ECE Lecture 32

Transcription

1 ECE Lecture 32 1 Microwave Radiometry 2 Properties of a Radiometer 3 Radiometric Calibration and Uncertainty 4 Types of Radiometer Measurements Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

2 Microwave Radiometry Microwave radiometers are used in passive microwave sensing Do not transmit; receive naturally emitted thermal noise in order to determine properties of observed scene This is the external noise from Chapter 4; there this noise was not desired, but in radiometry, it is the signal of interest! In chapter 4, we learned that the thermal noise power received by an antenna, described as an antenna temperature T A, can be related to the brightness temperature T B of the scene observed by the antenna: T A = 1 Ω=4π T B (Ω)G(Ω)dΩ + [1 υ] T p (1) 4π Ω=0 where G(Ω) is the antenna pattern, T p is the antenna physical temperature, and υ is the antenna efficiency Above involves an approximation to Planck s blackbody radiation law; the approximation is applicable for frequencies less than around 100 GHz Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

3 Brightness Temperature The brightness temperature T B of an object (measured in Kelvin = Celsius+273) is the temperature of a blackbody that would produce a thermal emission equal to that of the object A blackbody is an object that perfectly absorbs all incident radiation and re-radiates this energy as thermal noise Real objects aren t blackbodies so the brightness temperature is less than the physical temperature The emissivity e of an object (for an object at uniform physical temperature T phys ) is defined as e = T B T Phys We will learn that brightness temperature of real media can vary with frequency, polarization, and observation angle; emissivity is also a function of these parameters Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

4 Kirchhoff s Law For an object or scene at uniform temperature, Kirchhoff s Law can be used to determine the emissivity A blackbody is an object that perfectly absorbs any incident power density: brightness temperature equals physical temperature so emissivity equals 1 Kirchhoff s Law says that the emissivity of a non-blackbody is equal to the fraction of the incident power density that is absorbed when illuminated by an impinging field Works as a function of frequency, angle, and polarization too! To find the emissivity of an object in direction θ, frequency f, and polarization β, consider a plane wave of frequency f and polarization β impinging on the object from angle θ The fraction of the incident power density absorbed by the object or scene is the emissivity at frequency f into angle θ and polarization β! We ll use this later... Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

5 Properties of a radiometer Given T A = 1 Ω=4π T B (Ω)G(Ω)dΩ + [1 υ] T p (2) 4π Ω=0 it is clear that highly efficient antennas are desirable to maximize external brightness, not internal loss It is also clear that high gain antennas are desirable to focus on measuring brightness at a particular location (and angle) Since the total noise power measured by the receiver is k B B [(F 1)290 + T A ] it is clear that it is desirable to have a low noise figure receiver We want T A to be significant compared to the system temperature T sys = (F 1)290. Noise power is small: radiometer is a high gain receiver Need to perform microwave radiometry in protected bands where transmission is prohibited; otherwise we ll measure someone else s signal power instead of thermal noise Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

6 Radiometer Field of View Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

7 Frequency bands protected for microwave radiometry/radio astronomy , , MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz GHz, GHz, GHz, GHz Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

8 Spatial Resolution Because a radiometer is measuring thermal noise, there is no possibility (as in SAR) of producing a synthetic aperture Spatial resolution determined by the one-way antenna footprint Microwave radiometry from space is usually at spatial resolutions on the order of 10 km or worse Useful mainly for large scale phenomena: weather, climate, oceanography, etc. Resolutions better in airborne or ground measurements The term synthetic aperture radiometry refers to using an antenna array instead of a single antenna Array can beamform many look angles simultaneously Synthetic aperture radiometer therefore observes at many incidence angles simultaneously Pattern of array still determines spatial resolution for each angle Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

9 Radiometric Calibration The radiometer receiver essentially is a string of amplifiers and filters followed by a square-law detector (to change voltage into power), averaging, and digitization Gain of amplifiers is usually large, up to 100 db or more Digitizer will output a quantity, let s call it P, that ideally is linearly related to T B : P = AT B + B Calibration of radiometer refers to determining A and B by observing sources of known brightness, typically called hot and cold loads: P hot = AT B,hot + B P cold = AT B,cold + B Above equations can be solved for A and B, which enables determination of T B for other measurements of P Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

