Implementation of Vicarious Calibration for High Spatial Resolution Sensors Stephen J. Schiller Raytheon Space and Airborne Systems El Segundo, CA Collaborators: Dennis Helder- South Dakota State University Mary Pagnutti and Robert Ryan - Lockheed Martin Space Operations, Stennis Space Center Vicki Zanoni – NASA Earth Scinece Applications Directorate, Stennis Space Center

Overview Calibration Considerations for Absolute Radiometry Vicarious Calibration and its application to High Spatial Resolution Sensors Design of Ground Targets and Ground Truth Measurements Top-of-Atmosphere Radiance Estimates Using MODTRAN and Considering: – BRDF Effects – Adjacency Effect – Aerosol Modeling – Evaluating Model Radiance Accuracy Error Propagation Model

Sensor Absolute Calibration Absolute Calibration establishes the link to physical parameters and processes recorded in the remote sensing image. Multiple paths to SI units are necessary to evaluate systematic errors in calibration coefficients. Vicarious calibration provides a known at-sensor radiance independent of on-board calibration sources Goal of this presentation is to outline the process for not just obtaining a gain estimate at a single radiance level but to generate a Vicarious Calibration Curve over the operational dynamic range of the sensor

Reflectance Based Vicarious Calibration Methodology Measure surface/atmospheric optical properties at the site containing one or more uniform targets Constrain input parameters in a radiative transfer model (MODTRAN 4) to match surface and atmospheric conditions at the time of the sensor overpass Predict the top-of-atmosphere spectral radiance for the ground target (hyperspectral resolution) Extract target signal from sensor data for each band Integrate the at-sensor radiance spectrum with the sensor’s relative spectral response for each band Calculate the gain and bias for each band Method provides an absolute calibration established relative to the solar spectral constant

Ground-Based Vicarious Calibration of Sensor Gain and Bias S = (dS/dL) L +B Sensor Gain and Bias Solar Spectral Constant Radiative Transfer Calculation of At-Sensor Radiance (L) Sensor Signal (S) of Ground Targets Measure Target Reflectance Monitor Atmospheric Transmittance, Diffuse/Global Ratio

Traditional Approach to Vicarious Calibration of Remote Sensing Systems June 10, 2000 Blue Band Typical approach has been to characterize a large bright uniform target at a desert site to provide a known top- of-atmosphere radiance level. Provides a gain value based on a single radiance level Uncertainty is estimated to be ~ +/- 3% (RSS estimate of measurement and modeling errors) IKONOS Image of Lunar Lake, Nevada (Developed for Large Footprint Sensors Requiring Natural Targets)

White Sands Railroad Valley Playa Lunar Lake Playa Vegetation Cover (Brookings) Improvement is to Generate a Calibration Curve Over the Sensor’s Dynamic Range using Multiple Sites – IKONOS Deep Dense Vegetation or Water Bodies (~zero reflectance) Six Deployments

Calibration Curve Generation From A Single Field Campaign (Using Man-made Targets) Does the tight linear fit imply a better gain estimate? Does the data resolve detector non-linearity?

No! Not Yet. More Data shows There are Systematic Variations in Gain Estimates Between Sites and Dates However, we now be seeing differences due to: Stray light, Out of band leakage, Temperature variations of focal plane and readout electronics, Limitations of ground truth data and atmospheric modeling.

Enhanced application applied to high spatial resolution sensors Generate a Vicarious Calibration Curve covering the sensor dynamic range in a single image Same atmospheric effects, scattered light levels, adjacency effect, sensor responsivity conditions Evaluates both gain and bias. Potential to evaluate non-linear responsivity. Potential to reduce cost compared to multiple campaigns

Enhanced Ground Target Design Lay out six to eight targets covering ~ 0% to 85% reflectance Targets include -Spectrally flat (gray toned targets for calibration curve generation) -Strong spectral contrast (evaluate effects of spectral banding) -Sample of surround spectrum (location where image DN for each band is near the average of the entire image) Reflectance of each target is measured at the site close to the time of the sensor overpass Use a site that is similar to image sites collected in operational use. (reproduce scattered light and out-of- band leakage effects) -Ocean/coastal, vegetation, desert

Arrow indicates DN value of the surround target area Histogram of 11 km by 11 km IKONOS image of Brookings DN Histogram Of A Pre-Campaign Image Of The Target Area Provides Data To Identify A Surround Spectral Sample Location

Vicarious Calibration Curve Generation for Push Broom Sensors 1 Assumes a flat field image has been acquired for relative calibration of all detector channels on the focal plane (i.e. cloud, ice or desert scenes, side slither image) Relative gain for each channel is derived from its response in terms of the average response of all the channels Uniform cloud or ground scene Detector Array Side slither image

Next, apply the relative gain to the vicarious calibration image Raw signal (DN raw ) of calibration targets are converted to relative signal (DN rel ) and average over the target area Weighted least-squares regression of TOA Radiance,, vs relative signal gives absolute gain, with respect to average responsivity of focal plane, This relation defines the vicarious calibration curve Absolute gain of each channel, G chan,band,,is given by Vicarious Calibration Curve Generation for Push Broom Sensors 2 TOA Radiance (Watts/m 2 -ster) Slope = abs

Achieving Accurate Top of Atmosphere Radiance Estimates 1 Radiative transfer model (MODTRAN) must account for all major atmospheric effects Target Reflectance (BRDF) Surround Reflectance Multiple Scattering Direct Solar Irradiance Adjacency Effect Sky Path Radiance (Single scattering) Path Radiance Adjacency Effect Multiple Scattering

