ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

Characterization tools for estimate radar signals with partial obstructions Juan Antonio Romo Argota 1, Mercedes Maruri Machado 2, Ivan Iglesias 1, Sabina Ustamujic 1

1Department of Electronics and Telecomunications, E.T.S.I Bilbao, University of Basque Country. Alameda Urquijo s/n, Bilbao, Spain [email protected] 2Department of Applied Mathematics, E.T.S.I Bilbao, University of Basque Country. Alameda Urquijo, Bilbao, Spain [email protected]

1. Introduction When radar signals travel along paths close to the Earth’s surface, there is a possibility that the wave front is partially obstructed by terrain irregularities such as hills or mountains, or even by artificial structures (buildings). This phenomenon is called diffraction and it is a key factor as error source in weather radar estimations in complex orographic areas, specially for lowest radar antenna elevation angles. Under these conditions, when any diffraction is caused by terrain irregularities or obstacles the propagation of the signal energy will block partially (or even completely). Diffraction is studied through the analysis of the degree of obstruction suffered by the so called First Fresnel Ellipsoid or First Fresnel Zone. The energy contribution of the different ellipsoids to the total received power is a decreasing function of the order of ellipsoids. In consequence, the difraction losses are evaluated considering the first ellipsoid only and neglecting any effect due to the rest of ellipsoids. The received energy at any location is the contribution of the infinite paths that are contained by the plane which is perpendicular to the Pointing vector of a flat wave front. This concept is based on Huygens’ principle that states that any of the points of a flat wave front originates a spherical wave, that in turn, with all the spherical waves associated to other points of the flat wave front, will create an envelope that forms again a flat wave front at a distance r. The contribution of each path to the total received power will depend on the phase of each component associated to the flat wave front. Diffraction of direct ray of a microwave signal in the proximity to a partially blocking obstruction, creates a shadow zone in which diffracted signal energy is lost. When severe subrefraction conditions occur, the path followed by the wave front can be bent down and intersect with terrain obstacles. The first Fresnel ellipsoid will be free of obstacles (at least a 60% of its radius should be above any relevant terrain obstacle of the path profile). In exceptional cases where this condition cannot be fulfilled and for calculation purposes of diffraction associated to the subrefractive condition, there are different methods to estimate the diffraction loss value.

2. The abstract In this paper we develop a calculation algorithm to estimate diffraction losses. The method to be applied in each case will depend on the number and shape of the obstacles and the position of those obstacles in the propagation path. The main objective for this algorithm is the assessment of radar signals in scenarios within partial obstructions. Depending on the idealization used to characterize the obstacles encountered in the propagation path, different prediction models can estimate the path loss in vertical plane of a given point from ground level up to line of sight height. In this way power loss is calculated for different radar antenna elevation angles during rain events using a digital elevation model and different attenuation methods as function of the types of obstacles in the path. This power loss is compared with radar reflectivity at these points. Additional applications for this developed model are planning and interferences evaluation tools in the design and implementation of microwaves line of sight or satellite links.

3. Digital Elevation Model In general, most propagation prediction algorithms are based on detailed topographical information provided by Digital Terrain Elevation (DTE) models which are composed by digital terrain topographical databases and represented in the form of digital terrain maps. These models are used to evaluate the potential loss associated to diffraction. There is a variety of digital terrain models, with elevation data of different resolutions on a global scale that cover practically the whole surface of the Earth. Digital Elevation Models (DEM), in addition to digital terrain elevation data, require more details and features of the terrain including different soil types, vegetation layers, layers describing the existence of buildings and associated heights, etc. The first step of the suggested methodology involves the conversion of Digital Terrain Elevation files to X,Y,Z coordinates. This Digital Terrain Elevation is later combined with building height layers, available locally, to obtain the Digital Elevation Model (DEM), which are composed by digital topographical databases implemented in MySQL. ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

4. Profile extraction and obstacles identification and classification The path profile extraction is carried out directly from the topographical database and traced with the appropriate equivalent Earth radius. [1] The proposed tool detects automatically the obstacles in the path and the shape of them.

An obstacle is identified if the clearance from the ray tracing is at least 57.7 % of the first Fresnel zone radius R 1 on both sides of the obstacle, at a given equivalent Earth radius. It is considered isolated if there is no interaction between the obstacle itself and the surrounding terrain. In turn, to determine if two obstacles must be considered as one isolated obstacle the distance between adjacent obstacles is verified and compared with the radius of the first Fresnel elipsoide. To make diffraction fading calculations it is necessary to idealize the complex forms of real obstacles, either assuming a knife-edge of negligible thickness or a thick smooth obstacle with a well-defined radius of curvature at the top.