10 Radiometric Calibration 2 How frequently do we need to calibrate? Depends on how fast A and B vary in time (how stable radiometer receiver is) Because the gain of the radiometer receiver is high, small amplifier gain fluctuations can be a problem Radiometer hardware usually temperature controlled Dicke switching is an internal calibration cycle using a rapid switching process to observe internal calibration loads This allows calibration of internal gain variations on rapid time scales (typically msec) Internal loads are usually a temperature controlled termination (= blackbody) and a noise diode that produces a known amount of power Additional external calibration needed to calibrate system components between Dicke switch and external environment Ground based measurements often use ambient and liquid nitrogen cooled absorbers Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

11 Radiometer Internal Calibration Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

12 Radiometric Uncertainty Because we are measuring thermal noise, the received signals are again complex Gaussian fields (like speckle in radar) Single measurement power has an exponential distribution Mean and standard deviation are both the expected value of the received power As in radar, averaging measurements over independent samples reduces this large uncertainty After integration, measured power (or estimated brightness temperature) is a Gaussian random variable Mean is the expected value of the power (or brightness temperature), and variance is equal to the mean divided by N, the number of independent samples averaged Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

13 NEDT In radiometry, the standard deviation of the brightness temperature is called the noise equivalent delta temperature, which is NEDT = T sys + T B N = T sys + T B BTint In the above, the number of samples N averaged has been replaced by the product of the integration time T int and the radiometer bandwidth B (assumes Nyquist sampling) We want small values of NEDT, usually less than 1 K; this usually means large bandwidths and long integration times A radiometer is an extremely low data rate system; provides only one measurement of T B for multiple observations of a wide bandwidth channel Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

14 Example NEDT computation A microwave radiometer operates in the protected MHz range using a 23 MHz bandwidth The radiometer receiver has a noise figure of 3 db, and the antenna is 100 percent efficient. What integration time is needed to achieve an NEDT of 1 K when a 290 K scene is observed? Solution: Noise figure of 3 db means T sys = (F 1)290 = 290 K υ = 1 means that T A = T B Then NEDT = T sys + T B N NEDT = Solving yields T int = 14.6 msec = T sys + T B BTint (10 6 ) T int = 1 Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

15 Radiometer Geometries Nadir looking: Frequently used with radar altimeters to provide estimates of water vapor along radar path Pushbroom: Radiometer observes a fixed oblique incidence angle; spot moves along with satellite Cross-Track Scanning: Take a nadir looking radiometer and measure as radiometer (or footprint) is rotated perpendicular to flight direction Produces a swath with varying incidence angle across track Frequently used for atmospheric observations Conically Scanning: Radiometer observes at fixed oblique incidence angle, and is rotated in azimuth to create swath Most common type; can achieve large swath External cal targets observed over part of rotation Limb sounding: Observes atmosphere in a low grazing geometry Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

16 Radiometer Types Radiometers usually designed to focus on observing surface emission, atmospheric emission, or a combination of both Measurements are often performed at multiple frequencies and in multiple polarizations, especially for combined surface/atmospheric case Sounders are intended to measure atmospheric properties vs. altitude Imagers usually include measurements of surface emission Polarimetric radiometers measure not only horizontally and vertically polarized noise powers, but also the correlations between vertically and horizontally polarized fields It turns out the correlation information responds to surface features that are asymmetric in azimuth (for example wind direction over the sea surface) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

17 ECE Lecture 33 1 Passive Microwave Sensing of the Atmosphere 2 Homogeneous atmosphere approximation 3 Weighting Functions and Temperature Profile Retrieval 4 Columnar integrated Water Vapor Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

18 Passive Sensing of the Atmosphere Atmospheric sensing is a major application of microwave radiometry We need to think about thermal emission from the atmosphere to understand how this works First divide the atmosphere into layers; each layer can emit depending on its physical temperature and emissivity Atmospheric gases clearly aren t blackbodies since they re often transparent; can still treat as effective blackbodies How? We know from Chapter 5 that the attenuation due to atmospheric gases in traveling distance dz from altitude z at incidence angle θ is α Np,m (z) (dz sec θ) This power absorbed is re-radiated as thermal noise; Kirchhoff s law says that the brightness temperature of an atmospheric layer dz emitted at observation angle θ is dt B (z) = α Np,m (z)t phys (z) (dz sec θ) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

