro and A. Martellucci, “Development of a new global rainfall rate model based on ERA40, TRMM and GPCC products”, Proceedings of ISAP07, August 20-24 2007, Niigata, Japan

[5] A. Martellucci, “Use and development of climatological and experimental databases for radiowave propagation modelling in SatCom and SatNav systems”, invited paper, Proceedings of 3rd European conference on antennas and propagation, EuCAP 2009, 23-27 March 2009, Berlin, Germany, pp. 2002-2006

[6] Ref. for 3D/4D variational techniques

[7] Jeannin N, L. Féral, H. Sauvageot, L. Castanet (2008): “Statistical distribution of integrated liquid water and water vapour content from meteorological reanalysis”, IEEE Transactions on Antennas and Propagation, 56(10), pp 3350-3355.

ANNEX 1

List of FERAS station used for ERA40 maps validation

Station name

Country code

Latitude (° N)

Longitude (° E)

Altitude(m

a.m.s.l.)Sodankyla FI 67.22 26.39 178

Jokionen FI 60.49 23.30 103Stornoway UK 58.13 353.41 14

Hemsby UK 52.41 1.41 13De Bilt NL 52.06 5.11 2

Uccle BX 50.48 4.21 104Lyon FR 45.44 5.05 240

Berlin DE 52.29 13.25 46Wien OS 48.15 16.22 200

Milan IT 45.26 9.17 107Brindisi IT 40.39 17.57 7

Trapani IT 37.55 12.30 5

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Cagliari IT 39.15 9.03 4Moscow RUS 55.45 37.34 184

Tabuk SD 28.22 36.35 771Delhi IN 28.35 77.12 281

Hong Kong CH 22.19 114.10 65Singapore SR 1.22 103.59 14

Dal-El-Beida AL 36.43 3.15 25Cape Town ZA -33.58 18.36 46

San Diego US (CA) 32.49 242.52 124Denver US (CO) 39.45 255.08 1611

Mexico City MX 19.26 260.55 2231Lihue-On-Kauai US (HI) 21.59 200.39 36

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PART 2

Proposed update to the method for water vapour attenuation prediction in Recommendation ITU-R P.676-10

1 IntroductionThe second part of this document describes a method to improve the accuracy of the simplified method currently recommended by the ITU-R for the prediction of water vapour attenuation at millimeter-wave on Earth-space links (Annex 2, paragraph 2.3 of Recommendation ITU-R P.676-10), which receives as input only the local integrated water vapour content V. The main improvement to such model originates from taking into account the dependence of the water vapour mass absorption coefficient aV on the reference site altitude, which is investigated by taking advantage of an extensive set of radiosonde observations (RAOBS) collected in several sites worldwide and characterized by high accuracy and reliability. Tested against attenuation estimates obtained from mass absorption models coupled with the mentioned RAOBS data, the model’s prediction accuracy turns out to improve significantly with respect to the current Recommendation and to be less dependent both on the operational frequency (1-350 GHz range) and on the considered site.

The model for the prediction of water vapour attenuation, AV, included in Annex 1 of Recommendation ITU-R P.676-10, requires as input vertical profiles of pressure (P), temperature (T) and relative humidity (RH) to take into due account the dependence of the specific attenuation along the profile on pressure and temperature. As such kind of data is not easily retrievable worldwide, the same Recommendation defines a simplified approach in Annex 2 (paragraph 2.3) for the prediction of AV, henceforth referred to as “simplified ITU-R model”, which receives as input only the integrated water vapour content, V, rather than the full atmospheric profiles.

This information document focuses on enhancing the accuracy of such simplified model in the 1-350 GHz frequency range. The main improvement originates from taking into account the dependence of the water vapour mass absorption coefficient aV (lying at the basis of the said methodology) on the reference site altitude, which is investigated by taking advantage of an extensive set of radiosonde observations (RAOBS) collected in 24 sites worldwide and characterized by high accuracy and reliability.

2 The radiosonde observation datasetRadiosonde observations (RAOBS) are of key importance primarily for atmospheric sciences (for example, together with other sensors, they contribute to produce the boundary values to run meteorological forecasts using Limited Area Models), but are also of great usefulness for electromagnetic wave propagation, as they provide high-resolution key information on the state of the atmosphere, from which, in turn, the impact of water vapour and oxygen on millimetre waves can be accurately estimated [1]. In this work, we make use of the extensive set of RAOBS data already presented in part 1 of this document, which is characterized by worldwide coverage, long measurement duration and, most importantly, high accuracy and reliability.

