Radar MeteorologyTheoretical work (Mie scattering theory) in the late 1940s showed that weather clutter arose from the scattering of electromagnetic radiation by precipitation particles (resonant interaction between propagating EM wave and a dielectric such as water and ice).

Today modern radars can not only detect hydrometeors (both precipitation and cloud particles), but clear air targets such as insects and large aerosol particles, as well as changes in the index of refraction, the latter caused by turbulent motions in the atmosphere.

RADAR-Radio Detection and RangingRadar is the art of detecting by means of radio echoes the presence of objects, determining their direction and range, recognizing their characteristics and employing the data thus obtained.

Object refers to meteorological targets such as raindrops, hailstones, cloud ice and liquid particles and snowflakes. For the purpose of clear air detection, insects are considered the objects. Birds also are readily detected and hence are of interest.

Radar is based on the propagation of electromagnetic waves through the atmosphere, a non-vacuum. EM waves propagate at the speed of light in a vacuum, c = 2.998 x 108 ms-1.

Propagation speed in a non-vacuum determines the index of refraction, n = c/ where is the wave speed (Note : water and ice have different refractive index)

Electromagnetic Waves and Their Propagation Through the Atmosphere

Electromagnetic Waves are characterized by:Wavelength, [m, cm, mm, mm etc]

Frequency, [s-1, hertz (hz), megahertz (Mhz), gigahertz (Ghz)

where: c =

Polarization of electromagnetic wavesThe polarization is specified by the orientation of the electromagnetic field.

The plane containing the electric field is called the plane of polarization.

For a monochromatic wave:Electric field will oscillate in the x,y plane with z as the propagation directionwhere f is the frequency and d is the phase difference between Exm and Eym and the coordinate x is parallel to the horizon, y normal to x, and z in the direction of propagation.If Eym = 0, Electric field oscillates in the x directionand wave is said to be horizontally polarizedIf Exm = 0, Electric field oscillates in the y directionand wave is said to be vertically polarizedIf Exm = Eym, and d = /2 or - /2, electric field vector rotates in a circle and wave is circularly polarizedAll other situations: E field rotates as an ellipse

How does radar scan ?

Ground/ship radar

VCP 31clear air modeVCP 11severe weather modeVCP 21Wide-spread precipScanning strategies for scanning radars must take into account the propagation path of the beam if certain operational or scientific objectives are to be addressed. Here, 3 common NWS NEXRAD Volume Coverage Patters (VCPs) are illustrated. NEXRADs have a 5-6 minute scan update requirement for severe weather detection, so they vary their VCPs and scan rates depending on the weather situation.6 min update, slow scan rate5 min update, fast scan rate6 min update, slow scan rate

Airborne

Commercialairplanes

Airborne

Research airplanes

Space borne

What kind of electromagnetic pulse do we send?

Block Diagram of a Radar SystemTransmitter106 WAntennaReceiver10-14 WDisplayT/R switch

Why is wavelength important?Longer wave length -> sensitive to larger objects -> larger penetration ability (long range), but require a larger antenna to obtain enough return signalShorter wave length -> sensitive to smaller objects -> more scattering and more attenuation of signal, require a smaller antenna to obtain enough return signal

W and K band radars are cloud radarsX, C, S and L band radars are precipitation radarsAlso - Wind Profilers (UHF & VHF; ~50 to 900 MHz; ~6 to 0.3 m)

How does electromagnetic wave travel in the atmosphere?

Electromagnetic waves:Interact with matter in four ways:Reflection:Refraction:

Scattering:Diffraction:

Snells law:Where: i is the angle of incidence r is the angle of refraction Vi is the velocity of light in medium n Vr is the velocity of light in medium n - DnIn the atmosphere, n normally decreases continuously with height

Therefore: due to refraction, electromagnetic rays propagating upward away from a radar will bend toward the earths surface

Propagation of electromagnetic waves in the atmosphereSpeed of light in a vacuum: CSpeed of light in air: VRefractive index: n=C/VAt sea level: n = 1.0003In space: n = 1.0000c = 2.998 x 108 ms-1

The Refractive Index is related to:Density of air (a function of dry air pressure (Pd), temperature (T), vapor pressure (e)2. The polarization of molecules in the air(molecules that produce their own electric field in the absence of external forces)The water molecule consists of three atoms, one O and two H. Each H donates an electron to the O so that each H carries one positive charge and the O carries two negative charges, creating a polar molecule one side of the molecule is negative and the other positive.

