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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 12, 2013
1-Minute Integrated Rain Rate Statistics Estimated From Tropical Rainfall Measuring Mission Data Nor Azlan Mohd Aris, Lorenzo Luini, Jafri Din, Member, IEEE, and Hong Yin Lam, Student Member, IEEE
Abstract—This letter presents a new model for the prediction of the 1-min integrated complementary cumulative distribution function (CCDF) of the rain rate, , valid for tropical and to equatorial regions (specifically, latitudes ranging from 35 35 ). The proposed model inherits its analytical formulation from the method currently recommended by the International Telecommunication Union—Radiocommunication Sector (ITU-R) for global prediction (Annex 1 of recommendation P.837-6), but it relies on Tropical Rainfall Measuring Mission (TRMM) data, in place of the ERA40 database, for the extraction of the required local meteorological inputs. With respect to the ITU-R model, the proposed model requires a lower number of inputs (two instead of three) and, in addition, it shows a better prediction performance when tested against the experimental curves (tropical/equatorial sites) included in the global DBSG3 database of ITU-R. Index Terms—1-min integrated rain rate statistics, equatorial, radiowave propagation, tropical, Tropical Rainfall Measuring Mission (TRMM).
I. INTRODUCTION
T
HE MAJOR impairment to radiowave propagation at frequencies above 10 GHz is rain attenuation, for the prediction of which accurate knowledge of the 1-min integrated complementary cumulative distribution function (CCDF) of the rain rate (henceforth ) is required, as recommended by the International Telecommunication Union—Radiocommunication Sector (ITU-R) [1]. However, measured data are not easily retrievable worldwide because raingauges with much longer integration time are commonly deployed for meteorological purposes [2]. In order to overcome such limitation, several prediction methods have been proposed so far. On one side, conversion models, whose aim is to estimate from the knowledge of rain rate CCDFs with longer integration time (e.g., h), provide the best prediction accuracy [3]; their main drawback is that, as mentioned above, they require as input full local Manuscript received October 24, 2012; revised November 24, 2012; accepted January 22, 2013. Date of publication January 25, 2013; date of current version March 12, 2013. This work was supported by the Universiti Teknikal Malaysia Melaka (UTeM) and the Ministry of Higher Education (MoHE). N. A. Mohd Aris is with the Department of Telecommunication, Faculty of Electronic and Computer Engineering, Universiti Teknikal Malaysia Melaka (UTeM), 81310 UTM Skudai, Malaysia (e-mail:
[email protected]). L. Luini is with the DEI, Politecnico di Milano, 20133 Milan, Italy (e-mail:
[email protected]). J. Din and H. Y. Lam are with the Department of Communication Engineering, Faculty of Electrical Engineering, Universiti Teknologi Malaysia (UTM), 81310 UTM Skudai, Malaysia (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/LAWP.2013.2243103
rainfall rate statistics with coarse integration time. On the other side, meteorology-based methods rely on analytical models of the whose tuning parameters are directly dependent on general meteorological information to be provided as input. The most acknowledged model of the latter kind, included in Annex 1 of recommendation ITU-R P.837-6 [1] (henceforth simply referred to as “ITU-R model”), allows global prediction from the knowledge of the local convective and total mean yearly rain accumulations, and of the probability to have rain in a 6-h time interval . In turn, these values are extracted from the ERA40 database, made available by the European Centre for Medium-range Weather Forecast (ECMWF) [4], which, notwithstanding its global coverage and statistical stability, represents the main source of inaccuracy of the current ITU-R recommendation. In fact, its prediction performance is reduced on one side by the poor spatial resolution of the ERA40 database (1.125 1.125 latitude/longitude grid) and on the other side by the limited accuracy of the meteorological quantities extracted from it, which, although partially calibrated (i.e., only ) using global raingauge-derived and satellite-based rainfall products (e.g., the Global Precipitation Climatology Centre (GPCC) database, as explained in more detail in [5]), originate from meteorological reanalyses (henceforth we will refer to the meteorological database of the ITU-R model as “calibrated ERA40”). This letter presents a new prediction model, valid for tropical/equatorial regions (specifically latitudes ranging from 35 to 35 ), which receives as input local meteorological quantities derived from the data collected during the Tropical Rainfall Measuring Mission (TRMM). The proposed model retains the analytical formulation of the ITU-R model, but, as an advantage, besides offering a better prediction performance, it makes use of a reduced number of meteorological inputs (two instead of three). The remainder of this paper is organized as follows. Section II briefly introduces TRMM data and describes in detail the prediction method. Section III presents the assessment of the proposed model against rainfall rate statistics extracted from the DBSG3 database made available by ITU-R. Finally, Section IV draws some conclusions. II. METHODOLOGY A. TRMM The TRMM, born from the collaboration between the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA), was conceived to improve the understanding of rainfall in the tropics and its influence on the global climate. The mission satellite, whose