19 Adding up contribution of layers Our single layer contribution dt B (z) = α(z)t phys (z) (dz sec θ) which has to transit to the radiometer before being measured The attenuation along the path to the radiometer is: ( ) exp sec θ α(z ) dz Now add up all the layers: T B = sec θ 0 dz α(z)t phys (z) exp z ( sec θ z α(z ) dz ) Final equation predicts the upwelling brightness from the atmosphere given temperature profile T phys (z), specific attenuation α(z), and observation angle θ Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

20 Analysis This equation includes contributions only from atmospheric gas emission and attenuation Other atmospheric effects, e.g. rain attenuation or scattering, are not included This is therefore a clear air description of atmospheric emission Because atmospheric gases absorb power in either polarization identically, there are no significant effects of polarization We ve also neglected contributions from the Earth surface Method therefore most applicable as-is to cases where there is a lot of atmospheric attenuation so the Earth surface isn t seen (i.e. near gas absorption resonance frequencies) Also a component of observed brightness at frequencies where surface is seen; we ll put it all together later Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

21 Homogeneous atmosphere approximation If we approximate the atmosphere as existing from 0 to z max only, and as having a constant α and T phys vs. altitude, we get T B = T phys {1 exp ( α sec θ z max )} This is a big approximation, but often can be reasonable at frequencies where the atmosphere is nearly transparent (need to include surface here too!) Notice that if α is very small (i.e. very small attenuation), the brightness temperature gets small Expanding the exponential in two terms we get T B αt phys (z max sec θ) Same as for our one little layer! For large attenuations, T B will approach T phys T B increases with θ because of increasing path length through atmosphere Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

22 Homogeneous Layer T B s vs. angle Brightness Temperature (K) T =290 K, z =100 km phys max α =10 6 Np,m Incidence angle (deg) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

23 Weighting Functions For more lossy atmospheres (i.e. near gas resonance lines) the homogeneous approximation isn t applicable Take another look at ( ) T B = sec θ dz α(z)t phys (z) exp sec θ α(z ) dz 0 Let s define a weighting function as ( W (z, θ, f ) = sec θ α(z, f ) exp sec θ z z α(z, f ) dz ) which depends on α(z), θ, and now radiometer frequency f, but not T phys (z) We now have T B (θ, f ) = 0 dz W (z, θ, f )T phys (z) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

24 Temperature profile retrieval The brightness temperature is a combination of signals from individual atmospheric layers, each proportional to T phys of the layer weighted by the weighting function A single measurement can t tell us much about T phys (z) However if we make multiple measurements of T B as function of θ or f, potentially we could invert these data into information on T phys (z) It is desirable when doing so if there is distinct information in each measurement; do this by operating at multiple frequencies near an absorption line For example, the Advanced Microwave Sounding Unit (AMSU) radiometer uses 12 channels in the range GHz for temperature profiling Frequencies further from the absorption line have less attenuation and see deeper into the atmosphere; those closer to the absorption line see upper parts of the atmosphere Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

25 AMSU Channels Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

26 AMSU Weighting Functions Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

27 Line Shape The behavior of α Np,m vs. frequency can be complicated; we have routines from the ITU to model this An approximation to this frequency dependence can sometimes be useful in studies of atmospheric emission A Van Vleck/Weisskopf absorption line has α(f ) = α(f 0 ) f f 0 ( f ) 2 ( f ) 2 + (f f 0 ) 2 where f 0 is the center freq.& 2 f is the 3 db bandwidth f_0 df f_0 f_0+df Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

28 Columnar integrated values Temperature profile sensing is performed using the oxygen line: oxygen mixing ratio is relatively stable, so weighting functions are fixed and temperature is the key variable Water vapor on the other hand is highly variable, so both water vapor concentration and temperature can vary vs. altitude in our equation Parameter of interest is the water vapor concentration ρ V (z) in grams/cubic centimeter Some measurements instead provide a columnar integrated value, called V : V = 0 dz ρ V (z) which has units of grams/cm 2 V in grams/cm 2 can also be multiplied by 10 to produce V in mm (because 1 cm 3 of water weighs 1 g) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