Earth curvatureElectromagnetic ray propagating away from the radar will rise above the earths surface due to the earths curvature.

Ray Path GeometryConsider the geometry for a ray path in the Earths atmosphere. Here R is the radius of the Earth, h0 is the height of the transmitter above the surface, 0 is the initial launch angle of the beam, h is the angle relative to the local tangent at some point along the beam (at height h above the surface at great circle distance s from the transmitter).

Equation governing the path of a ray in the earths atmosphere:where R is the radius of the earth, h is the height of the beam above the earths surface, and s is distance along the earths surface.To simplify this equation we will make three approximations1. Large earth approximation2. Small angle approximation3. Refractive index ~ 1 in term: (1)

X1XX1/R1Approximate equation for the path of a ray at small angles relative to the earths surface:Or, in terms of the elevation angle of the beam(2)

Curvature of Ray Paths Relative to the EarthAn additional equation of interest is the equation that provides the great circle distance s, from the radar, for the r, h pair (slant range, beam height), which is

s = keR sin-1[rcos/(keR + h)]

Here ke=4/3We can get even simpler and consider a the height of the beam at slant range R and elevation angle ,

h (km) = R2/17000 + R sin hR

Non-Standard RefractionNon-standard refraction typically occurs with the temperature distribution does not follow the standard lapse rate (dn/dh -1/4 (R)). As a result, radar waves may deviate from their standard ray paths predicted by the previous model. This situation is known as abnormal or anomalous propagation (AP).

Abnormal downward bending ------- super-refraction (most common type of AP)Abnormal upward bending ----------- sub-refraction

Super-refraction is associated most often with cold air at the surface, giving rise to a near surface elevated temperature inversion in which the T increases with height. Most commonly caused by radiational cooling at night, or a cold thunderstorm outflow.

Since T increases with height, n decreases (rapidly) with height (dn/dh is strongly negative). Since n = c/v, v must increase with height, causing downward bending of the ray path.

Non-Standard RefractionSuper-Refraction (most common)dN/dZ < -79 km-1 and > -158 km-1Beam is bent downward more than standardSituations:Temperature inversions (warm over cold air; stable layers)Sharp decrease in moisture with height And (2) can occur in nocturnal and trade inversions, warm air advection (dry), thunderstorm outflows, fronts etc.Result:Some increased clutter ranges (side lobes)Overestimate of echo top heights (antenna has to be tilted higher to achieve same height as standard refracted beam)- see figure aboveMost susceptible at low elevation angles (e.g., typically less than 1o)0hh

Sub-Refraction (not as common)dN/dZ > 0 km-1 Beam is bent upward more than standardSituations:Inverted-V sounding (typical of desert/intermountain west and lee-side of mountain ranges; microburst sounding; late afternoon and early evening; see figure)Result:Underestimate of echo top heights (beam intersects top at elevation angles lower than in standard refraction case)- see figure above

Most susceptible at low elevation angles (e.g., typically less than 1o)0hh

Ducting or Trapping (common)dN/dZ < -158 km-1 Beam is severely bent downward and may intersect the surface (especially at elevation angles less than 0.5o) or propagate long distances at relatively fixed heights in an elevated duct.Situations: Strong temperature inversions (surface or aloft) Strong decreases in moisture with heightResult: Markedly Increased clutter ranges at low elevation angles Range increases to as much as 500% in rare instances (useful for tracking surface targets)Most susceptible at low elevation angles (e.g., typically less than 1o)Elevated ducts can be used as a strategic asset for military airborne surveillance and weapons control radars. E.g., if a hostile aircraft is flying in a ducting layer it could be detected a long way away, while its radar cannot detect above or below the ducting layer. Conversely, friendly aircraft may not want to be located in the duct.