5. Diffraction loss methods The used algorithmia to calculate the diffraction loss caused by different types, number and obstacles configurations along the path are basically derived from de the ITU-R models. [2] Different methods are used for the cases where there is a single isolated obstacle and for those where several irregularities are relevant in the path profile. 1) Single knife-edge obstacle: Attenuation due to diffraction J(ν) (dB) is calculated by the equation derived from the Fresnel-Kirchhoff diffraction theory: J (ν ) = 9.6 + 20 log ( (ν – )1.0 2 + 1 + ν – 1.0 ) dB Where ν is a dimensionless parameter

2  1 1  ν = h  +  λ    d1 d2  according to the geometrical parameters selected: λ wavelength (m) h clearance (m) d1 distance from de radar to the obstacle (km) d2 distance from the obstacle to the target (km)

2) Single rounded obstacle: Diffraction loss associated with this geometry, A, can be calculated from equation: A = J(ν ) + T J(ν) is the Fresnel-Kirchoff loss due to the equivalent knife-edge obstacle with a maximum height that equals the vertex of the parabola. T is the additional attenuation due to the curvature of the obstacle and can be calculated from geometric parameters of the obstacle. 3) Double obstacles: When there are two perfectly identified isolated obstacles in the route, either knife-edge or rounded, methods derived from the theory of diffraction on isolated obstacles are applied successively to the two obstacles, with the top of the first obstacle acting as a source for diffraction over the second obstacle. The total diffraction loss is then given by:

L = L1 + L2 + Lc. The first diffraction path gives a loss L1 (dB) and the second diffraction path gives a loss L2 (dB). L1 and L2 are calculated considering an isolated obstacle in the path. A correction term Lc (dB) is added to take into account the separation between the edges.

4) Multiple obstacles: When there are multiple obstacles in the route we use a method derived from the cascade cylinder method. Figure 1 illustrates the geometry for an obstruction consisting of more than one string point. The following points are indicated by: w: closest string point or terminal on the transmitter side of the obstruction which is not part of the obstruction; x: string point forming part of the obstruction which is closest to the transmitter; y: string point forming part of the obstruction which is closest to the receiver; z: closest string point or terminal on the receiver side of the obstruction which is not part of the obstruction; v: vertex point made by the intersection of incident rays above the obstruction. ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

Fig. 1 Geometry of a multipoint obstacle

The letters w, x, y and z will also be indices to the arrays of profile distance and height samples. For an obstruction consisting of an isolated string point, x and y will have the same value, and will refer to a profile point which coincides with the vertex. Note that for cascaded cylinders, points y and z for one cylinder are points w and x for the next, etc.

The total diffraction loss, in dB relative to free-space loss, may be written::

N N = ′ + ′′ + ′′ Ld ∑ Li L (w x)1 ∑ L (y z)i – 20 log C N dB i = 1 i = 1

L'i : diffraction loss over the i-th cylinder L"(w x)1 : sub-path diffraction loss for the section of the path between points w and x for the first cylinder

L"(y z)i : sub-path diffraction loss for the section of the path between points y and z for all cylinders

CN : correction factor to account for spreading loss due to diffraction over successive cylinders.

6. Results Figure 2 shows the graphical representation obtained for the propagation path from a radar site and different targets at several elevations, and a standard atmosphere with the effective Earth’s radius or k-factor from its median value of 4/3. For each direct beam at a given elevation, 57.7 % of first zone of Fresnel is also depicted in order to visualize obstacles in the path.

Fig. 2. Example of path propagation profile for different elevations

ERAD 2012 - THE SEVENTH EUROPEAN CONFERENCE ON RADAR IN METEOROLOGY AND HYDROLOGY

For a given elevation angle and a given effective Earth’s radius, path propagation loss are calculated depending on the topographical profile associated to the beam tracing. In the other hand for a given elevation angle and a given diffraction attenuation, k-factor is calculated and therefore the mean value in the path propagation for the vertical gradient of Radio Refractivity, or Refractive Index. This feature presents a high interest when anomalous radio refractivity gradient values are presented and duct region of the troposphere keeps the propagation of the signal confined between two layers of the troposphere or between a layer of the troposphere and the Earth’s surface. The performance of the algorithm has been checked, and calibrated using radiosonde measurements for gradient of Refractive Index and simultaneous meteorological observations derived from volume scan weather radar information for reflectivity which is function of propagation loss for a given type of target, in the Basque Country area, using three year, from 2006 to 2008, data series.

Acknowledgment Authors thank the Basque Met Service for providing the Radar and surface information and for their general support for this work.

References [1] ITU-R Rec. P.834-6: " Effects of tropospheric refraction on radiowave propagation". International Telecommunications Union. Radiocommunications Sector. ITU-R. Geneva. 2007 [2] ITU-R Rec. P.526-12: "Propagation by diffraction". International Telecommunications Union. Radiocommunications Sector. ITU-R. Geneva. 2012 [3] Perez-Fontan, F. and Hernando-Rabanos, J.M. “Comparison of irregular terrain propagation models for use in digital terrain data based radiocommunication system planning tools” IEEE Transactions on Broadcasting, 1995. [4] Barrios, A.E.,. Patterson, W.L: “Advanced Propagation Model (APM) ver. 1.3.1”. Computer Software Configuration Item (CSCI) Documents, SPAWAR Systems Center, San Diego CA, 339 p. 2002 [5] Chang, S.K.; Kim, S.W.; Kim, B.K.; Hong, U.S.; Baek, C.H.; Choi, B.J.; “A propagation loss prediction model for various types of finite width obstacles using numerical approach” Microwave Conference Asia-Pacific, 2000.