The FERAS (FUB-ESA Radiosonde, being FUB the acronym for Fondazione Ugo Bordoni) radiosounding dataset was assembled by the European Space Agency (ESA), starting from an NCAR (National Center for Atmospheric Research) database. Specifically, it consists of vertical profiles of pressure, temperature and relative humidity, collected routinely twice a day (0 and 12 Coordinated Universal Time UTC) for ten years (1980-1989) in non-rainy condition in 24 sites

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spread across different countries: for convenience, Table 1 summarizes the geographical coordinates and the altitude of the sites where RAOBS data were collected, showing coverage of different climates, e.g. from cold in Finland, to Mediterranean in Italy or to equatorial in Singapore.

A detailed description of the FERAS database can be found in the final report of the COST 255 project [2], which also lists the guidelines according to which all RAOBS data were accurately validated. First, original NCAR quality control marks were taken into account, if present, and, afterwards, plausibility and inconsistency checks were applied. For example: the validity range of ground pressure was set to 700-1100 hPa; RAOBS levels corresponding to inversions of pressure or height values were discarded; the validity range of temperature and dew point temperature was set to 183-333 K for the whole profile. Finally, after this pre-processing, outliers of the time series of integrated parameters such as the total water vapour content were identified and removed.

TABLE 1

Details on the rain rate time series used in this document (geographical coordinates of the raingauge and duration of the experiments)

Station name

Country code

Latitude (° N)

Longitude (° E)

Altitude(m

a.m.s.l.)Sodankyla FI 67.22 26.39 178Jokionen FI 60.49 23.30 103

Stornoway UK 58.13 353.41 14Hemsby UK 52.41 1.41 13

De Bilt NL 52.06 5.11 2Uccle BX 50.48 4.21 104

Lyon FR 45.44 5.05 240Berlin DE 52.29 13.25 46

Wien OS 48.15 16.22 200Milan IT 45.26 9.17 107

Brindisi IT 40.39 17.57 7Trapani IT 37.55 12.30 5

Cagliari IT 39.15 9.03 4Moscow RUS 55.45 37.34 184

Tabuk SD 28.22 36.35 771Delhi IN 28.35 77.12 281

Hong Kong CH 22.19 114.10 65Singapore SR 1.22 103.59 14

Dal-El-Beida AL 36.43 3.15 25Cape Town ZA -33.58 18.36 46

San Diego US (CA) 32.49 242.52 124Denver US (CO) 39.45 255.08 1611

Mexico City MX 19.26 260.55 2231Lihue-On-Kauai US (HI) 21.59 200.39 36

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3 Water vapour attenuation

3.1 The reference methodology

For propagation applications in the mm-wave region, the attenuation due to water vapour can be accurately calculated using mass absorption models such as those proposed by Liebe et al. (MPM93) [3] and by Rosenkranz [4]. Such models take into account the microphysical effects of atmospheric components, including water vapour and oxygen. Both gases cause absorption of the electromagnetic energy due to resonant effects (rotation of the electric and magnetic dipoles) associated to specific peak frequencies (typically referred to as lines). As for water vapour, the specific attenuation depends on pressure, temperature and relative humidity. Specifically, RH is necessary to estimate the water vapour density v, which, in turn, is used together with P and T to calculate the water vapour specific attenuation V. As a result, the accurate calculation of V requires knowledge of the full P, T and RH (or v) vertical profiles, which, in turn, can typically be obtained by exploiting data collected by radiosondes. Given their accuracy, the estimates of gaseous attenuation at millimetre-wave provided by mass absorption models are typically considered as the reference against which prediction models are tested.

As an example, Figure 1 shows P-RH-T vertical profiles measured by the radiosonde launched at Milano Linate airport (Figure 1.a), Figure. 1.b) and Figure. 1.c), respectively), as well as the associated profile of water vapour specific attenuation at 22 GHz (Figure. 1.d)) estimated using the MPM93 model (the total path attenuation AV is equal to 0.115 dB).

FIGURE 1

Sample P-RH-T vertical profiles measured by the radiosonde launched at Milano Linate airport, and associated profile of water vapour specific attenuation at 22 GHz

estimated using the MPM93 model [4].