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observation coverage falls within latitudes 35 –35 , was launched in November 1997. Its orbital altitude is 402.5 km, and the satellite completes about 16 orbits per day. Among the sensors on-board the TRMM satellite (e.g., the Microwave Imager, TMI, and the Visible Infrared Scanner, VIRS), the Precipitation Radar (PR), operating at 13.8 GHz, is the key instrument providing three-dimensional pictures of precipitation phenomena [6]. The datasets based on the TRMM PR are classified into three levels. Level-1 and 2 products are derived from TRMM PR instantaneous field of view (IFOV) data, while Level-3 products provide statistical precipitation parameters based on Level–1 and 2 products. Additional details on TRMM data are available in [7]. B. Proposed Prediction Model The proposed prediction model originates from the ITU-R model, which expresses as a function of , , and (1) where
and
(2)
In (1) and (2), all the input values are extracted from the calibrated ERA40 database through bilinear interpolation on the site of interest [5]. The proposed prediction model retains the analytical formulation of the method currently recommended by ITU-R. However, in order to improve the meteorological database on which it relies, both in terms of spatial resolution and accuracy, the input values required in (2) are extracted from TRMM data. In addition, as will be explained in detail in Sections III and IV, with being directly extracted from TRMM data, and are no longer required for prediction [refer to (2)]. C. Mean Yearly Rainfall Accumulation,
, From TMPA 3B43
values as input to the proIn order to employ accurate posed prediction model, we have considered the TRMM Multisatellite Precipitation Analysis (TMPA) 3B43 database [8]. Recently updated to version 7, such a database consists of longterm (14 years of TRMM observation from January 1998 until December 2011) mean monthly rainfall accumulations obtained by merging the information coming from the TRMM instruments and from other ground-based rainfall products. Besides its expected high accuracy, the TMPA 3B43 database is characterized by fine spatial resolution (regular 0.25 0.25 latitude/longitude grid between 35 and 35 ), which also allows tracking of small-scale spatial variations of . So far, several authors (see, e.g., [9] and [10]) have highlighted the good accuracy and reliability of the TMPA 3B43 database. As a further assessment, Fig. 1 shows the comparison between the mean yearly measured by some
Fig. 1. Comparison of mean yearly at four locations in Malaysia: measurements from raingauges and values extracted from the TMPA 3B43 database and the calibrated ERA40.
raingauges of the Malaysian Department of Irrigation and Drainage (DID) [11] and the one extracted from the TMPA 3B43 V7 database, as well as from the database on which the ITU-R model relies. As is clear from Fig. 1, for the selected locations, TRMM-derived values provide a better estimation of the measured , while the calibrated ERA40 tends to underestimate it. D. Probability of Rain,
, From TRMM PR 3A25
The probability to have rain in an average year (on 1-min basis), , is a critical quantity to be measured due to the limited resolution and accuracy of the instruments commonly deployed for this purpose (typically, tipping bucket raingauges or disdrometers). As a result, accurate and reliable values of are not commonly available as a reference to evaluate the accuracy of prediction formulas such as the first equation in (2), which is included in the ITU-R model as an intermediate step towards the prediction of . Instead of (2), which requires as input , , and , in this work we propose to directly infer the local value of from TRMM IFOV data. Specifically, the idea put forth here is to exploit the well-established ergodicity property of the rainfall process, which, in practice, implies that the long-term first-order statistics collected by a raingauge at one site (i.e., in this work), is equivalent to the one obtained by cumulating the information on the precipitation affecting the surrounding area of dimension approximately between 100 100 and 300 300 km (i.e., spatial rain rate statistics, ) [12], [13]. As a result, the probability to have rain as measured by a raingauge in time is equivalent to the average fractional rainy coverage relative to the area surrounding the raingauge. An opportunity to estimate the latter quantity is offered by Level-3 PR products, specifically by the TRMM PR 3A25 V7 database [8], which includes monthly statistics of the number of pixels flagged as affected by rain (the PR resolution on the ground is 5 5 km ), and of the total number of observed pixels, both relative to the same reference area. Such statistics are provided with high (0.5 0.5 )
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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 12, 2013
Fig. 2. Probability of rain 1 spatial resolution. 1
(%) derived from TRMM PR 3A25 V7 data,
TABLE I LOCATIONS SELECTED FOR MODEL TESTING
Fig. 3. Examples of the prediction performance of the proposed model and of the ITU-R model: (a) Kuala Lumpur and (b) Rio de Janeiro.