One moral of the whole refraction story..knowing the exact location of the beam can be problematic. Remember this when you have the opportunity to compare the measurements of two radars supposedly looking at the same storm volume!

Big implication of radar beam height increasing with range (under normal propagation conditions) combined with broadening of the radar beam: The radar cannot see the low level structures of storms, nor resolve their spatial structure as well as at close ranges. Thus, for purposes of radar applications such as rainfall estimation, the uncertainty of the measurements increases markedly with range.Storm 1Storm 2

*Beam Blockage in Complex TerrainBeam propagation is a function of the vertical refractivity gradient (dN/dz)N = 77.6(p/T) - 5.6(e/T) + 3.75x105(e/T2)dN/dz is sensitive to p, T, eThus, changes in the vertical profiles of these quantities can change the height of the ray path as it propagates away from the radarThis is especially important in complex terrain, because the amount of beam blockage will change depending on the vertical refractivity gradientdN/dZ = -40/kmdN/dZ = -80/km)

False DataGround ClutterPortion of radar beam hits buildings, trees, hillsAlso can be due to dust, aerosols in the air near the radarGives false indication that precip is presentRadar location is in the black area surrounded by blue/green reflectivities

False DataAnomalous propagation (AP)Occurs when temperature inversions are present in low-levelsRadar beam bent into ground, returning strong signalCommon during early morning hours after a clear nightAgain, no precip really present

False DataVirgaRadar detects precip occurring at upper levels, but not making it to the groundPrecip quickly evaporates in dry air below cloudPrecipitation is thus overestimated

False DataOvershooting BeamSome precip can form from clouds with minimal heightBeam may overshoot a large portion of the cloud, underestimating the intensity of the precipitation

False DataStorm InterferenceStorms closest to radar may absorb or reflect much of the radar energyLeaves reduced amount of energy available to detect distant stormsUnderestimates precipitation

False DataWind ShearFalling precip may be displaced by the wind as it fallsSome regions may be experiencing precip where the radar indicates nothing, and vice versa

Height of Lowest Unobstructed Sampling Volume Radar Coverage MapMid-Atlantic River Forecast Center (MARFC)

Height of Lowest Unobstructed Sampling Volume Radar Coverage MapWest Gulf River Forecast Center (WGRFC)

* Southeast

PRECIPITATION MOSAICRADAR COVERAGE MAP Northeast

Say youd like to site a radar for a research experiment. In a perfect worldyoud like to be able to take a swim after work, but AP and beam blockage may be a problem. Sidelobes may intersect the highly reflective ocean creating sea clutter

Mountains can be a problem

Local effects can be a problem too topographic maps and DEMs can help, butstill need to conduct a site survey to see trees, antennas, buildings, and overpasses.

Often times you end up in places like this

Height of a ray due to earths curvature and standard atmospheric refraction

Assignment #1Here we have reviewed the calculation of slant path of the radar beam. But I did not describe the equation for the beam width change with the distance. Here is the question: assuming you have a radar with beam width 1 degree. How big is the beam width at 100 km?

There is an airplane flying at 10 km altitude with a radar sending a 1 degree beam tangentially. At 200 km distance, a) what is the beam width? b) what are the heights of the top and bottom of the beam respect to the Earth surface? If there is a storm reaching 10 km at 200 km distance, can pilot see the storm on his screen? (assuming the standard atmospheric refraction)

ELECTRIC FIELDAn Electric field exists in the presence of a charged bodyELECTRIC FIELD INTENSITY (E)A vector quantity: magnitude and direction (Volts/meter)MAGNITUDE OF E: Proportional to the force acting on a unit positive charge at a point in the field