Pressure (hPa)200 400 600 800 1000

Hei

ght (

km)

0

1

2

3

4

5

6

7

8

9

10

Relative humidity (%)0 20 40 60 80

Hei

ght (

km)

0

1

2

3

4

5

6

7

8

9

10

a) b)

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Temperature (°C)-60 -40 -20 0

Hei

ght (

km)

0

1

2

3

4

5

6

7

8

9

10

Specific attenuation (dB/km)0 0.02 0.04 0.06 0.08

Hei

ght (

km)

0

1

2

3

4

5

6

7

8

9

10

c) d)

3.2 The simplified ITU-R model

The methodology outlined in section 3.1 certainly guarantees a high accuracy in the prediction of water vapour attenuation (it lies at the basis of Annex 1 of the current Recommendation ITU-R P.676-10, where all the detailed calculations can be found), but, on the other hand, it is quite demanding in terms of inputs, as accurate high-resolution vertical profiles of the atmosphere can be hardly retrieved on global basis.

In order to address this issue, Salonen et al. proposed in [5] and [6] an approximate method to predict AV, which, instead of making use of full vertical profiles of the atmosphere, receives as input V in mm, i.e. the water vapour content integrated along the path. Specifically, for a zenithal path:

(1)where:

f = frequency (GHz)fref = 20.6 (GHz)

aV (fref) = 0.0173 (dB/mm)Pref = 780 (hPa)hV = 4 (km)

ref = V/hV (g/m3)

Tref = (°C)

specific attenuation in dB/km due to water vapour, calculated using equations (23a)-(23d) in Recommendation ITU-R P.676-10, as a function of frequency f, pressure P, water-vapour density v and temperature T.

The model above was conceived by Salonen et al. [5] by observing that the ratio between the specific water vapour attenuation v at a reference frequency fref = 20.6 GHz and at the target frequency f is approximately equal to the ratio of the path attenuation AV(fref)/AV(f). Specifically, this occurs for a given reference pressure Pref = 780 hPa [6]. It is also worth noticing that the simplified model introduced by Salonen et al. also depends on V through ref: instead of considering the full

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vertical trend of the water vapour content with the height, ref is defined as a sort of “average value”, obtained as the ratio between the integrated liquid water content V (mm) and the so-called water vapour scale height hV (km), which regulates the decay of with height h (G is the water vapour content at sea level expressed in g/m3):

(2)

As a matter of fact, equation (1) offers a simplification to the calculation of AV by proposing an approach based on the concept of mass absorption coefficient [1], which, in the specific case of (1) depends both on f and V (see the right end side of (1)). Finally, it is worth pointing out that, as already noticed in [5] (and confirmed later on in Section 3.3), the model proposed by Salonen et al. relies on the observation that the variation of aV from site to site is fairly limited and generally negligible for the electromagnetic wave propagation applications addressed in this work.

3.3 Model refinement

Though the methodology described in the previous section, adopted in Recommendation ITU-R P.676-10 as well (Annex 2, paragraph 2.3), represents a simplified yet powerful approach to calculate water vapour attenuation, the accuracy of such a method might be restricted by the limited number of data used to tune its main parameters (e.g. the reference pressure Pref and water vapour scale height hV): indeed, to this aim, only one year of radiosonde observations (RAOBS) collected in five European sites were employed and the models’ accuracy was evaluated against the same dataset only for some sample frequencies in the range 12 GHz ≤ f ≤ 50 GHz [5].

In this section, we take advantage of the extensive RAOBS dataset presented in section 2 (24 sites spread worldwide, 10 years of measurements) to propose a refinement of the simplified approach described in Section 3.2, as well as to more extensively test its accuracy on global basis.

The key idea at the basis of (1) is to embed into the water vapour mass absorption coefficient aV the impact on AV of the variation of T, P and RH with altitude. While the latter typically has a fairly irregular trend with height, as exemplified in Figure 1, pressure and temperature are always associated to large negative gradients, such that, for instance, in the first 4 km, the value of P reduces to approximately half of its ground value, and T might decrease of 30 °C. This prompted us to investigate the possible variation of aV as a function of the site altitude using the radiosonde database in Section 2. Specifically, aV was calculated as if the reference RAOBS site lay at a fictitious height a.m.s.l. (h0), which means using as input to the MPM93 model RAOBS vertical profiles whose layers comprised between the sea level and h0 are removed.