29 Water Vapor Sensing V is commonly sensed using radiometer channels near the 23 GHz water vapor resonance; AMSU uses 23.8 GHz However, attenuation here may not be large so both surface and atmosphere contributions have to be considered Typical to measure 23.8 GHz plus another frequency having low atmospheric attenuation Measurement in the window channel used to remove surface effects from 23.8 GHz Multiple polarizations also used because surface returns can vary with polarization (we ll learn next time); works best over ocean where surface returns are more homogeneous V is retrieved from the corrected 23.8 GHz channel One simplification is that water vapor is present mostly at altitudes less than a few km; modeling the temperature profile here is simplified Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

30 Water Vapor Applications Measurements of V have a variety of applications Water vapor causes small changes in the refractive index in the air, leading not only to refraction but also to small changes in velocity Causes excess delay on signal paths through troposphere (similar to ionospheric changes in group velocity, but the latter can be much larger) These tropospheric delays can interfere with systems that try to measure range or time delays: e.g. GPS or altimeters Altimeter missions typically include a nadir looking microwave radiometer to try to measure V so that the tropospheric delay effect on the altimeter range measurement can be corrected Similar radiometer measurements are also used to estimate the cloud liquid water content; liquid water in clouds produces attenuation at frequencies beyond the water vapor line at 23 GHz Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

31 Frequencies for Atmospheric Sensing in Practice 23.8 GHz and a window channel: columnar integrated water vapor 23.8 GHz and a higher frequency channel: columnar integrated cloud liquid water 60 and 118 GHz: atmospheric temperature profiling 183 and 325 GHz: Water vapor profiling Resonances at higher frequencies can be used to sense trace gases and other components Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

32 ECE Lecture 34 1 Surface Thermal Emission and Kirchhoff s Law 2 Sea Surface Emission 3 Land Surface Emission Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

33 Surface Thermal Emission Now let s consider emission from the Earth s surface This can be complicated due to the variety of objects present on Earth s surface: rough terrain of varying dielectric constant, various kinds of vegetation, etc. We ll make an approximation that is most applicable at low frequencies and over the sea surface: the Earth surface is a flat plane Later we ll add a model for vegetation effects that is also applicable just at lower frequencies Let s consider what Kirchhoff s Law says about the emissivity of a flat surface Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

34 Kirchhoff s Law for a Flat Surface To find the emissivity of a flat surface at frequency f, angle θ, and polarization β, we need to find the fraction of the power density absorbed when the surface is illuminated by a plane wave of frequency f and polarization β impinging from angle θ From Chapter 6, we know the fraction of the incident power density that is reflected from a flat surface is Γ β (θ) 2 This means the brightness temperature of a flat surface at physical temperature T surf is ( T Bβ = T surf 1 Γ β (θ) 2) This depends on polarization and θ since the reflection coefficients depend on polarization! No explicit dependence on f but any dependence of ɛ on f will matter Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

35 Kirchhoff s Law for a Flat Surface Radiometer Θ Halfspace, Temperature T phys Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

36 Example Brightness Temps of a Flat Soil Surface Brightness temperature (K) T phys =293 K, 10% soil moisture Vertical Horizontal Observation angle (deg) Brightness temperature (K) T phys =293 K, 40 degrees Vertical Horizontal Soil Moisture (%/%) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

37 Effects of Roughness Even bare Earth surfaces aren t totally flat, so we should try to consider surface roughness effects It turns out as long as the roughness is moderate compared to the EM wavelength, roughness doesn t have a major effect on the brightness temperature This is a big difference from radar, where roughness was as large or larger than the effect of changes in permittivity This difference makes radiometry very desirable and effective in cases where it is the permittivity that is being sensed However spatial resolution of radiometer will usually be worse than that of radar, especially synthetic aperture radar! The small effects of roughness are important in some high precision applications but we will neglect in what follows Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

38 Sea surface emission Our flat surface model is a good starting point for understanding systems that measure sea surface salinity or sea surface temperature Given f, the sea surface temperature (SST), and salinity (psu), we can find ɛ Given ɛ, the observation angle, and the SST, we can find the brightness temperature It turns out that brightness temperature is fairly sensitive to salinity at frequencies near L-band Also sensitive to SST though; SST influences change in brightness temperature per unit salinity These types of behaviors were used to develop NASA s Aquarius mission (launched June 2011) for sea salinity measurements Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

