Sensitivity of Radar Wave Propagation Power to the Marine Atmospheric Boundary Layer Nathan E. Lentini and Erin E. Hackett

Coastal Carolina University, School of Coastal & Marine Systems Science, Conway, SC 29528, nelentini@coastal.edu

Model Domain • Range: 0-60 km • Altitude: 0-1000 m • Resolution: 0.05 km X 1 m

Antenna: Generic air-sea surveillance radar • 3, 9, and 15 GHz • HH and VV polarization • 25 m height • 15° vertical beam width • Beam directed horizontally

Symbol Parameter Range

SSS Sea Surface Salinity 30-38 psu

SST Sea Surface Temperature 1-35 °C

ΘS Swell Direction 0-359.9 °

ΘW Wind Direction 0-359.9 °

HS Swell Height 0.1-17 m

TS Swell Period 5-18 sec

U10 Wind Speed 0.1-35 m/s

Ω Wave Age 0.83-3

Symbol Parameter Range

Z0 Aerodynamic Roughness Height 7.5x10-5 – 1.5 m

C0 Potential Refractivity Gradient (Evaporation Duct Curvature)

0.05-1.5 M/m

Zd Evaporation Duct Height 0-50 m

HML Mixed Layer Height 0-400 m

mML Mixed Layer Refractivity Gradient

0-0.4 M/m

HIL Inversion Layer Height 0-100 m

ΔM Inversion Layer Strength 0-100 M

mU Upper Refractivity Gradient 0-0.4 M/m

Atmosphere Parameters

Ocean Parameters Designers of radar use long term averages of meteorological conditions to assess system performance, but instantaneous conditions like strong moisture gradients, land breezes, and fronts can cause unpredictable propagation phenomena, such as ducts. To better understand the relative importance of these effects, this study aims to quantify the sensitivity of propagation power to environmental parameters.

VTRPE is a physics-based wave propagation model that calculates the full wave solution of the parabolic wave equation, providing electromagnetic field strength and propagation loss in spatially varying environments over rough sea surfaces (wind seas and swell). VTRPE models radar waves with horizontal or vertical polarization and frequencies from 10 kHz – 300 GHz. The model accounts for refraction, diffraction, scattering, attenuation, and ducting.

Numerical Experiment

Propagation Loss: 𝑃𝑃𝑃𝑃 = 20 log 2𝑘𝑘0𝑅𝑅 − 20 log 𝐹𝐹

Radar Transmission Equation: 𝑃𝑃𝑟𝑟𝑃𝑃𝑡𝑡

= 𝐺𝐺𝑡𝑡[𝐹𝐹

2𝑘𝑘0𝑅𝑅]2

Introduction and Background

“Stacked” Refractivity Model (Gerstoft et al., 2003)

M-profile is assumed homogeneous with range

Area where the duct height has little effect on the propagation.

Variable Terrain Radio-wave Parabolic Equation Model (VTRPE; Ryan, 1991)

Standard Atmosphere

Evaporation Duct

Extended Fourier Amplitude Sensitivity Test (Saltelli et al., 2000)

Sensitivity Analysis

In order to evaluate the spatial variation of sensitivity, the domain is divided into regions (R) for localized results. Results (bar charts below) show average SI and TSI over the whole domain and for each region.

EFAST is a global, variance-based (V), method that accounts for multi-degree interaction effects (TSI). It is most suitable for complex models (i.e., non-linear, non-monotonic, non-additive), and computes sensitivity indices for main order (SI) and total order (TSI) effects for parameter i. Each case requires over 1,000 VTRPE model runs.

Example TSI Distribution over Domain

Sensitivity Index (SI) Total Sensitivity Index (TSI)

𝑆𝑆𝑖𝑖 =𝑉𝑉𝑖𝑖𝑉𝑉

𝑆𝑆𝑇𝑇𝑖𝑖 = 1 −𝑉𝑉−𝑖𝑖𝑉𝑉

R1 R2

R7 R8 R9

R4 R5 R6

R3

Area where the evaporation duct height has little effect on propagation

Extended Fourier Amplitude Sensitivity Test (Saltelli et al., 2000)

Sensitivity Analysis

Results: Whole Domain

Parameter

EFA

ST S

ensit

ivity

3 GHz VV

9 GHz VV

EFA

ST S

ensit

ivity

Parameter

15 GHz VV

Parameter

EFA

ST S

ensit

ivity

Polarization & Frequency

Aver

age T

SI

Parameter Rank (VV)

Frequency is more important than

polarization

Results: Regional

Discussion

Acknowledgements The authors would like to thank the Office of Naval Research, Grant N00014-13-1-0307, for funding this research, and Nathan Grimes and John Saeger for their contributions to the refractivity model used in this study. Also, special thanks to Frank Ryan for providing us the VTRPE model.

References 1. Gerstoft, P., L.T. Roger, J.L. Krolik, and W.S. Hodgkiss. 2003. Inversion for refractivity parameters from radar sea clutter. Radio Sci. 38(3):8053. 2. Ryan, F. 1991. Analysis of electromagnetic propagation over variable terrain using the parabolic wave equation. TR1453, Naval Oceans Systems Center, San Diego, 38 pp. 3. Saltelli, A., S. Tarantola, and F. Campolongo. 2000. Sensitivity analysis as an ingredient of modeling. Statistical Science 15:377-395.

EFA

ST S

ensit

ivity

0-10 km 10-30 km 30-60 km

0-20

0 m

60

0-10

00 m

20

0-60

0 m

3 GHz VV 9 GHz VV 15 GHz VV

This study calculates global sensitivity of radar wave propagation to the marine atmospheric boundary layer environment using the EFAST method. Results show there are significant interaction effects that need to be accounted for to correctly assess the importance of a given environmental parameter. These interactions are evident because TSI is generally much higher than SI, where the latter only considers leading order effects. Over the entire domain, parameter sensitivity varies more with frequency than polarization, which has little impact on the relative importance of the parameters. Atmospheric parameters are much more important than ocean surface parameters due to atmospheric refraction having a larger effect on propagation than multipath effects arising from ocean surface scattering. For the ocean surface, roughness parameters are most important, except at 3 GHz, where directionality dominates. For the atmosphere, in general, the mixed layer is the most important for leading order (SI) and total order (TSI) effects, presumably because of its centralized location within the domain. The relative importance of the parameters varies with location and frequency. For example, at low altitude, the evaporation duct height is the most important parameter at close range for all frequencies, but its importance decreases with range at a rate that is frequency-dependent. Thus, the most important environmental parameters for a given application depend on frequency and required radar coverage; and these results provide insight to help determine which parameters are most important for assessing a radar system’s performance.

Aver

age T

SI /

Max

imum

Ave

rage

TSI

kilometers

0-20

0

200-

600

600-

1000

m

eter

s

Evaporation Duct Height

Most important parameter at low

altitude, close range

𝑴𝑴 𝒛𝒛 = 𝑴𝑴𝟎𝟎 + 𝒄𝒄𝟎𝟎 𝒛𝒛 − 𝒛𝒛𝒅𝒅 𝒍𝒍𝒍𝒍𝒛𝒛 + 𝒛𝒛𝟎𝟎𝒛𝒛𝟎𝟎

Evaporation Layer

Mixed Layer 𝒎𝒎𝑴𝑴𝑴𝑴 𝑯𝑯𝑴𝑴𝑴𝑴

Inversion Layer 𝑯𝑯𝑰𝑰𝑴𝑴

∆𝑴𝑴

Upper Layer

𝒎𝒎𝑼𝑼

Numerical Experiment