Figure 2 shows, for some sample frequencies including the water vapour absorption peak at 22.235 GHz, the variation with h0 of aV*, defined as the ratio between aV(h0) and its value calculated close to the sea level, aV(0). The curves refer to the RAOBS station in Trapani, Italy, but very similar findings for aV* were obtained for all the other sites lying close to the average mean sea level, i.e. those allowing the full investigation of the aV–h0 relationship: according to Table 1, De-Bilt (The Netherlands), Brindisi (Italy), Trapany (Italy) and Cagliari (Italy).

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FIGURE 2

Variation with h0 of aV*, defined as the ratio between aV(h0) and its value calculated

close to the sea level, aV(0). Data from the RAOBS station in Trapani, Italy

Height (km)0 1 2 3 4

a V* =

aV(h

0)/aV(0

)

0.6

0.8

1

1.2

1.4

1.6

f = 20.6 GHzf = 22.235 GHzf = 22.7 GHzf = 23.1 GHzf = 25 GHzf = 26 GHzf = 28 GHzf = 29 GHzf = 35 GHzf = 60 GHzf = 100 GHz

Results in Figure 2 clearly indicate that, for the calculation of water vapour attenuation along the path, the change in aV with h0 is far from being negligible and that the rate of change varies with frequency: the most and less steep trends in the curves are associated to the water vapour absorption line at 22.235 GHz and to f = 20.6 GHz, respectively, while for f ≥ 28 GHz, aV* is fairly independent of the frequency, at least up to 100 GHz. Indeed, the same behaviour occur for the other water vapour absorption peaks which fall around 180 and 320 GHz.

Notwithstanding the marked differences shown in Figure 2, the following power-law expression can be used to accurately model all the reported curves:

for h0 ≤ 4 km (3)

where a, b and c are fitting coefficients. Figure 3 gives a hint of the high accuracy achieved by using (4) to fit the curves in Figure 2 (f = 20, 22.235, 23.1 and 60 GHz). As indicated in equation (3), the validity of the proposed expression is limited to h0 = 4 km: one the one side, most of the ground stations are likely to be installed at altitudes lower than 4 km and, on the other side, as also shown in Figure 1.d), the impact of water vapour reduces considerably for h0 > 4 km.

FIGURE 3

Fitting the trend of aV* with h0 using (4).

Height (km)0 1 2 3 4

a V* =

aV(h

0)/aV

(0)

0.6

0.8

1

1.2

1.4

1.6

Data (f = 20 GHz)Fit (f = 20 GHz)Data (f = 22.235 GHz)Fit (f = 22.235 GHz)Data (f = 23.1 GHz)Fit (f = 23.1 GHz)Data (f = 60 GHz)Fit (f = 60 GHz)

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As a matter of fact, c can be set to 1, as it turns out to be practically independent of the frequency (it ranges between 0.999 and 1.007), while the dependence of a, b on f (the former is reported as an example in Figure 4) can be accurately modelled using the following analytical formulations:

(4)

(5)

The three Gaussian functions in (4) are associated to the three water vapour absorption peaks in the 1-350 GHz range.

FIGURE 4

Trend of coefficient a in (3) with frequency and its fitting expression in (4).

Frequency (GHz)50 100 150 200 250 300 350

Coe

ffici

ent a

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

In the light of the dependence of aV on h0, and taking advantage of the availability of a more extensive RAOBS dataset than that employed in [5], we have investigated the value of aV(fref) in (1), i.e. the water vapour mass absorption coefficient at 20.6 GHz. This was done by using again the RAOBS data collected in the 24 sites. As an example, Figure 5 shows the calculation of aV(26 GHz) using data from Cagliari, Italy, which indicates a very high correlation coefficient of 0.998. Considering that the RAOBS sites listed in Table 1 lie at fairly different altitudes (as shown in the fifth column in Table 1, h0 ranges from 2 to 2231 m a.m.s.l.), all the aV(26 GHz) values where first scaled to the same reference altitude, i.e. the average mean sea level, by using the relationships in equations (3) to (5):

(6)

As a matter of fact, the variation of from site to site turns out to be practically negligible:

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indeed , the mean value of , is 0.0176 and its standard deviation, normalized to , is 1.5%. Thus, accounting also for the dependence of the water vapour mass absorption

coefficient with altitude, equation (1) becomes:

(7)

As is clear in (7), the factor scaling the water vapour mass absorption with the site altitude

( ) is set to 1 for 1 < f < 20 GHz, as in that frequency range the attenuation due to water vapour strongly decreases and the impact of the scaling factor turns out to be negligible.