Achieving Accurate Top Of Atmosphere Radiance Estimates 2 Requires extensive set of field data obtained with well calibrated radiometers and reference panels. –BRDF (Bi-directional Reflectance Distribution Function) of calibration panels and targets –Atmospheric transmittance, upwelling radiance, diffuse/global ratio, almucantor scans of sky path radiance (if possible - hyperspectral resolution) –Verticle profiles of water vapor and aerosols (altitude of boundary layer) –radiosonde / lidar / aircraft based measurements

Achieving Accurate Top Of Atmosphere Radiance Estimates 3 Requires MODTRAN parameters to be established via user supplied inputs (using a default atmosphere or surface reflectance is not adequate) –Target and surround reflectance spectrum (hyperspectral resolution, user supplied BRDF) –Wavelength characterized aerosol extinction known below and above the boundary layer (user supplied from sun photometry) –Surface Range in the boundary layer (adjusted to reproduce observed transmittance) –Aerosol scattering phase function ( adjust H-G asymmetry factor or input user-supplied)

Comments on MODTRAN Model Characterization BRDF Considerations Adjacency Effect Aerosol Vertical Profile

BRDF Knowledge of calibration panel and ground targets is essential BRDF effects are reduced with higher diffuse-to-global ratio

Multi-angle images should be collected to verify atmospheric and BRDF model Θ z =7 o Θ z =19 o

Comments on MODTRAN Model Characterization BRDF Considerations Adjacency Effect Aerosol Vertical Profile

Measuring Atmospheric Parameters To Characterize The Adjacency Effect Is Critical Target Surround Direct Solar Adjacency Effect Multiple Scattering Target Surround Direct Solar Adjacency Effect Multiple Scattering MODTRAN Modeling adjacency effect is required to reproduce measured upwelling radiance off ground targets Target spectrum= surround spectrum Grass spectrum used for surround

Surround Spectrum’s Influence On Sky Path Radiance Red edge of vegetation observed in the downwelling sky path radiance

Comments on MODTRAN Model Characterization BRDF Considerations Adjacency Effect Aerosol Vertical Profile

Aircraft Measurements Of Extinction At The Boundary Layer Improve Aerosol Model Solar radiometer observations at the top of the boundary layer (altitude defined in the MODTRAN model) revealed a significantly higher transmittance than available with MODTRAN model atmospheres. The 1976 standard atmosphere was scaled to fit the observations. Aerosol vertical profile plays a significant role in modeling the adjacency effect and extinction as a function of wavelength (composition varies with height). Solar radiometer observations at the top of the boundary layer (altitude defined in the MODTRAN model) revealed a significantly higher transmittance than available with MODTRAN model atmospheres. The 1976 standard atmosphere was scaled to fit the observations. Aerosol vertical profile plays a significant role in modeling the adjacency effect and extinction as a function of wavelength (composition varies with height).

Analysis Designed To Uses Multiple Paths to SI Units for Accuracy Assessment MODTRAN parameterization achieved with input of unitless quantities ties TOA radiance only to solar spectral constant –Transmittance –Reflectance –Diffuse/global ration –Assymetry factor Ground truth validation data from calibrated radiometers is traceable to NIST standards –Upwelling radiance at surface –Sky path radiance Direct comparison of MODTRAN predicted and measured upwelling radiance and sky path radiance evaluates systematic errors

Comparison of MODTRAN and Measured Upwelling Radiance: Grass Target

Comparison of MODTRAN and Measured Sky Path Radiance

TOA Error Propagation Model Apply error propation analysis to the following radiative transfer equation from ground to sensor. is the upwelling target radiance at ground level is the transmittance along the path between the target and the sensor is the sky path radiance contribution as seen from the sensor when viewing the target (the signal produced if looking at a surface of zero reflectance) Each component is directly related to calibrated ground measurements of which their uncertainty is known based on the measurement errors of the spectroradiometer and sunphotometer

Error Propagation Equation: Deriving the Uncertainty in the TOA Radiance Ratio of air mass from ground to sun and sensor MODTRAN calculated transmittance to sun and sensor MODTRAN calculated upwelling radiance at the ground Measurement uncertainty in transmittance from ground to sun Measurement uncertainty in upwelling radiance from target Measurement uncertainty in in sky path radiance from ground observation Uncertainty in estimating aerosol extinction at the MODTRAN input wavelengths from solar radiometry. A is a fraction of the total transmittance. uncertainty in TOA sky path radiance using the H-G scattering phase function characterized with ground measurements. B is a fraction of the TOA path radiance, Described in “Technique for estimating uncertainties in top-of-Atmosphere radiances derived by vicarious calibration”, S.J. Schiller, SPIE vol. 5151, 2003

Conclusion Progress made in vicarious claibration techniques for high spatial resolution sensors. –Natural targets to grey-toned deployed targets –Single radiance levels at different sites & dates to multiple levels evaluated in a single campaign event. Goal is to generate a vicarious calibration curve over the operational dynamic range of EO sensors (Vis to SWIR) Atmospheric model (i.e. MODTRAN) must be characterized using “user supplied” parameters Ground truth must address: –BRDF properties of targets –Adjacency effect (knowledge of surround spectrum) –Aerosol vertical profile –Radiometric accuracy knowledge of ground truth data for TOA radiance uncertainty estimates Working toward <3% absolute accuracy from environments consistent with operational use