39 Example sea surface T B plots T b (K) V pol, 40 degrees, 1.4 GHz V pol, 1.4 GHz, K Salinity (psu) 125 Change in T b from 20 to 40 psu (K) Angle (deg) K, 1.4 GHz H pol, 1.4 GHz, V H SST (K) SST (K) Salinity (psu) Salinity (psu) 70 Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

40 Typical sensitivities over the sea Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

41 Land surface emission We previously saw how the brightness temperature of a bare land surface varies with surface soil moisture Retrieving soil moisture from single brightness temperature measurements requires knowledge of the land surface temperature T surf Or we could use multiple channels (e.g. V-pol and H-pol) to try to retrieve both land surface temperature and soil moisture What about vegetation? At low frequencies (including L-band) we can model vegetation in a manner similar to how we modeled the atmosphere Basic assumption is that the vegetation acts as an absorbing and emitting (but not scattering) layer We need to consider the atmosphere and surface together to sort this out! Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

42 Land + atmosphere together When we have atmosphere over the surface we have three contributions: upwelling atmosphere, upwelling surface, and reflected downwelling atmosphere Space Atmosphere or Vegetation Temperature T phys Constant α Soil surface Temperature T surf z=zmax z=0 Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

43 Land + atmosphere together If we make a single layer model of the atmosphere, the up and downwelling radiation are identical and equal to T up = T dn = T phys {1 exp ( α sec θ z max )} The upward emission from the surface in polarization β is: ( T surf 1 Γ β (θ) 2) The upward emission from the surface is attenuated all the way through the atmosphere before reaching the radiometer The attenuation on this path is exp ( α sec θ z max ) = exp ( τ sec θ) The downwelling term reflects off the surface and is then attenuated by the same factor Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

44 Land + atmosphere together Final combination of terms is: T Bβ = T phys {1 exp ( τ sec θ)} +T surf (1 Γ β (θ) 2) exp ( τ sec θ) ( ) 1 + Γ β (θ) 2 exp ( τ sec θ) For vegetation layers, it is frequently assumed that T phys = T surf. Also a correction is applied for the up- and down-welling brightnesses by multiplying them with 1 Ω, where Ω is a term to account for scattering effects The resulting tau-omega model is: T Bβ = T surf {[1 Q 2 Γ β (θ) 2] Ω where Q = exp ( τ sec θ) [ 1 + Q Γ β (θ) 2] } [1 Q] Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

45 Tau-Omega Model Results The tau-omega model allows us to study the impact of vegetation (or a simple atmosphere) on surface emission As vegetation increases, it produces more up- and down-welling emission, which may increase the total brightness However vegetation also attenuates surface emission, so it can also decrease total brightness in some cases By doing a little calculus, it is possible to derive that the total brightness will increase with τ for [ 1 Γ β (θ) 2 τ < 1 sec θ log 2 Γ β (θ) 2 and will decrease with τ for larger values of τ ( Ω ) ] 1 Ω Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

46 Example Tau-Omega Plots Brightness (K) Ts=290 K, R=0.33,Omega= Brightness (K) Ts=290 K, R=0.33,Omega= Canopy Optical Depth Canopy Optical Depth Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

47 Tau-Omega Model for Vegetation Adding vegetation in the tau-omega model requires us to describe τ = αz max and Ω Instead of finding α and z max separately for varying vegetation types, it is more common just to find τ empirically A commonly used empirical form is: τ = b VWC where b is a vegetation parameter and VWC is the vegetation water content in kg/m 2 ; typical value for b at L-band is around 0.1 Ω is a parameter that varies with vegetation type, typical value for L-band is also around 0.1 Parameters of the model are then ɛ (which depends on frequency and soil moisture), VWC, surface temperature, and observation angle Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

48 SMAP Passive Sensing of Soil Moisture NASA s Soil Moisture Active/Passive (SMAP) mission will include a GHz radiometer observing at 40 degrees incidence angle for soil moisture sensing The tau-omega model is inverted to perform the retrieval of soil moisture Requires knowledge of VWC, b and τ parameters, surface temperature, soil texture, etc. All of these parameters are assumed to be available from other information sources in the baseline algorithm SMAP measurements performed near 6 AM local time because then the vegetation and surface temperatures are most similar You will examine some in your homework More info at smap.jpl.nasa.gov Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49

49 Typical sensitivities over land Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 20, / 49