DIRECTION OF E: The direction that the force acts

The Electric Field (E) is represented by drawing the Electric Displacement Vector (D), which takes into account the characteristics of the medium within which the Electric Field exists.e, the Electric Conductive Capacity or Permittivity, is related to the ability of a medium, such as air to store electrical potential energy.Vacuum:Air:Ratio:

The Electric Displacement Vector, D, is used to draw lines of force.Units of D:

MAGNETIC FIELDA Magnetic field exists in the presence of a currentMAGNETIC FIELD INTENSITY (H)A vector quantity: magnitude and direction (amps/meter)MAGNITUDE OF H: Proportional to the current

DIRECTION OF H: The direction that a compass needle points in a magnetic field

The Magnetic Field (H) is represented by drawing the Magnetic Induction Vector (B), which takes into account the characteristics of the medium within which the current flows.m, the Magnetic Inductive Capacity, or Permeability, is related to the ability of a medium, such as air, to store magnetic potential energy.Vacuum:Air:Ratio:

Magnetic Fields:Magnetic fields associated with moving charges (electric currents)I: CurrentB: Magnetic InductionMagnetic Field Lines are closed loops surrounding the currents that produce them

Maxwells Equations for time varying electric and magnetic fields in free space(where is the charge density)Simple interpretationDivergence of electric field is a functionof charge densityA closed loop of E field lines will exist whenthe magnetic field varies with timeDivergence of magnetic field =0(closed loops)A closed loop of B field lines will exist inThe presence of a current and/or time varying electric field

Electromagnetic Waves: A solution to Maxwells EquationsElectric and Magnetic Force FieldsPropagate through a vacuum at the speed of light:Electric and Magnetic Fields propagate as waves:where:or:, , are coordinates, A is an amplitude factor, is the frequency and is an arbitrary phase

All energy stored in electric fieldAll energy stored in magnetic fieldwavelengthTime variations in charge, voltage and current in a simple Dipole AntennaEnergy is 1) stored in E, B fields, 2) radiated as EM waves, 3) Dissipated as heat in antennaNear antenna: Energy stored in induction fields (E, B fields) >> energy radiated(near field)More than a few from antenna: Energy radiated >> energy stored in induction fields (far field)Pt. APt. B

Spherically Stratified Atmosphere; Ray Path EquationIntegrating (2) yields,

(dh/ds)2 = 2 (1/R + dn/dh) dh + constant (3)

Since dh/ds for small , (3) can be written as,

1/2(h2 - 02) = (h - h0)/R + n - n0 = (h/R + n) - (h0/R + n0)

Letting M = [h/R + (n-1)] x 106, we have

= (M - M0)10-6

M is the so-called modified index of refraction. M has a value of approximately 300 at sea level.

Curvature of Ray Paths Relative to the Earth

If the vertical profile of M is known (say through a sounding yielding p, T and q), h can be calculated at any altitude h, that is, the angle relative to the local tangent.

Lets now consider the ray paths relative to the Earth. For the case of no atmosphere, or if N is constant with height (dN/dh = 0), the ray paths would be straight lines relative to the curved Earth.

d/ds = 1/R + dn/dh 1/R for n constant with height(No atmosphere case?)(Flat earth case?)For n varying with height,

d/ds = 1/R + dn/dh < 1/R since dn/dh < 0

For the special case where dn/dh = -1/R, d/ds = 0. Hence the ray travels around the Earth concentric with it, at fixed radius, R + h. This is the case of a trapped wave. DUCTING

Curvature of Ray Paths Relative to the EarthFor convenience, it is is easier to introduce a fictitious Earth radius, 1/R = 1/R + dn/dh

For typical conditions, dn/dh = -1/4 R m-1

Hence R = R/(1 - 1/4) = 4/3 RThis is the effective Earth radius model, to allow paths to be treated as straight lines.

Doviak and Zrnic (1993) provide a complete expression for h vs. r, where r is the slant range (distance along the ray).

h = {r2 + (keR)2 + 2rkeRsin}1/2 - keR

where h is beam height as slant range r, is the elevation angle of the antenna, and ke is 4/3 (R is the actual Earth radius).

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