III. VALIDATION OF THE PROPOSED PREDICTION MODEL
or low (5 5 ) resolution, both covering 14 years of observation (from January 1998 to December 2011). Thus, can be calculated as (3) and are respectively the number of rainy pixel where and the number of total pixels (all 1998–2011 period) relative to the same reference area (e.g., 0.5 0.5 ). Although 0.5 0.5 is the finest resolution at which and are directly provided in the TRMM PR 3A25 V7 database, it is worth reminding that for the ergodicity property to hold, besides considering a long period, the lateral dimension of the reference area for calculation should range approximately between 100 100 and 300 300 km [13]. For this reason, in this work, 1 1 has been selected as the suitable resolution to calculate from TRMM PR 3A25 V7 data: In fact, this choice corresponds to considering area dimensions approximately equal to 110 110 and 90 110 km at the Equator and at latitudes 35 or 35 , respectively. As an example, Fig. 2 shows the values of calculated for an area over Malaysia .
In order to evaluate the performance of the proposed model, we have considered the tropical/equatorial sites included in the DBSG3 database made available by ITU-R [14]. Table I shows the selected sites where rainfall data have been collected with 1-min integration time: All the measured curves were derived from the DBSG3 database, except for the one relative to Padang, which has been extracted from [15]. For each of the available sites, has been estimated using the proposed model: [required in (1)] and [required in the second and third equations of (2)] have been extracted from TRMM PR 3A25 and TMPA 3B43 data, respectively, through bilinear interpolation on the site of interest. Despite the different spatial resolution of the two input databases, they represent the most effective choice to maximize the model’s prediction performance: As mentioned, on one side, 1 1 is necessary to increase the validity of the ergodicity, while on the other side, 0.25 0.25 allows to properly track also small-scale spatial variations of . The error figure for the testing activity is based on the relative rain rate difference, mathematically defined as (4) and are the rain rate values respectively where extracted from the estimated and measured curves, both associated to the same probability level . The prediction performance is quantified by calculating the average (E), standard deviation , and root mean square (RMS) values of , considering in order to maintain a suitable degree
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TABLE II DETAILED PERFORMANCE OF THE PROPOSED MODEL AND OF THE ITU-R FOR ALL THE TROPICAL/EQUATORIAL SITES MODEL IN PREDICTING INCLUDED IN THE DBSG3 DATABASE
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the use of input values with fine spatial resolution and high accuracy: When tested against the experimental curves included in the DBSG3 database of ITU-R, the proposed model shows a significantly better estimation accuracy with respect to the ITU-R model (overall RMS of the error equal to 20.9% and 28.3% for the former and the latter, respectively). Although the proposed model is only valid for tropical and equatorial regions because of the limited coverage of the TRMM PR 3A25 and TMPA 3B43 databases, its applicability could be extended by exploiting global precipitation datasets to be collected with high resolution and high accuracy in future Earth Observation missions (e.g., Global Precipitation Measurement (GPM) [16]). ACKNOWLEDGMENT Some data used in this study were acquired using the GESDISC Interactive Online Visualization And Analysis Infrastructure (Giovanni) as part of the NASA’s Goddard Earth Sciences (GES) Data and Information Services Center (DISC). REFERENCES
of statistical stability in the data (the lowest level considered corresponds to approximately 20 rain rate samples for experiments with the most limited duration, i.e., 2 years). As an example of the performed tests, Fig. 3 shows the for (a) Kuala Lumpur and (b) Rio de Janeiro, as extracted from the DBSG3 database (asterisk markers) and as predicted by the proposed model (solid line). For comparison, also the curves estimated by the ITU-R model (dashed line) are included in the figures. The two examples provide a qualitative indication of the better prediction performance achieved by the proposed model with respect to the ITU-R model. Table II, which lists the results on the testing activity for all the selected locations, clearly highlights the marked difference in the performance shown by the two models. For all sites, the RMS value of associated with the proposed model is lower than the one obtained using the ITU-R model and, in addition, the former also generally provides a considerably more limited bias than the latter. These results are confirmed by the last line of Table II, where the average (over all locations) E, , and RMS values are reported for the two models. Such an improvement in the prediction performance has to be ascribed to the use of meteorological inputs with high accuracy and fine resolution. IV. CONCLUSION A new model for prediction, valid for tropical and equatorial regions, is presented here. The model originates from the method currently recommended by ITU-R for global prediction (recommendation P.837-6—Annex 1), of which it retains the same analytical formulation. The novelty of the proposed model consists in the use of input local meteorological quantities (average probability to have rain, , and mean yearly rain accumulation, ) that are extracted from TRMM data (TRMM PR 3A25 and TMPA 3B43, respectively) instead of from the ERA40 database. Advantages clearly emerge from
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