FIGURE 5

Calculation of the mass absorption coefficient aV at 20.6 GHz using the RAOBS data collected

in Cagliari (MPM93 model)

The final elements investigated to refine the model in (1) are the reference pressure Pref and average water vapour scale height hV, respectively set to 780 hPa and 4 km in Annex 2 of Recommendation ITU-R P.676-10. As a matter of fact, both values are effective parameters: in this work they were derived using an optimization procedure aiming at maximizing the agreement between AV values calculated from the RAOBS dataset and the MPM93 model at frequencies in the range 1-350 GHz and path attenuation predictions obtained by applying (7) (V inputs extracted from RAOBS data as well). As a result, the following values were identified:

(8)

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As a final remark, only half of the 24 sites were selected (uniformly across the Globe) to derive Pref and hV in (8), while the remaining locations were employed only to perform independent tests on the model’s prediction accuracy (see Section 4).

Figure 6 and Figure 7 give a hint of the dependence of on the integrated water vapour content V and on site altitude h0: while the discrepancies in the former figure are fairly limited, the impact of h0 is definitely significant.

FIGURE 6

Trend of the water vapour mass absorption coefficient with frequency, for different values of V and fixed h0

Frequency (GHz)0 20 40 60 80 100

a V(f,

V,h 0) (

dB/m

m)

0

0.01

0.02

0.03

0.04

0.05

0.06

V = 5 mm and h0 = 0 km

V = 20 mm and h0 = 0 km

V = 40 mm and h0 = 0 km

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FIGURE 7

Trend of the water vapour mass absorption coefficient with frequency, for different values of h0 and fixed V

Frequency (GHz)0 20 40 60 80 100

a V(f,

V,h 0) (

dB/m

m)

0

0.01

0.02

0.03

0.04

0.05

0.06V = 10 mm and h0 = 0 km

V = 10 mm and h0 = 1 km

V = 10 mm and h0 = 2 km

4 Accuracy evaluationThe accuracy of the new expression proposed in (7) and (8) to estimate the water vapour attenuation along the path is assessed here against the complete set of RAOBS measurements introduced above. Figure 8 shows an example of the zenithal water vapour attenuation statistics (Complementary Cumulative Distribution Function, CCDF) at 80 GHz calculated according to the MPM93 model using as input the whole P-RH-T profiles, the expression in (7) and the Annex 2 of Recommendation ITU-R P.676-10, i.e. expression (1) (RAOBS data collected at Sodankyla, Finland).

The methods’ prediction accuracy is quantified by the average (E) and root mean square (RMS) values (also reported in the legend of Figure 8) of the following error figure (typically suggested by ITU-R in Recommendation ITU-R P.311-15 to compare tropospheric attenuation statistics):

(9)

where AV*(P) and AV(P) are the water vapour attenuation values extracted from the estimated and

reference attenuation statistics, respectively, relative to the same probability level P ≥ 0.05%.

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FIGURE 8

Zenithal water vapour attenuation CCDF at 80 GHz calculated according to the exact method (black solid line), the new approximate expression in (7) (gray line with

circles) and Annex 2 of Recommendation ITU-R P.676-10 (gray line with squares) for the RAOBS data collected at Sodankyla, Finland

Attenuation due to water vapor (dB)0 0.2 0.4 0.6 0.8 1 1.2

Pro

babi

lity

10-2

10-1

100

MPM93New expression (RMS = 1.5, E = -1.4)ITU-R (RMS = 6.8, E = -6.7)

Figure 9 gives a summary of the accuracy of the method by reporting the mean E (E) and mean RMS (RMS) values as a function of frequency. Results indicate a very accurate prediction performance (overall RMS = 5.1), which is fairly constant with frequency. The ITU-R method shows a lower accuracy (overall RMS = 7.4) with a tendency to underestimation and a slight dependency on the frequency. Figure 10 completes the prediction models’ assessment by reporting RMS as a function of the site. It is worth clarifying that the results in Figures 9 and 10 have been obtained by using as input to both models (the new expression in (8) and to the prediction method included in Recommendation ITU-R P.676-10) V values extracted from Recommendation ITU-R P.836-5, i.e. exactly a user would do.

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FIGURE 9

Mean E (E) and mean RMS (RMS) as a function of frequency (average over all stations). V inputs extracted from Recommendation ITU-R P.836-5

Frequency (GHz)50 100 150 200 250 300 350

App

roxi

mat

ion

erro

r (%

)

-4

-2

0

2

4

6

8

10

E ITU-R (mean = -2.5%)

E new expressions (mean = 0.3%)

RMS ITUR (mean = 7.4%)

RMS new expression (mean = 5.1%)

FIGURE 10

Mean RMS (RMS) as a function of the RAOBS site (average over all frequencies). V inputs extracted from Recommendation ITU-R P.836-5

Station number1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

App

roxi

mat

ion

erro

r (%

)

-10

-5

0

5

10

15

20E ITU-R (mean = -2.5%)

E new expression (mean = 0.3%)

RMS ITU-R (mean = 7.4%)

RMS new expression (mean = 5.1%)

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5 AcknowledgmentsDr Martellucci, from the European Space Agency, is acknowledged for the provision of FERAS radiosonde data.

6 References[1] L. Luini, C. Riva, C. Capsoni, A. Martellucci, “Attenuation in non rainy conditions at

millimeter wavelengths: assessment of a procedure,” IEEE Transactions on Geoscience and Remote Sensing, pp. 2150-2157, Vol. 45, Issue 7, July 2007.

[2] COST Action 255 Final Report, “Precipitation, Clouds and Other Related Non-Refractive Effects,” J. P. V. Poiares Baptista, Ed. Noordwijk, The Netherlands: ESA Publication Division, ch. 3.2.

[3] H. J. Liebe, G. A. Hufford, M. G. Cotton, “Propagation modeling of moist air and suspended water/ice particles at frequencies below 1000 GHz,” in Proc. AGARD 52nd Spec. Meeting EM Wave Propag.

[4] P. Rosenkranz, “Water vapour microwave continuum absorption: A comparison of measurements and models,” Radio Sci., vol. 33, no. 4, pp. 919–928, Jul./Aug 1998.

[5] E. Salonen, S. Karhu, P. Jokela, W. Zhang, S. Uppala, H. Aulamo, S. Sarkkula, “Study of propagation phenomena for low availabilities,” Helsinki University of Technology Radio Laboratory and Finnish Meteorological Institute, Finland, Final Report for the European Space Agency under ESTEC contract 8025/88/NL/PR, Nov. 1990.

[6] E. Salonen, S. Karhu, S. Uppala, R. Hyvönen, “Study of improved propagation predictions,” Helsinki University of Technology Radio Laboratory and Finnish Meteorological Institute, Finland, Final Report for the European Space Agency under ESTEC contract 9455/91/NL/LC(SC), Dec. 1994.

Overall conclusionsTests conducted on an extensive global RAOBS database covering different climates have shown that the statistics of integrated water vapour content obtained from the ERA40 database are more accurate than those extracted from the ERA15 dataset. This translates into an improved prediction accuracy delivered by the method included in Annex 2 of Recommendation ITU-R P.676-10 for water vapour attenuation estimation. This outcome is confirmed by an additional test involving integrated water vapour statistics derived from radiometric data. Moreover, for the purpose of using probabilistic models for channel dynamics (e.g. synthetic time series generators), analytical functions and input statistical parameters can be used to reproduce the original statistical distribution of integrated water vapour content at the expense of a residual error which is comparable to the current instrumental accuracy.

The methodology presented in the second part of this document represents an interesting chance to improve the accuracy of the simplified model currently included in Recommendation ITU-R P.676-10 (Annex 2) for the prediction of water vapour attenuation at millimeter-wave on Earth-space links. Taking advantage of the same set of RAOBS data mentioned above, the key model’s improvement over the current method originates from introducing the dependence of the water vapour mass absorption coefficient aV on the reference site altitude h0. In addition, two effective parameters, namely the “average” water vapour scale height hV and the reference pressure level Pref, are updated to 3.67 km and 815 hPa, respectively. The improved model shows an excellent accuracy in terms of overall prediction error (average RMS for the current ITU-R model and its improved version equal to 7.4 and 5.1, considering all sites and all frequencies).

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Future additional improvements to the accuracy in predicting water vapour attenuation will come from the use of new global NWP products with finer spatial resolution provided by ECMWF (e.g. the ERA-Interim dataset) or from NCAR.

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